An integrated decision-making approach to resilience-LCC Bridge network retrofitting using a genetic algorithm-based framework

Abstract

Bridge networks are essential components of civil infrastructure, supporting communities by delivering vital services and facilitating economic activities. However, bridges are vulnerable to natural disasters, particularly earthquakes. To develop an effective disaster management strategy, it is critical to identify reliable, robust, and efficient indicators. In this regard, Life-Cycle Cost (LCC) and Resilience (R) serve as key indicators to assist decision-makers in selecting the most effective disaster risk reduction plans. This study proposes an innovative LCC-R optimization framework to identify the most optimal retrofit strategies for bridge networks facing hazardous events during their lifespan. The proposed framework employs both single- and multi-objective optimization techniques to identify retrofit strategies that maximize the R index while minimizing the LCC for the under-study bridge networks. The considered retrofit strategies include various options such as different materials (steel, CFRP, and GFRP), thicknesses, arrangements, and timing of retrofitting actions. The first step in the proposed framework involves constructing fragility curves by performing a series of nonlinear time-history incremental dynamic analyses for each case. In the subsequent step, the seismic resilience surfaces are calculated using the obtained fragility curves and assuming a recovery function. Next, the LCC is evaluated according to the proposed formulation for multiple seismic occurrences, which incorporates the effects of complete and incomplete repair actions resulting from previous multiple seismic events. For optimization purposes, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) evolutionary algorithm efficiently identifies the Pareto front to represent the optimal set of solutions. The study presents the most effective retrofit strategies for an illustrative bridge network, providing a comprehensive discussion and insights into the resulting tactical approaches. The findings underscore that the methodologies employed lead to logical and actionable retrofit strategies, paving the way for enhanced resilience and cost-effectiveness in bridge network management against seismic hazards.

Keywords

Bridge network / Infrastructures management / Decision-making framework / Resilience / Life-cycle cost

Relevance to resilience

Resilience is increasingly becoming a central idea in designing, assessing, monitoring, maintaining, and managing infrastructure systems. Resilience can be defined as the ability of a system to withstand the effects of disruptive events and efficiently recover to pre-event performance. In infrastructure management, decision-makers need to develop disaster risk reduction methodologies to find the most optimal mitigation strategies. In this regard, this research proposes a logical optimization framework by investigating and comparing various objectives, such as resilience and life-cycle cost, through single- or multi-objective optimization. This framework presents a comprehensive understanding of the current and future states of the under-study system, enabling decision-makers to make informed decisions on how to effectively manage infrastructure throughout its life-cycle.

Compliance with ethical standards

Conflict of interest: The authors declare no conflict of interest.

Replication of results

Detailed information on the proposed methods, simulation models, and software used in this article can be found in the corresponding sections. This includes the algorithms and parameters used. The data that support the findings of this study are available from the first author upon reasonable request.

Author statements and declarations

Author Contributions: All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Pedram Omidian, Naser Khaji and Ali Akbar Aghakouchak. All authors read and approved the final manuscript

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

CRediT authorship contribution statement

Pedram Omidian: Writing - review & editing, Writing - original draft, Visualization, Validation, Supervision, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Naser Khaji: Writing - review & editing, Writing - original draft, Visualization, Validation, Supervision, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Ali Akbar Aghakouchak: Writing - review & editing, Writing - original draft, Visualization, Validation, Supervision, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors have no relevant financial or non-financial interests to disclose.

Acknowledgments

The authors would like to thank anonymous reviewers for their constructive comments, which greatly improved the quality of the initial manuscript.

References

[1] Feng K, Wang C, Li Q. Evaluating the role of transportation system in community seismic resilience. Resilient Cities Struct 2024; 3(3):65-78. doi: 10.1016/j.rcns.2024.05.003.

[2] Godazgar B, Balomenos GP, Tighe SL. Resilience surface for quantifying hazard resiliency of transportation infrastructure. Resilient Cities Struct 2023; 2(3):74-86. doi: 10.1016/j.rcns.2023.08.001.

[3] Van De Lindt JW, Kruse J, Cox DT, Gardoni P, Lee JS, Padgett J, McAllister TP, Barbosa A, Cutler H, Van Zandt Sh, Rosenheim N, Navarro CM, Sutley E, Hamideh A. The interdependent networked community resilience modeling environment (INCORE). Resilient Cities Struct 2023; 2(2):57-66. doi: 10.1016/j.rcns.2023.07.004.

