seismic assessment and retrofit of existing …

POLITECNICO DI MILANO Dipartimento di Ingegneria Strutturale Dottorato di Ricerca in Ingegneria Sismica, Geotecnica e dell’Interazione Ambiente-Struttura

SEISMIC ASSESSMENT AND RETROFIT OF EXISTING REINFORCED CONCRETE BRIDGES

Georgios Tsionis

Supervisor Prof. Giandomenico Toniolo

June 2004

POLITECNICO DI MILANO Dipartimento di Ingegneria Strutturale Dottorato di Ricerca in Ingegneria Sismica, Geotecnica e dell’Interazione Ambiente-Struttura


PhD candidate: Georgios Tsionis

Tutor / Supervisor: Prof. Giandomenico Toniolo

PhD course coordinator: Prof. Alberto Castellani

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TABLE OF CONTENTS

List of tables.......................................................................................................................vii

List of figures ......................................................................................................................ix

Aknowledgements............................................................................................................xvii

1. INTRODUCTION .......................................................................................................1

1.1. General – Motivation for the research .................................................................1

1.2. Objectives of the research....................................................................................3

1.3. Outline of the thesis .............................................................................................4

2. OPEN ISSUES IN SEISMIC DESIGN AND ASSESSMENT OF BRIDGES - A

LITERATURE REVIEW ....................................................................................................7

2.1. Asynchronous excitation......................................................................................7

2.2. Displacement-based design and assessment ........................................................9

2.3. Soil-structure interaction....................................................................................11

2.4. Bridges with isolation and dissipation devices ..................................................12

2.5. Damage assessment ...........................................................................................15

2.6. Seismic retrofit of reinforced concrete columns ................................................16

2.6.1. Retrofit by jacketing ..................................................................................17

Concrete jackets .....................................................................................................17

Steel jackets ...........................................................................................................18

FRP jackets ............................................................................................................19

2.6.2. Retrofit for enhancement of lapped splices ...............................................21

2.7. Analysis and modelling......................................................................................23

3. EXPERIMENTAL ASSESSMENT OF HOLLOW BRIDGE PIERS WITH

SEISMIC DEFICIENCIES................................................................................................27

3.1. Introduction........................................................................................................27

3.2. Bibliographic research .......................................................................................29

3.2.1. Experimental assessment of piers with seismic design..............................29

3.2.2. Experimental assessment of piers without seismic design ........................32

3.3. Design of the test models ...................................................................................33

3.3.1. Scaling of the specimens............................................................................33

3.3.2. Geometry of the specimens........................................................................34

3.3.3. Test set-up and instrumentation .................................................................38

3.4. Cyclic test on a model of a short bridge pier .....................................................40


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3.4.1. Experimental results...................................................................................40

Force-displacement diagram and observed damage ..............................................40

On the definition of yield displacement.................................................................42

Flexural and shear deformation .............................................................................46

Equivalent plastic hinge length..............................................................................47

Distribution of curvature........................................................................................50

Damage assessment ...............................................................................................51

3.4.2. Comparison to empirical predictions .........................................................55

3.4.3. Comparison to a squat pier designed according to EC8 ............................58

General ...................................................................................................................58

Equivalent damping ...............................................................................................59


3.5. Cyclic test on a model of a tall bridge pier ........................................................63

3.5.1. Experimental results...................................................................................63

Force-displacement diagram and observed damage ..............................................63

Flexural and shear deformation .............................................................................67

Distribution of curvature........................................................................................67

Equivalent plastic hinge length..............................................................................69


3.5.2. Comparison to empirical predictions .........................................................71

3.6. Performance of hollow cross-section bridge piers.............................................72

3.6.1. Effect of mechanical and geometrical parameters .....................................72

3.6.2. Estimation of deformation limits ...............................................................75

3.7. Concluding remarks ...........................................................................................77

4. SEISMIC ASSESSMENT OF AN EXISTING HIGHWAY BRIDGE ....................83

4.1. Introduction........................................................................................................83

4.2. The pseudodynamic testing method...................................................................85

4.2.1. The pseudodynamic testing method...........................................................85

4.2.2. The a-Operator Splitting scheme...............................................................86

4.2.3. The substructuring technique.....................................................................88

4.2.4. Substructuring in the case of asynchronous motion ..................................88

4.2.5. The continuous pseudodynamic testing with non-linear substructuring....89

4.2.6. Implementation for the Talübergang Warth Bridge tests ..........................92

4.3. Pre-test numerical simulation ............................................................................94

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4.3.1. Numerical models for the substructured piers ...........................................94

4.3.2. Numerical model of the bridge structure ...................................................96

Description of the model........................................................................................96

Damping matrix .....................................................................................................98

Modal analysis .......................................................................................................99

4.3.3. Input motion.............................................................................................101

4.3.4. Numerical simulation of the pseudodynamic tests ..................................101

4.4. Pseudodynamic testing of the bridge model ....................................................105

4.4.1. Testing programme ..................................................................................105

4.4.2. Low-level earthquake test ........................................................................106

4.4.3. Nominal earthquake test ..........................................................................108

4.4.4. High-level earthquake test .......................................................................111

4.4.5. Final collapse test.....................................................................................115

4.5. Seismic assessment of the bridge.....................................................................117

4.5.1. Deformation and curvature distribution in the physical piers..................117

4.5.2. Damage assessment .................................................................................119

4.5.3. Overall damage index ..............................................................................122

4.5.4. Vulnerability functions ............................................................................124

4.5.5. Effect of cycling.......................................................................................126

4.5.6. Irregularity issues.....................................................................................127

4.6. Application of simplified assessment methods................................................131

4.6.1. General .....................................................................................................131

4.6.2. HAZUS method .......................................................................................132

4.6.3. The substitute structure methods .............................................................135

4.6.4. Application to the Talübergang Warth Bridge tests ................................138

HAZUS ................................................................................................................138

Capacity Spectrum method ..................................................................................140

N2 method............................................................................................................145

4.7. Concluding remarks .........................................................................................150

5. NUMERICAL MODELLING OF AS-BUILT AND RETROFITTED BRIDGE

PIERS...............................................................................................................................153

5.1. Introduction......................................................................................................153

5.2. Fibre/Timoshenko Beam modelling ................................................................154

5.2.1. The Fibre/Timoshenko Beam element in Cast3m ...................................154


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5.2.2. Constitutive laws......................................................................................155

Concrete ...............................................................................................................155

Steel......................................................................................................................158

5.2.3. Alternative configurations for the cross-section and the beam element ..160

5.2.4. Validation of the numerical models.........................................................164

Piers with flexure-dominated behaviour ..............................................................164

Piers with combined flexural and shear behaviour ..............................................167

Piers with tension shift.........................................................................................170

Numerical models for the Talübergang Warth Bridge PSD tests ........................174

5.3. FEM modelling ................................................................................................178

5.3.1. Constitutive laws......................................................................................179

Concrete ...............................................................................................................179

Steel-to-concrete interface ...................................................................................182

5.3.2. Validation of the numerical model ..........................................................184

Piers with tension shift.........................................................................................184

Piers with lapped splices......................................................................................189

