Abstract
Civil structures and infrastructures are often subjected by design to the impacts of natural and human-caused hazardous events, and accordingly may suffer from damages, functionality loss, and failure. In order to quantitatively measure the associated likelihood and consequences for quantifying risks, an appropriate measure of structural reliability and resilience is essentially required. This paper presents an explicit measure for the time-dependent resilience of repairable structures as a natural extension of time-invariant and time-dependent structural reliability concepts, taking into account the effects of structural performance deterioration and nonstationary external loads. First, the resilience measure associated with a single load event is discussed, and an integral-free expression is developed for a special case of structural robustness and recovery. Subsequently, the resilience measure for a planning horizon, which is a function of the duration of considered service period, is proposed in a closed form. Remarkably, the time-dependent resilience can be treated as a generalized form of the time-dependent reliability. Motivated by this, the resilience-based design and cost optimization of structures are also discussed. A numerical example is presented to demonstrate the accuracy and applicability of the proposed resilience measure.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research described in this paper was supported by the Vice-Chancellor’s Postdoctoral Research Fellowship from the University of Wollongong. This support is gratefully acknowledged. The authors would like to acknowledge the thoughtful suggestions of three anonymous reviewers, which substantially improved the present paper.
References
Attoh-Okine, N. O., A. T. Cooper, and S. A. Mensah. 2009. “Formulation of resilience index of urban infrastructure using belief functions.” IEEE Syst. J. 3 (2): 147–153. https://doi.org/10.1109/JSYST.2009.2019148.
Ayyub, B. M. 2014. “Systems resilience for multihazard environments: Definition, metrics, and valuation for decision making.” Risk Anal. 34 (2): 340–355. https://doi.org/10.1111/risa.12093.
Ayyub, B. M. 2015. “Practical resilience metrics for planning, design, and decision making.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Mech. Eng. 1 (3): 04015008. https://doi.org/10.1061/AJRUA6.0000826.
Ayyub, B. M., and G. J. Klir. 2006. Uncertainty modeling and analysis in engineering and the sciences. New York: Chapman and Hall/CRC.
Ayyub, B. M., K. A. Stambaugh, T. A. McAllister, G. F. de Souza, and D. Webb. 2015. “Structural life expectancy of marine vessels: Ultimate strength, corrosion, fatigue, fracture, and systems.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 1 (1): 011001. https://doi.org/10.1115/1.4026396.
Biondini, F., E. Camnasio, and A. Titi. 2015. “Seismic resilience of concrete structures under corrosion.” Earthquake Eng. Struct. Dyn. 44 (14): 2445–2466. https://doi.org/10.1002/eqe.2591.
Bonstrom, H., and R. B. Corotis. 2016. “First-order reliability approach to quantify and improve building portfolio resilience.” J. Struct. Eng. 142 (8): C4014001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001213.
Bruneau, M., S. E. Chang, R. T. Eguchi, G. C. Lee, T. D. O’Rourke, A. M. Reinhorn, M. Shinozuka, K. Tierney, W. A. Wallace, and D. Von Winterfeldt. 2003. “A framework to quantitatively assess and enhance the seismic resilience of communities.” Earthquake Spectra 19 (4): 733–752. https://doi.org/10.1193/1.1623497.
Bruneau, M., and A. Reinhorn. 2007. “Exploring the concept of seismic resilience for acute care facilities.” Earthquake Spectra 23 (1): 41–62. https://doi.org/10.1193/1.2431396.
Chang, S. E., and M. Shinozuka. 2004. “Measuring improvements in the disaster resilience of communities.” Earthquake Spectra 20 (3): 739–755. https://doi.org/10.1193/1.1775796.
Cheung, M. S., and B. Kyle. 1996. “Service life prediction of concrete structures by reliability analysis.” Constr. Build. Mater. 10 (1): 45–55. https://doi.org/10.1016/0950-0618(95)00055-0.
Decò, A., P. Bocchini, and D. M. Frangopol. 2013. “A probabilistic approach for the prediction of seismic resilience of bridges.” Earthquake Eng. Struct. Dyn. 42 (10): 1469–1487. https://doi.org/10.1002/eqe.2282.
Dieulle, L., C. Bérenguer, A. Grall, and M. Roussignol. 2003. “Sequential condition-based maintenance scheduling for a deteriorating system.” Eur. J. Oper. Res. 150 (2): 451–461. https://doi.org/10.1016/S0377-2217(02)00593-3.
Ellingwood, B. R. 2005. “Risk-informed condition assessment of civil infrastructure: State of practice and research issues.” Struct. Infrastruct. Eng. 1 (1): 7–18. https://doi.org/10.1080/15732470412331289341.
Enright, M. P., and D. M. Frangopol. 1998. “Service-life prediction of deteriorating concrete bridges.” J. Struct. Eng. 124 (3): 309–317. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:3(309).
Goss, M., D. L. Swain, J. T. Abatzoglou, A. Sarhadi, C. A. Kolden, A. P. Williams, and N. S. Diffenbaugh. 2020. “Climate change is increasing the likelihood of extreme autumn wildfire conditions across California.” Environ. Res. Lett. 15 (9): 094016. https://doi.org/10.1088/1748-9326/ab83a7.
IPCC (Intergovernmental Panel on Climate Change). 2021. “Climiate change 2021: The physical science basis.” In Contribution of Working Group I to the 6th Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, UK: Cambridge University Press.
Kafali, C., and M. Grigoriu. 2005. “Rehabilitation decision analysis.” In Proc., 9th Int. Conf. on Structural Safety and Reliability (ICOSSAR05). New York: International Association for Structural Safety and Reliability.
