Reliability-Based Load and Resistance Factor Rating Using In-Service Data
Publication: Journal of Bridge Engineering
Volume 10, Issue 5
Abstract
Traditional bridge evaluation techniques are based on design-based deterministic equations that use limited site-specific data. They do not necessarily conform to a quantifiable standard of safety and are often quite conservative. The newly emerging load and resistance factor rating (LRFR) method addresses some of these shortcomings and allows bridge rating in a manner consistent with load and resistance factor design (LRFD) but is not based on site-specific information. This paper presents a probability-based methodology for load-rating bridges by using site-specific in-service structural response data in an LRFR format. The use of a site-specific structural response allows the elimination of a substantial portion of modeling uncertainty in live load characterization (involving dynamic impact and girder distribution), which leads to more accurate bridge ratings. Rating at two different limit states, yield and plastic collapse, is proposed for specified service lives and target reliabilities. We consider a conditional Poisson occurrence of identically distributed and statistically independent (i.i.d.) loads, uncertainties in field measurement, modeling uncertainties, and Bayesian updating of the empirical distribution function to obtain an extreme-value distribution of the time-dependent maximum live load. An illustrative example uses in-service peak-strain data from ambient traffic collected on a high-volume bridge. Serial independence of the collected peak strains and of the counting process, as well as the asymptotic behavior of the extreme peak-strain values, are investigated. A set of in-service load and resistance factor rating (ISLRFR) equations optimized for a suite of bridges is developed. Results from the proposed methodology are compared with ratings derived from more traditional methods.
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Acknowledgments
The writers would like to thank the Delaware Department of Transportation for its support of this work, with special thanks to Dennis O’Shea. The authors also appreciate the input provided by Bala Sivakumar of Lichtenstein Consulting Engineers.
References
American Association of State Highway and Transportation Officials (AASHTO). (1994). LRFD highway bridge design specifications, 1st Ed., AASHTO, Washington, D.C.
Aktas, E., Moses, F., and Ghosn, M. (2001). “Cost and safety optimization of structural design specification.” Reliability Eng. Sys. Safety, 73, 205–212.
Bakht, B., and Jaeger, L. G. (1990). “Bridge testing—a surprise every time.” J. Struct. Eng., 116(5), 1370–1383.
Bhattacharya, B., Basu, R., and Ma, K-T. (2001). “Developing target reliability for novel structures: the case of the Mobile Offshore Base.” Marine Struct., 14(1–2), 37–58.
Brockwell, P. J., and Davis, R. A. (1991). Time series: Theory and methods, 2nd Ed., Springer, New York.
Castillo, E. (1988). Extreme value theory in engineering, Academic, New York.
Chajes, M. J., Mertz, D. R., and Commander, B. (1997). “Experimental load rating of a posted bridge.” J. Bridge Eng., 2(1), 1–10.
Chajes, M. J., Shenton, H. W., III, and Finch, W. W. (2001). “Diagnostic and in-service testing of a transit railway bridge.” Transp. Res. Rec., 1770, 51–57.
Chajes, M. J., Shenton, H. W., III, and O’Shea, D. (2000). “Bridge condition assessment and load rating using nondestructive evaluation methods.” Transp. Res. Rec., 1696(2), 83–91.
Collins, K. R., Wen, Y.-K., and Foutch, D. (1996). “Dual-level seismic design: A reliability-based methodology.” Earthquake Eng. Struct. Dyn., 25, 1433–1467.
Corotis, R. B., and Dougherty, A. M. (2004). “Reliable design loads for natural phenomena: Illustration with wind speeds.” Nat. Hazards Rev., 5(1), 40–47.
de Haan, L. (1994). “Extreme value statistics.” Extreme value theory and applications, J. Galambos, J. Lechner, and E. Simiu, eds., Vol. 1, Kluwer Academic, Dordrecht, The Netherlands.
Det Norske Veritas (DNV). (1992). “Structural reliability analysis of marine structures.” Classification Notes No. 30.6, Det Norske Veritas, Hovik, Norway.
Ditlevsen, O. (1993). “Distribution arbitrariness in structural reliability.” Proc., 6th Int. Conf. on Structural Safety and Reliability, Innsbruck, Austria.
Ditlevsen, O. (2003). “Decision modeling and acceptance criteria.” Struct. Safety, 25, 165–191.
Ellingwood, B. R. (1996). “Reliability-based condition assessment and LRFD for existing structures.” Struct. Safety, 18(2/3), 67–80.
Ellingwood, B. R. (2000). “LRFD: implementing structural reliability in professional practice.” Eng. Struct., 22, 106–115.
Ellingwood, B. R., Galambos, T. V., MacGregor, J. G., and Cornell, C. A. (1980). “Development of a probability based load criterion for American National Standard A58.” NBS Spec. Publ. 577, United States Department of Commerce, National Bureau of Standards, Washington, D.C.
Faber, M. H., Val, D. V., and Stewart, M. G. (2000). “Proof load testing for bridge assessment and upgrading.” Eng. Struct., 22, 1677–1689.
Frangopol, D. M., Lin, K.-Y., and Estes, A. C. (1997). “Life-cycle cost design of deteriorating structures.” J. Struct. Eng., 123(10), 1390–1401.