5.4. Numerical modelling of piers with hollow cross-section and FRP jackets .....193

5.4.1. Experimental results.................................................................................193

5.4.2. FEM modelling of the confinement effect...............................................194

5.4.3. Global behaviour of retrofitted pier .........................................................199

5.5. Final remarks on the assessment of modelling tools .......................................203

6. SEISMIC RETROFIT OF EXISTING HOLLOW BRIDGE PIERS......................205

6.1. Introduction......................................................................................................205

6.2. Seismic retrofit of reinforced concrete bridge piers with hollow cross-section

206

6.2.1. Retrofit with steel jackets.........................................................................206

6.2.2. Retrofit with FRP jackets.........................................................................208

6.2.3. Performance of retrofitted bridge piers....................................................211

6.3. Design of retrofit of bridge piers with FRP .....................................................214

6.3.1. Global retrofit procedure..........................................................................214

6.3.2. Relocation of critical cross-section..........................................................216

Piers with curtailment of vertical reinforcement .................................................216

Piers with lapped splices......................................................................................216

6.3.3. Anchorage ................................................................................................217

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Overlaying............................................................................................................218

Mechanical anchorage .........................................................................................219

U-anchor ..............................................................................................................221

6.3.4. Retrofit for flexural strength enhancement ..............................................223

6.3.5. Retrofit for shear strength enhancement ..................................................225

6.3.6. Retrofit for confinement ..........................................................................231

General .................................................................................................................231

FRP-confined concrete.........................................................................................231

Design based on ultimate curvature.....................................................................237

Design based on upgrade index ...........................................................................241

Detailing...............................................................................................................243

6.3.7. Retrofit for enhancement of lapped splices .............................................244

6.4. Design of FRP jackets for piers with rectangular hollow cross-section ..........248

6.4.1. General .....................................................................................................248

6.4.2. Numerical analysis - effect on concrete properties..................................248

Description of the numerical model.....................................................................248

Effect of confinement within the cross-section ...................................................251

Effect of confinement on the concrete properties ................................................253

6.4.3. Numerical analysis - effect on cross-section ductility .............................259

Description of the numerical model.....................................................................259

Curvature ductility capacity.................................................................................260

Effectiveness index ..............................................................................................268

Enhancement of moment capacity .......................................................................271

Cyclic behaviour and energy-dissipation capacity ..............................................272

6.4.4. Design equations and recommendations..................................................272

Curvature ductility ...............................................................................................272

Effectiveness index ..............................................................................................275

Alternative definition of curvature ductility ........................................................276

Recommendations................................................................................................277

6.5. Concluding remarks .........................................................................................279

7. CONCLUSIONS AND FUTURE RESEARCH .....................................................283

7.1. Summary and conclusions ...............................................................................283

7.1.1. Performance of existing bridge piers with hollow cross-section .............283

7.1.2. Performance of existing bridge structures ...............................................284


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7.1.3. Assessment of numerical tools for existing bridge piers .........................286

7.1.4. Retrofit of bridge piers with hollow cross-section using FRP strips .......287

7.2. Suggestions for future research........................................................................288

REFERENCES ................................................................................................................291

APPENDIX A – EXPERIMENTAL DATA FOR BRIDGE PIERS...............................309

APPENDIX B – CONSTRUCTION DRAWINGS.........................................................321

APPENDIX C – PHOTOGRAPHIC DOCUMENTATION ...........................................329

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LIST OF TABLES

Table 3.1. Similitude relationship between the full-scale prototype (P) and the constructed

model (M) .........................................................................................................34

Table 3.2. Material properties of the specimens (average values).....................................36

Table 3.3. Mechanical properties of the specimens and seismic code requirements.........37

Table 3.4. Experimental and empirical values of plastic hinge length for the short pier ..49

Table 3.5. Park & Ang Damage Index [Park & Ang, 1985]..............................................52

Table 3.6. Bridge damage and performance assessment [Hose et al., 2000].....................53

Table 3.7. Damage assessment of the short pier ................................................................55

Table 3.8. Experimental and empirical displacement for the short pier ............................58

Table 3.9. Comparison of the two piers (values at ultimate displacement).......................62

Table 3.10. Experimental and empirical values of plastic hinge length for the tall pier ...70

Table 3.11. Damage assessment of the tall pier.................................................................70

Table 3.12. Experimental and empirical displacement for the tall pier .............................70

Table 3.13. Drift capacity of piers with hollow cross-section ...........................................75

Table 4.1. Longitudinal reinforcement steel ratio and characteristic values of

displacement for the scaled bridge piers ...........................................................95

Table 4.2. Eigenfrequencies of Warth Bridge .................................................................100

Table 4.3. Damage of the bridge piers .............................................................................121

Table 4.4. Maximum drift and ductility demand for the piers.........................................121

Table 4.5. Dissipated energy and Damage Index ............................................................121

Table 4.6. Overall Park and Ang Damage Index .............................................................124

Table 4.7. Displacement ductility and drift capacities for the cyclic and PSD tests .......129

Table 4.9. Damage ratios for highway bridges [FEMA, 1999] .......................................134

Table 4.10. Discrete values of restoration functions for highway bridges [FEMA, 1999]

.........................................................................................................................134

Table 4.11. Parameters for estimation of damage probability .........................................139

Table 4.12. Assessment of the Talübergang Warth Bridge according to HAZUS ..........140

Table 4.13. Equivalent damping (%) ...............................................................................141

Table 4.14. Displacement of control point (m) for mean ADRS.....................................144

Table 4.15. Displacement of control point (m) for EC8 ADRS and triangular distribution

of lateral forces ...............................................................................................144

Table 4.16. Characteristic values of the equivalent bilinear structures ...........................144


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Table 5.1. Material properties used in the numerical models of the piers .......................162

Table 5.2. Characteristics of different models .................................................................162

Table 5.3. Longitudinal reinforcement steel ratio for the scaled bridge piers .................175

Table 5.4. Values of dissipated energy (kNm) for the bridge piers .................................176

Table 5.5. Characteristic values of force and displacement for the bridge piers .............178

Table 5.6. Material properties for the tall pier A40 .........................................................188

Table 5.7. Material properties for the short pier A70 ......................................................191

Table 5.8. Material properties for concrete and FRP.......................................................197

Table 5.9. Concrete properties for different zones of the cross-section ..........................201

Table 6.1. Bridge pier test database .................................................................................213

Table 6.2. FRP material safety factors f? [fib, 2001]......................................................227

Table 6.3. Parameters k, α , β , γ and η from regression analysis [Monti et al., 1998] 242

Table 6.4. Material properties..........................................................................................250

Table A.1. Seismic-deficient piers with solid cross-section: geometrical and mechanical

properties and deformation capacity...............................................................309

Table A.2. Code-designed piers with solid cross-section: geometrical and mechanical


Table A.3. Retrofitted piers with solid cross-section: geometrical and mechanical


Table A.4. Seismic-deficient piers with hollow cross-section: geometrical and mechanical


Table A.5. Code-designed piers with hollow cross-section: geometrical and mechanical


Table A.6. Retrofitted piers with hollow cross-section: geometrical and mechanical


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LIST OF FIGURES

Figure 3.1. Talübergang Warth Bridge, Austria ................................................................28

Figure 3.2. Geometry of the scaled models of the short (a) and the tall (b) pier and typical

cross-section (c) ............................................................................................35

Figure 3.3. Instrumentation of the short (a) and the tall (b) pier .......................................39

Figure 3.4. Cyclic test on the short pier: force-displacement curve ..................................41

