桥梁评测_桥梁工程.pdf

Bridge Rating Using System Reliability Assessment II Improvements to Bridge Rating Practices Naiyu Wang M ASCE1 Bruce R Ellingwood Dist M ASCE2 and Abdul Hamid Zureick M ASCE3 Abstract The current bridge rating process described in AASHTO Manual for Bridge Evaluation First Edition permits ratings to be determined by allowable stress load factor or load and resistance factor methods These three rating methods may lead to different rated capacities 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 research program to developimprovements to the bridge rating process by using structural reliability methods The first paper provided background on the research program and summarized a coordinated program of load testing and analysis to support the reliability assessment leading to the recommended improvements This second paper presents the reliability basis for the recommended load rating develops methods that closely couple the rating process to the results of in situ inspection and evaluation and recommends specific improvements to current bridge rating methods 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 Introduction The AASHTO Manual for Bridge Evaluation MBE First Edition AASHTO 2008 allows bridge ratings to be determined through the traditional allowable stress rating ASR or load factor rating LFR methods or by the more recent load and resistance factor rating LRFR method which is consistent with the AASHTO LRFD Bridge Design Specifications 2007 These three rating methods may lead to different rated capacities and posted limits for the same bridge NCHRP 2001 Wang et al 2009 a situation that cannot be justified from a professional engineering viewpoint and has implications for the safety and economic well being of those affected by bridge postings or closures To address this issue the Georgia Institute of Technology has conducted a multiyear research program aimed at making improvements to the process by which the condition of existing bridge structures in Georgia are assessed The end product of this research program is set of recommended 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 element modeling which have been integrated within a structural reliability framework to determine practical bridge rating methods that are consistent with those used to develop the AASHTO LRFD Bridge Design Specifications AASHTO 2007 It is believed that bridge construction 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 United States CEUS The recent implementation of LRFD and its companion rating method LRFR both of which have been supported by structural reliability methods enable bridge design and condition assessment to be placed on a more rational basis Notwithstanding these ad vances improved techniques for evaluating the bridge in its in situ condition would minimize the likelihood of unnecessary posting For example material strengths in situ may be vastly different from the standardized or nominal values assumed in design and current rating practices attributable to strength gain of concrete on one hand and deterioration attributable to aggressive attack from physi cal or chemical mechanisms on the other Satisfactory performance of a well maintained bridge over a period of years of service pro vides additional information not available at the design stage that might be taken into account in making decisions regarding posting or upgrading Investigating bridge system reliability rather than solely relying on component based rating methods may also be of significant benefit Proper consideration of these factors is likely to contribute to a more realistic capacity rating of existing bridges This paper is the second of two companion papers that provide the technical bases for proposed improvements to the current LRFR practice The first paper Wang et al 2011 summarized the current bridge rating process and practices in the United States and presented the results of a coordinated bridge testing and analysis program conducted to support revisions to the current rating pro cedures This paper describes the reliability analysis framework that provides the basis for recommended improvements to the MBE and recommends specific improvements to the MBE that address the preceding factors 1Senior Structural Engineer Simpson Gumpertz and Heger Inc 41 Seyon St Waltham MA 02453 formerly Graduate Research Assistant School of Civil and Environmental Engineering Georgia Institute of Technology 2Professor School of Civil and Environmental Engineering Georgia Institute of Technology 790 Atlantic Dr Atlanta GA 30332 0355 corresponding author E mail ellingwood gatech edu 3Professor School of Civil and Environmental Engineering Georgia Institute of Technology 790 Atlantic Dr Atlanta GA 30332 0355 Note This manuscript was submitted on March 19 2010 approved on August 2 2010 published online on October 14 2011 Discussion period open 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 6 863 871 25 00 JOURNAL OF BRIDGE ENGINEERING ASCE NOVEMBER DECEMBER 2011 863 Downloaded 21 Mar 2012 to 180 95 224 53 Redistribution subject to ASCE license or copyright Visit http www ascelibrary org Reliability Bases for Bridge Load Rating Bridge design as codified in the AASHTO LRFD specifications 2007 is established by modern principles of structural reliability analysis The process by which existing bridges are rated must be consistent with those principles Uncertainties in the perfor mance of an existing bridge arise from variations in loads material strength 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 a rational and powerful theoretical basis for handling these uncertain ties in bridge evaluation The limit states for bridge design and evaluation can be defined in the general form G X 0 1 where X X1 X2 X3 Xn load and resistance random variables On the basis of bridge performance objectives these limit states may relate to strength for public safety or to excessive deformation cracking wear of the traffic surface or other sources of functional impairment A state of unsatisfactory performance is defined by convention when G X 0 Thus the probability of failure can be estimated as Pf P G X 0 Z fX x dx 2 where fX x joint density function of X and failure domain in which G x 0 In modern first order FO reliability analysis Melchers 1999 Eq 2 is often approximated by Pf 3 where standard normal distribution function and reliability index For well behaved limit states Eq 3 usually is an excellent approximation to Eq 2 and and Pfcan be used interchangeably as reliability measures Ellingwood 2000 When the failure surface in Eq 1 is complex or when the reliability of a structural system in which the structural behavior is modeled through 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 are established 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 load terms Nowak 1993 Bartlett and McGregor 1996 Moses and Verma 1987 an examination of existing bridge design practices led to a target reliability index equal to 3 5 based on a 75 year service period Nowak 1999 Moses 2001 Consistent with such reliability based performance objective the AASHTO LRFD spec ifications stipulate that in the design of new bridges 1 25D 1 5DA 1 75 L I Rn 4 where D dead load excluding weight of thewearing surface DA weight of the wearing surface asphalt L I represents live load including impact Rn design strength in which Rn nominal resistance 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 load