[4] Chaudhary RK, Gernay T, Van Coile R. Cost-optimization based target reliabilities for design of structures exposed to fire. Resilient Cities Struct 2024; 3(2):20-33. doi: 10.1016/j.rcns.2024.03.004.

[5] Omidian P, Khaji N. A total life-cycle cost-resilience optimization framework for infrastructures management using different retrofit strategies. Sustain Resilient Infrastruct 2023; 8(6):675-98. doi: 10.1080/23789689.2023.2257516.

[6] Wang H, Guo X, Luo Ch, Zhao J, Feng H. Life-cycle cost assessment of the base-isolated-reinforced concrete structure. J Earthquake Tsunami 2024. doi: 10.1142/S179343112450026X.

[7] Shekhar Sh, Ghosh J. A metamodeling based seismic life-cycle cost assessment framework for highway bridge structures. Reliabil Eng Syst Saf 2020;195:106724. doi: 10.1016/j.ress.2019.106724.

[8] Torti M, Venanzi I, Laflamme S, Ubertini F. Life-cycle management cost analysis of transportation bridges equipped with seismic structural health monitoring systems. Struct Health Monit 2021; 21(1):100-17. doi: 10.1177/1475921721996624.

[9] Roohi M, Ghasemi S, Sediek O, Jeon H, Van De Lindt JW, Shields M, Hamideh S, Cutler H. Multi-disciplinary seismic resilience modeling for developing mitigation policies and recovery planning. Resilient Cities Struct 2024; 3(2):66-84. doi: 10.1016/j.rcns.2024.07.003.

[10] Ke S-S, H Ch-H, Yang Ch-Y. Rapid crisis response in resilient cities: emergency response to and reconnaissance of earthquake disasters in Taiwan. J Earthquake Tsunami 2024; 18(4): 2450008. doi: 10.1142/S1793431124500088.

[11] Zhang Y, Ayyub BM, Feng JF, Labe ZM. Incorporating extreme event attribution into climate change adaptation for civil infrastructure: methods, benefits, and research needs. Resilient Cities Struct 2024; 3(1):103-13. doi: 10.1016/j.rcns.2024.03.002.

[12] Lu J, Atamturktur S, Huang Y. Bi-level resource allocation framework for retrofitting bridges in a transportation network. Transp Res Record: J Transp Res Board 2016; 2550(1):31-7. doi: 10.3141/2550-05.

[13] Patel DA, Lad VH, Chauhan KA, Patel KA. Development of bridge resilience index using multicriteria decision-making techniques. J Bridge Eng 2020; 25(10):04020090. doi: 10.1061/(ASCE)BE.1943-5592.0001622.

[14] Rasulo A, Pelle A, Briseghella B, Nuti CA. Resilience-based model for the seismic assessment of the functionality of road networks affected by bridge damage and restoration. Infrastructures (Basel) 2021; 6(8): 112. doi: 10.3390/infrastructures6080112.

[15] Yavuz C. Multi-hazard risk assessment of south Korean nuclear power plants. J Earthquake Tsunami 2023; 17(3):2350015. doi: 10.1142/S179343112350015X.

[16] Omidian P, Khaji N, Aghakouchck AA. A logical retrofit strategy optimization framework for resiliency bridge infrastructure management considering life-cycle cost. Sustain Struct 2024; 4(1):000036. doi: 10.54113/j.sust.2024.000036.

[17] Omidian P, Khaji N, Aghakouchck AA. Seismic time-dependent resilience assessment of aging highway bridges incorporating the effect of retrofitting. Structures 2024;63:106347. doi: 10.1016/j.istruc.2024.106347.

[18] Satyannarayana R, Rajesh BG. Spatial variation of earthquake hazard for Amaravati city of Peninsular India: a probabilistic approach. J. Earthquake Tsunami 2024; 18(6): 2450021. doi: 10.1142/S1793431124500210.

[19] Omidian P, Khaji N. A multi-objective optimization framework for seismic resilience enhancement of typical existing RC buildings. J Build Eng 2022;52:104361. doi: 10.1016/j.jobe.2022.104361.

[20] Deb K, Prata A, Agarwal A, Meyarivan T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2002; 6(2):182-97. doi: 10.1109/4235.996017.

