Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Chowdhury, Abu Obayed
Doctor of Philosophy - PhD
University of British Columbia
An intended performance of a structure under different seismic hazard levels can be obtained by applying the performance-based seismic design (PBSD) approach. Various performance levels and the respective limit states need to be set for employing PBSD. These limit states corresponding to different performance levels are unavailable in the latest codes and guidelines for existing seismically deficient bridges. Being major components, multi-column bents have notable effects on the seismic behaviour of these bridges. Thus, a typical deficient bent is retrofitted with different alternatives such as carbon fibre-reinforced polymer (CFRP), steel, engineered cementitious composite (ECC), and concrete jackets, and the development of limit states for each alternative is sought in this research. Incremental dynamic analyses were performed to come up with the limit states expressed in terms of limiting drifts and damage indices for different performance levels of retrofitted bents. A detailed example has been developed to demonstrate a retrofit design for achieving the target seismic performance with the proposed damage states. Fragility analysis was conducted to achieve the conditional probabilities of exceeding various damage states at different hazard levels under various earthquake scenarios. The effects of various performance-based damage states and earthquake sources on the life-cycle cost and seismic resilience were assessed for retrofitting a deficient bridge bent in this research. Performance-based seismic loss and seismic resilience assessments of as-built bent and bents retrofitted with different retrofit options were executed for life-cycle performance comparison and optimum retrofitting technique selection. ECC jacketed bent had the least crushing probability in most situations. CFRP and steel jacketed bents were subjected to the smallest and highest seismic losses, respectively. ECC jacket was selected as the optimum option for retrofitting the deficient bent because it produced the greatest benefit-cost ratio under most conditions over the other techniques. All retrofitted bents exhibited the highest and lowest seismic resilience under interface and intra-slab earthquakes, respectively. Each retrofitted bent showed the minimum seismic resilience when the yielded rebar proportion mostly increased by 40% for intra-slab earthquakes. CFRP jacket became the optimum technique for retrofitting the deficient bent with maximum seismic resilience and the shortest full-functionality restoration duration.
PERFORMANCE-BASED SEISMIC DESIGN FOR RETROFITTING OF BRIDGE BENTS by Abu Obayed Chowdhury M.E.Sc., Western University, 2007 B.Sc., Bangladesh University of Engineering and Technology, 2005 A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) November 2024 © Abu Obayed Chowdhury, 2024 ii The following individuals certify that they have read, and recommended to the College of Graduate Studies for acceptance, the dissertation entitled: Performance-Based Seismic Design for Retrofitting of Bridge Bents submitted by Abu Obayed Chowdhury in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Dr. M. Shahria Alam, School of Engineering Supervisor Dr. A.H.M. Muntasir Billah, University of Calgary Co-supervisor Dr. Kasun Hewage, School of Engineering Supervisory Committee Member Dr. Abbas Milani, School of Engineering Supervisory Committee Member Dr. Jian Liu, School of Engineering University Examiner Dr. Khaled Sennah, Toronto Metropolitan University External Examiner iii ABSTRACT An intended performance of a structure under different seismic hazard levels can be obtained by applying the performance-based seismic design (PBSD) approach. Various performance levels and the respective limit states need to be set for employing PBSD. These limit states corresponding to different performance levels are unavailable in the latest codes and guidelines for existing seismically deficient bridges. Being major components, multi-column bents have notable effects on the seismic behaviour of these bridges. Thus, a typical deficient bent is retrofitted with different alternatives such as carbon fibre-reinforced polymer (CFRP), steel, engineered cementitious composite (ECC), and concrete jackets, and the development of limit states for each alternative is sought in this research. Incremental dynamic analyses were performed to come up with the limit states expressed in terms of limiting drifts and damage indices for different performance levels of retrofitted bents. A detailed example has been developed to demonstrate a retrofit design for achieving the target seismic performance with the proposed damage states. Fragility analysis was conducted to achieve the conditional probabilities of exceeding various damage states at different hazard levels under various earthquake scenarios. The effects of various performance-based damage states and earthquake sources on the life-cycle cost and seismic resilience were assessed for retrofitting a deficient bridge bent in this research. Performance-based seismic loss and seismic resilience assessments of as-built bent and bents retrofitted with different retrofit options were executed for life-cycle performance comparison and optimum retrofitting technique selection. ECC jacketed bent had the least crushing probability in most situations. CFRP and steel jacketed bents were subjected to the smallest and highest seismic losses, respectively. ECC jacket was selected as the optimum option for retrofitting the deficient bent because it produced the greatest benefit-cost ratio under most iv conditions over the other techniques. All retrofitted bents exhibited the highest and lowest seismic resilience under interface and intra-slab earthquakes, respectively. Each retrofitted bent showed the minimum seismic resilience when the yielded rebar proportion mostly increased by 40% for intra-slab earthquakes. CFRP jacket became the optimum technique for retrofitting the deficient bent with maximum seismic resilience and the shortest full-functionality restoration duration. Keywords: Bridge bent; Damage states; Performance-based design; Seismic loss; Seismic resilience; Seismic retrofit. v LAY SUMMARY There exists no proper guideline in current codes and standards for executing PBSD to retrofit seismically deficient bridge bents. Thus, this research developed performance-based damage states and design guidelines for existing reinforced concrete bents retrofitted with CFRP, steel, ECC, and concrete jackets. Damage states expressed in terms of limiting drifts and damage indices of retrofitted bents for various performance levels have been developed. An optimum intensity measure has also been obtained to compare the seismic performances of all retrofitted bents. A design example has been developed to demonstrate the developed PBSD method. Moreover, performance-based seismic loss and resilience for bridge bents under various earthquake scenarios were obtained. The research findings will aid practitioners in adopting PBSD to retrofit existing bridge bents/piers. vi PREFACE • A version of chapter 3 has been published in the 4th IABSE-JSCE Joint Conference on Advances in Bridge Engineering proceedings. Chowdhury, A. O., A. H. M. M. Billah, and M. S. Alam. 2020. “Finite element modeling and development of performance-based damage states for retrofitted multi-column bridge bent.” In Proc., IABSE-JSCE Joint Conf. on Advances in Bridge Eng.-IV, edited by Amin, Okui, Bhuiyan, and Rahman, Dhaka, Bangladesh: IABSE (International Association for Bridge and Structural Engineering)-JSCE (Japan Society of Civil Engineers). I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. A version of Chapter 3 has been published in the 11th International Conference on Short and Medium Span Bridges proceedings. Chowdhury, A. O., A. H. M. M. Billah, and M. S. Alam. 2022. “Damage index-based performance evaluation of retrofitted bridge bent.” In Proc., 11th Int. Conf. on Short and Medium Span Bridges, Toronto, ON: CSCE (Canadian Society for Civil Engineering). I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. A version of chapter 3 has been published in the 2nd International Conference on Advances in Civil Infrastructure and Construction Materials proceedings. Chowdhury, A. O., A. H. M. M. Billah, and M. S. Alam. 2023. “Performance-based damage states for seismic retrofitting of reinforced concrete bridge bent.” In Proc., 2nd Int. Conf. on Advances in Civil Infrast. and Constr. Mater., Dhaka, Bangladesh: MIST (Military Institute of Science and Technology). I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. vii A version of chapter 3 has been published in the Journal of Bridge Engineering, ASCE. Chowdhury A. O., A. H. M. M. Billah, and M. S. Alam. 2024. “Performance-based seismic design for retrofitting bridges: Developing performance-based damage states.” J. Bridge Eng. 29 (7): 04024046. https://doi.org/10.1061/JBENF2.BEENG-6236. I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. A version of chapters 3 and 4 has been published in the 18th World Conference on Earthquake Engineering proceedings. Chowdhury, A. O., A. H. M. M. Billah, and M. S. Alam. 2024. “Performance-based seismic retrofitting of bridge bents with engineered cementitious composites.” In Proc., 18th World Conf. on Earthquake Eng., Milan, Italy: AIM Group International. I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. • A version of chapter 4 has been published in the Canadian Conference - Pacific Conference on Earthquake Engineering 2023 proceedings. Chowdhury, A. O., A. H. M. M. Billah, and M. S. Alam. 2023. “Performance-based seismic loss assessment of retrofitted RC bridge bents with different alternatives.” In Proc., Canadian Conf. - Pacific Conf. on Earthquake Engineering, Vancouver, BC: CAEE (Canadian Association for Earthquake Engineering)-NZSEE (New Zealand Society for Earthquake Engineering). I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. A version of chapter 4 has been submitted to Earthquake Engineering & Structural Dynamics, John Wiley & Sons Ltd. Chowdhury A. O., A. H. M. M. Billah, and M. S. Alam. 2024. “Performance-based seismic loss assessment of seismically deficient bridge bent retrofitted with different techniques.” Earthquake Eng. Struct. Dyn., Manuscript ID: EQE-24-0383. I viii conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. • A version of chapter 5 has been submitted to Resilient Cities and Structures, Elsevier. Chowdhury A. O., A. H. M. M. Billah, and M. S. Alam. 2024. “Performance-based seismic resilience assessments of retrofitted bridge bents.” Resilient Cities Struct., Manuscript No. RCNS-D-24-00156. I conducted the numerical analysis and wrote the manuscript, which was edited further by Dr. Billah and Dr. Alam. Generative AI was not used for any aspects of this work. ix TABLE OF CONTENTS ABSTRACT……..........................................................................................................................iii LAY SUMMARY...........................................................................................................................v PREFACE………..........................................................................................................................vi TABLE OF CONTENTS..............................................................................................................ix LIST OF TABLES......................................................................................................................xiii LIST OF FIGURES.....................................................................................................................xv LIST OF SYMBOLS AND ABBREVIATIONS.......................................................................xix ACKNOWLEDGEMENTS.....................................................................................................xxvi DEDICATION..........................................................................................................................xxvii Chapter 1. INTRODUCTION AND THESIS ORGANIZATION.............................................1 1.1 General...................................................................................................................................1 1.2 Research Gaps........................................................................................................................3 1.3 Objectives of the Research.....................................................................................................3 1.4 Contribution and Novelty.......................................................................................................4 1.5 Outline of the Thesis..............................................................................................................5 Chapter 2. LITERATURE REVIEW...........................................................................................7 2.1 General...................................................................................................................................7 2.2 Bridge Retrofit Options and Current Design Guidelines.......................................................7 2.2.1 Seismic retrofitting using CFRP jacket.........................................................................10 2.2.2 Seismic retrofitting using steel jacket...........................................................................10 2.2.3 Seismic retrofitting using ECC jacket..........................................................................12 2.2.4 Seismic retrofitting using concrete jacket.....................................................................13 x 2.2.5 Seismic retrofitting using UHPFRC jacket...................................................................14 2.3 Performance-Based Seismic Loss Assessments of Bridges.................................................15 2.4 Performance-Based Seismic Resilience Assessments of Bridges........................................18 2.5 Summary..............................................................................................................................21 Chapter 3. DEVELOPMENT OF PERFORMANCE-BASED DAMAGE STATES FOR RETROFITTED BRIDGE BENTS...........................................................................................22 3.1 General.................................................................................................................................22 3.2 Bridge Bent Details..............................................................................................................22 3.3 Retrofit Alternative Details..................................................................................................23 3.4 Design of Different Retrofit Options...................................................................................25 3.5 Finite Element Modeling.....................................................................................................29 3.5.1 Model validation with experimental results..................................................................32 3.6 IDA-Based Approach for Development of Performance-Based Damage States.................34 3.7 Selection of Earthquakes......................................................................................................36 3.8 Selection of Optimum Intensity Measure............................................................................38 3.9 Developments of Performance-Based Damage States.........................................................41 3.10 Design Example.................................................................................................................50 3.11 Effects of Retrofit Options and Earthquake Sources on Maximum Drifts........................54 3.12 Effects of Retrofit Options and Earthquake Sources on Damage Indices.........................59 3.13 Summary............................................................................................................................64 Chapter 4. BRIDGE BENT PERFORMANCE-BASED SEISMIC LOSS ASSESSMENTS...........................................................................................................................65 4.1 General.................................................................................................................................65 xi 4.2 Fragility Analyses and Seismic Loss Assessments of Bridge Bents....................................65 4.3 Effects of Retrofit Techniques on Performance-Based Seismic Loss..................................69 4.4 Effects of Earthquake Sources on Performance-Based Seismic Loss.................................80 4.5 Effect of Yielded Rebar Proportion on Seismic Loss..........................................................80 4.6 Effects of Retrofit Techniques on Benefit-Cost Ratio.........................................................81 4.7 Effects of Earthquake Sources on Benefit-Cost Ratio.........................................................83 4.8 Effect of Yielded Rebar Proportion on Benefit-Cost Ratio.................................................85 4.9 Selection of the Optimum Retrofit Technique.....................................................................86 4.10 Summary............................................................................................................................86 Chapter 5. PERFORMANCE-BASED SEISMIC RESILIENCE ASSESSMENTS OF RETROFITTED BRIDGE BENTS...........................................................................................88 5.1 General.................................................................................................................................88 5.2 Seismic Resilience Assessments of Retrofitted Bridge Bents.............................................89 5.3 Effects of Retrofit Options on Mean Expected Functionality..............................................94 5.4 Effects of Earthquake Sources on Mean Expected Functionality........................................98 5.5 Effects of Yielded Rebar Proportions on Mean Expected Functionality...........................100 5.6 Effects of Retrofit Options on Seismic Resilience............................................................101 5.7 Effects of Earthquake Sources on Seismic Resilience.......................................................104 5.8 Effects of Yielded Rebar Proportions on Seismic Resilience............................................105 5.9 Selection of the Optimum Retrofit Option.........................................................................106 5.10 Summary..........................................................................................................................107 Chapter 6. SUMMARY, CONCLUSIONS, AND FUTURE WORKS..................................108 6.1 Summary............................................................................................................................108 xii 6.2 Core Contributions.............................................................................................................108 6.3 Conclusions........................................................................................................................109 6.3.1 Performance-based damage states of different jacketed bridge bents........................109 6.3.2 Performance-based seismic loss assessments of bridge bents....................................111 6.3.3 Performance-based seismic resilience assessments of retrofitted bridge bents..........112 6.3.4 Selection of the optimum retrofit option.....................................................................113 6.4 Limitations of the Research...............................................................................................113 6.5 Recommendation for Future Works...................................................................................114 BIBLIOGRAPHY.......................................................................................................................115 xiii LIST OF TABLES Table 2.1. Mechanical properties, constructability, and cost of various retrofit options (Kennedy et al. 2015).....................................................................................................................9 Table 2.2. As-built and retrofitted column specimens’ ductility and ultimate lateral load comparison (Saiidi et al. 2004).....................................................................................11 Table 2.3. Effective retrofit options for the as-built bridge at various damage states (Stefanidou and Kappos 2021)........................................................................................................14 Table 2.4. Comparisons of LCCs, benefits, costs, and CBRs of various retrofit options for MSC steel bridge (Padgett et al. 2010)..................................................................................16 Table 3.1. Advantages and disadvantages of various retrofit options...........................................25 Table 3.2. Properties of different retrofit materials.......................................................................26 Table 3.3. Time periods of multi-column bents.............................................................................32 Table 3.4. Selected earthquake ground motion records.................................................................37 Table 3.5. Various intensity measure comparisons of different jacketed bridge bents under crustal earthquakes..................................................................................................................43 Table 3.6. Various intensity measure comparisons of different jacketed bridge bents under intra- slab earthquakes...........................................................................................................43 Table 3.7. Various intensity measure comparisons of different jacketed bridge bents under inter- face earthquakes...........................................................................................................44 Table 3.8. Proposed damage state framework...............................................................................46 Table 3.9. Drift-based damage state comparisons of different retrofit techniques and earthquake sources..........................................................................................................................48 Table 3.10. Bent material properties.............................................................................................51 xiv Table 3.11. Comparison of median maximum drifts for various retrofit options and earthquake sources........................................................................................................................59 Table 3.12. Proposed damage index-based damage states for various retrofit options.................63 Table 3.13. Median damage index comparisons of various retrofit options and earthquake sources........................................................................................................................63 Table 4.1. Traffic data used in seismic loss assessment of as-built and retrofitted bents..............68 Table 4.2. As-built and various jacketed bridge bents’ dispersion values for different performance levels........................................................................................................70 Table 4.3. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under crustal earthquakes.....................................................................74 Table 4.4. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under intra-slab earthquakes................................................................74 Table 4.5. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under interface earthquakes.................................................................75 Table 4.6. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under crustal earthquakes.....................................................................75 Table 4.7. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under intra-slab earthquakes................................................................76 Table 4.8. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under interface earthquakes.................................................................76 Table 5.1. Random variables for bridge functionality at various performance levels...................93 Table 6.1. Ranking of different retrofit options given seismic performance, benefit-cost ratios, seismic resilience, and full functionality recovery times............................................113 xv LIST OF FIGURES Figure 3.1. Bridge bent elevation (adapted from Pantelides and Gergely 2002)..........................23 Figure 3.2. Column and cap beam cross-sections (adapted from Pantelides and Gergely 2002).24 Figure 3.3. Retrofitted column elevations.....................................................................................27 Figure 3.4. Retrofitted column cross-sections..............................................................................28 Figure 3.5. Finite element model: (a) 3D bent model and (b) critical column section.................30 Figure 3.6. Stress-strain diagrams: (a) CFRP jacket, (b) steel jacket, (c) ECC jacket, and (d) concrete.......................................................................................................................31 Figure 3.7. Comparisons of lateral and flexural strengths of as-built and retrofitted bridge bents: (a) capacity curves and (b) bending moment-curvature responses of critical column sections........................................................................................................................31 Figure 3.8. First mode shape of the bent.......................................................................................32 Figure 3.9. Comparison of experimental and numerical results: (a) as-built bridge bent (Pantelides and Gergely 2002), (b) bent retrofitted with CFRP jacket (Pantelides and Gergely 2002), (c) column retrofitted with concrete jacket (Vandoros and Dritsos 2008), (d) column retrofitted with steel jacket (ElGawady et al. 2010), and (e) ECC column (Gencturk and Elnashai 2011).......................................................................35 Figure 3.10. Target and mean response spectra of the selected ground motions: (a) crustal, (b) intra-slab, and (c) interface earthquakes....................................................................39 Figure 3.11. Proposed drift-based damage states of different retrofitted bridge bents.................49 Figure 3.12. Flowchart of PBSD for retrofitting bents.................................................................52 Figure 3.13. Deflected shape of the bent under earthquakes........................................................52 Figure 3.14. IDA curves of bents retrofitted with different materials for crustal earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing...............................................55 xvi Figure 3.15. IDA curves of bents retrofitted with different materials for intra-slab earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing...............................................56 Figure 3.16. IDA curves of bents retrofitted with different materials for interface earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing...............................................57 Figure 3.17. Effects of different retrofit options on median maximum drifts of retrofitted bents for different earthquake sources: (a) crustal, (b) intra-slab, and (c) interface..........58 Figure 3.18. Effects of different earthquake sources on median maximum drifts of bents retrofitted with different materials: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing...................................................................................................................61 Figure 3.19. Effects of different retrofit options on median damage indices of retrofitted bents for different earthquake sources: (a) crustal, (b) intra-slab, and (c) interface..........62 Figure 4.1. Fragility curves for the as-built and retrofitted bridge bents under crustal earthquakes: (a) cracking, (b) yielding, and (c) crushing................................................................71 Figure 4.2. Fragility curves for the as-built and retrofitted bridge bents under intra-slab earthquakes: (a) cracking, (b) yielding, and (c) crushing...........................................72 Figure 4.3. Fragility curves for the as-built and retrofitted bridge bents under interface earthquakes: (a) cracking, (b) yielding, and (c) crushing...........................................73 Figure 4.4. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event.................................................................................................................78 Figure 4.5. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event......................................................................................................78 xvii Figure 4.6. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event......................................................................................................79 Figure 4.7. Comparisons of benefit-cost ratios of the retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event....................82 Figure 4.8. Comparisons of benefit-cost ratios of the retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event............................................................................................................................82 Figure 4.9. Comparisons of benefit-cost ratios of the retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event............................................................................................................................83 Figure 5.1. Schematic representation of resilience of a retrofitted bent.......................................91 Figure 5.2. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under crustal earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%..................................................................................................95 Figure 5.3. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under intra-slab earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%..................................................................................................96 Figure 5.4. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under interface earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%..................................................................................................97 xviii Figure 5.5. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under crustal earthquakes for 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%..................................................................................................98 Figure 5.6. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under intra-slab earthquakes for 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%.........................................................................................99 Figure 5.7. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under interface earthquakes for 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45%.................................................................................100 Figure 5.8. Comparisons of the seismic resilience of the retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event..........................................................................................................................102 Figure 5.9. Comparisons of the seismic resilience of the retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event..........................................................................................................................102 Figure 5.10. Comparisons of the seismic resilience of the retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event........................................................................................................................103 xix LIST OF SYMBOLS AND ABBREVIATIONS a Regression coefficient a1 Unscaled accelerogram b Regression coefficient 𝐴𝐴ℎ Transverse steel cross-sectional area 𝐵𝐵 Cross-section width c Neutral axis depth corresponding to crushing cATC Average hourly total compensation for truck driver cAW Average hourly wage for car driver CDS,i Direct and indirect losses creb Rebuilding cost of a bridge unit area CREP,i Bent repair cost at any damage state CRUN,i Running cost at any damage state crun,car Cost per unit length for car crun,truck Cost per unit length for truck CTL,i Time loss monetary value at any damage state D Jacket diameter 𝑑𝑑 Cross-section effective height 𝐷𝐷′ Diameter of transverse steel 𝑑𝑑𝑏𝑏𝑏𝑏 Longitudinal reinforcement diameter 𝑑𝑑𝑐𝑐 Column diameter dE Incremental hysteretic absorbed energy xx di Downtimes (times to repair the bent to full functionality) for different performance levels Dl Detour length Ds5-75 5%-75% significant duration E(LCLas-built) As-built bent total expected life-cycle loss 𝐸𝐸{𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖(𝑡𝑡𝑖𝑖𝑖𝑖𝑖𝑖)} Bent total expected life-cycle loss in any time interval (0, tint) E(LCLr) Retrofitted bent total expected life-cycle loss 𝑓𝑓𝑐𝑐′ Compressive strength of concrete fcc’ Compressive strength of confined concrete fuj Tensile strength of jacket material 𝑓𝑓𝑦𝑦 Longitudinal reinforcement yield strength fyh Yield strength of transverse steel fyj Yield strength of steel 𝐻𝐻(𝑡𝑡 − 𝑡𝑡0 − 𝛿𝛿𝑖𝑖) Heaviside step function equal to 0 when 𝑡𝑡 − 𝑡𝑡0 − 𝛿𝛿𝑖𝑖 is less than 0, otherwise it is 1 𝐼𝐼𝐼𝐼𝑖𝑖 IM median value k 1 and 2 for performance levels yielding and crushing, respectively L Effective column height l Route length including the bridge 𝑏𝑏𝑑𝑑 Shear span ratio 𝐿𝐿𝑏𝑏 Length of bridge Lc Clear column height Li Bent expected annual loss xxi ln (𝐼𝐼𝐼𝐼𝑖𝑖) Natural log of the median IM value for the selected damage state Lp Plastic hinge length Lpj Yield penetration length Mw Moment magnitude N Simulation case number 𝑁𝑁0 Axial force 𝑛𝑛0 Normalized axial stress ocar Average occupancy for car otruck Average occupancy for truck P Conditional probability of occurrence of an earthquake in the time interval ∆𝑡𝑡 PDS,i|IM Conditional probability of exceeding any damage state at the considered hazard levels 𝑃𝑃𝑓𝑓(𝑘𝑘) Probability of exceeding damage state k 𝑄𝑄(𝑡𝑡) Time-dependent functionality 𝑄𝑄(𝑡𝑡|𝐼𝐼𝐼𝐼) Expected functionality at any hazard level 𝑄𝑄(𝑘𝑘)(𝑡𝑡) Bridge functionality for damage state k at time t 𝑄𝑄𝑟𝑟 Residual functionality 𝑄𝑄𝑖𝑖 Target functionality 𝑄𝑄𝑦𝑦 Yield strength 𝑅𝑅 Seismic resilience Repi Distances of the stations where the selected motions were recorded from fault 𝑅𝑅𝑓𝑓 �𝑖𝑖−𝑖𝑖0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟� 1 − 𝑒𝑒−𝑤𝑤�𝑡𝑡−𝑡𝑡0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟 � (for yielding) or 𝑒𝑒−𝑤𝑤�1−𝑡𝑡−𝑡𝑡0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟 � (for crushing) xxii Rrcr Repair cost ratios for different performance levels S Average detour speed 𝑠𝑠 Spacing of transverse steel S0 Average vehicle speed on the intact route Sa(T1) First-mode spectral acceleration 𝑆𝑆𝑐𝑐 Median SD Average vehicle speed on the damaged route Sd(T1) First-mode spectral displacement t Time 𝑇𝑇0 Average daily truck traffic ratio 𝑡𝑡0 Time of earthquake occurrence 𝑡𝑡ℎ Investigated time horizon 𝑡𝑡𝑖𝑖 Time when idle time interval ends tint Time interval tj Thickness of the jacket Vs Shear wave velocity W Width of bridge 𝑤𝑤 Shape parameter equal to 10 𝛽𝛽𝑐𝑐 Dispersion value for the bridge bent damage states 𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Dispersion component 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 EDP’s dispersion relying on the IM 𝛿𝛿𝑖𝑖 Idle time interval δM Maximum displacement in ground motion xxiii ∆p Plastic displacement 𝛿𝛿𝑟𝑟 Recovery duration ∆𝑡𝑡 Time interval ∆u Ultimate displacement δu Ultimate displacement for quasi-static load ∆𝑦𝑦 Yield displacement εcu Ultimate compressive strain εs Longitudinal reinforcement yielding strain εsu Strain corresponding to the tensile strength of transverse steel (0.15) εt Concrete cracking strain εuj Ultimate tensile strain of jacket material ζ Proficiency 𝜃𝜃𝑐𝑐 Plastic rotation λ Scaling factor λf Poisson’s model mean rate 𝜌𝜌𝑖𝑖 Longitudinal steel ratio 𝜌𝜌𝑤𝑤 Confinement ratio τ Monetary discount rate 𝜑𝜑 Standard normal cumulative distribution function 𝜑𝜑𝑐𝑐 Plastic curvature 𝜑𝜑𝑢𝑢 Ultimate curvature 𝜑𝜑𝑦𝑦 Yield curvature ADT Average Daily Traffic xxiv ADTD Average Daily Traffic to Detour ADTE Average Daily Traffic on the Damaged Route CBR Cost-Benefit Ratio CESMD Center for Engineering Strong Motion Data CFRP Carbon Fibre-Reinforced Polymer CHBDC Canadian Highway Bridge Design Code DI Damage index DM Damage Measure EB Elastomeric Bearing ECC Engineered Cementitious Composite EDB Energy Dissipation Brace EDP Engineering Demand Parameter EPA Effective Peak Acceleration FRC Fibre-Reinforced Concrete FRP Fibre-Reinforced Polymer GFRP Glass Fibre-Reinforced Polymer HDB Elastomeric High Damping Bearing IDA Incremental Dynamic Analysis IM Intensity Measure LCC Life-Cycle Cost LRB Lead Rubber Bearing MCS Monte Carlo Simulation MSC Multi-Span Continuous xxv MSSS Multi-Span Simply Supported NIED National Research Institute for Earth Science and Disaster Resilience NSGA Non-Dominated Sorting Genetic Algorithm NSM Near-Surface Mounted PBSD Performance-Based Seismic Design PEER Pacific Earthquake Engineering Research Center PET Polyethylene Terephthalate PGA Peak Ground Acceleration PGD Peak Ground Displacement PGV Peak Ground Velocity PRC Prestressed Reinforced Concrete RC Reinforced Concrete RC Restrainer Cable SA Simulated Annealing SCEB Self-Centring Energy Dissipation Brace SE Seat Extender SJ Steel Jacket SK Shear Key SL Shear Link SMA Shape Memory Alloy UHPFRC Ultra-High Performance Fibre Reinforced Concrete xxvi ACKNOWLEDGEMENTS I say a grace to Allah for successfully completing this research. I earnestly thank my supervisor, Dr. M. Shahria Alam, for letting me pursue my Ph.D. at The University of British Columbia, Okanagan. Both my supervisor, Dr. Alam and co-supervisor, Dr. A.H.M. Muntasir Billah, supported, guided, and inspired me throughout my program. They gave me invaluable advice, which helped me carry out my research in an efficient way at UBC, and all my efforts led to a successful and rewarding end. I would like to acknowledge my supervisory committee members, Dr. Kasun Hewage and Dr. Abbas Milani, for their continuous support and important, timely advice to improve my research notably. I feel privileged by the great experience gained with the necessary resources provided by the School of Engineering at UBC (Okanagan) and would like to acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for funding my program. I would like to express my wholehearted appreciation to my wife, Rubaba Karim, for accompanying me all the time. Her invaluable advice, support, inspiration, and endless love have made this journey pleasant and successful. I am also sincerely grateful to my father-in-law, Mahbubul Karim, for his wise advice and inspiration toward a fruitful completion of my program. xxvii THIS DISSERTATION IS DEDICATED TO MY DEAR WIFE, RUBABA KARIM AND SON, ZAVIYAR KARIM CHOWDHURY. 1 CHAPTER 1. INTRODUCTION AND THESIS ORGANIZATION 1.1 General The performance-based seismic design (PBSD) approach has been given priority over the conventional force-based method over the last few decades for seismic design of bridges to restrict global and local deformations below allowable limits (Priestley et al. 2007). In the PBSD approach, drift must not exceed a certain limit for the expected performance level. PBSD needs to predict damage states with confidence in the design of any structure. The conventional method aims to resist the collapse of a structure under design ground motions. On the other hand, PBSD has control over damage at various performance levels. Past research on reinforced concrete (RC) column damage states has focused on how damage measures are related to design parameters. They mainly relied on post-seismic inspections and large-scale laboratory experiments (Kawashima et al. 1998; Lehman et al. 2004; Fahmy et al. 2009; Jean et al. 2012). Furthermore, the column damage states of specific geometry or innovative materials need to be reassessed to design or retrofit them. Numerical simulations can be used instead of expensive large-scale experimental programs to investigate the damage states of RC columns. Advancements in numerical approaches, such as incremental dynamic analysis (IDA) (Vamvatsikos and Cornell 2002), as well as increasing computational capacity, have expedited the application of numerical simulations in developing damage states in RC columns. For seismic retrofit of existing bridges, it is required to determine the acceptable damage levels and the corresponding damage states for decision-making. These damage measures are either noncumulative, e.g., maximum drift (Roy et al. 2010; Billah and Alam 2014; Upadhyay et al. 2019), or cumulative, e.g., damage index (Park and Ang 1985; Mander and Cheng 1995; Hindi and Sexsmith 2001). Noncumulative damage measures are used for their simplicity and 2 practicality, whereas cumulative ones are considered to represent the progress of damage and to compare motions of different durations (Mohammed 2016; Barbosa et al. 2017; Pan et al. 2018). Performance-based seismic loss evaluation can help decide and mitigate risks related to bridge retrofitting by fulfilling the current and future necessities. To make informed decisions, the life-cycle cost to retrofit the seismically deficient bridge is measured to quantify seismic loss (Padgett et al. 2010). Hence, as opposed to only the initial cost for retrofitting, life-cycle performance cost can allow funding allocation based on risk and assist in retrofit planning. Therefore, Padgett et al. (2010) obtained an optimum retrofit strategy for a deficient bridge from a life-cycle cost assessment. It not only takes into account the retrofit cost but also other costs that can be added from rebuilding, repair, and demolition. Moreover, seismic resilience has become gradually significant in predicting the ability of a bridge to be ready for and adjust to variable circumstances and to resist and get over service disruption quickly after earthquakes at the same time. It also measures the remaining functionality of a bridge as well as the social effort toward post-earthquake functionality. Seismic resilience is measured employing a probability-based method that considers uncertainties in seismic vulnerability and its consequences. Various bridge components affect how a bridge behaves and can become vulnerable following an earthquake. A single pier or double or multi-column RC bent is considered an important bridge component since it markedly influences the behaviour of the bridge under an earthquake. A double or multi-column RC bent is not only laterally stiffer to resist excessive displacement under service loads but also accommodates more vehicle lanes as opposed to a single-column pier. However, it attracts larger seismic force for higher lateral stiffness and eventually raises the probability of exceeding the seismic damage state that a bridge can have. 3 1.2 Research Gaps PBSD is included in the Canadian Highway Bridge Design Code (CHBDC) (CSA 2019) for achieving a targeted bridge performance under design-level earthquakes. Various steel and concrete strain limits are proposed in this code at different performance levels, e.g., limited service, immediate occupancy, life safety, and service disruption, when designing new bridges. These strain limits have to be met under different seismic hazard levels as prescribed in the design code. Furthermore, the code does not require existing bridges to meet these requirements. For retrofitting existing bridges, the code requires that the performance objectives be dictated by the regulatory authority, and they can vary depending on the intended purpose and service life for the design of the retrofit. Moreover, it is often difficult to meet the code prescribed strain limits for retrofitting existing bridges because of their existing deficiencies and other site constraints. Thus, the current PBSD approach in the code for new bridges is not suitable for retrofitting existing bridges. Existing bridges need to be retrofitted to provide desired performance under different seismic hazard levels. However, the current code does not provide any guidelines for performing PBSD for retrofitting seismically deficient bridges. In addition, the performance objectives and criteria of their corresponding limit states need to be defined first for retrofitting existing bridges using PBSD. In the past, performance-based seismic losses and resilience of deficient and retrofitted bridges were assessed considering different hazard levels. However, the effects of various damage states, such as different yielded rebar proportions and earthquake sources, were not included in those assessments. 1.3 Research Objectives This research aims to develop a performance-based design guideline for retrofitting existing 4 seismically deficient RC bridge bents using various retrofit options, including carbon fibre-reinforced polymer (CFRP), engineered cementitious composite (ECC), steel, and concrete jackets. This research particularly targets the following: 1. Developing performance-based damage states of different retrofit techniques expressed as limiting drifts and damage indices 2. Identification of an optimum intensity measure for comparisons of seismic performances of bents retrofitted with various retrofit options 3. Proposing a performance-based design guideline to retrofit a seismically deficient bridge bents 4. Evaluating performance-based seismic loss and resilience for different retrofitted bridge bents 1.4 Contribution and Novelty Past studies focused on forced-based seismic design to retrofit deficient bridge bents though CHBDC (CSA 2019) recommends performance-based seismic design, especially for lifeline bridges. Thus, this research will enrich CHBDC through the development of a design guideline for different performance levels for retrofitting existing reinforced concrete bents using various retrofit options. Successful completion of the research will quantify the effects of various retrofit options on how a deficient bridge bent’s seismic behaviour and collapse capacity are enhanced. Moreover, it will aid engineers in increasing service lives and users’ safety of such bridges through retrofitting, which will cost less than replacement. The developed framework will provide a solution space for researchers, practitioners, and stakeholders to uncover the coupled 5 complex threats of earthquakes, deficient design, and aging and deterioration of bridge safety and serviceability. 1.5 Thesis Outline Six chapters comprise the thesis. In this chapter, research gaps, goals, contributions, and novelty are discussed. The remaining thesis content is included in the chapters as follows: Chapter 2 provides different techniques used to retrofit seismically deficient bridge bents in the previous research. Furthermore, it provides a literature review of performance-based seismic loss and resilience assessments of retrofitted bents to obtain the optimum one with the most benefit-cost ratio and functionality. In Chapter 3, deficient and retrofitted bents’ numerical modeling and their validations with experimental results are discussed. A design example is included here to demonstrate the performance-based seismic design to retrofit a similar bent using the damage states proposed in this research. Chapter 4 discusses deficient and retrofitted bents’ fragility analyses performed to obtain probabilities of exceeding various damage states under different earthquakes. In this chapter, benefit-cost ratio analyses of various retrofitting techniques for selecting the optimum one that maximizes such a ratio are presented. In Chapter 5, retrofitted bents’ performance-based seismic resilience assessments are described. This chapter presents how the optimum retrofit option that maximizes seismic resilience and takes the least time to restore the full functionality is selected for the considered deficient bent. 6 At last, the core contributions and conclusions of this research are summarized in Chapter 6. Prospective research in this discipline has been recommended. 7 CHAPTER 2. LITERATURE REVIEW 2.1 General Deficient bridge piers and bents fail to provide the desired performance under major earthquakes. Thus, seismic performance assessments of such piers and bents retrofitted with different retrofit options have been the topic of interest for several decades. Furthermore, previous researchers evaluated performance-based seismic losses of as-built and retrofitted piers and bents to obtain the benefit-cost ratios of various retrofitting techniques. They measured the performance-based seismic resilience of retrofitted piers and bents to select the optimum retrofit option that maximized functionality and needed the least restoration period. Moreover, the next sections present past studies’ outcomes on the seismic performance, loss, and resilience assessment of retrofitted bridge piers and bents. 2.2 Bridge Retrofit Options and Current Design Guidelines Past studies have extensively investigated the seismic behaviour of single pier or multi-column bent retrofitted with different retrofit options. In this research, CFRP, ECC, steel, and concrete jacketing were utilized for retrofitting a seismically deficient RC bridge bent. Their comparisons in terms of mechanical properties, constructability, and cost are shown in Table 2.1. As observed from Table 2.1, the tensile strengths of CFRP and ECC range from 628 to 1800 and 1.75 to 6 MPa, respectively. Elastic modulus and elongation of CFRP lie between 64.73 and 115.70 GPa and 1.00 and 1.75 %, respectively. Conversely, steel jacket and transverse steel yield strengths differ from 248 to 361 and 275.0 to 599.2 MPa, respectively. Moreover, ECC and concrete compressive strengths vary between 54.5 and 80.0 and 17.8 and 34.0 MPa, respectively. On the contrary, the tensile strain of transverse steel corresponding to the maximum tensile stress ranges from 0.10 to 0.15. CFRP jackets are preferable to other jackets for their simple 8 application. However, steel jackets also require more effort to construct than CFRP. Furthermore, formwork is needed for both ECC and concrete jackets. More preparation work is needed for ECC jackets compared to CFRP and steel ones during repair. In contrast, rebars need to be placed for concrete jacket construction, which involves the most physical activity compared to other jackets. Moreover, the CFRP jacket costs the most among the considered retrofit options. Conversely, concrete, ECC, and steel jackets cost the same. Previous research outcomes on steel, CFRP, concrete, ECC, and ultra-high performance fibre reinforced concrete (UHPFRC) jacketed RC bridge piers and bents are presented in the next subsections. 9 Table 2.1. Mechanical properties, constructability, and cost of various retrofit options (Kennedy et al. 2015) Retrofit options Mechanical properties Constructability Cost CFRP • Tensile strength: 628-1800 MPa • Modulus of elasticity: 64.73-115.70 GPa • Elongation: 1.00-1.75% • Easiest to apply • Expensive Steel • Yield strength: 248-361 MPa • Ultimate tensile strain: 0.15-0.22 • Harder to apply than CFRP jacket • Can be cheaper than CFRP jacket ECC • Tensile strength: 1.75-6.00 MPa • Ultimate tensile strain: 0.04-0.06 • Compressive strength: 54.5-80.0 MPa • Requires formwork and more labour to apply than CFRP and steel jackets • Cost same as steel and concrete jackets Concrete • Concrete compressive strength: 17.8-34.0 MPa • Transverse steel yield strength: 275.0-599.2 MPa • Tensile strain of transverse steel corresponding to maximum tensile stress: 0.10-0.15 • Also requires formwork, rebar placement, and the most labour • Cost like steel and ECC jackets 10 2.2.1 Seismic retrofitting using CFRP jacket In this subsection, past research involving seismic performances of bridge piers retrofitted with CFRP jackets is discussed. Fahmy et al. (2009) examined how fibre-reinforced polymer (FRP) bridge columns performed under earthquakes to evaluate their recoverability. A condition for states of recoverability and irrecoverability of such columns was also specified in that study. Damage states of bridge piers retrofitted with CFRP jackets were suggested by Jean et al. (2012) in terms of ductility. The vulnerability of 12 RC circular bridge piers retrofitted with CFRP jackets subjected to different earthquakes was compared by Parghi and Alam (2017). Furthermore, various concrete compressive strengths, longitudinal steel rebar yield strengths, longitudinal steel rebar amounts, axial load levels, shear span-depth ratios, and CFRP confinement layers were taken into account. The nonlinear dynamic behaviours of these retrofitted bridge piers were studied under different ground motions conducting nonlinear static pushover and IDA. Shear span-depth ratios, reinforcement amounts, and axial load levels notably affected their collapse fragility curves. Moreover, McEntee et al. (2021) tested one as-built and two RC bridge wall piers retrofitted with near-surface mounted (NSM) CFRP rods and CFRP jackets, respectively, under quasi-static load. Though both retrofit options increased the as-built pier’s hysteretic energy dissipation and flexural capacity, the pier retrofitted with CFRP jackets showed less ductility compared to that retrofitted with NSM CFRP rods. However, the CFRP jacket was recommended for easy application. 2.2.2 Seismic retrofitting using steel jacket The effects of retrofitting bridge piers with steel jackets on seismic behaviour, as determined by various researchers, are presented in this subsection. Chai et al. (1991) retrofitted 11 RC circular bridge columns with steel jackets. Furthermore, retrofitting increased the seismically deficient columns’ ductility, energy absorptions, and stiffnesses. The retrofitted column’s plastic hinge region reinforcement fractured from low-cycle fatigue instead of experiencing bond failure. Priestley et al. (1994) studied seismic performances of as-built and steel-jacketed RC rectangular bridge columns. Moreover, the retrofitted column achieved ductility and drift angle of at least 8 and 4%, respectively. Retrofitting increased the as-built column’s elastic stiffness, and the column consequently failed in flexure instead of shear. Saiidi et al. (2004) tested as-built and retrofitted flared RC bridge column specimens on a shake table. The as-built column specimen was also retrofitted with steel, glass fibre-reinforced polymer (GFRP), and CFRP jackets. These jackets increased the as-built column specimen’s ductility and shear strength while providing a similar seismic performance that Table 2.2 presents. Table 2.2. As-built and retrofitted column specimens’ ductility and ultimate lateral load comparison (Saiidi et al. 2004) Column specimen type As-built Steel CFRP GFRP Ductility 5.4 6.9 7.9 7.4 Ultimate lateral load (kN) 263 360 324 341 All retrofitted column specimens failed in flexure instead of shear. Furthermore, Jeon et al. (2016) retrofitted damaged RC circular bridge columns with CFRP and steel jackets and conducted nonlinear time history analyses under different mainshock-aftershock sequences. The steel-jacketed bridge experienced a lower aftershock vulnerability compared to the CFRP-jacketed one. 12 Moreover, steel jackets did not markedly affect the longitudinal bridge vulnerability, but they did remarkably decrease transverse bridge vulnerability. Brodbeck et al. (2024) applied quasi-static load to as-built and steel-jacketed RC circular bridge columns. This repair improved energy dissipation and decreased the gradual strength reduction of the column by relocating the plastic hinge to an intact section. 