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Seismic performance evaluation of circular reinforced concrete bridge piers retrofitted with fibre reinforced… Parghi, Anantray M. 2016

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SEISMIC PERFORMANCE EVALUATION OF CIRCULAR REINFORCED CONCRETE BRIDGE PIERS RETROFITTED WITH FIBRE REINFORCED POLYMER   by  Anantray M. Parghi  B.Eng. (Civil Engineering), Saurashtra University, 2004 M.Tech. (Structural Engineering), S.V. National Institute of Technology, 2006  A THESIS 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)  August 2016  © Anantray M. Parghi, 2016 The undersigned certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled:    Seismic Performance Evaluation of Circular Reinforced Concrete Bridge Piers Retrofitted with Fibre Reinforced Polymer submitted by Anantray M. Parghi in partial fulfilment of the requirements of the degree of Doctor of Philosophy in Civil Engineering.    Dr. M. Shahria Alam, Associate Professor, School of Engineering  Supervisor, Professor   Dr. Dwayne Tannant, Professor, School of Engineering   Supervisory Committee Member, Professor    Dr. Ahmad Rteil, Assistant Professor, School of Engineering  Supervisory Committee Member, Professor    Dr. Thomas Johnson, Associate Professor, School of Engineering University Examiner, Professor   Dr. Ahmed El Refai, Associate Professor, Laval University  External Examiner, Professor   June 10th, 2016  (Date Submitted to Grad Studies)  Additional Committee Members include:   Dr. Lukas Bichler, Associate Professor, School of Engineering  Neutral Chair       ii Abstract A large number of researchers around the globe are currently conducting investigations on the use of fibre-reinforced polymer (FRP) for strengthening of reinforced concrete (RC) bridge piers. It has been observed that such strengthening technique can be a cost-effective method for restoring and increasing the strength and ductility of piers damaged during catastrophic events, like earthquakes. Material properties, amount of longitudinal and transverse steel, external confinement, axial load and shear span-depth ratio affect the lateral load capacity, ductility and failure mode of retrofitted bridge piers under seismic load. These parameters are considerably different in the pre-1970 code designed RC bridge piers compared to the current seismically designed bridges.         This research investigates the effect of different factors and their interactions on the limit states of FRP-confined seismically deficient RC circular bridge piers using factorial design method.  Nonlinear static pushover analyses of the non-seismically designed FRP retrofitted circular bridge piers are conducted in order to determine the sequence of different limit states such as yielding of reinforcement, and concrete crushing along with ductility capacity of the piers. In addition, nonlinear reverse cyclic, and dynamic time-history analyses are carried out in order to determine the lateral load carrying capacity, flexural ductility, and hysteretic behavior of such retrofitted piers. Fragility curves are developed for the FRP retrofitted RC bridge piers considering different limit states of displacement ductility as the demand parameter. The incremental dynamic analysis is conducted by considering 20 ground motion records to investigate the nonlinear dynamic behavior of the retrofitted piers. The fragility curves are described using lognormal distribution functions with two parameters developed as a function of peak ground acceleration. The impact of various parameters is evaluated on the bridge pier fragility curve based on the theory of probability. This study shows that the shear span-depth ratio, the yield strength of reinforcement, longitudinal reinforcement ratio, axial load and FRP confinement significantly affect the lateral load capacity, ductility and the failure mode of the retrofitted bridge piers under seismic load.   iii Preface   A portion of Chapter 2 is accepted in CINPAR 2016-International Conference on Structural Repair and Rehabilitation, 26-29 October-2016, Porto, Portugal. Anant Parghi, and M. Shahria Alam. Seismic repair and retrofit of reinforced concrete bridge columns: Review of research outcomes. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 2 will be submitted to the journal, Construction and Building Materials, 2016, Elsevier. Anant Parghi, and M. Shahria Alam. Seismic repair and retrofit of reinforced concrete bridge piers: Review of research finding. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 2 has been published in Conference Proceedings, CSCE May 27-30, 2015 Regina, SK, Canada. Anant Parghi, and M. Shahria Alam. Stress-strain behavior model of FRP-confined concrete: A state of the art review. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 2 will be submitted to the journal, Structures, 2016, Elsevier. Anant Parghi, and M. Shahria Alam. Stress-strain behavior model of FRP-confined concrete: A review. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 3 has been accepted in the journal, Engineering Structures. 2016, Elsevier. Anant Parghi, and M. Shahria Alam. Seismic behavior of deficient reinforced concrete bridge piers confined with FRP- a factorial analysis. I wrote the manuscript which was further edited by M. Shahria Alam  A portion of Chapter 3 has been submitted to the 11th International Conference on Earthquake Resistant Engineering Structures (ERES 2017). Anant Parghi, and M. Shahria Alam. Seismic behavior of non-seismically designed circular RC bridge piers retrofitted with FRP. I wrote the manuscript which was further edited by M. Shahria Alam.   A portion of Chapter 4 has been published in Conference Proceedings, CSCE May 27-30, 2015 Regina, SK, Canada. Anant Parghi, and M. Shahria Alam. Analysis of circular RC bridge piers retrofitted with the fibre-reinforced polymer under axial and  iv lateral cyclic load. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 4 has been submitted to Jjournal, Bulleting of Earthquake Engineering, August 8, 2016, Manuscript no. BEEE-S-16-00382. Springer. Anant Parghi, and M. Shahria Alam. Analysis of circular RC bridge piers retrofitted with the fibre-reinforced polymer under axial and lateral cyclic load. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 6 is accepted in CINPAR 2016 - International Conference on Structural Repair and Rehabilitation, 26-29 October-2016, Porto, Portugal. Anant Parghi, and M. Shahria Alam. Fragility analysis of deficient RC bridge columns retrofitted with FRP composites. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 6 has been prepared for the journal, Composite Structures, 2016, Elsevier. Anant Parghi, and M. Shahria Alam. Seismic collapse assessment of deficient RC bridge piers retrofitted with FRP composites. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 7 has been submitted to STRUCTURES CONGRESS 2017, 6-8 April-2017, Denver, Colorado. Anant Parghi, and M. Shahria Alam. Fragility analysis of deficient RC bridge piers retrofitted with FRP composites. I wrote the manuscript which was further edited by M. Shahria Alam.  A portion of Chapter 7 has been prepared for the journal, Composite Structures, Elsevier, 2016. Anant Parghi, and M. Shahria Alam. Fragility analysis of deficient RC bridge piers retrofitted with FRP composites. I wrote the manuscript which was further edited by M. Shahria Alam.    v Table of Contents  Thesis Committee …………………………………………………………………………...ii Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iii Table of Contents .................................................................................................................... v List of Tables .......................................................................................................................... xi List of Figures ....................................................................................................................... xiii List of Symbols, Abbreviations ............................................................................................ xx Acknowledgements ............................................................................................................. xxv Dedications......................................................................................................................... xxvii Chapter 1: Introduction and Thesis Organization ........................................................ 28 1.1 General ................................................................................................................................ 28 1.2 Research Background ......................................................................................................... 29 1.3 Problem Description ........................................................................................................... 30 1.4 Scope and Objectives of the Research ................................................................................ 31 1.5 Methodology of the Thesis ................................................................................................. 31 1.6 Thesis Organization ............................................................................................................ 33 Chapter 2: Literature Review ......................................................................................... 35 2.1 General ................................................................................................................................ 35 2.2 Old Seismic Design Criteria of Bridge Piers ...................................................................... 35 2.3 Performance of RC Bridge Piers in Past Earthquake .......................................................... 36 2.4 Seismic Retrofitting Techniques for Reinforced Concrete Piers ........................................ 37 2.4.1 Active confinement techniques ....................................................................................... 38 2.4.1.1 External prestressing strands ................................................................................. 38 2.4.1.2 Shape memory alloys (SMAs) spirals ................................................................... 39 2.4.2 Passive confinement technique ....................................................................................... 40 2.4.2.1 Concrete jacketing ................................................................................................. 40 2.4.2.2 Steel jacketing........................................................................................................ 41  vi 2.4.2.3 Engineered cementitious composite jacketing ....................................................... 43 2.4.2.4 Ferrocement jacketing ........................................................................................... 44 2.4.2.5 Fibre-reinforced polymer jacketing ....................................................................... 45 2.5 Fibre Reinforced Polymer Constituents .............................................................................. 45 2.5.1 FRP materials ................................................................................................................. 45 2.5.2 Application of FRP as confining materials ..................................................................... 46 2.6 Models of FRP-confined Concrete under Axial Compression............................................ 48 2.6.1 Mechanism of FRP confinement .................................................................................... 49 2.6.2 Constitutive stress-strain response of FRP-confined concrete........................................ 51 2.7 Axial Stress-Strain Models for FRP-Confined Concrete .................................................... 52 2.7.1 Design oriented stress-strain models (DOMs) ................................................................ 54 2.7.2 Analysis-oriented stress-strain models (AOMs) ............................................................. 58 2.7.3 Axial stress-strain curves based on active confinement models ..................................... 59 2.7.4 Peak axial stress equation for actively confined concrete .............................................. 61 2.7.5 Peak axial strain equation for actively confined concrete .............................................. 62 2.8 Experimental Test of FRP-Retrofitted RC Piers ................................................................. 63 2.9 Summary ............................................................................................................................. 63 Chapter 3: Finite Element Modeling of Non-Seismically Designed Circular RC Bridge Pier Retrofitted with FRP ........................................................................................ 65 3.1 General ................................................................................................................................ 65 3.2 Numerical Investigation of Bridge Piers ............................................................................. 65 3.2.1 Description of bridge pier model .................................................................................... 65 3.2.2 Finite element modeling of bridge piers ......................................................................... 67 3.2.2.1 Material constitutive relationship .......................................................................... 68 3.2.2.2 Constitutive models of concrete ............................................................................ 69 3.2.2.3 Constitutive model of steel reinforcement ............................................................. 72 3.2.2.4 Constitutive model of FRP reinforcement ............................................................. 73 3.3 Nonlinear reverse cyclic analyses ....................................................................................... 75 3.3.1 Loading protocol ............................................................................................................. 75 3.4 Numerical Model Validation .............................................................................................. 76 3.5 Summary ............................................................................................................................. 77   vii Chapter 4: Pushover Response of Non-Seismically Designed Circular RC Bridge Pier Retrofitted with FRP using Fractional Factorial Design – A Parametric Study ............ 78 4.1 General ................................................................................................................................ 78 4.2 Factor Affecting First Yielding of Longitudinal Rebar ...................................................... 79 4.3 Factors Affecting First Crushing of Concrete Core ............................................................ 80 4.4 Factors Affecting Buckling and Fracture of Rebar ............................................................. 83 4.5 Fractional Factorial Analyses for Different Propertied of Piers ......................................... 84 4.6 Flexural Limit States ........................................................................................................... 85 4.7 ANOVA Results for Fractional Factorial Design ............................................................... 86 4.8 Effect of Different Factors at First Yielding ....................................................................... 88 4.9 Effect of Different Factors at First Crushing ...................................................................... 92 4.10 Effect of Different Factors at First Buckling ...................................................................... 95 4.11 Effect of Different Factors at First Crushing ...................................................................... 97 4.12 Effect of Different Factors on Displacement Ductility ....................................................... 99 4.13 Summary ........................................................................................................................... 100 Chapter 5: Seismic Behavior of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP – A Parametric Study .................................................................... 101 5.1 General .............................................................................................................................. 101 5.2 Parametric Investigation of Piers ...................................................................................... 101 5.2.1 Nonlinear static pushover analysis (NSPA).................................................................. 102 5.3 Pushover Response of FRP Retrofitted Piers .................................................................... 103 5.3.1.1 Moment-curvature response ................................................................................ 104 5.3.1.2 Ductility capacity ................................................................................................. 106 5.3.1.3 Hysteretic response of retrofitted piers under cyclic load ................................... 107 5.3.1.4 Stress-strain response of rebar of the CFRP/GFRP retrofitted piers ................... 110 5.3.2 Nonlinear dynamic analyses of retrofitted RC piers ..................................................... 113 5.3.2.1 Ground motion database ...................................................................................... 113 5.3.3 Seismic response of the retrofitted piers ....................................................................... 115 5.3.3.1 Base shear ............................................................................................................ 115 5.3.3.2 Residual displacement ......................................................................................... 117 5.3.3.3 Stiffness ............................................................................................................... 118 5.4 Summary ........................................................................................................................... 120  viii Chapter 6: Seismic Collapse Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP .................................................................................... 121 6.1 General .............................................................................................................................. 121 6.2 Design of Bridge Piers ...................................................................................................... 121 6.3 Nonlinear Static Pushover Analysis and the Flexural Limit States .................................. 123 6.4 Incremental Dynamic Analysis of Pier ............................................................................. 129 6.4.1 Selection of ground motions ......................................................................................... 129 6.4.2 Incremental dynamic analysis for pier collapse capacity ............................................. 131 6.4.2.1 Dynamic pushover curve ..................................................................................... 131 6.4.2.2 Incremental dynamic analysis curve .................................................................... 136 6.5 Collapse Fragility Assessment .......................................................................................... 139 6.5.1 Effect of compressive strength of concrete on collapse fragility curve ........................ 143 6.5.2 Effect of yield strength of steel reinforcement on collapse fragility ............................ 144 6.5.3 Effect of amount of longitudinal reinforcement on collapse fragility .......................... 145 6.5.4 Effect of axial load on collapse fragility ....................................................................... 146 6.5.5 Effect of shear span-depth ratio on collapse fragility ................................................... 147 6.5.6 Effect of confinement on collapse fragility .................................................................. 148 6.5.7 Median peak ground acceleration ................................................................................. 150 6.5.8 Performance evaluation of bridge piers ........................................................................ 152 6.6 Summary ........................................................................................................................... 153 Chapter 7: Fragility Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP Using Full Factorial Design Method................................... 155 7.1 General .............................................................................................................................. 155 7.2 Fragility Function Methodology ....................................................................................... 155 7.3 Seismic Hazard for Vancouver and Selection of Ground Motion .................................... 160 7.4 Fragility Assessment of Retrofitted Bridge Piers .............................................................. 165 7.4.1 Factorial experimental design ....................................................................................... 165 7.4.2 Geometry of bridge piers .............................................................................................. 166 7.4.3 Representations of damage/limit states......................................................................... 168 7.4.4 Probabilistic seismic demand models ........................................................................... 175 7.4.5 Displacement ductility .................................................................................................. 175 7.5 Comparison of Fragility Results ....................................................................................... 180 7.5.1 Effect of strength concretes on the fragility curve ........................................................ 180  ix 7.5.2 Effect of yield strength of reinforcement on the fragility curve ................................... 182 7.5.3 Effect of longitudinal reinforcement ratio on the fragility curve .................................. 183 7.5.4 Effect of axial load ratio on the fragility curve ............................................................. 184 7.5.5 Effect of shear span-depth ratio on the fragility curve ................................................. 185 7.5.6 Effect of strength of FRP confinement on the fragility curve ...................................... 186 7.5.7 Median values of peak ground acceleration ................................................................. 188 7.6 Seismic Demand Hazard of FRP Retrofitted Bridge Piers ............................................... 189 7.7 Summary ........................................................................................................................... 190 Chapter 8: Summary, Conclusions, and Future Works ............................................. 192 8.1 General .............................................................................................................................. 192 8.2 Core Contributions ............................................................................................................ 192 8.3 Conclusions ....................................................................................................................... 193 8.3.1 Repair and retrofitting of earthquake damaged RC circular bridge piers, and constitutive              models of FRP-confined concrete ................................................................................. 193 8.3.2 Finite element modeling of non-seismically designed circular RC bridge piers retrofitted              with FRP ....................................................................................................................... 194 8.3.3 Pushover response of non-seismically designed circular RC bridge piers retrofitted with              FRP using fractional factorial design – A parametric study ......................................... 195 8.3.4 Sesicmic behavior of non-seismically designed circular RC bridge piers retrofitted with              FRP – A parametric study ............................................................................................. 196 8.3.5 Seismic behavior of collapse assessment of non-seismically designed circular RC bridge              piers retrofitted with FRP ............................................................................................. 197 8.3.6 Fragility assessment of non-seismically designed circular RC bridge piers retrofitted              with FRP through full factorial design ......................................................................... 199 8.4 Recommendation for Future Works .................................................................................. 201 References ............................................................................................................................ 203 Appendices ........................................................................................................................... 233 Appendix A Performance of Bridge Piers in the Past Earthquakes ................................................. 233 A.1 The San Fernando Earthquake, USA, 1971 ....................................................................................... 233 A.2 The Loma Prieta Earthquake, USA, 1989 ......................................................................................... 233 A.3 The Northridge Earthquake, USA, 1994 ........................................................................................... 234 A.4 Kobe Earthquake, Japan, 1995 .......................................................................................................... 235 A.5 Chi-Chi Earthquake, Taiwan, 1999 ................................................................................................... 236  x A.6 Kocaeli and Duzce Earthquakes, Turkey, 1999 ................................................................................. 237 A.7 Niigata-Keb Chuetsu Earthquake, Japan, 2004 ................................................................................. 237 A.8 Chile Earthquake, Chile, 2010 ........................................................................................................... 238 Appendix B Stress-Strain Model of FRP-Confined Concrete ......................................................... 240 Appendix C Experimental Test of FRP Retrofitted Piers ................................................................ 264 Appendix D Design Guidelines of FRP Retrofitting System .......................................................... 273 D.1 ACI Committee 440.2R-2008 ............................................................................................................ 277 D.2 CAN/CSA-S806-14 ........................................................................................................................... 278 D.3 Curvature-Based Approach ............................................................................................................... 279 D.4 Drift-Based Approach........................................................................................................................ 280 D.5 Concrete Society Technical Report No. 55 2004 ............................................................................... 281 D.6 Technical Report by the Federation International Du Beton (fib Bulletin 14) 2001 ......................... 282 D.7 CNR-DR 2000 R1/2013 .................................................................................................................... 284 Appendix E Fractional Factorial Design, Acceleration Time Histories, and Failure Drift .............. 286 E.1 Fractional Factorial Design for Pushover Analysis ........................................................................... 286 E.2 Acceleration Time Histories of EQ. 1-20 .......................................................................................... 287 E.3 Failure Drift of Piers Based on IDA Curve ....................................................................................... 290 Appendix F Full Factorial Design, IDA Results, PSDMs, Fragility and Hazard Analyses Results 291 F.1 Full Factorial Design for Incremental Dynamic Analysis ................................................................. 291 F.2 IDA Results of Pier 1-64 ................................................................................................................... 292 F.3 PSDMs of Pier 2-63 using Regression Ananysis ............................................................................... 303 F.4 Fragility Curve of Pier 1 to 64 ........................................................................................................... 314 F.5 Hazard Analysis Results of Pier 2 to 63 ............................................................................................ 325   xi List of Tables  Table 3.1 Material properties used in the numerical model .................................................... 67 Table 3.2 Parameters used in Mander et al. (1988a) model in  SeismoStruct (2015) ............ 71 Table 3.3 Parameters used in Menegotto and Pinto (1973)  model in SeismoStruct         (2015) ................................................................................................................... 73 Table 3.4 CFRP  material properties used in the numerical model                           (Kawashima et al. 2000) ...................................................................................... 76 Table 4.1 Levels of the factors considered for the nonlinear static pushover analyses .......... 78 Table 4.2 P-values from ANOVA of nonlinear static pushover analyses of drift results ....... 87 Table 4.3 P-values from ANOVA of nonlinear static pushover analyses of base shear     results ................................................................................................................... 88 Table 5.1 Properties of CFRP (Kawashima et al. 2000) and GFRP (Shin 2012) used in the four case studies ................................................................................................. 101 Table 5.2 Characteristics of the selected ten-ground motion records used in this study ...... 114 Table 6.1 Details of variable parameters considered in this study ....................................... 123 Table 6.2 Details of FRP retrofitted bridge piers .................................................................. 123 Table 6.3 Base shear and displacement at different limit states ........................................... 128 Table 6.4 Characteristic of ground motion records used in IDA .......................................... 130 Table 6.5 Median and dispersion values from the results of IDA using regression         analysis ............................................................................................................... 140 Table 6.6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g ...... 149 Table 6.7 Median values of PGA for piers with different parameters .................................. 151 Table 6.8 Collapse margin ratio for collapse safety of piers ................................................ 153 Table 7.1 Characteristics of the selected earthquake ground motion records ....................... 163 Table 7.2 Levels of the factors considered for the nonlinear dynamic analyses .................. 165 Table 7.3 Qualitative limit states (FEMA 2003) .................................................................. 170 Table 7.4 Description of damage/limit states of bridge pier ................................................. 171 Table 7.5 Ductility demand and limit state capacity of retrofitted bridge piers ................... 172 Table 7.6 Parameters (Regression coefficient) of fragility curves for the piers with respect to peak ground acceleration ................................................................................... 177  xii Table 7.7 P-Values from ANOVA of PSDMs of the piers ................................................... 177 Table 7.8 Parameters (Mean and standard deviation) of fragility curves for the piers with respect to peak ground acceleration, CFRP ....................................................... 179 Table 7.9 Median value of PGA for the CFRP retrofitted bridge ......................................... 188 Table 7.10 P-Values of median of PGA for the different damage states of CFRP retrofitted concrete .............................................................................................................. 240 Table B.2 Synopsis of peak stress-strain equation of AOMs for FRP-confined concrete ........ 274 Table D.2 Design guidelines, restrictions, and type of models used for circular section ..... 275 Table D.3 Outline of design guidelines for axial strength and model for circular piers piers .................................................................................................................... 189 Table B.1 Summary of strength and strain enhancement DOMs of FRP confined        equation for FRP confined concrete................................................................... 259 Table C.1 Summary of repair and retrofitted circular pier experimental test ....................... 270 Table D.1 Strength reduction and materials safety factors of various code/guidelines .... 257 Table B.3 Summary of existing analysis-oriented stress-strain models curve and dilation ....... 276 Table D.4 Tensile strength of FRP jacket and level of axial load ........................................ 281 Table E.1 Factorial design for pushover analysis ................................................................. 286 Table E.2 Failure drift of pier based on IDA results............................................................. 290 Table F.1 Factorial design for incremental dynamic analysis .............................................. 291   xiii List of Figures  Figure 1.1 Organization of thesis ............................................................................................ 34 Figure 2.1 Circular reinforced concrete piers prestressed with steel wires (Zong-Cai et al. 2014) .................................................................................................................... 39 Figure 2.2 Pier retrofitting using RC jacketing (a) plan view, and (b) sectional elevation .... 41 Figure 2.3 Pier retrofitting using steel jacket (a) circular pier plan, and (b) elevation (After Priestley et al. 1996)............................................................................................. 42 Figure 2.4 Pier retrofitting using FRP jacket (a) circular pier                                            (After Priestley et al. (1996) ................................................................................ 47 Figure 2.5 Confinement action of FRP-confined concrete in circular section (Lam and Teng 2003a)................................................................................................................... 49 Figure 2.6 Schematic of axial stress-strain relationship of unconfined and FRP-confined concrete ................................................................................................................ 52 Figure 2.7 Concept basis for confinement modeling (a) Two parts confinement DOM by Toutanji (1999), (b) passive confinement model (dots) (Jiang and Teng 2007) generated using active confinement stress-strain curves (Mander et al. 1988a) –AOM .................................................................................................................... 53 Figure 3.1 Reversed lateral cyclic loading test of RC piers specimen and geometry and reinforcement detailing/configuration .................................................................. 66 Figure 3.2 Schematic details of pier and its numerical model ................................................ 68 Figure 3.3 Schematic of effective confined concrete region with internal ties (Mander et al. 1988a)................................................................................................................... 70 Figure 3.4 Constitutive stress-strain response of confined concrete under (a) uniaxial and (b) cyclic loading (Mander et al. 1988a) ................................................................... 70 Figure 3.5 Schematic of hysteretic behavior of steel reinforcement based on (Menegotto and Pinto 1973)  cyclic model .................................................................................... 73 Figure 3.6 Schematic demonstration of constitutive response unconfined and FRP-confined concretes (Mander et al. 1988a, Spoelstra and Monti 1999) ............................... 75 Figure 3.7 Loading protocol of cyclic loading program ......................................................... 76  xiv Figure 3.8 Comparison of the force-displacement relationship of the numerical and experimental results ............................................................................................. 77 Figure 4.1 Typical pushover response curves showing various limit states with low, median and high levels ..................................................................................................... 86 Figure 4.2 Effect of (a) different shear span-depth ratios on the yield base shear and (b) percentage contribution of factors on the change of yield base shear ................. 89 Figure 4.3 Effect of (a) l/d ratio and fy of steel, (b) l/d ratio and 'cf , (c) l/d ratio and ρl of steel, (d) l/d ratio and axial load (e) l/d ratio and ρl of steel (f) 'cf and axial load on the yield base shear .................................................................................................... 90 Figure 4.4 Effect of (a) different shear span-depth ratios on the yield drift and (b) percentage contribution of factors on the change of yielding base shear of piers .................. 91 Figure 4.5 Effect of (a) l/d ratio and axial load (b) l/d ratio and tie spacing on drift at   yielding................................................................................................................. 91 Figure 4.6 Effect of (a) different shear span-depth ratios on the crushing base shear, and (b) percentage contribution of factors on the change on crushing base shear ........... 92 Figure 4.7 Effect of (a) fy of steel and l/d ratio (b) 'cf and l/d ratio on the base shear at  crushing ................................................................................................................ 93 Figure 4.8 Effect of (a) different shear span-depth ratios on the crushing drift, and (b) percentage contribution of factors on the change of crushing drift on the         piers ...................................................................................................................... 94 Figure 4.9 Effect of (a) fy and l/d ratio, (b) 'cf and axial load (c) ρl and fy of steel (d) l/d ratio and CFRP layers on the drift at crushing failure .................................................. 94 Figure 4.10 Effect of (a) different shear span-depth ratio on the buckling base shear, and (b) percentage contribution of factors on the change of buckling base shear on the piers ...................................................................................................................... 95 Figure 4.11 Effect of (a) fy of steel and l/d ratio (b) ρl and l/d ratio (c) l/d ratio and axial load (d) l/d ratio and CFRP layers on the base shear at buckling ................................ 96 Figure 4.12 Effect of (a) different shear span-depth ratios on the buckling drift, and (b) percentage contribution of factors on the change of buckling drift on the        piers ...................................................................................................................... 96  xv Figure 4.13 Effect of l/d ratio and axial load (b) axial load and CFRP layers on the drift at buckling of longitudinal steel ............................................................................... 97 Figure 4.14 Effect of (a) different l/d ratios on the fracture base shear, and (b) percentage contribution of factors on the change of fracture base shear on the piers ............ 98 Figure 4.15 Effect of (a) different shear span-depth ratios on the fracture drift and (b) percentage contribution of factors on the change of fracture drift on the           piers ...................................................................................................................... 98 Figure 4.16 Effect of (a) l/d ratio and axial load (b) l/d ratio and CFRP layer on the drift at buckling of longitudinal steel of piers.................................................................. 99 Figure 4.17 Range of ductility on different shear span-depth ratio of piers, (b) range of yield drift on different CFRP layer ............................................................................. 100 Figure 4.18 Effect of (a) axial load and l/d ratio and (b) axial load and CFRP layers on ductility .............................................................................................................. 100 Figure 5.1 Typical pushover analysis of pier (a) deformed and undeformed shape, and (b) load vs. drift curve with limit states ................................................................... 102 Figure 5.2 Pushover curves with different confinement ratios of (a) CFRP jacketed and (b) GFRP jacketed piers........................................................................................... 104 Figure 5.3 Moment-curvature response with different confinement ratios of (a) CFRP jacketed and (b) GFRP jacketed piers ................................................................ 105 Figure 5.4 Yield and ultimate displacement for defining the ductility ................................. 106 Figure 5.5 Ductility comparison of different confinement ratios of (ϕFRP) of          CFRP/GFRP ....................................................................................................... 107 Figure 5.6 Force-displacement relationship of CFRP retrofitted piers under cyclic         loading ................................................................................................................ 108 Figure 5.7 Force-displacement relationship of GFRP retrofitted piers under cyclic         loading ................................................................................................................ 109 Figure 5.8 Comparison of the envelope curve of (a) CFRP and (b) GFRP retrofitted         piers .................................................................................................................... 110 Figure 5.9 Axial stress vs strain behavior of core concrete of the CFRP and GFRP retrofitted pier under cyclic load (a) Case-1, (b) Case-2, (c) Case-3, (d) Case-4 ............... 111  xvi Figure 5.10 Axial stress vs strain behavior of longitudinal steel of the CFRP and GFRP retrofitted pier under cyclic load (a) Case-1, (b) Case-2, (c) Case-3,                   (d) Case-4 ........................................................................................................... 112 Figure 5.11 Suits of 10 unscaled ground motion records with 5% damping (a) response spectral acceleration, and (b) percentile of response spectral acceleration ........ 114 Figure 5.12 Suits of 10 scaled ground motion records with 5% damping (a) response spectral acceleration, and (b) percentile of response spectral acceleration ..................... 114 Figure 5.13 Base shear of CFRP retrofitted piers under ten ground motion records............ 116 Figure 5.14 Base shear of GFRP retrofitted piers under ten ground motion records ........... 116 Figure 5.15 Force-displacement behavior of case-4 (ϕFRP = 0.44) and as-built pier under the scaled Gazli-USSR, 1976 earthquake recorded at station 9201 Karakyer ......... 117 Figure 5.16 Residual displacement of CFRP retrofitted piers under ten ground motion   records ................................................................................................................ 