[21] Lewin Ch, Rossi M, Soultani E, Raj KR. Managing infrastructure resilience and adaptation. Sustain Resilient Infrastruct 2023; 9(2):107-23. doi: 10.1080/23789689.2023.2241728.

[22] Sun J, Bathgate K, Zhang Zh. Bayesian network-based resilience assessment of interdependent infrastructure systems under optimal resource allocation strategies. Resilient Cities Struct 2024; 3(2):46-56. doi: 10.1016/j.rcns.2024.06.001.

[23] Kim J-S, Park W-S, Han T-S. Framework to evaluate seismic fragility of bridges considering component damage correlations. J Earthquake Tsunami 2021; 15(5): 2150022. doi: 10.1142/S1793431121500226.

[24] Altuni şik AC, Sunca F, Sevim B. Ambient vibration-based seismic evaluation of long-span prestressed concrete box-girder bridges under long-duration, nearfault and far-fault ground motions. J Earthquake Tsunami 2024; 18(6): 2450019. doi: 10.1142/S1793431124500192.

[25] HAZUS-MH MR5 Multi-hazard loss estimation methodology-earthquake model. Department of Homeland Security, Washington DC; 2014. Accessed URL: https://www.hsdl.org/c/view?docid=12760.

[26] Hutt CM, Vahanvaty T, Kourehpaz P. An analytical framework to assess earthquake-induced downtime and model recovery of buildings. Earthquake Spectra 2022; 38(2):1283-320. doi: 10.1177/8755293021106085.

[27] Fu Zh, Wu D, Fang L, Chen D, Ji B. Influence factors and repair effects of seismic damage to a box section steel pier. J Earthquake Tsunami 2019; 13(3-4):1940001. doi: 10.1142/S1793431119400013.

[28] Fereshtehnejad H, Shafieezadeh A. A multi-type multi-occurrence hazard lifecycle cost analysis framework for infrastructure management decision making. Eng Struct 2018;167:504-17. doi: 10.1016/j.engstruct.2018.04.049.

[29] Yousfi N, Belkacem BA, Guessoum N, Bensaibi M. Seismic resilience scenario of Algerian buildings’ context: blida city case study. J Earthquake Tsunami 2024; 18(3): 2450005. doi: 10.1142/S1793431124500052.

[30] Li S-Q. Seismic risk model for regional buildings that considers the influence of temperature and intensity measures. Expert Syst Appl 2024;250:123962. doi: 10.1016/j.eswa.2024.123962.

[31] Li S-Q, Zhong J. Development of a seismic vulnerability and risk model for typical bridges considering innovative intensity measures. Eng Struct 2023;302:117431. doi: 10.1016/j.engstruct.2023.117431.

[32] Li S-Q, Gardoni P. Optimized seismic hazard and structural vulnerability model considering macroseismic intensity measures. Reliab Eng Syst Saf 2024;252:110460. doi: 10.1016/j.ress.2024.110460.

[33] Li S-Q. Hybrid seismic vulnerability models for regional structures considering bivariate intensity measures. Soil Dyn Earthquake Eng 2024;183:108763. doi: 10.1016/j.soildyn.2024.108763.

[34] Aristeidou S, O’Reilly GJ. Exploring the use of orientation-independent inelastic spectral displacements in the seismic assessment of bridges. J Earthquake Eng 2024; 28(12):3515-38. doi: 10.1080/13632469.2024.2343067.

[35] Xie Y, Zhang J, Desroches R, Padgett JE. Seismic fragilities of single-column highway bridges with rocking column-footing. Earthquake Eng Struct Dyn 2019; 48(7):843-64. doi: 10.1002/eqe.3164.

[36] Fakharifar M, Chen G, Sneed L, Dalvand A. Seismic performance of post-mainshock FRP/steel repaired RC bridge columns subjected to aftershocks. Compos Part B: Eng 2015;72:183-98. doi: 10.1016/j.compositesb.2014.12.010.

[37] Uenaga T, Omidian P, George RC, Mirzajani M, Khaji N. Seismic resilience assessment of curved reinforced concrete bridge piers through seismic fragility curves considering short- and long-period earthquakes. Sustainability 2023; 15(10): 7764. doi: 10.3390/su15107764.

[38] Padgett JE, DesRoches R. Methodology for the development of analytical fragility curves for retrofitted bridges. Earthquake Eng Struct Dyn 2008; 37(8):1157-74. doi: 10.1002/eqe.801.