Fu, G., and Tang, J. (1992). “Proof load formula for highway bridge rating.” Transp. Res. Rec., Transportation Research Board, Washington, D.C., 129–141.
Galambos, J. (1987). The asymptotic theory of extreme order statistics, 2nd Ed., Krieger, Malabar, Fla.
Galambos, J. (1993). “The development of the mathematical theory of extremes in the past half century.” Theory Probab. Appl., 39(2), 234–248.
Ghosn, M. (2000). “Development of truck weight regulations using bridge reliability model.” J. Bridge Eng., 5(4), 293–303.
Ghosn, M., and Moses, F. (1998). “Redundancy in highway bridge superstructures.” Rep. 406, Transportation Research Board, National Academy Press, Washington, D.C.
Goble, G., Schulz, J. and Commander, B. (1992). “Load prediction and structural response.” Final Rep. FHWA DTFH61-88-C-00053, Univ. of Colorado, Boulder, Colo.
Hastings, J. (2001). “Bridge rating using in-service data.” Master’s thesis, Univ. of Delaware, Newark, Del.
Hauptmanns, U., and Werner, W. (1991). Engineering risks: Evaluation and valuation, Springer, New York.
Imai, K., and Frangopol, D. M. (2001). “Reliability-based assessment of suspension bridges: Application to the Innoshima Bridge.” J. Bridge Eng., 6(6), 398–411.
International Organization for Standardization (ISO). (1998). ISO 2394 General principles on reliability for structures, 2nd Ed., ISO, Geneva.
Joint Commitee on Structural Safety (JCSS). (2001). “Probabilistic model code, 12th draft,” JCSS, www.jcss.ethz.ch, accessed September 5 2004.
Kendall, M. G., and Stuart, A. (1968). The advanced theory of statistics, Vol. 3, 2nd Ed., Hafner, New York.
Li, D. (2004). “Reliability-based load and resistance factor rating using site specific data.” PhD dissertation, Univ. of Delaware, Newark, Del.
Moan, T. (1997). “Target levels for reliability-based reassessment of offshore structures.” Proc., 7th Int. Conf. on Structural Safety and Reliability, Kyoto, Japan.
Moses, F., Lebet, J. P., and Bez, R. (1994). “Applications of field testing to bridge evaluation.” J. Struct. Eng., 120(6), 1745–1762.
Naess, A. (1998). “Statistical extrapolation of extreme value data based on the peaks over threshold method.” J. Offshore Mech. Arct. Eng., 120, 91–96.
National Cooperative Highway Research Program (NCHRP). (1998). “Manual for bridge rating through load testing.” Research Results Digest, 234, Transportation Research Board, National Research Council, Washington, D.C.
National Cooperative Highway Research Program (NCHRP). (1999a). “Manual for condition evaluation and load and resistance factor rating of highway bridges.” NCHRP 12-46, Pre-Final Draft, Transportation Research Board, National Research Council, Washington, D.C.
National Cooperative Highway Research Program (NCHRP). (1999b). “Calibration of LRFD bridge design code.” Rep. 368. Transportation Research Board, National Research Council, Washington, D.C.
National Cooperative Highway Research Program (NCHRP). (2001). “Calibration of load factors for LRFR bridge evaluation.” Rep. 454. Transportation Research Board, National Research Council, Washington, D.C.
Nowak, A. S. (1995). “Calibration of LRFD bridge code.” J. Struct. Eng., 121(8), 1245–1251.
Nowak, A. S., Szerszen, M. M., and Park, C. H. (1997). “Target safety levels for bridges.” Proc., 7th Int. Conf. on Structural Safety and Reliability, Kyoto, Japan.
Rackwitz, R., and Fiessler, B. (1978). “Structural reliability under combined random load sequences.” Comput. Struct., 9, 489–494.
Shenton, H. W., III, Chajes, M. J., and Holloway, E. S. (2000) “A system for monitoring live load strain in bridges.” CD Proc. Structural Materials Technology IV: An NDT Conference, S. Alampalli, ed., Technomic, Lancaster, Pa.
Simiu, E., and Heckert, N. A. (1996). “Extreme wind distribution tails: A ‘peaks over threshold’ approach.” J. Struct. Eng., 122(5), 539–547.
Stewart, M. G., and Melchers, R. E. (1997). Probabilistic risk assessment of engineering systems, Chapman Hall, London.
van Breugel, K. (1998). “How to deal with and judge the numerical results of risk analysis.” Comput. Struct., 67(1–3), 157–164.
Wen, Y. K. (2001a). “Minimum lifecycle cost design under multiple hazards.” Reliability Eng. Sys. Safety, 73, 223–231.
Wen, Y. K. (2001b). “Reliability and performance based design.” Struct. Safety, 23, 407–428.
Whitman, R. V. (1984). “Evaluating calculated risk in geotechnical engineering.” J. Geotech. Eng., 110(2), 145–188.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 10 • Issue 5 • September 2005
Pages: 530 - 543
Copyright
© 2005 ASCE.
History
Received: Apr 29, 2003
Accepted: Jul 6, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005
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