118 Figure 5.17 Residual displacement of GFRP retrofitted piers under ten ground motion records ................................................................................................................ 118 Figure 5.18 Effective stiffness of CFRP retrofitted piers under ten ground motion records 119 Figure 5.19 Effective stiffness of GFRP retrofitted piers under ten ground motion records 120 Figure 6.1 Specimen geometry and reinforcement detailing used in this study ................... 122 Figure 6.2 Results of pushover analysis considering different compressive strength of concrete .............................................................................................................. 124 Figure 6.3 Results of pushover analysis considering different yield strength of       reinforcement ..................................................................................................... 125 Figure 6.4 Results of pushover analysis considering different longitudinal steel ratio ........ 126 Figure 6.5 Results of Pushover analysis considering different axial load ratio .................... 127 Figure 6.6 Results of pushover analysis considering different shear span-depth ratio ......... 127 Figure 6.7 Results of pushover analysis considering different layer of FRP ........................ 128 Figure 6.8 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b) percentile of response spectral acceleration of a suit of earthquake ground motion records.................................................................................................... 131 Figure 6.9 Results of dynamic and static pushover curve for C-1-35 .................................. 132 Figure 6.10 Dynamic and static pushover curve for C-1-20 ................................................. 132  xvii Figure 6.11 Dynamic and static pushover curve for C-2-400 ............................................... 133 Figure 6.12 Results Dynamic and static pushover curve for C-2-250 .................................. 133 Figure 6.13 Results of dynamic and static pushover curve for C-3-2.5 ............................... 133 Figure 6.14 Results of dynamic and static pushover curve for C-3-1 .................................. 134 Figure 6.15 Results of dynamic and static pushover curve for C-4-0.20 ............................. 134 Figure 6.16 Results of dynamic and static pushover curve for C-4-0.10 ............................. 134 Figure 6.17 Results of dynamic and static pushover curve for C-5-7 .................................. 135 Figure 6.18 Results of dynamic and static pushover curve for C-5-4 .................................. 135 Figure 6.19 Results of dynamic and static pushover curve for C-6-2 .................................. 135 Figure 6.20 Results of dynamic and static pushover curve for C-6-3 .................................. 136 Figure 6.21 IDA results used to identify IM values related with collapse for each ground motions of all the bridge piers retrofitted with FRP .......................................... 138 Figure 6.22 Linear regression model for the median and dispersion from IDA results ....... 142 Figure 6.23 Effect of concrete strength on collapse fragility ................................................ 144 Figure 6.24 Effect of yield strength of longitudinal steel on collapse fragility .................... 145 Figure 6.25 Effect of amount of longitudinal steel on collapse fragility .............................. 146 Figure 6.26 Effect of axial load on collapse fragility ........................................................... 147 Figure 6.27 Effect of shear span-depth ratio on collapse fragility ........................................ 148 Figure 6.28 Effect of FRP confinement on collapse fragility ............................................... 149 Figure 6.29 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g ... 150 Figure 6.30 Difference between collapse probability of different parameters ..................... 150 Figure 6.31 Bar chart of median values of PGA for the piers with different parameters ..... 152 Figure 7.1 Example of fragility curves with four damage/limit states of bridge pier ........... 155 Figure 7.2 Schematic demonstration of methodology for the seismic vulnerability assessment of FRP retrofitted bridge piers ........................................................................... 160 Figure 7.3 Vancouver (Site Coordinates: 49.2827, °N 123.1207°W, Sa(0.2), site class C) seismicity in British Columbia, Canada (NRCC 2015) ..................................... 162 Figure 7.4 Design acceleration response spectrum for Vancouver, British Columbia, Canada with different seismic hazard level, for site class C (NBCC 2015) ................... 162  xviii Figure 7.5 Typical acceleration, velocity and displacement time histories of (a) Northridge (PGA 0.41g) earthquake recorded at same station Canyon Country-WLC, and (b) Chi-Chi, Taiwan (PGA 0.47g) earthquake recorded at same station TCU045 .. 164 Figure 7.6 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b) percentile of response spectral acceleration of a suit of earthquake ground motion records.................................................................................................... 165 Figure 7.7 Specimen geometry and reinforcement detailing with lower level factors (fc’ = 20 MPa, fy = 250 MPa, ρl = 1%, P = 10%, l/d = 4, n = 2) ....................................... 167 Figure 7.8 Specimen geometry and reinforcement detailing with higher-level factors ( 'cf = 35 MPa, fy = 400 MPa, ρl = 2.5%, P = 20%, l/d = 7, n = 3) .................................... 168 Figure 7.9 Damage limit state on base shear for low and high levels factors of piers ......... 171 Figure 7.10 PSDMs for displacement ductility (as EDP) of piers as a function of PGA (as IM) with (a) high and (b) low level of modeling parameter .............................. 176 Figure 7.11 Effect of low and high-level strength of concrete on the fragility curve for the retrofitted bridge piers ........................................................................................ 181 Figure 7.12 Effect of low and high yield strength of rebar on the fragility curves for the retrofitted bridge piers ........................................................................................ 183 Figure 7.13 Effect of low and high levels reinforcement ratio of rebar on the fragility curves for the retrofitted bridge piers ............................................................................ 184 Figure 7.14 Effect of low and high levels axial load ratio on the fragility curves for the retrofitted bridge piers ........................................................................................ 185 Figure 7.15 Effect of low and high levels shear span-depth ratio on the fragility curves for the retrofitted bridge piers ........................................................................................ 186 Figure 7.16 Effect of low and high levels CFRP layers on the fragility curves for the retrofitted bridge piers 1971 (USGS and Leyendecker 1971) ................................................................ 233 ........................................................................................ 187 Figure 7.17 Performance of damage of low-level factors..................................................... 190 Figure 7.18 Performance of damage high-level factor ......................................................... 190 Figure A.1 Damage of RC pier on Interstates 5 and 14 during the San Fernando earthquake,  xix Figure A.2 Failure of RC piers and collapsed upper deck on the Cypress viaduct of Interstate of 880 (USGS and Wilshite 1989) ..................................................................... 234 Figure A.3 Simi Valley Freeway Damage Buckling of freeway support piers under the Simi Valley Freeway at the North end of the San Fernando Valley (USGS and Teng 1994) .................................................................................................................. 235 Figure A.4 Premature shear failure of reinforced concrete pier, Fukae Viaduct Hanshin expressway (Kawashima 2011) ......................................................................... 236 Figure A.5 Wushi Bridge, shear failure of piers P2S, 1999 Taiwan earthquake (Hsu and Fu 2000) .................................................................................................................. 237 Figure A.6 Damaged RC pier of Uonogawa Bullet Train Bridge due to the 2004 Chuetsu earthquake in Japan (Shanmuganathan 2005) .................................................... 238 Figure A.7 Shear failure of a pier at the right dyke, Juan Pablo II Bridge (Kawashima et al. .............................................. 302 Figure F.2 PSDMs of pier 2 to 6 using regression analysis .................................................. 313 Figure F.3 Fragility curves of pier 1 to 64 ............................................................................ 324 Figure F.4 Hazard analysis results of pier 2 to 63 ................................................................ 332    2011) .................................................................................................................. 239 Figure D.1 Confining pressure exerted by the FRP strips (fib Bulletin No. 14 2001) (CNR-DT 2013) ............................................................................................................ 283 Figure E.1 Acceleraction time histories of selected 20 ground motion records ................... 289 Figure F.1 Iremental dynamic analysis results of pier 2 to 64  xx List of Symbols, Abbreviations   LVDTs Linear variable displacement transducers ACC Active-confined concrete DOMs Design oriented stress-strain models AOMs Analysis oriented stress-strain models FRP Fibre-reinforced polymer FCC FRP-confined concrete RC Reinforced concrete SSR Stress-strain response of FRP confined concrete DIC Digital image correlation CFRP Carbon fibre reinforced polymer GFRP Glass fibre reinforced polymer AFRP Aramid fibre reinforced polymer BFRP Basalt fibre reinforced polymer FRC Fibre reinforced concrete NSPA Non-linear static pushover analysis NDTA Non-linear dynamic time history analysis PEER Pacific earthquake engineering research center PGA Peak ground acceleration PGV Peak ground velocity PGD Peak ground displacement SI Spectral intensity ANOVA Analysis of variance IDA Incremental dynamic analysis IM Intensity measures EDP Engineering demand parameter ATC Applied technology council R Epicenter distance Mw Moment magnitude SCT Collapse median intensity CMR Collapse margin ratio SMT Design level earthquake intensity PSDMs Probabilistic seismic demand models FE Finite element FEMA Federal emergency management agency ACI American concrete institute JCI Japan concrete institute JSCE Japan society of civil engineers ASCE American society of civil engineers CSCE Canadian society of civil engineers NRCC National research council Canada NBCC National building code of Canada UHPC Ultra-high performance concrete HPFRC High-performance fibre reinforced concrete  xxi ECC Engineered cementitious composite SMAs Shape memory alloys fh Hoop tensile stresses of FRP jacket R Radius of the core concrete section D Diameter of pier εh,frp Hoop strain of FCC d Diameter of concrete core (mm) Ef Elastic modulus of fibres (MPa) εfu Ultimate tensile strain of fibre ffrp Ultimate tensile strain FRP tfrp Nominal thickness of the FRP jacket (mm) fc,res Residual compressive stress of actively confined concrete (MPa) fl Confining pressure (MPa) 'l cof f  Confinement ratio referred as the confinement pressure fl at FRP jacket rupture to the unconfined compressive strength of concrete 'cof  kε Strain reduction factor flu,a Actual confining pressure keff Effective confining coefficient nfrp Number of layers of FRP Sfrp Width of FRP sheets (mm) S Clear adjacent spacing of FRP sheets (mm) lf  Effective confining pressure 'ccf  Peak confined compressive strength of concrete 'cof  Strength of unconfined concrete εv Volumetric strain 1  Axial strain r  Lateral strain εcc Peak axial strain εcu Ultimate strain DI Ductility index  kl Coefficient of confinement effectiveness εca Axial strain of concrete flu,a Actual confining pressure of FRP at ultimate condition; flu,a = Elεh,rup (MPa) ,'lu acoff Confinement ratio of FRP-confined concrete *ccf  Peak axial compressive stress of actively confined concrete (MPa) 'cof  Peak axial compressive stress of unconfined concrete (MPa) 'cuf  Ultimate axial compressive stress of FRP-confined concrete (MPa) *lf  Active confining pressure (MPa) *'lcoff Confinement ratio of actively confined concrete H FRP confined concrete specimen height (mm)  xxii Kl Lateral confinement stiffness (MPa); Kl=2Eftf/d or Efrptfrp/d kε,f   Hoop strain reduction factor of fibres n Curve-shape parameter in dilation model tf Total nominal thickness of fibres (mm) εc Axial strain *cc  Axial strain of actively confined concrete at*ccf  εco Axial strain of unconfined concrete at 'cof  εc,res Axial strain of actively confined concrete at fc,res εcu Ultimate axial strain of FRP-confined concrete at 'cuf  E1 First slope (ascending branch) of the stress-strain curve '1 5500 cpE f (Yan 2005) (Yan 2005) E2 Second slope (post peak) of the stress-strain curve fo Plastic stress intercept of the second slope of stress-strain curve Eco Secant modulus Ai Constants of the initial slope and the descending part of the stress-strain curve Di Constants of the initial slope and the descending part of the stress-strain curve (Toutanji 1999) Ci Constants of the initial slope and the descending part of the stress-strain curve (Toutanji 1999) c1 Correction constant in the strength enhancement c2 Correction constant in the strain enhancement  k1 Strength enhancement coefficients for FCC k2 Strain enhancement coefficients for FCC kε Hoop strain reduction factor for FCC r Constant for the brittle response of concrete fc Axial stress of concrete,  '*ccf  Peak axial stress of concrete *cc  Peak axial strain of concrete 'cof  Compressive strength of unconfined concrete µt Tangent dilation ratio  εh Hoop strain εf Ultimate tensile strain of fibres εh,rup Hoop rupture strain of FRP shell ε∗lc Lateral strain of actively confined concrete at 'ccf  εlo Lateral strain of unconfined concrete at 'cof  εl,res Lateral strain of actively confined concrete at fc,res μt Dilation ratio of confined concrete υi Initial Poisson’s ratio of concrete μs Secant dilation ratio ρl Longitudinal steel reinforcement ratio As Area of longitudinal steel Ag Gross area of concrete 'cf  Specified compressive strength of concrete  xxiii 'ccf  Specified compressive strength of confined concrete εsu Steel strain at maximum tensile stress εcu Strain in the extreme fibre of the concrete core at ultimate fy  Yield strength of steel Vy  Base shear at first yielding My Moment at first yielding l Height of pier 𝜙s Resistance factor for steel reinforcement a Depth equivalent rectangular stress block 𝛼1 Ratio of average stress in rectangular compression block to the specified concrete strength 𝜙c Resistance factor for concrete 𝜙y Curvature at the onset of first yielding  Dy Yield drift Ec Modulus of elasticity of concrete fl Effective lateral stress of confined concrete Ic Cracked moment of inertia Vc Base shear at first cracking Δc Lateral displacement at first cracking Δcrush Displacement at first concrete crushing Δd Target displacement Δp Plastic displacement Δy Yield displacement Δu  Ultimate lateral displacement μ∆ Displacement ductility 𝜙u Curvature at first concrete crushing   Factor accounting for shear resistance of cracked concrete Es Modulus of elasticity of steel n’ Elastic modulus ratio n Number of CFRP layers εc Compressive strain at crushing of concrete ρ Ratio of longitudinal steel reinforcement at tension zone '  Ratio of longitudinal steel reinforcement at compression zone *lf  Effective confining pressure  keff Effective confinement coefficient S’ Clear spacing between transverse steel ρcc  Longitudinal reinforcement ratio fyh or fys  Yield strength of transverse reinforcement tF Thickness of the CFRP system F Resistance factor for CFRP wrap fF Ultimate strength of CFRP Dg Diameter of the circular section lp Plastic hinge length dv Effective depth of the section Av Gross area of the tie bars in a single layer  xxiv θ Angle of shear failure Δbb Displacements at buckling of bar Δbf Displacements at fracture of bar db Diameter of the longitudinal reinforcing bar P Axial load level Vcrush Base shear at crushing of concrete ρs Volumetric ratio of confining steel d Depth of the cross-section CDF Cumulative distribution function Sc Median  βc Dispersion βD|IM logarithmic standard deviation or dispersion of the demand Sd Median demand or the engineering demand parameter  λ Median ξ Standard dispersion (deviation) Pc(C|IM = x) Probability of collapse at a given ground motion with IM = x  Φ(.) Standard normal CDF θ Collapsed median intensity of the fragility function β Logarithmic standard deviation or sometimes mentioned as the dispersion of lnIM.        xxv Acknowledgements    At this time, as I complete this thesis, it is with a pleasure to recognize those who helped along the way to make this difficult taks possible. First, I would like to express my sincere gratitude to my supervisor Dr. M. Shahria Alam for providing me with this precious research opportunity to work on an interesting topic on advanced composite materials. I would like to express my sincere appreciation to him for his elaborate guidance, enthusiasm and inspiration, considerable encouragement, invaluable discussions, support and insightful comments, which helped me to understand this challenging topic.    Special thanks to my thesis supervisory committee members, Dr. Ahmad Rteil, and Professor Dwayne Tannant, for their valuable advice, comments, support, and inspiration since the early stage of the project. I would like to thank Dr. Solomon Tesfamariam from School of Engineering, University of British Columbia (UBC) for the fruitful discussion and help to understand the seismic vulnerability and fragility function of structures. I would like to thank our industrial research partner Mr. Eric Marciniak, Mr. Joseph Gardner and Mr. Brendan Pogue, PolyRAP Engineered Concrete Solutions, Kelowna, British Columbia, Canada for their help and support throughout my doctoral research at the University of British Columbia. Without you people, the completion of this work would have been much difficult.    I would like to express my gratefulness to UBC for the International Tuition Scholarship; Ministry of Human Resources Development (MHRD), Government of India, New Delhi for National Overseas Scholarship; PolyRAP Engineered Concrete Solutions, Kelowna, British Columbia (B.C.), Canada for Mitacs Accelerate Ph.D. Fellowship; and Natural Science Engineering and Research Council of Canada (NSERC) for providing me with financial support during my doctoral research at UBC. I would like to thank Sardar Vallabhbhai National Institute of Technology, (SV NIT), Surat, India for granting me a study leave for my doctoral research at UBC, Canada.   Beside my doctoral research, I conducted a large-scale experimental work on deficient bridge piers retrofitted using sprayed-FRP, and sprayed-FRP confined concrete cylinder. Thus, this thesis would not be smooth without the kind and timely support of laboratory staff Alec Smith, Kim Nordstrom, Durwin Bossy, Marc Nadeau, Ryan Mandau, Tim Giesbrecht,  xxvi Michele Cannon, Michelle Tofteland, Emily Zhang laboratory technicians from School of Engineering who generously helped me build the formwork and casting of specimens, test-set up for the experiments and granted access to different tools and facilities. Thanks go to administrative staff Shannon Hohl, Angela Perry and Karen Seddon from the School of Engineering, and Aaron Heck, Senior Manager, and Chase Tompkins Support Analyst II - Tech Lead IT Client Services, UBC for providing me an extra computing facility for conducting incremental dynamic analyses of piers.   Alongside my Ph.D. research, the experimental works on sprayed-FRP piers, and sprayed-FRP confined concrete cylinder research would not be possible without the support of local companies, namely, FormAShape 3D Architectural Design Solutions, and Product Design Engineer Charles Stuart for providing FRP materials; O.K. Builders  Supplies, LTD, and Desmond O’Brien, Quality Manager for providing reinforcement and ready mix concrete; Silver Springs Concrete Services for providing the concrete pump; Ed Rivard President & Board Member from R & R Reinforcing Ltd, for providing circular steel reinforcements; and Sprayed-FRP spraying facility by Mr. Eric,  Elite Fibre Glass, Kelowna, British Columbia, Canada.  I would like to thank all the people and friends that I have met in Kelowna during the past five years. Special thanks to Mr. Michael Hutchinson and Mr. Eric Marciniak for their help and moral support in my difficult time. I would like to thank my friends at UBC, Dr. Abu Hena MD Muntasir Billah, Dr. Farshad Hedayati Dezfuli, and Charles Rockson for their help and support in conducting data analyses and interpreting the numerical results.   Finally, yet important, my great respect to my parents who sacrifices their pleasure for the betterment of me throughout their lives, and they planted in me that every realistic goal is achievable. I would like to thank my brothers’ Mr. Harsharai Parghi and Mr. Rajendra Parghi for their constant belief and support throughout my life. My deepest gratitude and indebtedness to my beloved wife and best friend Vanita Parghi, loving daughter Kinjal Parghi and cherished son Renish Parghi for their understanding, love, support and continuous encouragement and sacrifice throughout my doctoral research at UBC. Without their continual support from a distance place, it would be extremely difficult for me to continue this long research journey.   xxvii Dedications This thesis is dedicated to  The Lord Krishna and  An Architect of Indian Constitution  Dr. B. R. Ambedkar Their words of inspiration and encouragement in pursuit of excellence in life       28 Chapter 1: Introduction and Thesis Organization  1.1 General There are more than 685,000 reinforced concrete (RC) bridges in North America, among them about 80,000 are in Canada (Huijbregts 2012). It is estimated that about 30% of the highway bridges in Canada have passed their service lives and they are dificient either structurally or functionally (Huijbregts 2012). In addition, since the seismic design guidelines have been updated, the deficient bridges do not meet the current seismic standard and are in need of seismic upgrade or retrofit. Therefore, huge amount of bridge rehabilitation and replacement works need to be done in the near future in North America for ensuring a safe and continuous transport facility. Recent destructive seismic events, including 2012 Emilia earthquakes Italy, 2011 Tohoku earthquake, 2011 Christchurch earthquake New Zealand, and 2011 Sikkim earthquake India have demonstrated that buildings and bridges designed and built according to older seismic design codes are vulnerable to catastrophic damages and collapse. Many of the concrete bridge failures occurred during past earthquakes were due to the failure of piers. Many existing bridges were designed without any seismic resistance guideline as they were constructed prior to seismic resistance design code. Although many bridges were designed to resist lateral loads, they may become deficient because of the fact that they might not been designed as per the principle of the capacity design, or they may have been constructed in a location where the seismic hazard level has been reevaluated and augmented (ATC-32 1996, CAN/CSA-S6 2014). Research studies reported that lack of concrete confinement due to the use of inadequate transverse reinforcement, and inadequate lap splice length at the plastic hinge region of the piers are few of the key causes for the poor flexural ductility and/or insufficient shear capacity found in many of the collapsed bridge piers (Priestley and Seible 1995, Haroun and Elsanadedy 2005).   One option is replacing the deficient structure with a new one, however, new construction in most cases is quite expensive, time-consuming, and even impractical. Hence, the other alternative is to strengthen these structures up to the current seismic standards.      29 1.2 Research Background Several rehabilitation/strengthening methods are available to upgrade the seismic performance of existing concrete bridges. A common method to strengthen poorly designed reinforced concrete (RC) bridge piers is to apply external confinement to concrete at the potential plastic hinge region of the piers. This could be the use of concrete, steel or fibre reinforced polymer (FRP) or fibre reinforced concrete (FRC) jackets (Priestley et al. 1996). Confinement approaches could be divided into two types, namely, passive confinement and active confinement. In the case of active confinement, the main advantage is the delay in damages sustained by the concrete, which leads to the early application of confining pressure; while in the case of passive confinement, the concrete has to deform laterally in order to fully activate the confining pressure. There are numerous studies which attempted on exploring the feasibility of active confinement technique for seismic retrofitting of concrete elements (Gamble et al. 1996, Saatcioglu and Yalcin 2003). Although, there are benefits for active confinement, its field implementation is limited due to the practical application related to the technique used in applying a confining pressure at the job site. Steel plates (Chai et al. 1991, Norris et al. 1997) and FRP wraps (Elsanadedy and Haroun 2005, Haroun and Elsanadedy 2005, Haroun et al. 2003) are the most common methods used for passive confinement techniques to improve the ductility capacity of vulnerable piers. The passive confinement technique has been popular and widely used all over the world where the past research has demonstrated excellent results.  For the last two decades, several researchers have conducted experimental investigations that focused on exploring the effect of passive confinement technique using FRP composites (Saadatmanesh et al. 1994, Seible et al. 1995, Samaan et al. 1998). While other studies attempted to describe analytically constitutive behavior and stress-strain model of concrete confined with FRP passive confinement technique (Spoelstra and Monti 1999, Toutanji 1999, Fam and Rizkalla 2001, Chun and Park 2002, Marques et al. 2004, Binici 2005, Teng et al. 2007), Youssef et al. 2007). There are numerous studies, which attempted to explore the feasibility of FRP passive confinement techniques for seismic retrofit of concrete piers. Some of these studies (Saadatmanesh et al. 1996, Xiao and Ma 1997, Saadatmanesh et al. 1997, Chang et al. 2004, Haroun and Elsanadedy 2005, Han et al. 2014) investigated lateral load carrying capacity of piers by applying FRP composites as passive confinement technique. The   30 results of these studies have demonstrated that shear failure was prevented and significant improvement was obtained in the ductility of retrofitted piers.  1.3 Problem Description In order to observe the effect of various factors on the seismic performance of deficient RC bridge piers, many experimental and analytical investigations have been conducted. Park and Paulay (1975) studied the effect of the amount of longitudinal reinforcement, the steel yield strength, and the compressive strength of concrete on the yield and crushing behavior, and the corresponding ductility. Mo and Nien (2002) reported that higher axial load reduces pier ductility. Stone and Cheok (1989), and McDaniel (1997) found that with the increasing height to diameter ratio, the flexural failure mode was observed with higher deformation capacity; whereas decreasing aspect ratio decreased the deformation capacity, and shear failure occurred. In order to observe the effect of lateral confinement, many researchers have conducted experimental and analytical investigations on the performance of bridge piers under reversed cyclic load along with constant axial load. They found that with the increase of lateral confinement, the flexural and shear strengths could be improved significantly (Mander et al. 1988a, Sheikh and Uzumeri 1982, Calderone et al. 2000, Razvi and Saatcioglu 1994, Papanikolaou and Kappos 2009). Gallardo-Zafra and Kawashima (2009) reported that the flexural strength and ductility of piers retrofitted with CFRP composite increased with increasing CFRP confinement ratio.  In the existing literature, most of the researches conducted experimental studies about the behavior of FRP retrofitted RC bridge piers under seismic ground motions. Further, the experimental studies are expensive and time-consuming, and cannot be easily extended to a wide range of cases. Moreover, there is no study available on the effect of modeling parameters/factors their variability with a practical range and their interaction on the seismic performance evaluation of the FRP-retrofitted bridge pier using factorial design method by assessing their seismic vulnerability using fragility curve. Mitchell et al. (2012) reported that about 40% highway bridges were constructed before 1970 when the probabilistic seismic hazard map for Canada was developed. Hence, it evidently demonstrates that numerous highway bridges were designed without considering seismic hazard provision. With time, continuing deterioration has taken place and fast aging of structures have substantially   31 increased the anticipated repair cost (Mirza 2007). Hence, this research has been undertaken to conduct an extensive and systematic seismic vulnerability assessment of pre-1970 designed RC bridge piers retrofitted with carbon fibre reinforced polymer (CFRP) using factorial design method.   1.4 Scope and Objectives of the Research  The research study presented herein assesses the effect of various parameters and their interactions on the seismic response of CFRP retrofitted circular bridge piers using numerical simulations. The parameters include those related to the material, for example, the strength of concrete and yield strength of rebar, whereas the other parameters include: longitudinal reinforcement ratio of steel, axial load, shear span-depth ratio, and CFRP confinement level. This study has two major objectives.  Identify important parameters/factors and their interactions that affect the seismic performance of the retrofitted bridge piers using factorial design.   Determining the effect of various parameters on the seismic vulnerability of deficient circular RC bridge piers retrofitted with CFRP by developing seismic fragility curves.  1.5 Methodology of the Thesis In Chapter 3, a numerical finite element (FE) model is generated for FRP retrofitted circular RC bridge pier using fibre modeling approach with reverse cyclic load and a constant axial load of the axial capacity of the pier. The numerical results were verified with the experimental results.  In Chapter 4, seven factors along with three levels (low, medium, and high) are considered to determine the effect of various factors on the seismic performance of deficient RC bridge piers retrofitted with CFRP. Here, fractional factorial design method has been employed. Nonlinear static pushover analysis (NSPA) of the CFRP retrofitted bridge piers are conducted for all possible combinations of considered factors in order to determine the sequence of different limit states. The important factors (within their practical ranges) and their interactions that have significant impact on the seismic performance of the retrofitted bridge piers are studied.    32  In Chapter 5, parametric investigations are conducted using nonlinear static pushover analysis (NSPA), reverse cyclic analysis and nonlinear dynamic time-history analysis (NDTA). In order to study the flexural limit states, the amount of confinement of CFRP/GFRP retrofitted piers are varied by using single, double, triple and four layers of 0.11 mm thick CFRP/GFRP jackets, which corresponds to volumetric confinement ratios (ϕFRP) of 0.11, 0.22, 0.33 and 0.44%, respectively. In order to provide a common base for the comparison between the two retrofitting methods, same confinement ratios are used by changing the thickness of jackets.   Chapter 6 focuses on quantifying the inelastic seismic demand and capacities of FRP retrofitted non-seismically designed circular RC bridge piers. Here, different level of parameters (low and high) are considered and the perforamnces are evaluated by using NSPA, and incremental dynamic analyses (IDA). IDA is conducted with finite element numerical models of the FRP retrofitted piers to a family of 20-earthquake ground motions scaled with different intensity measures (IM). With respect to IM, such as peak ground acceleration (PGA), the maximum responses in terms of governing engineering demand parameters (EDP), such as the maximum drift or deformation, and ductility demand of the structure are estimated to compare seismic performances of retrofitted bridge piers. The seismic collapse assessment of the deficient bridge pier retrofitted with CFRP is conducted and their damage states are determined with fragility curves.  To study the effect of different modeling parameters/factors along with their interactions, a factorial design method containing six factors with two levels (low and high) is considered for the seismic vulnerability assessment of retrofitted piers. NSPA and IDA are conducted using a set of 20 ground motions with different dynamic characteristics by means of the formulation of probabilistic seismic demand model (PSDM)'s framework based on analytical fragility curves for all possible combinations of six factors to determine the sequence of different damage/limit states (structural capacities) for bridge piers. Fragility curves are developed to provide practical information about the failure probability of retrofitted bridge piers and assist in expressing the impact of CFRP composites on the deficient bridge pier vulnerability.      33 1.6 Thesis Organization This thesis is organized into eight chapters. The organization of the thesis is depicted in Figure 1.1. In the present chapter, a brief preface, objectives and scope of research, and thesis methodology are discussed. The overall content of the dissertation is organized into the following chapters:   In Chapter 2, a comprehensive review of the currently available literature on FRP retrofitted circular piers is presented. Several important experimental studies on the seismic behavior of FRP retrofitted RC circular piers are reviewed.   In Chapter 3, discuss the finite element modeling of circular RC bridge pier retrofitted with FRP using fibre element approach. In this Chapter, the finite element numerical models have been generated and the numerical results are verified with the experimental results.  In Chapter 4, an extensive parametric study is conducted using fractional factorial design method in order to investigate the effect of various design and geometric parameters on the nonlinear static pushover analysis and reverse cyclic behavior of FRP retrofitted RC piers using fractional factorial design.  Chapter 5 presents a parametric study on the seismic performance of FRP retrofitted circular reinforced concrete piers under nonlinear static pushover and quasi-static cyclic analyses, and nonlinear dynamic time history analysis using finite element analysis.  Chapter 6 presents the seismic collapse assessment of FRP retrofitted non-seismically designed circular reinforced concrete bridge piers with different modeling parameters using incremental dynamic analysis. The collapse probabilistic seismic demand models are developed by assessing their seismic fragility curves.  In Chapter 7, seismic vulnerability analyses of FRP retrofitted deficient bridge piers are conducted using a factorial design method and probabilistic seismic demand models are developed by assessing their seismic fragility curves.  Finally, the results, concluding remarks, and recommendations for future studies are presented in Chapter 8.        34                                Figure 1.1 Organization of thesis Seismic Performance Evaluation of Circular Reinforced Concrete Bridge Piers Retrofitted with Fibre Reinforced Polymer Title Chapter 1: Introduction and Thesis Organization Seismic Performance of Bridge Piers in the Past Earthquakes and FRP Design Guidelines, and Constitutive Models of FRP Confined concrete Chapter 2: Review  Summary, Conclusions and Future Works  Chapter 8: Conclusions  Core Contribution Pushover Response of Non-Seismically Designed Circular RC Bridge Pier Retrofitted with FRP using Fractional Factorial Design -A Parametric Study Chapter 4: Seismic Behaviour of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP – A Parametric Study Chapter 5: Seismic Collapse Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP  Chapter 6: Fragility Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP Using Full Factorial Design Method Chapter 7: Finite Element Modelling of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP Chapter 3: Modelling    35 Chapter 2: Literature Review  2.1 General The aim of this chapter is to collect up-to-date information on seismic repair and retrofit of both standard and sub-standard reinforced concrete (RC) bridge piers in order to simplify the progress of seismic repair and retrofitting systems using composite materials. In this research, the sub-standard piers are defined as those having insufficient lateral reinforcements, and longitudinal bars, whereas the standard piers are reinforced with adequate lateral reinforcement and longitudinal bars with ductile detailing. This chapter summarizes the old seismic design criteria of bridge piers, the performance of bridge piers during the past earthquake; seismic tests on repair and retrofit of RC bridge piers with different damage levels using advanced composites, and numerical methods for analyzing their behavior under later cyclic load. The constitutive model and stress-strain behavior of FRP-confined concrete are also discussed. The last section summarizes the current design provision of circular RC bridge pier’s lateral confinement using fibre reinforced polymer composites to upgrade the seismic resistance of pier considering different codes and design guidelines.    2.2 Old Seismic Design Criteria of Bridge Piers Many existing bridges in North America built before the 1971 San Fernando earthquake may not have adequate seismic resistance capacity as specified by previous design code (ATC-32 1996), and the recent design guidelines (CAN/CSA-S6 2014). This was because of the application of elastic design philosophy in the earlier days. Recently bridge piers are mainly designed as energy dissipation elements during an earthquake. Poorly detailed RC bridge piers are vulnerable to loss of axial load carrying capacity at drift levels (2-3%) during a design level earthquake (Boys et al. 2008). Before 1970, the tie spacing of 300 mm was commonly used in the bridge piers. The inadequate lap splice length at the plastic hinge zone and inadequate transverse reinforcement in these piers were the most significant factors causing a lateral deficiency in resisting seismic force (Priestley and Seible 1995, Elsanadedy and Haroun, 2005). Ruth and Zhang (1999) conducted a survey on 33 RC bridges in Washington State, USA which was constructed between the years of 1957 and 1969. The spacing of the transverse reinforcement of piers was suggested to be about 305 mm regardless of pier   36 diameter. CAN/CSA-S6 (1974) code provisions specified the maximum spacing of transverse reinforcement was the least of 16 times the diameter of longitudinal reinforcement, 48 times diameter of stirrup rebar or smallest dimension of the pier. CSA CAN3-S6-M (1978) code provisions specified tie spacing of 300 mm or the smallest dimension of the member, and tie should cover every alternate bar. According to CAN/CSA-S6 (2006), the maximum tie spacing is the smallest of six times the longitudinal bar diameter or 0.25times the minimum dimension of pier or 150 mm and tie should cover every longitudinal bar. Thus, the recently updated CAN/CSA-S6 (2014) has specified lower tie spacing than that of 1974 and 1978 code provisions.   In old RC bridges, the yield strength of longitudinal reinforcement was in the range of 276-400 MPa, whereas in modern bridges, the yield strength of longitudinal reinforcement is in the range of 450-500 MPa. The moment/shear ratio decreases by decreasing the shear span-depth ratio, which causes an increasing tendency of shear failure rather than flexural failure. Khaled et al. (2004) found that piers with a small shear span-depth ratio of 2.5 behaved as combined flexural-shear failure mode. Whereas, the shear span-depth ratios of 4.5 and 6.4 piers failed in flexure with lower shear demand.   2.3 Performance of RC Bridge Piers in Past Earthquake Past earthquake reconnaissance report, such as the 1971 San Fernando, 1989 Loma Prieta, and the 1994 Northridge earthquakes in California; the 1995 Kobe earthquake in Japan; the 1999 Chi-Chi earthquake in Taiwan; the 1999 Kocaeli and Duzce earthquakes, Turkey; the Niigata-Keb Chuetsu earthquake, Japan 2004; and the Chile earthquake, Chile, 2010 showed that many bridges and their components have experienced some sort of damage that lead to structural collapse. The failure of the piers occurred at the base because of the inadequate transverse reinforcement at this critical region (Kawashima 2011). The failure of RC pier occurred due to the insufficient development length (only 20-time bar diameter was the development length) of longitudinal bars terminated at mid-height (Kawashima 2011). The highway bridges, including those built using recent seismic design codes, were severely damaged. As per Taiwanese Highway Bureau's preliminary report, minimum nine bridges were severely damaged, including three bridges that were under construction during Chi-Chi earthquake in Taiwan. Five bridges collapsed due to fault rupture, and seven bridges were   37 moderately damaged (Yen 2002). As explained earlier, the past destructive earthquake proved that existing bridges built prior to the 1971 seismic design code provisions have shown many drawbacks. Research studies (Chai et al. 1991, Priestley et al. 1994a,b, Maekawa and An 2000) reported that insufficient flexural ductility and shear capacity are the two main reasons for the failure of RC piers. Insufficient quantity of transverse reinforcement (in the form of ties and hoops, commonly provided as 13mm rebar at 300mm on center) and inadequate lap splice length at the plastic hinge zone of the piers is another main cause for the poor flexural ductility, and shear failure in many collapsed bridge piers (Priestley and Seible 1995, Seible et al. 1997, Elsanadedy and Haroun 2005). The RC bridge piers could experience a combination of axial, bending, shear and torsional forces during an earthquake (Belarbi et al. 2010). These combined damages lead to the development of cracking or spalling of concrete cover, yielding of longitudinal and lateral reinforcement, the crushing of concrete, and buckling or fracture of longitudinal rebar. The detailed description of the performance of RC bridge piers in the past earthquakes is presented in Appendix A.  2.4 Seismic Retrofitting Techniques for Reinforced Concrete Piers From the previous section, it could be observed that crushing of core concrete, yielding, buckling, and fracture of longitudinal reinforcement caused severe damage to RC piers. The buckling and fracture of longitudinal bars created more difficulty when restoring the original capacity of the damaged pier.  Over the years, engineers have developed various rehabilitation methods to upgrade the seismic performance of existing building and bridges. The influential factors, i.e., the transverse reinforcement and the axial load level on the ductility of piers have been gradually revealed by analytical and experimental studies. A common method had been used in the past to address the issue of poorly designed RC piers by providing an external confinement of concrete at the potential plastic hinge region of the piers. This could be the use of reinforced concrete, steel plate, fibre reinforced polymer (FRP), or fibre reinforced concrete (FRC) jackets.  