Figure 3.5. Cyclic test on the short pier: crack pattern at the end of the test.....................41

Figure 3.6. Cyclic test on the short pier: experimental and envelop force-displacement

curves ............................................................................................................45

Figure 3.7. Cyclic test on the short pier: flexural and shear displacement ........................46

Figure 3.8. Cyclic test on the short pier: distribution of average curvature along the height

.......................................................................................................................51

Figure 3.9. Cyclic test on the short pier: evolution of vertical deformation ......................52

Figure 3.10. Cyclic test on the short pier: Park & Ang Damage Index .............................53

Figure 3.11. Relation between wall parameters and ultimate curvature [Wallace &

Moehle, 1992] ...............................................................................................57

Figure 3.12. Force-drift diagrams for the short, A70, and the squat, PREC8, piers..........59

Figure 3.13. Equivalent damping – drift for the PREC8 and A70 piers ............................61

Figure 3.14. Equivalent damping – displacement ductility: theoretical expressions and

experimental values for the PREC8 and A70 piers.......................................61

Figure 3.15. Cyclic test on the tall pier: force-displacement curve ...................................63

Figure 3.16. Cyclic test on the tall pier: crack pattern at the end of the test......................64

Figure 3.17. Equilibrium of internal forces in diagonally cracked element with shear

reinforcement ................................................................................................66

Figure 3.18. Cyclic test on the tall pier: flexural and shear displacement .........................66

Figure 3.19. Cyclic test on the tall pier: distribution of average curvature along the height

.......................................................................................................................68

Figure 3.20. Cyclic test on the tall pier: evolution of vertical deformation.......................69

Figure 3.21. Cyclic test on the tall pier: Park & Ang Damage Index ................................71

Figure 3.22. Performance of seismic-deficient (left column) and code-designed (right

column) bridge piers with hollow cross-section ...........................................74

Figure 4.1. Talübergang Warth Bridge, Austria ................................................................84


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Figure 4.2. Parallel procedures: simple inter-field procedure (a), improved inter-field

procedure (b) and intra-field procedure (c) ...................................................91

Figure 4.3. PSD test with substructuring of the Warth Bridge at the ELSA laboratory....94

Figure 4.4. Cross-section of the deck.................................................................................97

Figure 4.5. Mode shapes of the bridge.............................................................................100

Figure 4.6. Input accelerograms for the abutments and the pier bases (see Figure 4.3 for

abutment and pier labels) ............................................................................102

Figure 4.7. Response spectra of the accelerograms for the nominal earthquake.............103

Figure 4.8. Displacement histories for the 0.4xNE test, pre-test numerical analysis ......104

Figure 4.9. Force-drift diagrams for the 0.4xNE test.......................................................107

Figure 4.10. Damage pattern of the tall pier for the 0.4xNE test.....................................108

Figure 4.11. Displacement histories for the 0.4xNE test, experimental (solid line) and

numerical (thin line) results ........................................................................109

Figure 4.12. Force-drift diagrams for the 1.0xNE test.....................................................110



Figure 4.14. Damage pattern of the tall pier for the 1.0xNE test.....................................112

Figure 4.15. Force-drift diagrams for the 2.0xNE earthquake test ..................................113



Figure 4.17. Damage pattern of the short pier for the 2.0xNE test..................................114

Figure 4.18. Final collapse test on the tall pier: force-displacement diagram .................116

Figure 4.19. Damage pattern of the tall pier for the final collapse test............................116

Figure 4.20. Flexural and shear deformation of the short pier.........................................118

Figure 4.21. Flexural and shear deformation of the tall pier ...........................................118

Figure 4.22. Distribution of average curvature along the height of the short pier...........120

Figure 4.23. Distribution of average curvature along the height of the tall pier..............120

Figure 4.24. Vulnerability functions: Park and Ang Damage Index (a), drift ratio (b),

displacement ductility (c) and overall Park and Ang Damage Index (d)....125

Figure 4.25. Distribution of ductility demand (a), drift demand (b), Park and Ang Damage

Index (c) and percentage of dissipated energy (d) among the piers............128

Figure 4.26. Fast Fourier Transforms of the pier top displacement.................................128

Figure 4.27. Change in stiffness between adjacent piers and distribution of stiffness ....130

Figure 4.28. Response spectrum used in HAZUS [FEMA, 1999]...................................132

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Figure 4.29. Suggested displacement shapes, adapted from [Fajfar et al., 1997]............136

Figure 4.30. Acceleration response spectra for 5% damping: mean experimental (a) and

EC8 Type 1, Soil Class B and PGA = 0.36 g (b) ........................................139

Figure 4.31. Fragility curves for the Talübergang Warth Bridge ....................................140

Figure 4.32. Distribution of lateral forces........................................................................141

Figure 4.33. Force-displacement curves from pushover analysis....................................141

Figure 4.34. Evaluation of performance point for mean experimental ADRS: trapezoidal

(a) and triangular distribution of forces (b).................................................142

Figure 4.35. Maximum displacement of the piers: experimental values and CS method for

control at top of pier A30 (left column) and control at top of pier A70 (right

column) .......................................................................................................143

Figure 4.36. Evaluation of performance point for EC8-compatible ADRS: trapezoidal (a)

and triangular distribution of forces (b) ......................................................143

Figure 4.37. Mean displacement spectra for use in N2 method: experiment (a) and EC8

Type 1 for Soil Class B (b) .........................................................................147

Figure 4.38. Maximum displacement of the piers: experimental values and N2 method for

control at top of pier A30 (left column) and control at top of pier A70 (right

column) .......................................................................................................147

Figure 4.39. Assessment of the bridge for the EC8 spectrum and N2 method................148

Figure 5.1. Monotonic constitutive law for in compression (a) and tension (b)..............156

Figure 5.2. Cyclic constitutive law for concrete in compression (a) and tension (b) ......157

Figure 5.3. Monotonic (a) and cyclic (b) constitutive law for steel.................................158

Figure 5.4. Discretisation of alternative models for the cross-section.............................161

Figure 5.5. Pier A20: force-displacement monotonic curves for different models .........162

Figure 5.6. Short pier A70: experimental and numerical force-displacement curves .....166

Figure 5.7. Short pier A70: experimental and numerical moment-curvature curves.......166

Figure 5.8. Short pier A70: experimental and numerical dissipated energy versus top

displacement................................................................................................167

Figure 5.9. Tall pier T250: experimental and numerical force-displacement curves ......169

Figure 5.10. Tall pier T250: experimental and numerical dissipated energy versus top

displacement................................................................................................169

Figure 5.11. Tall pier A40: distribution of average curvature along the height of the pier

for the original model..................................................................................170

Figure 5.12. Tall pier A40: force-displacement curves for alternative models ...............171


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Figure 5.13. Numerical model with elastic base for the tall pier A40: force-displacement

curves (a) and dissipated energy (b)............................................................172

Figure 5.14. Numerical model with increased steel at the base for the tall pier A40: force-

displacement curves (a) and dissipated energy (b) .....................................173

Figure 5.15. Numerical model with reduced steel at the critical cross-section for the tall

pier A40: force-displacement curves (a), dissipated energy (b) and

distribution of curvature along the height (c)..............................................173

Figure 5.16. Talübergang Warth Bridge piers: force-displacement curves for the fibre

model and the damage model......................................................................176