Knutson, T. R., J. L. McBride, J. Chan, K. Emanuel, G. Holland, C. Landsea, I. Held, J. P. Kossin, A. Srivastava, and M. Sugi. 2010. “Tropical cyclones and climate change.” Nat. Geosci. 3 (3): 157–163. https://doi.org/10.1038/ngeo779.
Kumar, R., D. B. Cline, and P. Gardoni. 2015. “A stochastic framework to model deterioration in engineering systems.” Struct. Saf. 53 (Mar): 36–43. https://doi.org/10.1016/j.strusafe.2014.12.001.
Li, Q., C. Wang, and B. R. Ellingwood. 2015. “Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation.” Struct. Saf. 52 (Part A): 132–141. https://doi.org/10.1016/j.strusafe.2014.10.003.
Ma, Y., J. Zhang, L. Wang, and Y. Liu. 2013. “Probabilistic prediction with bayesian updating for strength degradation of RC bridge beams.” Struct. Saf. 44 (Sep): 102–109. https://doi.org/10.1016/j.strusafe.2013.07.006.
McAllister, T. 2013. Developing guidelines and standards for disaster resilience of the built environment: A research needs assessment. Gaithersburg, MD: US Dept. of Commerce, National Institute of Standards and Technology.
Mori, Y., and B. R. Ellingwood. 1993. “Reliability-based service-life assessment of aging concrete structures.” J. Struct. Eng. 119 (5): 1600–1621. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1600).
Munich RE. 2021. “Record hurricane season and major wildfires—The natural disaster figures for 2020.”Accessed July 31, 2021. https://www.munichre.com/en/company/media-relations/media-information-and-corporate-news/media-information/2021/2020-natural-disasters-balance.html.
National Research Council. 2012. Disaster resilience: A national imperative. Washington, DC: National Academies Press.
NOAA (National Oceanic and Atmospheric Administration). 2021. “Billion-dollar weather and climate disasters: Events.” Accessed July 31, 2021. https://www.ncdc.noaa.gov/billions/events/US/2020.
Reda Taha, M., B. M. Ayyub, K. Soga, S. Daghash, D. Heras Murcia, F. Moreu, and E. Soliman. 2021. “Emerging technologies for resilient infrastructure: Conspectus and roadmap.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 7 (2): 03121002. https://doi.org/10.1061/AJRUA6.0001134.
Renschler, C. S., A. E. Frazier, L. A. Arendt, G. P. Cimellaro, A. M. Reinhorn, and M. Bruneau. 2010. A framework for defining and measuring resilience at the community scale: The PEOPLES resilience framework. Buffalo, NY: Univ. at Buffalo.
Salomon, J., M. Broggi, S. Kruse, S. Weber, and M. Beer. 2020. “Resilience decision-making for complex systems.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 6 (2): 020901. https://doi.org/10.1115/1.4044907.
Sanchez-Silva, M., G.-A. Klutke, and D. V. Rosowsky. 2011. “Life-cycle performance of structures subject to multiple deterioration mechanisms.” Struct. Saf. 33 (3): 206–217. https://doi.org/10.1016/j.strusafe.2011.03.003.
Schurman, G. 2017. “The exponential integral part I–Derivation and solution.” Accessed July 31, 2021. http://www.appliedbusinesseconomics.com/files/gvsexpint01.pdf.
Stewart, M. G., and D. V. Rosowsky. 1998. “Time-dependent reliability of deteriorating reinforced concrete bridge decks.” Struct. Saf. 20 (1): 91–109. https://doi.org/10.1016/S0167-4730(97)00021-0.
Stewart, M. G., D. V. Rosowsky, and D. V. Val. 2001. “Reliability-based bridge assessment using risk-ranking decision analysis.” Struct. Saf. 23 (4): 397–405. https://doi.org/10.1016/S0167-4730(02)00010-3.
Tierney, K., and M. Bruneau. 2007. “Conceptualizing and measuring resilience: A key to disaster loss reduction.” TR News 250: 14–17.
Vishwanath, B. S., and S. Banerjee. 2019. “Life-cycle resilience of aging bridges under earthquakes.” J. Bridge Eng. 24 (11): 04019106. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001491.
Wang, C., M. Beer, and B. M. Ayyub. 2021. “Time-dependent reliability of aging structures: Overview of assessment methods.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 7 (4): 03121003. https://doi.org/10.1061/AJRUA6.0001176.
Wang, C., and H. Zhang. 2020. “Assessing the seismic resilience of power grid systems considering the component deterioration and correlation.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 6 (2): 020903. https://doi.org/10.1115/1.4046394.
Wang, C., H. Zhang, and Q. Li. 2017. “Reliability assessment of aging structures subjected to gradual and shock deteriorations.” Reliab. Eng. Syst. Saf. 161 (May): 78–86. https://doi.org/10.1016/j.ress.2017.01.014.
Yang, D. Y., and D. M. Frangopol. 2019. “Life-cycle management of deteriorating civil infrastructure considering resilience to lifetime hazards: A general approach based on renewal-reward processes.” Reliab. Eng. Syst. Saf. 183 (Mar): 197–212. https://doi.org/10.1016/j.ress.2018.11.016.
Information & Authors
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8 • Issue 3 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 17, 2021
Accepted: Mar 3, 2022
Published online: Apr 23, 2022
Published in print: Sep 1, 2022
Discussion open until: Sep 23, 2022
ASCE Technical Topics:
- Analysis (by type)
- Construction engineering
- Construction methods
- Design (by type)
- Deterioration
- Engineering fundamentals
- Failure analysis
- Infrastructure
- Infrastructure resilience
- Load factors
- Materials characterization
- Materials engineering
- Measurement (by type)
- Rehabilitation
- Structural analysis
- Structural design
- Structural engineering
- Structural reliability
- Time dependence
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