Resilience-Based Optimal Seismic Retrofit and Recovery Strategies of Bridge Networks under Mainshock–Aftershock Sequences
Publication: Journal of Infrastructure Systems
Volume 30, Issue 3
Abstract
This paper proposes a mathematical framework for optimal retrofit and recovery strategies of bridge networks. The pre-earthquake and postearthquake management of the highway systems is addressed considering performance objectives based on seismic resilience and life-cycle costs. Structural capacity of vulnerable bridges and traffic performance of the transportation network are investigated accounting for the effects of aftershocks by state-dependent fragility curves informing cumulative damage scenarios. Optimal intervention sequences are identified under uncertainties related to bridge damage levels and mainshock–aftershock sequences based on a biobjective optimization problem aiming to maximize network resilience and minimize costs associated with pre-event retrofit and postrepair restoration activities.
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Data Availability Statement
Some data or models that support the findings of this study are available from the corresponding author upon reasonable request. These resources include the input data used for traffic analysis of the assumed network, as well as the models used to apply the proposed framework discussed in the paper.
Acknowledgments
A preliminary version of this paper has been drafted when the first author was a Ph.D. student at the University of Tehran. The paper has been extended and improved, both in the theoretical framework and application examples, when the first author was a visiting Ph.D. student at Politecnico di Milano.
References
Adey, B., R. Hajdin, and E. Brühwiler. 2004. “Effect of common cause failures on indirect costs.” J. Bridge Eng. 9 (2): 200–208. https://doi.org/10.1061/(ASCE)1084-0702(2004)9:2(200).
Ahmed, A. R. A. M., M. H. Gadallah, and H. Hegazi. 2016. “Multi-objective optimization indices: A comparative analysis.” Aust. J. Basic Appl. Sci. 8 (4): 1–12.
Ashrafifar, J., and H. Estekanchi. 2023. “Life-cycle seismic fragility and resilience assessment of aging bridges using the endurance time method.” Soil Dyn. Earthquake Eng. 164 (Feb): 107524. https://doi.org/10.1016/j.soildyn.2022.107524.
Baker, J. W. 2008. “An introduction to probabilistic seismic hazard analysis (PSHA).” In White paper version 1.3. Standord, CA: Stanford Univ.
Balakrishnan, S., and Z. Zhang. 2020. “Criticality and susceptibility indexes for resilience-based ranking and prioritization of components in interdependent infrastructure networks.” J. Manage. Eng. 36 (4): 04020022. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000769.
Banerjee, S., and C. Chi. 2013. “State-dependent fragility curves of bridges based on vibration measurements.” Probab. Eng. Mech. 33 (Jun): 116–125. https://doi.org/10.1016/j.probengmech.2013.03.007.
Baranov, S., and P. Shebalin. 2016. “Forecasting aftershock activity: 1. Adaptive estimates based on the Omori and Gutenberg–Richter laws.” Izv. Phys. Solid Earth 52 (3): 413–431. https://doi.org/10.1134/S1069351316020038.
Baranov, S., and P. Shebalin. 2017. “Forecasting aftershock activity: 2. Estimating the area prone to strong aftershocks.” Izv. Phys. Solid Earth 53 (3): 366–384. https://doi.org/10.1134/S1069351317020021.
Baranov, S., and P. Shebalin. 2018. “Forecasting aftershock activity: 3. Båth’s dynamic law.” Izv. Phys. Solid Earth 54 (6): 926–932. https://doi.org/10.1134/S1069351318060022.
Bindi, D., F. Pacor, L. Luzi, R. Puglia, M. Massa, G. Ameri, and R. Paolucci. 2011. “Ground motion prediction equations derived from the italian strong motion database.” Bull. Earthquake Eng. 9 (6): 1899–1920. https://doi.org/10.1007/s10518-011-9313-z.
Biondini, F., E. Camnasio, and A. Palermo. 2014. “Lifetime seismic performance of concrete bridges exposed to corrosion.” Struct. Infrastruct. Eng. 10 (7): 880–900. https://doi.org/10.1080/15732479.2012.761248.