[39] Oregon highways seismic plus. (2014). ODOT’s oregon highways seismic plus report, bridge and geo-environmental sections, Oregon department of transportation. Accessed URL: https://www.oregon.gov/odot/Bridge/Docs_Seismic/Seismic-Plus-Report_2014.pdf>.

[40] ISMEP. (2014). Istanbul seismic risk mitigation and emergency preparedness project (ISMEP), No.4 retrofitting and reconstruction works, 1-96, June 2014, Beyaz Gemi Social Project Agency. Accessed URL: https://www.ipkb.gov.tr/wp-content/uploads/2019/07/ISMEP4_GUCLENDIRME_EN140214.pdf.

[41] Washington state’s bridge seismic retrofit program. (2019). WSDOT’s bridge seismic retrofit program and bridge resiliency assessment Data, the Washington State Department of Transportation. Accessed URL: https://publications.anl.gov/anlpubs/2020/01/157924.pdf>.

[42] Kabir MR,Muntasi Billah AHM, Shahria Alam M. Seismic fragility assessment of a multi-span RC bridge in Bangladesh considering near-fault, far-field and long duration ground motions. Structures 2019;19:333-48. doi: 10.1016/j.istruc.2019.01.021.

[43] Speranza E, De Martino G, Conte Ch, Dolce M. Italian national seismic prevention plan: cost analyses for risk reduction policies. Procedia Struct Integr 2023;44:1784-91. doi: 10.1016/j.prostr.2023.01.228.

[44] Du A, Padgett JE, Shafieezadeh A. Adaptive IMs for improved seismic demand modeling of highway bridge portfolios. Los Angeles, CA, USA: Proceedings of the 11th National Conference in Earthquake Engineering; 2018. 25-29 June 2018.

[45] Raghunandan M, Liel AB, Luco N. Aftershock collapse vulnerability assessment of reinforced concrete frame structures. Earthquake Eng Struct Dyn 2015; 44(3):419-39. doi: 10.1002/eqe.2478.

[46] Naseem A, Kashif M, Schotte K, Backer HD. Seismic fragility curves of combined multiple tunnel complexes in soft soils. J Earthquake Tsunami 2023; 17(6): 2350026. doi: 10.1142/S1793431123500264.

[47] Liang Y, Kong Y-Zh, Zhao Ch-X, Liu R-Q, Luo J, Zhu RH. Time-varying seismic fragility analysis of ECC-RC composite bridge with high-strength steel bars. J Earthquake Tsunami 2024; 18(1):2350029. doi: 10.1142/S179343112350029X.

[48] Yaghmaei-Sabegh S, Neekmanesh Sh. Non-parametric seismic fragility curves of SDOF systems based on a clustering process. J Earthquake Tsunami 2023; 17(3): 2350008. doi: 10.1142/S1793431123500082.

[49] Sultan M., Kawashima K. (1993). Comparison of the seismic design of highway bridges in California and in Japan, ” Recent selected publications of Earthquake Engineering Div., Public Works Research Institute (PWRI), Japan (Technical Memorandum of PWRI No. 3276). Accessed URL: https://thesis.pwri.go.jp/public_detail/109658/.

[50] SeismoStruct. (2024). SeismoSoft, A computer program for static and dynamic nonlinear analysis of framed structures. Accessed URL: https://seismosoft.com/product/seismostruct/

[51] Madas P, Elnashai AS. A new passive confinement model for the analysis of concrete structures subjected to cyclic and transient dynamic loading. Earthquake Eng Struct Dyn 1992;21:409-31. doi: 10.1002/eqe.4290210503.

[52] Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete. J Struct Eng 1988;30:1804-26. doi: 10.1061/(ASCE)0733-9445(1988)114:8(1804.

[53] Martinez-Rueda JE, Elnashai AS. Confined concrete model under cyclic load. Mater Struct 1997;30:139-47. doi: 10.1007/BF02486385.

[54] Yassin MHN. Nonlinear analysis of prestressed concrete structures under monotonic and cyclic loads, Berkeley, USA:PhD Thesis, University of California; 1994. Accessed URL: https://search.worldcat.org/en/title/222312210.

[55] Filippou F.C., Popov E.P., Bertero V.V. (1983). Effects of bond deterioration on hysteretic behaviour of reinforced concrete joints, Report EERC 83-19, Earthquake Engineering Research Center, University of California, Berkeley, USA. Accessed URL: https://nehrpsearch.nist.gov/static/files/NSF/PB84192020.pdf.