Confinement approaches could be divided into two types, namely, active confinement and passive confinement techniques. In the active confinement technique, the confining pressure is applied in order to prestress the transverse reinforcement in the concrete section prior to   38 application of axial compression load. The passive confinement can be defined where the transverse reinforcement reacts to the expansion of concrete. The main difference between active and passive confinement techniques is the lateral confining pressure. In the case of active confinement, the main advantage is the early application of confining pressure that delays damages sustained by the concrete. Several researchers focused on exploring the feasibility of active confinement technique for seismic retrofitting of concrete elements (Gamble et al. 1996, Saatcioglu and Yalcin 2003). Although, there are benefits for active confinement, its field application is limited due to the practical application related to the technique used in applying a confining pressure at the job site.    Steel plates and FRP wraps are the most common methods used for passive confinement techniques to improve the ductility capacity of vulnerable piers (Chai et al. 1991, Norris et al. 1997, Elsanadedy and Haroun 2005). The passive confinement technique has been popular and widely used all over the world. Priestley et al. (1996) reported various seismic rehabilitation methods of RC bridge piers using concrete, steel and FRP composite jacketing. This section provides a comprehensive review of the literature on seismic retrofitting methods available for RC bridge piers.  2.4.1 Active confinement techniques  This section describes the active confinement technique such as external prestressing strands and shape memory alloys (SMAs) for the external strengthening of circular RC piers. Each technique application is briefly described through an experimental study carried out by numerous researchers for the circular RC piers in the following sections.  2.4.1.1 External prestressing strands The most common deficiency, such as failure of existing RC bridge piers is due to the inadequate confinement, insufficient lateral reinforcement and lack of reinforcement splicing.  In order to investigate the viability of applying active confinement in the field of seismic retrofitting, some researchers suggested that the active confinement model is superior compared to the passive confinement techniques. The methodology of applying active confinement pressure in each study was different. Figure 2.1 shows the active confinement technique using prestressing wire. Gamble et al. (1996) and, Saatcioglu and Yalcin (2003)   39 conducted an experimental investigation of lateral prestressed steel strands to confine RC piers. Gamble et al. (1996) studied full-scale RC circular piers to investigate the spliced region at the base of the piers. They used externally tensioned steel bands and prestressing strands to confine the RC piers. They reported that the performance of the RC piers was improved with the help of prestressing strands. Saatcioglu and Yalcin (2003) investigated two full-scale square piers, and five full-size circular piers confined with external prestressing strands under lateral cyclic load along with constant axial load. Their results showed that the flexural behavior was improved, and the shear failure was prevented. In addition, they reported that piers retrofitted with external prestressing exhibited enhanced performance in terms of strength and ductility. The enhanced performance is mainly because of the further concrete confinement and extra shear reinforcement provided by the external prestressing system.   Figure 2.1 Circular reinforced concrete piers prestressed with steel wires (Zong-Cai et al. 2014)  2.4.1.2 Shape memory alloys (SMAs) spirals Shin and Andrawes (2011) conducted an experimental investigation on 1/3 scale as-built RC circular pier, and actively confined RC piers with shape memory alloy (SMA) spiral wires. The pier was tested under lateral cyclic load along with an axial constant load (5% of the axial load capacity). They reported that the repaired and retrofitted piers using SMA spiral could fully restore the strength stiffness, and flexural ductility, even compared to the as-built pier.   40 The improved strength, stiffness, and ductility were attributed to the active confinement of SMA spiral, which could delay the propagation of further damage. In addition, they reported that overall displacement ductility was improved; however, the displacement capacity was lower compared to the original pier.  2.4.2 Passive confinement technique For the last two decades, several researchers have conducted experimental investigations that explicitly focused on exploring the effect of passive confinement technique using FRP composites (Elsanadedy and Haroun 2005,Gallardo-Zafra and Kawashima 2009). While other studies attempted to describe analytically the constitutive behavior and stress-strain model of concrete confined with FRP (Spoelstra and Monti 1999, Fam and Rizkalla 2001, Chun and Park 2002,  Marques et al. 2004, Binici 2005, Youssef et al. 2007, Teng et al. 2007). There are also numerous studies, which attempted to explore the feasibility of FRP passive confinement method for seismic retrofit of concrete piers. Some of these studies (Saadatmanesh et al. 1997, Ma and Xiao 1997, Chang et al. 2004,  Haroun and Elsanadedy 2005, Han et al. 2014) investigated the lateral load carrying capacity by applying FRP composites as passive confinement technique. The results of these studies demonstrated that shear failure was prevented and significant improvement was obtained in the ductility capacity of retrofitted piers.    The following section briefly explains the passive confinement techniques; such as reinforced concrete, steel plate, external prestressing, engineered cementitious composite, ferrocement, and fibre-reinforced polymer (FRP) jacketing techniques for the repair and retrofitting of RC circular bridge piers. Each application by different researchers for the circular RC piers is briefly described.  2.4.2.1 Concrete jacketing In the earlier days, concrete jacketing had been a popular method for rehabilitation of deficient infrastructure. It is more economical compared to other retrofit technique, and it is the most suitable method for retrofitting of piers in water. This type of jacketing method uses a thick layer of reinforced concrete jacket around the pier. The concrete jacketing can increase the stiffness, and flexural and shear strengths as well as the deformation capacity. The concrete   41 jacketing technique is effective in obtaining an improved confinement and flexural strength. In this regard, provided longitudinal reinforcement should be properly dowelled and anchored in the footing. Unjoh (2000) reported that the concrete jacketing should be accompanied by footing retrofit to ensure that the plastic hinge forms in the pier and not in the footing. A typical method of retrofitting using concrete jacketing is depicted in Figure 2.2 (Priestley et al. 1996). This technique has some drawbacks associated with its use. Concrete jacketing is a labor-intensive, time-consuming, and could have shrinkage and bonding problems with substrate concrete. Another main drawback is the reduction of available floor-space area, since jacketing increases the section size, which leads to a substantial mass increase, stiffness modification, and subsequent modification of the dynamic characteristics of the entire structure. Rodriguez and Park (1994) carried out an experimental study on rectangular RC pier retrofitted with concrete jacketing under simulated seismic loading. They observed that the damaged and undamaged piers encased using concrete jacketing could enhance the strength, stiffness, and ductility. Priestley et al. (1996) reported that the construction and effectiveness of concrete jacketing are convenient for circular piers using closely spaced ties. Bousias et al. (2006) conducted an experimental investigation on rectangular pier retrofitted with concrete jacketing under cyclic load. They reported that the concrete jacket is effective for retrofitting piers with a lap splice length of about 15-bar diameter.    Figure 2.2 Pier retrofitting using RC jacketing (a) plan view, and (b) sectional elevation   2.4.2.2 Steel jacketing In order to enhance the strength and ductility of deficient RC piers, steel jacket can be used as a lateral confinement. The circular piers are retrofitted with circular steel jackets while (a) (b)   42 rectangular pier is retrofitted by elliptical or rectangular jackets. Typical steel jackets for circular piers are depicted in Figure 2.3.  Chai et al. (1991) investigated the retrofit of circular piers by encasing plastic hinge regions with a bonded steel jacket. They found that steel jacketing results in a pier ductility as high as those available from confined piers designed based on current codes, and inhibits bond failures in lap splices of longitudinal reinforcement in plastic hinge regions. After Chai et al. (1991) and, Priestley and Seible (1991) steel jackets have been introduced to retrofit both circular and rectangular piers around the globe. Tsai and Lin (2001) introduced the octagonal shaped steel jacket for rectangular RC pier. They reported that proportioned octagonal steel jackets could improve the ductility and cyclic strength of deficient bridge piers.      Figure 2.3 Pier retrofitting using steel jacket (a) circular pier plan, and (b) elevation (After Priestley et al. 1996)   Kawashima (1990) conducted a series of experimental investigations to retrofit 50 piers. Some of the retrofitted options were implemented in actual bridge piers, which were tested under real ground shaking during the 1995 Kobe earthquake where none of them suffered any major damage. Chai et al. (1991) studied two aspects (pier lapped with starter bars and continuous reinforcement) of steel jacketing to enhance the lateral stiffness and ductility of piers under the 1989 Loma Prieta earthquake. They observed that the pier with lapped starter bars is likely to suffer bond failure at a strength lower than their nominal flexural strength, while in the pier reinforced with continuous bars, the strength degradation is likely to have a slower rate due to the confinement failure. In addition, they reported that the lateral stiffness is affected by the jacket thickness and length. Zhang et al. (1999) investigated various (a) (b)   43 combination of pier jacketing of multi-pier bridge bent. They used partial and full retrofitting using steel jacketing. They reported that both retrofit measures could enhance the ductility, but the level of effectiveness is predominant when the pier is retrofitted in its full section. Daudey and Filiatrault (2000) performed both experimental and numerical analyses for steel-jacketed RC bridge piers using complex cross-sectional shapes and lap-splices in the plastic hinge region. They concluded that a gap of approximately 50 mm is essential between the jacket and footing top in order to avoid stress concentration and premature bar failure. Xiao and Wu (2003) studied rectangular and circular RC piers using thin steel jackets, which were further stiffened using thick plates or angle iron in the plastic hinge region. They observed that the thin jacket exhibited sufficient shear strength and partial ductility, however ultimately the pier failed as a result of the jacket bulging at the end of the pier. Sun et al. (1993), and Seible et al. (1990) reported that the rectangular steel jackets are not active enough to extract the full benefit of the retrofitting method; however, rectangular jackets can enhance the shear strength and moment capacity of the rectangular pier. The failure mode of steel jacketed rectangular pier showed adequate lateral confinement (FHWA-HRT-06-032 2006, Priestley et al. 1996).   Priestley et al. (1994a,b) and Chai et al. (1991) conducted an extensive test of the single pier with a steel jacket and recommended not to use rectangular steel jackets for the rectangular pier, though they are capable of increasing shear strength. The steel jacketing needs specialized heavy equipment at the work place, and furthermore, high cost and the likelihood of steel corrosion at the interface of steel and concrete results in bond deterioration. Other disadvantages include: difficulty in manipulating heavy steel plates in a tight construction site, need for scaffolding, and limitation in available plate lengths.  2.4.2.3 Engineered cementitious composite jacketing From the last decades, ultra-high performance concrete (UHPC) have been used for the building and bridge constructions. However, the UHPC is brittle in nature. Sometimes, the brittleness which can be evaluated using brittleness number as suggested by Hillerborg (1983) increases by increasing the compressive strength. Therefore, this nature of brittleness showed the vulnerability of structures and limited the use of high strength concrete in structural applications. In the seismic prone region, ductile concrete could make a substantial change in the overall performance of a structure during an earthquake. In the late 1990s, Li (1992a, b)   44 and his research group developed a high-performance fibre reinforced concrete (HPFRC) in order to produce an engineered cementitious composite (ECC) materials with micromechanical principles. The ECC materials consist of Portland cement, water, silica fume or fly ash, fine silica sand, randomly distributed polymeric fibres (generally polyvinyl alcohol (PVA) or polyethylene, ≤ 2% by volume), and water reducer admixture (super plasticizers). Li et al. (2001), Kesner and Billington (2004), and Boshoff (2014) reported that the ECC showed high tensile strain capacity (0.03-0.05) with strain-hardening characteristics. Therefore, this high tensile strain capacity leads to the formation of closely spaced micro crack (~100µm) which makes it appropriate materials for seismic applications. Kesner et al. (2003) demonstrated that the ECC has a lower elastic stiffness than concrete because of the absence of coarse aggregates and a higher strain at the peak compressive strength.   Saiidi and Wang (2006) conducted shake table tests on ¼ scale flexural dominated circular concrete piers longitudinally reinforced with SMAs bars in the plastic hinge area. After the tests, the pier plastic hinge area was repaired with ECC and tested again. The experimental results demonstrated that the use of ECC in the plastic hinge area could reduce the concrete damage considerably, and as a result, needs little repair even after a strong earthquake excitation. Sun et al. (2015) conducted a seismic analysis on RC hollow rectangular bridge piers under lateral cyclic load along with constant axial load. The ECC was applied to retrofit the pier inside and outside of the section. They reported that the strength and ductility capacity of the piers could be enhanced substantially with the use of ECC.   2.4.2.4 Ferrocement jacketing The ferrocement is one kind of thin composite concrete shell produced from a hydraulic cement mortar reinforced with closely spaced layers of continuously and comparatively small size (≤ 1.5mm) of wire mesh. The small diameter of wire mesh leads to a higher specific surface area which offers more effective confinement and much larger bonded area between mortar and wire. As a result of confinement, this material demonstrates isotropic and homogeneous properties in two principal directions leading to a much higher ductility. The ferrocement is moderately cost effective compared to other materials and its manufacturing does not need any advanced skill or technique (Amanat et al. 2007). Low material cost, special fire and corrosion protection characteristics of ferrocement make it an appropriate   45 mean for jacketing materials (Williamson and Fisher 1983, ACI 549.1R 1993). Numerous researchers have reported the potential application of ferrocement jacketing in repair and rehabilitation of concrete structures (Alam et al. 2009). Kaushik et al. (1990) revealed that the ferrocement confined short concrete piers could enhance the strength and ductility of piers for both axial and eccentric loadings. Kumar and Rao (2006) reported that the uniform alignment of reinforcement improves the flexural and tensile strengths, toughness, crack control, impact and fatigue resistance of piers. Xiao et al. (2011) reported that the ferrocement-confined piers produce a more ductile behavior than the fibre-reinforced polymer confined piers. Fahmy et al. (1999) conducted an experimental study on repairing pre-loaded RC piers with ferrocement jacketing. Their experimental results revealed that improved performance could be achieved for all the specimens regardless of mesh type or pre-loading level compared to the original pier.  2.4.2.5 Fibre-reinforced polymer jacketing Fibre-reinforced polymer (FRP) composites are manufactured by combining high strength fibre and resins (vinyl ester or polyester resin). FRPs were initially developed in the early 1940’s for a different type of applications in mechanical and aerospace engineering (Fardis and Khalili 1982). The use of FRP composites as the confining material has attracted much attention in the construction industry due to their favorable and essential properties (e.g. high strength-to-weight ratio, high corrosion resistance, and electromagnetic neutrality) and this will be discussed in detail in section 2.5.  2.5 Fibre Reinforced Polymer Constituents 2.5.1 FRP materials The main function of the resin or the matrix is to transfer stress between the fibres and, the fibres and the concrete. The polymer matrix is an epoxy, vinyl ester or polyester thermosetting plastic. Phenol-formaldehyde resins are the most popularly used thermosetting polymers (ACI 440.2R 2008). A range of resins has been developed with optimized structural behavior for a variety of environments. An appropriate resin must be easy to apply and compatible with, and bond to the substrate (ACI 440.2R 2002).   46  Fibres are the load carrying elements in FRP composite material. The fibres provide the strength and stiffness of the FRP system (ACI 440.2R 2008). Normally, fibres have very small diameters and high aspect ratio. Continuous fibres are used in structural applications. Different orientations of  fibres including uni-directional, bi-directional, combination of both, or other orientations can be used depending on the type of application (ACI 440.2R 2008). Four types of fibres such as carbon fibre, glass fibre, aramid fibre and basalt fibre are available in the market.   Carbon fibre reinforced polymer (CFRP) composites offer many essential properties for engineering applications, such as high tensile strength and stiffness, an outstanding corrosion resistance, and a high strength to weight ratio. CFRP, with a low coefficient of thermal expansion, has the most resistant to creep rupture and fatigue failures compared to other fibres.   Glass fibre reinforced polymer (GFRP) composites production cost is less compared to carbon fibres. GFRP offers a higher tensile strength compared to steel, very good heat transfer resistance, and low electrical conductivity. However, GFRP composites show low stiffness and low specific strength relative to carbon fibres.  Aramid fibre is generally known as Kevlar, Nomex and Technora. Aramid fibre is commonly manufactured by the reaction amongst an amine group and a carboxylic acid halide group. Composites made of aramid fibres are stiffer than GFRP and less expensive than CFRP. They have a low density and low impact resistance, high tensile strength and, good fatigue and corrosion resistance.  Basalt fibre reinforced polymer (BFRP) shows higher modulus of elasticity, equivalent tensile strength and better alkaline resistance relative to glass fibre, and excellent interfacial and shear strength. In addition, basalt fibre has a density of only one-third and a tensile strength three times that of steel and high-temperature resistance. BFRP has a higher cost due to lack of manufacturer capacity, but a better strength than GFRP. The basalt fibre is environmentally friendly and economical compared to other fibrous materials.  2.5.2 Application of FRP as confining materials  The use of fibre-reinforced polymer (FRP) composites (e.g. glass, carbon, aramid, and basalt) as the confining material has found much attention in the construction industry (Seible et al.   47 1997, Xiao et al. 1999). Because of the lightweight, high strength and stiffness-to-weight ratio, durability properties, performance, and especially the ease of application, the FRP composites jacketing method offers great benefits compared to other jacketing system (steel, concrete, and FRC). Amongst all the fibres, CFRP is more robust because of its higher modulus of elasticity and high tensile strength compared to the other fibres. One of the most popular applications of FRP composites is confining materials for concrete, in both the retrofit of existing RC piers in the form of filaments windings and wraps, and in concrete-filled FRP tubes to achieve confinement in new construction of RC piers (Bakis et al. 2002) for improved seismic resistance. Figure 2.4 shows the application of CFRP confinement for RC circular piers.  Many researchers have explored the viability of FRP passive confinement techniques for upgrading the seismic performance of deficient RC bridge  piers (Saadatmanesh et al. 1994, Saadatmanesh et al. 1997, Ma and Xiao 1997, Samaan et al. 1998, Bakis et al. 2002, Chang et al. 2004, Haroun and Elsanadedy 2005, Han et al. 2014). From extensive experimental investigations, it has been observed that continuous fibre FRP wrapped piers can substantially improve the flexural  and shear capacities of deficient RC bridge piers (Haroun and Elsanadedy 2005, Chang et al. 2004, Gallardo-Zafra and Kawashima (2009).   Figure 2.4 Pier retrofitting using FRP jacket (a) circular pier (After Priestley et al. (1996)  Gallardo-Zafra and Kawashima (2009) reported that the flexural strength and ductility of piers retrofitted with CFRP composite increased with the increasing CFRP confinement ratio. Chang et al. (2004) performed pseudo-dynamic tests on as-built and CFRP strengthened rectangular RC bridge piers under near-fault ground motions. They discovered that the   48 flexural strength of damaged RC bridge piers improved after retrofitting with CFRP composite.  2.6 Models of FRP-confined Concrete under Axial Compression In order to design economical and reliable FRP retrofitting system for RC piers, the stress-strain response (SSR) and constitutive modeling of FRP-confined concrete (defined as FCC cylinder hereafter in this research) need to be understood clearly. In other words, the FRP retrofitted piers should be simulated under monotonic and lateral cyclic loads using the numerical method by considering the constitutive law defined in terms of axial stress-strain models of confined concrete. Numerous researchers studied the constitutive models and SSR of FCC under concentric compression and cyclic load for the circular unreinforced concrete section.   In the previous studies of FRP strengthened RC piers (Saadatmanesh et al. 1994, Seible et al. 1995, Mander et al. 1988a), active-confined concrete (ACC) model was directly adopted in the analysis. However, many researchers did not agree (Mirmiran and Shahawy 1996, Samaan et al. 1998, Miyauchi et al. 1997, Saafi et al. 1999, Spoelstra and Monti 1999) with the direct consideration of ACC model for the analysis of FRP strengthened piers. They reported that SSR of FRP sheet is linear elastic up to the brittle failure; whereas, the SSR of steel plate is elastoplastic until failure which is not capable of estimating the dilatancy of confined concrete (Mirmiran and Shahawy 1997). In addition, the steel confined concrete model proposed by Mander et al. (1988a), a constant confining pressure was presumed while the steel was in the yield state; conversely, the FRP materials do not exhibit yielding state, and as a result, exert a constant confining pressure on the concrete core. Accordingly, extensive studies have been carried out for the development of analytical and experimental models of FCC. However, several of these models were generated with inadequate test results available to the scientists. Hence, the performance of these models degrades when the accuracy of these models is evaluated with a larger number of experimental results (Lam and Teng 2003b, De Lorenzis and Tepfers 2003, and Bisby et al. 2005). In addition, the correctness and statistics of these models are mostly affected by the test data used in the regression analysis of the models (Lee and Hegemier 2009).       49 2.6.1 Mechanism of FRP confinement  In order to analyze the concentric compression behavior of FCC, it is important to recognize the confinement mechanism of FCC, and the interaction between FRP jacket and concrete core (Benzaid et al. 2010). Under the application of concentric compression load on confined concrete, the axial compression strain increases whereas, due to the Poisson’s effect the lateral strain increases (Benzaid et al. 2010). When the axial stress/strain surpasses particular limits, vertical cracks occur and then, the lateral strain magnitude increases with axial strain at a high rate (Lam and Teng 2003a). Subsequently, FCC hoop stress increases and limits the lateral expansion, which increases the strength and deformability of concrete (Lam and Teng 2003a). In other words, the lateral confinement pressure (fl) is exerted by FRP wraps after concrete experiences a significant radial expansion under the axial compression load (Lam and Teng 2003a). Figure 2.5 shows the schematic representation of the confinement action exerted on the FCC (Lam and Teng 2003a). At the FRP-concrete interaction, the confinement pressure, fl on the concrete core can be computed based on the force equilibrium and the displacement compatibility characteristic using Eq. (2.1)  h frplf tfR  (2.1) where fh is the hoop tensile stress in FRP jacket, and R is the radius of the core concrete section. The FRP composites show linear SSR until rupture, thus the hoop stress of FRP jacket is proportional to the hoop strain εh,frp, which could be calculated as fh = Efrp × εh,frp where Efrp is the elastic modulus of FRP composite.          Figure 2.5 Confinement action of FRP-confined concrete in circular section (Lam and Teng 2003a) 2R + 2tfrp Cross-section fl fc 2R  Plain concrete 2R frp frp frpf n t  frp frp frpf n t  tfrp FRP layer fl Cylinder fully wrapped with FRP  Free body diagram of FRP-confined concrete  Tri-axial stress state of concrete fl fc fl fc 2R    50  The axial compressive stress increases due to the uniform radial stress exerted by FRP jacket, which produces hoop tensile stresses (De Lorenzis and Tepfers 2003, and Teng and Lam 2002). The extreme confinement stresses exerted by the FRP is achieved when the peripheral strain in the FRP reaches its ultimate strain capacity and the rupture of fibre leads to brittle failure of the confined concrete (Benzaid et al. 2010). At the ultimate strength (flu) of FCC, the lateral confining pressure could be estimated using Eq. (2.2). However, numerous researchers, (Mirmiran et al. 1998, Matthys et al. 1999 , Xiao and Wu 2000, Pessiki et al. 2001, Harries and Carey 2002, (Lam and Teng 2003b), De Lorenzis and Tepfers 2003, Lam and Teng 2004, Theriault et al. 2004, Matthys et al. 2006, and, Ozbakkaloglu and Oehlers 2008) reported that the hoop strain (εh,rup) at rupture of FRP jacket in confined concrete is considerably lower than the ultimate hoop rupture statin of (εfrp) of FRP coupons (Benzaid et al. 2010 and, Seffo and Hamcho 2012).  2 22frp frp fu frp frp frp frplE t t f ffd d     (2.2) where fl, Efrp, εfu, ffrp, and tfrp are the lateral confining pressure, modulus of elasticity, ultimate tensile strain and strength, and nominal thickness of the FRP jacket, respectively. d is the diameter of the core concrete, and ρfrp is the volumetric ratio of FRP jacket to the core concrete that can be estimated using Eq. (2.3) (Figure 2.6) (Xiao and Wu 2001).  24/ 4frp frpfrpdt td d   (2.3)  Ozbakkaloglu and Lim (2013) demonstrated that FRP fabrics’ hoop rupture strain and ultimate tensile strain were different. They showed that the change in the hoop rupture strain and the material ultimate tensile strain depends on (i) the quality of workmanship (ii) fibre sheets overlap in the FRP shell; (iii) manufacturing deficiencies (e.g., misalignment of fibres); (iv) contraction of the concrete (for FRP tube-encased concrete); (v) localized or non-uniform effects caused by failures in FRP shells and/or heterogeneity of cracked concrete; (vi) load eccentricities caused by specimen failures and/or test setup inaccuracies; (vii) multi-axial stress condition generated on the FRP shell; and (viii) curvature effect of the FRP shell. Pessiki et al. (2001) proposed a strain reduction factor (kε) in Eq. (2.4) to introduce a relationship between the hoop rupture strain and the ultimate tensile strain (εfrp,u) of FRP composite based on (a) different shape of FRP coupons, (b) laboratory flat coupons, and (c) in-situ FRP jacket. The strain reduction/efficiency factor (kε) is defined as the ratio of ultimate   51 hoop rupture strain (εh,rup) of FRP jacket to the ultimate hoop rupture strain (εfrp,u) of FRP flat coupon test or fibres. The actual confining pressure (flu,a) (Eq. (2.5)) could be calculated by substituting the material ultimate tensile strain (εfrp,u) with the hoop rupture strain of the FRP shell (εh,rup) in Eq. (2.2) (Lam and Teng 2003a).  , , ,h rup frp frp uk  (2.4) where εfrp is the ultimate rupture strain of FRP which could be obtained from the coupon tests.  ,,2 frp frp h ruplu aE tfd  (2.5)  2.6.2 Constitutive stress-strain response of FRP-confined concrete The FCC stress-strain characteristics  mostly depend on the FRP-concrete interaction, type of FRP, and method of confinement (Samaan et al. 1998). On the other hand, at low axial stress, the FCC stress-strain curve follows a trend similar to that of unconfined concrete (Wu et al. 2006). Due to the dilatancy effect of FCC, the lateral expansion of confined concrete increases considerably at the peak compressive strength of unconfined concrete, and then it is followed by micro cracks. Fukuzawa et al. (1998), Miyauchi et al. (1997), Miyauchi et al. (1999), and Nakatsuka et al. (1998) reported that if the confinement is not adequate, the stress will decrease at the peak strength until the FRP composite fails. When the confinement is adequate, the composite will be activated at the peak strength of unconfined concrete and increase the uniformly distributed stress on the concrete until the composite ruptures (Wu et al. 2006). At the relaxation and evolution states, the peak stress of unconfined concrete change its original dimension; and accordingly, the FCC reveal a new bilinear stress-strain curve (Mirmiran and Shahaway 1997, Toutanji 1999, Xiao and Wu 2000, and, Xiao and Wu 2001). Figure 2.6 represents the schematic of the stress-strain curve of FCC with a constant confining pressure along with unconfined concrete under compressive loading.   The FRP confined concrete typically shows a monotonically bilinear ascending stress-strain curve (line OBD in Figure 2.6) at the ultimate strain ' '( )cc cu  of the peak confined compressive strength, 'ccf  (i.e.,' 'cc cu  ) of 7% confining pressure. Whereas, when the value of confinement pressure, fl is less than 7%, the stress-strain curve displays a post-peak softening offset, and, the peak strength, 'ccf  is achieved prior to the rupture of FRP (line OAC in Figure 2.6) (therefore, ' '( )cu cc  (Realfonzo and Napoli 2011). Benzaid et al. (2010) reported that the   52 high strength (' 50cof  MPa) FCC with a ratio of' 0.095l cof f  , considered as inadequately confined as the high strength FCC fails in a brittle fashion. Jiang and Teng (2007) indicated three kinds of confinement fashion, namely, low, fair, and extra confined concrete. They reported that the stress-strain curve, which follows a descending order represents the behavior of low-confined concrete. While the stress-strain curves which show a bilinear ascending order referred to fair and extra-confined concrete. After the ascending-bilinear curve, the confinement could be differentiated using ' 'cu cof f ratio (where'cuf  and 'cof are the axial compressive stress of FRP-confined and unconfined concrete, respectively). In addition, they also reported that when the ratio of' ' 2cu cof f  , the concrete is considered to be fair-confined, while all other cases with the ratio of' ' 2cu cof f   are considered to be extra confined concrete.            Figure 2.6 Schematic of axial stress-strain relationship of unconfined and FRP-confined concrete  2.7 Axial Stress-Strain Models for FRP-Confined Concrete Numerous researchers have proposed constitutive models of FCC under concentric compression load. The current models are categorized into two sets (Lam and Teng 2003a) (a) the design-oriented stress-strain models (DOMs) (Fardis and Khalili 1982, Karbhari and Gao 1997, Samaan et al. 1998, Miyauchi et al. 1997, Saafi et al. 1999, Toutanji 1999, Lillistone and Jolly 2000, Lam and Teng 2003a, Xiao and Wu 2000, Berthet et al. 2006, Harajli 2006, cof  B A D Unconfined concrete Confined concrete with strain hardening region o 'cc Confined concrete with strain softening region C 'cu  'cu  c  'cuf  ccf  FRP rupture cuf  c Confined concrete A = strain softening point B = strain-hardening point C = Ultimate point D = rupture point   FRP rupture Increasing type Decreasing type with' 'cu cof f 1 0.07lf   0.07lf   co    53 Saenz and Pantelides 2007, Wu et al. 2007, Youssef et al. 2007) and (b) the analysis-oriented stress-strain models (AOMs) (Mirmiran and Shahawy 1996,  Spoelstra and Monti 1999, and  Fam and Rizkalla 2001,  Harmon et al. 1998, Chun and Park 2002,  Harries and Kharel 2002, Marques et al. 2004, Binici 2005, Teng et al. 2007, Jiang and Teng 2007, Marques et al. 2012). The details of these DOMs and AOMs are presented in Appendix B (Table B.1 and Table B.2), respectively. In the DOM, the stress-strain curve and the ultimate state are derived based on regression analysis and closed-form solutions using experimental data which are simple to be directly used in the design process of FRP retrofitting system. However, the stress-strain curve of AOM is derived by means of an incremental-iterative procedure which makes them unsuitable for the direct use in the design process (Marques et al. 2012). In AOMs, the stress-strain curves with different active confinement levels generate a passive confinement curve as shown in Figure 2.7(a) and Eqs. (2.1)-(2.5) based on ACC stress-strain model. The incremental technique is iterative in most of the stress-strain models, therefore, AOMs is not popular in engineering communities (Marques et al. 2012). However, Lam and Teng (2003b) reported that AOMs show advantages for the interface of concrete and confining materials. For the computer-based numerical methods and advanced analyses, AOMs are ideal to produce numerical data for the development of DOMs (Teng et al. 2009). The open interaction was observed in the AOMs with different materials (FRP, steel, and concrete). In addition, the AOMs adopt the compatibility between the lateral strains, εl of actively confined concrete for the calculation of fl produced by FRP jacket. Figure 2.7 Concept basis for confinement modeling (a) Two parts confinement DOM by Toutanji (1999), (b) passive confinement model (dots) (Jiang and Teng 2007) generated using active confinement stress-strain curves (Mander et al. 1988a) –AOM   54  Toutanji (1999) and Saafi et al. (1999) DOMs are based on the same approximation from the two-state SSR (Figure 2.7a) using incremental techniques without iteration  (Richart et al. 1928). In the first state of the stress-strain curve, the response was similar to that of plain concrete, and the second state of stress-strain curve showed the fully activated FRP jacket. Ahmad and Shah (1982) adopted Richart et al. (1928) models  (see Eq. (3.9)) which was the first region of concrete confined with lateral hydrostatic stress and the spiral steel. Richart et al. (1928) revealed that the confined concrete axial strain (εco) increases with increasing the lateral pressure at the corresponding maximum stress (Eq.(3.10)).  cc co l lf f k f  (2.6)  1 5lca o lccfkf      (2.7) Where,  fcc is the strength of confined concrete, fco, is the strength of unconfined concrete, fl, is the lateral pressure, kl is the coefficient of confinement effectiveness, and εca is the axial strain of concrete. Richart et al. (1928) presumed a constant value for the kl equal to 4.1. Toutanji (1999) modified Richart et al. (1928) model (Eqs. (3.9) and Eq. (3.10)) to estimate the axial stress (Eq.(3.11)) and axial strain (Eq.(2.9)) at each point of the second state of FCC. Toutanji (1999) model was studied by Matthys et al. (2006) considering the 2nd part of the failure strain in the hoop direction which was  0.06 times  the ultimate strain of the CFRP (Figure 2.7(a)).     0.851 3.5a cc l ccf f f f   (2.8)  1 (310.57 1.9) aa o lccff             (2.9)  2.7.1 Design oriented stress-strain models (DOMs) The existing DOMs (Lam and Teng 2003b, Teng et al. 2009) are established through closed-form equations from the regression analysis with large numbers of experimental tests database on FCC circular section. Therefore, these models are considered as more accurate and uniform models to represents the response of FCC (Teng et al. 2013, Ozbakkaloglu and Lim 2013). The DOMs are simple; hence, they could be directly used in the design. However, the accuracy of these models depends on the test database adopted in the regression analysis. The DOMs proposed by Moran and Pantelides (2002) is complex compared to the other DOMs, hence it cannot be directly used in design. Most of the DOMs predict an increasing kind of   55 stress-strain curve, but some of the models (Xiao and Wu 2000, Miyauchi et al. 1999, Moran and Pantelides 2002) follow both increasing and decreasing trends of the stress-strain curve. The following subsection explains the increasing, decreasing and bilinear stress-strain curves of FRP confined concrete.  In order to model the transition point (Figure 2.6) in the initial part of the stress-strain curve of FCC, most of the researchers (Miyauchi et al. 1998, Youssef et al. 2007, Miyauchi et al. 1999, Jolly and Lilistone 1998, Jolly and Lilistone 2000, and Matthys et al. 2006) adopted the parabolic shape stress-strain curve from Hognestad (1951). The next part of the stress-strain curve was approximated by joining the initial peak with the ultimate condition through straight lines defined with Eqs. (2.10) and (2.11).  2'11 12 forc cc c c clc cf f                   (2.10)   '1 2 1 forc c c c c clf f E         (2.11)  where ' '121cc ccu cf fE   (2.12)  Richard and Abbott (1975) proposed a confinement stress-strain model using a continuous function to describe the elastic plastic (bilinear) constitutive law using a four-parameter formulation of FCC piers according to Eq. (2.13).    1 221/1 21cc cnncoE Ef EE Ef          (2.13) where, fc and εc are the axial stress and the axial strain of FCC, respectively; E1 and E2 are the first slope (ascending branch) and second slope (post peak) of the stress-strain curve, respectively (Figure 2.6); and n is the shape parameter which controls curvature in the transition zone using the two linear portions of the curve based on Eq. (2.14). fo is the plastic stress intercept of the second slope with the stress axis which could be estimated using Eq. (2.15). The initial elastic modulus 1E of FCC can be determined using '1 5500 cpE f in psi (Yan 2005) or '1 4730 cpE f  in MPa (ACI Committee 318 1995). After the peak, Richard and Abbott (1975) stress-strain model displays a hardening slope when E2 > 0, E1 < 0 indicates   56 strain softening behavior. According to Yan (2005), β increases as the jacket effective confinement ratio 'lu cof f decreases; β can be calculated using empirical Eq. (2.16).   1 2111nE E  (2.14)   ' '2o cc ccf f E    (2.15)    0.8'190 lu cof f  (2.16)   '2 'cc occ of fE  (2.17)   ' '2 ' 'cu cccu ccf fE  (2.18)  Plastic stress fo and slope E2 for FCC piers with strain hardening nature could be estimated using Eqs. (2.15) and (2.17), respectively. For piers with the softening response, E2 can be estimated using Eq. (2.18). Eco is the secant modulus associated with the slope of the line passing through the origin and the point at which the slope changesco co coE f  .  Samaan et al. (1998), Lam and Teng (2003b), Moran and Pantelides (2002), Jiang and Teng (2006), Yan and Pantelides (2007), Teng et al. (2009), Fahmy and Wu (2010) corrected the initial form of the stress-strain formula and established a new form of stress-strain model of FCC. The corrected formulas of stress-strain models are different from the initial models and are presented in Appendix B (Table B.1). In the earlier FCC models, the stress-strain curves were depicted with two slopes, such as the initial increasing part (E1) of the elastic zone, and the second slope of the post peak part (E2) (Eq. (2.13)). Appendix Table B.1 shows the various formulae for estimating of E1 of FCC.   Ahmad and Shah (1982) advised a bilinear stress-strain curve (Eq. (2.19)) for confined concrete using Sargin (1971) steel confined concrete.     22'11 2c ci ico coccoc ci ico coA DffA D                          (2.19) where   1 4.2556 ,    (if 0.68 ) 1.7757 3.1171 ,    (if 0.68 ) c l rco co coc l rco co cof f ff f ff f ff f f                (2.20)   57  The FCC model proposed by Toutanji (1999) (Eq.(2.21)) which was the modified model of Ahmad and Shah (1982) for steel spiral confined concrete. Consequently, several researchers adopted Toutanji (1999) model to represent the stress-strain relationship of FCC. To define the stress-strain curve, these models used the slopes of the 1st part (increasing E1) and after the peak stress in 2nd part (E2). It can be observed that in Figure 2.6, the slope of the 2nd part (Eoc2) refers to the tangential slope of the stress-strain curve taken instantly after the 1st peak stress ( '1cf ).  21i cci c i cAfC D   (2.21)   where 2iA E  (2.22)   '1 2 12' '21 1 12 cic c cE EECf f    (2.23)  '1 22 '21 11ic cE EDf   (2.24) whereiA , iC and iD are constants of the initial slope and the descending part of the stress-strain curve to be obtained from the boundary conditions.  Appendix B (Table B.1) presents a summary of the ultimate strength '( )ccf and the ultimate strain (εcu) of FCC stress-stain model equations. However, few of the models provided equations only for the ultimate strength without the ultimate strain and a comprehensive SSR has not been explained in these models. The majority of the researchers used Richart et al. (1928) Eq. (2.25) actively or (steel) confined concrete model for estimating the compressive strength '*( )ccf  and the corresponding ultimate strain (εcu). According to Ozbakkaloglu et al. (2013), the overall form of this strength and strain enhancement models can be found in Eqs. (2.26) and (2.27).   In Appendix B (Table B.1, Table B.2, and Table B.3), it should be noted that the models adopted by both the ACI 440.2R (2002) and FIB Bulletin 14 (2002) were based on Mander et al. (1988a) active or steel-confined concrete. The FCC model introduced by Spoelstra and Monti (1999) was the revised model of Mander et al. (1988a) steel or active confined concrete model. The FIB Bulletin 14 (2002) recommended design guidelines of the FCC model which was proposed by Spoelstra and Monti (1999). According to CAN/CSA-S806 (2002), the peak compressive strength of FCC could be estimated using Eq. (2.28). Based on the experimental   58 investigation, Razvi and Saatcioglu (1999) proposed the confinement coefficient kl using Eq. (2.21) by Richart et al. (1928) model, where 1sk   and  0.176.7l s lk k f . The Concrete Society Technical Report No. 55 (2004) proposed DOMs based on (Lam and Teng 2003a).   ' 'cc co l luf f k f   (2.25)   '1 1' 'cc luco cof fc k kf f      (2.26)   '2 2' 'cc luco cof fc k kf f      (2.27)   '' '0.85cc ll sco cof fk kf f   (2.28) where c1 and c2 are the correction constants, and k1, k2 and kε are the strength and strain enhancement coefficients, and hoop strain reduction factor for FCC, respectively. 'ccf and 'cof are the maximum compressive strength of confined and unconfined concrete, respectively. The lateral confinement stress, fl is computed based on the equilibrium of forces in the FCC cylinder.   2.7.2 Analysis-oriented stress-strain models (AOMs) Analysis oriented stress-strain models explicitly capture the interaction among the expanding concrete core and FRP wraps using static equilibriums and strain compatibility equations of ACC (Teng et al. 2007, Jiang and Teng 2007). Generally, AOMs, in which the stress-strain curves are developed using an incremental approach in an explicit manner, are more resourceful and exact; hence they could be used for numerical analyses (i.e., nonlinear finite element analysis) of FRP jacketed reinforced concrete piers (Teng et al. 2007). Conversely, the incremental technique is complex and time-consuming. Hence it makes AOMs unsuitable for the direct use in design calculation of FRP jacketed reinforced concrete piers (Teng and Lam 2004). The theory of FCC passive stress-strain model using an incremental approach had been earlier applied with the base model of ACC by Ahmad and Shah (1982) Richart et al. (1928) and, Madas and Elnashai (1992). After that, Mirmiran and Shahawy (1996), and Mirmiran and Shahaway (1997) extended Madas and Elnashai (1992) approach for FCC stress-strain model as a base model of ACC using an incremental approach as depicted in Figure 2.7(a) and Figure 2.7(b). Several researchers used Mander et al. (1988a) ACC stress-  59 strain model using (Mirmiran and Shahawy 1996) model in order to propose the FCC stress-strain model. Succeeding the stress-strain model proposed by Mirmiran and Shahawy (1996), and Mirmiran and Shahaway (1997), various researchers have generated FCC stress-strain models (Spoelstra and Monti 1999, Fam and Rizkalla 2001, Chun and Park 2002, Harries and Kharel 2002, Marques et al. 2004, Binici 2005, Teng et al. 2007). Most of the AOMs were proposed for a normal strength FCC which shows a typical bilinear stress-strain behavior. Some of the AOMs do not show a bilinear stress-strain behavior (Xiao and Wu 2000, Miyauchi et al. 1999). A detailed review of the majority of these models can be found in Jiang and Teng (2007), however, a brief summary of AOMs is presented in this thesis. Appendix B (Table B.2 and Table B.3) present a summary of the existing AOMs reported in the open literature.   The models were developed using an incremental approach assuming that the axial stress and strain of FCC are similar to concrete but with different levels of active confinement (Figure 2.7 (a)) and a constant confining pressure of FRP (Teng et al. 2007). In other words, the initial confinement pressure exerted under concentric compression load remains constant throughout the loading procedure (Teng et al. 2013). The accuracy of AOM mostly depends on the extrapolation of axial and lateral strains of concrete and adopted ACC base model (Teng et al. 2013). For the AOMs, the incremental approach needs a lateral-to-axial strain or dilation relationship for FCC  and explicit manner in order to be extended to  other materials (concrete filled-FRP tube) (Teng et al. 2013). The incremental approach includes the estimation of stress-strain curves of FCC as explained in the subsequent section.   2.7.3 Axial stress-strain curves based on active confinement models The confinement offered by FRP to concrete core is passive rather than active due to the confining pressure from the FRP generated by increasing the lateral expansion of the concrete core (Jiang and Teng 2007). The AOMs of FCC reviewed in this article assumed that the confining pressure applied externally remains uniform as the axial stress increases similar to ACC (Jiang and Teng 2007). These models are referred as active confinement stress-strain models. As shown in Appendix B (Table B.2 and Table B.3), the models developed are based on the assumption that the axial stress and strain of FCC  at a given lateral strain are the same as those of the concrete actively confined with a constant confining pressure equal to that   60 exerted by the FRP shell (Mirmiran and Shahawy 1996, Spoelstra and Monti 1999, Fam and Rizkalla 2001, Chun and Park 2002, and Harries and Kharel 2002).    A well-known an active confinement model proposed by Mirmiran and Shahawy (1996), Marques et al. (2004), Binici (2005), Teng et al. (2007), Spoelstra and Monti (1999), Fam and Rizkalla (2001), Chun and Park (2002), and Harries and Kharel (2002) have been briefly discussed here and evaluated using stress-strain curves of FCC with a significant level of confinement. To predict the SSR of the actively confined concrete and estimate its peak axial stress '*( )ccf  and corresponding strain*( )cc , a stress-strain equation along with a set of equations. Most of the existing AOMs (Saadatmanesh et al. 1994, Mirmiran and Shahawy 1996, Spoelstra and Monti 1999, Teng et al. 2007, Xiao et al. 2010, Jiang and Teng 2007, Fam and Rizkalla 2001, Chun and Park 2002, Marques et al. 2004 and Aire et al. 2010) except Harries and Kharel (2002) and Binici (2005) adopted the stress-strain model proposed by Popovics (1973) (Eq.(2.26)), and later adopted by Mander et al. (1988a), to estimate the shape of the actively confined concrete base curves. In the model of Popovics (1973), the stress-strain curve of concrete is defined using an energy balance approach as Eq. (2.29).    *'* *1c cccrcc c ccrff r    (2.29) where r is constant for the brittle response of concrete, fc is the axial stress of concrete, '*ccf and *cc are the peak axial stress and corresponding axial strain of concrete, respectively. Every model reviewed in this thesis  adopted the original or modified version of Popovics (1973) model to calculate  constant, r, using Carreira and Chu (1985) Eq. (2.30) where Ec is the elastic modulus of concrete.  '* *cc cc ccErE f  (2.30)  The stress-strain equation of actively-confined concrete defined by Eq. (2.26) is the modified version of Popovics (1973) model using a factor which was employed in Harries and Kharel (2002) model to control the slope of the decreasing part. The modified versions of the equations are presented in Appendix B (Table B.2 and Table B.3). The model introduced by Binici (2005) adopted the three separate equations to define the full stress-strain curve. The majority of the reviewed models in this thesis adopted ACI Committee 318 (1995) equation as   61 '4700c coE f in MPa to estimate the initial elastic modulus of concrete. Few of the models (Spoelstra and Monti 1999, Marques et al. 2004, Binici 2005, and Aire et al. 2010) implemented  different equations for  determining Ec These equations are presented in Appendix B (Table B.2 and Table B.3).   2.7.4 Peak axial stress equation for actively confined concrete  To determine the peak stress and corresponding peak strain on the stress-strain curve of actively confined concrete in AOMs, which are presented in Appendix B (Table B.2 and Table B.3) can be used. To define the peak axial stress (failure surface of concrete) Mirmiran and Shahawy (1996), Spoelstra and Monti (1999), Fam and Rizkalla (2001), Chun and Park (2002) adopted a “five-parameter” multiaxial failure surface which was suggested by Willam and Warnke (1975) in Eq. (2.31) proposed by Mander et al. (1988a). While in other four models, Harries and Kharel (2002) adopted Eq. (2.32) which was proposed by Mirmiran and Shahaway (1997). Marques et al. (2004) model employed Eq. (2.33) proposed by Razvi and Saatcioglu (1999). Binici (2005), and Binici (2008) model adopted Pramono and Willam (1989) criterion which is written in Eq. (2.34) if the tensile strength of unconfined concrete is assumed to be 0.1 times its compressive strength. Teng et al. (2007) and, Jiang and Teng (2007) proposed a linear function to define the peak axial stress Eq. (2.35). Albanesi et al. (2007) also proposed a linear function to define the peak axial stress Eq. (2.36). Xiao et al. (2010) proposed Eq. (2.37) for NSC and HSC by regression analysis to define the peak axial stress.  * *' ''* '2.254 1 7.94 2 1.254l lco cocc cof ff ff f        (2.31)   '* ' 0.587 '* ' 0.5874.269 4.269cc co l cc co lf f f ff f    (2.32)   '* ' 0.176.7cc co lf f f   (2.33)   '* ' 1 9.99 l lcc coco cof ff ff f     (2.34)   '* ' 3.5cc co lf f f   (2.35)   ' ' 3.609cu co luf f f   (2.36)   62   0.80'' '1 3.24cc lco cof ff f      (2.37) where '*ccf is the peak axial stress of concrete under a specific constant confining pressure (fl) and 'cof  is the compressive strength of unconfined concrete.  2.7.5 Peak axial strain equation for actively confined concrete  All existing reviewed models employed  Eq. (2.38) which was originally proposed by Richart et al. (1928) to describe the axial strain at peak axial stress.  '**'5 0.8cccc cocoff      (2.38)   '**'1 5 1cccc cocoff          (2.39)   ' '18.045 , for 0.7lu lucu co coco cof ff f      (2.40)   1.2* *'1 17.5cc lco coff      (2.41)   1.06* *'1 17.4cc lco coff      (2.42) where *cc is the axial strain at peak axial stress '*( )ccf  of concrete under a specific constant confining pressure andco is the axial strain at peak axial'*( )ccf stress of unconfined concrete'cof . Marques et al. (2004) and Aire et al. (2010) used Eq. (2.39) for normal strength concrete (NSC)' 40cof  MPa.  For high strength concrete (HSC), Eq. (2.39) was modified by a factor introduced by Razvi and Saatcioglu (1999) to account for the reduced effectiveness in the enhancement of axial strain. Albanesi et al. (2007) proposed a linear function to define the peak axial strain Eq. (2.40). Jiang and Teng (2007) also proposed a linear function to define the peak axial strain Eq. (2.41). Xiao et al. (2010) proposed Eq. (2.42) for NSC and HSC by regression analysis to define the peak axial strain.       63 2.8 Experimental Test of FRP-Retrofitted RC Piers Numerous experimental investigations have been conducted on the seismic behavior of FRP jacketed RC pier. In this section, the experimental test results of FRP retrofitted RC  circular piers have been collected from the existing works (Xiao et al. 1999, Sheikh and Yau 2002, Haroun et al. 2003, Li and Sung 2004, Haroun and Elsanadedy 2005, Gu et al. 2010,  and Wang et al. 2010). In the collected database, the height of the pier is in the range of 630-2045mm, the diameter is in between 150mm and 760mm, and the shear span- depth ratio is in the range of 1.5-7.4. The compressive strength of concrete is in the range of 18.6-95 MPa, and the applied axial load is in the range of 3-68% of the axial capacity of the pier. The thickness, ultimate tensile strength, and elastic modulus of FRP are in the range of 0.11-10.16mm, 552-4300 MPa, and 38-260 GPa, respectively. The wet-layup FRP jackets used in the original study were formed using carbon, glass, and aramid fibres and applied pier only in the hoop direction of the piers. The FRP retrofitted pier presented in the database  mostly encountered flexural failure, and the pier tested by (Xiao et al. 1999) failed in flexural-shear mode. The detailed descriptions of the experimental test of FRP retrofitted piers are presented in Appendix C. Summary of repair and retrofitted circular piers from the experimental tests are presented in Appendix C (Table C.1).  2.9 Summary  The relevant research reported in the existing literature was summarized in this Chapter. The first section described the performance of bridge piers in the past earthquakes. The second section reported the seismic repair and retrofitting techniques, (e.g. active and passive confinement methods). In the active confinement techniques, application of external prestressing strands, and shape memory alloys (SMAs) were discussed. In the passive confinement techniques, reinforced concrete, steel plate, engineered cementitious composites (ECC), ferrocement, and fibre reinforced polymer (FRP) jacketing methods were explained. Next section presented the axial stress-strain models of FRP-confined concrete. The design-oriented and analysis-oriented FRP-confined concrete stress-stain models are also presented where the axial peak stress and strain equations are presented in Appendix B (Table B.1 and Table B.2). A summary of dilation behavior and stress-strain curves of analysis-oriented models are presented in Appendix B (Table B.3). The next section described the selected   64 experimental investigations in which all the specimens were transversely confined with steel and FRP jacketing and tested under seismic loading (lateral cyclic and shake table tests) with a constant axial load. A summary of these experimental studies along with the repair and retrofitting methods and research findings were presented in Appendix C (Table C.1). Application of different design procedure using various codes, including ACI Committee 440.2R (ACI 440.2R 2008), CAN/CSA-S806 (2012), Technical Report of Concrete Society (TR 55 2004), Technical Report of fib Bulletin No. 14 (2001), Council of National Research (CNR-DT 2013), and Turkey Earthquake Code (TEC 2007) were discussed in detail about  externally bonded FRP jacket for circular RC piers were presented in Appendix D.                        65 Chapter 3: Finite Element Modeling of Non-Seismically Designed Circular RC Bridge Pier Retrofitted with FRP  3.1 General To consider a variation of more parameters in the effect analysis of seismic performance of retrofitted bridge piers, numerical models validated with the experimental results can be utilized to portray the energy dissipation capacity and stiffness degradation of retrofitted piers. Numerical models are generated using a finite element software, Seismosoft (2015) to conduct nonlinear static, cyclic and dynamic time history analyses. This program has capabilities for modeling and analyzing the nonlinear behavior of structures using wider range of material models, elements and algorithm solutions. The circular piers tested by researchers in the past are analyzed and validated with the experimental test results. To investigate the efficacy of the proposed numerical method in predicting the response of such piers, comprehensive nonlinear static pushover, and reverse cyclic analyses are carried out.   3.2 Numerical Investigation of Bridge Piers In this part of the thesis, the numerical model of circular RC bridge pier was generated based on the experimental investigation performed by Kawashima et al. (2000) and Yoneda et al. (2001). They tested a series of scaled RC bridge piers retrofitted with CFRP composite under lateral cyclic load and a constant axial load. The experimental results help validate the numerical model.   3.2.1 Description of bridge pier model The dimensions and material properties of deficient bridge piers are selected from the previous literature on RC bridge piers built before 1970 (Kawashima et al. 2000). The schematic of a detailed drawing of the adopted bridge pier is presented in Figure 3.1, which is reinforced with 12-15M (dia. of 16 mm) longitudinal reinforcement ratio of 1.89%, and 0.128% transverse steel (dia. of 6 mm) with 300 mm center-to-center spacing. As illustrated in Figure 3.1, the pier specimens have a diameter of 400 mm and an effective height of 1350 mm with a clear concrete cover of 35 mm. An infinitely rigid foundation was assumed. The pier was restrained in the out of plane motion. Cyclic horizontal displacement was applied at the   66 top of the pier, forcing it to move in the horizontal direction only. Table 3.1 depicts the material properties and dimensions adopted in this study. The specified compressive strength of the unconfined concrete is 30 MPa, and the yield strength of longitudinal and transverse reinforcements are 374 and 363 MPa, respectively. The height of the confined region where FRP jackets are applied is 1000mm from the base of the pier (see Figure 3.1(a)). An axial compressive load of 188.4 kN representing 5% axial capacity of the pier is applied at the top of the pier. The FRP retrofitting techniques adopted in this study are adapted from Kawashima et al. (2000), and Shin (2012). The CFRP and GFRP composites, respectively have initial stiffnesses of 266 and 19.13GPa, and ultimate strains of 1.63% and 1.80%.                   Figure 3.1 Reversed lateral cyclic loading test of RC piers specimen and geometry and reinforcement detailing/configuration   The efficiency of confinement techniques in bridge piers is examined by performing the nonlinear static pushover analysis, reverse cyclic analysis on cantilever circular RC bridge   67 piers retrofitted with CFRP and GFRP jackets. In order to numerically validate/calibrate the bridge pier numerical model, experimental investigations performed by Kawashima et al. (2000) and Yoneda et al. (2001) on the circular RC pier are compared with the numerical results. Table 3.1 Material properties used in the numerical model Description of properties Values Units Dia. of pier  400 (mm) Effective height of pier  1350 (mm) Longitudinal reinforcement ratio  1.89 (%) Volumetric ratio of lateral reinforcement  0.128 (%) Compressive strength of concrete  35 (MPa) Yield strength of longitudinal rebar  374 (MPa) Yield strength of transverse rebar  363 (MPa) Axial load  188.4 (kN)  3.2.2 Finite element modeling of bridge piers  The finite element model of the bridge pier is approximated as a continuous 2-D finite element frame using the computer software, Seismosoft (2015). This program has advanced capabilities for modeling and analyzing the nonlinear response of a structure. Figure 3.2(a) and Figure 3.2(b) show a schematic and model representation of the pier, respectively.   To simulate the experimental behavior of piers, they need to be idealized by discrete numerical model. In this research, the fibre modeling approach is employed in order to represent the distribution of material nonlinearity along the height and cross-sectional area of the members. The advantage of fibre modeling approach is that yielding height and the exact value of plastic  rotation can be estimated without considering the idea of equivalent plastic hinge length (Mortezaei and Ronagh 2012).   In order to consider material nonlinearity, a nonlinear beam-column element with five integration points was implemented, which was discretized with 3-D inelastic displacement-based frame elements for modeling of piers. In addition to the fibre elements, a nonlinear rotational spring element was used in the model to capture the bond-slip rotations at the pier-footing interface. The rotational spring element was defined with a zero-length element in SeismoStruct (2015). A rotational spring at the bottom of the pier indicates the longitudinal reinforcement pullout from the footing due to lap splicing of rebar. Its properties were used from Gallardo-Zafra and Kawashima (2009). At the numerical integration points, each   68 element is characterized by numerous cross-sections where each section is sub-divided into a number of fibres under a uniaxial state of stress. Figure 3.2(c) and Figure 3.2(d) show the fibre discretization of a typically retrofitted pier including concrete fibres, steel fibres, steel rebar fibres, and FRP fibres in the longitudinal and cross-section level, respectively.   Figure 3.2 Schematic details of pier and its numerical model    The considered components are assigned to the model with corresponding material properties. In order to mimic the effect of gravity load on the pier, a structural lumped mass is applied on the pier as a vertical point load on the pier. The pier footing was considered to be fixed, and its upper cantilever part free to rotate and move.  3.2.2.1 Material constitutive relationship While modeling the cross-section of the pier, confined and unconfined concretes, as well as the longitudinal steel reinforcement of each fibre element, their own constitutive stress-strain relationships were used. In this study, various constitutive models were adopted to describe the response of internal ties of confined concrete and external confined concrete using FRP composite. By specifying cross-section pieces along the height of the element, the distribution of inelastic deformation and forces is determined. However, this model does not consider into   69 account the shear deformation. The succeeding section explains the constitutive material models adopted in the numerical simulations.  3.2.2.2 Constitutive models of concrete  To predict the stress-strain behavior of actively confined concrete a stress-strain equation along with a set of equations are required to predict the peak stress '*( )ccf  and the corresponding peak strain *( )cc of confined concrete. In this study, the stress-strain model proposed by Madas (1993) following the constitutive behavior developed by Mander et al. (1988a), and the cyclic rules proposed by Madas and Elnashai (1992) with Martinez-Rueda and Elnashai (1997) are employed for confined (i.e. core) concrete and unconfined (i.e. cover) concrete constitutive models. In these models, a constant confining pressure is assumed throughout the entire stress-strain range resulting from the yielding of the steel lateral reinforcement since this model follows the constitutive model introduced by Popovics (1973). For a slow strain rate and monotonic loading, the peak compressive stress '*( )ccf  and the corresponding peak strain *( )cc could be determined using Eqs. (3.1) and (3.2).  * *' '' '2.254 1 7.94 2 1.254l lco cocc cof ff ff f        (3.1)  ''1 5 1cccc cocoff          (3.2) where 'ccf and'cof are the maximum compressive strength of confined and unconfined concrete, respectively. Figure 3.3 demonstrates the schematic of the effective confining region of confined concrete with internal ties (Mander et al. 1988a).      70  Figure 3.3 Schematic of effective confined concrete region with internal ties (Mander et al. 1988a)    Figure 3.4 Constitutive stress-strain response of confined concrete under (a) uniaxial and (b) cyclic loading (Mander et al. 1988a)   For the uniaxial stress-strain behavior of the confined concrete, Mander et al. (1988a) constitutive model is adopted as shown in Figure 3.4(a). This model is capable of considering the tensile strength of concrete where the Young’s modulus of concrete, peak compressive stress, and corresponding compressive strain of the concrete are the main input parameters.   71 The materials properties of concrete used in Mander et al. (1988a) are depicted in Table 3.2. For developing a cross-section discretization scheme, the concrete is assumed to crack at a tensile stress of zero. For the uniaxial cyclic behavior of confined concrete with different loading and unloading cycles, Mander et al. (1988a) cyclic model is adopted as shown in Figure 3.4(b).    Table 3.2 Parameters used in Mander et al. (1988a) model in  SeismoStruct (2015) Parameter Value Young’s modulus of elasticity (MPa) 23500 Mean compressive strength (MPa) 35.0 Mean tensile strength (MPa) 0.00 Strain at peak stress (mm/mm) 0.002 Specific weight (N/mm3) 2.4 × 10-5 Fracture/buckling strain 0.1 specific mass (kg/m3) 7800   As recommended by Richart et al. (1928), 'cof  and εco (0.002) are the unconfined concrete strength and corresponding strain, respectively. The constitutive law is then described using Eq. (4.3)    '1c cccrcc c ccrff r    (3.3) where r is a constant for the brittle behavior of concrete, secccErE Ewhere '5000c coE f in MPa for estimating the initial elastic modulus of concrete; and 'sec cc ccE f  . The effective lateral pressure of the confined concrete at the peak compressive strength can be calculated as follows:  *l l efff f k   (3.4) where *lf is the effective confining pressure and keff is the effective confinement coefficient, which could be determined using Eq. (3.5) for circular hoop ties.   2'121seffccSdk    (3.5)   72 where s' is the clear spacing between transverse reinforcement and ρcc is the longitudinal reinforcement ratio. Then, the effective lateral pressure can be calculated using Eq. (3.4).  3.2.2.3 Constitutive model of steel reinforcement To simulate the behaviour of steel reinforcement under cyclic load, Menegotto and Pinto (1973) steel model with Zulfiqar and Filippou (1990) isotropic strain hardening property is adopted as the constitutive model (Figure 3.5), which can be expressed as a bilinear kinematic hardening model. This model can capture the hysteretic behavior of steel reinforcing bars under simulated cyclic load. In addition, this model has a clear yielding point with a transient state from elastic to plastic response. Figure 3.5 exhibits the typical hysteretic behavior of steel reinforcing bars under cyclic load (Menegotto and Pinto 1973). The monotonic behavior with a bilinear curve is defined through Young’s modulus, Es, yield slope (εy, fy) and a hardening law with the modulus of E1 = (ft - fy)/( εt - εy), where (εt, ft) defines steel failure. According to this model, unloading curve starting from point S(εS, σS) along the hardening branch is given by an exponential law:  ** * 1( )1ee  (3.6) where ε*= (ε - εs)/(εF - εs), σ* = (σ - σS)/(σF - σS) are normalized strain and stress parameters, respectively, so that (ε*, σ*) = (0, 0) for S(εS, σS) and (ε*, σ*) = (1, 1) for F(εF, σF). Moreover, exponent λ is the solution of the nonlinear equation, which can be estimated using Eq. (3.7). A detailed description of the model can be found in Menegotto and Pinto (1973). Table 3.3 shows the parameters used in Menegotto and Pinto (1973) model for longitudinal steel reinforcement.  1F SoF SEe    (3.7)          73 Table 3.3 Parameters used in Menegotto and Pinto (1973)  model in SeismoStruct (2015) Parameter Value Young’s modulus of elasticity (GPa) 200 Yield strength (MPa) 374 Strain hardening parameter 0.009 Transition curve initial shape parameter 20.5 Transition curve shape calibrating coefficient, A1 18.5 Transition curve shape calibrating coefficient, A2 0.15 Isotropic hardening calibrating coefficient, A3 0.01 Isotropic hardening calibrating coefficient, A4 1 Fracture/buckling strain 0.1 specific mass (kg/m3) 7800   Figure 3.5 Schematic of hysteretic behavior of steel reinforcement based on (Menegotto and Pinto 1973)  cyclic model  3.2.2.4 Constitutive model of FRP reinforcement When RC piers are retrofitted with FRP sheets, the confinement pressure, fl depends on the lateral strain, εl of FRP reinforcement through an elastic behavior. The confinement pressure, fl is the summation of pressure exerted by transverse steel reinforcement and FRP (fl,FRP) lateral confining pressure, where fl,FRP can be determined by simplifying the calculation method which was described in the previous section.  , ,l l steel l FRPf f f   (3.8)   74   ,4with.sl steel eff S yh ssAf k fs d      (3.9)   ,2 .F Fl FRPgt ffD  (3.10) where ke = arching-effect coefficient, s = spacing (pitch) of hoops (spiral), and ds = diameter of hoops (spiral), keff , ρs, fyh are the effective lateral confining pressure, reinforcement ratio and effective yield strength of transverse reinforcements, respectively. tF is the thickness of the FRP system, F is the resistance factor for the FRP wrap, fF is the ultimate strength of the FRP and Dg is the diameter of the circular section. Finally, lateral strain εl can be obtained as a function of current axial strain, εco and stress, f’c adopting the damage model proposed in  (Pantazopoulou 1995)  ''( . )2. .c co clcE ff  (3.11) where 5700/ | | 500cof   . Considering Spoelstra and Monti (1999), an iterative procedure based on Eqs. (3.3), (3.10), and (3.11) is adopted to obtain the axial stress, 'cf for a given value of axial strain, εco of the confined concrete. It was assumed that FRP rupture suddenly causes the concrete failure in a brittle mode when it reaches its ultimate strain.   For FRP-confined concrete, the constitutive model of Ferracuti and Savoia (2005), which follows the constitutive relationship and cyclic rules proposed by Mander et al. (1988a) and, Yankelevsky and Reinhardt (1989) for compression and tension, respectively is employed. In this model, the confinement effect of the FRP wrapping follows the rules proposed by Spoelstra and Monti (1999). A bilinear stress-strain relation characterizes the model where the initial stiffness is governed by the properties of the unconfined concrete and the second stiffness is influenced by the amount of FRP jacket. The backbone curve of Mander et al. (1988a) model can be expressed as an ascending branch with a polynomial equation and linear descending branch. The concrete tensile strength is considered to be zero under tension. To develop the numerical model, the input parameter of the concrete strength, and the corresponding strain, the ultimate stress and the corresponding ultimate strain at the failure point are needed. Figure 3.6 demonstrates a typical uniaxial stress-strain material model, along with the constitutive behavior to indicate the relation of unconfined and FRP-confined   75 concrete. The residual stress is assumed to be 0.20 of the ultimate strength of concrete at the rupture of FRP, and the unconfined concrete residual stress is ignored.   Figure 3.6 Schematic demonstration of constitutive response unconfined and FRP-confined concretes (Mander et al. 1988a, Spoelstra and Monti 1999)    3.3 Nonlinear reverse cyclic analyses 3.3.1 Loading protocol  The studied pier is subjected to a displacement controlled-quasi-static cyclic analysis with an increment of 0.5% drift until reaching a maximum drift of 5.5%. Figure 3.7 shows the loading protocol of cyclic load used in this section (Kawashima et al. 2000).   76  Figure 3.7 Loading protocol of cyclic loading program   3.4 Numerical Model Validation Kawashima et al. (2000) investigated the cyclic behavior of one as-built reinforced concrete pier and one pier retrofitted with CFRP jacket. Figure 3.8(a) and Figure 3.8(b), respectively illustrate the hysteretic behavior of as-built pier and CFRP retrofitted pier. In order to validate the numerical model  in this study, the CFRP retrofitted pier was modeled and analyzed using a finite element program (SeismoStruct 2015) under same displacement-controlled reverse cyclic loading history (Kawashima et al. 2000). The circular RC cantilever pier was displaced with an increment of 0.5% drift until reaching a maximum drift of 5.5%. The numerical model of pier retrofitted with a single layer of CFRP sheets, which represents the volumetric confinement ratio of 0.11 has been validated with the experimental results of Kawashima et al. (2000) (see Figure 3.8). Table 3.4 depicts the CFRP materials properties used for the validation of numerical model (Kawashima et al. 2000).   Table 3.4 CFRP  material properties used in the numerical model (Kawashima et al. 2000) Material properties CFRP Young’s modulus (GPa) 230 Ultimate tensile strength (MPa) 3680 Ultimate strain  0.016 One-layer thickness (mm) 0.111    77  Figure 3.8 Comparison of the force-displacement relationship of the numerical and experimental results   The numerical analysis demonstrates a good agreement with the experimental results reported by Kawashima et al. (2000). As a result, the numerical model can simulate the initial stiffness, post-elastic stiffness, and the ultimate lateral load capacity with a sufficient level of precision. Compared to the experimental results, the maximum relative differences between experimental and numerical results in predicting the stiffness and lateral capacity were 3.5 and 3%, respectively.  3.5 Summary  This chapter presented a detailed 3D nonlinear numerical modeling technique for reinforced concrete bridge pier retrofitted with FRP. The nonlinear response of retrofitted circular RC pier under seismic action has been investigated using the fibre element approach, which is based on the cyclic constitute models of longitudinal reinforcement and concrete confined with lateral ties and FRP composites. The fibre element approach using constitutive models of concrete confined with advanced composite and lateral ties provided a good agreement with the experimental results of Kawashima et al. (2000). From the numerical investigation, the hysteretic results showed that retrofitting piers with advanced composites could improve the seismic performance of substandard RC piers by increasing its flexural strength and ductility.     78 Chapter 4: Pushover Response of Non-Seismically Designed Circular RC Bridge Pier Retrofitted with FRP using Fractional Factorial Design – A Parametric Study  4.1 General In order to investigate the effect of different factors along with their interactions, all of the factors need to be varied together using a factorial design method through the analysis of variance (ANOVA) (Montgomery 2012). ANOVA is a collection of statistical models for analyzing the difference between the effect of more than two factors and levels through the breakdown of the total variability of factors (Montgomery 2012). For example, if a factorial experiment contains n factors and three levels of each factor, this will result in 3n full factorial design combinations. For experiments with numerous factors and three levels for each factor, the full factorial design can lead to large number of data. It should be noted that  high order interactions often have a negligible effect on the response (Montgomery 2012). As a result, a well-designed experiment needs fewer runs for estimating the model parameter. In order to use the sparsity effect principle (Montgomery 2012), and to minimize a large amount of data, fractional factorial design can be used to run the experiment. Fractional factorial designs are experimental designs containing a carefully chosen fraction of the experimental runs in a full factorial design. In order to exploit the sparsity-of-effects principle, a fraction is selected from the experimental runs of a full factorial design to expose information about the most significant features of the problem (Montgomery 2012).   Table 4.1 Levels of the factors considered for the nonlinear static pushover analyses Sr. No. Factors/Parameters Level (treatment) Low (-1) Medium (0) High (+1) 1. Compressive strength of concrete, 'cf , (MPa) 25 30 35 2. Yield strength of steel, fy, (MPa) 250 300 350 3. Longitudinal steel reinforcement ratio, ρl, (%) 1.5 2 2.5 4. Spacing of stirrups, s, (mm) 300 250 200 5. Axial load, P (%) 5 10 15 6. Shear span-depth ratio (l/d) 3 5 7 7. CFRP layer (n) 1 2 3   79  In this study, seven factors including the compressive strength of concrete, the yield strength and amount of longitudinal steel, tie spacing, CFRP confinement layers, axial load level, and the shear span-depth ratio along with three levels (low, medium, and high) have been considered for the factorial design. A seven-factor factorial design (with three levels for each factor) leads to 37 = 2187 models, which needs more computational time, and may generate numerical errors. In this study, a fractional factorial design method is employed to save the computational time and reduce the numerical errors in the model. Then nonlinear static pushover analyses (NSPA) of the CFRP-confined bridge piers are conducted for all possible combinations of considered factors in order to determine the sequence of different limit states (see Table 4.1). The complete fractional factorial design is presented in Appendix E (Table E.1). The main objective of this part of the thesis is to identify the important factors (within their practical ranges) and as their interactions that have a significant influence on the seismic performance of the retrofitted bridge piers. The second objective of the study is to enhance understanding of how different levels (treatments) of factors can affect the seismic performance of deficient retrofitted bridge piers.   4.2 Factor Affecting First Yielding of Longitudinal Rebar The analytical solution of base shear at the first yielding of longitudinal steel reinforcement can be determined as Vy = My/l, where My is the moment capacity at the onset of first yielding of longitudinal steel reinforcement. Here, My = Asfy (d-a/2), where As and fy are the amount of longitudinal steel reinforcement and yield strength of steel, respectively. d is the distance from the extreme fibre in compression to the centroid of the steel on the tension side of the member. l is the height of the pier. The depth of equivalent rectangular stress block, a = As.fy /(𝛼1.D 'cf ) is a function of As, .fy, 'cf , 𝛼1 a coefficient (𝛼1 = 0.85 - 0.0015'cf ≥ 0.67) (CAN/CSA-A23.3-04 (R2010), Cl. 10.1.7 2004), D diameter of pier. Thus, the base shear at yielding of longitudinal steel reinforcement is a function of ρl,  fy, d and 'cf  Meanwhile, the compression stress block parameter, a, is much smaller than d, hence, the controlling parameters of the yield base shear include the longitudinal steel reinforcement (ρl) and yield strength (fy,) of the steel. The compressive strength of concrete has a little effect on the yield base shear (Vy), as it is affected by the compression stress block parameter, a.   The yield displacement can be estimated as   80  23yyl   (4.1)  yyc crackedME I   (4.2)  100yyDl   (4.3) where ϕy  is the curvature at the onset of the first yielding and Dy is the yield drift in %, and l is the effective height of the pier where the lateral load is applied. From the preceding discussion ρl and fy mostly affect My. Icracked depends on the amount of longitudinal steel reinforcement, while Ec is related to the square root of compressive strength of concrete. To account for flexural cracking, the cracked moment of inertia can be calculated as, Icracked = My/y. Ec,where My is the moment of onset of the first yielding of longitudinal rebar, y is the yield curvature, and Ec is the modulus of elasticity of concrete. Thus, Δy depends on both fy and 'cf .  4.3 Factors Affecting First Crushing of Concrete Core According to Park and Paulay (1975), the curvature ductility ratio of unconfined concrete ( 'cf ) (without FRP) can be estimated from Eq. (4.4), for FRP-confined concrete pier curvature ductility ratio can be estimated from Eq. (4.5) (Youssf et al. 2015).   1/2' '' ' 2 211/22' '' '1' ' '1 ( ) ( ) 2. .1.7 0.85 1.7u s cy ys c y s c ys cc c cdn n ndEfE f E fE df f d f                                      (4.4)   110013 0.052.45 0.18 0.7 0.25uyyoPDP       (4.5) where ϕu is the ultimate curvature when the extreme concrete compression fibre reaches its ultimate strain, ϕy is the curvature when the tension reinforcement first reaches the yield strength. ρ (=As/D) and ' '( / )sA D  are the ratio of longitudinal steel reinforcement at tension and compression zones, respectively; εc is the compressive strain at the crushing of concrete,   81 Es and fy are the modulus of elasticity and the yield strength of steel, respectively. n’ is the modular ratio (n’ = Es/Ec). β1 is the depth of the equivalent rectangular stress block. d is the effective depth of tension steel, d’ is the distance from extreme compression fibre to the centroid of compression steel. εy is the yield strain of the longitudinal rebar, λ1 is the confinement ratio, P is the pier axial load and Po is the pier axial load capacity. The 'cf in Eq. (4.4) can be substituted by the 'ccf  according to Mander et al. (1988b) Eq. (4.6)  * *' '' '2.254 1 7.94 2 1.254l lc ccc cf ff ff f        (4.6) The effective lateral pressure for the confined concrete at the peak compressive strength can be calculated as follows:  *l l efff f k   (4.7) where *lf is the effective confining pressure and keff is the effective confinement coefficient which could be determined from Eq. (4.8)  '121seffccSdk (4.8) where S’ is the clear spacing between the transverse steel reinforcement and ρcc is the longitudinal reinforcement ratio. When RC piers are retrofitted with CFRP sheets, the confinement pressure fl (in Mander constitutive model for confined concrete) contains stirrups (flsteel) and CFRP (fl,FRP). The lateral confining pressure depends on the reinforcement lateral strain εl through an elastic behavior. fl is the summation of pressure exerted by transverse steel and external reinforcement of CFRP (fl,FRP), where fl,FRP can be determined by a simplified method as shown in Eq. (4.11). A similar approach was used by Han et al. (2014) to determine the confining pressure exerted by stirrups (flsteel) and CFRP (fl,FRP).  , ,l l steel l FRPf f f   (4.9)  ,l steel eff S yhf k f    (4.10)  ,2 F F Fl FRPgt ffD  (4.11)   82 where keff is the effective lateral confining pressure of transverse steel, ρs is the reinforcement ratio of transverse steel; and fyh is the effective yield strength of transverse reinforcement. tF is the thickness of the CFRP system, F is the resistance factor for the CFRP wrap, fF is the ultimate strength of the CFRP and Dg is the diameter of the circular section. The total displacement and drift at the plastic hinge area can be estimated using Eq. (4.12) and Eq. (4.13), respectively.   Δcrushing = Δy + Δp (4.12)  100crushingcrushingDl   (4.13) where Δp, the plastic displacement can be estimated using Eq. (4.14), Eq. (4.2) and Eq. (4.4) and (4.5) can be used to determine ϕy and ϕu, respectively. The plastic hinge length lp, can be estimated using Eq. (4.15).  Δp = (ϕu – ϕy)lp × (l-lp/2) (4.14)  lp = 0.08lλ1 + 0.022fyds ≥ 0.044fyds (4.15) where l is the height of the pier; fy is the yield strength of longitudinal bar; λ1 is the confinement ratio, and ds is the diameter of the longitudinal bar. While applying CFRP confinement in bridge pier, it was ensured that the confinement length far exceeds the plastic hinge length of the pier. In this study, Paulay and Priestley (1992) model was modified considering the effect of FRP-confinement. To determine the lp of the CFRP-confined pier, a similar approach was used by Youssf et al. (2015). Hence, in the plastic deformation zone, all factors have effects on the crushing displacement, and interactions of different factors are expected to be noticeable. According to CAN/CSA-A23.3-04 (R2010), Cl. 11.3 and 11.4 (2004) based on modified compression field theory (Bentz et al. 2006), and strut and tie methods), the shear contribution of concrete and lateral steel reinforcement can be estimated from Eqs. (4.16) and (4.17), respectively. The shear resistance capacity, Vshear of CFRP wrapped piers can be calculated by using Eq. (4.18) from CAN/CSA S-806 (2012). According to CAN/CSA S-806 (2012), the total shear resistance capacity can be calculated by using Eq. (4.19).  ', .shear conc c c g vV f D d   (4.16)   83  ,v s y vshear steelA f d cotVS   (4.17)  , 2shear CFRP F F F F gV n t f D  (4.18)  '. 0.22r conc steel CFRP c c cvV V V V f A     (4.19) where fF = 0.006Ef ≤ fFu, Dg and dv are the diameter and effective depth of the section, respectively, and s is the spacing of transverse reinforcement, Av is the gross area of the tie bars in a single layer, θ is the angle of shear failure, failure which can be set as 35o in the design (for fy = 400 MPa, and 'cf  ≤ 60 MPa) (CAN/CSA-A23.3-04 (R2010) 2004) and β is a factor which depends on the average tensile stress in the cracked section (if the section contains minimum lateral steel reinforcement, Av = 0.06'cf Dg.S/fy, the value of β can be taken as 0.18). ϕc and ϕs are the strength reduction factors for concrete and reinforcing bars, respectively. ϕF, n, tf and fF, are the resistance factor, a number of layer, thickness and ultimate tensile strength of CFRP system, respectively.  4.4 Factors Affecting Buckling and Fracture of Rebar The bar buckling and fracture are estimated based on the longitudinal reinforcement steel tensile strain. The tensile strain at the onset of the bar buckling and fracture is expected to increase with an increase in effective confinement ratio. Berry and Eberhard (2007) proposed a model for the onset of the bar buckling and fracture in flexural dominated RC piers based on an imposed pier deformation. The estimated displacement drift at the onset of the bar buckling and fracture can be determined with Eq. (4.20) and Eq. (4.21), respectively based on the known pier properties of the pier.  '(%) 3.25 1 150 1 110bb beffg g c gd P ll D A f D                (4.20)   '(%) 3.5 1 150 1 110bf beffg g c gd P ll D A f D                (4.21)   's yseffcff   (4.22)   84 where, Δbb and Δbf are the displacements at the buckling and fracture of bar, respectively; ρs is the volumetric transverse reinforcement ratio; ƒys is the yield stress of the transverse reinforcement; db is the diameter of the longitudinal reinforcing bar; P is the applied axial load; Ag is the gross area of the cross section; 'cf is the concrete compressive strength; l is the distance from the pier face to the point of inflection; and Dg is the pier diameter.   4.5 Fractional Factorial Analyses for Different Propertied of Piers  Based on the discussion presented in previous sections, different factors affecting the performance of retrofitted bridge piers have been selected. The compressive strength of concrete, '( )cf , yield strength of steel (fy), longitudinal steel reinforcement ratio (ρl =As/Ag), tie spacing (s), axial load level (P), shear span-depth ratio (l/d) of pier and the CFRP wrapping layer (n) have been found as the contributing factors. A seven-factor with the three-level fractional factorial design of 37-3 (Connor 1959) is adopted in this research for the numerical investigation of retrofitted bridge piers to observe the effect of different factors and their interactions (see Table 4.1). This experimental design capitalizes on reducing the number of simulation from a full combination of modeling factor levels or from varying single factors at a time in order to achieve a more economical design where the significance of each factor can be statistically analyzed. According to Connor (Connor 1959), the fractional factorial design replicates the fraction of 1/27 for 7 factors in 27 blocks of 3 units each. Thus, 1/27 of 2187 (37) fractional factorial design (Connor 1959) needs 81 numerical models with different combinations of high, medium and low levels (treatments) with seven factors of the retrofitted bridge piers (Table 4.1).   In the case of low level, the 'cf , fy, ρl, s, P, l/d and n are considered to be 25 MPa, 250 MPa, 1.5 %, 300 mm, 5, 3, and 1, respectively. In the case of medium level, the 'cf , fy, ρl, s, P, l/d and n are considered to be 30 and 300 MPa, 2 %, 250 mm, 10, 5, and 2, respectively. In the case of high level, the 'cf , fy, ρl, s, P, l/d and n are considered to be 35 and 350 MPa, 2.5 %, 200 mm, 15, 7, and 3, respectively. First yielding, first crushing, first buckling and first fracture points are specified on the pushover curves as the performance indicators.      85 4.6 Flexural Limit States For the three levels and seven factors of each combination, nonlinear static pushover analysis is conducted using an incremental load in the form of displacement. In order to establish the curvature relationship of circular RC bridge pier with its limit states, Kowalsky (2000) proposed a simple relationship between curvature,  displacement ductility (µΔ) and drift ratio (D) with serviceability and damage control limit states. In order to study the effect of different factors on deficient CFRP-confined circular RC bridge piers, four performance criteria are considered based on displacements (Δ) and base shear (V) at the onset of first yielding (Δy, Vy) of longitudinal steel corresponding to steel strain, and first crushing of core concrete (Δcrush, Vcrush). The pushover analysis has been conducted for 81 piers. Figure 4.1 shows typical pushover response curves with the combination of seven factors. The yielding of longitudinal steel reinforcement is assumed to take place at a tensile strain of steel fy/Es. The crushing strain of unconfined concrete varies from 0.0025-0.006 (MacGregor and Wight 2012). Paulay and Priestley (1992) recommended that the crushing strain of confined concrete is much higher and varies from 0.012 to 0.05. In the present analysis, the crushing of confined concrete takes place when the extreme compressive fibre of core reaches the maximum strain estimated using Eq. (4.23) proposed by Paulay and Priestley (1992). The CFRP rupture strain value was also assigned to the program. When the rupture strain reaches the specified value, the program will notify the time of occurrence of FRP rupture. By post-processing, the corresponding base shear force and top displacement of the pier can be determined at that point in time.  '1.40.004s yh sucuccff     (4.23) where, εsu is the steel strain at maximum tensile stress and ρs = 4Asp/(Dc.s) is the volumetric ratio of confining steel, fyh is the yield strength of transverse steel reinforcement and 'ccf  is the confined concrete compressive strength. Typical damage states observed during pushover responses are depicted in Figure 4.1. The buckling and fracture of longitudinal reinforcement are determined according to the equations proposed by Berry and Eberhard (2007). They proposed that the onset of the bar buckling and the fracture are best predicted as a function of the effective confinement ratio, ρeff. Buckling and fracture of the longitudinal reinforcement are defined as the points when the tensile strain in the extreme tensile steel fibre reaches 0.045 and 0.046, respectively. Failure or ultimate conditions defined in the analysis are based on the   86 first occurrence of a concrete failure. The pier will  fail by concrete failure if the strain in the extreme fibre of the concrete core reaches the ultimate strain (εcu) as defined by the Chang and Mander (1994) concrete model. The pier will fail by steel failure if the strain in the extreme fibre of the reinforcing steel reaches ultimate strain (εsu) as defined in the previous section. The pier will fail by the loss of capacity if the load-carrying capacity of the structure falls below 80% of the maximum force as determined from the element analysis before reaching failure of concrete or steel as described above.   Figure 4.1 Typical pushover response curves showing various limit states with low, median and high levels   4.7 ANOVA Results for Fractional Factorial Design The ANOVA results for drift limits and base shear at different damage states are shown in Table 4.2 and Table 4.3, respectively. It estimates the P-value for main factors and the second order interaction for different response variables. Regarding two-factor interaction, analyses are presented for those factors that have a significant interaction effect on the performance of retrofitted piers. The analysis is conducted considering significant confidence level of 95%, which means that factors with P-value less than 5% have significant effects on the corresponding response.       87 Table 4.2 P-values from ANOVA of nonlinear static pushover analyses of drift results  Code Factors/Parameters P-values of drift limits for Yielding Crushing Buckling Fracture Main Factors Effect A Compressive strength of concrete, 'cf  0.627 0.888 0.774 0.949 B Yield strength of steel, fy < 0.001 0.046 0.456 0.144 C Longitudinal steel reinforcement ratio, ρl 0.025 0.894 0.888 0.464 D Spacing of stirrups, s 0.434 0.399 0.188 0.620 E Axial load, P 0.001 0.868 0.109 0.009 F Shear span-depth ratio, l/d < 0.001 0.805 < 0.001 < 0.001 G No. of CFRP layer, n 0.581 0.070 0.078 0.131 Two Factors Interaction AE 'cf × P 0.828 0.047 0.942 0.411 BF fy × l/d  < 0.001 0.016 0.813 0.951 EF P × l/d 0.003 0.122 0.896 0.519 FG l/d × n 0.574 0.031 0.865 0.852      Note: Italics red boldface letter shows a significant factor p-value ≤ 5% and known as significantly                 affecting the limit state regression coefficient responses, which are labeled the “most important”                 factors   From the analysis results, it can be observed that the l/d, fy, P, and the interactions of fy and l/d, and, P and l/d are the most significant factors on the yield drift limit states of the piers. These factors affect the initial stiffness, flexural and shear strengths as well as deformation capacity of the pier (Li 1994). In addition, the mode of failure could be changed by changing an axial load of the pier (Li 1994). 'cf and n have an insignificant contribution to the yield drift limit states of the piers. fy and the interaction of 'cf and P, and l/d and n are the most significant factors for the crushing drift limit states of the piers. The l/d has a significant contribution to the buckling and fracture drift limit states of the piers. The 'cf , fy, ρl, P and l/d, and the interaction of 'cf and P, l/d and ρl, and P are the most significant factors on the yield base shear of the piers. n has little contribution to the yield base shear of the piers. For the crushing base shear, similar to the yield base shear, n  and the interaction of P and l/d, and n have a major contribution. The fy, ρl, P, l/d and n, are the most significant factors affecting the buckling and fracture base shear of the piers. The interactions between 'cf and fy, fy, and ρl, and P, l/d, and n have a significant effect on the buckling and fracture of base shear of the piers. The significance of these factors can be seen from Eqs. (4.20) to (4.22) where the buckling and fracture drift limit states are functions of transverse reinforcement ratio, yield stress, axial load, concrete compressive strength, height, and the diameter of the pier. They could affect the buckling and fracture base shear of the piers. Tie spacing shows the insignificant contribution   88 to the yielding, crushing, buckling, and fracture drift limit states and base shear of the piers (Table 4.2 and Table 4.3). Gallardo-Zafra and Kawashima (2009) found that increasing tie spacing does not show much improvement on the hysteretic behavior for low tie spacing ratios. However, it should be noted that since the stirrup spacing did not vary widely in this study, and also in the presence of further confinement provided by FRP wrap, the results could not capture much effect of stirrup spacing on the bar buckling phenomenon.  Table 4.3 P-values from ANOVA of nonlinear static pushover analyses of base shear results  Code Factors/Parameters P-values of base shear limits for Yielding Crushing Buckling Fracture Main Factors Effect A Compressive strength of concrete, 'cf  < 0.0001 < 0.0001 0.517 0.764 B Yield strength of steel, fy < 0.0001 < 0.0001 0.014 0.057 C Longitudinal steel reinforcement ratio, ρl < 0.0001 < 0.0001 < 0.0001 < 0.0001 D Spacing of stirrups, s 0.547 0.596 0.855 0.368 E Axial load, P < 0.0001 0.001 < 0.0001 < 0.0001 F Shear span-depth ratio, l/d < 0.0001 < 0.0001 < 0.0001 < 0.0001 G No. of CFRP layer, n 0.093 0.001 < 0.0001 0.001 Two Factors Interaction AB 'cf × fy 0.150 0.383 0.082 0.041 AE 'cf × P < 0.0001 0.003 0.489 0.349 AF 'cf × l/d < 0.0001 0.003 0.935 0.946 BC fy × ρl 0.278 0.025 0.965 0.506 BF fy × l/d 0.259 < 0.0001 0.013 0.038 CF ρl × l/d < 0.0001 0.004 < 0.0001 < 0.0001 EF P × l/d < 0.0001 0.103 0.024 0.023 EG P × n 0.368 0.042 0.186 0.775 FG l/d × n 0.159 0.003 0.003 0.007      Note: Italics red boldface letter shows a significant factor p-value ≤ 5% and known as significantly affecting                 the limit state regression coefficient responses, which are labeled the “most important” factors  4.8 Effect of Different Factors at First Yielding Figure 4.2(a) shows decreases in yield base shear with the increase in the shear span-depth ratio. This is similar to Vy = My/l, where My = Asfy (d-a/2). As depicted in Figure 4.2(b), the shear span-depth ratio play a significant role on the base shear at yielding, while the yield strength, reinforcement ratio, and axial load also show a considerable effect on the yield base shear. The interaction effects of the square of the shear span-depth ratio (l/d × l/d) are also significant on the yielding base shear as shown in Figure 4.2(b). The shear span-depth ratio has the most significant effect (79% contribution) on the base shear at yielding.    89   Figure 4.2 Effect of (a) different shear span-depth ratios on the yield base shear and (b) percentage contribution of factors on the change of yield base shear   The effect of fy of steel, 'cf , amount of longitudinal reinforcement and axial load ratio have less effect on the yield base shear as shown in Figure 4.3(a)-Figure 4.3(e). This behavior may be attributed to the values of fy and 'cf in a close range is close (i.e. 250-350 MPa and 25-35 MPa, respectively, hence the difference in the value is less). The yield base shear increases with increase in 'cf and axial load level as shown in Figure 4.3(f), although as depicted in Figure 4.3(a)-Figure 4.3(e) their effect is less than that of other factors.          90               Figure 4.3 Effect of (a) l/d ratio and fy of steel, (b) l/d ratio and 'cf , (c) l/d ratio and ρl of steel, (d) l/d ratio and axial load (e) l/d ratio and ρl of steel (f) 'cf and axial load on the yield base shear    91  As shown in Figure 4.4(a), the drift at yielding shows more deviation for higher shear span-depth ratios in response to changes in factors, as found in Eq. (5.12). While determining the percentage contribution of different factors on the yield drift, it was found that shear span-depth ratio has a major contribution on the drift for first yielding as shown in Figure 4.4(b). The fy of steel has 13% contribution to the yield drift while the axial load level has a little contribution (Figure 4.4(b)). The tie spacing, CFRP layers and 'cf  show little contribution to the yield drift (Figure 4.4(b)). The effect of interactions between the fy of steel and shear span-depth ratio has a little contribution on the yield drift, while other factors are not significant. As shown in Figure 4.5(a) and Figure 4.5(b), the yield drift increases with increasing the l/d ratio and tie spacing.     Figure 4.4 Effect of (a) different shear span-depth ratios on the yield drift and (b) percentage contribution of factors on the change of yielding base shear of piers      Figure 4.5 Effect of (a) l/d ratio and axial load (b) l/d ratio and tie spacing on drift at yielding (a)    92 4.9 Effect of Different Factors at First Crushing Figure 4.6(a) shows the range of base shear at crushing which is the similar fashion to the yield base shear for all considered shear span-depth ratios of piers. Figure 4.6 (b) shows that the shear-span-depth ratio has a significant effect (72% contribution) on the crushing base shear capacity of the pier. As can be seen from Eqs. (4.17) and (4.18), the fy and ρl of steel, and the number of CFRP layers, respectively play a significant role in the crushing base shear capacity of the pier. The 'cf  and tie spacing do not have a significant effect on the base shear at crushing of flexural dominated piers as shown in Figure 4.6(b). However, the CFRP confinement shows some influence on the crushing base shear. Longitudinal steel ratio, ρl and fy of steel are the most critical factors in flexural dominated piers with the shear span- depth ratio in the range of 3 to 7. The effect of fy and ρl of steel is more significant in smaller shear span-depth ratios (l/d = 3 and 5) as shown in Figure 4.7(a). Figure 4.7 (b) shows that crushing base shear is not much affected by 'cf  whereas when the l/d increases the crushing base shear decreases. This behavior completely matches with Eqs. (4.16) to (4.18).     Figure 4.6 Effect of (a) different shear span-depth ratios on the crushing base shear, and (b) percentage contribution of factors on the change on crushing base shear   (a) (b)   93   Figure 4.7 Effect of (a) fy of steel and l/d ratio (b) 'cf and l/d ratio on the base shear at crushing   As shown in Figure 4.8(a), the range of drift at crushing or shear failure was broader with the decrease of the shear span-depth ratio as expected from Eq. (4.14). As shown in Figure 4.8(b), the yield strength of steel, fy, tie spacing and CFRP layers, n mostly affect the crushing drift of piers. The interaction among fy, ρl, l/d, 'cf , tie spacing, n  and axial load P also affect the crushing drift of piers. The interaction of CFRP layers with shear span-depth ratio; l/d and axial load mostly affect the crushing drift of piers. Higher order interactions play a significant role (see Figure 4.8(b)). Figure 4.9(a) shows that the drift at crushing decreases with the increase of fy of steel at lower l/d ratio; however, this effect gradually diminishes with higher l/d ratio. Figure 4.9(b) shows that the drift at crushing increases with increasing 'cf  at low axial load level. As axial load increases, the drift at crushing gradually decreases. At low 'cf  drift at crushing increases with increasing axial load level; however, this effect declines and gradually reverses with higher 'cf . With the increase of ρl, the crushing drift increases where the effect of ρl is low at higher values of fy as shown in Figure 4.9(c). Figure 4.9(d) shows that the effect of CFRP confinement on crushing is significant at low l/d ratio, i.e. as the number of CFRP layers increases drift decreases; however, at higher l/d ratio, this effect diminishes.     94    Figure 4.8 Effect of (a) different shear span-depth ratios on the crushing drift, and (b) percentage contribution of factors on the change of crushing drift on the piers       Figure 4.9 Effect of (a) fy and l/d ratio, (b) 'cf and axial load (c) ρl and fy of steel (d) l/d ratio and CFRP layers on the drift at crushing failure   (a) (b)   95 4.10 Effect of Different Factors at First Buckling Figure 4.10(a) shows that the spread of base shear at bar buckling increases as l/d ratio decreases and in general, the base shear at bar buckling has a negative effect on the l/d ratio where its contribution is the highest (68%) to base shear at bar buckling (Figure 4.10(b)). The base shear at buckling is also affected by fy, ρl and n, as shown in Figure 4.10(a) which matches with Eq. (4.20).    Figure 4.10 Effect of (a) different shear span-depth ratio on the buckling base shear, and (b) percentage contribution of factors on the change of buckling base shear on the piers    Figure 4.11 shows the interaction between fy and l/d ratio; ρl and l/d ratio; l/d ratio and axial load; and l/d ratio and CFRP layers on the base shear at bar buckling. fy, ρl, axial load level, and CFRP layers do not have a significant effect on the base shear at bar buckling at higher l/d  ratio; however, some effects are observed at lower l/d  ratio.    (a) (b)   96      Figure 4.11 Effect of (a) fy of steel and l/d ratio (b) ρl and l/d ratio (c) l/d ratio and axial load (d) l/d ratio and CFRP layers on the base shear at buckling    Figure 4.12 Effect of (a) different shear span-depth ratios on the buckling drift, and (b) percentage contribution of factors on the change of buckling drift on the piers   The variation of drift at bar buckling is wider than the crushing drift for all the shear span-depth ratio of piers (Figure 4.12(a)). Figure 4.12(b) shows that the shear span-depth ratio has a (a)  (b)    97 significant effect (37% contribution) on the drift at buckling where other influencing factors include fy, tie spacing, axial load level, the number of CFRP layers and interaction between axial load level and CFRP layer. Figure 4.13(a) shows that the drift at bar buckling decreases as the shear span-depth ratio increases except at H/d ratio around 3. However, axial load level does not have any major effect on drift at bar buckling. Figure 4.13(b) shows that with the increase of axial load, the drift decreases at CFRP layer = 1 whereas this effect reverses at a higher number of CFRP layer. At low axial load level, drift at bar buckling is not affected significantly by the number of CFRP layer; however, at higher axial load level CFRP layer has significant positive effect on drift at bar buckling.  It should be noted that stirrup spacing also affects the bar buckling (Figure 4.12(b)). Since the stirrup spacing did not vary widely, and in the presence of further confinement provided by FRP wrap, the results could not capture much effect of stirrup spacing on the bar buckling phenomenon.     Figure 4.13 Effect of l/d ratio and axial load (b) axial load and CFRP layers on the drift at buckling of longitudinal steel  4.11 Effect of Different Factors at First Crushing  The range of base shear at fracture is broader compared to buckling base shear for all considered shear span-depth ratios of piers Figure 4.14(a). This figure also shows that the trend is negative, i.e. base shear at fracture decreases with increases l/d ratio. Figure 4.14(b) shows that the shear span-depth ratio has a significant effect (74% contribution) on the base shear at fracture of longitudinal steel reinforcement. The longitudinal steel, ρl, and axial load, P, and interaction of l/d ratio and ρl and l/d ratio and n have little effect on the base shear at   98 fracture of rebar. The effect of 'cf , fy of steel, and s have an insignificant effect on the base shear at fracture of longitudinal steel reinforcement.    Figure 4.14 Effect of (a) different l/d ratios on the fracture base shear, and (b) percentage contribution of factors on the change of fracture base shear on the piers    Figure 4.15 Effect of (a) different shear span-depth ratios on the fracture drift and (b) percentage contribution of factors on the change of fracture drift on the piers   Figure 4.15(a) demonstrates that the range of drift at fracture of longitudinal steel reinforcement gets wider with the increase of pier shear span-depth ratio as expected in Eq.(4.22). The effect of shear span-depth ratio, axial load and interaction between 'cf and fy mostly affect the fracture drift of the piers. The shear span-depth ratio has 39% contribution to the fracture drift of the piers. Figure 4.16(a) show that the drift at rebar fracture decreases with increasing l/d where the effect is higher at higher l/d ratio and the effect of axial load level is insignificant. The drift at rebar fracture slightly increases with increasing number of CFRP layers (Figure 4.16(b)). (a)  (b)  (a)  (b)    99    Figure 4.16 Effect of (a) l/d ratio and axial load (b) l/d ratio and CFRP layer on the drift at buckling of longitudinal steel of piers  4.12 Effect of Different Factors on Displacement Ductility As shown in Figure 4.17(a), the range of ductility is wider at lower l/d ratio. As l/d ratio increases the ductility level decreases. Here, 'cf , ρl, axial load, l/d ratio, CFRP layer, and the interaction between axial load and l/d ratio, and the interaction between l/d ratio and CFRP layer are found to be significant on the ductility, as shown in Figure 4.17(b). Among them, the axial load and l/d ratio play the most important roles in the ductility of piers. Figure 4.18 (a) shows the interaction among ductility, axial loads, and l/d ratio where ductility around l/d = 3 increases with increasing l/d and beyond that ductility decreases. The effect of axial load on ductility is not significant with increasing axial load level the ductility decreases. Figure 4.18(b) shows that the number of CFRP layers n does not have a significant effect on ductility.      100   Figure 4.17 Range of ductility on different shear span-depth ratio of piers, (b) range of yield drift on different CFRP layer        Figure 4.18 Effect of (a) axial load and l/d ratio and (b) axial load and CFRP layers on ductility  4.13 Summary In this research, the variation of different limit states i.e., the first yielding of longitudinal rebar, first crushing of core concrete, first buckling and fracture of longitudinal reinforcement of CFRP-confined concrete piers with different factors (e.g. 'cf , fy, ρl, s, P, l/d and n) were investigated using fractional factorial design method. Moreover, the effects of individual parameters and their interactions on the limit states of the CFRP jacketed bridge piers were estimated. In order to determine the flexural limit states in terms of base shear and drift, nonlinear static pushover analyses were conducted with 81 numerical models.    (a)  (b)    101 Chapter 5: Seismic Behavior of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP – A Parametric Study  5.1 General In this Chapter, a parametric study of non-ductile circular RC piers retrofitted with different confinement ratios of carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) jackets under nonlinear static pushover analyses (NSPA), nonlinear static reverse cyclic analyses, and nonlinear dynamic time history analyses (NDTA) were studied. The nonlinear response of retrofitted circular RC pier under seismic action has been investigated using the fibre element approach, which is based on the cyclic constitute models of longitudinal reinforcement and concrete confined with lateral ties and FRP composites.   5.2 Parametric Investigation of Piers In Chapter 3, a numerical finite element (FE) model was generated for FRP retrofitted circular RC bridge pier using a fibre modeling approach (SeismoStruct 2015). The FE model was used to conduct a comparison between different confinement ratios of CFRP/GFRP jackets with the purpose of enhancing the behavior of cantilever RC piers under reverse cyclic loading. Here, the amount of the confinement of CFRP/GFRP retrofitted piers varied by using single, double, triple and four layers of 0.12 mm / 1.41 mm thick CFRP/GFRP jackets, respectively which correspond to volumetric confinement ratios (ϕFRP) of 0.11, 0.23, 0.34 and 0.45%. In order to provide a common base for the comparison between the two retrofitting methods, the same confinement ratios were used by changing the thickness of jackets. Table 5.1 shows the number of jackets, volumetric ratios of the jacket and lateral confining pressure corresponding to each of the four case considered herein.  Table 5.1 Properties of CFRP (Kawashima et al. 2000) and GFRP (Shin 2012) used in the four case studies Properties description CFRP jacketing system GFRP jacketing system Case-1 Case-2 Case-3 Case-4 Case-1 Case-2 Case-3 Case-4 t (mm) 0.12 0.23 0.34 0.45 1.41 2.80 4.19 5.59 Efrp (GPa) 266 266 266 266 19.1 19.1 19.1 19.1 εfrp (%) 1.63 1.63 1.63 1.63 1.80 1.80 1.80 1.80 fl (MPa) 1.20 2.41 3.61 4.81 1.21 2.41 3.61 4.81   102 5.2.1 Nonlinear static pushover analysis (NSPA) In order to conduct seismic assessment and inelastic behavior of the pier, nonlinear analysis is unavoidable. Usually, the nonlinear method consists of NSPA and NDTA. In the pushover analysis, a monotonically increasing lateral load with constant axial load is applied to the pier to a predefined lateral displacement. With the numerical modeling, and accurate definition of nonlinear material properties of structural components, and selection of proper ground motion records, NDTA would give a more precise prediction of the seismic response of the structure. However, within the boundary of its constraint, pushover analysis could provide a good prediction of the seismic response of the structures in lieu of an NDTA.  The pushover analysis of bridge pier is carried out by pushing the pier with a prescribed load distribution (uniform load distribution and first mode proportional load pattern) (Eurocode 8 2005) as shown in Figure 5.1(a). Figure 5.1(b) demonstrates the schematic representation of flexural limit states. In this study, a nonlinear static pushover analysis is conducted for as-built and retrofitted piers. The pier is subjected to an axial load of 188.4 kN (0.05fc.Ag where fc is the specified compressive strength of concrete, and Ag is the gross cross-sectional area of the pier). For the pushover analysis, an incremental load is applied in the form of displacement.          Figure 5.1 Typical pushover analysis of pier (a) deformed and undeformed shape, and (b) load vs. drift curve with limit states   (a) D = 400 mm (b)   103 5.3 Pushover Response of FRP Retrofitted Piers Figure 5.2(a) and Figure 5.2(b) show the total base shear versus top lateral displacement curve for the as-built and CFRP/GFRP retrofitted pier (ϕFRP = 0.11, 0.22, 0.33 and 0.44 %). As seen from Figure 5.2(a) and Figure 5.2(b) the pushover response curve exhibits that CFRP retrofitted pier has a higher lateral load capacity (18%) than the as-built pier, whereas the GFRP jackets lead to a slightly higher lateral load capacity (4%). The tensile reinforcement yielded before the lateral resistance reached the peak load, and the cracks suddenly opened up and extended to the base of the as-built pier, which resulted in the lateral load carrying capacity dropping from the maximum load compared to the retrofitted piers. The cracks and crushing of concrete core that occurred in the as-built piers were prevented by the composite wrapping for the retrofitted pier. The composite jacketing was able to offer additional flexural capacity, and jacketing at the potential plastic hinge zone that allowed the piers to undergo large inelastic deformation. The variation in the lateral load capacity is smaller in GFRP confinement and higher in CFRP confinement. The higher lateral load capacity of CFRP confinement was attributed to the higher stiffness of CFRP composites which resulted in less deformation compared to the GFRP retrofitted pier. The CFRP confinement in terms of lateral load capacity, CFRP jacketed piers with different confinement ratios (ϕFRP = 0.11, 0.22, 0.33 and 0.44%) show similar performance, and as a result, the retrofitted design can be considered adequate and comparable. The bridge piers confined with FRP jackets can achieve a higher displacement and deformability at a higher base shear load compared to the as-built pier. Similar observation was reported by Ozbakkaloglu and Saatcioglu (2006), Sheikh and Yau (2002).  The performance of a bridge can be established by limit states, and its related strain limits. The retrofitting methods used in this study are compared together in terms of different performance criteria. Four performance criteria considered here are the onset of first concrete cracking, spalling, first yielding of longitudinal reinforcement, and first crushing of concrete. The yielding of longitudinal reinforcement is assumed to take place at a tensile strain of 0.0025 while the cracking strain of concrete is considered to be 0.00014. Crushing strain of unconfined concrete differs about 0.0025-0.006 (MacGregor and Wight 2005). Thus, Paulay and Priestley (1992) recommended that the crushing strain of confined concrete is much higher and it varies from 0.015 to 0.05. In the present analysis, the crushing of confined   104 concrete is assumed to take place at a concrete compressive strain of 0.035. The onset of spalling of cover concrete is determined according to the maximum compression strain in unconfined concrete cover considered as 0.007 (Berry and Eberhard 2007, and Sheikh and Legeron 2014).   Figure 5.2 Pushover curves with different confinement ratios of (a) CFRP jacketed and (b) GFRP jacketed piers   It can be observed that the cracking of concrete and yielding of steel started at all the CFRP and GFRP jacketed piers almost at the same level of displacement and base shear. The base shear at spalling of concrete for 0.44% confinement ratio of CFRP and GFRP jacketed piers are 124.27 and 116.72 kN which is 18.6 and 13.9% higher than that of the as-built pier, respectively. In the case of GFRP retrofitted piers, the crushing of core concrete found at the displacement and base shear force in the range of 142.4-150.4 mm, and 56.35-67.25 kN, respectively for the confinement ratio of 0.11-0.33. Whereas, in the case of CFRP retrofitted pier no crushing occurred at the strain limit of 0.035 because of higher tensile strength and modulus of elasticity of CFRP jacket compared to GFRP jacket.   5.3.1.1 Moment-curvature response In order to compare the capacity of retrofitting techniques, the moment curvature analysis of retrofitted sections and as-built section are also conducted using SeismoStruct (2015). The   105 results are depicted in Figure 5.3(a) and Figure 5.3(b) for CFRP and GFRP retrofitting techniques, respectively. The ultimate moment and curvature, Mu and ϕu, are related to the ultimate state of section response. In this study, the ultimate stage of the section is defined as the one corresponding to the occurrence of the extreme compression strain, which reaches the ultimate value at the jacket of the steel hoop ruptures, or the strain in the extreme tension rebar, which reaches the “maximum tensile strain”. In this analysis, the maximum tensile strain for steel reinforcement is taken at 60% of the ultimate strain. The ultimate strains of the CFRP and GFRP jackets are 0.0163 and 0.018, respectively.  The higher load carrying capacity of the CFRP jacketed pier could be attributed to the high elastic modulus and tensile strength of CFRP jacket; in the case of GFRP retrofitted pier, the lower load capacity is attributed to the lower tensile and elastic modulus compared to CFRP jackets. The following figure also shows that the curvature drops quickly in the case of GFRP retrofitted piers compared to CFRP retrofitted piers, which again reflects back to the higher modulus of elasticity of CFRP jacket. Lower modulus of GFRP let the concrete dilate easily compared to CFRP, which eventually reduces the deformation capacity of GFRP retrofitted piers.     Figure 5.3 Moment-curvature response with different confinement ratios of (a) CFRP jacketed and (b) GFRP jacketed piers        106 5.3.1.2 Ductility capacity The displacement ductility factor (μ∆) is an important parameter in the seismic design procedure. The displacement ductility factor is defined as µ∆ = Δu/Δy, where Δy is the yield lateral displacement and Δu is the ultimate lateral displacement. The yield displacement in the load displacement envelop curve is defiend as the displacement using the secant stiffness considering the stiffness reduction due to cracks in the range of the elastic region to the yield displacement (Park 1988). As shown in the load-displacement envelope curve (Figure 5.4), the displacement for the point and the point of intersection with the horizontal and straight lines through the origin to the maximum lateral secant to 75% of the maximum lateral load. The ultimate displacement point is considered as the point on the backbone curve, which correspond to 85% times pier strength. Figure 5.4 shows the parameters used in calculating the definition of ductility.    Figure 5.4 Yield and ultimate displacement for defining the ductility    A comparison of ductility factors of the retrofitted piers with different FRP confinement ratios is shown in Figure 5.5. The specimens with a larger µ have a better ductility. The displacement ductility ratio of the as-built pier is 2.7, and the retrofitted specimen using CFRP and GFRP with a confinement level of 0.44 had a ductility ratio of 15.5 and 9.5, respectively. Figure 5.5 indicates that the ductility of the retrofitted specimen increases as the level of confinement increases.    107   Figure 5.5 Ductility comparison of different confinement ratios of (ϕFRP) of CFRP/GFRP   In the case of CFRP jacketed piers, the ductility factor was found higher compared to the GFRP jacketed piers. The higher ductility factor in the case of CFRP retrofitted pier is attributed due to the higher modulus of elasticity of CFRP jacket (266 GPa) which resulted in higher confinement pressure compared to GFRP jacket (19 GPa). It should be noted that the ductility at low confienement ratio of GFRP was insignificant where the increase in ductility for GFRP jacket is almost linear. Whereas, the CFRP jacket does improve the ductility significantly up to a certain level of confinement ratio, and beyond that the increase in ductility is not significant as observed between the confinement ratios of 0.33 and 0.44.   5.3.1.3 Hysteretic response of retrofitted piers under cyclic load The hysteretic behavior of CFRP and GFRP retrofitted piers of varying confiment ratios (Table 5.1) are depicted in Figure 5.6 and Figure 5.7, respectively. It can be observed that in all cases, the pier jacketed with CFRP shows a superior and stable load carrying capacity compared to the GFRP jacketed pier. The lower load carrying capacity of GFRP retrofitted system was attributed to the accumulation of a significant portion of plastic deformation at the interface of the pier and the footing, which considerably reduces the overall deformation capacity of the GFRP retrofitted pier. Since the deformation capacity is important for   108 satisfactory seismic performance, enhancement in ductility is highly desirable during retrofitting. CFRP retrofitted piers were able to maintain their load-carrying capacity until the end of the loading protocol. The GFRP jacketed piers show that the increase in resistance force is more pronounced up to 4% drift (33mm); however, the resistance is significantly affected in the subsequent cycles. In the case of GFRP retrofitting system, the strength degradation was higher compared to the CFRP system. This could be attributed to early stage rupturing and higher lateral deformation of GFRP sheet that help dilating the concrete at the same level of force compared to that of the CFRP sheet, as CFRP has higher Young’s modulus of elasticity (266 GPa for CFRP and 19 GPa for GFRP). Hence, CFRP retrofitting system showed much improved performance compared to GFRP retrofitting system. Overall, both the retrofitting system performed better than that of the as-built pier.    Figure 5.6 Force-displacement relationship of CFRP retrofitted piers under cyclic loading    109  It was observed that for piers retrofitted with GFRP, the flexural cracks develop within 300mm from the base of the pier and the top of the footing (Gallardo-Zafra and Kawashima 2009). Whereas, the piers retrofitted with CFRP, fewer cracks occurred within 300mm from the base. A similar observation has been reported in the previous study (Gallardo-Zafra and Kawashima 2009).    Figure 5.7 Force-displacement relationship of GFRP retrofitted piers under cyclic loading    The analytical results show that improved flexural strength and ductility was achieved with an increased ratio of CFRP and GFRP confinement. The lateral load vs. top lateral displacement envelope curves are depicted in Figure 5.8, where restoring force and maximum pier displacement increased as the confinement ratio increased. The increased lateral force and top lateral displacement attributed because of the concrete confinement with CFRP and GFRP,   110 in both cases, the retrofitted pier shows higher ductility compared to the as-built piers. However, other than improved ductility no substantial stiffness and strength improvement was found for the retrofitted specimen compared to the as-built pier.    Figure 5.8 Comparison of the envelope curve of (a) CFRP and (b) GFRP retrofitted piers  5.3.1.4 Stress-strain response of rebar of the CFRP/GFRP retrofitted piers In order to have a better understanding of the level of damage occurred during cyclic analysis on the pier, comparisons between stress-strain behavior of core concrete and longitudinal rebar in CFRP and GFRP jacketed piers are presented in Figure 5.9 and Figure 5.10, respectively. The CFRP jacketed pier in all four cases resulted in an early increase in the compressive strength compared to the GFRP jacketed pier. Because of GFRP’s lower modulus of elasticity compared to CFRP, concrete quickly dilates while wrapped with GFRP as observed in Figure 5.9.     111  Figure 5.9 Axial stress vs strain behavior of core concrete of the CFRP and GFRP retrofitted pier under cyclic load (a) Case-1, (b) Case-2, (c) Case-3, (d) Case-4    The reduction in the core concrete maximum strain of CFRP retrofitted piers with 0.11, 0.22, 0.33 and 0.44 % confinement ratios were 59, 64, 62 and 59%, respectively compared to those of GFRP retrofitted piers as portrayed in Figure 5.9. The results of axial strain in the longitudinal steel bars presented in Figure 5.10 also shows that in the case of CFRP confinement there is a reduction in the deformation demand of longitudinal steel reinforcement by 11, 10, 8 and 6 % with the confinement ratio of 0.11, 0.22, 0.33 and 0.44 %, respectively compared to those of GFRP retrofitted piers as portrayed in Figure 5.10.   112  Figure 5.10 Axial stress vs strain behavior of longitudinal steel of the CFRP and GFRP retrofitted pier under cyclic load (a) Case-1, (b) Case-2, (c) Case-3, (d) Case-4   The analytical results show that CFRP and GFRP jacketed piers could enhance the load carrying capacity and ductility of the retrofitted RC bridge pier compared to the as-built pier under nonlinear pushover and cyclic loadings. In addition, less damage observed in the concrete core and longitudinal reinforcement when the pier is jacketed with CFRP and GFRP. On the other hand, the pier retrofitted by CFRP has considerably improved seismic behavior compared to the GFRP wraps in terms of load carrying capacity and ductility. The CFRP shows a better strength and ductility due to the early increase in the concrete strength that reduces the damage experienced by both concrete and steel.     113 5.3.2 Nonlinear dynamic analyses of retrofitted RC piers  In this section, the bridge pier is subjected to a suite of recorded ground motions to determine its seismic performance under real earthquake records. Seismic ground motion records often vary in terms of predominant frequency, duration, peak ground acceleration (PGA), and peak ground velocity (PGV). Therefore, time history analysis of a structure for one ground motion may not truly represent the actual condition. Time history analysis with a suite of ground motions having different characteristics gives a reasonable prediction of structural response under seismic events.   5.3.2.1 Ground motion database To conduct a nonlinear dynamic analysis, a ground motion database has been compiled to constitute a representative number of earthquake ground motion records. Ten ground motion records are selected to cover a different range of durations, frequency, amplitudes, and epicenter distances. All the ground motion records have been chosen from the Pacific Earthquake Engineering Research Center, Next Generation Attenuation Project, Strong Motions Database (PEER NGA Database). The selected ground motion records belong to a bin of comparatively big magnitudes (Mw) ranging from 6 to7.6 on the Richter scale where the epicenter distance, R is in the range of 10.4-34.8 km. The pertinent information of these unscaled and scaled ground motions datasets, including the station, epicenter distance, and PGA are listed in Table 5.2.   Nonlinear dynamic analysis of retrofitted RC piers has been conducted using a set of 10 historic earthquake ground motions in order to assess the effect of most significant FRP confinement ratios on the seismic behavior of piers. At the fundamental period of the pier (T1 = 0.16 s), the average spectral acceleration of the records was found to be 0.98g. In order to introduce a level of seismic damage to the pier and compare their nonlinear behaviors under a suite of ten ground motions, all the ground motions are scaled to a uniform spectral acceleration value of 1.5g at the fundamental period of the pier. A uniform scaling spectral acceleration value of 1.5g will make the pier retrofitting option necessary and effective.       114 Table 5.2 Characteristics of the selected ten-ground motion records used in this study Historical Earthquake Year Record station R (km) Mw PGA (g) Sa(g) |T1 Unscaled  Scaled Victoria-Mexico  1980 6604 Cerro Prieto 34.8 6.4 0.62 0.93 0.57 Loma Prieta  1989 57217 Coyote Lake Dam 21.8 7.1 0.48 0.73 0.57 Northridge  1994 90014 Beverly Hills 20.8 6.7 0.62 0.93 0.51 Imperial Valley  1979 5115 El Centro Array #2 10.4 6.9 0.32 0.47 0.40 Cape Mendocino  1992 89324 Rio Dell Overpass 18.5 7.1 0.55 0.82 0.39 Mammoth Lakes  1980 54214 Long Valley Dam 20.0 6.0 0.92 1.38 0.55 Kobe, Japan 1995 JMA 99999 KJMA 25.6 6.9 0.82 1.23 1.83 Chi-Chi, Taiwan  1999 CWB 99999 CHY080-E 32.9 7.6 0.97 1.45 2.88 Morgan Hill  1984 CDMG 57217 Coyote Lake Dam (SW Abut) 26.0 6.2 0.71 1.07 0.90 Gazli, USSR  1976 9201 Karakyr 22.3 6.8 0.61 0.91 1.17    Figure 5.11 Suits of 10 unscaled ground motion records with 5% damping (a) response spectral acceleration, and (b) percentile of response spectral acceleration    Figure 5.12 Suits of 10 scaled ground motion records with 5% damping (a) response spectral acceleration, and (b) percentile of response spectral acceleration     115  Figure 5.11(a) and Figure 5.12(a) show the acceleration response spectra of the selected 10 unscaled and scaled ground motions, respectively with 5% damping ratio. The mean acceleration response spectrum (red line) of 10 ground motions with 5% damping ratio is also shown in the figure. Figure 5.11(b) and Figure 5.12(b) show different percentiles of acceleration response spectra for the selected ground motions. These figures represent that the selected earthquake records fall in the range of medium to strong intensity earthquake motion histories.  