Figure 5.17. Talübergang Warth Bridge piers: dissipated energy versus lateral

displacement for the fibre model and the damage model ...........................177

Figure 5.18. Talübergang Warth Bridge piers: force-displacement curves from pushover

analysis and bilinear envelope ....................................................................179

Figure 5.19. Concrete constitutive law: loading (a) and unloading (b) of a crack ..........180

Figure 5.20. Steel-to-concrete bond constitutive law: Eligehausen- Balázs model.........184

Figure 5.21. Evolution of damage for pier A40: numerical (a) and experimental (b) results

.....................................................................................................................186

Figure 5.22. Deformed shape for pier A40, numerical results (displacements magnified

x15) .............................................................................................................187

Figure 5.23. Tall pier A40: experimental and numerical force-displacement curves......188

Figure 5.24. Mesh of the numerical model: concrete (a), longitudinal steel (b), and

transverse steel (c) elements........................................................................190

Figure 5.25. Close-up at the base of the mesh: concrete and steel elements ...................190

Figure 5.26. Short pier A70: experimental and numerical force-displacement curves ...191

Figure 5.27. Crack pattern of the short pier A70: numerical analysis for continuous

reinforcement (a), numerical analysis with joint elements (b) and

experimental data (c)...................................................................................193

Figure 5.28. Tall pier T250: force-displacement curves of the as-built and retrofitted

specimens [Peloso, 2003]............................................................................195

Figure 5.29. Numerical stress-strain curves for concrete under uniform compression ...196

Figure 5.30. Tall pier T250-FRP: numerical stress-strain curves for FRP-confined

concrete (a) and definition of zones (b) ......................................................198

Figure 5.31. Tall pier T250-FRP: distribution of maximum axial stress within the cross-

section .........................................................................................................199

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Figure 5.32. Tall pier T250-FRP: different zones of concrete in the cross-section mesh200

Figure 5.33. Tall pier T250-FRP: numerical force-displacement monotonic curves ......200

Figure 5.34. Tall pier T250-FRP: experimental and numerical force-displacement curves

.....................................................................................................................202

Figure 5.35. Tall pier T250-FRP: experimental and numerical dissipated energy versus

lateral displacement.....................................................................................202

Figure 6.1. Drift capacity versus aspect ratio, transverse reinforcement ratio, splicing

length and normalised axial load for seismic-deficient (left) and code-

designed (right) piers...................................................................................212

Figure 6.2. Increase in drift capacity versus aspect ratio (a), transverse reinforcement ratio

(b), splicing length (c) and normalised axial load (d) .................................213

Figure 6.3. Global retrofit procedure for seismic-deficient bridge piers .........................215

Figure 6.4. Anchorage of flexural FRP reinforcement with external confinement

reinforcement ..............................................................................................220

Figure 6.5. Anchorage of shear FRP reinforcement in the compression zone by

embedment in concrete (a) and using bolts (b) ...........................................220

Figure 6.6. Anchorage of CFRP strips [Zehetmaier, 2000] .............................................222

Figure 6.7. Cross-section of an after-corner U-anchor [Khalifa et al., 1999]..................222

Figure 6.8. Cross-section analysis: (a) geometry, (b) strain distribution and (c) stress

distribution ..................................................................................................224

Figure 6.9. Bilinear constitutive model for FRP-confined concrete ................................232

Figure 6.10. Average absolute error: prediction of strength (a) and ultimate deformation

(b) of FRP-confined concrete [De Lorenzis, 2001] ....................................236

Figure 6.11. Moment – axial force interaction diagrams (a) and moment – curvature

monotonic curves (b) for different constitutive laws for FRP-confined

concrete [Yuan et al., 2001] ........................................................................236

Figure 6.12. Effectiveness of confinement for rectangular jacket ...................................237

Figure 6.13. Confinement of circular column with circular jacket ..................................239

Figure 6.14. Confinement of rectangular column with rectangular (a) and oval (b) jacket

.....................................................................................................................239

Figure 6.15. Failure of lapped splices ..............................................................................244

Figure 6.16. Confinement of circular column with circular jacket, equilibrium of internal

forces ...........................................................................................................246

Figure 6.17. Definition of cross-section geometry ..........................................................249


xiv

Figure 6.18. Concrete (blue) and FRP (red) jacket mesh ................................................250

Figure 6.19. Stress-strain curve of concrete for uniaxial compression............................250

Figure 6.20. Effect of jacket height and thickness on the compressive strength of concrete

.....................................................................................................................252

Figure 6.21. Stress-strain curves for confined concrete ( jh = 0.00 m) ............................254





Figure 6.26. Effect of jacket on the compressive strength of concrete............................258

Figure 6.27. Effect of jacket on the residual strength of concrete ...................................258

Figure 6.28. Effect of jacket on the softening stiffness of concrete ................................259

Figure 6.29. Concrete and steel mesh for the moment-curvature analysis ( jh = 0.05 m) 261

Figure 6.30. Material constitutive laws: concrete (a) and steel (b)..................................261

Figure 6.31. Definition of failure criteria and curvature ductility: at maximum moment (a)

and at 20% loss of strength (b)....................................................................261

Figure 6.32. Effect of axial load and amount of reinforcement on the curvature ductility

(as-built cross-section) ................................................................................262


( jh = 0.00 m) ...............................................................................................263


( jh = 0.05 m) ...............................................................................................263


( jh = 0.10 m) ...............................................................................................264


( jh = 0.15 m) ...............................................................................................264


( jh = 0.20 m) ...............................................................................................265

Figure 6.38. Effect of reinforcement ratio ( jh = 0.10 m, jt = 5 mm, ν = 0.1) .................266

Figure 6.39. Effect of axial load ( jh = 0.10 m, jt = 5 mm, sρ = 1.02%)..........................266

xv

Figure 6.40. Effect of jacket thickness ( jh = 0.10 m, sρ = 1.02%, ν = 0.1).....................267

Figure 6.41. Effect of jacket height ( jt = 5 mm, sρ = 0.17%, ν = 0.1) ............................267

Figure 6.42. Effect of axial load and amount of reinforcement on the effectiveness index

( jh = 0.00 m) ...............................................................................................269


( jh = 0.05 m) ...............................................................................................269


( jh = 0.10 m) ...............................................................................................270


( jh = 0.15 m) ...............................................................................................270


( jh = 0.20 m) ...............................................................................................271

Figure 6.47. Cyclic behaviour: moment-curvature diagrams for the as-built and jacketed

cross-section ( ν =0.2, jt = 5 mm, sρ = 1.02%)............................................272

Figure 6.48. Empirical fit to the numerical values of curvature ductility: ν ≤ 0.1 (a) and

ν > 0.1 (b)....................................................................................................274

Figure 6.49. Comparison between empirical and numerical values of curvature ductility:

ν ≤ 0.1 (a) and ν > 0.1 (b) ..........................................................................275

Figure 6.50. Comparison between empirical and numerical values of effectiveness index:

ν ≤ 0.1 (a) and ν > 0.1 (b) ..........................................................................276

Figure 6.51. Empirical fit to the numerical values of curvature ductility........................278

Figure 6.52. Empirical (5% characteristic) and numerical values of the effectiveness

index............................................................................................................278

Figure B.1. Vertical reinforcement of pier A70 (side view)............................................321