[56] Monti G., Nuti C., Santini S. (1996). CYRUS -cyclic response of upgraded sections, Report No. 96-2, University of Chieti, Italy. Accessed URL: https://hdl.handle.net/11590/191035.

[57] Fragiadakis M, Pinho R, Antoniou S.Modelling inelastic buckling of reinforcing bars under earthquake loading. Book: computational structural dynamics and earthquake engineering: structures and infrastructures book series, 2. 1st ed. CRC Press; 2008. doi: 10.1201/9780203881637.

[58] FIB (Fédération International du Béton). (2006). Retrofitting of concrete structures by externally bonded FRPS, with emphasis on seismic applications, FIB Bulletin No. 35, Federation Internationale du Beton, 220. DOI: 10.35789/fib.BULL.0035

[59] Ferracuti B, Savoia M.Cyclic behavior of CFRP-wrapped piers under axial and flexural loading. In:Proceedings of the International Conference on Fracture, Turin, Italy; 2005. Accessed URL: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=8b61f15de5c256d85fbf9eb8e8e02d4d1872aa33.

[60] Spoelstra MR, Monti G. FRP-confined concrete model. J Compos Construct 1999;3:143-50. doi: 10.1061/(ASCE)1090-0268(1999)3:3(143.

[61] Yankelevsky DZ, Reinhardt HW. Uniaxial behavior of concrete in cyclic tension. J Struct Eng 1989;115:166-82. doi: 10.1061/(ASCE)0733-9445(1989)115:1(166.

[62] Choi E. Seismic analysis and retrofit of Mid-America bridges, USA:PhD Thesis, Georgia Institute of Technology; 2002. Accessed URL: https://www.researchgate.net/deref/http%3A%2F%2Fhdl.handle.net%2F1853%2F21538?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InB1YmxpY2F0aW9uIiwicGFnZSI6InB1YmxpY2F0aW9uIiwicG9zaXRpb24iOiJwYWdlSGVhZGVyIn19.

[63] Maroney B, Kutter B, Romstad K, Chai YH, Vanderbilt E.Interpretation of large scale bridge abutment test results. In:Proceedings of 3rd Annual Seismic Research Workshop, California Department of Transportation, CA, June 27-29; 1994.

[64] Caltrans. (2013). Seismic design criteria version 1.7, California department of transportation. Accessed URL: https://dot.ca.gov/-/media/dot-media/programs/engineering/documents/seismicdesigncriteria-sdc/f0006116-justification-ofcaltrans-seismic-design-criteria-sdc-1.pdf.

[65] Muthukumar S, DesRoches R. A Hertz contact model with non-linear damping for pounding simulation. Earthquake Eng Struct Dyn 2006; 35(7):811-28. doi: 10.1002/eqe.557.

[66] Omidian P, Saffari H. Comparative analysis of seismic behavior of RC buildings with shape memory alloy rebar in regular, torsional irregularity and extreme torsional irregularity cases. J Build Eng 2018;20:723-53. doi: 10.1016/j.jobe.2018.09.020.

[67] Shome N., Cornel C.A. (1999). Probabilistic seismic demand analysis of nonlinear structures, Reliability of Marine Structures Program Technical Report RMS-35, Stanford Digital Repository. Accessed URL: https://purl.stanford.edu/qp089qb1141.

[68] PEER. (2024). Pacific earthquake engineering research center, PEER, online strong motion database. Accessed URL: https://ngawest2.berkeley.edu/

[69] Abbasi M, Zakeri B, Amiri GG. Probabilistic seismic assessment of multiframe concrete box-girder bridges with unequal-height piers. J Perform Construct Facil 2015; 30(2):04015016. doi: 10.1061/(asce)cf.1943-5509.0000753.

[70] Petersen M.D., Frankel A.D., Harmsen S.C., Mueller C.S., Haller K.M., Wheeler R.L., Wesson R.L., Zeng Y., Boyd O.S., Perkins D.M., Luco N., Field E.H., Wills C.J., Rukstales S. (2008). Documentation for the 2008 update of the united states national seismic hazard maps, U.S. Geological Survey (USGS) Open-File Report 2008- 1128, U.S. Geological Survey, Reston, VA DOI: 10.3133/ofr20081128

[71] Caltrans. (2005). Historic bridge inventory, sample plans of actions. Division of Maintenance, Structure Maintenance. Accessed URL: http://www.dot.ca.gov/hq/structur/strmaint/poa_samp.pdf>.