2.2.3 Seismic retrofitting using ECC jacket In this subsection, past research on seismic performances of bridge piers retrofitted with ECC jackets is discussed. Zhang et al. (2019) performed cyclic tests on as-built and ECC-jacketed RC rectangular bridge column specimens. Furthermore, as-built column specimens experienced more damage and had lower ductility, lateral strength, energy dissipation, and stiffness than the retrofitted ones. One seismically deficient and three ECC-jacketed RC rectangular bridge column specimens’ quasi-static behaviours were investigated by Zhang et al. (2022). They employed two different jacket thicknesses of 25 and 50 mm with jacket heights of 200 and 400 mm. Higher jacket thickness provided more elastic stiffness and lateral strength for deficient bents. Jacket thickness affected the deficient bent’s seismic performance more than jacket height. Zhou et al. (2023) also conducted cyclic tests on one uncorroded RC bridge pier, two piers with 10% and 30% corrosion rates, and six polyethylene terephthalate (PET) FRP and CFRP jacketed RC corroded piers. Corroded piers failed from the corroded area’s shear compression instead of the pier end’s flexure compression. The ultimate displacement, cumulative dissipated energy, and ultimate lateral load of the pier decreased with increasing corrosion rate. Furthermore, an engineered cementitious composite (ECC) coated FRP jacketed non-uniformly corroded piers, having a greater corrosion rate, performed better under 13 earthquakes. Such a pier exhibited higher lateral load capacity and ultimate displacement than the uncorroded pier. Retrofitting the portion between the corroded area and the foundation provided improved seismic performance compared to retrofitting only the corroded area of the pier. Moreover, the CFRP jacket showed higher cumulative energy dissipation and ductility compared to the PET one due to better confinement, whereas the latter experienced greater strain capacity than the former at failure. 2.2.4 Seismic retrofitting using concrete jacket The effects of retrofitting bridge piers with concrete jackets on seismic behaviour, as determined by various researchers, are presented in this subsection. Suarjana et al. (2020) retrofitted an RC hollow rectangular bridge pier with a concrete jacket and studied its seismic performance. Furthermore, retrofitting enhanced lateral strengths of the as-built and damaged piers by 15% and 46%, respectively. The flexural strength of the retrofitted section changed at best 7% when plastic hinge models with old and new concrete composite sections and initial load, respectively were considered. It markedly decreased with an interface slip coefficient smaller than 0.5. Stefanidou and Kappos (2021) also proposed a procedure to select retrofit options to achieve particular performance considering the as-built and retrofitted bridges' fragility. A continuous deck FRP and RC jacketed bridge pier as well as a base-isolated simply-supported deck bridge was taken into account to assess how effective such retrofit options were. Two FRP types such as CFRP and GFRP were considered. Similarly, lead rubber bearings (LRB), as well as high damping bearings (HDB), were provided for base isolation. The authors proposed an equivalent efficiency criterion to choose different retrofit option properties to compare the retrofit options at the considered performance levels. Table 2.3 shows the effective retrofitting 14 techniques that produced the least as-built bridge seismic vulnerability for various damage states. CFRP jacket decreased as-built bridge seismic vulnerability more than the GFRP one for these damage states. Table 2.3. Effective retrofit options for the as-built bridge at various damage states (Stefanidou and Kappos 2021) Bridge type Slight damage Moderate damage Extensive damage Imminent collapse Monolithic CFRP jacket RC jacket RC jacket CFRP jacket Bearing supported LRB LRB LRB LRB 2.2.5 Seismic retrofitting using UHPFRC jacket In this subsection, past research on UHPFRC jacketed bridge piers’ seismic performance is discussed. Degnais et al. (2018) tested five UHPFRC jacketed RC bridge piers and one as-built pier under cyclic loading. Furthermore, all piers had longitudinal reinforcement ratios between 1.30% and 1.67% with different bar diameters. To be consistent with pre-code seismic design requirements, 300 mm and 24 times the bar diameter were provided as stirrup spacing and pier base splice length, respectively, in all piers. All retrofitted piers experienced progressive and ductile failure because of the consecutive rupture of footing dowel bars. Thus, the use of the UHPFRC jacket avoided all concrete failure modes such as spalling, crushing, etc. and no lap splice failure and buckling of flexural reinforcement were observed. Moreover, Tong et al. (2019) 15 experimented with one as-built and UHPFRC-jacketed rectangular RC piers with high and small ratios of height to width and longitudinal rebars under cyclic load. They considered two jacket heights of 400 mm and 850 mm, which raised the as-built pier’s lateral strength by 16.2% and 37.8%, respectively. The 400-mm jacket provided higher ductility and dissipated more energy. 2.3 Performance-Based Seismic Loss Assessments of Bridges Previous researchers considered seismic loss to optimize seismically deficient bridges’ retrofits. A method for ranking seismically deficient bridges of various service lives and importance categories considering life cycle cost was suggested by Sato et al. (2004). Furthermore, a bridge pier’s maintenance and seismic risk-related loss were minimized by utilizing bridge maintenance actions assessed through multi-criteria optimization techniques (Furuta et al. 2006). The efficiencies of different retrofit options, e.g., restrainer cables and elastomeric bearings, were compared based on minimum life-cycle cost by performing probabilistic seismic damage analysis of 2D steel bridge models in Korea following first-order reliability methods (Cho et al. 2007). Life-cycle costs were availed to obtain an optimal retrofit technique in this study without considering the effects of various bridge types or hazard locations. Moreover, Mackie and Stojadinovi´c (2007) developed a non-iterative method to figure out the geometric properties of a bridge using PBSD. They suggested equations for design at various performance levels expressed in loss as well as bridge damage, considering uncertainty for hazard level and demand. Design examples were provided to demonstrate how the developed method could be applied to representative RC California bridges. Padgett et al. (2010) also proposed an approach to obtain the optimum retrofit options for four seismically deficient bridges in three locations representing different seismic hazards considering cost-benefit ratios 16 (CBRs) as well as life-cycle costs (LCCs). Seven retrofit techniques such as seat extender (SE), elastomeric bearing (EB), steel jacket (SJ), shear key (SK), restrainer cable (RC), a combination of shear key and seat extender or shear key and restrainer cable were taken into account in this study. They performed as-built and retrofitted bridges’ fragility analyses at various damage states to obtain retrofit costs. Furthermore, the optimum retrofit technique for a specific bridge was found to vary depending on the site's seismic characteristics, as the effects of retrofit techniques at various damage states differed. LCCs, benefits, costs, and CBRs of considered retrofit options for the deficient bridge multi-span continuous (MSC) steel bridge in Los Angeles are displayed in Table 2.4. Table 2.4. Comparisons of LCCs, benefits, costs, and CBRs of various retrofit options for MSC steel bridge (Padgett et al. 2010) Retrofit option LCC ($) Benefit ($) Cost ($) CBR Deficient 386,164 - - - SJ 313,208 83,160 36,000 2.31 EB 295597 48,206 21,912 2.20 RC 319,497 104,340 11,280 9.25 SK 333,333 95093 23,250 4.09 SE 332,075 70,200 9000 7.80 SE+SK 264,151 194,145 32,250 6.02 RC+ SK 289,308 159,529 34,530 4.62 17 RC was selected as the optimum retrofit option for providing the maximum CBR in the case of the MSC steel bridge at the location. Moreover, the effects of various performance-based damage states and earthquake sources on life-cycle costs and cost-benefit ratios were not considered in this study. Ghosh and Padgett (2011) introduced a method to evaluate the life-cycle costs of aging seismically deficient multi-span simply supported (MSSS) concrete and MSC steel bridges in Tennessee. The proposed method considered each element’s repair cost, repair method’s variability, and relationship of element damages for obtaining life-cycle cost. They also found that life-cycle cost was mostly affected by the damage in the columns and bearings. The comparative effects of column and bearing damages on life-cycle cost vary depending on the types of aging of those bridges. Consideration of deterioration raised this cost by 44% and 14% for MSSS concrete and MSC steel bridges, respectively at a 3% discount rate with 75-year remaining service life. Furthermore, Miano et al. (2016) applied the available methods in the literature to obtain repair cost probability distribution of highway bridges in Italy subjected to the Irpinia earthquake that took place in 1980. This research improved earthquake forecast, vulnerability, and cost models using data obtained from the literature. The authors proposed different hypotheses on earthquake correlation that markedly influenced direct economic loss distribution. Moreover, direct economic loss dispersion can be notably decreased using improved earthquake forecast. Perdomo and Monteiro (2021) obtained expected annual loss for an MSC RC bridge using an iterative response spectrum analysis with the higher mode effects for direct expected annual loss evaluation. They concluded that displacement obtained from nonlinear response history analysis provided less loss using probabilistic assessment relative to the suggested methods. 18 2.4 Performance-Based Seismic Resilience Assessments of Bridges Performance-based seismic resilience has been used for obtaining optimum retrofitting techniques of as-built bridges with deficiencies like inadequate ductility and low shear strength. Decò et al. (2013) suggested a probability-based approach to determine performance-based seismic resilience and to estimate the consequence expressed in indirect as well as direct costs of bridges. Furthermore, the performance-based seismic resilience of a highway bridge located in California was evaluated using this method. The indirect consequences were substantially controlled by the most expensive option. For this option, the maximum performance-based seismic resilience was obtained in the shortest duration required for the full recovery. Moreover, such an option can be the most useful for decision-makers who do not have budget constraints to curb the overall loss. Thus, this method can help in choosing the optimum technique based on the desired performance level, expected consequence, and funds used in bridge rehabilitation. Minaie and Moon (2017) suggested a simple multistep approach for evaluating bridge resilience based on several past significant natural events. A basic restoration time series was also proposed for a simple single-path recovery, considering the extremity of the event and affected area size. Performance loss of the bridge for an event is estimated according to the hazard level, vulnerability and importance of the bridge. Basic recovery time is modified depending on how prepared the community is to face major events, such as events’ histories and the bridge type. Furthermore, the area under the post-major event performance curve divided by that under the target performance curve over a year is measured as bridge resilience. The resilience of two bridges subjected to a major event was evaluated by this method. Pang et al. (2020) suggested a probability-based method for assessing the life-cycle performance of a highway bridge having fibre-reinforced concrete (FRC) as well as corroded RC 19 piers expressed in seismic resilience. Moreover, cloud analysis was improved to produce fragility curves used to measure seismic resilience considering the corroded bridge’s residual functionality before the occurrence of an earthquake. FRC was found to improve the bridge’s seismic resilience by about 25% over the bridge’s lifespan as opposed to RC which decreased it by around 20%. ChienKuo et al. (2021) suggested a procedure to show how seismically deficient and retrofitted RC bridges' resilience is related to the effective peak acceleration (EPA) of an earthquake. They also used a bridge in Taipei to demonstrate this procedure to select the optimum retrofit option considering resilience indices for different EPAs. Four concrete jackets with different longitudinal rebar spacings and various transverse rebar sizes and spacings and two steel jackets with different sheet thicknesses were considered in this study. The concrete jacketed bridge with smaller longitudinal rebar spacing showed a greater probability of exceeding the complete damage state compared to the steel jacketed one, which had a smaller sheet thickness due to more strength. Furthermore, the bridge retrofitted with each option became more resilient than the seismically deficient bridge. This study did not take into account how different performance-based damage states and earthquake sources could affect the resilience index. Qian et al. (2022) suggested a method for comparing RC as well as steel-SMA reinforced concrete bridges’ seismic resilience. Moreover, SMA’s corrosion resistance and self-centring ability resulted in 35% improved seismic resilience compared to the RC bridge. Ghaffarpasand et al. (2023) studied various techniques: simple, simulated annealing (SA), non-dominated sorting genetic algorithm (NSGA)-II, and NSGAII-SA for optimizing options such as CFRP and seat extender to retrofit a curved bridge located in Tehran. Different thicknesses and widths were considered for CFRP and seat extender, respectively. The optimum retrofit option also maximized seismic resilience and minimized recovery time and retrofit cost. Both as-built 20 and retrofitted bridges were subjected to 20 crustal earthquakes to perform IDA. Seat extenders and CFRP used to retrofit the bents and abutments increased seismic resilience and decreased recovery time. On the other hand, seat extenders only provided for abutments reduced retrofit cost. Furthermore, Hong et al. (2023) used shear links (SLs) to retrofit prestressed reinforced concrete (PRC) bridge bents and performed IDA for both as-built and retrofitted bridges subjected to 18 far-field as well as 18 near-fault crustal earthquakes. SLs increased the seismic resilience but reduced seismic loss and fragility. Omidian et al. (2024) suggested a straightforward probabilistic framework for a typical RC box girder bridge seismic resilience assessment while the bridge reinforcements were considered to rust away. Moreover, bridge piers were retrofitted with 9.53, 12.70, 19.05, and 25.40 mm thick steel jackets and 1.24 and 1.27 mm thick CFRP and GFRP jackets of 2, 4, 7, and 10 plies. Various cases, such as all piers, 75% piers, 50% piers, and 25% piers retrofitted with different jackets, were considered. IDA of retrofitted as well as as-built bridges was performed under 20 different crustal earthquakes. Various retrofit options were also found to increase the bridge's seismic resilience, counteracting corrosion and earthquake joint effects. Dong et al. (2024) conducted cyclic experiments on a pure energy dissipation brace (EDB), and a self-centring energy dissipation brace (SCEB) comprised of steel U-shaped plates and shape memory alloy (SMA), respectively. IDA was also performed for RC bridges where the bents were retrofitted with SCEB-SMAUs and EDB-SUs under 60 far-field as well as 60 near-fault crustal earthquakes. Furthermore, EDB-SUs and SCEB-SMAUs increased seismic resilience and decreased economic loss at lower and higher hazard levels, respectively. 21 2.5 Summary A literature review of various techniques used for retrofitting deficient bridges, their current design guidelines, and past studies on performance-based seismic resilience as well as loss assessments of retrofitted bridges, are presented in this chapter. Such a review helped identify the research objectives and recommend further work that could be done in the future. 22 CHAPTER 3. DEVELOPMENT OF PERFORMANCE-BASED DAMAGE STATES FOR RETROFITTED BRIDGE BENTS 3.1 General For implementing performance-based seismic design (PBSD) to retrofit older bridges, different performance objectives and criteria must be defined to identify the respective damage states. This research targets performance-based damage state development to retrofit seismically deficient RC bridge bents, given various retrofit options and earthquake hazard levels. The study mainly aims to present a framework to develop a performance-based design for seismic retrofitting and provide a design example for demonstrating how the suggested methodology can be applied to retrofit deficient multi-column bridge bent. IDA of retrofitted bents were performed at different performance levels to express performance-based damage states using damage indices and limiting drifts. The proposed damage states are used in a design example for the demonstration of the PBSD to retrofit seismically deficient bridge bents. The seismically deficient bent in this research is considered to exist in Vancouver in southwestern British Columbia, Canada. The Cascadia subduction zone, in which the bridge is located, may generate earthquakes from different tectonic sources such as crustal, intra-slab, and interface, and thus were considered (CSA 2019; Todorov and Billah 2021; Mottier et al. 2021). Since the bridge seismic performance depends on ground motion intensity, an optimum intensity measure has also been obtained to achieve the comparative seismic performances of all retrofitted bents expressed in damage indices and maximum drifts for different intensity levels. 3.2 Bridge Bent Details A bridge bent that represents a typical multi-column bent located in Vancouver, BC was considered in this study. The characteristics of the considered bridge bent belong to a study 23 conducted by Pantelides and Gergely (2002). The details of the original bent are presented in Figure 3.1. Seismic design guidelines were not followed when designing this bridge. Hence, it fails to meet current seismic performance standards. As per CHBDC, the bent is deficient under earthquake for not having adequate stirrups in column-cap beam connections, pile caps and cap beam not having column rebars with proper embedment, and column lap-splice and plastic-hinge regions with insufficient ties as portrayed in Figure 3.2. The bent carries eight girders at uniform spacing, each applying 240 kN gravity load on the bent cap. Reinforcement yield and concrete compressive strengths are 275 MPa and 21 MPa, respectively. Figure 3.1. Bridge bent elevation (adapted from Pantelides and Gergely 2002) 3.3 Retrofit Alternative Details Various techniques such as steel, CFRP, concrete, and ECC jackets; external prestressing using steel (Coffman et al. 1993); precast concrete segment (Iverson et al. 1999); ferrocement jacketing (Kumar et al. 2005), infill shear wall (Pulido et al. 2004), bracings (Xiang and Alam 24 2019), etc. can be used to retrofit deficient bridge bents. The comparisons of different retrofitting techniques are shown in Table 3.1. Figure 3.2. Column and cap beam cross-sections (adapted from Pantelides and Gergely 2002) The research considered a deficient bent retrofitted with steel, CFRP, ECC, and concrete jackets, which are cost-effective, can be easily obtained, simply applicable, and efficient at improving the deficient bridge bent seismic performance while achieving targeted performance objectives. The next section presents the considered retrofit technique designs. 25 Table 3.1. Pros and cons of various retrofit techniques Retrofit options Pros Cons CFRP • Non-corrosiveness, high elastic modulus, as well as high-strength (Seible et al. 1997) • Can increase the hysteretic energy dissipation and flexural strength (McEntee et al. 2021) • Easy application (McEntee et al. 2021) • Susceptible to fire/high temperature (Zarifian et al. 2020) Steel • Strength enhancement (Chai et al. 1994) • Cannot increase ductility as much as shear strength (Xiao and Wu 2003) ECC • Reduces crack width and enhances ductility as well as shear strength (Li et al. 2000) • Can improve how nonuniformly corroded piers having greater corrosion rate perform under earthquakes (Zhou et al. 2023) • Increases the component size compared to CFRP and steel jacketing Concrete • The most economic and also contributes to greater ductility, shear strength, stiffness, and lateral strength (Rodriguez and Park 1994) • Increases the component size in contrast with other jacketing 3.4 Design of Different Retrofit Options The mechanical properties of CFRP considered in this study are displayed in Table 3.2. The 26 thickness of the CFRP jacket was calculated using Equation (3.1) (Priestley et al. 1996) and properties presented in Table 3.2. 𝑡𝑡𝑗𝑗 = 0.1(𝜀𝜀𝑐𝑐𝑐𝑐−0.004)𝐸𝐸𝑓𝑓𝑐𝑐𝑐𝑐′𝑓𝑓𝑐𝑐𝑢𝑢𝜀𝜀𝑐𝑐𝑢𝑢 (3.1) where εcu is the ultimate compressive strain, tj is the thickness of the jacket, εuj is the ultimate tensile strain of jacket material, fuj is the tensile strength of jacket material, fcc’ is the compressive strength of confined concrete, and D is the jacket diameter. Table 3.2. Properties of different retrofit materials (Priestley et al. 1996; Pantelides and Gergely 2002; Fischer and Li 2003) Retrofit options Tensile strength of jacket material (MPa) Ultimate tensile strain of jacket material Jacket thickness (mm) CFRP 628 0.01 1.32 Steel 248 0.15 2 Concrete - - 100 ECC 6 0.06 40 Furthermore, the steel jacket which possesses the properties as shown in Table 3.2 was considered in this research. Such a tensile strength of the steel sheet helped avoid local buckling and handling without any problem. Equation (3.2) (Priestley et al. 1996) also provided steel jacket thickness with the properties as portrayed in Table 3.2. 𝑡𝑡𝑗𝑗 = 0.18(𝜀𝜀𝑐𝑐𝑐𝑐−0.004)𝐸𝐸𝑓𝑓𝑐𝑐𝑐𝑐′𝑓𝑓𝑦𝑦𝑢𝑢𝜀𝜀𝑐𝑐𝑢𝑢 (3.2) 27 where fyj is the yield strength of steel and D is the jacket diameter. The entire length of bent columns was covered with the CFRP and steel jackets as displayed in Figure 3.3. In the case of the steel jacket, a gap of 50 mm was kept between the jacket and the pile cap or/and cap beam so that it did not compress, pushing them for high drift. This arrangement did not increase plastic hinge region moment capacity, which consequently restricted pile cap and cap beam internal forces from increasing in such a situation. Figure 3.3. Retrofitted column elevations Moreover, concrete jacket thickness was calculated from Equation (3.3) (Priestley et al. 1996) using the properties presented in Table 3.2. 𝜀𝜀𝑐𝑐𝑢𝑢 = 0.004 + 1.4𝜌𝜌𝑠𝑠𝑓𝑓𝑦𝑦ℎ𝜀𝜀𝑠𝑠𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐′ (3.3) 28 where εsu is the strain corresponding to the tensile strength (0.15) and fyh is the yield strength of transverse steel. Figure 3.4 presents cross-sections of columns retrofitted with various retrofit options. The original column material properties were used in the concrete jacket to ensure consistency. This consistency provided numerical modelling convenience such that original column materials’ (concrete, steel) experimental stress-strain responses could be used to make the concrete jacket compatible and to simulate its seismic behaviour accurately. Otherwise, separate material property calibration studies would be required to obtain stress-strain responses of the concrete jacket materials. Furthermore, ECC properties, as portrayed in Table 3.2, were considered in this study. ECC jacket thickness was obtained using Equation (3.1). Moreover, columns were retrofitted with ECC and concrete jackets, as displayed in Figure 3.3, such that concrete outside the jacketed regions does not spall off. Figure 3.4. Retrofitted column cross-sections 29 3.5 Finite Element Modeling For this research, the full bridge was not modelled. Only one multi-column bent of the bridge, which was experimentally tested in a past study (Pantelides and Gergely 2002) is numerically modelled. SeismoStruct (2020) was used to model the cap beam as well as the columns using fibre-based 3D inelastic displacement-based frame elements as shown in Figure 3.5a. These elements can be used to model the bent components, including geometric and material nonlinearities. Column and beam cross-sections were divided into 200 fibres as presented in Figure 3.5b. The stress-strain curve of each fibre was used to model unconfined and confined concrete and steel reinforcement. Menegetto-Pinto (1973), Mander et al. (1988), Trilinear fib (2001, 2006), and Han et al. (2003) suggested constitutive models used to simulate steel, concrete, CFRP, and ECC behaviours, respectively as shown in Figure 3.6. Integrating the nonlinear uniaxial material responses of all fibres, stress-strain states of the cross-sections were obtained, considering inelasticity distribution over each component depth and length. The bent considered in this study is assumed to be a major-route bridge component. The site lies on stiff soil (Class D). As per CHBDC, the bent requires to have a lateral strength of 1452 kN, corresponding to a 2,475-year return period hazard level. However, the as-built bent has a lateral strength of 1277 kN, rendering it inadequate according to the current seismic performance requirements. Consequently, the same bent was retrofitted with steel, CFRP, ECC, as well as concrete jackets. Bents retrofitted with steel, CFRP, concrete, and ECC jackets have lateral strengths of 1914, 1902, 1923, and 1761 kN, respectively as portrayed in Figure 3.7a. Conversely, flexural strengths of steel, CFRP, ECC, and concrete jacketed critical column sections are 2750, 2810, 2560, and 2720 kN.m, respectively, which are higher than that of the deficient one of 1830 kN.m as shown in Figure 3.7b. Therefore, the lateral and flexural strengths of the retrofitted 30 bents are identical and comparable. For the research, 5% was taken into account as Rayleigh damping. Given the bridge deck tributary areas, each girder transfers 240 kN gravity load, which is used to model the mass as a lumped mass on the cap beam. Eigenvalue analyses were performed to obtain deficient and retrofitted bents’ time periods, as shown in Table 3.3. The first mode shape of the bent is presented in Figure 3.8. These periods were obtained from linear modal analyses considering the deficient and retrofitted bents’ cracked stiffnesses. Although only the bent was modelled, the mass contribution from the superstructure was considered in the model to correlate to the actual bridge period. Deficient and four retrofitted bridges’ natural periods and those of the respective bridge bents in the transverse direction are the same. Modelling methods were validated with previous experimental results of bridge piers and bents retrofitted with steel, CFRP, concrete, and ECC jackets. Figure 3.5. Finite element model: (a) 3D bent model and (b) critical column section Retrofit fibre Rebar fibre Confined concrete fibre (a) (b) 31 Figure 3.6. Stress-strain diagrams: (a) CFRP jacket, (b) steel jacket, (c) ECC jacket, and (d) concrete Figure 3.7. Comparisons of lateral and flexural strengths of as-built and retrofitted bridge bents: (a) capacity curves and (b) bending moment-curvature responses of critical column sections 01002003004005006007000 0.004 0.008 0.012Stress (MPa)Strain(a)0501001502002503000 0.06 0.12 0.18Stress (MPa)Strain(b)-100-75-50-25025-2 0 2 4 6 8Stress (MPa)Strain (%)05101520250 0.002 0.004 0.006 0.008Stress (MPa)StrainUnconfinedConfined05001000150020000 0.5 1 1.5 2 2.5 3 3.5 4Lateral Load (kN)Limiting Drift (%)As-BuiltCFRPSteelECCConcrete(a)0500100015002000250030000 0.01 0.02 0.03 0.04 0.05Bending Moment (kN.m)Curvature (1/m)As-BuiltCFRPSteelECCConcrete(b)(c) (d) 32 Figure 3.8. First mode shape of the bent Table 3.3. Time periods of multi-column bents Bent type Deficient CFRP Steel ECC Concrete Period (s) 0.60 0.59 0.53 0.55 0.47 3.5.1 Model validation with experimental results As-built seismically deficient bent’s experimental and numerical hysteretic behavioural comparison is shown in Figure 3.9a (Pantelides and Gergely 2002). The numerical model accurately simulated both the experimental maximum load and stiffness. It predicted loads at yielding and failure, differing by only 11% and 5%, respectively, from those of the experiment. Pantelides and Gergely (2002) experimentally studied the cyclic behaviour of the as-built seismically deficient bent retrofitted with CFRP jacket. The retrofitted bent considered in that experiment exhibited the quasi-static behaviour presented in Figure 3.9b. Figure 3.9b also displays the numerical model’s base shear–drift response, which closely matches the experimental result. The loads at failure and yielding were predicted as 2088 kN and 976 kN, respectively, only 7.91% and 2.09% higher than those of the experimental ones, i.e., 1935 kN and 956 kN. 33 Vandoros and Dritsos (2008) studied how three options of concrete jacketed columns performed under cyclic load. Figure 3.9c shows a concrete jacketed column’s (Specimen-N) performance under cyclic loading. Figure 3.9c portrays that the developed numerical model and test specimen exhibited nearly the same cyclic response. Ultimate, failure and cracking loads were predicted as 143 kN, 92.34 kN, and 127 kN, respectively, differing by only 4.54%, 6.42%, and 11.40%, respectively, from the experimental ones. Loading stiffness was different in all cycles, but the deviation of peak numerical drift from the experimental one was not more than 8.12% for any cycle. The axial load applied on the specimen varied from 720 kN to 770 kN in the experiment because of the test setup. It increased and decreased depending on the sway of the specimen. As the loading stiffness relies on axial load level (Priestley et al. 1996), experimental and numerical values differed since the numerical model could not simulate the change in the level of axial load as the experiment. ElGawady et al. (2010) studied how scaled CFRP and steel jacketed columns behaved when subjected to quasi-static load. The quasi-static behaviour of the specimen retrofitted with steel jacket (Specimen-SJ) used in that investigation is shown in Figure 3.9d. The numerical ultimate drift and load were 3.33% and 67.52 kN, respectively, whereas the experimental ones were 3.40% and 65 kN, respectively, varying by only 2.12% and 3.88%, respectively from each other. Stiffness and strength did not match in the small displacement cycles, but the deviations of numerical drift and base shear from experimental ones did not exceed 2.70% and 6.84%, respectively, for any cycle. In small displacement cycles, the column did not experience notable cracks, which eventually contributed to higher numerical model stiffness. Conversely, the column faced significant damage in large displacement cycles, so the numerical model almost simulated the stiffness of the experiment. 