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.
Biondini, F., and D. M. Frangopol. 2016. “Life-cycle performance of deteriorating structural systems under uncertainty.” J. Struct. Eng. 142 (9): F4016001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001544.
Biondini, F., and D. M. Frangopol. 2019. Life-cycle design, assessment, and maintenance of structures and infrastructure systems. Reston, VA: ASCE.
Bocchini, P., and D. M. Frangopol. 2011a. “Resilience-driven disaster management of civil infrastructure.” In Computational methods in structural dynamics and earthquake engineering, edited by M. Papadrakakis, M. Fragiadakis, and V. Plevris, 1–11. Athens, Greece: National Technical Univ. of Athens.
Bocchini, P., and D. M. Frangopol. 2011b. “A stochastic computational framework for the joint transportation network fragility analysis and traffic flow distribution under extreme events.” Probab. Eng. Mech. 26 (2): 182–193. https://doi.org/10.1016/j.probengmech.2010.11.007.
Bocchini, P., and D. M. Frangopol. 2012a. “Optimal resilience-and cost-based postdisaster intervention prioritization for bridges along a highway segment.” J. Bridge Eng. 17 (1): 117–129. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000201.
Bocchini, P., and D. M. Frangopol. 2012b. “Restoration of bridge networks after an earthquake: Multicriteria intervention optimization.” Earthquake Spectra 28 (2): 427–455. https://doi.org/10.1193/1.4000019.
Brookshire, D. S., S. E. Chang, H. Cochrane, R. A. Olson, A. Rose, and J. Steenson. 1997. “Direct and indirect economic losses from earthquake damage.” Earthquake Spectra 13 (4): 683–701. https://doi.org/10.1193/1.1585975.
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.
Cantelmi, R., G. Di Gravio, and R. Patriarca. 2021. “Reviewing qualitative research approaches in the context of critical infrastructure resilience.” Environ. Syst. Dec. 41 (3): 341–376. https://doi.org/10.1007/s10669-020-09795-8.
Capacci, L., and F. Biondini. 2020. “Probabilistic life-cycle seismic resilience assessment of aging bridge networks considering infrastructure upgrading.” Struct. Infrastruct. Eng. 16 (4): 659–675. https://doi.org/10.1080/15732479.2020.1716258.
Capacci, L., F. Biondini, and D. Frangopol. 2023. “Review of advances in life-cycle seismic risk and resilience of bridges and bridge networks.” In Life-cycle of structures and infrastructure systems, edited by F. Biondini and D. M. Frangopol, 883–891. London: Taylor & Francis Group.
Capacci, L., F. Biondini, and D. M. Frangopol. 2022. “Resilience of aging structures and infrastructure systems with emphasis on seismic resilience of bridges and road networks.” Resilient Cities Struct. 1 (2): 23–41. https://doi.org/10.1016/j.rcns.2022.05.001.
Capacci, L., F. Biondini, and A. S. Kiremidjian. 2021. “Damage disaggregation for seismic resilience assessment of aging bridge networks.” In Proc., 17th World Conf., on Earthquake Engineering (17WCEE), 1–12. Tokyo: International Association of Exhibitions and Events.
Capacci, L., F. Biondini, and A. Titi. 2020. “Lifetime seismic resilience of aging bridges and road networks.” Struct. Infrastruct. Eng. 16 (2): 266–286. https://doi.org/10.1080/15732479.2019.1653937.
Christopher, R., and L. Roland. 1985. ATC-13: Earthquake damage evaluation data for California. Redwood City, CA: Applied Technology Council.
Cimellaro, G. P., A. M. Reinhorn, and M. Bruneau. 2010. “Framework for analytical quantification of disaster resilience.” Eng. Struct. 32 (11): 3639–3649. https://doi.org/10.1016/j.engstruct.2010.08.008.
Cimellaro, G. P., D. Solari, V. Arcidiacono, C. S. Renschler, A. Reinhorn, and M. Bruneau. 2014. “Community resilience assessment integrating network interdependencies.” In Proc., Tenth US National Conf. on Earthquake Engineering (10NCEE). Buffalo, NY: Univ. at Buffalo.