[72] Calvi GM, O’reilly GJ, Andreotti G. Towards a practical loss-based design approach and procedure. Earthquake Eng Struct Dyn 2021; 50(14):3741-53. doi: 10.1002/eqe.3530.

[73] Abarca A, Monteiro R, O’reilly GJ. Simplified methodology for indirect loss-based prioritization in roadway bridge network risk assessment. Int J Disaster Risk Reduct 2022;74:102948. doi: 10.1016/j.ijdrr.2022.102948.

[74] Soliman M, Frangopol DM. Life-cycle cost evaluation of conventional and corrosion resistant steel for bridges. J Bridge Eng 2014; 20(1):06014005. doi: 10.1061/(ASCE)BE.1943-5592.0000647.

[75] Gallivan F., Ang-Olson J., Papson A., Venner M. (2010). Greenhouse gas mitigation measures for transportation construction, maintenance, and operations activities. San Francisco: AASHTO Standing Committee on the Environment. Accessed URL: http://onlinepubs.trb.org/onlinepubs/nchrp/docs/NCHRP25-25(58)_FR.pdf.

[76] Kendall A, Keoleian GA, Helfand GE. Integrated life-cycle assessment and lifecycle cost analysis model for concrete bridge deck applications. J Infrastruct Syst 2008; 14(3):214-22. doi: 10.1061/(ASCE)1076-0342(2008)14:3(214.

[77] CaltransAnnual average daily truck traffic on the California state highway system. Traffic Data Branch 2016. Accessed URL: https://dot.ca.gov/-/media/dot-media/programs/traffic-operations/documents/census/f0017681-2016-aadttruck-a11y.pdf.

[78] Abarca A, Monterio R, O’reilly GJ. Seismic risk prioritisation schemes for reinforced concrete bridge portfolios. Struct Infrastruct Eng 2023:1-21. doi: 10.1080/15732479.2023.2187424.

[79] Fereshtehnejad E, Hur J, Shafieezadeh A, Brokaw M. Ohio bridge condition index: multilevel cost-based performance index for bridge systems. Transp Res Record: J Transp Res Board 2017; 2612(1):152-60. doi: 10.3141/2612-17.

[80] Bocchini P, Frangopol DM. Optimal resilience- and cost-based postdisaster intervention prioritization for bridges along a highway segment. J Bridge Eng 2010; 17(1):117-29. doi: 10.1061/(ASCE)BE.1943-5592.0000201.

[81] ODOT. (2010). Ohio Department of Transportation, Innovative contracting manual, Division of Construction Management. Accessed URL: https://www.dot.state.oh.us/Divisions/ConstructionMgt/Admin/Innovative%20Contracting/Innovative_Contracting_Manual.PDF

[82] Porter K, Shoaf K, Seligson H. Value of injuries in the Northridge earthquake. Earthquake Spectra 2006; 22(2):555-63. doi: 10.1193/1.2194529.

[83] Caltrans. (2011). High occupancy vehicle lanes status report. Sacramento metropolitan area. District 3. Office of Freeway Operations, Sacramento. Accessed URL: https://dot.ca.gov/programs/traffic-operations/hov

[84] Nims D.K., Miranda E., Aiken I.D., Whttaker A.S., & Bereto V.V. (1989). Collapse of the cypress street viaduct as a result of the Loma Prieta earthquake. Earthquake Engineering Research Center, University of California, Berkeley, CA. Accessed URL: 10.13140/RG.2.1.4863.1924

[85] Kliesen K.L., Mill J.S. (1994). The economics of natural disasters. The regional economist. Federal Reserve Bank of St. Louis, p. 332. Accessed URL: https://www.stlouisfed.org/publications/regionaleconomist/april-1994/the-economics-of-natural-disasters.

[86] Bianchi F, Sousa R, Pinho R.Blind prediction of a full-scale RC bridge column tested under dynamic conditions. In:Proceedings of 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2011; 2011. Paper no. 294, Corfu, Greece. Accessed URL: http://congress.cimne.com/eccomas/proceedings/compdyn2011/compdyn2011_full/294.pdf.

[87] Caltrans Bridge design practices. California Department of Transportation; 2004. Accessed URL: https://dot.ca.gov/programs/engineeringservices/manuals/bridge-design-practice.