Figure B.2. Horizontal reinforcement of pier A70 ..........................................................321

Figure B.3. Vertical reinforcement of pier A70 (sections A-A, B-B) .............................322

Figure B.4. Vertical reinforcement of pier A70 (sections C-C, D-D) .............................323

Figure B.5. Vertical reinforcement of pier A40 (side view)............................................324

Figure B.6. Horizontal reinforcement of pier A40 ..........................................................325

Figure B.7. Vertical reinforcement of pier A40 (sections A-A, B-B) .............................326

Figure B.8. Vertical reinforcement of pier A40 (sections C-C, D-D) .............................327


xvi

Figure C.1. Talübergang Warth Bridge in Austria (both independent lanes are shown).329

Figure C.2. General view of the tested piers A40 and A70 inside the laboratory ...........329

Figure C.3. Cyclic test on the short pier A70: crack pattern of the flange (a) and the web

(b) at the end of the test...............................................................................330

Figure C.4. Cyclic test on the short pier A60: crack pattern of the flange (a) and the web

(b) at the end of the test...............................................................................330

Figure C.5. 0.4xNE test: crack pattern of the flange (a) and the web (b) of pier A40.....331

Figure C.6. 2.0xNE test: crack pattern of the flange (a) and the web (b) of pier A70.....331

Figure C.7. Final collapse test on the tall pier A40: crack pattern of the web.................332

Figure C.8. Pier A40: buckling of longitudinal reinforcement at 3.5m...........................332

Figure C.9. 1.0xNE test: hysteresis loops for substructured piers A20 and A30 (a) and on-

line comparison of experimental and pre-test displacement histories (b)...333

xvii

AKNOWLEDGEMENTS

The present thesis is submitted to the Department of Structural Engineering of the

Technical University of Milan (Politecnico di Milano - Dipartimento di Ingegneria

Strutturale) for the fulfilment of the PhD degree within the course on Earthquake and

Geotechnical Engineering and Soil-Structure Interaction (Ingegneria Sismica, Geotecnica

e dell’Interazione Ambiente-Struttura).

The author is sincerely grateful to Professor Giandomenico Toniolo, tutor and supervisor

of the thesis, for the excellent collaboration and his useful comments throughout the

whole duration of the research.

The greatest part of the work was performed while the author was a grant holder at the

ELSA laboratory of the JRC, Contract No: 15775-2000-03 P1B20 ISP IT, financed by the

SAFERR research network, CEC Contract No: HPRN-CT-1999-00035. The experiments

were partly financed by the VAB research programme, Environment & Climate Project

ENV4-CT97-0574. The financial support of the European Commission is acknowledged.

To Dr Artur Vieira Pinto, scientific responsible of the author at the JRC, are due deeply-

felt thanks for his friendship and support, for the joy of working together and for his

continuous encouragement to improve the quality of the work.

The author expresses his gratitude to Dr Javier Molina for the meticulous preparation and

control of the tests, to Dr Pierre Pegon for his continuous support on numerical

modelling, to Professor Michel Géradin, ELSA Head of Unit, and to all ELSA staff for

the warm welcome and for providing all the means and support that allowed to

successfully perform the work in the laboratory.

To the, unexpectedly many, new friends from the JRC and DIS, as well as to the old ones

from Greece, the author is thankful for they rendered pleasant the few pauses.

I thank the above for their interest that provided a motivation to continue my work at the

times when I mostly needed it; more than that, for supporting me in pursuing a passion.

To my family I dedicate my most personal thoughts during the periods of questioning and

doubts.


xviii

INTRODUCTION

1

1. INTRODUCTION

1.1. GENERAL – MOTIVATION FOR THE RESEARCH

This thesis deals with the seismic assessment and retrofit of existing reinforced concrete

bridges, with focus on piers with rectangular hollow cross-section. To what regards

assessment, an experimental campaign was followed and the test results were exploited

for the study of the seismic performance of single piers and complete bridge structures. A

numerical approach was adopted for the study of retrofitted hollow bridge piers. This first

chapter intends to introduce the subject by highlighting the importance of bridges, which,

combined with the seismic vulnerability of existing structures designed without

earthquake resistance, calls for the development of appropriate retrofit techniques.

Compared to buildings, bridges are less redundant and thus they have limited potential of

avoiding total collapse through the distribution of damage to a large number of plastic

zones within the structure. Indeed, collapse of a single beam/span and, even more, of a

column will most probably result in failure of the complete structure. In addition, most

bridges are valuable during the immediate post-earthquake emergency, since they are

required to ensure transport of heavy machinery, first-aid supplies and eventual victims

between earthquake-struck and surrounding areas. Being parts of complex

communication lifelines, bridges need to maintain a high level of occupancy, even in the

event of a strong earthquake. This is contrary to normal buildings for which significant,

but repairable, damage is accepted. Severe earthquake-induced damage on bridges results

in economic losses in the form of repair, or replacement, costs and disruption of traffic.

The above explain why particular attention and special studies are dedicated to bridges,

even though in most cases they can be considered as simple plane-frame structures.

The poor seismic behaviour of existing bridge structures has been verified during all the

recent important earthquakes, such as the 1987 Whittier Narrows earthquake [Gates et al.,

1988], the 1989 Loma Prieta earthquake [Housner & Thiels, 1990], the 1994 Northridge

earthquake [Housner & Thiels, 1995], the 1995 Hyogo-Ken Nambu (Kobe) earthquake

[Seible et al., 1995a; Kawashima & Unjoh, 1997] and the 1999 Kocaeli-Duzce

earthquakes [Imbsen et al., 2000]. Field and experimental observations allowed to

identify the main seismic deficiencies of existing bridges. They concern the abutments,


2

deck, columns, cap beams and foundation elements. Considering columns in particular,

the most common problems are the limited shear strength, presence of lapped splices in

the critical zones, limited ductility capacity and premature termination of longitudinal

reinforcement. It is argued that older bridge piers were designed with focus on strength

rather than deformation and without provisions to ensure stability of the response in the

post-elastic range [Pinto & Monti, 2000]. These observations support the need for retrofit

and also provide guidance on the targets to be sought.

Rectangular, octagonal, circular or wall-type solid cross-sections are often used for bridge

piers. In the case of tall piers, it is desirable to reduce the mass of the pier and

consequently the seismic loads it has to resist. In the USA the trend is to use solid

sections and to reduce the cross-sectional dimensions with height. In contrast, piers with

rectangular hollow cross-section are commonly used in Japan and Europe for highway

bridges that cross deep valleys [Hooks et al., 1997]. Despite the large population of

existing bridge piers with hollow cross-section, their seismic performance and appropriate

retrofit techniques have not been studied until recently. This provided the motivation to

focus the research presented herein to the assessment and retrofit of bridge piers with

rectangular hollow cross-section.

While various alternatives exist for the seismic upgrading of buildings [Fardis, 1998], the

practical solutions for bridges are rather limited. It is either desired to reduce the seismic

demand by modifying the structural response, or to increase the available strength and

deformation capacity. The use of isolation/dissipation devices for the seismic retrofit of

bridges often requires iterative procedures, or the study of alternative combinations of the

properties and position of the devices. Keeping in mind the code requirements for the

analysis of isolated bridges and the characterisation of the isolation/dissipation devices, it

seems that rather onerous studies are needed for each and every structure. Increasing the

capacity of the structure appears therefore as an appealing alternative, provided the

effectiveness of retrofit is verified and reliable design tools are available. The choice

between response modification and structural improvement should be supported by cost-

effectiveness studies and remains somehow at conceptual level. Without further

discussing this choice, the research described in this thesis follows the direction of

increasing the capacity of members.

