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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: ellingwood3Professor, 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 3. Redistribution subject to ASCE license or copyright. Visit Reliability 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 3. Redistribution subject to ASCE license or copyright. Visit structural 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.JOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011 / 865Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit The static push-down analysis is illustrated in Fig. 1 for the RCT-beam bridge (ID 129-0045). The FE modeling was performedwith ABAQUS (2006), with random material properties determinedby their respective mean values. The point of initial yielding occursat approximately 4.31 times the HS 20-44 design load configura-tion, at a deflection of approximately 36 mm (1.4 in.), which isequal to approximately 1=345 times the span. The ultimate live-load capacity of the bridge is approximately 4.8 times the appliedHS 20-44 loads. From Fig. 1, this 52-year-old bridge shows a con-siderable degree of ductility in behavior. The level of load imposedby the four fully loaded trucks during the load test described in thecompanion paper is also shown in Fig. 1; the test load (in maximumgirder moment) was approximately 1.3 times the two side-by-sideHS 20-44 loads. The capacity of this bridge system is substantiallyin excess of what a girder-based calculation would indicate. Similarpush-down analyses were performed on the other bridges describedin the companion paper, yielding the results summarized in Table 2.The elastic ranges of all four bridges are in excess of 4 times thedesign load level, indicating the level of conservatism associatedwith traditional design and rating procedures.As part of the effort to develop the AASHTO LRFD BridgeDesign Specifications, extensive databases were developed todescribe the strength of individual bridge girders and vehicle liveloads probabilistically (Nowak 1999; Moses 2001). (The HL-93live-load model is an outgrowth of this previous research.) Thatresearch focused on the capacity of individual bridge girders; sys-tem effects were included indirectly and approximately throughnew girder distribution factors that were developed in the courseof the project. The capacity of a bridge structural system is likelyto be different from the capacity predicted from an analysis of indi-vidual girders. To determine the additional level of conservatism(if any) that arises from system behavior, a finite-element-basedsystem reliability analysis of all four study bridges was conducted.This system reliability analysis provides additional perspectiveon the (unknown) level of conservatism furnished by the currentgeneration of reliability-based condition evaluation and rating pro-cedures embodied in the AASHTO Manual for Bridge Evaluation,and has implications for the use of such methods in permit ratingsfor extreme vehicle loads.To accelerate the FE-based reliability analysis, efficient FEmodels of the sample bridges were developed with the open-sourceplatform, OpenSees Version 2.2.2. The more detailed ABAQUSmodels, which had been validated from the load-test results, wereemployed to confirm the bridge structural behavior predicted by theOpenSees models as the system was loaded beyond its design limit.By using the RC T-beam bridge again as an example, Fig. 1 illus-trates the consistency achieved between the ABAQUS (2006) andthe OpenSees models through a complete push-down analysis, inwhich the bridge is loaded well into the inelastic range. Followingthis validation, the system performance of the sample bridges wascharacterized statistically by propagating the uncertainties inmaterial strengths, stiffnesses, and geometry through the OpenSeesanalysis by using a Latin Hypercube Sampling technique (Imamand Conover 1980) to achieve efficient coverage of the samplespace with a relatively few FE analyses. The random variablesinvolved in these FE analyses to capture bridge structural perfor-mance are described with statistics defined in the LRFD databasesmentioned previously. The limit state of performance was assumedas the point at which the bridge system exits the elastic range, asidentified from its load-deflection curve (see Fig. 1).The flexural capacities so determined from this system reliabil-ity analysis were rank-ordered and plotted on lognormal probabilitypaper, as illustrated in Fig. 2 for the straight approach RC bridge(ID 129-0045). The lognormal distribution provides a good fit tothese data. The mean and coefficient of variation in the systemcapacity of this bridge (at first yield) are 4.31 times the appliedFig. 