34 Gencturk and Elnashai (2011) tested eleven scaled ECC columns of four different ECC-mix designs under cyclic load. Figure 3.9e displays how one of the ECC columns with a 1.29% rebar ratio and no tie (Mix Design-ECC HFA) performed under quasi-static load. The load-drift response obtained from the experiment seems to be simulated accurately by the numerical model with only a 1.31% difference in peak load prediction, as presented in Figure 3.9e. 3.6 IDA-Based Approach for Development of Performance-Based Damage States The performance objectives and the respective damage state criteria need to be defined to employ PBSD for retrofitting deficient bridges. In this research, damage states of steel, CFRP, concrete, as well as ECC jacketed bents at various performance levels were developed from the response obtained from dynamic analysis using an IDA-based approach. Seismic performance predictions of bridges under different intensity levels can be obtained using IDA. IDA aims to analyze a numerical model under one or more earthquakes at various hazard levels to capture its overall behaviour by observing the demand, e.g., drift. Scaling each ground motion to several intensity levels and analyzing the model under the corresponding scaled motion continues until it fails for dynamic instability. First, four retrofit options were selected, and the seismically deficient bridge bent was retrofitted with each option, as discussed in the preceding section. In the next section, three representative earthquake suites were chosen, and IDA was performed for each ground motion. Limiting drifts at various damage states were obtained by tracking material strains from IDA under each ground motion. Finally, the results of all ground motions from IDA were used to obtain limiting drifts at various damage states. 35 Figure 3.9. Comparison of experimental and numerical results: (a) as-built bridge bent (Pantelides and Gergely 2002), (b) bent retrofitted with CFRP jacket (Pantelides and Gergely 2002), (c) column retrofitted with concrete jacket (Vandoros and Dritsos 2008), (d) column retrofitted with steel jacket (ElGawady et al. 2010), and (e) ECC column (Gencturk and Elnashai 2011) -1800-1200-600060012001800-2 -1 0 1 2Base Shear (kN)Drift (%)NumericalExperimental(a)-2400-1600-800080016002400-4 -3 -2 -1 0 1 2 3 4Base Shear (kN)Drift (%)NumericalExperimental(b)-180-120-60060120180-4 -3 -2 -1 0 1 2 3 4Base Shear (kN)Drift (%)NumericalExperimental(c)-90-60-300306090-4 -3 -2 -1 0 1 2 3 4Base Shear (kN)Drift (%)NumericalExperimental(d)-4-2024-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Base Shear (kN)Drift (%)NumericalExperimental(e) 36 3.7 Selection of Earthquakes Table 3.4 presents three suites of ground motions representing three different earthquake sources, each containing 11 earthquakes. These records are used to perform IDA. These accelerograms were chosen from the National Research Institute for Earth Science and Disaster Resilience (NIED 2019), Pacific Earthquake Engineering Research Center (PEER 2013), and Center for Engineering Strong Motion Data (CESMD n.d.) for representing bridge site seismic characteristics, such as tectonic source, source to site distance, earthquake magnitude, local geotechnical conditions, as well as fault type. Furthermore, Vancouver is located in southwestern British Columbia and has been jolted by over 100 earthquakes with magnitudes 5 or more between the west of Vancouver Island and the offshore region for the last 70 years (Salami and Goda 2014). The interaction of four tectonic plates in this region may generate earthquakes of moment magnitudes (Mw), 8 to 9 in the Cascadia subduction zone. Moreover, crustal, intra-slab, and interface earthquakes of various features, expressed in duration and frequency content, markedly influence seismic hazard in Vancouver (Atkinson and Goda 2011). Distances of the stations where the selected motions were recorded from fault (Repi) varied between 11.16 km and 148 km. The selected ground motions possess shear wave velocities (Vs) from 256 m/s to 359 m/s, peak ground velocities (PGV) between 12.70 cm/s and 3249.49 cm/s, and peak ground accelerations (PGA) between 0.12g and 1.39g. The PGA-PGV ratios, which show the frequency contents of ground motions, differed from 0.03 to 4.21. On the other hand, they are 0.62 and 0.56 for 475 and 2475-year return period hazard levels, respectively, in Vancouver, according to CHBDC. Therefore, the average PGA-PGV ratio of the 33 selected ground motions, 0.81, is closer to these values. Bommer and Martinez-Pereira (1999) also investigated and categorized about thirty definitions of ground motion durations. 37 Table 3.4. Selected earthquake ground motion records No. Earthquake Source Year Mw Repi (km) Vs (m/s) PGA (g) PGV (cm/s) PGA/PGV Ds5-75 (s) Source 1 Taiwan SMART1(45) Crustal 1986 7.30 57.13 285.09 0.24 27.29 0.89 - PEER 2 58.00 303.36 0.16 23.52 0.68 3 Landers 1992 7.28 89.69 291.03 0.12 12.70 0.94 4 21.78 359.00 0.15 20.88 0.74 5 Petrolia 1992 7.10 17.60 - 0.39 45.57 0.85 CESMD 6 Cape Mendocino 1992 7.01 41.97 337.46 0.18 28.29 0.63 PEER 7 Kobe, Japan 1995 6.90 11.34 256.00 0.28 33.57 0.82 8 22.50 312.00 0.32 26.87 1.21 9 Spitak, Armenia 1988 6.77 23.99 343.53 0.20 28.36 0.71 10 San Fernando 1971 6.61 22.77 316.46 0.22 21.72 1.03 11 Superstition Hills-02 1987 6.54 11.16 316.64 0.29 29.02 0.99 12 El Salvador Intra-slab 2001 7.60 91.00 - 0.43 48.92 0.88 - CESMD 13 98.00 0.65 49.52 1.31 14 Olympia 1949 7.10 39.00 0.30 45.54 0.66 15 Alaska 2018 7.00 27.80 0.83 19.85 4.21 16 Miyagi 2003 54.00 1.07 3249.49 0.03 K-NET 17 Nisqually 2001 6.80 72.70 1.39 147.65 0.94 CESMD 18 19.00 0.45 57.64 0.78 19 Tokachi 2013 6.50 102.00 0.33 309.01 0.11 KiK-net 20 Puget Sound 1965 6.50 89.00 0.22 15.04 1.46 CESMD 21 Geiyo 2001 6.40 19.00 0.43 174.13 0.25 K-NET 22 0.41 285.94 0.14 23 Tohoku Interface 2011 9.00 137.00 0.47 489.02 0.10 57.85 KiK-net 24 Chile 2010 8.80 65.60 0.68 50.02 1.36 29.84 CESMD 25 38.70 0.55 120.42 0.46 31.86 26 Michoacan 1985 8.10 47.80 0.13 24.06 0.53 32.43 27 Hokkaido 2003 8.00 148.00 0.36 179.70 0.20 15.80 K-NET 28 Valparaiso 1985 25.84 - 0.29 83.90 0.35 34.23 CESMD 29 59.98 0.43 123.31 0.35 40.73 30 Amberley 2016 7.80 34.40 0.31 26.45 1.17 28.48 31 11.80 0.24 29.81 0.81 22.14 32 Ishinomaki 2005 7.20 144.00 82.86 0.29 12.81 KiK-net 33 Kushiro 2004 7.10 34.00 0.34 35.31 0.84 2.52 K-NET 38 Of them, 5%-75% significant duration (Ds5-75) is the most recommended one to study the behaviour of bridges subjected to interface earthquakes (Barbosa et al. 2017). Thus, Ds5-75 was also considered in this research for evaluating the strong motion duration and determined using SeismoSignal (2021). SeismoMatch (2020) was used to adjust the selected ground motions based on the extreme intensity of the return period of 2475 years event in Vancouver. Each response spectrum was matched with the target response spectrum using a period range of interest, 0.075–1.5 s, proposed in CHBDC. Moreover, every earthquake was adjusted using a scale factor between 0.5 and 4 inclusive so that its response spectrum at least equals the target response spectrum within this range of period. All ground motions of each suite were scaled such that their mean response spectrum did not lie over 10% below the target response spectrum in any period on this period range. Figure 3.10 presents the target spectrum as well as the mean spectra of three earthquake sources. 3.8 Selection of Optimum Intensity Measure Intensity measure (IM) presents site seismic hazard and is generally expressed as ground motion intensity e.g., PGA (Ciampoli and Giovenale 2004). It determines how a ground motion affects a structure and is a positive monotonic scalable scalar in the form of a function, IM = fa1(λ), related to the accelerogram, a1, unscaled and that increases as the scaling factor, λ increases (Vamvatsikos and Cornell 2002; Baker 2005). Intensity measure is important because its efficiency determines the accuracy of structural damage estimation (Ciampoli and Giovenale 2004; Baker 2005; Luco and Cornell 2007; Padgett et al. 2008). 39 Figure 3.10. Target and mean response spectra of the selected ground motions: (a) crustal, (b) intra-slab, and (c) interface earthquakes An optimum intensity measure is selected depending on the structure type, its damage level, and the damage measure (DM) so that it produces comparatively little variability of the DM and correlates well with the DM (Giovenale et al. 2004; Ciampoli and Giovenale 2004). A suitable IM is chosen considering sufficiency, computability, and efficiency as criteria suggested by Luco and Cornell (2007). First-mode spectral acceleration (Sa(T1)), PGA, PGV, velocity intensity, cumulative absolute velocity, peak ground displacement (PGD), first-mode spectral displacement (Sd(T1)), Arias intensity, cumulative absolute displacement, Housner intensity, etc. are generally used IMs (Housner 1952; Mackie and Stojadinovic 2007; Padgett et al. 2008). PGA is less 0.050.550.05 0.5 5Spectral Acceleration (g)Vibration Period (sec)Target Response SpectrumMean Response Spectrum(a)0.050.550.05 0.5 5Spectral Acceleration (g)Vibration Period (sec)Target Response SpectrumMean Response Spectrum0.050.550.05 0.5 5Spectral Acceleration (g)Vibration Period (sec)Target Response SpectrumMean Response Spectrum(c)(b) 40 efficient than a structure-dependent IM, Sa(T1), which can better represent the earthquake damage potential of a particular structure than the former (Shome 1999). Furthermore, it can better correlate with energy-based and deformation-based damage measures (Conte et al. 2003). Sa(T1) was also found to be the most practical, proficient, and efficient IM for the MSSS steel girder bridge class (Padgett et al. 2008). However, PGA was reported as the most practical, proficient, and efficient IM for the retrofitted bridge bent with square columns under unscaled near-fault and far-field ground motions (Billah et al. 2013). Moreover, Conte et al. (2003) and Baker (2005) suggested several vector IMs, however, their way of scaling and hazard calculations are more complex (Giovenale et al. 2004) and hence not considered in this study. Vector IM requires all ground motion IMs’ variance-covariance matrix, scalar probability-based seismic hazard analysis disaggregation results, and the considered IMs’ site-specific seismic hazard curves (Kohrangi et al. 2016) that make the whole process complicated and time-consuming. To evaluate different IMs’ relative efficiencies, the engineering demand parameter (EDP)’s corresponding spread relying on the IM, 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼, is evaluated by Equation (3.4) and compared (Baker 2005). 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 = �∑ {ln(𝐸𝐸𝐸𝐸𝐸𝐸)−ln(𝑎𝑎𝐼𝐼𝐼𝐼𝑏𝑏)}2𝑁𝑁𝑖𝑖=1 𝑁𝑁−2 (3.4) where b and a are the regression coefficients evaluated using IDA results and N is the simulation case number. A smaller 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼, which shows a smaller spread from the median estimated using the IDA outcomes, indicates an efficient IM (Padgett et al. 2008). Conversely, the parameter b obtained by regression analysis, as Equation (3.4) involves, evaluates how practical an IM is. Practicality shows how EDP depends on IM and was measured by b, which is the slope of this logarithmic correlation (Khosravikia and Clayton 2020). A near zero value of b indicates that IM has 41 negligible influence on EDP, so consequently, IM becomes impractical. However, greater b values show EDP relies heavily on IM. A less practical IM gives a smaller b value. Proficiency (ζ) is a composite measure that evaluates the efficiency and practicality of an IM and is also calculated by Equation (3.5) to compare different IMs (Padgett et al. 2008). ζ = 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼𝑏𝑏 (3.5) Tables 3.5-3.7 present the comparison of four different IMs, found to be significant by previous researchers (Shome 1999; Conte et al. 2003; Padgett et al. 2008; Billah et al. 2013) and thus selected for this study, based on how efficient, practical, and proficient they are given the crustal, intra-slab, and interface ground motions. The optimum IM was found considering efficiency, practicality, and proficiency by comparing the corresponding 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼, b, and ζ values of different intensity measures, respectively. From Tables 3.5-3.7, it is clear that Sa(T1) came out as the most efficient IM producing the lowest spread for all situations. Furthermore, Sa(T1) turned out to be the most practical IM to predict the demand experienced by the steel, CFRP, concrete, as well as ECC jacketed bridge bents. Of four IMs, Sa(T1) became the most proficient IM for crustal, intra-slab, and interface ground motions depending on the ζ-values shown in Tables 3.5-3.7. 3.9 Developments of Performance-Based Damage States PBSD targets limiting the damage and the corresponding cost of repair resulting from the earthquake (Jean et al. 2012). It requires the prediction of different damage states or performance levels once a structure is subjected to various earthquake intensities (Todorov and Billah 2021). Every damage state represents how functional a bridge is at a specific level. Furthermore, earthquake-induced damage of a bridge depends on EDPs such as deformation, ductility, energy 42 dissipation, as well as stiffness and strength degradation. Damage measures quantify an RC member's damage. This study considered both noncumulative and cumulative damage measures as damage depends on various structural and demand parameters. Maximum drift was considered as the noncumulative damage measure, whereas damage index (Park and Ang 1985) was considered as cumulative one. Previous researchers (Roy et al. 2010; Billah and Alam 2014; Upadhyay et al. 2019) considered maximum drift (%) an important and adequate EDP for representing how a retrofitted bridge bent behaves under an earthquake. On the other hand, the damage indices, which are noncumulative, such as the one based on stiffness degradation, proposed by Kunnath et al. (1997), cannot represent fatigue damage that a bridge experiences at low cycle for the seismic load reversal. Cumulative damage indices are classified into energy-based (Hindi and Sexsmith 2001) and low-cycle fatigue (Mander and Cheng 1995) formulations. Damage index, developed by Hindi and Sexsmith (2001), was not considered as it requires energy evaluation of specimen under a monotonic load by experiment or numerical analysis. Mander and Cheng (1995) presented a fatigue-life expression that considers low-cycle fatigue in steel under flexure not well capturing the damage in some cases. Park and Ang damage index, represented by Equation (3.6), shows a combined damage index (DI) involving the hysteretic absorbed energy as well as the maximum displacement. It is the most popular damage index verified by test results and gets to anticipate damage once a structure is subjected to distinct situations of loading. Besides, the DI appeared to be the perfect damage index to assess structure damage for interface earthquakes (Mohammed 2016; Barbosa et al. 2017; Pan et al. 2018). 43 Table 3.5. Various intensity measure comparisons of different jacketed bridge bents under crustal earthquakes Intensity measure Steel CFRP Concrete ECC a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ PGA 2.73 1.03 0.24 0.23 3.26 1.05 0.23 0.22 3.28 1.16a 0.29 0.25 3.44 1.13a 0.20 0.18 PGV 0.02 1.01 0.29 0.29 0.02 1.02 0.28 0.27 0.01 1.14 0.35 0. 31 0.01 1.13 0.24 0. 21 PGD 0.04 0.96 0.39 0.41 0.04 0.94 0.38 0.40 0.03 1.05 0.50 0.48 0.03 1.04 0.41 0.39 Sa(T1) 1.29 1.04a 0. 22a 0.21a 1.64 1.06a 0. 19a 0.18a 1.37 1.17 0. 28a 0.24a 1.52 1.13 0. 19a 0.17a aMost efficient, proficient, as well as practical Table 3.6. Various intensity measure comparisons of different jacketed bridge bents under intra-slab earthquakes Intensity measure Steel CFRP Concrete ECC a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ PGA 2.25 1.03 0.37 0.36 2.84 0.95 0.30 0.32 2.62 1.10 0.34 0.31 2.78 1.05 0.30 0.29 PGV 0.07 0.54 0.86 1.59 0.12 0.47 0.74 1.57 0.07 0.58 0.95 1.64 0.08 0.57 0.91 1.60 PGD 0.27 0.15 1.10 7. 33 0.41 0.12 0.94 7. 83 0.34 0.14 1.22 8.71 0.35 0.15 1.19 7.93 S a(T1) 1.10 1.06a 0. 30a 0.28a 1.43 0.99a 0. 22a 0.22a 1.21 1.13a 0.28a 0.25a 1.34 1.09a 0.20a 0.18a aMost efficient, proficient, as well as practical 44 Table 3.7. Various intensity measure comparisons of different jacketed bridge bents under interface earthquakes Intensity measure Steel CFRP Concrete ECC a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ a b 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 ζ PGA 2.87 1.00 0.28 0.28 3.55 1.00 0.28 0.28 3.02 1.06 0.31 0.29 3. 74 1. 15 0.30 0.26 PGV 0.05 0.67 0.68 1.01 0.05 0. 71 0.64 0.90 0.04 0.70 0.71 1.01 0.03 0.77 0.75 0.97 PGD 0.51 0.09 1.00 11.11 0. 47 0. 12 1.04 8.67 0.44 0.12 1. 06 8.83 0.45 0.12 1. 16 9.67 S a(T1) 1.34 1.01a 0.26a 0.26a 1. 79 1.01a 0.26a 0.26a 1. 39 1.09a 0.27a 0.25a 1. 59 1.16a 0.26a 0.22a aMost efficient, proficient, as well as practical 45 𝐷𝐷𝐼𝐼 = 𝛿𝛿𝐼𝐼𝛿𝛿𝑐𝑐+ 𝛽𝛽𝑄𝑄𝑦𝑦𝛿𝛿𝑐𝑐∫ 𝑑𝑑𝐸𝐸 (3.6) where, δu is the ultimate displacement for quasi-static load, δM is the maximum displacement in ground motion, 𝑄𝑄𝑦𝑦 is the yield strength, dE is the incremental hysteretic absorbed energy, and 𝛽𝛽 = 0.7𝜌𝜌𝑤𝑤(−0.447 + 0.073 𝑏𝑏𝑑𝑑+ 0.24𝑛𝑛0 + 0.314𝜌𝜌𝑖𝑖) (Park and Ang 1985) (3.7) where, 𝜌𝜌𝑤𝑤 is the confinement ratio which equals 4𝑖𝑖𝑢𝑢𝐸𝐸 (CFRP, steel, and ECC jackets) or 4𝐴𝐴ℎ𝐸𝐸′𝑠𝑠 (concrete jacket) (Priestley et al. 1996), where, D is the jacket diameter, 𝐴𝐴ℎ is the transverse steel cross-sectional area, tj is the thickness of jacket, 𝑠𝑠 is the spacing of transverse steel, and 𝐷𝐷′ is the diameter of the transverse steel. 𝑛𝑛0 is the normalized axial stress, which equals 𝑁𝑁0𝑓𝑓𝑐𝑐′𝐵𝐵𝑑𝑑, where, 𝑁𝑁0 is the axial force, 𝑑𝑑 is the cross-section effective height, 𝑓𝑓𝑐𝑐′ is the compressive strength of concrete, and 𝐵𝐵 is the cross-section width. 𝜌𝜌𝑖𝑖 is the longitudinal steel ratio, and 𝑏𝑏𝑑𝑑 is the shear span ratio. Drift is frequently used to define damage states. Discrete notable damage states such as concrete crushing, rebar yielding, bar fracture, longitudinal bar buckling, etc. are commonly used to define damages (Marsh and Stringer 2013). CHBDC defined four damage states at various performance levels: immediate service, limited service, service disruption, and life safety, depending on the material strain limit. For example, performance levels such as limited service represent repairable damage that does not let the reinforcement tensile strain of the concrete structure exceed 0.025 and any primary member of the steel structure buckle. Hose et al. (2000) suggested different performance levels and qualitative damage states for describing a bridge pier’s damage state, which is considered in this research to define three performance levels and their corresponding quantitative damage states in terms of limiting drifts. 46 Three performance levels, their corresponding damage states, repair description, and bridge operation levels are presented in Table 3.8 (CSA S6 2019). Table 3.8. Proposed damage state framework Performance level Damage state Repair description Bridge operation level Cracking Onset of hairline cracks 𝜀𝜀𝑖𝑖 ≤ 0.0001 No repair Fully operational Yielding Theoretical first yield of longitudinal reinforcement 𝜀𝜀𝑠𝑠 ≤ 0.0014 Possible repair Operational Crushing Crushing of core concrete 𝜀𝜀𝑐𝑐𝑢𝑢 ≤ 0.0069 Replacement Collapse Different defined performance levels are cracking, yielding, and crushing, whose respective damage states limit drifts corresponding to hairline crack initiation, longitudinal reinforcement’s theoretical first yield, and core concrete’s crushing, respectively. Table 3.8 presents that a bridge does not need to be repaired, so it can fully operate at cracking. On the contrary, it may require repair and can have limited post-seismic operation at yielding. As longitudinal rebars of each column yield gradually depending on the lateral drift level, various yielded rebar proportions were used to present progressive damage states of yielding. Since only one outermost longitudinal rebar of each column yielded first, the corresponding 5% yielded rebar was obtained 47 by dividing one by the total longitudinal rebar number, 16, which Figure 3.2 displays. Similarly, the increasing 20%, 30%, and 45% yielded rebars were also considered to identify the effects of different yielded rebar proportions. Table 3.8 also shows that a bridge experiences failure and needs to be replaced for the crushing of core concrete. However, the number of columns in a bent as well as the number of bent in a bridge, determine how the performance levels, yielding and crushing and the bridge operation, as shown in Table 3.8, are related. Multiple columns and bents may keep a bridge operational once several column rebars yield and adequate shoring in such a situation can keep it functional. Moreover, a bridge with multiple columns and bents will not fail once any column experiences the crushing of core concrete as other columns will support the bridge even if it makes the bridge unsafe under gravity loads and post-seismic events. Strain-based damage detection was used in this research to define the limiting drifts corresponding to various performance levels. Cracking strain (εt) is used to define the cracking of concrete and calculated as tensile strength divided by the elastic modulus of concrete. Moreover, yielding strain (εs) is used to identify the yielding of longitudinal reinforcement, is obtained by dividing tensile strength by the elastic modulus of longitudinal reinforcement, and was monitored to know when yielding first took place. Conversely, the ultimate compressive strain (εcu) of 0.0069, required to design capacity-protected critical column sections based on CHBDC, was used to recognize the crushing of core concrete and observed to figure out when core concrete first crushed. The respective strain values at various performance levels were used to determine the limiting drift values based on the IDA results of each retrofitted bent subjected to each earthquake. For this purpose, each motion was applied multiple times by increasing the scale factors in IDA and the first occurrence of limiting drift at each performance level for each individual run was obtained. This procedure was repeated for all motions for three earthquake 48 sources and the mean of the limiting drifts for individual earthquake suites at each performance level for various retrofitted bents, as shown in Table 3.9, was obtained. Table 3.9. Drift-based damage state comparisons of different retrofit techniques and earthquake sources Retrofit options Limiting drift (%) Cracking Yielding Crushing Crustal Intra-slab Interface Crustal Intra-slab Interface Crustal Intra-slab Interface CFRP 0.06 0.06 0.06 0.39 0.38 0.39 2.73 2.81 2.75 Steel 0.06 0.06 0.06 0.38 0.39 0.38 2.90 2.86 2.82 ECC 0.06 0.06 0.06 0.37 0.37 0.38 4.11 4.16 4.13 Concrete 0.06 0.06 0.06 0.38 0.38 0.38 3.96 4.02 3.96 Moreover, the largest of the mean limiting drifts of three earthquake suites, with 11 earthquakes each at each performance level for each retrofitted bent, as shown in Figure 3.11, was obtained from Table 3.9 based on CHBDC. 49 Figure 3.11. Proposed drift-based damage states of different retrofitted bridge bents Figure 3.11 presents an important insight into the damage states of steel, CFRP, concrete as well as ECC jacketed bents proposed for various performance levels. It can be identified from Figure 3.11 that, ● Cracking appeared in the concrete of each retrofitted bent at a limiting drift of 0.06% as its tensile strength was not influenced by retrofitting the bent with each technique. ● Furthermore, yielding occurred in longitudinal reinforcements of CFRP and steel jacketed bents at a limiting drift of 0.39%. On the other hand, longitudinal reinforcements of ECC and concrete jacketed bents yielded at a 0.38% limiting drift. The longitudinal reinforcement tensile strength was not affected by retrofitting the bent with each option, so the limiting drifts of the considered jacketed bents at yielding were nearly equal. ● Moreover, confined concrete of ECC jacketed bent crushed at a limiting drift of 4.16%. Such concrete of steel, concrete, and CFRP jacketed bents underwent crushing at 43%, 3%, and 48% less limiting drifts, respectively. ECC jacket was subjected to the highest curvature which led to the highest drift. In contrast, greater tension producing more neutral axis depths and less 01.534.5Cracking Yielding CrushingLimiting Drift (%)Performance Level CFRP SteelECC Concrete50 curvature was obtained for other sections retrofitted with CFRP, steel, and concrete jackets for 0.0069 concrete compressive strain. Figure 3.11 presents the limiting drifts used to perform the PBSD retrofit of the case study bent considered in this study. Following this proposed approach, seismically deficient bridge bents located in similar site conditions and having similar geometric configurations can be retrofitted. However, the limiting drifts presented in Figure 3.11 can not be generalized and can serve as an example for PBSD retrofit of seismically deficient RC bridge bents. A detailed design example provided in the following section shows this method demonstration. 