INTRODUCTION

3

When designing the retrofit of a bridge structure, an important requirement is to consider

the cost of application, the large scale of the structure and the disruption of traffic. This is

the reason why fibre-reinforced polymer (FRP) materials have been extremely popular for

the seismic retrofit of bridges. Although the material is more expensive than reinforced

concrete and steel, the low transportation and application cost make it more attractive.

This lead to their use as a remedy to all problems and in some cases in over-designed

applications. Only recently they are seen with some scepticism and their absolute

effectiveness is questioned. While a sound background exists for the calculation of

flexural and shear strength [Seible et al., 1995b; fib, 2001], there is scarce confidence

with respect to design for confinement [De Lorenzis, 2001]. This provided the motivation

to study the effectiveness and eventual limitations of the use of FRP reinforcement for the

seismic retrofit of hollow piers with large dimensions.

The research was partly developed as contribution to two EC-funded research projects.

The VAB1 (Vulnerability Assessment of Bridges) project originated from the need to

assess the existing bridge stock, as a result of the inadequate seismic design of older

bridge structures, in combination with the recent revision of seismic hazard maps across

Europe. Particular attention was devoted to irregular highway bridges with rectangular

hollow piers. The evaluation of the deformation capacity of members with no seismic

detailing and the study of strengthening schemes and guidelines were among the tasks of

the SAFERR2 (Safety Assessment for Earthquake Risk Reduction) project.

1.2. OBJECTIVES OF THE RESEARCH

With the aim of assessing the cyclic behaviour of existing bridge piers with hollow cross-

section, cyclic tests on two large-scale (1:2.5) specimens of piers were performed. This is

seen as a contribution to the limited information available in the international literature on

bridge piers with this particular geometry. In fact, these are the first tests on large-scale

specimens of piers with rectangular hollow cross-section without earthquake detailing,

corresponding to an existing highway bridge situated in Austria. A second objective was

the calibration of non-linear numerical models that were employed for the substructured

piers during the pseudodynamic tests that followed.

1 www.arsenal.ac.at/vab 2 www.saferr.net


4

Aiming at the experimental assessment of a reinforced concrete bridge for increasing

intensity of the seismic input, a series of pseudodynamic tests on a complete bridge

structure were performed. A parallel objective was to implement the substructuring

technique in pseudodynamic testing with non-linear models for the numerical

substructure.

Having verified the seismic vulnerability of substandard bridges, a final objective related

to retrofitting was set. It is recognised that there is adequate knowledge and confidence on

the techniques and design tools for flexural and shear strength enhancement of seismic-

deficient bridge piers. In contrast, there is limited confidence in the effectiveness of

jacketing for increase of confinement for bridge piers with rectangular hollow cross-

section. Therefore, it was decided to undertake a numerical study on the effectiveness of

FRP jackets for confinement of rectangular hollow cross-sections.

1.3. OUTLINE OF THE THESIS

The thesis comprises seven chapters. Three appendices are given at the end, presenting

the main geometrical and mechanical characteristics of the examined bridge piers,

construction drawings for the tested specimens and a photographic documentation. A

short description of the contents of each chapter follows.

Following the present Chapter 1 which gives the motivation and objectives of the

research, Chapter 2 presents a bibliographic research on the effects of asynchronous input

motion and soil-structure interaction, innovative displacement-based methods, use of

isolation and dissipation devices in bridge engineering, procedures and indices for

damage assessment, methods of analysis and modelling and finally, techniques for the

seismic retrofit of bridge piers.

Chapter 3 deals with the cyclic tests on large-scale models of one short and one tall bridge

pier. The original piers belong to an existing highway bridge, situated in Austria and

designed in 1975. The experimental results are presented in terms of damage evolution,

force-displacement hysteretic curves, deformation and energy-dissipation capacity. A

literature review of experimental results on hollow bridge piers is presented and a

preliminary estimation of performance limits is based on the experimental results. This

INTRODUCTION

5

highlights the different capacities of piers designed before and after the introduction of

modern seismic codes and the need for retrofitting of seismic-deficient piers.

A series of pseudodynamic (PSD) tests performed on a large-scale (1:2.5) model of an

existing highway bridge are presented in Chapter 4. The research was focused on the

Talübergang Warth Bridge, which is considered representative of European highway

bridges designed before the modern seismic codes came into practice. The PSD testing

method is briefly presented, considering the particular cases of asynchronous input

motion and non-linear substructuring. The test results are presented in terms of hysteretic

curves, dissipated energy, deformation demands and distribution of damage. Standard

assessment procedures are checked against the experimental results. A simplified

procedure, appropriately corrected for the given structure, is applied for the assessment of

the bridge situated in a high-seismicity area: collapse is predicted for the design

earthquake (475 years return period) and therefore, retrofit of the bridge is imperative.

Numerical modelling is discussed in Chapter 5. Simplified fibre/beam models with

different configurations are calibrated on the results of the cyclic tests. Certain

modifications are introduced to surmount the limitations of these models, necessary for

the successful completion of the PSD tests. Refined FEM analyses allow overcoming the

restrictions of simplified models, at the expense of much larger computational demand.

Finally, a combination of these two approaches, namely FEM analysis for the material

properties and fibre modelling of the structural element, is validated against experimental

results for the study of hollow bridge piers retrofitted with FRP strips.

Chapter 6 deals with retrofitting and in particular with the problem of confinement for

rectangular hollow cross-sections with large dimensions. The effect of FRP wrapping on

the concrete properties in different parts of the cross-section is studied first and the

empirical constitutive laws for FRP-confined concrete are found inadequate for the

examined case. The results of these analyses are integrated in moment-curvature analyses

performed with the aim to study the effect of jacket dimensions, amount of reinforcement

and axial load on the ductility capacity of the cross-section. The effectiveness and

limitations of this retrofit method are discussed and finally, an empirical design equation

is formulated on the basis of more than 1000 numerical simulations.


6

The main achievements are recapitulated and the principal conclusions are put forward in

Chapter 7. Some suggestions for future research are given, on the grounds of the

difficulties encountered during the development of the research and on the limitations of

the findings.

OPEN ISSUES IN SEISMIC DESIGN AND ASSESSMENT OF BRIDGES – A LITERATURE REVIEW

7

2. OPEN ISSUES IN SEISMIC DESIGN AND ASSESSMENT OF BRIDGES -

A LITERATURE REVIEW

2.1. ASYNCHRONOUS EXCITATION

In design practice the effect of asynchronous input motion is not fully understood and due

to the complexity of the issue (representation of the seismic motion and time-consuming

non-linear dynamic analyses) it is usually ignored. According to Part 2 of Eurocode 8

(EC8-2) [CEN, 2002], the spatial variability of the input motion at the supports of bridges

must be taken into consideration for bridges in the presence of geological discontinuities

or marked topographical features and for bridges that are longer than 600 m. The effects

of the variability of the input motion on the response of the bridge are expected to be in

general small. Therefore, it is allowed to disregard them, or to use an idealised model.