1. Push-down analysis of RC T-beam bridge ID 129-0045(1 in 25:4 mm)Table 2. Analysis of Bridge Capacity Determined as the Point of First YieldBridge IDCountyTypeDesign loadLoad factor on design loadLoad factor on HS-20129-0045-0GordonRC; Tstraight; not postedH-157.464.31015-0108-0BartowRC; Tskewed; postedHS-156.004.50223-0034-0PauldingPrestressed; straight; not postedHS-205.945.94085-0018-0DawsonSteel girder; straight; postedH-159.935.37Fig. 2. Lognormal fit of the bridge system resistance of the RC Bridge(ID 129-0045)866 / JOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit two HS-20 loads and 15%, respectively. The variability is of thesame order as the individual girder capacities (Nowak 1999),but the larger mean is characteristic of the beneficial system effectsin a system reliability assessment. When used in a reliability assess-ment with the same statistical load models used to develop theLRFD bridge specifications, one obtains a system reliability indexof 3.51, which is comparable to the safety level stipulated for a newbridge in AASHTO-LRFD. The rating factor based on the systemcapacity see Eq. (4) for the HS-20 vehicle at Operating level is1.74, presenting an 86% increase in rated load capacity than thatcalculated at the component level as stipulated in AASHTO-LRFR.It may be appropriate to factor in this additional conservatism inbridge evaluation on a case-by-case basis.Revisions to Capacity Reduction Factor, con theBasis of Condition RatingCondition rating numbers (09) assigned by bridge inspectorsaccording to the National Bridge Inspection Standard (2004; assummarized in Table 3) identify whether deterioration is occurringin the bridge and, ideally, at what level. These inspection datashould be considered in computing the load rating and real-timereliability of the bridge. In the AASHTO-LRFR method, the physi-cal condition of the bridge is partially reflected in the capacityrating equation (AASHTO 2008, Eq. 6A.4.2.1-1) through the con-dition factor, c, as mentioned previously. The MBE stipulates thatcequals 1.0, 0.95, and 0.85 when the condition rating is greaterthan or equal to 6, equal to 5, and less than or equal to 4, respec-tively, to account for the change in uncertainty associated with theestimated resistance. This assignment of cis judgmental and doesnot have a reliability basis. A revised set of values of care de-veloped in this study to be consistent with the structural reliabilityphilosophy embodied in the MBE and to incorporate recent devel-opments in bridge resistance degradation modeling and compre-hensive databases on bridge condition rating.Quantitative models of bridge degradation have been developedin many research studies (Albrecht and Naeemi 1984; Mori andEllingwood 1993; McCuen and Albrecht 1995; Thoft-Christensen1998; Enright and Frangopol 1998). These models can be incorpo-rated in the real-time bridge reliability assessment. The uncertain-ties in resistance of an existing intact bridge are at least equalto those of a newly designed bridge. Once the bridge begins todeteriorate, its mean resistance is usually decreased and the uncer-tainty in resistance is generally greatly increased. Time-dependentstructural resistance can be modeled as (Mori and Ellingwood1993)Rt R0gt7where t = elapsed time; R0= resistance variable of a newlyconstructed bridge; and gt = degradation rate. The mean andCOV of random variable gt can be expressed as following bycoefficients k1and k2Egt? ?1;t T01 ? k1t ? T0;t T0Vgt? k2t8where T0= mean corrosion initiation time. Enright and Frangopol(1998) indicated that for reinforced concrete bridges subjected toenvironmental attack with medium degradation rate, T0is approx-imately 10 years and k1and k2equal 0.0031 and 0.0027, respec-tively. The mean and COVof gt as a function of time are plottedin Fig. 3.On the other hand, the average condition rating history of non-interstate RC bridges is commonly modeled by using a third orderpolynomial, in which the coefficients are determined from regres-sion analysis of data available in the National Bridge Inventory(NBI). Bolukbasi et al. (2004) provided the following model asshown in Fig. 4:Ct 8:662 ? 0:146t 0:003t2?3:09E5t39where Ct = condition rating of the bridge at age, t, of the bridge inyears. This model translates to 70 years to condition state 4. Jiangand Sinha (1989) developed a similar polynomial model withslightly different coefficients, which indicated 71 years to a condi-tion state 4.A relationship between condition rating Ct and the statisticalcharacteristics of degradation gt is developed by mapping theaverage condition rating history of noninterstate concrete bridges(Bolukbasi et al. 2004) in Fig. 4 onto the 75-year stochastic bridgeresistance model with medium degradation rate in Fig. 3. Thisrelationship is shown in Fig. 5 by the solid lines. When flexuralresistance is considered, Rois described by a lognormal distributionwith a mean of 1.14 times the nominal flexural strength RnandCOVof13%,respectively(Nowak 1999).The dashed lines inFig. 