Fatigue Reliability Assessment for Orthotropic Steel Deck Details Using Copulas: Application to Nan-Xi Yangtze River Bridge
Publication: Journal of Bridge Engineering
Volume 23, Issue 1
Abstract
In this study, the correlation between the fatigue equivalent stress and the stress cycle was considered using the copula function in the fatigue reliability assessment. In most earlier studies, the variables for the fatigue reliability function were assumed to be independent. However, based on the structural health monitoring (SHM) data in this study, they show that there are correlation properties in part of the variables. Hence, using the traditional method, the calculated fatigue reliability index is not accurate. For this reason, a new calculation method that considers the correlation between the variables was developed. The Gaussian copula was used to solve this problem because of its powerful connect function and concise expression. The study shows that there is a correlation between the fatigue stress and the fatigue stress cycle in the Nan-Xi Yangtze River Bridge. The values of the fatigue reliability index that consider the correlation between the variables are smaller than those calculated by the traditional method.
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Acknowledgments
This research was supported by a project from the National Key Fundamental Research Development Program (Program 973) (Grant 2015CB055701), and by a project from the National Natural Science Foundation of China (Grants 51378081 and 51308073).
References
AASHTO. (2010). LRFD bridge design specifications, 5th Ed., Washington, DC.
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, 19(6), 716–723.
Attema, T., Acharige, A. K., Morales-Nápoles, O., and Maljaars, J. (2017). “Maintenance decision model for steel bridges: A case in the Netherlands.” Struct. Infrastruct. Eng., 13(2), 242–253.
British Standards Institution. (1980). Steel, concrete and composite bridges, part10: Code of practice for fatigue.” BS 5400, London.
Demarta, S., and McNeil, A. J. (2005). “The t copula and related copulas.” Int. Stat. Rev., 73(1), 111–129.
Deng, Y., Ding, Y., Li, A., and Zhou, G. (2011). “Fatigue reliability assessment for bridge welded details using long-term monitoring data.” Sci. China Technol. Sci., 54(12), 3371–3381.
Downing, S. D., and Socie, D. F. (1982). “Simple rainflow counting algorithms.” Int. J. Fatigue, 4(1), 31–40.
Eryilmaz, S. (2014). “Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components.” Struct. Saf., 51:23–28.
Fengler, M. R., and Okhrin, O. (2016). “Managing risk with a realized copula parameter.” Comput. Stat. Data Anal., 100, 131–152.
Frangopol, D. M. (2008). “Probability concepts in engineering: Emphasis on applications to civil and environmental engineering.” Struct. Infrastruct. Eng, 4(5), 413–414.
Goda, K. (2010). “Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands.” Struct. Saf., 32(2), 112–123.
Grooteman, F. (2008). “Adaptive radial-based importance sampling method for structural reliability.” Struct. Saf., 30(6), 533–542.
Guo, T., and Chen, Y. W. (2011). “Field stress/displacement monitoring and fatigue reliability assessment of retrofitted steel bridge details.” Eng. Fail. Anal., 18(1), 354–363.
Guo, T., Frangopol, D. M., and Chen, Y. (2012). “Fatigue reliability assessment of steel bridge details integrating weigh-in-motion data and probabilistic finite element analysis.” Comput. Struct., 112–113, 245–257.
Guo, T., Li, A., and Li, J. (2008). “Fatigue life prediction of welded joints in orthotropic steel decks considering temperature effect and increasing traffic flow.” Struct. Health Monit., 7(3), 189–202.
Jiang, C., Zhang, W., Wang, B., and Han, X. (2014). “Structural reliability analysis using a copula-function-based evidence theory model.” Comput. Struct., 143, 19–31.
Keissar, K., Maestri, R., Pinna, G. D., La Rovere, M. T., and Gilad, O. (2010). “Non-invasive baroreflex sensitivity assessment using wavelet transfer function-based time-frequency analysis.” Physiol. Meas., 31(7), 1021–1036.
Kwon, K., and Dan, M. F. (2010). “Bridge fatigue reliability assessment using probability density functions of equivalent stress range based on field monitoring data.” Int. J. Fatigue, 32(8), 1221–1232.
Liu, M., Frangopol, D. M., and Kwon, K. (2010). “Fatigue reliability assessment of retrofitted steel bridges integrating monitored data.” Struct. Saf., 32(1), 77–89.
Liu, Y., Lu, N. W., and Yin, X. F. (2016). “A hybrid method for structural system reliability-based design optimization and its application to trusses.” Qual. Reliab. Eng. Int., 32(2), 595–608.
Liu, Y., Zhang, H. P., Liu, D. R., Deng, Y., Jiang, N., and Lu, N. (2017). “Fatigue reliability assessment for orthotropic steel deck details under traffic flow and temperature loading.” Eng. Fail. Anal., 71, 179–194.
Lu, N. W., Noori, M., and Liu, Y. (2017). “Fatigue reliability assessment of welded steel bridge decks under stochastic truck loads via machine learning.” J. Bridge Eng, 04016105.
Miner, M. A. (1945). “Cumulative damage in fatigue.” J. Appl. Mech., 12(3), A159–A164.
Nelsen, R. B. (2006). An introduction to copulas (Springer series in statistics), Springer, New York.
Ni, Y. Q., Ye, X. W., and Ko, J. M. (2010). “Monitoring-based fatigue reliability assessment of steel bridges: Analytical model and application.” J. Struct. Eng., 1563–1573.
Noh, Y., Choi, K. K., and Du, L. (2009). “Reliability-based design optimization of problems with correlated input variables using a Gaussian copula.” Struct. Multidiscip. Optim., 38(1), 1–16.
Singh, V., and Zhang, L. (2006). “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng., 150–164.
Sklar, M. (1960). “Fonctions de répartition À n dimensions et leurs marges.” Publ. Inst. Statist. Univ. Paris, 8, 229–231.
Tang, X. S., Li, D. Q., Zhou, C. B., and Phoon, K. K. (2015). “Copula-based approaches for evaluating slope reliability under incomplete probability information.” Struct. Saf., 52, 90–99.
Tang, X. S., Li, D. Q., Zhou, C. B., Phoon, K. K., and Zhang, L. M. (2013a). “Impact of copulas for modeling bivariate distributions on system reliability.” Struct. Saf., 44(2334), 80–90.
Tang, X. S., Li, D. Q., Zhou, C. B., and Zhang, L. M. (2013b). “Bivariate distribution models using copulas for reliability analysis.” Proc. Inst. Mech. Eng. Part O: J. Risk Reliab., 227(5), 499–512.
Wirsching, P. H. (1984). “Fatigue reliability for offshore structures.” J. Struct. Eng., 2340–2356.
Wu, X. Z. (2015). “Assessing the correlated performance functions of an engineering system via probabilistic analysis.” Struct. Saf., 52(Part A), 10–19.
Yazdani, N., and Albrecht, P. (1987). “Risk analysis of fatigue failure of highway steel bridges.” J. Struct. Eng, 483–500.
Zhao, Z., Haldar, A., and Breen, F. J., Jr. (1994). “Fatigue-reliability evaluation of steel bridges.” J. Struct. Eng., 1608–1623.
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Published In
Journal of Bridge Engineering
Volume 23 • Issue 1 • January 2018
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Nov 2, 2016
Accepted: Jun 27, 2017
Published online: Nov 8, 2017
Published in print: Jan 1, 2018
Discussion open until: Apr 8, 2018
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