3.10 Design Example A demonstration of a performance-based design procedure for retrofitting a multi-column bridge bent using the proposed damage state is shown in this example. Figure 3.1 shows a seismically deficient multi-column bent located in site soil class D, which is assumed to be a major-route bridge component in Vancouver, British Columbia, Canada. This bent consists of the following seismic deficiencies: column and cap beam connections with no stirrup, plastic-hinge and lap-splice regions of columns with insufficient ties, as well as pile caps and cap beam with inadequately embedded column rebars. Based on CHBDC, at a 2475-year return period hazard level, it needs 1452 kN lateral strength more than its actual lateral strength of 1277 kN. Thus, it has to be retrofitted to remain operational after possible repair for the chosen seismic hazard level. At the performance level considered, a 0.39% limiting drift (Figure 3.10) is chosen so that the performance objective is met. CFRP is used to retrofit this bent in the example. Table 3.10 presents the bent’s material properties. 51 Table 3.10. Bent material properties Material name Mechanical property Magnitude CFRP Ultimate tensile strain 0.01 Tensile strength (MPa) 628 Initial stiffness (MPa) 64730 Concrete Elastic modulus (GPa) 23.54 Compressive strength (MPa) 21 Steel Yield strength (MPa) 275 Elastic Modulus (GPa) 200 Figure 3.12 shows a flowchart that summarizes the steps taken in the design example. Step 1: Yield curvature (𝜑𝜑𝑦𝑦) calculation Based on Figure 3.13, using the moment-area theorem, yield displacement, ∆𝑦𝑦= 𝜑𝜑𝑦𝑦𝐿𝐿24 ∴ 𝜑𝜑𝑦𝑦 = 4∆𝑦𝑦𝐿𝐿2 (3.8) In this research, the proposed limiting drift corresponding to yielding for bent retrofitted with CFRP is 0.39% (Figure 3.11). 52 Figure 3.12. Flowchart of PBSD for retrofitting bents Figure 3.13. Deflected shape of the bent under earthquakes Choose performance level and limiting drift from Figure 3.11 Determine yield curvature (𝜑𝜑𝑦𝑦) Determine plastic curvature (𝜑𝜑𝑐𝑐) Determine ultimate curvature (𝜑𝜑𝑢𝑢) Determine jacket thickness (tj) Determine the site location and seismic hazard 53 Effective column height, L = Distance from seismic force to column top + clear column height (Lc) + yield penetration length (Lpj) ; (Priestley et al. 1996) = 762 + 7315 + 0.044𝑓𝑓𝑦𝑦𝑑𝑑𝑏𝑏𝑏𝑏 = 8077 + 0.044 × 275 × 32 = 8077 + 387.2 = 8464.2 mm From Equation (3.8), 𝜑𝜑𝑦𝑦 = 4×0.39×8077/1008464.22 = 1.76 × 10−6/mm Step 2: Plastic curvature (𝜑𝜑𝑐𝑐) calculation Plastic displacement, ∆p = ultimate displacement (∆u) – ∆y (3.9) In this research, the ultimate drift corresponding to crushing for bent retrofitted with CFRP is 2.81% (Figure 3.11). From Equation (3.9), ∆𝑐𝑐= (2.81−0.39)8077100 = 195.46 mm Plastic rotation, 𝜃𝜃𝑐𝑐 = ∆𝑝𝑝𝐿𝐿 = 195.468464.2 = 0.0231 rad 𝜑𝜑𝑐𝑐 = 𝜃𝜃𝑝𝑝𝐿𝐿𝑝𝑝 (3.10) Alemdar (2010) proposed Equation (3.11) for plastic hinge length (Lp) to evaluate ultimate drift. 𝐿𝐿𝐸𝐸 = �14 + 3𝑓𝑓𝑦𝑦𝑑𝑑𝑏𝑏𝑏𝑏10000�𝑓𝑓𝑐𝑐′+ 𝐿𝐿𝑐𝑐25000�𝑑𝑑𝑐𝑐 (3.11) = �14 + 3 × 275 × 3210000√21 + 731525000�1032 = 1154.49 mm From Equation (3.10), 𝜑𝜑𝑐𝑐 = 0.02311154.49 = 2 × 10−5/mm Step 3: Ultimate curvature (𝜑𝜑𝑢𝑢) calculation 54 𝜑𝜑𝑢𝑢 = 𝜑𝜑𝑦𝑦 + 𝜑𝜑𝑐𝑐 = 1.76 × 10−6 + 2 × 10−5 = 2.18 × 10−5/mm Using the preliminary moment-curvature analysis for the section retrofitted, the neutral axis depth corresponding to crushing, c is 334.86 mm. Step 4: Thickness of jacket (tj) calculation 𝑡𝑡𝑗𝑗 = 0.1(𝜀𝜀𝑐𝑐𝑐𝑐−0.004)𝐸𝐸𝑓𝑓𝑐𝑐𝑐𝑐′𝑓𝑓𝑐𝑐𝑢𝑢𝜀𝜀𝑐𝑐𝑢𝑢 (Priestley et al. 1996) = 0.1(𝜑𝜑𝑐𝑐𝑐𝑐−0.004)1032×24628×0.01 = 0.1(2.18 × 10−5 × 334.86 − 0.004)1032 × 24628 × 0.01 = 1.30 mm A layer of 1.30-mm thick CFRP sheet has to be provided over the entire height of the column. 3.11 Effects of Retrofit Options and Earthquake Sources on Maximum Drifts Relationships between the different retrofit options and earthquake sources with the maximum drift, obtained from each run of each motion are discussed in this section. Based on the analysis results, IDA curves of bents retrofitted with different materials for crustal, intra-slab, and interface earthquakes were generated and are shown in Figures 3.14-3.16, respectively. These curves show how significantly diverse and scattered the achieved results of various retrofitted bents are under various ground motions. Each curve exhibits a distinct elastic linear region that terminates when the first nonlinearity appears. The slope of this segment of each IDA curve is called the elastic stiffness of the corresponding retrofitted bent. Based on Figures 3.14-3.16, bent retrofitted with concrete and ECC jackets were stiffer on the elastic domain in comparison with bents having a steel or CFRP jacket. However, the IDA curves were not the same in the inelastic region of response as some softened and accelerated to high drift followed 55 by consequent failure and the others looked meandering about the slope on the elastic domain, showing successive regions of softening and hardening. As each IDA curve is an individual deterministic entity, the natural random variability among the ground motions needs a statistical assessment of demand. In order to summarize the IDA curves plotted for each suite of 11 ground motions, the IDA curves based on 16% fractile, median, and 84% fractile are defined (Vamvatsikos and Cornell 2002). More reasonable data is obtained from this summary for application and comprehension. Seismic design usually depends on median or mean maximum drift (Billah and Alam 2014). To plot the 16% fractile, median, and 84% fractile curves, 16% fractiles, medians, and 84% fractiles of maximum drifts for different spectral accelerations were evaluated. Figure 3.14. IDA curves of bents retrofitted with different materials for crustal earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing 012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(b)012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(c)012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(d)(a) 56 To compare the effects of different retrofit options on maximum drifts of retrofitted bents for different earthquake sources, 16% fractile, median, and 84% fractile IDA curves as shown in Figures 3.14-3.17 were developed. Besides, the median curves from IDA present the curves considering seismic demand for the bents retrofitted with different retrofit options and are availed in assessing their performances in comparison to acceptable drift for a particular spectral acceleration of any hazard level. For instance, for crustal, intra-slab, and interface earthquakes, maximum drifts are shown in Table 3.11 for bents retrofitted with CFRP, steel, ECC, and concrete jackets, respectively, at the design spectral accelerations of 0.50g and 0.87g. These design spectral accelerations were calculated for hazard levels with probabilities of exceedance of 10% and 2% in 50 years, respectively for major route bridges based on CHBDC. Figure 3.15. IDA curves of bents retrofitted with different materials for intra-slab earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing 012340 1 2 3 4 5 6 7 8S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(a)012340 1 2 3 4 5 6 7 8S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(b)012340 1 2 3 4 5 6 7 8S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(c)012340 1 2 3 4 5 6 7 8S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(d)57 The retrofitted bent experiencing the smallest median maximum drift under a certain hazard level and ground motion suite is considered to be the most effective one. It was found that the efficiency of various retrofitting techniques varied under different hazard levels as well as ground motion suites. It can be inferred based on this analysis that the steel jacket was the most efficient in decreasing the retrofitted bent’s median maximum drift for each earthquake source except under interface earthquakes and at the spectral acceleration of 0.50g under crustal earthquakes, in which the concrete jacket became the most efficient. Although the concrete jacket seemed to be the second most effective technique under intra-slab and crustal earthquakes at the spectral accelerations of 0.50g and 0.87g, respectively, the ECC jacket was the more efficient one at the spectral acceleration of 0.87g under intra-slab earthquakes. Figure 3.16. IDA curves of bents retrofitted with different materials for interface earthquakes: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing 012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(a)012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(b)012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(c)012340 1 2 3 4 5 6 7 8 9 10S a(T1)(g)Maximum Drift (%)Median16% Fractile84% Fractile(d)58 Furthermore, the ECC jacket was the third most effective technique under interface earthquakes and at the spectral acceleration of 0.87g under crustal earthquakes. However, the CFRP jacket appeared to be the least effective one under all earthquake scenarios. The median IDA curves shown in Figure 3.18 compare the effects of different earthquake sources on median maximum drifts of different retrofitted bents. Based on Figure 3.18a, CFRP jacketed bent experienced the lowest maximum drifts both at the spectral accelerations of 0.50g and 0.87g under intra-slab earthquakes. It was also observed from Figure 3.18b that the steel-jacketed bent underwent the least maximum drifts both at the spectral accelerations of 0.50g and 0.87g under intra-slab earthquakes. Figure 3.17. Effects of different retrofit options on median maximum drifts of retrofitted bents for different earthquake sources: (a) crustal, (b) intra-slab, and (c) interface 01230 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)CFRPSteelECCConcrete(a)01230 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)CFRPSteelECCConcrete(b)01230 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)CFRPSteelECCConcrete(c)59 On the other hand, the ECC-jacketed bent was subjected to the lowest maximum drift at the spectral acceleration of 0.50g under crustal earthquakes (Figure 3.18c), whereas it encountered the least maximum drift at the spectral acceleration of 0.87g under intra-slab earthquakes. Furthermore, concrete-jacketed bent faced the smallest maximum drift both at the spectral acceleration of 0.50g and 0.87g under interface earthquakes (Figure 3.18d). 3.12 Effects of Retrofit Options and Earthquake Sources on Damage Indices This section presents how the different retrofit options and earthquake sources are related to the damage index. Damage indices for each retrofitted bent at different spectral accelerations were calculated using Equation (3.6). Table 3.11. Comparison of median maximum drifts for various retrofit options and earthquake sources Retrofit options Median maximum drift (%) Crustal Intra-Slab Interface Hazard level probability of exceedance in 50 years (%) 10 2 10 2 10 2 CFRP 0.85 1.45 0.84 1.16 0.94 1.47 Steel 0.70 0.97 0.68 0.96 0.69 1.01 ECC 0.66 1.28 0.68 1.04 0.70 1.19 Concrete 0.64 1.03 0.69 1.11 0.44 0.99 60 Median IDA curves were plotted to show how different retrofit options affect the damage indices of retrofitted bents for different earthquake sources, as shown in Figure 3.19. Furthermore, the median curves from IDA show the curves considering seismic demand for retrofitted bents availed for evaluating their performances in comparison to damage indices for different performance levels as Table 3.12 displays. According to Table 3.12, concrete in CFRP, steel, ECC, and concrete jacketed bents cracked once the respective damage indices varied within the ranges of [0.03, 0.16), [0.03, 0.17), [0.02, 0.12), and [0.02, 0.13), respectively. Reinforcement in CFRP, steel, ECC, and concrete jacketed bents also reached yielding when the corresponding damage indices lay on the intervals of [0.16, 0.23], [0.17, 0.22], [0.12, 0.18], and [0.13, 0.17], respectively. Furthermore, core concrete in CFRP, steel, ECC, and concrete jacketed bents crushed as the respective damage indices were 2.05, 2.12, 1.91, and 1.92 or over, respectively. Even if Park and Ang (1985) suggested maximum damage index for an RC column as 1 at complete collapse represented by crushing of core concrete as one of the four failure modes considered in that study, the lower limit of damage index of each retrofitted bent at the same performance level is greater than 1. For example, median damage indices for CFRP, steel, ECC, and concrete jacketed bents at the design spectral accelerations of 0.50 and 0.87g under crustal, intra-slab, and interface earthquakes are presented in Table 3.13. 61 Figure 3.18. Effects of different earthquake sources on median maximum drifts of bents retrofitted with different materials: (a) CFRP, (b) steel, (c) ECC, and (d) concrete jacketing At the spectral accelerations of 0.50g and 0.87g for all earthquake scenarios, reinforcement in all retrofitted bents experienced yielding because their damage indices exceeded the upper limits of intervals of the damage indices at yielding displayed in Table 3.12. Based on the median damage index, the ECC jacket appeared the most effective in reducing the damage of retrofitted bridge bent subjected to intra-slab earthquakes and at the spectral acceleration of 0.87g under interface earthquakes, whereas the concrete jacket was the most useful under crustal earthquakes and at spectral acceleration of 0.50g under interface earthquakes. 00.61.21.82.430 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)Crustal EarthquakesIntra-Slab EarthquakesInterface Earthquakes(a)00.61.21.82.430 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)Crustal EarthquakesIntra-Slab EarthquakesInterface Earthquakes(b)00.61.21.82.430 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)Crustal EarthquakesIntra-Slab EarthquakesInterface Earthquakes(c)00.61.21.82.430 1 2 3 4 5 6S a(T1) (g)Maximum Drift (%)Crustal EarthquakesIntra-Slab EarthquakesInterface Earthquakes(d)62 Figure 3.19. Effects of different retrofit options on median damage indices of retrofitted bents for different earthquake sources: (a) crustal, (b) intra-slab, and (c) interface Even though the concrete jacket became the second most effective technique under intra-slab earthquakes and at the spectral acceleration of 0.87g under interface earthquakes, the ECC jacket was the second most useful one under crustal earthquakes and at spectral acceleration of 0.50g under interface earthquakes. On the other hand, the CFRP jacket showed up as the third most efficient technique under crustal and interface earthquakes. Nevertheless, the steel jacket turned out to be the least useful one for crustal and interface earthquakes. However, the steel jacket was more useful than the CFRP jacket under intra-slab earthquakes. 00.511.522.530 2 4 6 8 10S a(T1) (g)DICFRPSteelECCConcrete(a)00.511.522.530 2 4 6 8 10S a(T1) (g)DICFRPSteelECCConcrete(b)00.511.522.530 2 4 6 8 10S a(T1) (g)DICFRPSteelECCConcrete(c)63 Table 3.12. Proposed damage index-based damage states for various retrofit options Retrofit options Damage index Cracking Yielding Crushing CFRP 0.03 ≤DI< 0.16 0.16 ≤DI≤ 0.23 DI≥ 2.05 Steel 0.03 ≤DI< 0.17 0.17 ≤DI≤ 0.22 DI≥ 2.12 ECC 0.02 ≤DI< 0.12 0.12 ≤DI≤ 0.18 DI≥ 1.91 Concrete 0.02 ≤DI< 0.13 0.13 ≤DI≤ 0.17 DI≥ 1.92 Table 3.13. Median damage index comparisons of various retrofit options and earthquake sources Retrofit options Median damage index Crustal Intra-Slab Interface Hazard level probability of exceedance in 50 years (%) 10 2 10 2 10 2 CFRP 0.46 0.98 0.46 1.02 0.63 1.61 Steel 0.48 1.08 0.39 1.00 0.72 1.80 ECC 0.37 0.76 0.26 0.54 0.57 1.25 Concrete 0.30 0.64 0.31 0.65 0.46 1.31 64 3.13 Summary This chapter exhibits the seismically deficient bridge bent considered in this research, along with different retrofit options that have been used to retrofit the bent. Finite element models of both the as-built and retrofitted bents and their validations with experimental results are explained. The IDA-based approach utilized to develop performance-based damage states is presented. Moreover, it is discussed how various ground motions from different earthquake sources are selected. Performance-based damage states are developed and proposed for the considered retrofitted bents. A design example is illustrated to demonstrate the applications of proposed performance-based damage states to similar deficient bent. It also explained how the optimum intensity measure is obtained to study the effects of retrofit options and earthquake sources on maximum drifts and damage indices. 65 CHAPTER 4. BRIDGE BENT PERFORMANCE-BASED SEISMIC LOSS ASSESSMENT 4.1 General PBSD forms the basis for measuring the life-cycle cost of retrofitting a seismically deficient bridge bent (Padgett et al. 2010). Recently, life-cycle cost assessment has become a popular tool for providing the most economic retrofit solution for deficient bridge bents (Padgett et al. 2010). In the past, no research was conducted to obtain life-cycle cost for a retrofitted seismically deficient bridge bent under various earthquake scenarios, e.g., crustal, intra-slab, and interface for different proportions of yielded rebars. Thus, this research aimed to measure the performance-based seismic loss of a deficient multi-column bent retrofitted with well-known techniques like steel, CFRP, concrete, and ECC jackets. In this research, the benefit-cost ratios of the considered retrofit options were also calculated. Evaluations of these benefit-cost ratios eased to select the optimum retrofit of the deficient bent that maximized the ratio. Proposed damage states in the previous chapter were used to perform fragility analysis to obtain the conditional probabilities of exceeding different damage states for 475 and 2,475-year return period hazard levels. These damage probabilities were also used to calculate the total expected life-cycle losses of both as-built and all retrofitted bents and benefit-cost ratios of various retrofitting techniques. 4.2 Fragility Analyses and Seismic Loss Assessments of Bridge Bents As-built and retrofitted bridge bents’ performance-based seismic losses were evaluated to compare their life-cycle performances and to obtain the optimum retrofit option. Thus, performing fragility analysis the conditional probability of exceeding a specific damage state was obtained for 475 and 2,475-year return period hazard levels for major route bridges based on CHBDC using Equation (4.1) (Nielson 2005). 66 𝑃𝑃𝐸𝐸𝐷𝐷,𝑖𝑖|𝐼𝐼𝐼𝐼 = 𝜑𝜑 �ln( 𝐼𝐼𝐼𝐼)−ln (𝐼𝐼𝐼𝐼𝑛𝑛)𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝 � (4.1) where, PDS,i|IM is the conditional probability of exceeding any damage state at the considered hazard levels, 𝜑𝜑 is the standard normal cumulative distribution function, and ln(𝐼𝐼𝐼𝐼𝑖𝑖) = ln(𝐷𝐷𝑐𝑐)−ln(𝑎𝑎)𝑏𝑏 (4.2) where, 𝐼𝐼𝐼𝐼𝑖𝑖 is the IM median value, ln (𝐼𝐼𝐼𝐼𝑖𝑖) is the natural log of the median IM value for the selected damage state (no damage, slight, or collapse), 𝑆𝑆𝑐𝑐 is the median, b and a are the regression coefficients evaluated using IDA results, and the dispersion component was obtained using Equation (4.3) (Nielson 2005). 𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = �𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼2 +𝛽𝛽𝑐𝑐2𝑏𝑏 (4.3) where, 𝛽𝛽𝑐𝑐 is the dispersion value for the bridge bent damage states and 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 is the EDP’s dispersion relying on the IM. Seismic loss is the sum of direct and indirect losses, expressed in repair and running costs and the time loss monetary value of drivers as well as transported goods directed via the detour (Xiang et al. 2020). The bent expected annual loss (Li) was evaluated using Equation (4.4) (Dong et al. 2013). 𝐿𝐿𝑖𝑖 = ∑ 𝐿𝐿𝐸𝐸𝐷𝐷,𝑖𝑖𝑃𝑃𝐸𝐸𝐷𝐷,𝑖𝑖|𝐼𝐼𝐼𝐼3𝑖𝑖=1 (4.4) where, CDS,i is the direct and indirect losses. The direct loss represented by the bent repair cost at any damage state (CREP,i) was evaluated using Equation (4.5) (Stein et al. 1999). 67 𝐿𝐿𝑅𝑅𝐸𝐸𝐸𝐸,𝑖𝑖 = 𝑅𝑅𝑟𝑟𝑐𝑐𝑟𝑟𝑐𝑐𝑟𝑟𝑟𝑟𝑏𝑏𝑊𝑊𝐿𝐿𝑏𝑏 (4.5) where, Rrcr is the repair cost ratios of 0, 0.08, and 0.25 (Mander 1999) for different performance levels: cracking, yielding, and crushing, respectively, creb is the rebuilding cost of a bridge unit area, 𝐿𝐿𝑏𝑏 is the length of the bridge, and W is the width of the bridge. Indirect loss was measured by the running cost (CRUN,i) (Dong and Frangopol 2015) and the time loss monetary value (CTL,i) (Stein et al. 1999) at any damage state using Equations (4.6) and (4.7), respectively. 𝐿𝐿𝑅𝑅𝑅𝑅𝑁𝑁,𝑖𝑖 = �𝑐𝑐𝑟𝑟𝑢𝑢𝑖𝑖,𝑐𝑐𝑎𝑎𝑟𝑟 �1 − 𝑇𝑇0100� + 𝑐𝑐𝑟𝑟𝑢𝑢𝑖𝑖,𝑖𝑖𝑟𝑟𝑢𝑢𝑐𝑐𝑘𝑘 𝑇𝑇0100�𝐷𝐷𝑏𝑏𝐴𝐴𝐷𝐷𝑇𝑇𝐷𝐷𝑑𝑑𝑖𝑖 (4.6) where crun,car is the cost per unit length for car, T0 is the average daily truck traffic ratio, crun,truck is the cost per unit length for truck, Dl is the detour length, ADTD is the average daily traffic to detour, and di is the downtimes (times to repair the bent to full functionality) of 0, 18 (as-built) or 2 (CFRP) or 32 (steel) or 29 (ECC) or 26 (concrete), and 78 days for performance levels: cracking, yielding, and crushing, respectively (Zhou et al. 2015; Benedetti et al. 2016; ChienKuo et al. 2021). 𝐿𝐿𝑇𝑇𝐿𝐿,𝑖𝑖 = �𝑐𝑐𝐴𝐴𝐴𝐴𝑜𝑜𝑐𝑐𝑎𝑎𝑟𝑟 �1 − 𝑇𝑇0100� + 𝑐𝑐𝐴𝐴𝑇𝑇𝐴𝐴𝑜𝑜𝑖𝑖𝑟𝑟𝑢𝑢𝑐𝑐𝑘𝑘 𝑇𝑇0100� �𝐸𝐸𝑏𝑏𝐴𝐴𝐸𝐸𝑇𝑇𝐸𝐸𝐷𝐷 + 𝐴𝐴𝐷𝐷𝑇𝑇𝐸𝐸( 𝑏𝑏𝐷𝐷𝐸𝐸 − 𝑏𝑏𝐷𝐷0)� 𝑑𝑑𝑖𝑖 (4.7) where cAW is the average hourly wage for a car driver, ocar is the average occupancy for a car, cATC is the average hourly total compensation for a truck driver, otruck is the average occupancy for a truck, S is the average detour speed, ADTE is the average daily traffic on the damaged route, l is the route length including the bridge, SD is the average vehicle speed on the damaged route, and S0 is the average vehicle speed on the intact route. Parameter values used in Equations (4.5) – (4.8) are presented in Table 4.1. 68 Table 4.1. Traffic data used in seismic loss assessment of as-built and retrofitted bents (BC Ministry of Transportation and Infrastructure 2012; Dong and Frangopol 2015; Kriger et al. 2015; Apex Engineering Limited 2018; WSP Canada Group Limited 2019; XYZ Engineering 2020) 𝑐𝑐𝑟𝑟𝑟𝑟𝑏𝑏 ($/m2) crun,car ($/km) T0 (%) crun,truck ($/km) Dl (km) ADT cAW ($/h) ocar cATC ($/h) otruck S (km/h) l (km) S0 (km/h) 3540 0.32 10.38 0.47 2 66100 21.81 1.5 27.43 1.05 50 6 70 Ratios of ADTE to average daily traffic (ADT) were considered as 100%, 75%, and 0% for performance levels: cracking, yielding, and crushing, respectively (Dong and Frangopol 2015). Equations (4.5) – (4.7) were substituted into Equation (4.4) to evaluate the bent expected annual loss at the considered hazard level. An earthquake that occurs in any time interval (0, tint) is assumed to follow Poisson’s process. Thetotal expected life-cycle loss in any time interval (0, tint), was determined using Equation (4.8) (Zheng et al. 2018). 𝐸𝐸{𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖(𝑡𝑡𝑖𝑖𝑖𝑖𝑖𝑖)} = 𝜆𝜆𝑓𝑓𝐸𝐸(𝐿𝐿𝑖𝑖)𝜏𝜏 (1 − 𝑒𝑒−𝜏𝜏𝑖𝑖𝑖𝑖𝑛𝑛𝑡𝑡) (4.8) where τ is the monetary discount rate and λf is the Poisson’s model mean rate which equals −ln(1−𝐸𝐸)∆𝑖𝑖 (Dong and Frangopol 2016) where P is the conditional probability of occurrence of an earthquake in the time interval ∆𝑡𝑡. Moreover, with a risk-based framework (Padgett et al. 2010), a benefit-cost analysis was conducted to determine how effective any retrofit option is. The benefit of any retrofit option was determined using Equation (4.9). Benefit = 𝐸𝐸(𝐿𝐿𝐿𝐿𝐿𝐿𝑎𝑎𝑠𝑠−𝑏𝑏𝑢𝑢𝑖𝑖𝑏𝑏𝑖𝑖) − 𝐸𝐸(𝐿𝐿𝐿𝐿𝐿𝐿𝑟𝑟) (4.9) 69 where E(LCLas-built) is the as-built bent total expected life-cycle loss and E(LCLr) is the retrofitted bent total expected life-cycle loss. Material costs of steel, CFRP, concrete, and ECC jackets required for retrofitting the deficient bent were obtained as $1498, $9529, $3924, and $2374, respectively from different sources (Fischer and Li 2003; Sika Canada Inc. n.d.; Harris Rebar n.d.; Sakrete Canada n.d.). These costs do not include construction, labour, and other associated costs. 4.3 Effects of Retrofit Techniques on Performance-Based Seismic Loss The seismic fragility analysis and loss assessment outcomes are explained in this section. Table 3.10 presents various retrofitted bents’ limiting drift (𝑆𝑆𝑐𝑐) values. Furthermore, values of a, b, and 𝛽𝛽𝐸𝐸𝐸𝐸𝐸𝐸|𝐼𝐼𝐼𝐼 are displayed in Tables 3.5-3.7. Dispersion (𝛽𝛽𝑐𝑐) values of the demand obtained using the IDA results are also shown in Table 4.2. At cracking, 𝛽𝛽𝑐𝑐 of different retrofitted bents vary between 2.67 and 2.77, representing almost constant dispersion values. Moreover, these values range from 1.79 to 1.96, and thus have a maximum deviation of 10% under yielding. For crushing, dispersion values fall between 0.63 and 0.65, mainly differing by 3%. On the contrary, for as-built bent, such values are 2.46, 1.58, and 0.60, which are lower than those of each retrofitted bent at cracking, yielding, and crushing, respectively. The effects of different retrofit options on the damage probability for different earthquake sources are shown in Figures 4.1-4.3. Here, the results are compared at the design spectral accelerations (Sa(T1)) of 0.50g and 0.87g, which correspond to 475 and 2,475 year earthquake return periods in Vancouver, respectively. Tables 4.3-4.8 present the probabilities of exceeding considered damage states of the as-built and different jacketed bents under crustal, intra-slab, and interface earthquakes, respectively, for different yielded rebar proportions. 70 Table 4.2. As-built and various jacketed bridge bents’ dispersion values for different performance levels Bent type 𝛽𝛽𝑐𝑐 Cracking Yielding Crushing As built 2.46 1.58 0.60 CFRP 2.69 1.82 0.64 Steel 2.67 1.79 0.63 ECC 2.76 1.95 0.64 Concrete 2.77 1.96 0.65 The effects of retrofitting techniques on the cracking probability were found to be insignificant because its values have maximum ranges of 0.796-0.830 and 0.847-0.870, respectively at lower and higher hazard levels, as portrayed in Tables 4.3-4.8. Thus, cracking probabilities only varied by 4% and 3% for 0.5g and 0.87g, respectively. On the other hand, at smaller and greater Sa(T1)s, earthquake sources also did not remarkably affect the probability of exceeding cracking damage as their magnitudes differ from 0.790 to 0.815 and 0.848 to 0.865, respectively. Therefore, the probabilities of cracking damages slightly changed by 3% and 2% for 475 and 2475-year return period hazard levels, respectively. Furthermore, retrofit options hardly influenced the probability of yielding damage since the values lie between 0.529 and 0.588 and 0.620 and 0.675 under spectral accelerations of 0.50g and 0.87g, respectively. 71 Figure 4.1. Fragility curves for the as-built and retrofitted bridge bents under crustal earthquakes: (a) cracking, (b) yielding, and (c) crushing Consequently, yielding probabilities experienced little variations of 11% and 9% at lower and higher hazard levels, respectively. Moreover, earthquake sources had insubstantial impacts on the yielding probability at both hazard levels. Consequently, negligible changes of 13% and 8% for 475 and 2475-year return period hazard levels, respectively, were observed in the probability of yielding damage. However, the yielded rebar proportion affected yielding probability depending on the number of yielded rebars. When this proportion rose by 15% or 25%, the probability of exceedance did not vary markedly, as shown in Tables 4.3-4.8. 00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(a)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(b)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(c)72 Figure 4.2. Fragility curves for the as-built and retrofitted bridge bents under intra-slab earthquakes: (a) cracking, (b) yielding, and (c) crushing On the contrary, the increase in the yielded rebar proportion from 5% to 40% greatly influenced the probability of exceeding yielding damage owing to its value reductions from 0.565 to 0.471 and 0.687 to 0.62 at smaller and greater Sa(T1)s, respectively. Hence, the probability of yielding damage changed by 17% and 10% under 0.50g and 0.87g, respectively. However, retrofitting substantially reduced the probability of crushing damage for each earthquake source because of higher limiting drift and dispersion value, which led to a higher median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) and dispersion component, respectively, than those of the as-built bent at crushing, as presented in Tables 3.10 and 4.2. Interface and intra-slab earthquakes produced maximum and minimum drifts, which minimized and maximized median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖), respectively. 