Following the Italian seismic code [Ordinanza 3274, 2003], the total response of the

structure is obtained by adding the dynamic effects calculated from a response-spectrum

analysis and the pseudo-static effects for relative movement between the pier bases and

abutments.

Similar guidelines are provided by the Caltrans Seismic Design Criteria [Caltrans, 1999].

The Japanese seismic code [JSCE, 1996] requires the consideration of the epicentral

characteristics and amplification of the surface layer in defining the input motion for the

design earthquake with a rare probability of occurrence. The New Zealand Standards

[SNZ, 1995] recognise the need to increase the seismic loading due to site effects, but do

not directly take into consideration asynchronous motion of multi-support structures.

Following the Swiss code SIA 160 [SIA, 1989], a relative displacement at the base of

different piers or abutments due to travelling seismic waves is considered, in order to

prevent fall-down of the superstructure. Alternatively, it is recommended to provide the

structure with movement joints that subdivide the structure in simpler frames [Priestley et

al., 1996].

The main sources of the spatial variability of the ground motion are the finite dimensions

of the seismic source, the material heterogeneities and geometrical irregularities of the

earth surface and the wave-passage effects. The latter being easier to consider in defining

the asynchronous motion, more significant are the geological and topographical


8

irregularities, which are more complex and require detailed studies [Faccioli & Paolucci,

1990; Faccioli, 2002].

Dynamic analyses indicate that the effect of asynchronous motion is to decrease the

dynamic component and increase the pseudo-static component of the structural response.

From the structural point of view, it has been proved that designing for synchronous

motion, as is the common practice, provides a global upper bound of the response [Monti

et al., 1996]. Experimental results of an irregular bridge tested under asynchronous

earthquake input verify the above findings [Calvi & Pinto, 1996; Pinto et al., 1996].

On the other hand, an analytical study of a regular bridge subjected to non-stationary

multi-support random excitation suggests that the internal forces are in general reduced

for both the superstructure-deck and the substructure-piers, but in certain cases an

increase was observed [Perotti, 1990].

A theoretical study considering asynchronous motion due to wave-passage and

incoherence effects as well as local soil conditions proved that in certain cases, e.g. stiff

structures, the differential support motion may result in larger internal forces [Der

Kiureghian & Neuenhofer, 1992].

Dynamic analysis of an existing regular bridge showed that for small variability of the

ground motion the shear forces are decreased and the displacements increased, compared

to synchronous input, for both longitudinal and transverse excitation [Kahan et al., 1996].

Dynamic analysis of a regular bridge considering local soil amplification suggests

significant increase of shear forces and displacements in the case of substantial soil

amplification [Zembaty & Rutenberg, 1998].

A statistical approach has been adopted to study the importance of asynchronous motion

on the response of bridges [Lupoi et al., 2003]. Both regular and irregular bridges were

analysed, considering different combinations of the soil properties and levels of loss of

coherence and wave-passage effects. The results show that in presence of spatial

variability, the displacement ductility demands increase in the majority of the cases.

The coupling of spatial variability, soil-structure interaction and site effects was studied

through numerical parametric analyses [Sextos et al., 2003]. It was found that the effect


9

of spatial variability might increase up to 3.5 times the displacement demand and 50% the

bending moments, with respect to synchronous motion. In addition, the actual ductility

demand might be underestimated by a factor of 3, at the most unfavourable case, when

synchronous motion is considered in the design process.

From the above discussion it becomes clear that, although the importance of

asynchronous excitation is recognised for the design of bridges, there is absence of

general guidelines. This is due to the large scatter of the values that quantify the causes of

spatial variability of the ground motion. This in turn, makes their effects case-sensitive

and calls for relatively detailed analysis for each bridge and site.

2.2. DISPLACEMENT-BASED DESIGN AND ASSESSMENT

In recognition of the fact that earthquakes impose displacements, and not forces, on the

structures, several displacement-based procedures for the design and assessment of

structures have been proposed. At seismic code level, EC8-2 [CEN, 2002] introduces the

verification of deformation capacity of plastic hinges, in terms of rotation, for the case of

non-linear dynamic time-history analysis. In all other cases for new structures,

verification is performed for strength against applied forces. Part 3 of EC8 (EC8-3)

[CEN, 2003b], which deals with the strengthening and repair of buildings, makes the

distinction between ductile and brittle components and mechanisms and requires

verifications for three limit states, namely Near Collapse, Severe Damage and Damage

Limitation. Depending on the type of member and limit state, verifications are based on

either force or deformation. The Caltrans Seismic Design Criteria require that demand-

versus-capacity verifications of the members be performed for displacements and not

forces. The AASHTO Specifications [Buckle & Friedland, 1995] design approach is

based on forces, while displacements are mainly checked for bearing lengths.

Concerning design and assessment procedures, the basic concept is to substitute the real

structure with an equivalent linear single-degree-of-freedom (SDOF) one [Shibata &

Sozen, 1976]. Then, having estimated the equivalent damping, the effective period can be

derived for the target displacement from a displacement spectrum. Finally, the base shear

is defined from the stiffness corresponding to the effective period. This procedure is

called direct displacement-based design. In an early work [Iwan & Gates, 1979] that


10

compares different methods for the estimation of the properties of the equivalent linear

structure, the basic principles of the method are clarified. An overview of the recent

developments on the displacement-based design and assessment procedures can be found

elsewhere [Calvi, 1999; Priestley, 1998]. One drawback of the method is that damping

properties are estimated on the basis of semi-empirical expressions, although it is

understood that they play an important role in the procedure.

Displacement-based procedures have been applied for the design of single reinforced

concrete (RC) bridge columns and the validity of the method has been verified by

dynamic inelastic time history analyses [Kowalsky et al., 1995]. Concerning multi-

degree-of-freedom (MDOF) bridges, the concept works well for symmetrical structures,

but suffers some shortcomings for the case of irregular bridges [Calvi & Kingsley, 1995;

Fajfar et al., 1997]. This is due to the fact that a deflected shape, similar to the dominant

vibration mode, is assumed for the equivalent structure in order to achieve uniform

damage levels in the piers. Such assumption is true for regular bridges, but is not the case

for irregular structures, for which higher modes have a significant contribution to the

dynamic response.

To overcome these problems, a more elaborated procedure for the displacement-based

design of MDOF bridges, with either flexible or rigid superstructure, has been proposed

[Kowalsky, 2002]. In this, an effective mode shape is assumed for the equivalent

structure, as a combination of the modes calculated on the basis of the secant stiffness of

the piers and abutments and the elastic stiffness of the deck. The damping of the system is

a work-weighted sum of the values of damping of the components and then the standard

procedure for direct displacement-based design is followed. The accuracy of the proposed

method was verified for bridges with varying geometry and boundary conditions against

accurate dynamic analyses and consistency was observed.

An alternative procedure, supplementary to the current force-based ones, has been

proposed for RC buildings [Fardis & Panagiotakos, 1997]: the deformation demand is

estimated for a given lateral loading, corresponding to the serviceability earthquake, and

then the members are detailed to provide adequate deformation capacity. An expression

of the chord rotation capacity of members has been fit to a large databank of experimental

results on columns, beams and shear walls.