5show the mean, ER=Rn?, and COV, VR=Rn?, of the normalizedTable 3. NBI Instruction for Superstructure Condition RatingConditionratingDescription9Excellent condition8Very good condition; no problems noted7Good condition; some minor problems6Satisfactory condition; structural elements show some minor deterioration5Fair condition; all primary structural elements are sound but may have minor section loss, cracking, spalling, or scour4Poor condition; advanced section loss, deterioration, spalling, or scour3Serious condition; loss of section, deterioration, spalling, or scour have seriously affected primary structural components. Local failures arepossible. Fatigue cracks in steel or shear cracks in concrete.2Critical condition; advanced deterioration of primary structural elements. Fatigue cracks in steel or shear cracks in concrete may be present orscour may have removed substructure support. Unless closely monitored, it may be necessary to close the bridge until correctiveaction is taken.1Imminent failure condition; major deterioration or section loss present in critical structural components or obvious vertical or horizontalmovement affection structure stability. Bridge is closed to traffic but corrective action may put back in light service.0Failed condition; out of service, beyond repairJOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011 / 867Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit resistance modal as a function of condition rating. By mappingresistance model with an average degradation rate on the meancondition rating history of noninterstate RC bridges from NBIdatabase, this proposed model for the statistical description of re-sistance as a function of condition rating is independent of degra-dation rate.With the statistics in Fig. 5 along with the load models used inthe AASHTO-LRFD (Nowak 1999), the bridge condition ratingnumber can be included in the estimation of failure probabilityand reliability index of a given bridge. To further facilitate thebridge-rating practices that utilize a deterministic format, a setof c-values necessary to achieve the target reliability requirementsconsistent with AASHTO-LRFR was obtained by minimizingthe mean-square error between the target Tand the reliabilityachieved by the use of specific values of c, as illustrated in Fig. 6.The proposed condition factors are presented in Table 4. The pro-posed condition reduction factors reflect both the changes in theestimated nominal resistance and in the uncertainty in resistance.In contrast, the cin MBE is to account for the increase in uncer-tainty in estimating the strength of deteriorated members, whereasthe nominal value is to be estimated separately on the basis of theresult of the inspection.Service-Proven StrengthMany older bridges show no signs of damage and yet havebeen rated as structurally deficient without considering the fact thatthey have performed satisfactorily over the years under the ever-increasing traffic volume and lighter truck loads. These bridgesgenerally were designed for lighter loads but for greater factorsof safety and, if well-maintained, may have reliability levels thatare substantially higher than those in modern construction. Surviv-ing a service load history that is stochastic in nature provides evi-dence of structural reliability that may be comparable towhat mightFig. 3. Time-dependent mean and coefficient of variation of bridgecapacityFig. 5. Time-dependent statistics mean and COV of bridge flexuralcapacityFig. 6. Optimal condition factors for different condition ratingsFig. 4. Condition rating versus age (adapted from Bolukbasi et al.2004)Table 4. Proposed Condition FactorsStructural condition rating (Table 3)c 81.0070.9560.8550.75 40.70868 / JOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit be learned from a proof load test (Ellingwood 1996; Stewart andVal 1999). Satisfactory service history should be considered, espe-cially for old bridges, in designing in-service inspection programsand making decisions for updating analytical ratings and load post-ings. The AASHTO MBE does not provide a mechanism for up-dating structural resistance for service-proven bridges.A proof test of a bridge enables the lower tail of the resistancedistribution to be truncated at the level of the maximum load car-ried. In contrast, for a service-proven bridge, the magnitude of themaximum load carried is unknown; however, it can be determinedstatistically by using the weigh-in-motion data described earlier(e.g., Nowak 1999). For a structure surviving a sequence of randomvehicle loads, the magnitude of which is described by the proba-bility distribution function FQr determined by using weigh-in-motion data, the revised strength f00Rr can be written as follows(Ellingwood 1996):f00Rr FQ?rfRrR?FQ?rfRrdr10where fRr and FQ?r = previous probability density function ofresistance and the cumulative load distribution function of themaximum load to occur during the service period of interest, re-spectively. This updated density can be used in a structural reliabil-ity assessment to determine the beneficial effect of successfulservice performance.To illustrate the benefit of previous successful bridge perfor-mance on rating, consider the concrete T-beam bridge (ID 129-0045), which gave 52 years of serviceable performance. Beforeconsidering the benefit of successful bridge performance, theuse of the mean and COVof bridge capacity presented by (Nowak1999) for new bridges in Eqs. (2) and (3) leads to the previoussafety index 2:54. The updated distribution of resistance, asdetermined from Eq. (9) by Monte Carlo simulation, is illustratedin Fig. 7. As a result, with the updated resistance, the estimatedreliability index will increase as the successfully service life ofthe bridge increases, as illustrated in Fig. 8. This increase in reli-ability translates to an increase in bridge capacity rating factors, asindicated