5.3.3 Seismic response of the retrofitted piers Three types of response parameters namely, pier base shear, stiffness and residual displacement are determined as the main factors that would contribute to the efficacy of the retrofitting methods.   5.3.3.1 Base shear Figure 5.13 and Figure 5.14 show the base shear values of CFRP and GFRP retrofitted piers, respectively under the scaled ground motion. The effect of pier confinement pressure is included by varying the thickness in all cases of I, II III, and IV, which represent different values of the volumetric confinement ratio of FRP composites. From Figure 5.13 and Figure 5.14, it can be observed that the CFRP and GFRP composite jackets are effective in increasing the pier strength and deformability compared to the as-built pier. For the similar confinement ratios of 0.11, 0.22, 0.33, and 0.44%, the base shear value increases to 6, 11, 16, and 21%, for CFRP jacket and 2, 5, 7 and 10%, for GFRP jacket, respectively compared to the as-built pier. Since the stiffness of the piers does not significantly increase with composite jacketing, the retrofitted piers did not attract much larger shear forces as compared to the as built pier. The results in Figure 5.13 and Figure 5.14 demonstrate that increasing the level of confinement slightly increases the base shear for CFRP/GFRP jacketed piers. Overall, compared to GFRP confinement, the CFRP jackets increases the average base shear by 5, 6, 8, and 9% for similar confinement ratios of 0.11, 0.22, 0.33 and 0.44%, respectively. This higher base shear was found due to the high strength, and high modulus of elasticity of CFRP jacket compared to the GFRP jacket. Figure 5.15 illustrates an example of the sample base shear-displacement behavior typically obtained from the dynamic analysis. The relationship presented in Figure   116 5.15 reveals the comparison for the case-4 along with the as-built pier under the scaled Gazli-USSR, 1976 earthquake recorded at station 9201 Karakyr.   Figure 5.13 Base shear of CFRP retrofitted piers under ten ground motion records  Figure 5.14 Base shear of GFRP retrofitted piers under ten ground motion records   117  Figure 5.15 Force-displacement behavior of case-4 (ϕFRP = 0.44) and as-built pier under the scaled Gazli-USSR, 1976 earthquake recorded at station 9201 Karakyer  5.3.3.2 Residual displacement Residual displacement is an important parameter for performance-based earthquake engineering as it indicates the functionality of a member after an earthquake. Figure 5.16 and Figure 5.17 show the residual displacements of the CFRP and GFRP retrofitted piers, respectively under the considered ground motions. The effect of pier confinement pressure is included by varying the thickness in all cases of I, II III, and IV, which represent different values of the confinement volumetric ratio of FRP composites. From Figure 5.16 and Figure 5.17, it can be observed that the CFRP and GFRP composite jackets are effective in deformability compared to the as-built pier. For the similar confinement ratios of 0.11, 0.22, 0.33 and 0.44, the residual displacement value decreases by 11, 21, 30 and 41%, respectively for CFRP jacket, and 4, 11, 20, and 29%, for GFRP jacket, compared to as-built pier. The results in Figure 5.16 and Figure 5.17 demonstrate that increasing the level of confinement decreases the residual displacement of CFRP/GFRP jacketed piers. Overall, with similar confinement ratios of 0.11, 0.22, 0.33 and 0.44%, and the CFRP jackets could reduce the average residual displacement by 7, 11, 12, and 16%, respectively compared to GFRP confinement.     118  Figure 5.16 Residual displacement of CFRP retrofitted piers under ten ground motion records  Figure 5.17 Residual displacement of GFRP retrofitted piers under ten ground motion records  5.3.3.3  Stiffness The degradation of structural stiffness is a representation of the amount of damage experienced by the structure during a seismic event. Therefore, it is considered as an important factor, which defines the seismic behavior of structure in a quantitative way. For all dynamic loads, the average stiffness values using Eq. (5.12) in the positive or negative   119 directions are estimated by dividing the maximum load reached within a dynamic load by the corresponding displacement. K+ and K- are the stiffness values in positive and negative directions, respectively.  2avgK KK     (5.12)  Figure 5.18 Effective stiffness of CFRP retrofitted piers under ten ground motion records   Figure 5.18 and Figure 5.19 illustrate the effective stiffness of RC pier when it is retrofitted by CFRP and GFRP composite wraps and subjected to a suite of ground motion records. In general, it can be seen that in all groups, the effective stiffness of CFRP retrofitted piers is higher than that of the GFRP wrapped piers. Based on the average of all groups, using the CFRP jackets could enhance the effective strength and stiffness, compared to GFRP jackets. These results show the superiority of the CFRP confining technique in limiting the progressive damage in the retrofitted pier. For similar confinement ratios of 0.11, 0.22, 0.33, and 0.44%, the effective stiffness value respectively increases by 20, 36, 57, and 69%, for CFRP jacket and 10, 21, 38 and 48%, for GFRP jacket compared to as-built pier. The results in Figure 5.18 and Figure 5.19  reveal that increasing the level of confinement increases the effective stiffness of CFRP/GFRP jacketed piers. These observations are expected because the seismic demand of all retrofitted piers in all four cases is considered to be the same. Overall,   120 the CFRP jackets could increase the average effective stiffness by 8, 11, 11.5, and 12% compared to the GFRP confinement with similar confinement ratios of 0.11, 0.22, 0.33, and 0.44%, respectively. This higher effective stiffness is due to the high strength, and high modulus of elasticity of CFRP jacket compared to the GFRP jacket.   Figure 5.19 Effective stiffness of GFRP retrofitted piers under ten ground motion records  5.4 Summary In this chapter, the behavior of non-ductile circular RC piers retrofitted with different confinement ratios of CFRP and GFRP jackets under nonlinear static pushover analyses, nonlinear static reverse cyclic analyses, and nonlinear dynamic time history analyses were studied. The nonlinear response of retrofitted circular RC pier under seismic action has been investigated using the fibre element approach, which is based on the cyclic constitute models of longitudinal reinforcement and concrete confined with lateral ties and FRP composites. The fibre element approach using constitutive models of concrete confined with advanced composite and lateral ties provided a good agreement with the experimental results. From the analytical investigation, the hysteretic results showed that retrofitting piers with advanced composites could improve the seismic performance of substandard RC piers in terms of flexural strength and ductile failure mode.   121 Chapter 6: Seismic Collapse Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP   6.1 General In this chapter, seismic vulnerability assessment of non-seismically designed RC bridge piers retrofitted with FRP jacketing is conducted. The structural response of the retrofitted bridge piers under severe seismic events is considerably different compared to regular bridge pier. The chapter focuses on quantifying the inelastic demand and capacities of FRP retrofitted non-seismically designed circular RC bridge piers using nonlinear static pushover analyses (NSPA), and incremental dynamic analyses (IDA). The seismic behavior of the FRP retrofitted piers are investigated by using finite element model with suitable cyclic constitutive laws of FRP-confined concrete. IDA is conducted numerically on the FRP retrofitted piers with a family of 20-earthquake ground motions scaled with different intensity measures (IM). With respect to IM, such as peak ground acceleration (PGA), the maximum responses in terms of governing engineering demand parameters (EDP), such as the maximum drift or deformation, and ductility demand of the structure are estimated to compare performances of retrofitted bridge piers.   6.2 Design of Bridge Piers This section briefly explains the design and configuration of different RC bridge piers. The RC circular bridge piers are assumed to be located in Vancouver, BC, Canada and is non-seismically designed without consideration of the current seismic design guidelines. The diameter of piers is fixed to be 400 mm in all the piers. Several parameters affect the design and behavior of the bridge piers.   The important variables of this parametric study are selected as the compressive strength of concrete, 'cf , the yield strength, fy, and amount of longitudinal reinforcement, ρl, FRP confinement layers, n, axial load, P, and shear span-depth ratio, l/d.  Table 6.1 lists the factors and associated values considered in this chapter. These parameters are selected based on literature (Paulay and Priestley 1992, Hines et al. 2004, Bae and Bayrak 2008). For each parameter, two different values (levels) are considered.    122 Table 6.2 shows a summary of the FRP retrofitted piers analyzed in this chapter. A total of 12 non-seismically RC circular bridge piers are designed in order to study the effect of different parameters on the seismic vulnerability of FRP retrofitted piers. One parameter at a time is varied and the others are kept constant. As explained in Chapter 5, sections 5.12 to 5.14, the interaction of parameters has an insignificant effect on the response, and therefore, they are not considered in this chapter. The diameter and number of longitudinal rebars change for different rebar percentages. 6mm circular stirrups are used at 250mm spacing as the lateral reinforcement in all of the piers. Figure 6.1 displays the geometry and reinforcement detailing of the RC pier. In order to ensure that the dominant failure mode will be a flexural failure (i.e. avoiding shear failure), and two different aspect ratios (4 and 7) are considered.    Figure 6.1 Specimen geometry and reinforcement detailing used in this study    123 Table 6.1 Details of variable parameters considered in this study Modeling factors/parameters Code Values Units Compressive strength of concrete, ( 'cf )  A 20 35 (MPa) Yield strength of steel, (fy)  B 250 400 (MPa) Longitudinal steel reinforcement ratio, (ρl) C 1 2.5 (%) Axial load, (P) D 10 20 (%) Shear span-depth ratio, (l/d) E 4 7 -- FRP confinement layer, (n) F 2 3 No.  Table 6.2 Details of FRP retrofitted bridge piers Variable Pier-ID 'cf  (MPa) fy (MPa) ρl (%) P= 'cf /Ag l/d  n (No.) Compressive strength, 'cf  C-1-35 35 400 2.5 0.20 2800/400 3 C-1-20 20 400 2.5 0.20 2800/400 3 Yield strength, fy  C-2-400 35 400 1 0.20 2800/400 3 C-2-250 35 250 1 0.20 2800/400 3 Longitudinal reinforcement, ρl  C-3-2.5 35 400 2.5 0.10 2800/400 3 C-3-1 35 400 1 0.10 2800/400 3 Axial load, P C-4-0.20 35 400 2.5 0.20 1600/400 3 C-4-0.10 35 400 2.5 0.10 1600/400 3 Shear span-depth  ratio, l/d C-5-7 35 400 2.5 0.10 2800/400 2 C-5-4 35 400 2.5 0.10 1600/400 2 FRP confinement  layer, n   C-6-2 35 250 2.5 0.20 1600/400 2 C-6-3 35 250 2.5 0.20 1600/400 3  6.3 Nonlinear Static Pushover Analysis and the Flexural Limit States According to the performance-based design guidelines, structures are designed based on a damage limit state at which the loss of life is prohibited. However, the structure would be out of service for a certain time, which could withstand extensive structural and non-structural damages. The performance of the bridge pier can be quantified in terms of limit states with corresponding strain limits. In order to study the effect of different parameters of retrofitted circular bridge piers, four performance criteria have been considered: the displacements (Δ) and base shear (V) at the onset of first yielding of longitudinal steel (Δy, Vy), first crushing of core concrete (Δcrush, Vcrush), first buckling of longitudinal steel (Δbuck, Vbuck) and first fracture of longitudinal steel (Δfract, Vfract) pier. In order to identify the limit states for all combinations of the retrofitted piers (Table 6.4), nonlinear static pushover analyses are conducted. The yielding of longitudinal steel reinforcement is assumed to take place at a tensile strain of steel fy/Es. The crushing strain of unconfined concrete varies from 0.0025 to 0.006 (MacGregor and   124 Wight 2005). Consequently, Paulay and Priestley (1992) recommended that the crushing strain of confined concrete is much higher and changes from 0.015 to 0.05. In the present analysis, the crushing of confined concrete is assumed to occur when the concrete compressive strain reaches 0.035. Longitudinal bar buckling and fracture are determined according to the equations proposed by Berry and Eberhard (2007). They proposed that the onset of bar buckling and fracture are best predicted as functions of the effective confinement ratio, ρeff. Buckling and fracture of the longitudinal bar are defined as the points when the tensile strain in the extreme tensile steel fibre reaches 0.045 and 0.046, respectively (Berry and Eberhard 2007).  As depicted in Table 6.3 and Figure 6.2 - Figure 6.7, different parameters affect the flexural performance of the FRP retrofitted bridge piers. For instance, as shown in Figure 6.2-Figure 6.7, it can be observed that higher values of the parameters can increase the capacity of the piers. Yielding, bucking, and fracture of reinforcement, and crushing of core concrete are also presented in Figure 6.2 - Figure 6.7.    Figure 6.2 Results of pushover analysis considering different compressive strength of concrete   From Figure 6.2, it is observed that 35MPa concrete increases the pier yielding and crushing base shear capacities of 14 and 8.3%, respectively; while the buckling and fracture   125 base shear capacities decrease by 4.4 and 4.3% compared to 20MPa concrete. It could be attributed to the fact that for the low strength concrete (20 MPa), the FRP confinement is more effective which could give a higher deformability compared to the high strength concrete (35 MPa). Thus, low strength concrete shows a higher displacement for crushing, buckling, and fracture of the rebar. There is no difference in the yield displacement for 20 and 35MPa concrete. The results presented in Figure 6.3 indicate that the stiffness of both piers is quite similar until the yielding of the rebar. The results show that the stiffnesses of both piers are quite similar until cracking of the concrete. Once the concrete is cracked, the 20MPa pier exhibits comparatively lower stiffness compared to 35MPa concrete due to a lower modulus of elasticity of the concrete.    Figure 6.3 Results of pushover analysis considering different yield strength of reinforcement   From Figure 6.3, it can be observed that the yield strength of longitudinal reinforcement significantly affects the flexural performance of the FRP retrofitted bridge piers. For the high yield strength (400 MPa) reinforcement shows higher yielding, crushing, buckling and fracture base shear of 24.3, 27.3, 30.1 and 4.5%, and larger displacement by 28.6, 15.4, 27.3, 6.8, and 4.7%, respectively compared to the lower yield strength (250 MPa).  From Figure 6.4, it is observed that the amount of longitudinal steel considerably affects the flexural strength and limit states of the retrofitted bridge piers. For 2.5% longitudinal   126 reinforcement ratio, the yielding, crushing, buckling and fracture base shear capacities are improved by 44.9, 48.7, 55.8, and 56.1% compared to that of 1% longitudinal steel. For 2.5% longitudinal reinforcement ratio, the yielding, buckling, and fracture displacements increase by 14.3, 9.5, and 9.3%, respectively, but the crushing displacement decreases by 14.3% compared to that of 1% longitudinal steel.    Figure 6.4 Results of pushover analysis considering different longitudinal steel ratio   From Figure 6.5, it can be observed that at 20% axial load, the yielding, crushing, buckling, and fracture base shear increases by 41.5, 14.3, 7.4, and 7.2% compared to that of 10% axial load. The yielding displacement increases by 14.3% for 20% axial load compared to 10% axial load; and crushing, buckling and fracture displacements are almost the same for 20 and 10% axial load. The results presented in Figure 6.5 reveal that the stiffnesses of both piers are quite similar. The pier with 10% axial load has a higher deformation compared to 20% axial load pier.    127  Figure 6.5 Results of Pushover analysis considering different axial load ratio  Figure 6.6 Results of pushover analysis considering different shear span-depth ratio   From Figure 6.6, it can be observed that the shear span-depth ratio significantly affects the flexural performance of the FRP retrofitted bridge piers. For the shear span-depth ratio of 7 shows 52.6, 44.3, 100.6, and 101.7% lower yielding, crushing, buckling, and fracture base shear capacities, respectively compared to those having shear span-depth ratio of 4. For the shear span-depth ratio of 7, yielding, crushing, buckling, and fracture displacements increase by 57.1, 64.3, 67.4 and 65.9%, respectively compared to those for the shear span-depth ratio of 4. According to the results presented in Figure 6.6, the shear span-depth ratio of 4 shows higher stiffness and lower deformability compared to the shear span-depth ratio of 7.    128  From Figure 6.7, it can be observed that the FRP-confinement layer does not affect the flexural performance of the piers in terms of yielding, crushing, buckling, and fracture base shears and displacements. Similar base shear and displacement limit states are observed from 2 and 3 layers of FRP confinement.    Figure 6.7 Results of pushover analysis considering different layer of FRP  Table 6.3 Base shear and displacement at different limit states  Variable Pier-ID Yielding Crushing Bucking Fracture Disp. (mm) Base shear (kN) Disp. (mm) Base shear (kN) Disp. (mm) Base shear (kN) Disp. (mm) Base shear (kN) Compressive strength C-1-35 28 63.15 52 74.50 172 60.02 176 59.56 C-1-20 28 55.26 56 68.78 180 63.60 184 63.38 Yield strength C-2-400 28 63.09 52 74.62 176 57.55 176 57.55 C-2-250 20 47.74 44 54.26 164 40.23 168 38.92 Longitudinal reinforcement  C-3-2.5 28 58.08 56 71.11 168 66.99 172 66.88 C-3-1 24 31.99 64 36.47 152 29.58 156 29.35 Axial load C-4-0.20 12 133.74 20 138.94 56 138.63 60 138.50 C-4-0.10 8 94.52 20 129.08 56 133.78 56 133.78 Shear span-depth ratio C-5-7 28 56.77 56 69.15 172 65.41 176 65.28 C-5-4 12 119.87 20 124.20 56 131.22 60 131.68 FRP confinement layer C-6-2 8 97.16 16 107.44 56 102.62 56 102.62 C-6-3 8 97.17 16 105.69 56 103.17 56 103.17    129 6.4 Incremental Dynamic Analysis of Pier  In order to predict the structural response under lateral load, NSPA is widely used. Conversely, during a seismic event the lateral load experienced by the structures is dynamic in nature; hence, nonlinear dynamic time history analysis will provide accurate estimation of structural response under a seismic load. Luco and Cornell (1998) developed incremental dynamic analysis (IDA) method which is well explained in detail in Vamvatsikos and Cornell (2002), and Yun et al. (2002). IDA needs multiple nonlinear dynamic time history analyses of a structural model by scaling sets of seismic ground motion records based on adopted intensity measures (IM). Then, regression equations of engineering demand parameters (EDP), such as maximum drift at different intensity levels will be developed. The suite of different ground motions is properly chosen to cover the entire range of the model’s response from elastic to yield, and nonlinear inelastic which leads to global dynamic instability of structures. In IDA, different scaling factors should be selected for different piers. Here, PGA is selected as IM and the incremental scaling series in IDA ranges from 0.1g to 3.0g. Overall, when the maximum top drift of the piers exceeds certain level, it experiences dynamic instability with a large deformation or drift. In this chapter, a “collapse point” is considered as the first incidence of such large deformation or drift (Vamvatsikos and Cornell 2002). Though, Konstantinidis and Nikfar (2015) reported that increase of an actual ground motion PGA value  by a scaling factor does not certainly lead to reliable results; however, it will provide a better understanding of the behavior of the inelastic system over the range of different intensity measures. In portraying the inelastic demand, non-linear behavior in the collapsed state are defined. The collapse results are modeled by developing fragility curves at the collapse limit state.  6.4.1 Selection of ground motions  The properties of seismic ground motion differ in terms of frequency content, peak ground acceleration (PGA), and duration. Thus, dynamic time history analyses of structure for one ground motion record might not characterize the worst-case scenario. In order to incorporate the uncertainties and variability of ground motion records and their impact on the behavior of bridge piers, a suite of earthquake ground motions are required. Due to limited number of available earthquake records in Vancouver, British Columbia region (western Canada), a suite   130 of 20 ground motion histories are obtained from the Applied Technology Council (ATC 2009) ground motion database. Table 6.4 shows the characteristics of the un-scaled seismic ground motion records including PGA, peak ground velocity (PGV), epicenter distance (R), and moment magnitude (Mw) of the earthquake. These ground motion records have low to medium values of PGA, R, Mw and PGV, which are in the range of 0.22-0.73g, 8.7-98.2km, 6.5-7.6 and 17-70cm/sec, respectively. It is assumed that these ground motions are considered to be representative of an earthquake motion in Vancouver. In this study, the horizontal components of ground motion records are applied to the pier. The specified magnitude and distance ranges cover the predominant magnitudes and distances for Vancouver.   Table 6.4 Characteristic of ground motion records used in IDA EQ No. Mw Year Earthquake Name Earthquake Recording Station R (km) PGAmax (g) PGV (cm/s) 1 6.7 1994 Northridge Beverly Hills - Mulhol 13.3 0.42 58.95 2 7.3 1992 Landers Yermo Fire Station 86.0 0.24 52.00 3 6.7 1994 Northridge Canyon Country-WLC 26.5 0.41 42.97 4 7.3 1992 Landers Coolwater 82.1 0.28 26.00 5 7.1 1999 Duzce, Turkey Bolu 41.3 0.73 56.44 6 6.9 1989 Loma Prieta Capitola 9.80 0.53 35.00 7 7.1 1999 Hector Mine Hector 26.5 0.27 28.56 8 6.9 1989 Loma Prieta Gilroy Array #3 31.4 0.56 36.00 9 6.5 1979 Imperial Valley Delta 33.7 0.24 26.00 10 7.4 1990 Manjil, Iran Abbar 40.4 0.51 43.00 11 6.5 1979 Imperial Valley El Centro Array #11 29.4 0.36 34.44 12 6.5 1987 Superstition Hills El Centro Imp. Co. 35.8 0.36 46.00 13 6.9 1995 Kobe, Japan Nishi-Akashi 8.70 0.51 37.28 14 6.5 1987 Superstition Hills Poe Road (temp) 11.2 0.45 36.00 15 6.9 1995 Kobe, Japan Shin-Osaka 46.0 0.24 38.00 16 7.0 1992 Cape Mendocino Rio Dell Overpass 22.7 0.39 44.00 17 7.5 1999 Kocaeli, Turkey Duzce 98.2 0.31 59.00 18 7.6 1999 Chi-Chi, Taiwan CHY101 32.0 0.35 71.00 19 7.5 1999 Kocaeli, Turkey Arcelik 53.7 0.22 17.69 20 7.6 1999 Chi-Chi, Taiwan TCU045 77.5 0.47 37.00   131  Figure 6.8 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b) percentile of response spectral acceleration of a suit of earthquake ground motion records   Figure 6.8(a) shows the acceleration response spectrum of the recorded suits of 20 ground motions with a 5% damping ratio. Figure 6.8(b) depicts different percentiles of acceleration response spectra with a 5% damping ratio, showing that the selected earthquake ground motions records are well representing the medium to strong intensity earthquake ground motion histories. Acceleration time histories of all the earthquakes used in the IDA are described in Appendix E (Figure E.1).   6.4.2 Incremental dynamic analysis for pier collapse capacity For the retrofitted bridge piers, inelastic demands are estimated by conducting IDA. IDA curve is also known as dynamic pushover curve, which is the relationships between IM and EDP. These curves are generated using numerous ground motions, and each ground motion records are scaled to multiple levels of intensities (Vamvatsikos and Cornell 2002).  6.4.2.1 Dynamic pushover curve The incremental dynamic analysis is conducted for all the retrofitted bridge piers using the suite of 20 earthquake ground motion records. Figure 6.9 (a) - Figure 6.20 show the dynamic pushover curve of total base shear versus top lateral displacement for different compressive   132 strengths of concrete, yield strengths and amount of longitudinal reinforcement, axial loads, shear span-depth ratios, and FRP layers. The dynamic pushover points closely coincide with the static pushover curves before the first yielding of the longitudinal reinforcement. It can be observed from Figure 6.9  - Figure 6.20  that the dynamic pushover curves demonstrate higher base shear values compared to those from the static pushover curves between first yielding and crushing of core concrete.   Figure 6.9 Results of dynamic and static pushover curve for C-1-35    Figure 6.10 Dynamic and static pushover curve for C-1-20   133  Figure 6.11 Dynamic and static pushover curve for C-2-400  Figure 6.12 Results Dynamic and static pushover curve for C-2-250  Figure 6.13 Results of dynamic and static pushover curve for C-3-2.5   134  Figure 6.14 Results of dynamic and static pushover curve for C-3-1  Figure 6.15 Results of dynamic and static pushover curve for C-4-0.20  Figure 6.16 Results of dynamic and static pushover curve for C-4-0.10   135  Figure 6.17 Results of dynamic and static pushover curve for C-5-7  Figure 6.18 Results of dynamic and static pushover curve for C-5-4  Figure 6.19 Results of dynamic and static pushover curve for C-6-2   136  Figure 6.20 Results of dynamic and static pushover curve for C-6-3  6.4.2.2 Incremental dynamic analysis curve IDA curve results with all the combinations of parameters are used to identify IM values related to the collapse. Figure 6.21 - Figure 6.21 show the IDA curves of all the retrofitted piers with different adopted parameters (Table 6.2) and a set of IM values related to the onset of collapse for each ground motions. The overall characteristics of the IDA curves for maximum top drift ratio are different, the initial drift increases gradually with the seismic intensity level. Afterward, the drift increases rapidly when the seismic intensity level reaches a range of 0.2g to 0.4g for all of the piers (Figure 6.21). According to the results of IDA curves shown in Figure 6.21(a) - Figure 6.21(l), the non-seismically designed piers show more vulnerability compared to the other bridge piers. Failure modes obtained from the IDA curves at collapse level are summarized in Appendix E (Table E.2).    137       138    Figure 6.21 IDA results used to identify IM values related with collapse for each ground motions of all the bridge piers retrofitted with FRP   139 6.5 Collapse Fragility Assessment The fragility curves can be produced by using various methods, for instance, an expert opinion, damage  data observed from field, laboratory testing, based on numerical simulations, or a combination of them (Kennedy and Ravindra 1984, Kim and Shinozuka 2004, Calvi et al. 2006, Villaverde 2007, Porter et al. 2007, Shafei et al. 2011, Billah and Alam 2015) . In this research, analytical collapse fragility curves were generated based on IDA results using suits of 20 ground motion records scaled until it causes the collapse of the pier (Vamvatsikos and Cornell 2002). The analytical fragility curve exhibits advantages compared to other methods. For instance, in the case of analytical fragility curve, the analyst is free to choose the IM , at which analysis is to be conducted, and the number of analysis at each IM (Baker 2015). Generally, the fragility curves are mathematical functions which describe the conditional probability that a structure can experience damage by exceeding or reaching a specific level of damage state as a function of demand (drift or ductility), represented by EDP IM (e.g. PGA). In the seismic vulnerability assessment of structure, fragility curves are obtained from IDA (ATC 2012).. The collapse fragility function gives a probability that a structure would collapse as a function of a specific IM. The collapse fragility assessment can be described using Eq. (6.1) as a lognormal cumulative distribution function (CDF) reported by (Baker 2015).    ln|cxP C IM x      (6.1) where Pc(C|IM = x) represents the probability of collapse at a given ground motion with IM = x, Φ(.) is the standard normal CDF, θ is the collapsed median intensity of the fragility function (IM level with 50% probability of collapse not being exceeded), and β is the logarithmic standard deviation. Eq. (6.1) indicates the assumption of lognormality of the IM values of the ground motions causing the collapse of specific structures (Baker 2015). Calibrating Eq. (6.1) of the pier needs an estimation of θ and β from the IDA results. Figure 6.22(a) - Figure 6.22(l) shows the linear regression models of the median and standard lognormal dispersion for all the combinations of parameters. Table 6.5 depicts a summary of the values of linear regression models of the median and standard lognormal dispersion for all the combinations.   The probability of collapse can be assessed at a given IM level, x can then be determined as a part of records for which collapse occurs at a level lower than x. Fragility function   140 parameters can be assessed from the regression analyses of their median θ, and dispersion β, values, and by taking the logarithm of each ground motion’s IM value related to the onset of collapse.   Table 6.5 Median and dispersion values from the results of IDA using regression analysis Variable Pier-ID Median (θ) Dispersion (β)  R2 Compressive strength C-1-35 -0.32 0.55 0.97 C-1-20 0.09 0.47 0.98 Yield strength  C-2-400 0.20 0.42 0.97 C-2-250 -0.24 0.54 0.99 Longitudinal reinforcement  C-3-2.5 -0.11 0.47 0.98 C-3-1 -0.21 0.49 0.94 Axial load C-4-0.20 0.27 0.38 0.98 C-4-0.10 -0.34 0.53 0.97 Shear span-depth ratio C-5-7 -0.48 0.59 0.99 C-5-4 0.21 0.45 0.98 FRP confinement  layer  C-6-2 -0.28 0.54 0.95 C-6-3 0.15 0.42 0.95           141      142    Figure 6.22 Linear regression model for the median and dispersion from IDA results   143  Based on the obtained collapse mode of IDA results and using fragility curves, the probability of collapse of all the combination of parameters is plotted in Figure 6.23-Figure 6.28. In order to compare the obtained probability of collapse for the combination of different parameters, these curves are plotted together and presented in one figure. In Figure 6.23-Figure 6.28,  the curve drawn with a black solid line indicates a higher collapse fragility, and the dotted red line shows a lower collapse fragility as obtained by fitting the lognormal distribution to the data. These data are obtained from the IDAs results. It can be observed from the Figure 6.23 - Figure 6.28 that the probability of collapse of the lower value has a significant shift to the left and has a smaller PGA for a specific probability of collapse. It leads to an increase in the probability of collapse for a given seismicity. In Figure 6.23 - Figure 6.28, SCT represents the median collapse probability.  6.5.1 Effect of compressive strength of concrete on collapse fragility curve Figure 6.23 shows the effect of concrete compressive strength on the collapse fragility of retrofitted bridge piers based on the maximum collapse drift ratio. The solid black line and the red dotted line represent the probability of collapse with the specified compressive strength of concrete of 35 and 20 MPa, respectively. The fragility curve clearly demonstrates the probability of structural collapse for measuring definite intensity. From Figure 6.23, it can be observed that the difference between fragility curves of 35, and 20 MPa concrete is significant. It is important to note that 35MPa concrete pier is more fragile compared to 20MPa concrete piers. For instance, as shown in Table 6.6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the relative probability of collapse of 35 MPa concrete pier is higher compared to 20 MPa concrete pier. 35 MPa concrete pier has higher stiffness that attracts more seismic forces causing more damages to the pier compared to the 20 MPa concrete pier. Since 20 MPa concrete has lower modulus of elasticity compared to 30 MPa concrete, larger strain experienced by the 20 MPa concrete activated the FRP composite confinement and thus, was more effective in resisting seismic forces compared to the 30 MPa concrete at similar drift level. From Figure 6.23 it can be observed that the 20 MPa concrete pier will have 50% probability of collapse at a PGA value of 1.1g whereas the 35 MPa concrete will be able to sustain an earthquake with a PGA of only 0.72g to experience similar   144 damage level. In other words, during an earthquake with a PGA of 0.72g the probability of collapse of the 20 MPa concrete is only 20% whereas for the 35 MPa concrete it is 50%.    Figure 6.23 Effect of concrete strength on collapse fragility  6.5.2 Effect of yield strength of steel reinforcement on collapse fragility  Figure 6.24 shows the effect of yield strength of longitudinal reinforcement on the collapse fragility of retrofitted bridge piers based on maximum collapse drift ratio. The solid black line and the red dotted line indicates the probability of collapse fragility with the yield strength of longitudinal reinforcement of 400, and 250MPa, respectively. The fragility curve clearly demonstrates the probability of structural collapse for measuring definite intensity. From Figure 6.24, it can be observed that the difference between fragility curves of 400, and 250 MPa reinforcements are significant. For example, as shown in Table 6.6, for the peak ground intensity levels, PGA, in the range of 0.5g-2.0g, the relative probability of collapse for the 400MPa steel RC pier is lower compared to the 250 MPa steel RC pier. For the intensity level of 2.0g, the difference in the collapse probabilities is insignificant. Since both steel has the same modulus of elasticity, the 400 MPa steel experiences yielding at a much larger strain value compared to the 250 MPa steel. Hence, the 400 MPa steel gets an added advantage to experience lower damage level at the same ground motion level compared to the 400 MPa steel. From Figure 6.24 it can be observed that the 400 MPa steel RC pier will have 50%   145 probability of collapse at a PGA value of 0.71g whereas the 250 MPa steel RC pier will be able to sustain an earthquake with a PGA of only 0.62g. In other words, during an earthquake with a PGA of 0.62g the probability of collapse of the 400 MPa steel is 40% whereas for the 250 MPa steel it is 50%.   Figure 6.24 Effect of yield strength of longitudinal steel on collapse fragility  6.5.3 Effect of amount of longitudinal reinforcement on collapse fragility  Figure 6.25 shows the effect of the amount of longitudinal reinforcement on the collapse fragility of retrofitted bridge piers. The solid black line and the red dotted line represents the probability of collapse of the amount of longitudinal reinforcement of 1, and 2.5%, respectively. The fragility curve clearly demonstrates the probability of structural collapse for measuring definite intensity. From Figure 6.25, it can be observed that the difference between fragility curves with the longitudinal reinforcement of 2.5% is significant compared to 1% reinforcement. Larger amount of rebar increases the stiffness and strength of the pier and hence, it experiences lesser deformation compared to the pier having reduced amount of longitudinal bar. As shown in Table 6.6, for the peak ground intensity levels, PGA, in the range of 0.5g-2.0g, the relative probability of collapse for the 2.5% longitudinal steel is lower compared to 1% longitudinal steel. From Figure 6.25 it can be observed that the 1% longitudinal steel pier will have 50% probability of collapse even at a PGA value of 0.8g   146 whereas the 2.5% steel RC pier will be able to sustain an earthquake with a PGA of 1.22g. In other words, during an earthquake with a PGA of 0.8g the probability of collapse of the 1% steel pier is 50% whereas for the 2.5% steel pier it is only 14%.   Figure 6.25 Effect of amount of longitudinal steel on collapse fragility  6.5.4 Effect of axial load on collapse fragility  Figure 6.26 shows the effect of axial load on the collapse fragility of retrofitted bridge piers based on maximum collapse drift ratio. The solid black line and the red dotted line represent the probability of collapse with the axial load ratios of 0.20 and 0.10, respectively. The fragility curves clearly demonstrate the probability of structural collapse. From Figure 6.26, it can be observed that the difference between fragility curves with the axial load ratios of 0.20 and 0.10 is significant. For example, as shown in Table 6.6, for PGA values in the range of 0.5g-2.0g, the relative probability of collapse at the axial load of 0.20 is higher compared to 0.10 axial load. From Figure 6.26, it can be observed that the higher axial load pier will have 50% probability of collapse at a PGA value of 0.9g whereas the lower axial load pier will be able to sustain an earthquake with a PGA of 1.31g. In other words, during an earthquake with a PGA of 0.9g the probability of collapse of the higher axial load pier is 50% whereas for the lower axial load pier it is only 16%.   147  Figure 6.26 Effect of axial load on collapse fragility  6.5.5 Effect of shear span-depth ratio on collapse fragility  Figure 6.27 shows the effect of shear span-depth ratio on collapse fragility of retrofitted bridge piers. The solid black line and the red dotted line represent probabilities of collapse with the shear span-depth ratios of 4 and 7, respectively. The fragility curves clearly demonstrate the probability of structural collapse. From Figure 6.27, it can be observed that the difference between fragility curves with shear span-depth ratios of 4 and 7 is not very significant. As shown in Table 6.6, for the peak ground intensity levels, PGA in the range of 0.5g-2.0g, the relative probability of collapse at the shear span-depth ratio of 7 is lower compared to the shear span-depth ratio of 0.10. From Figure 6.27, it can be observed that the pier with larger shear span-depth ratio will have 50% probability of collapse at a PGA value of 1.16g whereas the pier with lower shear span-depth ratio will be able to sustain an earthquake with a PGA of only 1.24g. In other words, during an earthquake with a PGA of 1.16g the probability of collapse of the larger shear span-depth ratio is 50% whereas for the lower shear span-depth ratio it is 45%.   148  Figure 6.27 Effect of shear span-depth ratio on collapse fragility  6.5.6 Effect of confinement on collapse fragility  Figure 6.28 shows the effect of FRP confinement on the collapse fragility of circular RC bridge piers. The solid black line and the red dotted line represent the probabilities of collapse with 2 and 3 layers of FRP confinement, respectively. From Figure 6.28, it can be observed that the difference between fragility curves for 2 and 3 layers of FRP confinement is insignificant at PGA values beyond 1.5g. However, from 0.2g to 1.5g, there are some differences. As shown in Table 6.6, the relative probability of collapse for the 2 FRP confinement layers is higher compared to 3 layers of FRP confinement. From Figure 6.28 it can be observed that the 2 layer FRP pier will have 50% probability of collapse at a PGA value of 0.75g whereas the 3 layer FRP pier will be able to sustain an earthquake with a PGA of 0.82g. In other words, during an earthquake with a PGA of 0.75g the probability of collapse of the 3 layer FRP pier is 44% whereas for the 2 layer FRP pier it is 50%   149  Figure 6.28 Effect of FRP confinement on collapse fragility  Table 6.6 Collapse probability of different variables at PGAs of 0.5, 1.0, 1.5 and 2.0g Variable Pier-ID 0.5g 1.0g 1.5g 2.0g Pc ∆ (%) Pc ∆ (%) Pc ∆ (%) Pc ∆ (%) Compressive  strength C-1-35 0.25 - 0.72 - 0.91 - 0.97 - C-1-20 0.05 -74.8  0.43  -27.8 0.75 -9.3  0.90  -3.2 Yield strength  C-2-400 0.02  - 0.31  - 0.69 -  0.88 -  C-2-250 0.20 79.8 0.67 32.8 0.88 11.7 0.96 4.3 Longitudinal  reinforcement  C-3-2.5 0.11  - 0.59  - 0.86  - 0.95  - C-3-1 0.16 83.8 0.66 33.9 0.89 10.8 0.97 3.5 Axial load C-4-0.20 0.01 -  0.24 -  0.64  - 0.87  - C-4-0.10 0.25 -74.8 0.74 -26.4 0.92 -8.2 0.97 -2.7 Shear span-depth ratio C-5-7 0.36 - 0.79 - 0.93  0.98 - C-5-4 0.02  64.2 0.32  21.0 0.67  6.8 0.86 2.4  FRP confinement layer  C-6-2 0.22 - 0.70 - 0.90 - 0.97 - C-6-3 0.02  -77.7 0.36 -29.9 0.73  -10.0 0.90 -3.4      Pc: probability of collapse, (- negative sign indicates the reduction in the probability of damage)     ∆: relative difference between collapse probabilities of different parameters    The collapse probability difference, ∆, for fragilities of all combination of parameters are reported in a bar chart (see Figure 6.29 and Figure 6.30) for four peak ground accelerations of 0.5g, 1.0g, 1.5g, and 2.0g. As expected with higher PGA values, the differences in collapse probability gradually decrease.   150  Figure 6.29 Collapse probability of the piers at four PGA, 0.5, g, 0.1.0g, 1.5g, and 2.0g   Figure 6.30 Difference between collapse probability of different parameters  6.5.7 Median peak ground acceleration The median values of the intensity measure, PGA, for a different combination of FRP, retrofitted bridge piers are given in Table 6.7 and the corresponding bar chart is depicted in Figure 6.31. The median values of PGA are determined as a level of PGA at which the probability of collapse at each pier reaches 50%. For the same level of collapse probability,   151 lower values of median correspond to the higher probability of collapse, hence it demonstrates that the pier with a lower median value is more fragile compared to other piers. For example, piers with a concrete compressive strength of 35 MPa, a reinforcement yield strength of      250 MPa, a longitudinal reinforcement ratio of 1%, and axial load of 0.20, a shear span-depth ratio of 4, and 2 confinement layers have the lowest value of median, respectively, 0.72g, 0.62g, 0.79g, 0.90g, 1.16g and 0.78g. It demonstrates that the lowest median values of piers have the inferior performance. It can be noted that the pier with 20MPa concrete gives higher median value of 1.1g.  As a result, it indicates that the FRP confinement is more effective in 20MPa concrete compared to 35MPa concrete (PGA = 0.72g) in the case of FRP retrofitted piers.    