Cornell, C. A., F. Jalayer, R. O. Hamburger, and D. A. Foutch. 2002. “Probabilistic basis for 2000 sac federal emergency management agency steel moment frame guidelines.” J. Struct. Eng. 128 (4): 526–533. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:4(526).
Dijkstra, E. W. 1959. “A note on two problems in connexion with graphs.” Numer. Math. 1 (1): 269–271. https://doi.org/10.1007/BF01386390.
Dueñas-Osorio, L., and A. Kwasinski. 2012. “Quantification of lifeline system interdependencies after the 27 February 2010 mw 8.8 offshore Maule, Chile, earthquake.” Supplement, Earthquake Spectra 28 (S1): 581–603. https://doi.org/10.1193/1.4000054.
Evans, S. P. 1976. “Derivation and analysis of some models for combining trip distribution and assignment.” Transp. Res. 10 (1): 37–57. https://doi.org/10.1016/0041-1647(76)90100-3.
Forcellini, D. 2019. “A new methodology to assess indirect losses in bridges subjected to2011 multiple hazards.” Innovative Infrastruct. Solutions 4 (1): 10. https://doi.org/10.1007/s41062-018-0195-7.
Frangopol, D. M., and P. Bocchini. 2011. “Resilience as optimization criterion for the rehabilitation of bridges belonging to a transportation network subject to earthquake.” In Proc., ASCE Structures Congress, Las Vegas, Nevada, edited by D. Ames, T. L. Droessler, and M. Hoit, 2044–2055. Reston, VA: ASCE. https://doi.org/10.1061/41171(401)178.
Frank, M., and P. Wolfe. 1956. “An algorithm for quadratic programming.” Nav. Res. Logist. Q. 3 (1–2): 95–110. https://doi.org/10.1002/nav.3800030109.
Gibbons, A. 1985. Algorithmic graph theory. Cambridge, UK: Cambridge University Press.
Goda, K., A. Pomonis, S. C. Chian, M. Offord, K. Saito, P. Sammonds, S. Fraser, A. Raby, and J. Macabuag. 2013. “Ground motion characteristics and shaking damage of the 11th March 2011 m w9. 0 Great East Japan earthquake.” Bull. Earthquake Eng. 11 (1): 141–170. https://doi.org/10.1007/s10518-012-9371-x.
HAZUS. 2003. “Multi-hazard loss estimation methodology.” In Earthquake model (HAZUS MH. MR4) technical manual. Washington, DC: FEMA.
Huang, C., and S. Huang. 2021. “Seismic resilience assessment of aging bridges with different failure modes.” In Vol. 33 of Structures, 3682–3690. Amsterdam, Netherlands: Elsevier.
Iervolino, I., E. Chioccarelli, and A. Suzuki. 2020. “Seismic damage accumulation in multiple mainshock–aftershock sequences.” Earthquake Eng. Struct. Dyn. 49 (10): 1007–1027. https://doi.org/10.1002/eqe.3275.
Iervolino, I., M. Giorgio, and E. Chioccarelli. 2016. “Markovian modeling of seismic damage accumulation.” Earthquake Eng. Struct. Dyn. 45 (3): 441–461. https://doi.org/10.1002/eqe.2668.
Iervolino, I., M. Giorgio, and B. Polidoro. 2014. “Sequence-based probabilistic seismic hazard analysis.” Bull. Seismol. Soc. Am. 104 (2): 1006–1012. https://doi.org/10.1785/0120130207.
Jalayer, F. 2003. Direct probabilistic seismic analysis: Implementing non-linear dynamic assessments. Stanford, CA: Stanford Univ.
Karamlou, A. 2017. Multi-scale methodologies for probabilistic resilience assessment and enhancement of bridges and transportation systems. Bethlehem, PA: Lehigh Univ.
Karamlou, A., and P. Bocchini. 2014. “Optimal bridge restoration sequence for resilient transportation networks.” In Proc., Structures Congress 2014, 1437–1447. Reston, VA: ASCE. https://doi.org/10.1061/9780784413357.127.