in Fig. 9. Rating factors for this bridge in relation to HL-93 design loading at inventory level, before and after consideringthe 52-year successful service life of this bridge, are summarized inTable 5. These results indicate a 16% increase in flexural ratingsand a 40% increase in shear ratings by considering the 52-year ser-vice load history. The rating in shear increases more than that inflexure. The COV of the previous distribution of the shear resis-tance is much larger than the COVof resistance in flexure; knowl-edge of successful performance causes the effect of the larger COVon the updated reliability to be diminished.Fig. 7. Influence of service load on updated distribution of structuralresistance for RC bridge (ID 129-0045)Fig. 8. Updated failure probabilities and reliability indices for RCbridge (ID 129-0045)Fig. 9. Updated rating factors in relation to HL93 at inventory level forRC bridge (ID 129-0045)Table 5. Comparison of Rating Factors Computed before and afterConsidering Service Load History for RC Bridge (ID 129-0045)Rating factorFlexureShearInteriorgirderExteriorgirderInteriorgirderExteriorgirderBefore updating byservice load history0.750.650.450.46After updating byservice load history0.870.810.630.64JOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011 / 869Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit Conclusions and Recommendations forImprovements in the Bridge-Rating AnalysisThis paper has presented a structural reliability basis for possibleimprovements to bridge rating by using the LRFR option in theAASHTO Manual of Bridge Evaluation. The beneficial effect ofin situ material testing on load rating has been examined. A newset of condition factors couples the rating procedure more closely tothe results of bridge inspections, material tests, observed field data,and load tests incorporating real-time resistance of bridges in therating process. Routine biannual inspections can play an enhancedrole by providing in situ information to support the real-time bridgereliability assessment and can be incorporated into reliability-basedload rating and maintenance decisions. Application of the proposedevaluation criteria to existing steel, reinforced concrete, or pre-stressed concrete bridges with simple spans ranging from 12.221.3 m (4070 ft) indicates that posting requirements establishedby current bridge evaluation practices without further incorporatingavailable site-specific knowledge in the processes can be undulyconservative from a structural reliability viewpoint. The proposedimprovements recognize the uniqueness of each existing bridge andtake advantage of accessible in situ information to produce bridgeratings that provide for public safety without undue economicimpact on the community served. The proposed changes are madewithin the framework of the familiar LRFD/LRFR methods,and have been incorporated in the Recommended Guidelines forthe Evaluation of Existing Bridges in Georgia (Ellingwood et al.2009).AcknowledgmentsThe research described in this paper was supported by the GeorgiaDOT under an award entitled Condition Assessment of ExistingBridge Structures. This support is gratefully acknowledged. How-ever, the views are solely those of the writers and may not representthe positions of the Georgia DOT.ReferencesAASHTO. (2007). LRFD bridge design specifications, 4th Ed., AASHTO,Washington, DC.AASHTO. (2008). Manual for bridge evaluation, 1st Ed, AASHTO,Washington, DC.ABAQUS Version 6.8 Computer software. (2006). Dassault SystmesSimulia, Providence, RI.Albrecht, P., and Naeemi, A. H. (1984). “Performance of weatheringsteel in bridges.” NCHRP Rep. 272, Transportation Research Board,Washington, DC.American Concrete Institute (ACI). (2005). Building code requirementsfor structural concrete, ACI 318-05, ACI, Detroit.ASTM. (1995). “Standard Test Method for Obtaining and TestingDrilled Cores and Sawed Beams of Concrete.” ASTM C 42-94, ASTM,Philadelphia, 2427.Bakht, B., and Jaeger, L. G. (1990). “Bridge testingA surprise everytime.” J. Struct. Eng., 116(5), 13701383.Barker, M. G. (2001). “Quantifying field-test behavior for rating steelgirder bridges.” J. Bridge Eng., 6(4), 254261.Bartlett, M. F., and MacGregor, J. G. (1996). “Statistical analysis of the com-pressive strengthofconcrete instructures,ACI Mater.J., 93(2), 158168.Bhattacharya, B., Li, D., Chajes, M., and Hastings, J. (2005). “Reliability-based load and resistance factor rating using in-service data.” J. BridgeEng., 10(5), 530543.Bolukbasi, M., Mohammadi, J., and Arditi, D (2004). “Estimating thefuture condition of highway bridge components using National BridgeInventory data.” Pract. Period. Struct. Des. Constr., 9(1), 1624.Ellingwood, B. (1996). “Reliability-based condition assessment and LRFDfor existing structures.” Struct. Saf., 18(2), 6780.Ellingwood, B. (2000). “LRFD: Implementing structural reliability inprofessional practice.” Eng. Struct., 22(2), 106115.Ellingwood, B., MacGregor, J. C., Galambos, T. V., and Cornell, C. A.(1982). “Probability based load criteria: Load factors and load combi-nations.” J. Struct. Div., 108(5), 978997.Ellingwood, B., Zureick, A.-H., Wang, N., and OMalley, C.
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