Table 6.7 Median values of PGA for piers with different parameters Variable Pier-ID Pc ∆ Compressive  strength C-1-35 0.72g - C-1-20 1.10g -10 Yield strength  C-2-400 0.71g - C-2-250 0.62g 29 Longitudinal  reinforcement C-3-2.5 1.23g - C-3-1 0.79g 23 Axial load C-4-0.20 0.90g - C-4-0.10 1.31g 31 Shear span-depth ratio C-5-7 1.23g - C-5-4 1.16g 23 FRP confinement layer  C-6-2 0.76g - C-6-3 0.82g -18 Pc: probability of collapse,  ∆: relative difference between collapse probabilities of different parameters    152  Figure 6.31 Bar chart of median values of PGA for the piers with different parameters   The relative difference between the median values of PGA is found to be 10% for 35 and 20 MPa concretes. It represents that the 35MPa concrete pier leads to a 10% higher fragility compared to the 20 MPa concrete pier. It is because the FRP confinement is more effective for 20MPa concrete compared to the 35MPa concrete. Thus, it is concluded that the deficient pier performance can be improved with FRP.  6.5.8 Performance evaluation of bridge piers Results of IDA curve can be used to evaluate the collapse performance of the RC bridge piers. The collapse median intensity (SCT) obtained from the fragility fitting curves (Figure 6.23 - Figure 6.28) and the performance of bridge piers can be assessed using collapse margin ratio (CMR) (ATC 2009). The CMR can be expressed at the ratio of the SCT to the design level earthquake intensity (SMT). The CMR ratio is calculated by dividing the SCT by a specific level of SMT, which is equal to 0.185g, 0.256g and 0.363g for 10, 5, and 2% probabilities of exceedance in 50 years at the return period of 475, 975 and 2475 years, respectively for Vancouver, British Columbia. Table 6.8 exhibits the CMR values for different combinations of parameters. From Table 6.8, it can be observed that as the ground motion return period decreases the collapse probability of exceedance increases. For instance, for a pier with a compressive strength of concrete of 35 MPa, the collapse probability value under an earthquake with a return period of 2475 years is 1.98, which is 3.38 and 2.11% lower than a   153 return period of 975 and 475 years, respectively. As the earthquake return period increases, its intensity also increases. Hence, the probability of exceeding collapse of a certain pier will increase, which, means that the median collapse spectral acceleration will increase with the increase of earthquake return period. Since, the  spectral acceleration at maximum considered earathquake will also increase with the increase of earthquake return period, the results presented in Table 6.8 show the CMR values gradually decrease with increasing return period.  For instance, when the yield strength of longitudinal reinforcement increases, the CMR ratio increases from 3.35% to 3.84% at 475 years return period. In the case of increasing compressive strength, the CMR ratio decreases from 5.95% to 3.89% with a return period of 475 years. It is because of the lower strength concrete (20 MPa); the FRP confinement is more effective compared to higher strength (35 MPa) concrete.”  Table 6.8 Collapse margin ratio for collapse safety of piers Variable Pier-ID Probability of Exceedance of collapse 10% in 50 years 5% in 50 years  2% in 50 years  Compressive  strength C-1-35 3.89 2.81 1.98 C-1-20 5.95 4.30 3.03 Yield strength  C-2-400 3.84 2.77 1.96 C-2-250 3.35 2.42 1.71 Longitudinal  reinforcement  C-3-2.5 6.65 4.80 3.39 C-3-1 4.27 3.09 2.18 Axial load C-4-0.20 4.86 3.52 2.48 C-4-0.10 7.08 5.12 3.61 Shear span-depth ratio C-5-7 6.65 4.80 3.39 C-5-4 6.27 4.53 3.20 FRP confinement layer  C-6-2 4.08 2.95 2.08 C-6-3 4.43 3.20 2.26  6.6 Summary The seismic fragility assessment of the bridge can be analyzed using fragility curve, which is a method to estimate the probability of damage to the structure at specific levels of ground motion. The piers are the most vulnerable structural element in the bridge structures, which have a significant contribution to the failure probability of the bridge system. This chapter presented the nonlinear static pushover analyses, and collapse fragility curves for non-seismically designed RC circular bridge piers located in Vancouver, British Columbia,   154 Canada, using different combinations of parameters. Probabilistic seismic demand models were produced using the results obtained from the incremental dynamic analyses. Considering collapse drift as demand parameters, fragility curves were generated with different parameters of non-seismically designed RC circular bridge piers. It was observed that amount of reinforcement, shear span-depth ratio, and axial load significantly affect the collapse fragility curve of the retrofitted bridge piers.                             155 Chapter 7: Fragility Assessment of Non-Seismically Designed Circular RC Bridge Piers Retrofitted with FRP Using Full Factorial Design Method  7.1 General In order to conduct a seismic vulnerability assessment of existing highway bridge piers, the probabilistic seismic demand model (PSDM) is widely used in the literature (Shinozuka et al. 2000b, Monti and Nistico 2002, Franchin et al. 2006, Padgett and DesRoches 2008, Zanini et al. 2013, Carturan et al. 2014, Billah and Alam 2015b). Figure 7.1 demonstrates the example of seismic fragility curve representing the probability of pier being damaged beyond various performance damage/limit states, such as slight (damage with cracking), moderate (damage that is repairable), extensive (irreparable damage at the limit of life safely) and collapse under certain intensity measure (IM) in terms of peak ground acceleration (PGA) or spectral acceleration (Sa).   Figure 7.1 Example of fragility curves with four damage/limit states of bridge pier  7.2 Fragility Function Methodology To ensure structural safety and serviceability under extreme events, it is vital to conduct a seismic vulnerability study to assess the expected economic losses. Seismic vulnerability investigation is a widely popular and useful method for prioritizing the seismic retrofitting and   156 evaluating the loss of structural function of existing highway bridges in the seismic events. There are various methods available to assess the bridge pier performance under extreme events. Seismic vulnerability analysis is normally expressed in the form of fragility functions which shows the conditional probability of structural demands due to ground motions that exceed the structural capacities defined by different damage/limit states (Hwang et al. 2001). For the seismic evaluation of the bridges, fragility curves are used as a common tool, which shows the probability of structural damage as a function of ground motion intensities. The fragility curve is created using two-parameter lognormal distribution functions, and the assessment of the median and dispersion is conducted using a probabilistic framework based on seismic demand model under seismic intensity measure (Kim and Shinozuka 2004). In order to represent the severity of the ground motion, the peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), spectrum intensity (SI), and spectral acceleration (SA) at the first mode shape are widely used and recommended as optimum intensity measures (Nielson and DesRoches 2007, Padgett et al. 2008). Four different procedures are available for the development of seismic fragility curves, such as (a) professional opinion (Jaiswal et al. 2012), (b) experimental and visual observation (Rossetto and Elnashai 2003), (c) analytical method (Banerjee and Shinozuka 2007, Mander et al. 2007, Avsar et al. 2011, Tavares et al. 2012, Yazgan 2015, Alam et al. 2012, Billah et al. 2013,  Choine et al. 2015) and (d) hybrid method (Shinozuka et al. 1988, Komura et al. 1989, Billah and Alam 2015b). In the first method, the expert opinion is considered (ATC 1985). In the second method, the analysis is conducted based on the visual damages observed after an earthquake. The third analytical method is more popular for development of the fragility curve and vulnerability assessment because the analytically produced curves can be directly used and are beneficial to bridges where the damage data from an earthquake is insufficient or not available (Hwang et al. 2001, Jernigan and Hwang 2002, Mackie and Stojadinovic 2006, Nielson and DesRoches 2007). The fourth hybrid fragility curve method is a combination of three aforementioned methods (Rossetto et al. 2013). There is different analytical methods available for the fragility curve development, such as nonlinear static analysis (Mander and Basoz 1999, Monti and Nistico 2002, Moschonas et al. 2009), nonlinear time history analysis (Hwang et al. 2001, Choi et al. 2004, Ramanathan et al. 2010, Billah and Alam 2012) elastic-spectral analysis, and Bayesian approach. The literature shows that about 85% researcher used   157 the analytical methods for the seismic fragility assessment of bridges while remaining studies are based on experimental and empirical methods (Billah and Alam 2014).   The seismic vulnerability analysis of structures is affected by many input parameters (Nielson and DesRoches 2007a). Seismic fragility represents the conditional probability of damage at which the seismic demand (D) of a structure is equal to or greater than its capacity (C). The conditional probability can be described using Eq. (7.1)  Fragility = P[LS|IM] = P[D ≥ C|IM] = P [D – C ≥ 0 IM] (7.1) where LS is the limit state of damage of the bridge pier.   For the seismic venerability analysis of bridge piers, PSDMs can be established using cloud approach (Choi et al. 2004, Nielson and DesRoches 2007) and the scaling approach (Zhang et al. 2009). In the cloud approach, unscaled earthquake records are used in the nonlinear dynamic time history analyses (NDTA), and based on the obtained results, a PSDM is generated (Mackie and Stojadinovic 2001, Choi et al. 2004, Nielson and DesRoches 2007, Billah et al. 2013) . In the scaling approach, all records are scaled to selective intensity levels and IDA is conducted for each intensity level (Alam et al. 2012, Bhuiyan and Alam 2013). In this research, the scaling approach has been adopted in order to develop the analytical seismic fragility curve of the deficient CFRP retrofitted piers (Table 7.1). It is worth to mention that IDA is conducted to generate an adequate amount of data for the development of fragility curve.  Displacement ductility (µd) and PGA are used as the engineering demand parameter (EDP) and the ground intensity measure (IM), respectively. In the PSDMs, it is assumed that the distribution of EDPs follows a two-parameter logarithm correlation between median and IM (Song and Ellingwood 1999, Kim and Shinozuka 2004, Cornell et al. 2002). In this chapter, the relationship between the intensity measure and the engineering demand parameter (median demand, Sd) can be defined as a power model (Cornell et al. 2002) Eq. (7.2)  bdEDP S aIM   (7.2) According to the probability theory, if the variable EDP has a lognormal distribution, ln(EDP) will have a normal distribution. Hence, using logarithm transformation, Eq. (7.3) becomes   ( ) = (a) + . ( )dln(EDP)= ln S ln b ln IM  (7.3) where, a and b are linear regression coefficient of the demand which can be estimated from the response obtained through IDA.    158  Maximum top drift ratio is a widely used EDP, since its calculation using dynamic analyses is straightforward, and its relation to the damage to the pier can be performed using empirical correlations. The scope of this research in this chapter is limited to the estimation of the structural response. The fragility function depends on the structural demand and the selected damage/limit states. The structural demand was determined using IDA. In this research, a probabilistic relation between EDP and limit state (LS) or damage state (DS) can be assumed. The distributions of demand and capacity of bridge piers follow a lognormal function and the associated standard deviations are recommended in the HAZUS framework (NIBS 2004). This approach is represented in Eq.(7.4).      2 2|ln /| |d cD IM CS SP LS IM P D C IM         (7.4) where Φ[.] is the standard normal cumulative distribution function (SCDF); Sd and Sc are the median values for the structural demand (spectral displacement) and structural capacity at a specific limit state in terms of seismic intensity, respectively ; D and C are the demand and capacity, respectively; βD|IM is the logarithm standard deviation or dispersion of the demand condition on the IM; and βc is the log-standard dispersion (deviation) of the fragility curve for different damage states   (e.g. slight, moderate, extensive and collapse). It is assumed that the structural demand and capacity are random variables and showed by standard lognormal functions (Shinozuka et al. 2000a, Choi et al. 2004, Hancilar et al. 2013, Razzaghi and Eshghi 2014).  The likelihood function can then be introduced by substituting Eq. (7.3) in to Eq. (7.4) and considering the characteristic of natural logarithm function. The fragility function of each bridge pier for specified limit states can be written as below   159    2 2|ln( ) ln ( ) ln( ) ln( )|cD IM Cb IM S a IMP LS IM               (7.5) where λ and ξ are the median, Eq. (7.6), and the standard dispersion (deviation), (7.7), of the intensity measure, IM, respectively.  ln( ) ln( )cS ab  (7.6)  2 2|D IM Cb   (7.7) The conditional dispersion (standard deviation) of the  mean demand, βD|IM, can be calculated using Eq. (7.8) (Baker and Cornell 2006)     21|ln ln .2Nbi iiD IMEDP a IMN    (7.8) where N is the total number of simulations and EDPi is the peak demand. It should be noted that the statistical degree of freedom is equal to the number of data points (N) minus the number of estimated parameter. Figure 7.2 exhibits the schematic representation of methodology for the seismic vulnerability assessment of the FRP retrofitted bridge piers. As displayed in Figure 7.2, following procedure is adopted for the development of PSDMs and fragility curves of FRP retrofitted piers.   Selecting the earthquake ground motion records which could represent the interest of the site and include a satisfactory range of PGA as IM.  Developing Nm numerical models of the FRP retrofitted bridge piers considering a number of ground motion records, NEQ, with factorial design parameters, NPR, (i.e., Nm = NPR × NEQ).  Performing an incremental dynamic analysis, for each pier model. A number of dynamic time history analysis in each IDA is equal to the number of the scaling factor.  Extracting IDAs results, plotting the peak response versus peak value of IM for each IDA.  Conducting regression analyses to determine the regression coefficients, a, b, and βD|IM.  Defining limit states for FRP retrofitted piers considering the median and dispersion values of capacity models at each limit states, and developing fragility curves of the FRP retrofitted pier.   160                         Figure 7.2 Schematic demonstration of methodology for the seismic vulnerability assessment of FRP retrofitted bridge piers  7.3 Seismic Hazard for Vancouver and Selection of Ground Motion  In order to generate fragility curve, a carefully selected ground motion parameter must represent the seismic hazard at the site of interest. According to Luco and Cornell (2007), efficiency, sufficiency, and computability are the three main criteria for the section of suitable Select Suits of Earthquake Records (NEQ) Intensity Measure IM = PGA 0 < PGA < 1.16 Location (Western Canada) 0.8 < PGA/PGV < 1.2 Nm = NPR × NEQ = 1280   Developed Nm Models for FRP Confined Piers Modelling Parameters, 6 with 2 level NPR = 26 = 64 Earthquake Records (NEQ = 20) Conduct Incremental Dynamic Analysis  Scaling Factors: 0.2, 0.4, 0.6…5  Extracting Results Peak Response vs. Peak Value of Displacement Ductility of Pier, µd    Conduct Regression Analysis to Develop PSDMs Coefficients: a, b and βD|IM   Define Damage States (Capacity Models) Coefficients: Sc and βc Slight Moderate Extensive Collapse P [D > C|IM] = Φ  λ = , ξ =   Obtaining Fragility Curves of Pier  Fragility Curves   161 IM for the better accuracy in the PSDMs. Typically, the spectral acceleration at the fist mode period, Sa(T1) is the most commonly used IMs (Billah et al. 2013). However, as recommended by Mackie and Stojadinovic (2006), and Padgett et al. (2008), peak ground acceleration, PGA, is the optimal selection to represent the severity of the ground motion due to its risk computability, efficiency, sufficiency, and practicality. If IM is efficient, it will have a less dispersion for the median of the IDA results. Padgett et al. (2008) reported that a lower value of the dispersion, and a higher value of b in Eq. (7.3) results in a more efficient, practical and proficient IM. However, it is not always correct that higher intensity level of seismic ground motion causes severe structural damage, such as peak ground velocity (Nielson 2005). The different indices, such as peak ground displacement (PGD), PGV, spectrum intensity (SI) (Katayama et al. 1988), time duration of motion (Td) (Trifunac and Brady 1975), distance to epicenter (R), and spectral characteristic are also used for the damage estimation (Molas and Yamazaki 1995). For PSDMs, Billah et al. (2013) reported that PGA is the most efficient IM for the fragility analysis of CFRP retrofitted piers. In this research, PGA is adopted as the IM due to its utility, efficacy, and sufficiency in vulnerability assessment.  The Geological Survey of Canada conducted a seismic hazard analysis for the National Building Code of Canada (NBCC 2015). Figure 7.3 displays the seismicity in Vancouver with a site coordinates of 49.2827°N, and 123.1207°W with Sa(0.2) for site class C in British Columbia, Canada (NBCC 2015). In the NBCC (2015), the seismic hazard is signified in terms of 5% damped spectral acceleration with a uniform probability of exceedance of 2, 5, and 10% in 50 years or return period of 2475, 975, and 475 years, respectively, for the minimum performance level. The spectral accelerations are represented for a period of 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0 s. Figure 7.4 shows the design acceleration response spectra of Vancouver, British Columbia, Canada with different seismic hazard level of a Site class C as specified in NBCC (NRCC 2015). In order to accurately represent any earthquake, which has the biggest contribution to the seismic hazard, it is important to know the magnitude (Mw) and the epicenter distance (R) of the earthquake. Halchuk et al. (2007) studied the seismic hazard by estimating the contributions to the hazard of selected bins of magnitude (ΔMw = 0.25) and distance (ΔR = 20 km) intervals. They showed that at 2% probability exceedance in 50 years, the corresponding Mw and R mean values are 6.4 and 54 km, and 6.8 and 49 km for a period of   162 0.2s and 2.0 s, respectively. 0.2 s and 2.0 s are considered as short and long period earthquake records.    Figure 7.3 Vancouver (Site Coordinates: 49.2827, °N 123.1207°W, Sa(0.2), site class C) seismicity in British Columbia, Canada (NRCC 2015)  Figure 7.4 Design acceleration response spectrum for Vancouver, British Columbia, Canada with different seismic hazard level, for site class C (NBCC 2015)   The deficient RC circular bridge piers retrofitted using CFRP designed for Vancouver City are used in this study to conduct a seismic vulnerability assessment. In order to incorporate the uncertainties and variability of ground motions and their impact on the bridge   163 pier responses, suites of earthquake ground motions are needed to generate fragility curves. Since, such records are not available from the earthquake in Vancouver, British Columbia region, suites of 20 ground motion histories are obtained from the Applied Technology Council (ATC 2009) ground motion database. It is assumed that these ground motions are considered to be representative of earthquake motions in Vancouver. Table 7.1 lists the characteristics of the seismic ground motion records including PGA, PGV, epicenter distance (R), and a moment magnitude (Mw) of the earthquake. These ground motion records have low to medium PGA, R, and Mw, shear wave velocity in the range of 0.22-0.73g, 8.7-98.2 km, 6.5-7.6 Mw, and 17-70 cm/s respectively. Figure 7.5(a) and Figure 7.5(b) show the typical acceleration, velocity, and displacement time histories of Northridge (PGA = 0.41g) earthquake, and Chi-Chi, Taiwan (PGA = 0.47g) earthquake, respectively. The Northridge earthquake and the Chi-Chi Taiwan earthquake have Mw and R of 6.7 and 26.5 km, and 7.6 and 77.5 km, respectively. In this chapter, the horizontal components of ground motion records are applied to the pier. The specified magnitude and distance ranges cover the predominant magnitude and distance scenarios for Vancouver City.   Table 7.1 Characteristics of the selected earthquake ground motion records EQ No Mw Year Earthquake Name Earthquake Recording  Station R (km) PGAmax           (g) PGVmax           (cm/sec) 1 6.7 1994 Northridge Beverly Hills - Mulhol 13.3 0.42 58.95 2 7.3 1992 Landers Yermo Fire Station 86.0 0.24 52.00 3 6.7 1994 Northridge Canyon Country-WLC 26.5 0.41 42.97 4 7.3 1992 Landers Coolwater 82.1 0.28 26.00 5 7.1 1999 Duzce, Turkey Bolu 41.3 0.73 56.44 6 6.9 1989 Loma Prieta Capitola 9.80 0.53 35.00 7 7.1 1999 Hector Mine Hector 26.5 0.27 28.56 8 6.9 1989 Loma Prieta Gilroy Array #3 31.4 0.56 36.00 9 6.5 1979 Imperial Valley Delta 33.7 0.24 26.00 10 7.4 1990 Manjil, Iran Abbar 40.4 0.51 43.00 11 6.5 1979 Imperial Valley El Centro Array #11 29.4 0.36 34.44 12 6.5 1987 Superstition Hills El Centro Imp. Co. 35.8 0.36 46.00 13 6.9 1995 Kobe, Japan Nishi-Akashi 8.70 0.51 37.28 14 6.5 1987 Superstition Hills Poe Road (temp) 11.2 0.45 36.00 15 6.9 1995 Kobe, Japan Shin-Osaka 46.0 0.24 38.00 16 7.0 1992 Cape Mendocino Rio Dell Overpass 22.7 0.39 44.00 17 7.5 1999 Kocaeli, Turkey Duzce 98.2 0.31 59.00 18 7.6 1999 Chi-Chi, Taiwan CHY101 32.0 0.35 71.00 19 7.5 1999 Kocaeli, Turkey Arcelik 53.7 0.22 17.69 20 7.6 1999 Chi-Chi, Taiwan TCU045 77.5 0.47 37.00   164    Figure 7.5 Typical acceleration, velocity and displacement time histories of (a) Northridge (PGA 0.41g) earthquake recorded at same station Canyon Country-WLC, and (b) Chi-Chi, Taiwan (PGA 0.47g) earthquake recorded at same station TCU045   Figure 7.6(a) shows the acceleration response spectrum of the recorded suites of 20-ground motion with 5% damping ratio. Figure 7.6(b) depicts different percentiles of acceleration response spectra with a 5% damping ratio. It shows that the selected earthquake ground motions are well representing the medium to strong intensity earthquake ground motion histories.  (a) (b)   165  Figure 7.6 A suit of 20 earthquake ground motion records (a) Response spectral acceleration (b) percentile of response spectral acceleration of a suit of earthquake ground motion records   7.4 Fragility Assessment of Retrofitted Bridge Piers 7.4.1 Factorial experimental design In order to investigate the effect of different modeling parameters/factors along with their interactions, all factors need to be varied together using factorial design through the analysis of variance (ANOVA) (Montgomery 2012). ANOVA is a collection of statistical models for analyzing differences between the effect of more than two factors and levels through the breakdown of the total variability of factors (Montgomery 2012). A factorial experiment containing n factors, each with two levels, results in 2n factorial design combinations.   Table 7.2 Levels of the factors considered for the nonlinear dynamic analyses Sr. no. Modeling factors/parameters Code Low High Units 1. Compressive strength of concrete, ( 'cf )  A 20 35 (MPa) 2. Yield strength of steel, (fy)  B 250 400 (MPa) 3. Longitudinal steel reinforcement ratio, (ρl) C 1 2.5 (%) 4. Axial load, (P) D 10 20 (%) 5. Shear span-depth ratio, (l/d) E 4 7 -- 6. FRP Layer, (n) F 2 3 No.     166  In this study, the strength of concrete, 'cf , the yield strength of steel, fy, amount of longitudinal reinforcement, ρl, CFRP confinement layers, n, axial load P, and shear span-depth ratio, l/d, with two levels (low and high) are considered for the factorial design as reported in Table 7.2. Six factors, each of them with two levels lead to a full factorial design with 26 = 64 runs (i.e. models). The complete factorial design is presented in Appendix F (Table F.1). High and low levels of each factor are set to encompass reasonable ranges. The NSPA and IDA using a set of 20 ground motion records are conducted for all possible combinations of six factors to determine the sequence of different damage limit states.   7.4.2 Geometry of bridge piers A RC single circular non-seismically designed pier, which represents a typical single circular bridge pier and is located in Vancouver, British Columbia, (western Canada) is used. In order to consider different longitudinal rebar ratio (ρl) of 1 and 2.5%, the rebar area is adjusted (i.e. ρl = As/Ag). Figure 7.7 and Figure 7.8 show the low and high level (treatment) pier reinforced with 13-16mm (ρl = 1%), and 16-16mm (ρl = 2.5%),  longitudinal reinforcements, respectively. For low and high levels (treatments), 400mm diameter pier is reinforced with a circular lateral tie of 6mm with a spacing of 250mm irrespective of the height of the piers. The clear cover of concrete is considered as 35mm in all of the piers. The ratio of vertical load to the design axial load is considered in the range of 10%  to 20%. Based on the reinforcement configuration, the confinement factor is estimated according to Mander et al. (1988a).    167  Figure 7.7 Specimen geometry and reinforcement detailing with lower level factors (fc’ = 20 MPa, fy = 250 MPa, ρl = 1%, P = 10%, l/d = 4, n = 2)   168    Figure 7.8 Specimen geometry and reinforcement detailing with higher-level factors ( 'cf = 35 MPa, fy = 400 MPa, ρl = 2.5%, P = 20%, l/d = 7, n = 3)  7.4.3 Representations of damage/limit states  In order to conduct seismic vulnerability assessment and develop fragility curve, the damage/limit states of bridge piers should be quantified in terms of engineering demand parameters (EDPs). The damage state should have a qualitative representation (Hwang et al. 2000) of the pier. In order to assess the bridge condition, Dutta and Mander (1999) used drift ratio, Hwang et al. (2000) used the capacity/demand ratio of the bridge pier, whereas Park and Ang (1985) developed a damage index (DI) using energy dissipation capacity and ductility demand of the structure as the EDP to develop fragility curves.   In order to estimate the limit states of bridge piers, a capacity model is needed in terms of EDPs (FEMA 2003, Choi et al. 2004, and Nielson 2005). There are two methods available in order to estimate the limit/damage state capacity of bridge piers, such as descriptive   169 (judgmental) method and/or prescriptive (physical) method (Hwang et al. 2000). In the descriptive (judgmental) method, the functionality levels are assigned to the structure using visual inspection by decision makers for various levels of observed damages during seismic events (Hwang et al. 2000). While in the prescriptive (physical) method the mechanics of the problem is studied and some functional levels are prescribed to be assigned to the structure for various level of damage (Mackie and Stojadinovic 2006). Previous research showed that the prescriptive method is a preferred method compared to the descriptive method because it involves engineering analysis and probability  and as a result, it does not need an expert or decision makers (Nielson and DesRoches 2007b). The Bayesian method, which is a combination of the descriptive and physics-based methods can estimate damage/limit states of the bridge pier.  For the ease of demonstration of the analytical procedure, it is assumed that there are five damage states including the state of almost no damage. A set of five damage states is considered including  Ds0, Ds1, Ds2, Ds3 and Ds4, which respectively that represent the state of almost no, at least slight, moderate, extensive damages and complete collapse according to the FEMA loss assessment document HAZUS-MH (FEMA 2003). Table 7.3 shows the qualitative definition and description of these damage states for bridge pier (FEMA 2003). Bridge piers are considered as the main vulnerable elements of highway bridges since it shows nonlinear behavior under severe ground motions. Based on strain limit in the pier section, crack width and repair cost, many statistical damage/limit states have been advised by different researchers (Hose et al. 2000, Karim and Yamazaki 2001, Kawashima et al. 2011, Mander 1999). Shinozuka et al. (2002) and, Kim and Shinozuka (2004)  used the drift limits introduced by Dutta and Mander (1999) for seismic fragility assessment of pier retrofitted by steel jackets. Roy et al. (2010) proposed various limit state value for CFRP jacketed pier which is similar to those introduced by Dutta and Mander (1999). Billah and Alam (2016) introduced residual drift based limit states for RC brider piers reinforced with supeleastic alloys. However, the displacement ductility demand is one of the most typical quantitative damage parameters used for the bridge pier (Hwang et al. 2001, Mosleh et al. 2015).      170 Table 7.3 Qualitative limit states (FEMA 2003) Damage/limit state Descriptions of damage limit state Failure pattern of pier  Slight  (Ds1) Minor cracking and spalling to the abutment cracks in shear keys at abutments, minor spalling and cracks at hinges, minor spalling at eh pier or minor cracking at the deck  Moderate (Ds2) Pier experiencing moderate cracking and spalling, moderate movement of the abutment, extensive cracking of shear keys, any connection having cracked shear keys of bent bolts, keeper bar failure without unseating rocker bearing failure   Extensive (Ds3) Pier degrading without collapse-shear failure, significant residual movement at connections, or major settlement approach, vertical offset of the abutment, differential settlement at connections, shear key failure at abutments  Collapse (Ds4) Pier collapsing, tilting of substructure due to foundation failure   Based on the experimental study, Dutta and Mander (1999) suggested five different damage/limit states (DLS) using drift limit for the non-seismically designed bridge piers. Since, retrofitting technique affect the demand and the seismic response of bridge piers, new damage state must be quantified. Hereafter, these damage states are defined as the maximum drift demand of the piers (DR, %). Damage/limit states (DLS) for all retrofitted pier are obtained by considering the drift limits introduced by Dutta and Mander (1999). Table 7.4 shows a set of five different damage/limit states of a typical bridge pier suggested by Dutta and Mander (1999) which depicts the description of these five damage states and the corresponding drift limits. Figure 7.9 shows the base shear-drift curves obtained from pushover analyses for low and high level factors along with drift limits related to the damage states (DS1-DS4). From Figure 7.9, it can be observed that the damage states on the pushover curves represent multiple levels of structural performance for the low and high levels factors, such as points close to yielding before and after reaching the maximum base shear capacity. For example, slight and extensive damages occur at a drift limit of 0.7 and 2.5%, respectively. In this study, the drift limit can be transformed to peak ductility demand of the pier for each limit state. For the CFRP jacketed piers, this limit is reached when the pier encounters a displacement in the   171 range of 11-20mm. The yield displacement of the CFRP jacketed pier is found in the range of 8-28 mm. The ductility demand of the CFRP retrofitted piers is obtained by dividing the ultimate displacement corresponding to the slight damage by the yield displacement. Following the same procedure, the ductility demand of the piers with different variables is obtained for different damage states. It is assumed that the drift limit can be quantified as a two-parameter lognormal distribution with a median (Sc) and a dispersion (βc). It is also assumed that the drift limit corresponds to Sc and βc values of the related limit state as used in a previous study (Billah et al. 2013). Sc and βc values of the limit state capacities defined by the dispersion (Nielson 2005) are presented in Table 7.5.  Table 7.4 Description of damage/limit states of bridge pier Damage state Description Drift limits (%) (Ds0) Almost No damage First yielding DLS0(DR = 0.5) (Ds1) Slight Cracking, spalling DLS1(DR = 0.7) (Ds2) Moderate Loss of anchorage DLS2(DR = 1.5) (Ds3) Extensive Incipient pier collapse DLS3(DR = 2.5) (Ds4) Collapse Pier collapse DLS4(DR = 5.0)  Note: adapted from (Dutta and Mander 1999)  Figure 7.9 Damage limit state on base shear for low and high levels factors of piers      172 Table 7.5 Ductility demand and limit state capacity of retrofitted bridge piers Pier No. Damage state Ductility  capacity Limit state  capacity  Pier No. Damage state Ductility capacity Limit state capacity Sc βc Sc βc P1 Slight 0.7 0.7 0.59  P33 Slight 0.7 0.7 0.59 Moderate 1.5 1.5 0.51  Moderate 1.5 1.5 0.51 Extensive 2.5 2.5 0.64  Extensive 2.5 2.5 0.64 Collapse 5.0 5.0 0.65  Collapse 5.0 5.0 0.65 P2 Slight 0.7 0.7 0.59  P34 Slight 1.0 1.0 0.59 Moderate 1.5 1.5 0.51  Moderate 2.1 2.1 0.51 Extensive 2.5 2.5 0.64  Extensive 3.5 3.5 0.64 Collapse 5.0 5.0 0.65  Collapse 7.0 7.0 0.65 P3 Slight 1.0 1.0 0.59  P35 Slight 1.0 1.0 0.59 Moderate 2.1 2.1 0.51  Moderate 2.1 2.1 0.51 Extensive 3.5 3.5 0.64  Extensive 3.5 3.5 0.64 Collapse 7.0 7.0 0.65  Collapse 7.0 7.0 0.65 P4 Slight 1.2 1.2 0.59  P36 Slight 1.0 1.0 0.59 Moderate 2.6 2.6 0.51  Moderate 2.1 2.1 0.51 Extensive 4.4 4.4 0.64  Extensive 3.5 3.5 0.64 Collapse 8.8 8.8 0.65  Collapse 7.0 7.0 0.65 P5 Slight 0.8 0.8 0.59  P37 Slight 0.8 0.8 0.59 Moderate 1.8 1.8 0.51  Moderate 1.8 1.8 0.51 Extensive 2.9 2.9 0.64  Extensive 2.9 2.9 0.64 Collapse 5.8 5.8 0.65  Collapse 5.8 5.8 0.65 P6 Slight 0.8 0.8 0.59  P38 Slight 0.8 0.8 0.59 Moderate 1.8 1.8 0.51  Moderate 1.8 1.8 0.51 Extensive 2.9 2.9 0.64  Extensive 2.9 2.9 0.64 Collapse 5.8 5.8 0.65  Collapse 5.8 5.8 0.65 P7 Slight 1.2 1.2 0.59  P39 Slight 1.2 1.2 0.59 Moderate 2.6 2.6 0.51  Moderate 2.6 2.6 0.51 Extensive 4.4 4.4 0.64  Extensive 4.4 4.4 0.64 Collapse 8.8 8.8 0.65  Collapse 8.8 8.8 0.65 P8 Slight 1.2 1.2 0.59  P40 Slight 1.2 1.2 0.59 Moderate 2.6 2.6 0.51  Moderate 2.6 2.6 0.51 Extensive 4.4 4.4 0.64  Extensive 4.4 4.4 0.64 Collapse 8.8 8.8 0.65  Collapse 8.8 8.8 0.65 P9 Slight 0.7 0.7 0.59  P41 Slight 0.7 0.7 0.59 Moderate 1.5 1.5 0.51  Moderate 1.5 1.5 0.51 Extensive 2.5 2.5 0.64  Extensive 2.5 2.5 0.64 Collapse 5.0 5.0 0.65  Collapse 5.0 5.0 0.65 P10 Slight 0.7 0.7 0.59  P42 Slight 0.7 0.7 0.59 Moderate 1.5 1.5 0.51  Moderate 1.5 1.5 0.51 Extensive 2.5 2.5 0.64  Extensive 2.5 2.5 0.64 Collapse 5.0 5.0 0.65  Collapse 5.0 5.0 0.65 P11 Slight 1.2 1.2 0.59  P43 Slight 1.0 1.0 0.59 Moderate 2.6 2.6 0.51  Moderate 2.1 2.1 0.51 Extensive 4.4 4.4 0.64  Extensive 3.5 3.5 0.64 Collapse 8.8 8.8 0.65  Collapse 7.0 7.0 0.65    173 Pier No. Damage state Ductility  capacity Limit state  capacity  Pier No. Damage state Ductility capacity Limit state capacity Sc βc Sc βc P12 Slight 1.2 1.2 0.59  P44 Slight 1.2 1.2 0.59 Moderate 2.6 2.6 0.51  Moderate 2.6 2.6 0.51 Extensive 4.4 4.4 0.64  Extensive 4.4 4.4 0.64 Collapse 8.8 8.8 0.65  Collapse 8.8 8.8 0.65 P13 Slight 0.8 0.8 0.59  P45 Slight 0.8 0.8 0.59 Moderate 1.8 1.8 0.51  Moderate 1.8 1.8 0.51 Extensive 2.9 2.9 0.64  Extensive 2.9 2.9 0.64 Collapse 5.8 5.8 0.65  Collapse 5.8 5.8 0.65 P14 Slight 0.8 0.8 0.59  P46 Slight 0.8 0.8 0.59 Moderate 1.8 1.8 0.51  Moderate 1.8 1.8 0.51 Extensive 2.9 2.9 0.64  Extensive 2.9 2.9 0.64 Collapse 5.8 5.8 0.65  Collapse 5.8 5.8 0.65 P15 Slight 1.2 1.2 0.59  P47 Slight 1.2 1.2 0.59 Moderate 2.6 2.6 0.51  Moderate 2.6 2.6 0.51 Extensive 4.4 4.4 0.64  Extensive 4.4 4.4 0.64 Collapse 8.8 8.8 0.65  Collapse 8.8 8.8 0.65 P16 Slight 1.2 1.2 0.59  P48 Slight 1.2 1.2 0.59 Moderate 2.6 2.6 0.51  Moderate 2.6 2.6 0.51 Extensive 4.4 4.4 0.64  Extensive 4.4 4.4 0.64 Collapse 8.8 8.8 0.65  Collapse 8.8 8.8 0.65 P17 Slight 0.9 0.9 0.59  P49 Slight 0.9 0.9 0.59 Moderate 2.0 2.0 0.51  Moderate 2.0 2.0 0.51 Extensive 3.3 3.3 0.64  Extensive 3.3 3.3 0.64 Collapse 6.7 6.7 0.65  Collapse 6.7 6.7 0.65 P18 Slight 1.4 1.4 0.59  P50 Slight 0.9 0.9 0.59 Moderate 3.0 3.0 0.51  Moderate 2.0 2.0 0.51 Extensive 5.0 5.0 0.64  Extensive 3.3 3.3 0.64 Collapse 10.0 10.0 0.65  Collapse 6.7 6.7 0.65 P19 Slight 1.4 1.4 0.59  P51 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P20 Slight 1.4 1.4 0.59  P52 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P21 Slight 1.4 1.4 0.59  P53 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P22 Slight 1.4 1.4 0.59  P54 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65     174 Pier No. Damage state Ductility  capacity Limit state  capacity  Pier No. Damage state Ductility capacity Limit state capacity Sc βc Sc βc P23 Slight 1.4 1.4 0.59  P55 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P24 Slight 1.4 1.4 0.59  P56 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P25 Slight 1.4 1.4 0.59  P57 Slight 0.9 0.9 0.59 Moderate 3.0 3.0 0.51  Moderate 2.0 2.0 0.51 Extensive 5.0 5.0 0.64  Extensive 3.3 3.3 0.64 Collapse 10.0 10.0 0.65  Collapse 6.7 6.7 0.65 P26 Slight 1.4 1.4 0.59  P58 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P27 Slight 1.4 1.4 0.59  P59 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P28 Slight 1.4 1.4 0.59  P60 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P29 Slight 1.4 1.4 0.59  P61 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P30 Slight 1.4 1.4 0.59  P62 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P31 Slight 1.4 1.4 0.59  P63 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65 P32 Slight 1.4 1.4 0.59  P64 Slight 1.4 1.4 0.59 Moderate 3.0 3.0 0.51  Moderate 3.0 3.0 0.51 Extensive 5.0 5.0 0.64  Extensive 5.0 5.0 0.64 Collapse 10.0 10.0 0.65  Collapse 10.0 10.0 0.65        175 7.4.4 Probabilistic seismic demand models  The displacement ductility with major contributions to the fragility analysis of the retrofitted bridge piers is considered as the engineering demand parameter in this chapter of the thesis.  7.4.5 Displacement ductility  The stiffness of the pier reduces when the pier undergoes a large amount of deformation under seismic load. According to Park (1988), if the stiffness loss exceeds a specific level, the structure can collapse. The displacement ductility (µd) is defined as the ratio of the relative ultimate displacement (∆u) at the top of a pier to its yield displacement (∆y). In other words, ductility is the capacity of the structure to undergo a large deformation without excessive loss of its strength or stiffness. According to the aforementioned definition, a ductile structure experiences a large amount of inelastic deformation and can dissipate a substantial amount of energy during seismic events. Here, the µd factor is considered as the quantitative measure of the damage state index (Hwang et al. 2001) for RC bridge pier. Pier damage/limit states are described in terms of relative displacement ductility ratio (Hwang et al. 2001). µd is quantified using Eq. (7.9)   udy (7.9) where ∆u is the ultimate displacement at the top of the pier achieved from the seismic analysis of the pier and ∆y is the yield displacement of a pier when the longitudinal reinforcements under tension reach the first yield.   Here, the yielding of longitudinal steel rebar is assumed to take place at a tensile strain of fy/Es as a performance criterion.    To estimate the seismic demand on different pier NSPA and IDA for 1280 pier models are conducted using nonlinear program SeismoStruct (2015). After conducting NSPA and IDA, the numerical results are extracted in terms of the yield displacement and corresponding relative ultimate displacement. The IDA curves of all the piers are presented in Appendix F (Figure F.1). Based on the yield displacement and corresponding ultimate displacement, the displacement ductility ratio (μd) is obtained using Eq. (7.9) for a range of PGAs. According to Eq. (7.2), engineering demand parameters are considered with a lognormal probability distribution. The logarithm of displacement ductility ratio, ln(μd), versus the logarithm of intensity measure ln(PGA), is plotted. This plot will follow a linear trend.    176  In order to estimate the coefficients of PSDMs, a linear regression analysis is conducted. The coefficients a and b are calculated using Eq. (7.3), and the standard deviation (dispersion) of the demand, (βEDM|IM) value is estimated from Eq. (7.8). Figure 7.10 demonstrates the PSDMs. Rest of the PSDMs are presented in Appendix F (Figure F.2). Based on Figure 7.10, it can be observed that each figure shows R2 value greater than 70 which exhibits that the relationship between ln(μd), and ln(PGA) is almost linear. In the linear regression equation, ln(a) and b are representing the intercept and the slope, respectively.    Figure 7.10 PSDMs for displacement ductility (as EDP) of piers as a function of PGA (as IM) with (a) high and (b) low level of modeling parameter             177 Table 7.6 Parameters (Regression coefficient) of fragility curves for the piers with respect to peak ground acceleration Pier No. a b βEDM|IM R2 Pier No. a b βEDM|IM R2 P1 6.66 0.80 0.47 0.72 P33 6.85 0.81 0.45 0.83 P2 7.10 0.90 0.43 0.76 P34 10.62 0.89 0.44 0.78 P3 8.42 0.76 0.45 0.68 P35 9.37 0.78 0.50 0.68 P4 11.37 0.83 0.50 0.70 P36 9.23 0.85 0.53 0.70 P5 8.27 0.78 0.50 0.65 P37 8.23 0.77 0.49 0.83 P6 8.37 0.86 0.51 0.71 P38 8.33 0.85 0.48 0.73 P7 13.44 0.82 0.46 0.71 P39 12.59 0.80 0.46 0.83 P8 12.58 0.83 0.50 0.68 P40 12.94 0.87 0.50 0.71 P9 7.00 0.88 0.44 0.77 P41 6.73 0.88 0.43 0.80 P10 5.90 0.99 0.42 0.82 P42 6.22 0.91 0.47 0.79 P11 11.73 0.89 0.49 0.73 P43 9.80 0.84 0.50 0.73 P12 11.18 1.04 0.46 0.81 P44 10.75 1.01 0.46 0.81 P13 8.24 0.79 0.48 0.70 P45 8.10 0.80 0.48 0.71 P14 7.93 0.92 0.50 0.75 P46 8.02 0.91 0.46 0.78 P15 13.82 0.89 0.43 0.75 P47 12.23 0.85 0.48 0.71 P16 12.87 0.91 0.54 0.71 P48 11.97 0.89 0.52 0.73 P17 9.34 1.09 0.43 0.85 P49 8.98 1.00 0.45 0.81 P18 10.79 1.14 0.43 0.87 P50 7.22 1.14 0.41 0.88 P19 15.15 1.09 0.48 0.82 P51 14.56 1.06 0.50 0.81 P20 12.49 1.20 0.49 0.85 P52 12.86 1.22 0.47 0.85 P21 15.64 0.99 0.50 0.70 P53 16.42 1.01 0.52 0.77 P22 14.53 1.11 0.49 0.82 P54 15.24 1.13 0.50 0.82 P23 16.83 1.07 0.61 0.73 P55 18.20 1.04 0.50 0.77 P24 16.80 1.16 0.53 0.81 P56 17.37 1.17 0.52 0.81 P25 9.40 1.15 0.43 0.86 P57 6.10 1.10 0.43 0.86 P26 6.35 1.20 0.38 0.90 P58 6.35 1.19 0.38 0.88 P27 11.35 1.19 0.51 0.83 P59 11.07 1.17 0.50 0.84 P28 8.06 1.24 0.49 0.86 P60 7.79 1.29 0.43 0.83 P29 14.21 1.11 0.42 0.85 P61 13.66 1.07 0.48 0.81 P30 10.74 1.25 0.44 0.87 P62 10.84 1.19 0.43 0.87 P31 16.26 1.18 0.47 0.84 P63 15.92 1.15 0.49 0.83 P32 12.92 1.32 0.52 0.84 P64 12.62 1.21 0.50 0.84  Table 7.7 P-Values from ANOVA of PSDMs of the piers Sr. No. Code Factors/Parameters a b βEDM|IM 1 A Compressive strength of concrete, 'cf   0.059 0.000 0.687 2 B Yield strength of steel, fy 0.000 0.000 0.000 3 C Longitudinal steel reinforcement ratio, ρl 0.000 0.003 0.000 4 D Axial load, P 0.000 0.000 0.012 5 E Shear span-depth ratio, l/d 0.000 0.000 0.687 6 F CFRP layer, n 0.532 0.054 0.872 Note: Italic red boldface letter shows a significant factor p-value ≤ 5% and known as significantly affecting the PSDM regression coefficient responses, which are labeled as the “most important” factors.   178  The effect of different parameters on the displacement ductility, and regression parameter (a, b), logarithm dispersion (βEDM|IM) and regression coefficient, R2 values of PSDMs are presented in Table 7.6. From Table 7.6, it is revealed that the low value of parameters affect both the intercept (ln(a)) and slope (b) of the regression model. In addition, for most of the piers, dispersion of the demand (βEDM|IM) is less than 0.50 which shows that the PGA is a correct and efficient intensity measure. The ANOVA results with P-values of PSDMs are shown in Table 7.7. The analysis is conducted by considering a confidence level of 95% which means that modeling factors with P-value less than 5% have significant effects on the corresponding response. From the results, it can be observed that the l/d ratio, fy and ρl of reinforcement, and P are the most significant modeling factors. These factors could influence the initial stiffness, flexural and shear strengths, as well as the deformation capacity of the pier (Li 1994). 'cf and n have insignificant contribution to the PSDMs of the piers. The mean and standard deviation values of the PSDMs are presented in Table 7.8. From Table 7.8, it can be seen that the fragility curves depend on the ground motion history.                   