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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: 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- 863871/$25.00. JOURNAL OF BRIDGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2011 / 863 Downloaded 21 Mar 2012 to 3. Redistribution subject to ASCE license or copyright. Visit 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 GX 01 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 GX 0. Thus, the probability of failure can be estimated as Pf PGX 0? Z fXxdx2 where fXx = joint density function of X; and = failure domain in which Gx 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 1:75L I Rn4 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 PGX 0jH? PT5 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 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 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 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 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?X1 ? kV6 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 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 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 bridges 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 d