00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(a)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(b)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(c)73 Figure 4.3. Fragility curves for the as-built and retrofitted bridge bents under interface earthquakes: (a) cracking, (b) yielding, and (c) crushing Thus, the core concrete of the retrofitted bents also had the highest probability of crushing damage when subjected to interface earthquakes, whereas it is the least expected to crush under intra-slab earthquakes. Moreover, higher median intensity measure ( 𝐼𝐼𝐼𝐼𝑖𝑖) and dispersion component, resulting from higher limiting drift (Table 3.10) caused by greater curvature and less rate of drift change in regard to intensity measure, respectively, provide a smaller conditional probability of exceeding any damage state at the considered hazard levels. 00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(a)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(b)00.20.40.60.810 0.5 1 1.5 2Probability of Damage Sa(T1) (g)As-BuiltCFRPSteelECCConcrete(c)74 Table 4.3. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under crustal earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.830 0.667 0.035 0.830 0.654 0.035 0.830 0.642 0.035 0.830 0.585 0.035 CFRP 0.830 0.650 0.029 0.830 0.632 0.029 0.830 0.608 0.029 0.830 0.562 0.029 Steel 0.810 0.604 0.011 0.810 0.598 0.011 0.810 0.570 0.011 0.810 0.516 0.011 ECC 0.811 0.620 0.003 0.811 0.607 0.003 0.811 0.584 0.003 0.811 0.550 0.003 Concrete 0.796 0.592 0.004 0.796 0.582 0.004 0.796 0.555 0.004 0.796 0.542 0.004 Table 4.4. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under intra-slab earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.810 0.620 0.020 0.810 0.610 0.020 0.810 0.590 0.020 0.810 0.520 0.020 CFRP 0.810 0.620 0.020 0.810 0.610 0.020 0.810 0.588 0.020 0.810 0.520 0.020 Steel 0.790 0.565 0.007 0.790 0.559 0.007 0.790 0.529 0.007 0.790 0.471 0.007 ECC 0.801 0.600 0.002 0.801 0.586 0.002 0.801 0.562 0.002 0.801 0.520 0.002 Concrete 0.787 0.575 0.003 0.787 0.564 0.003 0.787 0.537 0.003 0.787 0.520 0.003 75 Table 4.5. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.50g under interface earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.830 0.660 0.040 0.830 0.650 0.040 0.830 0.630 0.040 0.830 0.570 0.040 CFRP 0.830 0.660 0.040 0.830 0.650 0.040 0.830 0.630 0.040 0.830 0.570 0.040 Steel 0.815 0.616 0.016 0.815 0.611 0.016 0.815 0.584 0.016 0.815 0.532 0.016 ECC 0.813 0.624 0.005 0.813 0.612 0.005 0.813 0.588 0.005 0.813 0.555 0.005 Concrete 0.804 0.608 0.005 0.804 0.598 0.005 0.804 0.572 0.005 0.804 0.560 0.005 Table 4.6. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under crustal earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.883 0.788 0.188 0.883 0.782 0.188 0.883 0.775 0.188 0.883 0.748 0.188 CFRP 0.879 0.758 0.153 0.879 0.747 0.153 0.879 0.732 0.153 0.879 0.704 0.153 Steel 0.862 0.720 0.078 0.862 0.716 0.078 0.862 0.697 0.078 0.862 0.661 0.078 ECC 0.865 0.732 0.041 0.865 0.723 0.041 0.865 0.707 0.041 0.865 0.684 0.041 Concrete 0.856 0.713 0.041 0.856 0.706 0.041 0.856 0.687 0.041 0.856 0.678 0.041 76 Table 4.7. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under intra-slab earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.870 0.749 0.110 0.870 0.740 0.110 0.870 0.731 0.110 0.870 0.694 0.110 CFRP 0.870 0.737 0.110 0.870 0.724 0.110 0.870 0.708 0.110 0.870 0.675 0.110 Steel 0.848 0.687 0.055 0.848 0.683 0.055 0.848 0.662 0.055 0.848 0.620 0.055 ECC 0.856 0.712 0.026 0.856 0.703 0.026 0.856 0.685 0.026 0.856 0.660 0.026 Concrete 0.847 0.693 0.028 0.847 0.686 0.028 0.847 0.666 0.028 0.847 0.656 0.028 Table 4.8. Probabilities of exceeding considered damage states of as-built and retrofitted bents at Sa(T1) = 0.87g under interface earthquakes Bent type Yielded rebar proportion (%) 5 20 30 45 Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing Cracking Yielding Crushing As-built 0.870 0.770 0.180 0.870 0.760 0.180 0.870 0.749 0.180 0.870 0.720 0.180 CFRP 0.870 0.770 0.180 0.870 0.760 0.180 0.870 0.749 0.180 0.870 0.720 0.180 Steel 0.865 0.725 0.095 0.865 0.722 0.095 0.865 0.703 0.095 0.865 0.668 0.095 ECC 0.868 0.738 0.052 0.868 0.730 0.052 0.868 0.714 0.052 0.868 0.691 0.052 Concrete 0.859 0.718 0.042 0.859 0.711 0.042 0.859 0.693 0.042 0.859 0.684 0.042 ` 77 Therefore, bent retrofitted with an ECC jacket experienced the smallest probability of crushing damage at lower hazard levels under all earthquake scenarios. On the other hand, at higher hazard levels, it is subjected to the same for crustal and intra-slab earthquakes. ECC-jacketed bent also encountered the least vulnerability for the considered damage states under far-field crustal ground motions in another research (Billah et al. 2013). On the contrary, bent retrofitted with concrete jacket had the smallest probability of crushing damage at the same hazard level when subjected to interface earthquakes. The total expected life-cycle losses of the bents have been evaluated considering the remaining service life and monetary discount rate (τ) of 50 years and 3.79% (BC Ministry of Transportation and Infrastructure 2022), respectively. As-built and different jacketed bridge bents’ total expected life-cycle losses were obtained with Equation (4.8) for the two hazard levels considered in this study. These losses are shown in Figures 4.4-4.6 when the as-built and different jacketed bridge bents experienced crustal, intra-slab, and interface earthquakes for different proportions of yielded rebars. Effects of various retrofit options on the bent total expected life-cycle loss were compared in this subsection. The bent expected annual loss has a linear relationship with the probabilities of cracking, yielding, and crushing damages. The as-built bent was subjected to higher probabilities of yielding and crushing damages due to a lower median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) and dispersion component obtained from smaller limiting drift and dispersion value, respectively than each retrofitted bent that Tables 3.10 and 4.2 present at both hazard levels under all earthquake scenarios regardless of the proportion of yielded rebars as displayed in Tables 4.3-4.8. The lower hazard level was more frequent than the higher one. 78 Figure 4.4. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event Figure 4.5. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event Thus, maximum total expected life-cycle losses of CFRP, steel, ECC, and concrete jacketed bents were $39522, $95342, $79377, and $70114, respectively compared to that of as-built one $106637 with 5% yielded rebars at lower hazard level that Figure 4.6a portrays. 0200004000060000800001000001200005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete010000200003000040000500005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete0200004000060000800001000005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete0100002000030000400005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete(a) (b) (a) (b) 79 Figure 4.6. Comparisons of total expected life-cycle losses of the as-built and retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event Furthermore, these retrofit options decreased the seismic loss of the deficient bent by 63%, 11%, 26%, and 34%, respectively. On the contrary, for higher hazard levels with the same proportion of yielded rebars, such losses of CFRP, steel, ECC, and concrete jacketed bents are $26508, $33721, $25248, and $21502, respectively in relation to that of the as-built bent of $40600 that Figure 4.6b presents. Therefore, the total expected life-cycle loss of deficient one incurred reductions of 35%, 17%, 38%, and 47% for these techniques, respectively. The expected annual loss of the bent is also linearly related to downtime. CFRP jacketed bent required the lowest downtime of 2 days at yielding. Consequently, it experienced the lowest total expected life-cycle losses of $21402 and $16216 at lower and higher hazard levels, respectively, under various earthquake scenarios except at 0.87g for interface earthquakes with different yielded rebar proportions, as shown in Figures 4.4-4.6. However, the concrete jacketed bent had such a loss of $20795 at higher hazard level under interface earthquakes that Figure 4.6b presents owing to the least probabilities of cracking, yielding, and crushing damages owing to the greatest values of 0200004000060000800001000001200005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete010000200003000040000500005 20 30 45E (LCL) ($)Proportion of Yielded Bars (%) As-Built CFRP Steel ECC Concrete(a) (b) 80 median intensity measures (𝐼𝐼𝐼𝐼𝑖𝑖) influenced by the smallest drift. Moreover, the bent retrofitted with steel jacket incurred the highest total expected life-cycle losses of $95342 and $33721 under Sa(T1) of 0.5g and 0.87g, respectively, considering all earthquake sources and yielded rebar proportions as displayed in Figures 4.4-4.6 since it needed the largest downtime of 32 days at yielding. 4.4 Effects of Earthquake Sources on Performance-Based Seismic Loss In this subsection, comparisons of how different earthquake sources affected the total expected life-cycle loss are made. The as-built, CFRP, steel, ECC, and concrete jacketed bents had the smallest total expected life-cycle losses of $30948, $16216, $24656, $19371, and $18011, respectively, under the 2475-year event due to 45% yielded rebars when subjected to intra-slab earthquakes (Figure 4.5b) because of the least cracking, yielding, and crushing probabilities owing to the maximum median intensity measures (𝐼𝐼𝐼𝐼𝑖𝑖) resulting from the minimum drifts. On the other hand, as-built bent faced the greatest total expected life-cycle loss of $107110 for crustal earthquakes as displayed in Figure 4.4a, whereas CFRP, steel, ECC, and concrete jacketed ones underwent such losses of $39522, $95342, $79377, and $70114, respectively under interface earthquakes with 5% yielded rebars at lower hazard level that Figure 4.6a portrays since the probabilities of exceeding considered damage states were the most thanks to the lowest median intensity measures (𝐼𝐼𝐼𝐼𝑖𝑖) caused by the highest drifts. 4.5 Effect of Yielded Rebar Proportion on Seismic Loss The influences of various yielded rebar proportions on the total expected life-cycle loss are explained in this subsection. Higher limiting drift raised the median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) for 81 a higher yielded rebar proportion. Hence, the probability of exceeding such a damage state affected by the median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) was smaller at any hazard level too. Thus, the as-built and different jacketed bents’ total expected life-cycle losses decreased according to the yielded rebar proportion increase. When this proportion went up by 15% or 25%, such losses were affected a little as shown in Figures 4.4-4.6. On the other hand, seismic losses of as-built, CFRP, steel, ECC, and concrete jacketed bents mostly reduced from $90193, $22487, $81141, $74086, and $64700 to $77901, $21402, $68625, $65223, and $59139, respectively at 0.5g under intra-slab earthquakes when yielded rebar proportion is increased by 40% (Figure 4.5a). Therefore, such losses of these bents went down by 14%, 5%, 15%, 12%, and 9%, respectively. 4.6 Effects of Retrofit Techniques on Benefit-Cost Ratio Benefit-cost ratios of the retrofitted bents as portrayed in Figures 4.7-4.9 were also calculated using Equation (4.9) at lower and higher hazard levels under different earthquake scenarios considering various yielded rebar proportions. Furthermore, in this subsection, comparisons are made to present how different retrofitting techniques influence these ratios. The benefit was less, while as-built and retrofitted bents experienced simultaneous smaller and greater probabilities of exceeding considered damage states, respectively. CFRP-jacketed bent had the smallest benefit-cost ratio of 0.17 for higher hazard levels due to 45% yielded rebars when subjected to interface earthquakes that Figure 4.9b displays because of its highest cracking, yielding, and crushing probabilities arising from the lowest median intensity measures ( 𝐼𝐼𝐼𝐼𝑖𝑖) caused by the least limiting drifts as shown in Table 3.10, and the greatest drift. On the other hand, steel, ECC, and concrete jacketed ones faced such ratios of 0.49, 0.61, and 0.41, respectively for intra-slab earthquakes as shown in Figures 4.8b since the probabilities of exceeding considered damage 82 states of the as-built bent were the least due to maximum value of median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) obtained from the smallest drift. Figure 4.7. Comparisons of benefit-cost ratios of the retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event Figure 4.8. Comparisons of benefit-cost ratios of the retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event However, CFRP, steel, ECC, and concrete jacketed bents underwent the greatest benefit-cost ratios of 1.06, 1.56, 1.61, and 1.27, respectively, at 0.5g under crustal earthquakes that Figure 4.7a presents. Such ratios resulted from the maximum probabilities of cracking, yielding, and 00.511.522.55 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete00.511.55 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete00.250.50.7515 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete00.250.50.755 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete(b)(a) (b) (a) 83 crushing damages of the as-built bent caused by the lowest median intensity measures (𝐼𝐼𝐼𝐼𝑖𝑖) and dispersion components thanks to the most drift and rate of change of drift with respect to intensity measure. Figure 4.9. Comparisons of benefit-cost ratios of the retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event 4.7 Effects of Earthquake Sources on Benefit-Cost Ratio In this subsection, the effects of various earthquake sources on benefit-ratio are compared. The ECC-jacketed bent experienced the most benefit-cost ratios of 1.61 and 1.02 at lower and higher hazard levels, respectively, when subjected to crustal earthquakes with 30% yielded rebars as portrayed in Figure 4.7 facing the smallest crushing probabilities obtained from the greatest limiting drift that Table 3.10 displays. On the contrary, bents retrofitted with steel and CFRP jackets had the second most and least benefit-cost ratios of 1.56 and 1.06; 1.01 and 0.28 under 0.5g and 0.87g, respectively. The expected yearly loss of the bent has a linear relationship with the downtime. CFRP jacketed bent needed the least downtime of 2 days at yielding, so it incurred the smallest seismic losses of $22487 and $22270 for 0.5g under intra-slab earthquakes for 5% and 20% yielded rebars, respectively that Figure 4.5a shows. Therefore, CFRP jacketed 00.511.55 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete00.250.50.7515 20 30 45Benefit-Cost RatioYielded Rebar Proportion (%) CFRP Steel ECC Concrete(b)(a) 84 one encountered the greatest benefit-cost ratios of 0.89 and 0.87 with these proportions, respectively, as presented in Figure 4.8a. Conversely, ECC jacketed bent experienced such ratios of 0.62, 0.62, 0.63, and 0.61 at higher hazard levels for similar earthquakes owing to 5%, 20%, 30%, and 45% yielded rebars, respectively, that Figure 4.8b portrays since its crushing probability was the smallest for the most value of median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) caused by the maximum limiting drift that Table 3.10 displays. ECC jacketed one also faced the second highest benefit-cost ratios of 0.85 and 0.83 for lower hazard levels when subjected to intra-slab earthquakes, for 5% and 20% yielded rebars, respectively. Nevertheless, concrete jacketed bent had the lowest benefit-cost ratios of 0.82 and 0.60 for 30% and 45% yielded rebars, respectively. Furthermore, bent retrofitted with ECC jacket experienced the maximum benefit-cost ratios of 1.44, 1.43, 1.49, and 1.31 at lower hazard levels under interface earthquakes due to 5%, 20%, 30%, and 45% yielded rebars, respectively as shown in Figure 4.9a because of its minimum probability of crushing damage resulting from the greatest value of median intensity measure (𝐼𝐼𝐼𝐼𝑖𝑖) due to the most limiting drift that Table 3.10 presents and the lower material cost of $2374 for the ECC jacket than for the concrete jacket, which is $3924. It also had such ratios of 0.81, 0.81, 0.82, and 0.80, respectively for higher hazard levels with these proportions, respectively, as portrayed in Figure 4.9b, since concrete jackets cost more. Moreover, bent retrofitted with concrete one was subjected to the second most benefit-cost ratio of 0.61 for the same earthquakes for all yielded rebar proportions except 45% at higher hazard levels. Notwithstanding, bent retrofitted with CFRP jacket faced the smallest benefit-cost ratios of 0.88, 0.86, 0.84, and 0.75; 0.18, 0.18, 0.18, and 0.17 for 0.5g; and 0.87g, respectively under interface earthquakes. The probabilities of exceeding considered damage states of the as-built and retrofitted bents at higher hazard levels were more than those at lower 85 ones that Tables 4.3-4.8 display. Consequently, for example, CFRP, steel, ECC, and concrete jacketed bents underwent benefit-cost ratios of 0.28, 0.99, 1.02, and 0.68 lower compared to those of 1.02, 1.56, 1.61, and 1.27, respectively for the latter under crustal earthquakes with 30% yielded rebars as shown in Figure 4.7. 4.8 Effect of Yielded Rebar Proportion on Benefit-Cost Ratio The influences of different yielded rebar proportions on the benefit-cost ratio are discussed in this subsection. Both the probabilities of exceeding a higher yielded rebar proportion of as-built and retrofitted bents were less caused by greater limiting drifts leading to higher median intensity measures (𝐼𝐼𝐼𝐼𝑖𝑖) at any hazard level, too. The benefit-cost ratios of the retrofitted bents differed according to the hazard level and how the yielded rebar proportion varied. For lower hazard levels, the benefit-cost ratios of CFRP, steel, ECC, and concrete-jacketed bents decreased at most from 0.89, 0.76, 0.85, and 0.81 to 0.87, 0.66, 0.83, and 0.79, respectively owing to the increase in such proportion to 20% that Figure 4.8a presents. Thus, the ratios of these retrofitted bents went down by 2%, 13%, 2%, and 2%, respectively. On the contrary, when the yielded rebar proportion rose from 20% to 30%, the benefit-cost ratios of CFRP, steel, ECC, and concrete jacketed bents changed to 0.84, 0.84, 0.89, and 0.82, respectively. Therefore, such ratios of the bents retrofitted with these retrofit options faced variations of 3%, 27%, 7%, and 4%, respectively. However, the benefit-cost ratios of CFRP, steel, ECC, and concrete-jacketed bents reduced to 0.74, 0.77, 0.67, and 0.60, respectively, with a change of this proportion from 30% to 45%. Consequently, the ratios of these retrofitted bents differed by 12%, 8%, 25%, and 27%, respectively. Conversely, the benefit-cost ratios of CFRP, steel, ECC, and concrete jacketed bents had maximum ranges of 0.21-0.19, 0.49-0.53, 0.62-0.61, and 0.43-0.41, respectively as the yielded rebar proportion 86 varied by 40% at 0.87g as portrayed in Figure 4.8b. As a result, such ratios of the bents retrofitted with these retrofit options experienced changes of 10%, 8%, 2%, and 5%, respectively. 4.9 Selection of the Optimum Retrofit Technique In this subsection, the retrofit option that provides the maximum benefit-cost ratio for the various yielded rebar proportions at 475 and 2475-year return period hazard levels under all earthquake scenarios is considered the optimum one. In the descending order of benefit-cost ratios, the jackets were ECC, steel, concrete, and CFRP for any hazard level and yielded rebar proportion under crustal earthquakes. They were CFRP, ECC, steel, and concrete at lower hazard levels when subjected to intra-slab ones. However, higher hazard levels provided this order as ECC, steel, concrete, and CFRP for similar earthquakes. The jackets were ECC, concrete, steel, and CFRP when benefit-cost ratios were ordered descendingly when subjected to interface earthquakes. Thus, the ECC jacket became the optimum option for retrofitting the considered seismically deficient multi-column bent, comparing its life-cycle performance in terms of benefit-cost ratios with those of the other jackets. The other jackets in the descending order of life-cycle performances were steel, concrete, and CFRP. 4.10 Summary This chapter presents as-built and different jacketed bents’ fragility analyses to obtain the conditional probabilities of exceeding cracking, yielding, and crushing damage states. It provides the performance-based seismic loss assessments of such bents considering these probabilities. Furthermore, the effects of different retrofit options, earthquake sources, and yielded rebar proportions on such loss are discussed. This chapter shows benefit-cost ratio evaluations of 87 various retrofitting techniques with considered yielded rebar proportions under all earthquake scenarios. It explains how different retrofit options, earthquake sources, and yielded rebar proportions affect this ratio. Moreover, the selection of the optimum retrofit option that maximizes the benefit-cost ratio to retrofit the deficient bent is presented. 88 CHAPTER 5. PERFORMANCE-BASED SEISMIC RESILIENCE ASSESSMENTS OF RETROFITTED BRIDGE BENTS 5.1 General Modern civilization uses infrastructure networks to tackle post-seismic situations and restore them to improved conditions. Infrastructure designed and maintained according to the current standards can serve people in normal and emergency situations. Infrastructure network components such as bridges connect different places and help people through easing emergency transportation and evacuation. Hence, rapid restorations of bridges affected by earthquakes are required considering their valuable services. However, creating alternative routes for such bridges used to cross a barrier is not always possible. Furthermore, the interactions of the bridges with people make them crucial to mitigate interruption and discomfort. Seismic resilience has become gradually significant in predicting the ability of a bridge to be ready for and adjust to variable circumstances and to resist and get over service disruption quickly after earthquakes at the same time (Dong and Frangopol 2015; Frangopol et al. 2017; Aghaeidoost and Billah 2023; Wei et al. 2023; Li et al. 2024). It also measures how functional a bridge remains as well as the social effort toward post-earthquake functionality (Decò et al. 2013; Aghaeidoost and Billah 2023; Wei et al. 2023). Seismic resilience is measured with a probability-based method considering uncertainties in the seismic vulnerability and consequence assessments (Venkittaraman and Banerjee 2014; Dong and Frangopol 2015; Frangopol et al. 2017; Aghaeidoost and Billah 2023; Li et al. 2024). Moreover, bridges with deficiencies like inadequate ductility and low shear strength are retrofitted to enhance seismic performance. Though retrofitting reduces seismic vulnerability, it also matters how different retrofit options like steel, CFRP, concrete, and ECC jackets affect the bridge's post-seismic functionality. For many years, performance-based seismic resilience has been used as an effective measure to 89 indicate the post-seismic functionality of bridges. Furthermore, no research has previously been attempted to measure it for a seismically deficient multi-column bridge bent retrofitted with various alternatives considering different earthquake sources like crustal, intra-slab, and interface with various yielded rebar proportions. Hence, performance-based seismic resilience of a deficient bent retrofitted with popular techniques, e.g., CFRP, steel, ECC, and concrete jackets have been assessed considering the conditional probabilities of exceeding various damage states at 475 and 2,475-year return period hazard levels obtained in the previous chapter. The retrofit option with the maximum performance-based seismic resilience and least recovery time was considered optimum for such a bent. 5.2 Seismic Resilience Assessments of Retrofitted Bridge Bents Performance-based seismic resilience of steel, CFRP, concrete, and ECC jacketed bridge bents, were obtained to achieve the most resilient retrofit option for the seismically deficient bridge bent. Infrastructure resilience can be ensured through the minimization of functionality loss after an earthquake and fast recovery to full functionality (Bruneau and Reinhorn 2019). Seismic resilience (𝑅𝑅) also is the organizational and community capacity to mitigate hazards, control post-disaster effects, and conduct recovery activities for minimization of social disruption and mitigation of probable seismic effects (Bruneau et al. 2003). As resilience has a wide coverage of societal and technical aspects, its quantification can have a few different definitions. This research considered the following definition which has been extensively used by many previous researchers (Frangopol and Bocchini 2011; Decò et al. 2013; Dong and Frangopol 2015; ChienKuo et al. 2021): 𝑅𝑅 = ∫ 𝑄𝑄(𝑖𝑖)𝑑𝑑𝑖𝑖𝑡𝑡ℎ𝑡𝑡0𝑖𝑖ℎ−𝑖𝑖0 (5.1) 90 where, t is the time, 𝑄𝑄(𝑡𝑡) is the time-dependent functionality, 𝑡𝑡0 is the time of earthquake occurrence, and 𝑡𝑡ℎ is the investigated time horizon. The classic schematic representation of a retrofitted bent resilience after an earthquake is presented in Figure 5.1. The pre-seismic level of functionality of the bent corresponds to point A. The bent loses functionality to a residual value 𝑄𝑄𝑟𝑟 corresponding to B owing to an earthquake at the time 𝑡𝑡0 based on the assessed post-seismic damage. Later on, the post-seismic recovery is achieved in two steps. Moreover, its pattern is related to the physical rehabilitation or reconstruction method, which includes construction methods and timing. Segment BC displays the first step of the recovery executed in an idle time interval 𝛿𝛿𝑖𝑖 when the functionality does not change till the time 𝑡𝑡𝑖𝑖. During an idle time interval, it is planned when the bent is rehabilitated considering available resources, a damaged bent is demolished, and the debris is removed. Furthermore, segment CD presents the second step of recovery in recovery duration 𝛿𝛿𝑟𝑟 when the functionality of the damaged bent is restored to a target value 𝑄𝑄𝑖𝑖 that corresponds to point D. Therefore, the recovery pattern relies on four independent random variables, 𝑄𝑄𝑟𝑟, 𝛿𝛿𝑖𝑖, 𝛿𝛿𝑟𝑟, and 𝑄𝑄𝑖𝑖 that Table 5.1 presents. Segment CD follows a negative exponential-type pattern at performance level yielding due to faster recovery of functionality when the restoration starts. On the other hand, a positive exponential-type pattern was used for segment CD at performance level crushing considering that the bridge is fully operational only when the restoration ends. The bridge functionality 𝑄𝑄(𝑘𝑘)(𝑡𝑡) for damage state k at time t is calculated from Equation (5.2) (Pang and Wang 2021; Aghaeidoost and Billah 2023). 𝑄𝑄(𝑘𝑘)(𝑡𝑡) = 𝑄𝑄𝑟𝑟 + 𝐻𝐻(𝑡𝑡 − 𝑡𝑡0 − 𝛿𝛿𝑖𝑖)𝑅𝑅𝑓𝑓 �𝑖𝑖−𝑖𝑖0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟 � (𝑄𝑄𝑖𝑖 − 𝑄𝑄𝑟𝑟) (5.2) where k is 1 and 2 for performance levels yielding and crushing, respectively, 𝐻𝐻(𝑡𝑡 − 𝑡𝑡0 − 𝛿𝛿𝑖𝑖) is the Heaviside step function equal to 0 when 𝑡𝑡 − 𝑡𝑡0 − 𝛿𝛿𝑖𝑖 is less than 0, otherwise it is 1, and 91 𝑅𝑅𝑓𝑓 �𝑖𝑖−𝑖𝑖0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟� = 1 − 𝑒𝑒−𝑤𝑤�𝑡𝑡−𝑡𝑡0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟 � (for yielding) = 𝑒𝑒−𝑤𝑤�1−𝑡𝑡−𝑡𝑡0−𝛿𝛿𝑖𝑖𝛿𝛿𝑟𝑟 � (for crushing) where, 𝑤𝑤 is the shape parameter equal to 10. Figure 5.1. Schematic representation of resilience of a retrofitted bent Moreover, the expected functionality 𝑄𝑄(𝑡𝑡|𝐼𝐼𝐼𝐼) at any hazard level is obtained using Equation (5.3) (Pang and Wang 2021; Aghaeidoost and Billah 2023). 𝑄𝑄(𝑡𝑡|𝐼𝐼𝐼𝐼) = ∑ 𝑃𝑃𝑓𝑓(𝑘𝑘)2𝑘𝑘=1 𝑄𝑄(𝑘𝑘)(𝑡𝑡) (5.3) where, 𝑃𝑃𝑓𝑓(𝑘𝑘) is the probability of exceeding damage state k. 𝑃𝑃𝑓𝑓(𝑘𝑘) values are presented in the past chapter. Monte Carlo simulation (MCS) was also performed considering a time interval of 0.1 month using different random variable values shown in Table 5.1 with 10000 trials (Pang and Wang 2021; ChienKuo et al. 2021; Aghaeidoost and Billah 2023) to obtain the mean expected functionality from Equation (5.3) using MATLAB. MCS evaluated an uncertain value range rather than obtaining results using particular values of random variables. It provided a probable outcome model using random variable probability 𝛿𝛿𝑖𝑖 𝛿𝛿𝑟𝑟 92 distributions. The outcome calculation is repeated with a different random value set. A great deal of possible outcomes were obtained by performing MCS many times. 