testing material tests or traffic surveys if available can be utilized to modify the probability distributions describing the structural behavior and response in Eq 2 The metric for acceptable perfor mance is obtained by modifying Eq 2 to reflect the additional information gathered Pf P G X 0jH PT 5 where H represents what is learned from previous successful performance in service inspection and supporting in situ testing if any The target probability PT should depend on the economics of rehabilitation repair consequences of future outages and the bridge rating sought In the AASHTO LRFR method 2007 the target for design level checking by using HL 93 load model at inventory level is 3 5 which is comparable to the reliability for new bridges whereas the target for HL 93 operating level and for legal and permit loads is reduced to 2 5 owing to the reduced load model and reduced exposure period 5 years Moses 2001 The presence of H in Eq 5 is a conceptual departure from Eqs 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 daily truck traffic ADTT Furthermore the component nominal resis tance in LRFR is factored by a system factor sand a member condition factor cin addition to the basic resistance factor for a particular component limit state The system factor depends on the perceived redundancy level of a given bridge in its rating whereas the condition factor is to account for the bridge s 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 further examined later in this paper The LRFR option in the AASHTO MBE extends the limit state design philosophy to the bridge evaluation process in an attempt to achieve a uniform target level of safety for existing highway bridge systems However the uncertainty models of load and resistance embedded in the LRFR rating format represent typical values for a large population of bridges involving different materials con struction practices and site specific traffic conditions Although the LRFR live load model has been modified for some of the spe cific cases as discussed previously the bridge resistance model should also be customized for an individual bridge by incorpo rating available site specific knowledge to reflect the fact that each bridge is unique in its as built condition A rating procedure that does not incorporate in situ data properly may result in inaccurate ratings and consequent unnecessary rehabilitationor postingcosts for otherwise well maintained bridges as indicated by many load tests Nowak and Tharmabala 1988 Bakht and Jaeger 1990 Moses et al 1994 Fu and Tang 1995 Faber et al 2000 Barker 2001 Bhattacharya et al 2005 Improvements in practical guidance would permit the bridge engineer to include more site specific knowledge 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 Using Reliability Based Methods In this section the bridge ratings in light of the reliability based updating of in service strength described in the previous section are examined The possibilities of incorporating available site specific data obtained from material tests load tests advanced 864 JOURNAL OF BRIDGE ENGINEERING ASCE NOVEMBER DECEMBER 2011 Downloaded 21 Mar 2012 to 180 95 224 53 Redistribution subject to ASCE license or copyright Visit http www ascelibrary org structural analysis and successful service performance to make fur ther recommendations for improving rating analysis are explored Incorporation of In Situ Material Testing The companion paper summarized the load test of Bridge ID 129 0045 a reinforced concrete T beam bridge that was designed according to the AASHTO 1953 design specification for H 15 loading 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 the bridge before its demolition Seven cores were taken from the slab at seven different locations along both the length and width of the bridge Cores also were taken from three of the girders that were in good condition after demolition these were cut into 203 mm 8 in lengths and the jagged ends were smoothed and capped resulting in a total of 14 girder test cylinders Tests of these 102 203 mm 4 8 in cylinders conformed to ASTM Standard C42 ASTM 1995 and the results are presented in Table 1 An analysis of these data indicated no statistically significant difference in the concrete compression strength in the girders and slab and the data were therefore combined for further analysis The mean average com pression strength of the concrete is 33 MPa 4 820 psi and the coefficient of variation COV is 12 which is representative of good quality concrete Bartlett and MacGregor 1996 The mean strength is 1 93 times the specified compressionstrength of the con crete This increase in compression strength over a period of more than 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 concrete bridges the in situ concrete strength is likely to be substantially greater than the 28 day strength that is customarily specified for bridge design or condition evaluation Accordingly the bridge en gineer should be provided incentives in the rating criteria to rate a bridge by using the best possible information from in situ material strength testing whenever feasible Ellingwood et al 2009 It is customary to base the specified compression strength of concrete on 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 by fc X 1 kV 6 where X sample mean V sample coefficient of variation and k p lower confidence interval on the 10th percentile compres sion strength By using the 21 tests from Bridge ID 129 0045 with p 75 as an example k 1 520 Montgomery 1996 and fc can be expressed as fc 1 1 520 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 strength tests the concrete compression strength was set at 17 2 MPa 2 500 psi which was the only information available before the material test To determine the impact of using the actual concrete strength in an older bridge on the rating process the finite element model was revised to account for the increased concrete compres sion strength and the corresponding increase in stiffness into the analysis of the bridge Only a modest enhancement in the estimated bridge capacity in flexure was obtained but a 34 increase was achieved in the shear capacity ratings for the girders by using the results of Table 1 Bridge System Reliability Assessment on the Basis of Static Push Down Analysis Although component based design of a new bridge provides ad equate safety at reasonable cost component based evaluation of an existing bridge for rating purposes may be overly conservative and result in unnecessary repair or posting costs It is preferable to perform load rating regarding bridge posting or road closure through a system level analysis A properly conducted proof load test can be an effective way to learn the bridge s structural perfor mance as a system and to update the bridge load capacity assess ment in situations in which the analytical approach produces low ratings or structural analysis is difficult to perform because of deterioration or lack of documentation Saraf and Nowak 1998 However a proof load test represents a significant investment in capital time and personnel and the trade off between the informa tion gain and the riskof damaging the bridge during the test mustbe considered 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 Wang et al 2011 in which bridge response measurements obtained from the load tests of the four bridges were compared with the results of finite element analyses of 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