Karamlou, A., P. Bocchini, and V. Christou. 2016. “Metrics and algorithm for optimal retrofit strategy of resilient transportation networks.” In Maintenance, monitoring, safety, risk and resilience of bridges and bridge networks, 335. Boca Raton, FL: CRC Press.
Khansefid, A., and A. Bakhshi. 2022. “New model for simulating random synthetic stochastic earthquake scenarios.” J. Earthquake Eng. 26 (2): 1072–1089. https://doi.org/10.1080/13632469.2019.1699207.
Knowles, J., and D. Corne. 1999. “The Pareto archived evolution strategy: A new baseline algorithm for Pareto multiobjective optimisation.” In Proc., 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 98–105. New York: IEEE.
Lee, C., and R. B. Machemehl. 2005. Combined traffic signal control and traffic assignment: Algorithms, implementation and numerical results. New York: Association for Computing Machinery.
Levinson, D. M., and A. Kumar. 1994. “Multi-modal trip distribution: Structure and application.” Transp. Res. Rec.: J. Transp. Res. Board 1446 (1): 124–131.
Liu, Y., S. McNeil, J. Hackl, and B. T. Adey. 2022. “Prioritizing transportation network recovery using a resilience measure.” Sustainable Resilient Infrastruct. 7 (1): 70–81. https://doi.org/10.1080/23789689.2019.1708180.
Masiero, L., and R. Maggi. 2012. “Estimation of indirect cost and evaluation of protective measures for infrastructure vulnerability: A case study on the transalpine transport corridor.” Transp. Policy 20 (Sep): 13–21. https://doi.org/10.1016/j.tranpol.2011.10.002.
Merschman, E., M. Doustmohammadi, A. M. Salman, and M. Anderson. 2020. “Postdisaster decision framework for bridge repair prioritization to improve road network resilience.” Transp. Res. Rec. 2674 (3): 81–92. https://doi.org/10.1177/0361198120908870.
Messore, M. M., L. Capacci, and F. Biondini. 2020. “Life-cycle cost-based risk assessment of aging bridge networks.” Struct. Infrastruct. Eng. 17 (4): 515–533. https://doi.org/10.1080/15732479.2020.1845752.
Nielson, B. G., and R. DesRoches. 2007. “Seismic fragility methodology for highway bridges using a component level approach.” Earthquake Eng. Struct. Dyn. 36 (6): 823–839. https://doi.org/10.1002/eqe.655.
Padgett, J. E. 2007. “Seismic vulnerability assessment of retrofitted bridges using probabilistic methods.” Ph.D. thesis, School of Civil and Environmental Engineering, Georgia Institute of Technology.
Padgett, J. E., and R. DesRoches. 2007. “Bridge functionality relationships for improved seismic risk assessment of transportation networks.” Earthquake Spectra 23 (1): 115–130. https://doi.org/10.1193/1.2431209.
Padgett, J. E., and R. DesRoches. 2009. “Retrofitted bridge fragility analysis for typical classes of multispan bridges.” Earthquake Spectra 25 (1): 117–141. https://doi.org/10.1193/1.3049405.
Pang, Y., and L. Wu. 2018. “Seismic fragility analysis of multispan reinforced concrete bridges using mainshock-aftershock sequences.” Math. Prob. Eng. 2018 (Dec): 1–12. https://doi.org/10.1155/2018/1537301.
Reasenberg, P. A., and L. M. Jones. 1989. “Earthquake hazard after a mainshock in California.” Science 243 (4895): 1173–1176. https://doi.org/10.1126/science.243.4895.1173.
Shadabfar, M., M. Mahsuli, Y. Zhang, Y. Xue, B. M. Ayyub, H. Huang, and R. A. Medina. 2022. “Resilience-based design of infrastructure: Review of models, methodologies, and computational tools.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 8 (1): 03121004. https://doi.org/10.1061/AJRUA6.0001184.