93 Table 5.1. Random variables for bridge functionality at various performance levels (Decò et al. 2013; Zhou et al. 2015; Benedetti et al. 2016; ChienKuo et al. 2021) Random variable Distribution category Distribution parameter Performance level Cracking Yielding Crushing CFRP Steel ECC Concrete CFRP Steel ECC Concrete 475 years 2475 years 𝑄𝑄𝑟𝑟 Triangular Min. 1 (deterministic) 0.7 0.5 0 (deterministic) Mode 0.85 0.65 Max. 1 0.8 𝛿𝛿𝑖𝑖 (months) Uniform Min. - 1 Max. 2 𝛿𝛿𝑟𝑟 (days) Triangular Min. - 1 22 28 18 43 64 70 60 Mode 1.5 27 28.5 22 61.5 87 88.5 82 Max. 2 32 29 26 80 110 107 104 𝑄𝑄𝑖𝑖 Triangular Min. - 1 Mode Max. 94 The parameter evaluation related to the recovery process was not straightforward, so the distribution types and the corresponding parameters were obtained from literature and engineering judgment. Statistical independence of random variables was assumed as suggested by Decò et al. (2013). Different 𝑄𝑄𝑟𝑟 triangular distributions were considered at yielding for events with return periods of 475 and 2475 years to account for various damage states. On the other hand, deterministic 𝑄𝑄𝑟𝑟 values of 1 and 0 were used for cracking and crushing, respectively. Determination of bridge importance required network-level analysis which was beyond scope. Thus, the 𝛿𝛿𝑖𝑖 values were assumed to follow a uniform distribution having a range of [1, 2] months for each recovery pattern. The 𝛿𝛿𝑟𝑟 values were assumed to have a triangular distribution and are shown in Table 5.1 at yielding and crushing for different retrofit options. 𝑄𝑄𝑖𝑖 could be considered as a random variable in this research. However, it was assumed that the bridge functionality was fully recovered using various patterns e.g. negative and positive exponential types at yielding and crushing, respectively. The area under the mean expected functionality vs time graph, ∫ 𝑄𝑄(𝑡𝑡)𝑑𝑑𝑡𝑡𝑖𝑖ℎ𝑖𝑖0 was calculated using the trapezoidal rule. Furthermore, 𝑅𝑅 was obtained considering the 𝑡𝑡ℎ at which mean expected functionality tended to 1. 5.3 Effects of Retrofit Options on Mean Expected Functionality Seismic resilience assessment outcomes are discussed in this section. Mean expected functionalities of the retrofitted bents for various yielded rebar proportions under 475 and 2475-year return period earthquakes considering different earthquake scenarios are shown in Figures 5.2-5.7. Each mean expected functionality vs time graph consists of three portions. The initial portion of the graph is flat up to the minimum idle time interval of 1 month because the mean expected functionality remains the same. Since idle time interval is a random variable with a 95 maximum 2-month limit, and the value can be different for various performance levels, yielding and crushing, the middle portion of the graph is linear. Figure 5.2. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under crustal earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% As the recoveries for yielding and crushing are fast and slow, respectively, the last portion of the graph has a positive exponential-type pattern. In this subsection, comparisons of how various retrofit options affected the mean expected functionality of the bent are made. Expected functionality had a linear relationship with yielding and crushing probabilities based on Equation (5.3). CFRP-jacketed bent exhibited the maximum mean expected functionality slightly differing from those of other retrofitted ones with any 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)96 yielded rebar proportion for all earthquakes with return periods of 475 and 2475 years because its probabilities of exceeding yielding and crushing damage states were the highest. Figure 5.3. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under intra-slab earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% For example, at t = 0, this bent functionality was 0.57, 8% higher than that of the ECC-jacketed one, having the second most value of 0.53 with 5% yielded rebar proportion at lower hazard level under interface events (Figure 5.4a). However, bent retrofitted with an ECC jacket presented the second greatest mean expected functionality, having a marginal variation from those of other jacketed ones. For instance, such a bent had this functionality of 0.53, which is 3% more compared to that of one retrofitted with steel jacket with the third highest value of 0.51 for 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)97 5% yielded rebar proportion when subjected to 475-year return period crustal earthquakes at t = 0 (Figure 5.2a). Figure 5.4. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under interface earthquakes for 475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% Furthermore, steel-jacketed bent showed the third most mean expected functionality insignificantly deviating from those of other retrofitted ones except when subjected to intra-slab events which provided the minimum yielding probabilities. For example, at t = 0, this bent functionality was 0.51, 2% greater in comparison with that of concrete jacketed one having the smallest value of 0.50 with 5% yielded rebar proportion at lower hazard level under crustal earthquakes (Figure 5.2a). Nevertheless, bent retrofitted with the concrete jacket was expected to 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)98 exhibit the least functionality nominally varying from those of other jacketed ones except for intra-slab earthquakes, producing the second lowest probabilities of exceeding yielding and crushing damages. Figure 5.5. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under crustal earthquakes for a 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% 5.4 Effects of Earthquake Sources on Mean Expected Functionality The influences of different earthquake sources on the mean expected functionality of the bents are discussed in this subsection. Under interface earthquakes, all retrofitted bents presented the highest mean expected functionalities, having a minor difference from those for other earthquake sources at both hazard levels for the considered yielded rebar proportions since 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)99 yielding and crushing probabilities were the greatest. For instance, when subjected to 475-year return period interface earthquakes, CFRP, steel, ECC, and concrete jacketed bents showed functionalities of 0.54, 0.49, 0.50, and 0.48, 4%, 2%, 2%, and 2% higher than those under crustal events, respectively with 30% yielded rebar proportion at t = 0 (Figures 5.2c and 5.4c). Figure 5.6. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under intra-slab earthquakes for a 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% On the other hand, for intra-slab earthquakes that caused the smallest probabilities of exceeding yielding and crushing damage states, these bents exhibited the lowest mean expected functionalities negligibly varying from those when subjected to crustal and interface ones under similar circumstances. For example, at t = 0 at lower hazard levels under such events, CFRP, 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)100 steel, ECC, and concrete jacketed bents had these functionalities of 0.50, 0.45, 0.48, and 0.46, which were 3%, 7%, 3%, and 4% less compared to those for crustal earthquakes, respectively with 30% yielded rebar proportion (Figures 5.2c and 5.3c). Figure 5.7. Mean expected functionalities for different yielded rebar proportions of retrofitted bents under interface earthquakes for a 2475-year return period events: (a) 5%, (b) 20%, (c) 30%, and (d) 45% 5.5 Effects of Yielded Rebar Proportions on Mean Expected Functionality The effects of various yielded rebar proportions on the mean expected functionality of the bents are compared in this subsection. The mean expected functionality of each retrofitted bent decreased depending on the increase in yielded rebar proportion due to more damage at considered hazard levels when subjected to earthquakes from any source. CFRP-jacketed bent 00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(a)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(b)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(c)00.20.40.60.810 1 2 3 4 5 6Mean Expected Functionality Time (months)CFRPSteelECCConcrete(d)101 exhibited the most reduction of 14% in the mean expected functionality with the highest increase in the yielded rebar proportion of 40% for any 475-year return period intra-slab event because of the greatest change in its probability of exceeding yielding damage state. Conversely, such a bent mean expected functionality was subjected to the greatest decrease of 8% for the same yielded rebar proportion increase under the 2475-year return period similar events since yielding probability changed by 8%. Furthermore, while the yielded rebar proportion increased by 40%, bent retrofitted with steel jacket had the mean expected functionality reduced by 17% at lower hazard levels when subjected to intra-slab earthquakes. On the contrary, this bent was expected to be 10% less functional for the higher hazard level under the same conditions. Moreover, the ECC-jacketed bent presented a 12% mean expected functionality reduction for 40% yielded rebar proportion increment when subjected to an intra-slab event with a return period of 475 years. Conversely, the ECC-jacketed one showed a 7% mean expected functionality loss for a similar change in yielded rebar proportion under the same event with a 2475-year return period. 40% increment of yielded rebar proportion also decreased the mean expected functionality of the bent retrofitted with concrete jacket by 9% at lower hazard levels when subjected to intra-slab earthquakes. In contrast, such a bent had a 5% smaller mean expected functionality for the higher hazard level for similar yielded rebar proportion increase under interface ones since its yielding probability was reduced by 6%. 5.6 Effects of Retrofit Options on Seismic Resilience Performance-based seismic resilience of the retrofitted bents with different yielded rebar proportions when subjected to various 475 and 2475-year return period events from different sources were presented in Figures 5.8-5.10. The influence of different retrofit options on seismic 102 resilience was discussed in this subsection. Seismic resilience was proportional and inversely proportional to the area under the mean expected functionality vs time graph and investigated time horizon, respectively according to Equation (5.1). Figure 5.8. Comparisons of the seismic resilience of the retrofitted bents under crustal earthquakes: (a) 475-year return period event and (b) 2475-year return period event Figure 5.9. Comparisons of the seismic resilience of the retrofitted bents under intra-slab earthquakes: (a) 475-year return period event and (b) 2475-year return period event Bent retrofitted with CFRP jacket exhibited the most seismic resilience, having a slight deviation from those of other jacketed bents under various 475-year return period earthquakes, except for 00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(a)00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(b)00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(a)00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(b)103 45% yielded rebar proportion for crustal ones, which generated the smallest area of 1.96 under the mean expected functionality vs time graphs as shown in Figure 5.2d. For instance, this bent presented such a resilience of 0.64 with 5% yielded rebar proportion at a lower hazard level for interface events (Figure 5.10a). Figure 5.10. Comparisons of the seismic resilience of the retrofitted bents under interface earthquakes: (a) 475-year return period event and (b) 2475-year return period event On the other hand, ECC-jacketed bent had the highest seismic resilience marginally differing from those of other retrofitted ones with the considered yielded rebar proportions at higher hazard levels when subjected to different events creating the maximum areas under the mean expected functionality vs time graphs (Figures 5.5-5.7). For example, such a bent showed the resilience and area of 0.67 and 3.16 with 5% yielded rebar proportion for 2475-year return period interface earthquakes as displayed in Figures 5.10b and 5.7a, respectively. Furthermore, bent retrofitted with ECC jacket exhibited the second most seismic resilience, insignificantly varying from those of other jacketed bents under various 475-year return period earthquakes except for 45% yielded rebar proportion for crustal ones. For instance, this bent presented seismic resilience of 0.62 with 5% yielded rebar proportion at a lower hazard level for interface events (Figure 00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(a)00.250.50.755 20 30 45Seismic ResilienceProportion of Yielded Bars (%) CFRP Steel ECC Concrete(b)104 5.10a). On the contrary, CFRP-jacketed bent had the second greatest seismic resilience, nominally deviating from those of other retrofitted bents at higher hazard levels for different earthquakes except with 5% and 20% yielded rebar proportions under interface ones and 45% yielded rebar proportion. For example, this bent showed a resilience of 0.66 with 5% yielded rebar proportion for 2475-year return period interface earthquakes as portrayed in Figure 5.10b. Moreover, bent retrofitted with concrete jacket exhibited the minimum seismic resilience having a minor difference from those of other jacketed bents when subjected to various 475 and 2475-year return period events from different sources except for 30% yielded rebar proportion under intra-slab ones, and 45% yielded rebar proportion for crustal and interface ones. For instance, this bent presented resilience of 0.60 and 0.65 with 5% yielded rebar proportion at lower and higher hazard levels, respectively for interface earthquakes (Figures 5.10a and 5.10b). 5.7 Effects of Earthquake Sources on Seismic Resilience In this subsection, comparisons are made to present how various earthquake sources influence seismic resilience. Each retrofitted bent had the most seismic resilience at considered hazard levels with different yielded rebar proportions when subjected to interface earthquakes. This is owing to the highest areas under the mean expected functionality vs time graphs, which resulted from the greatest mean expected functionalities obtained by the maximum probabilities of exceeding yielding and crushing damage states, as shown in Figure 5.7. Seismic resilience for interface earthquakes negligibly varied from those under other earthquake sources. For example, for such events with a 475-year return period, CFRP, steel, ECC, and concrete jacketed bents showed resilience of 0.57, 0.53, 0.56, and 0.55, that are 5%, 1%, 2%, and 3% more in comparison with those when subjected to crustal ones, respectively with 45% yielded rebar 105 proportion (Figures 5.8a and 5.10a). Conversely, under all situations for intra-slab earthquakes, thanks to the lowest values of the areas under the mean expected functionality vs time graphs caused by the smallest mean expected functionalities (Figure 5.6) evaluated from the least yielding and crushing probabilities, these bents exhibited the minimum seismic resilience having slight deviations from those when subjected to crustal and interface earthquakes. For instance, at lower hazard levels under these events, CFRP, steel, ECC, and concrete jacketed bents presented resilience of 0.53, 0.47, 0.53, and 0.51, 3%, 9%, 4%, and 5% smaller than those for crustal ones, respectively with 45% yielded rebar proportion (Figures 5.8a and 5.9a). 5.8 Effects of Yielded Rebar Proportions on Seismic Resilience In this subsection, the effects of different yielded rebar proportions on seismic resilience are compared. All retrofitted bents exhibited less seismic resilience with an increase in the extent of damage resulting from gradually increasing yielded rebar proportion under various earthquakes with return periods of 475 and 2475 years. As the yielded rebar proportion increased by 40%, bent retrofitted with CFRP jacket had seismic resilience mostly reduced by 14% at lower hazard levels when subjected to intra-slab ones since the yielding probability faced the maximum decrease. On the contrary, this bent presented 8% less seismic resilience for the higher hazard level under the same conditions. Furthermore, steel-jacketed bent showed the most reduction of 16% in seismic resilience resulting from the highest reduction in the probability of exceeding the yielding damage state with the highest yielded rebar proportion increase of 40% for any 475-year return period intra-slab event. On the other hand, seismic resilience of such a bent was subjected to the greatest decrease of 10% for the same yielded rebar proportion increase under the 2475-year return period similar events. Moreover, the 40% increment of the yielded rebar proportion 106 decreased seismic resilience of the bent retrofitted with ECC jacket by 11% at lower hazard levels when subjected to intra-slab earthquakes. In contrast, such a bent exhibited 7% smaller seismic resilience caused by a 7% lower yielding probability for the higher hazard level for similar yielded rebar proportion increase under intra-slab ones. Concrete-jacketed bent also had a 9% seismic resilience reduction for 40% yielded rebar proportion increment when subjected to an intra-slab event with a return period of 475 years. Conversely, the concrete-jacketed one presented a 5% less seismic resilience for a similar change in yielded rebar proportion under 2475-year return period interface earthquakes because its probability of exceeding yielding damage state mostly decreased. 5.9 Selection of the Optimum Retrofit Option In this subsection, the retrofit option that maximized seismic resilience and required the shortest duration to restore the full bent functionality with the different yielded rebar proportions under various earthquakes with return periods of 475 and 2475 years was chosen as the optimum. In the descending order of seismic resilience having marginal differences, the jackets were ECC, CFRP, steel, and concrete for any hazard level and yielded rebar proportion when subjected to crustal events. These jackets were ordered as ECC, CFRP, concrete, and steel, considering the decreasing trend of seismic resilience with nominal variations under similar conditions for intra-slab ones. Their such order was ECC, CFRP, steel, and concrete for the considered yielded rebar proportions under interface earthquakes with return periods of 475 and 2475 years. However, the CFRP jacket needed the least full-functionality recovery periods with the considered yielded rebar proportions when the retrofitted bent was subjected to different earthquakes with return periods of 475 and 2475 years, as shown in Figures 5.2-5.7. Hence, it came up as the optimum 107 technique for retrofitting the seismically deficient multi-column bent considered in this study, comparing both its seismic resilience and restoration time with those of the other jackets. 5.10 Summary This chapter exhibits performance-based seismic resilience assessments of bents retrofitted with different alternatives. Expected functionality evaluations at various times for each retrofitted bent with different yielded rebar proportions under all earthquake scenarios are presented. Furthermore, the effects of various retrofitting techniques, earthquake sources, and different yielded rebar proportions on mean expected functionality are explained. It describes how the seismic resilience of all retrofitted bents for the considered conditions is calculated using the mean expected functionality vs time graphs. Effects of different retrofitting techniques, earthquake sources, and different yielded rebar proportions on seismic resilience are illustrated. Moreover, the selection of the optimum retrofitting technique with the highest seismic resilience and lowest full-functionality recovery period for the deficient bent is shown. 108 CHAPTER 6. SUMMARY, CONCLUSIONS, AND FUTURE WORKS 6.1 Summary CHBDC highlights PBSD to control the post-seismic condition of the bridge. Damage states available in CHBDC solely apply to new or seismically well-detailed ductile bridge substructures. Furthermore, they cannot be applied to retrofit old bridges if not modified to avoid premature brittle and unexpected failure. Damage states need to be selected considering strains, deformations, and performance corresponding to old bridge perspective details, materials, and arrangements. As a result, such states were developed using IDA for a seismically deficient multi-column bridge bent retrofitted with popular options such as steel, CFRP, concrete, and ECC jackets subjected to 475 as well as 2475-year return period events from different earthquake sources like crustal, intra-slab, and interface in Vancouver, BC, Canada. Moreover, a design example is presented to demonstrate the proposed damage state application to the seismic retrofitting of similar bents. An optimum intensity measure was obtained to observe the effects of retrofitting techniques and earthquake sources on the considered damage measures: maximum drift and damage index. Fragility analysis was performed to achieve probabilities of exceeding cracking, yielding, and crushing damage states. Such probabilities were also used to assess performance-based seismic loss and resilience of each retrofitted bent. The optimum retrofit option was selected based on the benefit-cost ratios, seismic resilience, and the full-functionality restoration periods of the retrofitted bents. Effects of retrofit options, earthquake sources, and yielded rebar proportions on seismic loss, benefit-cost ratio, mean expected functionality and seismic resilience of each retrofitted bent were studied. 6.2 Core Contributions This research contributed to performance-based design guideline development for retrofitting 109 seismically deficient RC multi-column bents with different techniques like CFRP, steel, ECC, and concrete jackets at various hazard levels under different earthquake scenarios. The following are this research's core contributions. 1. Performance-based damage state development for different retrofitting techniques expressed as limiting drifts and damage indices 2. Identifying an optimum intensity measure to compare seismic performances of retrofitted bridge bents 3. Performance-based design guideline development to retrofit deficient bridge bents 4. Assessing and comparing performance-based seismic losses and resilience of retrofitted bridge bents 6.3 Conclusions 6.3.1 Performance-based damage states of different jacketed bridge bents For developing the performance-based design to retrofit deficient bridge bents, both the performance level and its corresponding limit must be known. As the behaviours of retrofitted bents and new bridges are different, the damage states of new bridges available in design codes should not be used for retrofitting existing bents. Thus, steel, CFRP, concrete, and ECC jackets were used to retrofit a seismically deficient bent. Then, every jacketed bent experienced different suites, with 11 far-field earthquakes, each from various sources such as crustal, intra-slab, and interface. IDA was conducted for every jacketed bent to develop performance-based damage states expressed in damage indices as well as limiting drifts that Chapter 3 presents. An example to illustrate the performance-based seismic design to retrofit a deficient bent using proposed damage states is also presented in this chapter. First-mode spectral acceleration (Sa(T1)) was 110 identified as the optimum intensity measure for comparing all retrofitted bents’ performances expressed in damage measures: damage indices and maximum drifts for different intensity levels. The conclusions inferred from the study results are as follows: Concrete and rebar tensile strengths were used to obtain the cracking and yielding strains, respectively. These tensile strengths do not depend on retrofitting. Therefore, the respective limiting drifts of different jacketed bents matched at cracking and yielding. Conversely, the retrofit technique influenced the limiting drift corresponding to core concrete crushing. Furthermore, the bent retrofitted with the ECC jacket was subjected to the highest limiting drift of various jacketed bents. The order of the remaining retrofitted bents was concrete, steel, and CFRP, considering descending limiting drifts. The steel jacket turned out to be the most efficient in decreasing the median maximum drift of the retrofitted bent at the considered intensity levels of 0.50g and 0.87g under crustal, intra-slab, and interface earthquakes, whereas concrete and CFRP jackets were the second most and least effective, respectively. Core concrete of CFRP, steel, ECC, and concrete jacketed bents experienced crushing, provided their damage indices surpassed 2.05, 2.12, 1.91, and 1.92, respectively. Furthermore, the ECC jacket reduced the median damage index the most at the intensity levels of 0.50g and 0.87g under all three earthquake scenarios. Concrete and steel jackets proved to be the second most and least useful, respectively for such reductions of the median damage indices. ECC jacket stood out as the most appropriate option for retrofitting the seismically deficient bent, comparing its performance expressed in the median maximum drift as well as damage index with those of other jackets. In the descending order of efficiencies, the other jackets were concrete, steel, and CFRP. 111 6.3.2 Performance-based seismic loss assessments of bridge bents The study aims to compare the performance-based seismic losses of a seismically deficient retrofitted bent at different hazard levels considering crustal, intra-slab, and interface earthquakes. The benefit-cost ratios of the retrofitting techniques were also determined, and the ECC jacket with the maximum ratio was selected as the optimum one for such a multi-column bent. This study provided the inferences as mentioned below: 1. CFRP jacketed bent was subjected to the greatest yielding probabilities with 5% yielded rebar proportion for different 475 and 2475-year return period events. 2. Maximum probabilities of core concrete crushing were obtained for all retrofitted bents regardless of the hazard level under interface earthquakes. 3. Intra-slab earthquakes minimized total expected life-cycle losses of as-built and all retrofitted bents irrespective of hazard level and yielded rebar proportion. However, crustal and interface ones maximized their losses, respectively, under similar circumstances. 4. Furthermore, bent retrofitted with CFRP jacket incurred the least total expected life-cycle loss for any yielded rebar proportion. However, under interface earthquakes at higher hazard levels, the lowest life-cycle loss was incurred by the concrete jacketed bent. On the contrary, the steel jacketed bent experienced the highest life-cycle loss for any considered earthquake scenarios. 5. Interface earthquakes brought about the minimum benefit-cost ratios for bent retrofitted with CFRP jacket, whereas intra-slab ones did so for the other retrofitted bents under all hazard levels for the considered yielded rebar proportions. Nevertheless, crustal earthquakes maximized such ratios of the retrofitted bents under the same situation. 112 6.3.3 Performance-based seismic resilience assessments of retrofitted bridge bents The study aimed to compare the performance-based seismic resilience of a seismically deficient bridge bent retrofitted with various options such as steel, CFRP, concrete, and ECC jackets for crustal, intra-slab, and interface earthquakes with different return periods. Based on the calculated seismic resilience and full-functionality recovery periods of various retrofit options, the optimum retrofit technique was selected. The study came up with the inferences as follows: 1. In the descending order of mean expected functionality with minor deviations, the jackets were CFRP, ECC, steel, and concrete. 3. All retrofitted bents presented the highest mean expected functionality reductions when yielded rebar proportion went up by 40% under intra-slab earthquakes. However, concrete-jacketed bent had the most reduction in mean expected functionality under 2475-year return period interface earthquakes. 