179 Table 7.8 Parameters (Mean and standard deviation) of fragility curves for the piers with respect to peak ground acceleration, CFRP Pier  No. Slight Moderate  Extensive Collapse λ ξ λ ξ λ ξ λ ξ P1 -2.83 0.94 -1.87 0.87 -1.23 0.99 -0.36 1.00 P2 -2.58 0.81 -1.73 0.74 -1.16 0.86 -0.39 0.87 P3 -2.82 0.97 -1.82 0.89 -1.15 1.02 -0.24 1.03 P4 -2.68 0.93 -1.77 0.86 -1.15 0.98 -0.32 0.99 P5 -2.95 0.99 -1.98 0.91 -1.33 0.03 0.44 1.04 P6 -2.71 0.91 -1.82 0.84 -1.23 0.95 -0.42 0.96 P7 -2.91 0.91 -1.98 0.84 -1.36 0.96 -0.52 0.97 P8 -2.81 0.93 -1.89 0.86 -1.27 0.98 -0.44 0.99 P9 -2.60 0.83 -1.74 0.76 -1.16 0.88 -0.38 0.89 P10 -2.15 0.73 -1.38 0.67 -0.87 0.77 -0.17 0.78 P11 -2.55 0.86 -1.69 0.80 -1.11 0.91 -0.33 0.92 P12 -2.12 0.72 -1.39 0.66 -0.90 0.76 -0.24 0.76 P13 -2.94 0.97 -1.97 0.89 -1.32 1.02 -0.44 1.03 P14 -2.48 0.84 -1.65 0.78 -1.09 0.88 -0.34 0.89 P15 -2.72 0.82 -1.87 0.75 -1.29 0.87 -0.51 0.88 P16 -2.59 0.88 -1.75 0.81 -1.19 0.92 -0.42 0.93 P17 -2.12 0.67 -1.42 0.61 -0.95 0.71 -0.31 0.72 P18 -1.79 0.64 -1.12 0.59 -0.67 0.68 -0.07 0.68 P19 -2.19 0.70 -1.49 0.65 -1.02 0.74 -0.38 0.75 P20 -1.82 0.64 -1.19 0.59 -0.76 0.67 -0.19 0.68 P21 -2.44 0.78 -1.67 0.72 -1.15 0.82 -0.45 0.83 P22 -2.12 0.69 -1.43 0.64 -0.96 0.73 -0.34 0.74 P23 -2.33 0.80 -1.62 0.75 -1.14 0.83 -0.47 0.84 P24 -2.14 0.68 -1.14 0.63 -1.04 0.72 -0.45 0.72 P25 -1.66 0.64 -0.99 0.58 -0.55 0.67 0.05 0.68 P26 -1.26 0.59 -0.63 0.53 -0.20 0.62 0.38 0.63 P27 -1.75 0.65 -1.11 0.60 -0.69 0.68 -0.11 0.69 P28 -1.41 0.62 -0.80 0.57 -0.38 0.65 0.17 0.65 P29 -2.08 0.65 -1.40 0.60 -0.94 0.69 -0.32 0.70 P30 -1.63 0.59 -1.02 0.54 -0.61 0.62 -0.06 0.63 P31 -2.07 0.64 -1.43 0.59 -1.00 0.67 -0.41 0.68 P32 -1.69 0.60 -1.11 0.55 -0.72 0.63 -0.19 0.63 P33 -2.83 0.92 -1.88 0.84 -1.25 0.97 -0.39 0.98 P34 -2.67 0.82 -1.82 0.75 -1.25 0.87 -0.47 0.88 P35 -2.88 0.99 -1.91 0.92 -1.26 1.04 -0.37 1.05 P36 -2.64 0.93 -1.74 0.86 -1.14 0.98 -0.33 0.99 P37 -2.98 0.99 -2.00 0.91 -1.34 1.04 -0.44 1.05 P38 -2.75 0.90 -1.85 0.83 -1.24 0.94 -0.42 0.95 P39 -2.92 0.94 -1.96 0.86 -1.32 0.99 -0.46 1.00 P40 -2.70 0.89 -1.83 0.82 -1.24 0.93 -0.45 0.94 P41 -2.57 0.83 -1.70 0.76 -1.12 0.88 -0.34 0.89 P42 -2.41 0.83 -1.57 0.76 -1.00 0.87 -0.24 0.88 P43 -2.73 0.92 -1.83 0.85 -1.22 0.96 -0.40 0.97 P44 -2.15 0.74 -1.39 0.68 -0.89 0.78 -0.20 0.79    180 Pier  No. Slight Moderate  Extensive Collapse λ ξ λ ξ λ ξ λ ξ  P45 -2.87 0.95 -1.92 0.87 -1.28 1.00 -0.41 1.01 P46 -2.52 0.83 -1.68 0.76 -1.12 0.87 -0.35 0.88 P47 -2.72 0.90 -1.82 0.83 -1.22 0.95 -0.40 0.96 P48 -2.56 0.88 -1.71 0.82 -1.13 0.93 -0.35 0.94 P49 -2.82 0.75 -1.51 0.69 -1.00 0.79 -0.30 0.80 P50 -1.80 0.63 -1.13 0.57 -0.68 0.67 -0.07 0.67 P51 -2.20 0.73 -1.49 0.67 -1.00 0.76 -0.35 0.77 P52 -1.82 0.62 -1.19 0.57 -0.78 0.65 -0.21 0.66 P53 -2.43 0.78 -1.67 0.72 -1.17 0.81 -0.49 0.82 P54 -2.12 0.69 -1.44 0.64 -0.99 0.72 -0.37 0.73 P55 -2.47 0.75 -1.74 0.69 -1.25 0.78 -0.58 0.79 P56 -2.15 0.67 -1.50 0.62 -1.06 0.70 -0.47 0.71 P57 -1.70 0.66 -1.01 0.60 -0.55 0.70 0.08 0.71 P58 -1.27 0.59 -0.63 0.54 -0.20 0.63 0.38 0.63 P59 -1.77 0.66 -1.12 0.61 -0.68 0.69 -0.09 0.70 P60 -1.33 0.56 -0.74 0.52 -0.34 0.60 0.19 0.60 P61 -2.14 0.71 -1.42 0.65 -0.94 0.75 -0.29 0.76 P62 -1.72 0.62 -1.08 0.56 -0.65 0.65 -0.07 0.66 P63 -2.11 0.67 -1.45 0.61 -1.01 0.70 -0.40 0.71 P64 -1.82 0.64 -1.19 0.59 -0.77 0.67 -0.19 0.68  7.5 Comparison of Fragility Results In order to study the effect of low and high level (treatment) on the fragility of CFRP retrofitted piers, two sets of fragility curves are plotted in each figure. The fragility of low and high levels (treatments) associated with their damage states (i.e. slight, moderate, extensive and collapse) are depicted in Figure 7.11 to Figure 7.16. The fragility curves of all other piers are presented in Appendix F (Figure F.3). The fragility is estimated from the PSDM parameters, from the linear regression analysis and limit state capacities as shown in Table 7.5. The fragility curves of all the pier were produced using these PSDM parameters, and Eq. (7.5). The fragility curves relate the influence of the low and high-level modeling parameters of the piers. In addition, these fragility curves exhibit the most vulnerable condition of the piers under seismic loads.   7.5.1 Effect of strength concretes on the fragility curve  Figure 7.11 demonstrates the effect of low and high level strength of concrete on the fragility of CFRP retrofitted piers where the two piers considered here are P3 [ 'cf = 35 MPa, fy = 250 MPa, ρl = 2.5%, P = 20%, l/d = 7, n = 3] and P4 [ 'cf = 20 MPa, fy = 250 MPa, ρl = 2.5%,           181 P = 20%, l/d = 7, n = 3]. It can be observed from Figure 7.11 that when 'cf = 20 MPa, the probability of damage is found in the range of 100, 85-100, 40-91, and 3-35% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of 'cf = 35 MPa, the probability of damage is found in ranges of 100, 88-100, 43-90, and 3-31% for the slight, moderate, extensive and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. It is revealed that the probability of damage increases for 'cf = 20 MPa compared to 'cf = 35 MPa, at extensive and collapse limit states for PGAs in the range of 0.5g-2.0g. There is a 100% probability of slight and moderate damage for low and high level of concrete strength at all seismic hazard levels in 50 years. Variation in concrete strength (i.e. 'cf = 20 MPa, to 35 MPa) has relatively small effect on slight, moderate and extensive damage limit states. However, the probability of damage at collapse limit state for the pier with higher compressive strength of concrete is much lower compared to low concrete strength. As concrete strength increases the stiffness of the pier increases leading to lower drift level compared to the pier with lower concrete strength. Hence, the probability of damage of for high strength concrete pier was lower compared to the low strength concrete pier.   Figure 7.11 Effect of low and high-level strength of concrete on the fragility curve for the retrofitted bridge piers     182 7.5.2 Effect of yield strength of reinforcement on the fragility curve Figure 7.12 compares the effect of the yield strength of longitudinal reinforcement on the fragility curve of CFRP retrofitted piers where the two piers considered here are P5 [ 'cf = 35 MPa, fy = 400 MPa, ρl = 1%, P = 20%, l/d = 7, n = 3] and P7 [ 'cf = 35 MPa, fy = 250 MPa,     ρl = 1%, P = 20%, l/d = 7, n = 3]. It is postulated from Figure 7.12 that the probability of failure in the major damage mode for high yield strength rebar shows less probability of damage compared to the low yield strength of rebar. The variation in steel yield strength (fy = 250-400 MPa) has a considerable effect on the collapse limit state, while a relatively less effect is found at the slight, moderate, and extensive damage mode. It can be observed from Figure 7.12 that when fy = 250 MPa, the probability of damage is found in the ranges of 100, 95-100, 57-96, and 6-51% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of fy = 400 MPa, the probability of damage is found in the ranges of 100, 94-100, 57-94, and 7-46% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. It is revealed that the probability of damage increases for fy = 250 MPa piers compared to fy = 400 MPa, at extensive and collapse limit states for PGAs in the range of 0-0.5g. There is a 100% probability of slight and moderate damages for low and high levels of concrete strength at all the seismic hazard levels in 50 years. Variation of the yield strength of steel has relatively small effect on the slight and moderate damage limit states. Although fy is different for P5 and P7, both piers will have similar stiffness. However, P5 will experience yielding at a lower drift level compared to P7 due to P5’s lower yield strength. This increases the vulnerability of P5 compared to that of P7.      183  Figure 7.12 Effect of low and high yield strength of rebar on the fragility curves for the retrofitted bridge piers   7.5.3 Effect of longitudinal reinforcement ratio on the fragility curve Figure 7.13 shows the effect of longitudinal reinforcement ratio on the fragility curve of CFRP retrofitted piers where the two piers considered here are P3 [ 'cf = 35 MPa, fy = 250 MPa,         ρl = 2.5%, P = 20%, l/d = 7, n = 3] and P7 [ 'cf = 35 MPa, fy = 250 MPa, ρl = 1%, P = 20%,    l/d = 7, n = 3]. Variation of the area of longitudinal steel strongly influences the probability of damage. Reducing the longitudinal reinforcement ratio decreases the displacement ductility and governs the failure mode of the pier in tension mode. Decreasing the longitudinal steel content from 2.5% to 1% increases the probability of damage at moderate, extensive, and collapse limit state. Similar observasion was made by Zhang et al. (2016) while evaluating the performance of a bridge with more longitudinal reinforcement in concrete piers. While at the slight damage states, the reinforcement ratio does not affect the results. As longitudinal rebar increases, the stiffness of the bridge improves significantly, which in turn reduces the drift level as well as the vulnerability to various damage state of the bridge pier with higher reinforcement ratio compared to the bridge pier with lower reinforcement ratio.    184  Figure 7.13 Effect of low and high levels reinforcement ratio of rebar on the fragility curves for the retrofitted bridge piers    It can be observed from Figure 7.13 that when ρl = 1%, the probability of damage is found in the ranges of 100, 95-100, 57-96, and 6-51 for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of ρl = 2.5%, the probability of damage is found in the ranges of 100, 88-100, 43-90, and 3-31% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5 and 2% seismic hazard levels in 50 years, respectively. As discussed, the probability of damage increases when ρl = 1% compared to the case where ρl = 2.5%, at extensive and collapse limit states for PGAs in the range of 0-0.5g.   7.5.4 Effect of axial load ratio on the fragility curve It is well known that the level of applied axial load affects the lateral load and deformation capacity of the CFRP retrofitted piers considerably. Increasing the axial load decreases the lateral load and drift ratio which leads to an increase in the damage probability. Atalay and Penzien (1975), and Sheikh and Khoury (1993) reported that increasing the axial load can reduce the displacement ductility of the pier. Figure 7.14 shows the effect of axial load ratio on the fragility curve of CFRP retrofitted piers where the two piers considered here are P19   185 [ 'cf = 35 MPa, fy = 250 MPa, ρl = 2.5%, P = 20%, l/d = 4, n = 3] and P27 ['cf = 35 MPa, fy = 250 MPa, ρl = 2.5, P = 10%, l/d = 4, n = 3].   Figure 7.14 Effect of low and high levels axial load ratio on the fragility curves for the retrofitted bridge piers    It can be observed from Figure 7.14 that when P = 20%, the probability of damage is found in the ranges of 99-100, 44-100, 9-92, and 0-27% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of P = 10%, the probability of damage is found in the ranges of 82-100, 2-98, 0-62, and 0-4% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. The probability of damage increases for P = 20% compared to P = 10%, at extensive and collapse limit states for PGAs in the range of 0-0.5g because of additional compressive strain coming from higher axial load level that further increases the damage potential.   7.5.5 Effect of shear span-depth ratio on the fragility curve The effect of shear span-depth ratio on the fragility curve can be investigated by comparing the behavior of CFRP retrofitted piers having different l/d, where the two piers considered here are P3 [ 'cf = 35 MPa, fy = 250 MPa, ρl = 2.5%, P = 20%, l/d = 7, n = 3] and P19 ['cf = 35   186 MPa, fy = 250 MPa, ρl = 2.5%, P = 20%, l/d = 4, n = 3]. Figure 7.15 shows the effect of shear span-depth ratio on the fragility curve of CFRP retrofitted piers.  It can be observed from Figure 7.15 that when l/d = 4, the probability of damage was found in the ranges of 99-100, 44-100, 9-92, and 0-27% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of l/d = 7, the probability of damage is found in the ranges of 100, 88-100, 43-80, and 3-11% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. It is revealed that the probability of damage increases for l/d = 4 compared to l/d = 7, at extensive and collapse limit states for PGAs in the range of 0-0.5g. Although the pier with l/d = 4 has higher stiffness compared to the pier with l/d = 7, the pier with lower l/d will will experience yielding and other damage states at a much lower drift level and thus an increase in the shear span-depth ratio leads to an increase in the probability of damage.    Figure 7.15 Effect of low and high levels shear span-depth ratio on the fragility curves for the retrofitted bridge piers   7.5.6 Effect of strength of FRP confinement on the fragility curve Figure 7.16 shows the effect of CFRP confinement layers on the fragility of CFRP retrofitted piers where the two piers considered here are P1 [ 'cf = 35 MPa, fy = 400 MPa, ρl = 2.5%, P =   187 20%, l/d = 7, n = 3] and P33 [ 'cf = 35 MPa, fy = 400 MPa, ρl = 2.5?%, P = 20%, l/d = 7, n = 2]. The dotted and solid lines in the figure are the fragility curves of the pier with 2 and 3 layers of CFRP confinement, respectively. This figure demonstrates that how the probability of damage increases by changing the amount of CFRP confinement. When the amount of CFRP confinement is low (n = 2), the probability of damage increases with increased PGA value, while an increase in the amount of confining CFRP does not significantly reduce the probability of damage compared to that of low confinement.   Figure 7.16 Effect of low and high levels CFRP layers on the fragility curves for the retrofitted bridge piers    It can be observed from Figure 7.16 that when n = 2, the probability of damage is found in the ranges of 100, 91-100, 48-94, and 3-40% for the slight, moderate, extensive and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. While, in the case of n = 3, the probability of damage is found in the ranges of 100, 90-100, 48-93, and 4-39% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. It is revealed that the probability of damage increases for n = 2 compared to n = 3, at extensive and collapse limit states for PGAs in the range of 0-0.5g.     188 7.5.7 Median values of peak ground acceleration The median value of the intensity measure for the CFRP retrofitted are given in Table 7.9. The median values of PGA are determined as the level of PGA at which the probability of damage limit state reaches 50%. At the same level of damage probability (i.e. moderate damage probability of P1 and P2), the lower median values link to more probability of damage showing that the specific pier is more vulnerable or fragile. As depicted in Table 7.9, at slight, moderate, extensive, and collapse limit states, the median values are found in ranges of 0-0.33g, 0.02-0.38g, 0.02-0.73g, and 0.35-1.87g, respectively.  Table 7.9 Median value of PGA for the CFRP retrofitted bridge Pier No. DS1 DS2 DS3 DS4 Pier No. DS1 DS2 DS3 DS4 P1 0.00g 0.03g 0.09g 0.49g P33 0.00g 0.03g 0.08g 0.46g P2 0.01g 0.05g 0.11g 0.49g P34 0.01g 0.04g 0.09g 0.42g P3 0.00g 0.03g 0.10g 0.61g P35 0.00g 0.03g 0.08g 0.47g P4 0.01g 0.04g 0.10g 0.53g P36 0.01g 0.04g 0.11g 0.53g P5 0.00g 0.02g 0.07g 0.41g P37 0.00g 0.02g 0.06g 0.40g P6 0.01g 0.04g 0.10g 0.44g P38 0.01g 0.03g 0.09g 0.45g P7 0.00g 0.03g 0.07g 0.36g P39 0.00g 0.03g 0.07g 0.40g P8 0.01g 0.03g 0.08g 0.42g P40 0.01g 0.04g 0.09g 0.42g P9 0.01g 0.05g 0.11g 0.50g P41 0.01g 0.05g 0.12g 0.53g P10 0.02g 0.10g 0.21g 0.75g P42 0.01g 0.06g 0.15g 0.63g P11 0.01g 0.05g 0.12g 0.53g P43 0.00g 0.03g 0.09g 0.46g P12 0.03g 0.10g 0.02g 0.66g P44 0.02g 0.10g 0.20g 0.70g P13 0.00g 0.02g 0.07g 0.41g P45 0.00g 0.03g 0.08g 0.44g P14 0.01g 0.05g 0.13g 0.53g P46 0.01g 0.05g 0.12g 0.52g P15 0.01g 0.04g 0.09g 0.38g P47 0.01g 0.04g 0.09g 0.46g P16 0.01g 0.04g 0.11g 0.44g P48 0.01g 0.05g 0.11g 0.51g P17 0.03g 0.10g 0.20g 0.59g P49 0.02g 0.08g 0.17g 0.58g P18 0.05g 0.17g 0.32g 0.90g P50 0.05g 0.17g 0.32g 0.89g P19 0.02g 0.09g 0.17g 0.51g P51 0.02g 0.09g 0.17g 0.53g P20 0.05g 0.15g 0.28g 0.73g P52 0.05g 0.16g 0.28g 0.71g P21 0.01g 0.06g 0.12g 0.43g P53 0.01g 0.06g 0.12g 0.41g P22 0.03g 0.10g 0.19g 0.56g P54 0.03g 0.09g 0.19g 0.53g P23 0.02g 0.06g 0.12g 0.41g P55 0.01g 0.05g 0.11g 0.35g P24 0.03g 0.09g 0.17g 0.47g P56 0.03g 0.09g 0.16g 0.45g P25 0.07g 0.21g 0.40g 1.10g P57 0.06g 0.20g 0.40g 1.15g P26 0.14g 0.38g 0.72g 1.87g P58 0.33g 0.38g 0.73g 1.87g P27 0.06g 0.17g 0.32g 0.84g P59 0.05g 0.17g 0.31g 0.87g P28 0.10g 0.29g 0.53g 1.35g P60 0.12g 0.33g 0.58g 1.36g P29 0.03g 0.11g 0.21g 0.59g P61 0.03g 0.09g 0.19g 0.60g P30 0.07g 0.21g 0.37g 0.91g P62 0.06g 0.19g 0.34g 0.89g P31 0.03g 0.10g 0.19g 0.51g P63 0.03g 0.10g 0.18g 0.50g P32 0.01g 0.18g 0.31g 0.73g P64 0.05g 0.15g 0.28g 0.73g   189 Table 7.10 P-Values of median of PGA for the different damage states of CFRP retrofitted piers Sr. No. Code Factors/Parameters DS1 DS2 DS3 DS4 1 A Compressive strength of concrete, 'cf   0.005 0.005 0.000 0.000 2 B Yield strength of steel, fy 0.290 0.290 0.148 0.073 3 C Longitudinal steel reinforcement ratio, ρl 0.009 0.009 0.000 0.000 4 D Axial load, P 0.004 0.004 0.000 0.000 5 E Shear span-depth ratio, l/d 0.000 0.000 0.000 0.000 6 F CFRP layer, n 0.560 0.560 0.952 0.882 Note: Italics red boldface letter shows a significant factor p-value ≤ 5% and known as significantly affecting the PSDMs regression coefficient responses which are labelled the “most important” factors.  The ANOVA results with P-values of the median of PGA are presented in Table 7.10. From the analysis results, it can be observed that 'cf  ρl, P, and l/d ratio are the most significant factors affecting the median values of PGA. Because these factors could influence the initial stiffness, the flexural and shear strengths, as well as the deformation capacity of the pier (Li 1994). fy and n show the insignificant contribution to the median value of the PGA.  7.6 Seismic Demand Hazard of FRP Retrofitted Bridge Piers In order to study the performance-based earthquake engineering (PBEE) methodology for deficient CFRP retrofitted bridge piers, it is crucial to conduct the probabilistic seismic demand analysis in terms of exceeding damage probability. The fragility hazard analysis results are presented in Figure 7.17 and Figure 7.18. The fragility hazard results of other piers are presented in Appendix F (Figure F.4).    190  Figure 7.17 Performance of damage of low-level factors  Figure 7.18 Performance of damage high-level factor   7.7 Summary Fibre reinforced polymer (FRP) composites have emerged as an effective external confinement technique compared to steel jacketing, and concrete jacketing for improving the seismic performance of deficient bridge piers during severe seismic events. This chapter presented the seismic vulnerability assessment of deficient CFRP retrofitted RC bridge piers based on analytical fragility curves. The deficient bridge piers do not conform to the current seismic design standard. A particular focus was on different parameters such as the strength of   191 concrete, yield strength and amount of longitudinal reinforcement, the level of applied axial load, shear span-depth ratio and CFRP confinement layers using a full factorial design. Total 64 CFRP retrofitted pier models were generated by considering low and high levels for each parameter. Probabilistic seismic demand models were generated using the response achieved from the incremental dynamic analyses in terms of displacement ductility. The amount of longitudinal reinforcement, the level of applied axial load and shear span-depth ratio were found to be the most significant parameters resulting in a high probability of damage for the CFRP retrofitted piers.                          192 Chapter 8: Summary, Conclusions, and Future Works  8.1 General Fibre reinforced polymer (FRP) composites are promising retrofitting material for improving the seismic performance of existing reinforced concrete (RC) bridge piers. This thesis presented a comprehensive summary of the existing application of FRP in order to improve the seismic resistant capacity of non-seismically designed RC circular bridge piers. This study also presented an up-to-date information on the seismic repair and retrofit of both standards and sub-standard RC circular bridge piers in order to simplify the progress of seismic repair and retrofitting systems using FRP composites. The thesis also presented the current design provision for the lateral confinement of RC circular bridge pier using FRP to upgrade their seismic resistance based on different codes and design guidelines. A state-of-the-art criticism and review were also offered with highlighting the axial compressive response and the constitutive modeling of FRP-confined concrete. This study mainly focused on the seismic performance evaluation of non-seismically designed RC circular bridge piers retrofitted using advanced composite materials.   8.2 Core Contributions The findings of this research work will help practicing engineers use the fibre-reinforced polymer as an external reinforcement for improving the seismic resistant capacity of the existing RC bridge piers, which were designed prior to 1970 with no consideration of seismic design provision. The core contributions of this thesis are as follows:  Identified the most significant parameters and quantitatively evaluate their interactions such as the amount of longitudinal reinforcement, shear span-depth ratio, and the level of axial load affecting the seismic performance of damaged RC bridge piers retrofitted with FRP.  Determined the seismic collapse damage states for FRP retrofitted bridge piers.  Determined the seismic vulnerability of deficient bridge pier built in the pre-1970 retrofitted with FRP in terms of probability of damage at each limit state.     193 8.3 Conclusions The following conclusion can be drawn based on the current research program.  8.3.1 Repair and retrofitting of earthquake damaged RC circular bridge piers, and constitutive models of FRP-confined concrete From the last two decades, many experimental and numerical studies are conducted on repair and retrofitting of earthquake-damaged RC circular bridge piers. The research presented in Chapter 2, provides a better understanding concerning the repair and retrofitting of seismically damaged RC bridge piers, and constitutive models of FRP confined concrete. Based on the comprehensive literature review, the following conclusion can be derived.  For the seismically damaged RC circular piers, repairing and retrofitting technique including concrete, steel plate, FRP jacketing, and SMA active confinement techniques demonstrated the purpose of restoring the strength and ductility of piers.   The experimental results exhibited that initial stiffness changes for most of the jacketing methods.   The shear failure can be prevented and dramatic improvement is found in the ultimate lateral force and ductility of piers using FRP jacketing.   The experimental results reported that the combination of epoxy injection and damaged concrete following FRP jacketing is an effective repair and retrofitting technique to restore the strength and ductility of damaged piers.  Based on the comprehensive literature review on FRP-confined concrete, it was found that most of the existing models adopted Richart et al. (1928) model which was derived using active hydrostatic pressure to evaluate the compressive strength of FCC concrete.   It can be observed that actively (or steel) confined concrete models are not able to capture the response of FCC, because of the fact that the FRP confinement exerts a continuously increasing pressure as opposed to steel at the yield state.  Based on the reviewed models, it can be revealed that for the prediction of ultimate axial stress and corresponding strain, the design-oriented models (DOMs) perform better than the analysis-oriented models (AOMs).    194  In general, the DOM's performance increases with an increase in the number of the database used in the model development.   The explicitly derived dilation responses of AOMs perform better compared to the implicitly adopted dilation responses.  For the prediction of ultimate strength and strain enhancement ratios, a model of Lam and Teng (2003a), and model of Tamuzs et al. (2006), respectively are the most accurate models.  The DOMs developed with less database are found to be less accurate, such as Fardis and Khalili (1982), Miyauchi et al. (1998), Toutanji (1999) models, and the AMOs models developed by Spoelstra and Monti (1999), Fam and Rizkalla (2001) and Chun and Park (2002) models and derived based on implicitly dilation responses found less accurate models.   The models that use the hoop rapture strain (εh,rup) are more accurate compared to  once that directly use the ultimate tensile strain of fibres (εf). The majority of the well-performing models employs rupture strain efficiency factor (kε) in their equations for the prediction of the ultimate strain enhancement ratios.   Based on the previous research, the stress-strain behavior of FRP-confined concrete was conducted on small-scale cylinder. However, the scale effect shows an important contribution to the FRP retrofit design of full-size piers; thus, more research needs to be conducted considering the scale effect.  8.3.2 Finite element modeling of non-seismically designed circular RC bridge piers retrofitted with FRP The finite element modeling of non-seismically designed circular RC bridge pier is presented in Chapter 3. The fibre element approach using constitutive models of concrete confined with advanced composite and lateral ties provided a good agreement with the experimental results of Kawashima et al. (2000). From the numerical investigation, the hysteretic results showed that the numerical model of retrofitting piers with advanced composites could predict the seismic behaviour in terms of strength and failure mode accurately.     195 8.3.3 Pushover response of non-seismically designed circular RC bridge piers retrofitted with FRP using fractional factorial design – A parametric study In Chapter 4, the variation of different limit states i.e., the first yielding of longitudinal rebar, first crushing of core concrete, first buckling and fracture of longitudinal reinforcement of CFRP-confined concrete piers with different factors (e.g. 'cf , fy, ρl, s, P, l/d and n) were investigated using fractional factorial design method. Moreover, the effects of individual parameters and their interactions on the limit states of the CFRP jacketed bridge piers were estimated. In order to determine the flexural limit states in terms of base shear and drift, nonlinear static pushover analyses were conducted with 81 numerical models. Because of the simplicity of chosen model, the static inelastic analysis is less time consuming (less than 2 minutes), less expensive and equally reliable.   Based on the numerical analysis results of CFRP-confined concrete bridge piers and using the design of experiment principles the following observations are made.  Height-to-depth ratio of the pier is the most important factor which affects the seismic performance and limits states criteria of the CFRP-confined bridge pier.  Although the tie spacing does not show a significant effect on the lateral load resistance of a CFRP retrofitted pier, it shows some effect on the drift at yield, crushing and bar buckling. Similar conclusions were observed from the experimental and numerical investigations conducted by Gallardo-Zafra and Kawashima (2009).   The amount of longitudinal steel reinforcement shows a significant effect on the yield and crushing drift limit states and base shear of the CFRP-confined bridge piers.  The yield strength of longitudinal steel and interactions among longitudinal steel, compressive strength, axial load and the shear span-depth ratio significantly affect the drift and base shear at yielding and crushing of the CFRP-confined bridge piers. The interactions among the shear span-depth ratios, CFRP confinement, and axial load show significant contributions to the crushing drift and base shear of the CFRP-confined bridge piers.  The compressive strength of concrete does not affect the yielding and crushing drift significantly; however, it shows some contribution to the yielding and crushing base shear to the seismic performance of CFRP-confined bridge piers.   196  Shear span-depth ratio and axial load level, and the interactions between yield strength and concrete compressive strength, axial load and a number of CFRP layer affect the buckling and fracture of longitudinal steel reinforcements of the CFRP-confined deficient bridge piers.   8.3.4 Sesicmic behavior of non-seismically designed circular RC bridge piers retrofitted with FRP – A parametric study Chapter 5 reported the behavior of non-seismically designed RC circular bridge piers retrofitted with different confinement ratios of CFRP/GFRP jacket under nonlinear static pushover analyses (NSPA), reverse cyclic analyses, and nonlinear time history analyses (NTHA). The nonlinear response of retrofitted circular bridge piers under seismic load was studied using fibre element model. The fibre element approach using constitutive models of concrete confined with FRP and lateral ties could simulate the behavior of FRP retrofitted piers where the numerical results were in good agreement with the experimental results. From the numerical investigation of NSPA, reverse cyclic and dynamic time history analyses, the following concluding remarks can be drawn.  In the case of NSPA, the base shear at spalling of concrete for 0.44% confinement ratio of CFRP and GFRP jacketed piers were 124.27 kN and 116.72 kN which were 18.6% and 13.9% higher than those of the as-built pier, respectively. In the case of GFRP retrofitted piers, the crushing of core concrete found at the displacement and base shear force was in the range of 142.4-150.4 mm, and 56.35-67.25 kN, respectively for the confinement ratio of 0.11-0.33.  In the case of reverse cyclic analysis, the displacement ductility ratio of the as-built pier was 2.7, and the retrofitted specimen using CFRP and GFRP with a confinement level of 0.44 had a ductility ratio of 15.5 and 9.5, respectively.   In the case of dynamic analysis, for CFRP and GFRP jackets with similar confinement ratios of 0.11, 0.22, 0.33 and 0.44, the base shear value increased by 6, 11, 16, and 21%, and 2, 5, 7, and 10%, respectively compared to the as-built pier. The CFRP jackets increased the average base shear of 5, 6, 8, and 9% compared to GFRP confinement with a similar confinement ratio of 0.11, 0.22, 0.33, and 0.44% respectively.    197  For CFRP and GFRP jacket with similar confinement ratios of 0.11, 0.22, 0.33, and 0.44, the residual displacement value decreased by 11, 21, 30, and 41%, and 4, 11, 20, and 29%, respectively compared to the as-built pier. Overall, the CFRP jackets reduced the average residual displacement by 7, 11, 12, and 16% compared to the GFRP confinement with similar confinement ratios of 0.11, 0.22, 0.33, and 0.44% respectively.  For CFRP and GFRP jacket with similar confinement ratios of 0.11, 0.22, 0.33, and 0.44, the effective stiffness value increased by 20, 36, 57, and 69%, and 10, 21, 38, and 48%, respectively compared to the as-built pier. The CFRP jackets increased the average effective stiffness by 8, 11, 11.5, and 12% compared to GFRP confinement with similar confinement ratios of 0.11, 0.22, 0.33, and 0.44% respectively.  8.3.5 Seismic behavior of collapse assessment of non-seismically designed circular RC bridge piers retrofitted with FRP Chapter 6 presented the nonlinear static pushover analyses (NSPA) and collapse fragility curves of non-seismically designed RC circular bridge piers located in Vancouver, British Columbia, Canada with a different combination of parameters. Probabilistic seismic demand models were produced using the results obtained from the incremental dynamic analyses (IDA). Considering collapse drift as demand parameter, fragility curves were generated with different parameters of non-seismically designed RC circular bridge piers. It was observed that the amount of reinforcement, shear span-depth ratio, and level of the axial load could significantly affect the collapse fragility curve of the retrofitted bridge piers. Based on the NSP and results obtained from IDA curves, and collapse fragility curve, the following conclusions can be drawn.  It can be observed from the NSPA that higher values of parameters could increase the capacity of the piers.  It is observed that 35MPa concrete increased the pier yield and crushing base shear capacity by 14 and 8.3%, respectively; while the buckling and fracture base shear capacities were decreased by 4.4 and 4.3% compared to 20MPa concrete.   198  For piers with 400 MPa yield strength of longitudinal reinforcements, yielding, crushing, buckling and fracture base shear and displacement capacities increased by 24.3, 27.3, 30.1 and 4.5%, and 28.6, 15.4, 27.3, 6.8, and 4.7%, respectively, compared to those of the pier with reinforcements having 250 MPa yield strength.  For piers with longitudinal reinforcement ratios of 2.5%, the yielding, crushing, buckling and fracture base shear capacities improved by 44.9, 48.7, 55.8, and 56.1% compared to those for 1% longitudinal reinforcement ratios.   For piers with longitudinal reinforcement ratios of 2.5%, the yielding, buckling and fracture displacements increased by 14.3, 9.5, and 9.3%, respectively, but the crushing displacement decreased by 14.3% compared to those for 1% longitudinal reinforcement ratios.   It can be observed that at 20% axial load, the yielding, crushing, buckling, and fracture base shear increased by 41.5, 14.3, 7.4, and 7.2% compared to those for 10% axial loads.   The yielding displacement increased by 14.3% for 20% axial load compared to 10% axial load, and crushing, buckling and fracture displacements were almost the same for 20 and 10% axial loads.  For the shear span-depth ratio of 7, yielding, crushing, buckling, and fracture base shears decreased by 52.6, 44.3, 100.6, and 101.7%, respectively compared to those for 4 shear span-depth ratio.   The shear span-depth ratio of 7 resulted in an increase in yielding, crushing, buckling and fracture displacements by 57.1, 64.3, 67.4 and 65.9%, respectively compared to those of 4 shear span-depth ratios.  The dynamic pushover points closely coincided with the static pushover curves before the first yielding of the longitudinal reinforcement.  The dynamic pushover curved demonstrated higher base shear value compared to f the static pushover curves between first yielding and crushing of core concrete.  It can be observed that 35MPa concrete pier is more fragile compared to 20MPa concrete piers. For PGA values in the range of 0.5g-2.0g, the relative probability of collapse of 35MPa concrete pier is higher (in the range of 74.8-3.2% compared to 20MPa concrete pier).   199  At PGA values from 0.5g to 2.0g, for 400 MPa yield strength, a relatively lower probability of collapse (i.e. in the range of 79.8-4.3%) was observed compared to 250 MPa yield strength.  At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in the range of 83.5-3.2%) for the amount of longitudinal steel of 2.5% is compared to 1% longitudinal steel.   At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in the range of 74.8-2.7%) for the axial load of 0.20 compared to 0.10 axial load. The higher axial load reduced the deformability.  At PGAs from 0.5g-2.0g, a relatively lower probability of collapse was observed (i.e. in the range of 64.8-2.4%) for the shear span-depth ratio of 7 compared to the shear span-depth ratio of 4.  At PGAs from 0.5g-2.0g, a relatively higher probability of collapse was observed (i.e. in the range of 77.7-3.4%) for 2 layers of FRP confinement compared to the 3 layers of confinement.  8.3.6 Fragility assessment of non-seismically designed circular RC bridge piers retrofitted with FRP through full factorial design Chapter 7 presented the seismic vulnerability assessment of non-seismically designed CFRP retrofitted RC circular bridge piers based on analytical fragility curves. A particular focus was given to parameters such as the strength of concrete, yield strength and amount of longitudinal reinforcement, the level of applied axial load, shear span-depth ratio, and CFRP confinement layers using full factorial design. Total 64 CFRP retrofitted pier models were generated by considering low and high levels for all the parameters. Probabilistic seismic demand models were generated using the response achieved from the incremental dynamic analysis results in terms of displacement ductility as a demand parameter. Based on the study presented in this chapter, following conclusions can be drawn.  When 'cf = 20 MPa, the probability of damage was found to be in the range of 100, 85-100, 40-91, and 3-35% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case of 'cf = 35 MPa, the probability of damage was found to be in the range of 100, 88-100, 43-90,   200 and 3-31% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5 and 2% seismic hazard levels in 50 years, respectively.  when fy = 250 MPa, the probability of damage was found to be in the range of 100, 95-100, 57-96, and 6-51% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case fy = 400 MPa, the probability of damage was found to be in the range of 100, 94-100, 57-94, and 7-46% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively.  When ρl = 1%, the probability of damage was found to be in the range of 100, 95-100, 57-96, and 6-51% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case ρl = 2.5%, the probability of damage was found to be in the range of 100, 88-100, 43-90, and 3-31% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5 and 2% seismic hazard levels in 50 years, respectively.   When P = 20%, the probability of damage was found to be in the range of 99-100, 44-100, 9-92, and 0-27% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case P = 10%, the probability of damage was found to be in the range of 82-100, 2-98, and 0-62 and 0-4% for the slight, moderate, extensive, and collapse limit state at 40, 10, 5 and 2% seismic hazard levels in 50 years, respectively.   When l/d = 4, the probability of damage was found to be in the range of 99-100, 44-100, 9-92, and 0-27% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case, l/d = 7, the probability of damage was found to be the range of 100, 88-100, and 43-80 and 3-11% for the slight, moderate, extensive, and collapse limit state at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively.  When n = 2, the probability of damage was found to be in the range of 100, 91-100, 48-94, and 3-40% for the slight, moderate, extensive, and collapse limit states at 40, 10, 5, and 2% seismic hazard levels in 50 years, respectively. In the case n = 3, the probability of damage was found to be in the range of 100, 90-100, and 48-93 and 4-  201 39% for the slight, moderate, extensive, and collapse limit state at 40, 10, 5 and 2% seismic hazard levels in 50 years, respectively.  The amount of longitudinal reinforcement, the level of applied axial load and shear span-depth ratio are most significant parameters which result in a high probability of damage for the CFRP retrofitted piers.  8.4 Recommendation for Future Works  Based on the numerical study conducted in the thesis, following recommendations can be made for the future research.  From a large number of experimental investigations on the behavior of FRP-confined concrete, it was observed that most of them are based on the results obtained from scaled cylinder tests. A research on large-scale FRP-confined concrete is still limited and hence, further research needs to be performed.  Chapter 5 considers seven factors with a limited range of data. For example, the strength of concrete of 20-35MPa, yield strength of longitudinal reinforcement of 250-400 MPa, the amount of longitudinal steel of 1-2.5%, the level of axial load of 10-20%, the shear span-depth ratio of 10-20%, and FRP confinement layers of 2-3. Thus, further studies are required with parameters having wider ranges of values. For example, in order to better understand the effect of transverse reinforcement spacing on the lateral load capacity of CFRP retrofitted bridge piers very low to very large values should be considered. Shear span to depth ratio should be considered below 3 to understand the performance of shear dominated bridge piers.   The incremental dynamic analysis was conducted by using far-filed earthquakes having epicenter distances greater than 10 km. Therefore, a future research can be conducted considering the near-fault record.  In this research, single circular pier bent retrofitted with FRP was considered.  Future research should be conducted by considering multi-pier bridge bent retrofitted with FRP.  In the present research, the lateral reinforcement spacing and diameter of the pier were considered to be 250 and 400 mm respectively. Therefore, different lateral reinforcement spacings and diameters of pier should be considered in the future.   202  The seismic collapse analyses were carried out and fragility curves were developed by considering CFRP jacket.  Future research can be conducted by considering different properties of CFRP or different FRP composites such as GFRP, BFRP, and AFRP jackets.  In the present research, the CFRP jacket was applied at a length of 1000 mm from the base of the pier. 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National Cooperative Highway Research Program, Transportation Research Board, Washington, D.C., USA.                             233 Appendices Appendix A  Performance of Bridge Piers in the Past Earthquakes A.1 The San Fernando Earthquake, USA, 1971 The 1971 San Fernando earthquake with a moment magnitude of 6.5 or 6.7 (as estimated by many independent institutions) was occurred in the early morning of February 9 in the foothills of the San Gabriel Mountains in Southern California. This destructive earthquake continued about 60 seconds, which resulted in the death of 65 lives, more than 2,000 injuries, and the collapse of several bridges. The destructive earthquake caused property damage estimated at the US $505 million (Jennings 1971). The main reasons for bridge failures were the excessive damage sustained by the bridges of RC piers. Figure A.1 shows an example of bridge pier damaged on Interstates 5 and 14, as seen in the 1971 San Fernando earthquake. Research studies reported that lack of concrete confinement due to the use of inadequate transverse reinforcement at the plastic hinge region of the piers were few of the important causes for the poor flexural ductility and/or insufficient shear capacity found in many of the collapsed bridge piers.   Figure A.1 Damage of RC pier on Interstates 5 and 14 during the San Fernando earthquake, 1971 (USGS and Leyendecker 1971)  A.2 The Loma Prieta Earthquake, USA, 1989 The 1989 Loma Prieta earthquake occurred in Northern California on October 17 with a moment magnitude of 6.9 at 5:04 p.m. local time. This earthquake was one of the most   234 notorious earthquake resulted in an estimated property loss of US $6 billion. This destructive major earthquake caused the death of 63 lives, 3,757 injuries, 12000 damaged homes, 40 collapsed buildings, and 2 major bridges. Among these bridges, the well-known bridge  Cypress Street Viaduct of Interstate 880 in West Oakland collapsed during the Loma Prieta earthquake and claimed 43 lives (Priestley et al. 1996). Figure A.2 shows the example of the RC bridge piers collapsed of the Cypress Viaduct on Interstate 880 as seen in the 1989 Loma Prieta earthquakes. The Viaduct was constructed in 1950 with inadequate lateral reinforcement, which was one of the main reason for RC piers failure. As shown in Figure A.2, this collapse was mainly caused by pier joint shear failures, and the result of the lack of a strong pier through the joint, which were preventing the transfer of force from piers to the cross beams.   Figure A.2 Failure of RC piers and collapsed upper deck on the Cypress viaduct of Interstate of 880 (USGS and Wilshite 1989) A.3 The Northridge Earthquake, USA, 1994 The 1994 Northridge earthquake occurred on January 17, at 4:30:55 a.m. local time in the north-central San Fernando Valley region of Los Angeles, California. Since the 1933 long Beach earthquake, the 1994 Northridge earthquake has generated the strongest ground motion ever instrumentally recorded with the moment magnitude of 6.7 in an urban region of North America. The damage was widespread, parking structures, office buildings, and sections of major freeways collapsed, and numerous apartment buildings experienced irrep