Shcherbakov, R., M. Nguyen, and M. Quigley. 2012. “Statistical analysis of the 2010 mw 7.1 Darfield earthquake aftershock sequence.” N. Z. J. Geol. Geophys. 55 (3): 305–311. https://doi.org/10.1080/00288306.2012.676556.
Shinozuka, M., Y. Murachi, X. Dong, Y. Zhou, and M. J. Orlikowski. 2003. “Effect of seismic retrofit of bridges on transportation networks.” Earthquake Eng. Eng. Vib. 2 (2): 169–179. https://doi.org/10.1007/s11803-003-0001-0.
Skokandić, D., A. Vlašić, M. Kušter Marić, M. Srbić, and A. Mandić Ivanković. 2022. “Seismic assessment and retrofitting of existing road bridges: State of the art review.” Materials 15 (7): 2523. https://doi.org/10.3390/ma15072523.
Srinivas, N., and K. Deb. 1994. “Muiltiobjective optimization using nondominated sorting in genetic algorithms.” Evol. Comput. 2 (3): 221–248. https://doi.org/10.1162/evco.1994.2.3.221.
Sun, W., P. Bocchini, and B. D. Davison. 2020. “Resilience metrics and measurement methods for transportation infrastructure: The state of the art.” Sustainable Resilient Infrastruct. 5 (3): 168–199. https://doi.org/10.1080/23789689.2018.1448663.
Titi, A., and F. Biondini. 2013. “Resilience of concrete frame structures under corrosion.” In Proc., 11th Int. Conf. on Structural, Safety & Reliability, edited by G. Deodatis, B. R. Ellingwood, and D. M. Frangopol, 16–20. London: Taylor and Francis Group.
Wardrop, J. G. 1952. “Road paper. Some theoretical aspects of road traffic research.” Proc. Inst. Civ. Eng. 1 (3): 325–362. https://doi.org/10.1680/ipeds.1952.11259.
Wei, F., E. Koc, N. Li, L. Soibelman, and D. Wei. 2022. “A data-driven framework to evaluate the indirect economic impacts of transportation infrastructure disruptions.” Int. J. Disaster Risk Reduct. 75 (Jan): 102946. https://doi.org/10.1016/j.ijdrr.2022.102946.
Wu, Y., G. Hou, and S. Chen. 2021. “Post-earthquake resilience assessment and long-term restoration prioritization of transportation network.” Reliab. Eng. Syst. Saf. 211 (Jul): 107612. https://doi.org/10.1016/j.ress.2021.107612.
Yeo, G. L. 2005. Stochastic characterization and decision bases under time-dependent aftershock risk in performance-based earthquake engineering. Stanford, CA: Stanford Univ.
Yeo, G. L., and C. A. Cornell. 2009. “A probabilistic framework for quantification of aftershock ground-motion hazard in California: Methodology and parametric study.” Earthquake Eng. Struct. Dyn. 38 (1): 45–60. https://doi.org/10.1002/eqe.840.
Yin, C., M. M. Kassem, and F. Mohamed Nazri. 2022. “Comprehensive review of community seismic resilience: Concept, frameworks, and case studies.” Adv. Civ. Eng. 19 (Apr): 7668214. https://doi.org/10.1155/2022/7668214.
Zitzler, E. 1999. “Evolutionary algorithms for multi-objective optimization: Methods and applications.” Doctoral dissertation, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology.
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Published In
Journal of Infrastructure Systems
Volume 30 • Issue 3 • September 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Feb 2, 2023
Accepted: Apr 22, 2024
Published online: Jun 17, 2024
Published in print: Sep 1, 2024
Discussion open until: Nov 17, 2024
ASCE Technical Topics:
- Bridge engineering
- Bridges
- Construction engineering
- Construction methods
- Earthquake engineering
- Earthquakes
- Engineering fundamentals
- Geohazards
- Geotechnical engineering
- Highway and road management
- Highway transportation
- Infrastructure
- Infrastructure resilience
- Rehabilitation
- Seismic effects
- Seismic tests
- Structural engineering
- Tests (by type)
- Transportation engineering
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