4. All retrofitted bents showed maximum and minimum seismic resilience when subjected to interface and intra-slab ones, respectively. 5. Moreover, the seismic resilience of each retrofitted bent decreased the most for 40% yielded rebar proportion increase under intra-slab earthquakes. Nevertheless, bent retrofitted with the concrete jacket exhibited the greatest seismic resilience reduction at higher hazard levels for interface ones. 6. CFRP jacket was selected as the optimum retrofit option for providing slightly higher seismic resilience and taking the shortest duration to recover the full bent functionality. 113 6.3.4 Selection of the optimum retrofit option Considered retrofit options for the seismically deficient bent are ranked based on seismic performance, benefit-cost ratios, seismic resilience, and full functionality restoration periods, as shown in Table 6.1. The higher the rank is, the better the retrofit option is. Though the ECC jacket became the best retrofit option considering seismic performance, benefit-cost ratios, and seismic resilience, CFRP one was selected as optimum for requiring the least full functionality recovery duration. Table 6.1. Ranking of different retrofit options given seismic performance, benefit-cost ratios, seismic resilience, and full functionality recovery times Retrofit options Seismic performance Benefit-cost ratios Seismic resilience Full functionality recovery times CFRP 4 4 2 1 Steel 3 2 3 3 ECC 1 1 1 4 Concrete 2 3 4 2 6.4 Limitations of the Research Only one multi-column bent of specific geometric and material properties and axial loads was used in this research. Also, the mechanical properties of four retrofitting materials, e.g., CFRP, steel, ECC, and concrete jacketing were not varied. However, in reality, such properties and axial loads of a multi-column bent will vary. For example, the CFRP type utilized in the 114 study had a lower modulus of elasticity. This means that higher-grade CFRP use could notably affect the outcomes. This research identified an optimal retrofit solution based on the bridge seismic performances, benefit-cost ratios, seismic resilience, and full-functionality restoration times. It did not assess the time-variant vulnerability of the bridge given the deterioration effect and included interaction between different seismic hazards e.g. liquefaction and effects of mainshock-aftershock sequences. Moreover, it was not examined how climate change could affect seismic resilience, changing the seismic performance and functionality. 6.5 Recommendation for Future Works In the future, multi-column bents of various geometric and material properties and axial loads can be considered to study how these parameters affect performance-based damage states of retrofitted bents while considering the uncertainty in the mechanical properties of retrofitted materials. Furthermore, loading scenarios for multi-column bents are likely to vary and should be considered in future research. Future research should focus on identifying the optimal retrofit strategy through multi-criteria optimization techniques that consider bridge seismic performance, benefit-cost ratio, seismic resilience, and full-functionality recovery period. 115 BIBLIOGRAPHY Aghaeidoost, V., and A. H. M. M. Billah. 2023. “Life-cycle seismic resilience assessment of isolated bridges equipped with different isolation systems.” Struct. Infrastruct. Eng. 1-23. Alemdar, Z. F. 2010. “Plastic hinging behavior of reinforced concrete bridge columns.” Ph.D. thesis, Dept. of Civil, Environmental and Architectural Engineering, Univ. of Kansas. Apex Engineering Limited. 2018. Default values for benefit cost analysis in British Columbia. BC Ministry of Transportation and Infrastructure. Atkinson, G. M., and K. Goda. 2011. “Effects of seismicity models and new ground motion prediction equations on seismic hazard assessment for four Canadian cities.” Bull. Seismol. Soc. Am. 101 (1): 176–189.https://doi.org/10.1785/0120100093. Baker, J. W. 2005. Vector-valued ground motion intensity measures for probabilistic seismic demand analysis. Stanford, CA: Stanford Univ. Barbosa, A. R., F. L. A. Ribeiro, and L. A. C. Neves. 2017. “Influence of earthquake ground-motion duration on damage estimation: application to steel moment resisting frames.” Earthquake Eng. Struct. Dyn. 46 (1): 27-49. https://doi.org/10.1002/eqe.2769. BC Ministry of Transportation and Infrastructure. 2012. Construction and rehabilitation cost guide. BC Ministry of Transportation and Infrastructure. 2022. B.C. highway construction cost indexes. Benedetti, A., P. Fernandes, J. L. Granja, J. Sena-Cruz, and M. Azenha. 2016. “Influence of temperature on the curing of an epoxy adhesive and its influence on bond behaviour of NSM-CFRP systems.” Compos. Part B: Eng. 89: 219-229. Billah, A. H. M. M., and M. S. Alam. 2014. “Seismic performance evaluation of multi-column bridge bents retrofitted with different alternatives using incremental dynamic analysis.” Eng. Struct. 62-63: 105-117. http://dx.doi.org/10.1016/j.engstruct.2014.01.005. 116 Billah, A. H. M. M., M. S. Alam, and M. A. R. Bhuiyan. 2013. “Fragility analysis of retrofitted multicolumn bridge bent subjected to near-fault and far-field ground motion.” J. Bridge Eng. 18 (10): 992-1004. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000452. Bommer, J. J., and A. Martinex-Pereira. 1999. “The effective duration of earthquake strong motion.” J. Earthquake Eng. 3 (2): 127-172. https://doi.org/10.1080/13632469909350343. Brodbeck, T. J., Z. A. Shurow, R. Seracino, and M. J. Kowalski. 2024. “Impact of confinement on bar anchorage in relocated plastic hinges.” ACI Struct. J. 121 (3): 57-67. Bruneau, M., and A. M. Reinhorn. 2019. “Structural engineering dilemmas, resilient EPCOT, and other perspectives on the road to engineering resilience.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. 5 (3): 02519001. https://doi.org/10.1061/AJRUA6.0001011. Bruneau, M., S. E. Chang, R. T. Eguchi, G. C. Lee, T. D. O’Rourke, A. M. Reinhorn, M. Shinozuka, K. Tierney, A. W. 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. CESMD (Center for Engineering Strong Motion Data). n.d. “Strong motion data.” Accessed September 1, 2020. http://www.strongmotioncenter.org/. Chai, Y. H., M. J. N. Priestley, and F. Seible. 1991. “Seismic retrofit of circular bridge columns for enhanced flexural performance.” ACI Struct. J. 88 (5): 572-584. Chai, Y. H., M. J. N. Priestley, and F. Seible. 1994. “Analytical model for steel-jacketed RC circular bridge columns.” J. Struct. Eng. 120 (8): 2358-2376. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:8(2358). 117 ChienKuo, C., Y. Eiki, and D. Santoso. 2021. “Seismic resilience analysis of a retrofit-required bridge considering moment-based system reliability.” Struct. Infrastruct. Eng. 17 (6): 757-778. https://doi.org/10.1080/15732479.2020.1767658. Cho, H. N., H. H. Choi, K. M. Lee, and K. H. Park. 2007. “Optimal seismic retrofit and maintenance strategy for steel bridges using life-cycle cost analysis.” In Proc., Life-Cycle Cost and Performance of Civil Infrastructure Systems, edited by H. Cho, D. M. Frangopol, and A. H. Ang. London: Taylor and Francis Group. Ciampoli, M., and P. Giovenale. 2004. “Optimal intensity measures for the characterization of the ground motion in performance-based seismic design.” In Proc., Probabilistic Safety Assessment and Management, edited by C. Spitzer, U. Schmocker, and V. N. Dang, 2932–2937. London, UK: Springer. Coffman, H. L., M. L. Marsh, and C. B. Brown. 1993. “Seismic durability of retrofitted reinforced-concrete columns.” J. Struct. Eng. 119 (5): 1643-1661. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1643). Conte, J. P., H. Pandit, J. P. Stewart, and J. W. Wallace. 2003. “Ground motion intensity measures for performance-based earthquake engineering.” In Proc., 9th Int. Conf. on Applications of Statistics and Probability in Civil Engineering. Rotterdam, Netherlands: Millpress. CSA (Canadian Standards Association). 2019. Canadian highway bridge design code. CSA S6:19. Toronto, ON: CSA. Dagenais, M. A., B. Massicotte, and G. B. Proulx. 2018. “Seismic retrofitting of rectangular bridge piers with deficient lap splices using ultrahigh-performance fiber-reinforced concrete.” J. Bridge Eng. 23 (2): 04017129. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001173. 118 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. Dong, Y., and D. M. Frangopol. 2015. “Risk and resilience assessment of bridges under mainshock and aftershocks incorporating uncertainties.” Eng. Struct. 83: 198–208. https://doi.org/10.1016/j.engstruct.2014.10.050. Dong, Y., and D. M. Frangopol. 2016. “Probabilistic time-dependent multihazard life-cycle assessment and resilience of bridges considering climate change.” J. Performance Constructed Facilities 30 (5): 1–12. Dong, Y., D. M. Frangopol, and D. Saydam. 2013. “Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards.” Earthquake Eng. Struct. Dyn. 42 (10): 1451–1467. https://doi.org/10.1002/eqe.2281. Dong, H., R. Ma, Q. Han, and X. Du. 2024. “Seismic resilience of RC bridge with self-centering energy dissipation braces using SMA U-shaped plates.” Soil Dyn. Earthquake Eng. 181: 108632. https://doi.org/10.1016/j.soildyn.2024.108632. ElGawady, M., M. Endeshaw, D. McLean, and R. Sack. 2010. “Retrofitting of rectangular columns with deficient lap splices.” J. Compos. Constr. 14 (1): 22-35. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000047. Fahmy, M. F. M., Z. Wu, and G. Wu. 2009. “Seismic performance assessment of damage-controlled FRP-retrofitted RC bridge columns using residual deformations.” J. Compos Constr. 13 (6): 498-513. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000046. fib (Federation Internationale du Beton). 2001. Externally bonded FRP reinforcement for RC structures. fib Bulletin No. 14, 138. Lausanne, Switzerland: fib. 119 fib (Federation Internationale du Beton). 2006. Retrofitting of concrete structures by externally bonded FRPS, with emphasis on seismic applications. fib Bulletin No. 35, 220. Lausanne, Switzerland: fib. Fischer, G., and V. C. Li. 2003. “Deformation behavior of fiber-reinforced polymer reinforced engineered cementitious composite (ECC) flexural members under reversed cyclic loading conditions.” ACI Struct. J. 100 (1): 25-35. 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., Structures Congress, edited by D. Ames, T. L. Droessler, and M. Hoit, 2044–2055. Las Vegas, NV: ASCE (American Society of Civil Engineers). Frangopol, D. M., Y. Dong, and S. Sabatino. 2017. “Bridge life-cycle performance and cost: analysis, prediction, optimisation and decision-making.” Struct. Infrastruct. Eng. 13 (10): 1239–1257. Furuta H., K. Koyama, and M. Ohi. 2006. “Life-cycle cost analysis of bridge structures considering maintenance cost and seismic risk.” In Proc., Advances in Reliability and Optimization of Structural Systems, edited by J. D. Sorensen and D. M. Frangopol, 51–58. Taylor and Francis Group. Gencturk, B., and A. S. Elnashai. 2011. Multi-objective optimal seismic design of buildings using advanced engineering materials. Urbana, IL: Mid-America Earthquake Center. Ghaffarpasand, B., D. Samadian, M. R. Dehkordi, P. Bocchini, and M. Eghbali. 2023. “Investigation of different resilience-based optimisation strategies for retrofitting curved bridges.” Struct. Infrastruct. Eng. 1-15. https://doi.org/10.1080/15732479.2023.2165690. 120 Ghosh, J., and J. E. Padgett. 2011. “Probabilistic seismic loss assessment of aging bridges using a component-level cost estimation approach.” Earthquake Eng. Struct. Dyn. 40 (15): 1743-1761. https://doi.org/10.1002/eqe.1114. Giovenale, P., C. A. Cornell, and L. Esteva. 2004. “Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses.” Earthquake Eng. Struct. Dyn. 33 (8): 951-979. https://doi.org/10.1002/eqe.386. Han, T. S., P. H. Feenstra, and S. L. Billington. 2003. “Simulation of highly ductile fiber-reinforced cement-based composite components under cyclic loading.” ACI Struct. J. 100 (6): 749-757. Harris Rebar. n.d. Accessed January 1, 2023. www.harrisrebar.com. Hindi, R. A., and R. G. Sexsmith. 2001. “A proposed damage model for RC bridge columns under cyclic loading.” Earthquake Spectra. 17 (2): 261-290. https://doi.org/10.1193/1.1586175. Hong, Y., L. Ye, and W. Xie. 2023. “Seismic fragility and resilience improvement of conventional bridges supported by double-column piers utilizing shear links.” Structures 57: 105309. https://doi.org/10.1016/j.istruc.2023.105309. Hose, Y., P. Silva, and F. Seible. 2000. “Development of a performance evaluation database for concrete bridge components and systems under simulated seismic loads.” Earthquake Spectra. 16 (2): 413-442. https://doi.org/10.1193/1.1586119. Housner, G. 1952. “Spectrum intensities of strong motion earthquakes.” Symp. on Earthquake and Blast Effect on Structures, 20-36. Los Angeles. Iverson, J. K., C. Banchik, R. Brantley, and J. Sage. 1999. “Precast segmental seismic retrofit for the San Mateo Hayward Bridge.” PCI J. 44 (6): 28-40. https://doi.org/10.15554/pcij.11011999.28.40. 121 Jean, M., C. St-Martin, N. Roy, P. Rivard, Z. Moradian, E. C. Jr, and J. Proulx. 2012. “Limit states of reinforced concrete bridge piers confined with carbon fiber reinforced polymer (CFRP).” In Proc., 15th World Conf. Earthquake Engineering. Red Hook, NY: Curran Associates, Inc. Jeon, J.-S., R. DesRoches, and D. H. Lee. 2016. “Post-repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes.” Earthquake Eng. Struct. Dyn. 45 (7): 1149-1168. https://doi.org/10.1002/eqe.2700. Kawashima, K., G. A. MacRae, J. Hoshikuma, and K. Nagaya. 1998. “Residual displacement response spectrum.” J. Struct. Eng. 124 (5): 523-530. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:5(523). Kennedy, D., K. Habel, and G. Fraser. 2015. “Ultra high-performance concrete column jacket retrofit for the mission bridge.” In Proc., 11th Can. Conf. Earthquake Engineering. Victoria, BC: Canadian Association for Earthquake Engineering. Khosravikia, F., and P. Clayton. 2020. “Updated evaluation metrics for optimal intensity measure selection in probabilistic seismic demand models.” Eng. Struct. 202: 109899. https://doi.org/10.1016/j.engstruct.2019.109899. Kohrangi, M., P. Bazzurro, and D. Vamvatsikos. 2016. “Vector and scalar IMs in structural response estimation, part I: Hazard analysis.” Earthquake Spectra 32 (3): 1507–1524. https://doi.org/10.1193/053115EQS080M. Kriger, D., A. Rose, E. Baydar, J. Moore, L. Frank, J. Chapman, and A. Pisarki. 2015. Urban transportation indicators fifth survey. Ottawa, ON: Transportation Association of Canada. 122 Kumar, P. R., T. Oshima, S. Mikami, and T. Yamazaki. 2005. “Seismic retrofit of square reinforced concrete piers by ferrocement jacketing.” Struct. Infrastruct. Eng. 1 (4): 253–262. https://doi.org/10.1080/15732470500031065. Kunnath, S. K., A. El-Bahy, A. W. Taylor, and W. C. Stone. 1997. Cumulative seismic damage of reinforced concrete bridge piers. Gaithersburg: National Institute of Standards and Technology. Lehman, D., J. Moehle, S. Mahin, A. Calderone, and L. Henry. 2004. “Experimental evaluation of the seismic performance of reinforced concrete bridge columns.” J. Struct. Eng. 130 (6): 869-879. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(869). Li, V. C., H. Horri, P. Kabele, T. Kanda, and Y. M. Lin. 2000. “Repair and retrofit using engineered cementitous composites.” Eng. Fract. Mech. 65 (2-3): 317-334. Li, Y., Z. Sun, Y. Li, J. Dong, and W. He. 2024. “Time-dependent combined index seismic resilience assessment of shear-critical RC bridge piers with height-varying corrosion.” Eng. Struct. 308: 117957. https://doi.org/10.1016/j.engstruct.2024.117957. Luco, N., and C. A. Cornell. 2007. “Structure-specific scalar intensity measures for near source and ordinary earthquake ground motions.” Earthquake Spectra 23 (2): 357–392. https://doi.org/10.1193/1.2723158. Mackie, K. R., and B. Stojadinovic. 2007. “Performance-based seismic bridge design for damage and loss limit states.” Earthquake Eng. Struct. Dyn. 36 (13): 1953-1971. https://doi.org/10.1002/eqe.699. Mander, J. B. 1999. Fragility curve development for assessing the seismic vulnerability of highway bridges. New York: Univ. at Buffalo, State Univ. of New York. 123 Mander, J., and C-T Cheng. 1995. “Renewable hinge detailing for bridge columns.” In vol. 187 of Proc., Pacific conf. on earthquake engineering, 197–206. Melbourne. Mander, J. B., M. J. N. Priestley, and R. Park. 1988. “Theoretical stress-strain model for confined concrete.” J. Struct. Eng. 114 (8): 1804-1826. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804). Marsh, M. L., and S. J. Stringer. 2013. Performance-based seismic bridge design, a synthesis of highway practice. Washington, DC: National Academies Press. MATLAB. 2023. MATLAB. Natick, MA: The MathWorks, Inc. McEntee, V., B. Kunwar, C. P. Pantelides, and T. Alkhradji. 2021. “Flexural strengthening of substandard reinforced concrete bridge wall piers with CFRP systems under cyclic loads.” J. Compos. Constr. 25 (3): 04021010. https://doi.org/10.1061/(ASCE)CC.1943-5614.0001120. Menegetto, M., and P. E. Pinto. 1973. “Method of analysis for cyclically loaded R.C. plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” In Proc., Symp. on the Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, 15-22. Zurich, Switzerland: International Association for Bridge and Structural Engineering. Miano, A., F. Jalayer, R. De Risi, A. Prota, and G. Manfredi. 2016. “Model updating and seismic loss assessment for a portfolio of bridges.” Bull. Earthquake Eng. 14: 699-719. https://doi.org/10.1007/s10518-015-9850-y. Minaie, E., and F. Moon. 2017. “Practical and simplified approach for quantifying bridge resilience.” J. Infrastruct. Syst. 23 (4): 04017016. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000374. 124 Mohammed, M. S. 2016. Effect of earthquake duration on reinforced concrete columns. Reno: University of Nevada. Mottier, P., R. Tremblay, and C. Rogers. 2021. “Shake table test of a two-story steel building seismically retrofitted using gravity-controlled rocking braced frame system.” Earthquake Eng. Struct. Dyn. 50 (6): 1576–1594. https://doi.org/10.1002/eqe.3411. NIED (National Research Institute for Earth Science and Disaster Resilience). 2019. “NIED K-NET, KiK-net.” Accessed September 1, 2020. https://www.doi.org/10.17598/NIED.0004. Nielson, B. G. 2005. Analytical fragility curves for highway bridges in moderate seismic zones. Atlanta, GA: Georgia Institute of Technology. Omidian, P., N. Khaji, and A. A. Aghakouchak. 2024. “Seismic time-dependent resilience assessment of aging highway bridges incorporating the effect of retrofitting.” Structures 63: 106347. https://doi.org/10.1016/j.istruc.2024.106347. Padgett, J. E., B. G. Nielson, and R. DesRoches. 2008. “Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios.” Earthquake Eng. Struct. Dyn. 37 (5): 711–725. https://doi.org/10.1002/eqe.782. Padgett, J. E., K. Dennemann, and J. Ghosh. 2010. “Risk-based seismic life-cycle cost–benefit (LCC-B) analysis for bridge retrofit assessment.” Struct. Safety 32 (3): 165–173. Pan, Y., C. E. Ventura, and W. D. L. Finn. 2018. “Effects of ground motion duration on the seismic performance and collapse rate of light-frame wood houses.” J. Struct. Eng. 144 (8): 04018112. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002104. Pang, Y., K. Wei, and W. Yuan. 2020. “Life-cycle seismic resilience assessment of highway bridges with fiber-reinforced concrete piers in the corrosive environment.” Eng. Struct. 222: 111120. https://doi.org/10.1016/j.engstruct.2020.111120. 125 Pang, Y., and X. Wang. 2021. “Cloud-IDA-MSA conversion of fragility curves for efficient and high-fidelity resilience assessment.” J. Struct. Eng. 147 (5): 04021049. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002998. Pantelides, C. P., and L. Gergely. 2002. “Carbon-fiber-reinforced polymer seismic retrofit of RC bridge bent: Design and in situ validation.” J. Compos. Constr. 6 (1): 52-60. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:1(52). Parghi, A., and M. S. Alam. 2017. “Seismic collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP composites.” Compos. Struct. 160: 901–916. http://dx.doi.org/10.1016/j.compstruct.2016.10.094. Park, Y. J., and A. H. S. Ang. 1985. “Mechanistic seismic damage model for reinforced concrete.” J. Struct. Eng. 111 (4): 722–739. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(722). PEER (Pacific Earthquake Engineering Research Center). 2013. “PEER ground motion database.” Accessed September 1, 2020. https://ngawest2.berkeley.edu/. Perdomo, C., and R. Monteiro. 2021. “Extension of displacement-based simplified procedures to the seismic loss assessment of multi-span RC bridges.” Earthquake Eng. Struct. Dyn. 50 (4): 1101-1124. https://doi.org/10.1002/eqe.3389. Priestley, M. J. N., F. Seible, Y. Xiao, and R. Verma. 1994. “Steel jacket retrofitting of reinforced concrete bridge columns for enhanced shear strength-part 2: Test results and comparison with theory.” ACI Struct. J. 91 (5): 537-551. Priestley, M. J. N., F. Seible, and G. M. Calvi. 1996. Seismic design and retrofit of bridges. New York: Wiley. Priestley, M. J. N., G. M. Calvi, and M. J. Kowalski. 2007. Displacement-based seismic design of structures. Pavia: IUSS Press. 126 Pulido, C., M. S. Saiidi, D. Sanders, A. Itani, and S. El-Azazy. 2004. “Seismic performance of two-column bents-Part II: Retrofit with infill walls.” ACI Struct. J. 101 (5): 642–649. Qian, J., Y. Zheng, Y. Dong, H. Wu, H. Guo, and J. Zhang. 2022. “Sustainability and resilience of steel – shape memory alloy reinforced concrete bridge under compound earthquakes and functional deterioration within entire life-cycle.” Eng. Struct. 271: 114937. https://doi.org/10.1016/j.engstruct.2022.114937. Rodriguez, M., and R. Park. 1994. “Seismic load tests on reinforced concrete columns strengthened by jacketing.” ACI Struct. J. 91 (2): 150-159. Roy, N., P. Paultre, and J. Proulx. 2010. “Performance-based seismic retrofit of a bridge bent: Design and experimental validation.” Can. J. Civ. Eng. 37 (3): 367–379. https://doi.org/10.1139/L09-138. Saiidi, M. S., F. Martinovic, B. McElhaney, D. Sanders, and F. Gordaninejad. 2004. “Assessment of steel and fiber reinforced plastic jackets for seismic retrofit of reinforced concrete columns with structural flares.” J. Struct. Eng. 130 (4): 609-617. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(609). Sakrete Canada. n.d. Accessed January 1, 2023. www.sakretecanada.com. Sato, T., I. Yoshida, and M. Masumoto. 2004. “Prioritization of seismic reinforcement for road bridges based on the concept of life-cycle cost.” In Proc., Life-Cycle Performance of Deteriorating Structures, edited by D. M. Frangopol, E. Bruhwiler, M. H. Faber, and B. Adey, 219–227. ASCE (American Society of Civil Engineers). Seible, F., M. J. N. Priestley, G. A. Hegemier, and D. Innamorato. 1997. “Seismic retrofit of RC columns with continuous carbon fiber jackets.” J. Compos. Constr. 1 (2): 52-62. https://doi.org/10.1061/(ASCE)1090-0268(1997)1:2(52). 127 SeismoMatch. 2020. SeismoMatch. Pavia, Italy: Seismosoft. SeismoSignal. 2021. SeismoSignal. Pavia, Italy: Seismosoft. SeismoStruct. 2020. SeismoStruct. Pavia, Italy: Seismosoft. Shome, N. 1999. Probabilistic seismic demand analysis of nonlinear structures. Stanford, CA: Stanford Univ. Sika Canada Inc. n.d. Accessed January 1, 2023. www.sika.ca. Stefanidou, S. P., and A. J. Kappos. 2021. “Fragility-informed selection of bridge retrofit scheme based on performance criteria.” Eng. Struct. 234: 111976. https://doi.org/10.1016/j.engstruct.2021.111976. Stein, S. M., G. K. Young, R. E. Trent, and D. R. Pearson. 1999.“Prioritizing scour vulnerable bridges using risk.” J. Infrastruct. Sys. 5 (3): 95–101. Suarjana, M., D. D. Octora, and M. Riyansyah. 2020. “Seismic performance of RC hollow rectangular bridge piers retrofitted by concrete jacketing considering the initial load and interface slip.” J. Eng. Technol. Sci. 52 (3): 343-369. https://doi.org/10.5614/j.eng.technol.sci.2020.52.3.4. Todorov, B., and A. H. M. M. Billah. 2021. “Seismic fragility and damage assessment of reinforced concrete bridge pier under long-duration, near-fault, and far-field ground motions.” Structures 31: 671–685. https://doi.org/10.1016/j.istruc.2021.02.019. Tong, T., S. Yuan, W. Zhuo, Z. He, and Z. Liu. 2019. “Seismic retrofitting of rectangular bridge piers using ultra-high performance fiber reinforced concrete jackets.” Compos. Struct. 228: 111367. https://doi.org/10.1016/j.compstruct.2019.111367. 128 Upadhyay, A., C. P. Pantelides, and L. Ibarra. 2019. “Residual drift mitigation for bridges retrofitted with buckling restrained braces or self centering energy dissipation devices.” Eng. Struct. 199: 109663. https://doi.org/10.1016/j.engstruct.2019.109663. Vamvatsikos, D., and C. A. Cornell. 2002. “Incremental dynamic analysis.” Earthquake Eng. Struct. Dyn. 31 (3): 491–514. https://doi.org/10.1002/eqe.141. Vandoros, K. G., and S. E. Dritsos. 2008. “Concrete jacket construction detail effectiveness when strengthening RC columns.” Constr. Build. Mater. 22 (3): 264-276. https://doi.org/10.1016/j.conbuildmat.2006.08.019. Venkittaraman, A., and S. Banerjee. 2014. “Enhancing resilience of highway bridges through seismic retrofit.” Earthquake Eng. Struct. Dyn. 43 (8): 1173-1191. https://doi.org/10.1002/eqe.2392. Wei, B., J. Jia, Y. Bai, X. Du, B. Guo, and H. Guo. 2023. “Seismic resilience assessment of bridges considering both maximum and residual displacements.” Eng. Struct. 291: 116420. https://doi.org/10.1016/j.engstruct.2023.116420. WSP Canada Group Limited. 2019. Traffic reports user documentation. BC Ministry of Transportation and Infrastructure. Xiang, N., and M. S. Alam. 2019. “Displacement-based seismic design of bridge bents retrofitted with various bracing devices and their seismic fragility assessment under near-fault and far-field ground motions.” Soil Dyn. Earthquake Eng. 119: 75–90. https://doi.org/10.1016/j.soildyn.2018.12.023. Xiang, N., X. Chen, and M. S. Alam. 2020. “Probabilistic seismic fragility and loss analysis of concrete bridge piers with superelastic shape memory alloy-steel coupled reinforcing bars.” Eng. Struct. 207: 110229. https://doi.org/10.1016/j.engstruct.2020.110229. 129 Xiao, Y., and H. Wu. 2003. “Retrofit of reinforced concrete columns using partially stiffened steel jackets.” J. Struct. Eng. 129 (6): 725-732. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:6(725). XYZ Engineering. 2020. Traffic management plan Highway 19 Lantzville median gate. Zarifian, A., R. A. I. Fard, and A. Khalighi. 2020. “Experimental study on the behavior of thermally insulated RC beams strengthened with CFRP after their exposure to high temperatures compared to non-insulated ones.” Can. J. Civ. Eng. 47 (7): 875–883. http://dx.doi.org/10.1139/cjce-2019-0001. Zhang, R., Q. Meng, Q. Shui, W. He, K. Chen, M. Liang, and Z. Sun. 2019. “Cyclic response of RC composite bridge columns with precast PP-ECC jackets in the region of plastic hinges.” Compos. Struct. 221: 110844. https://doi.org/10.1016/j.compstruct.2019.04.016. Zhang, R., R. Zhao, Z. Liu, K. Chen, P. Hu, and Z. Liu. 2022. “Cyclic behavior of existing flexure-dominated RC bridge columns retrofitted by ECC jackets in the region of plastic hinge.” Eng. Struct. 269: 114820. https://doi.org/10.1016/j.engstruct.2022.114820. Zheng, Y., Y. Dong, and Y. Li. 2018. “Resilience and life-cycle performance of smart bridges with shape memory alloy (SMA)-cable-based bearings.” Constr. Build. Mater. 158: 389–400. https://doi.org/10.1016/j.conbuildmat.2017.10.031. Zhou, J., J. Pan, and C. K. Y. Leung. 2015. “Mechanical behavior of fiber-reinforced engineered cementitious composites in uniaxial compression.” J. Mater. Civ. Eng. 27 (1): 04014111. Zhou, Y., X. Wang, B. Hu, Lili Sui, and F. Yuan. 2023. “Seismic retrofit of nonuniformly corroded coastal bridge piers with FRP and engineered cementitious composite overlays.” J. Compos. Constr. 27 (1): 04022088. https://doi.org/10.1061/JCCOF2.CCENG-3993.
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Billah, A.H.M. Muntasir
Performance-based seismic design for retrofitting of bridge bents
Text
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