11

2.3. SOIL-STRUCTURE INTERACTION

Soil-structure interaction (SSI) and its effects on the response of structures are known for

well 30 years now. It is recognised that ignoring SSI may introduce errors on the unsafe

side when the spectral acceleration increases for periods higher than the fundamental

period of the structure [Newmark & Rosenblueth, 1971]. Apart from such extreme cases,

SSI is generally considered beneficial for structures.

At seismic code level, in EC8-5 [CEN, 2001] the lengthening of the fundamental period

of the structure, the increase in damping and the change of the eigenmodes and the modal

participation factors are recognised. Consequently, EC8 demands the consideration of SSI

for structures where P- δ effects are significant, for structures with massive or deep

foundations (e.g. bridge piers, offshore caissons and silos) or founded on very soft soil

and for very tall structures. The same criterion is adopted by the Italian seismic code

[Ordinanza 3274, 2003]. Following the New Zealand seismic code and the Caltrans

Seismic Design Criteria, SSI is always considered beneficial, as it reduces the seismic

design forces.

In order to quantify the effects of SSI, the lengthening of the fundamental period and the

increase in damping are typically estimated. Non-parametric methods using simple

transfer functions, e.g. [Paolucci, 1993], as well as parametric ones that study numerical

models for the transfer functions, e.g. [Stuart & Fenves, 1998], have been proposed for

the estimation of the dynamic properties of the structure based on the recordings of its

response during earthquakes. In addition, theoretical expressions, based on the soil and

structure properties as well as the geometry of the structure-foundation system, have been

proposed, e.g. [Stuart et al., 1999].

With the aim of studying the effects of SSI on inelastic structures, numerical

investigations are complementary to observations of data from instrumented structures.

Numerical analyses of 240 cases concerning a single bridge pier subjected to artificial

accelerograms matching the EC8 design spectrum, lead to the conclusion that the effects

of SSI are significant only in the extreme case of very stiff structures on soft soil

[Ciampoli & Pinto, 1995]. In terms of displacement ductility, the phenomenon seems to

have little effect, if not slightly beneficial. SSI results in increase of the displacement, but

only in terms of rocking motion due to the deformability of the soil and not in terms of


12

inelastic deformation of the pier. Similar results were obtained from non-linear pushover

analyses of bridge piers with various configurations [Elnashai & McClure, 1996].

In contrast, dynamic non-linear analyses of a similar model using accelerograms recorded

on soft-soil sites suggest significant increase of the ductility demand [Gazetas &

Mylonakis, 2001]. In fact, SSI effects are considered to have contributed to the collapse

of the Hanshin Expressway during the Kobe earthquake [Mylonakis & Gazetas, 2000].

The coupling between spatial variability of the ground motion, site effects and SSI was

studied considering different cases of symmetry, regularity and boundary conditions for a

bridge structure [Sextos et al., 2002]. It was found that the effects on the calculated

displacement ductility of the piers are important in the case of ground motions rich in low

frequencies, abrupt changes of soil stiffness, significant site response phenomena and

wave-passage effects.

2.4. BRIDGES WITH ISOLATION AND DISSIPATION DEVICES

Seismic isolation is an attractive alternative to design for ductility. In other words, the

effort on earthquake design of bridges is focused on minimising the forces to be resisted

by the piers. Isolation and dissipation devices can be used with the aim either to lengthen

the period of the structure (decrease the force but increase the displacement), or to

increase the damping (decrease both force and displacement), or for a combination of the

two. For the first case, particular attention should be paid for input motions with

significant amplification in the longer periods. For flexible bridges the reduction of forces

is insignificant, while displacements still increase linearly [Priestley et al, 1996].

The simplest device is the laminated rubber bearing consisting of horizontal steel plates

inserted in a block of rubber. This device offers small increase in damping. Inserting a

lead plug in the rubber bearing provides restoring force and damping [Robinson, 1982].

In addition, lead has good fatigue performance (actually, lead-rubber bearings retained

most of their dissipation capacity after five earthquake tests) and reliable mechanical

properties. Sliding bearings exhibit unreliable response, no centering force and should be

combined with dissipation devices.


13

Sliding bearings with a pendulum-type response constitute the principle of the friction

pendulum device (FPD). Experimental studies of a simple bridge structure isolated with

FPD verified the insensitivity of the device to the amplitude and frequency content of the

input motion, the stability of the response for a large number of cycles and also the

reduction of the shear forces and drift of the piers to almost half of the values for the non-

isolated bridge [Tsopelas et al., 1996]. Analytical studies of a regular bridge with FPD

between all piers and the deck showed that for the case of hard foundation soil, a

reduction in forces and displacements was obtained, with respect to the non-isolated

bridge, while a more complex distribution of the devices among the piers was needed for

efficient isolation in the case of soft foundation soil [Wang et al., 1998].

Steel hysteretic dampers (of cantilever, butterfly or crescent moon shape) are used to

dissipate energy and increase the damping of the structure in the desired directions.

Hydraulic dampers have been originally used to accommodate displacements at thermal

joints, but can be used as isolation/dissipation devices. Similar dissipation capacity

originates from the plastic deformation of lead in lead-extrusion dampers. The dampers

have no centering effect, but could be used as jacks to reposition the deck after the

earthquake. Shock transmitters, that allow slow displacements and prevent dynamic ones,

can be used between selected structural elements so that the structure remains isostatic for

normal use, while it becomes hyperstatic during an earthquake shacking [FIP, 2002].

Considering modelling and analysis methods, increasing degrees of sophistication,

namely: static linear, dynamic modal and time-history analysis, are proposed for

increasing importance of the bridge structure [Priestley et al., 1996]. It is recognised,

though, that safety factors that account for the reliability of the properties of the devices

have yet to be codified.

At seismic code level, EC8-2 [CEN, 2002] dedicates a section to the design of isolated

bridges and allows only fully isolated bridges, i.e. both the superstructure and

substructure should remain essentially elastic. Either elastic response spectrum

(fundamental mode or multimode) analysis or non-linear dynamic analysis can be

performed. Prototype tests of the devices are required for the characterisation of the

deformation and damping properties, as well as the effects of bilateral load, temperature,

aging and load history; a testing sequence and acceptance criteria are prescribed. The

isolating system is also demanded to provide a certain level of lateral restoring force.


14

A comprehensive review of analysis methods required by seismic codes in the USA and

Japan can be found in [Hwang et al., 1994]. One approach is to define via semi-empirical

expressions the damping of the isolation devices and then enter the elastic design

spectrum with a combination of them. Either SDOF or MDOF structures are considered.

Alternatively, the effective damping and stiffness of the devices are determined and a

strain energy-based combination of the damping of all components is used to define the

overall structural damping. A tributary mass-based sum of the damping ratios has also

been proposed [Priestley et al., 1996].

Application to a sample bridge has shown that all the aforementioned methods provide

accurate results for the purposes of bridge design. Nevertheless, the accuracy of each

method seems to depend on the characteristics of the input earthquake. Linear time-

history analysis was found to be more accurate than response-spectrum analysis [Hwang,

1996]. Different simplified methods for the analysis of isolated bridges were compared

for three types of regular and irregular bridges [Franchin et al., 2001]. It was found that

the results of simplified response spectrum analyses were consistent with those of more

elaborated ones. The difficulties in identifying, in a comprehensive way, the damping

properties of the equivalent linear system were discussed and such procedure was found

as time-consuming as non-linear time-history analysis.

Considering the design of isolation for existing bridges, an iterative procedure is proposed

[Fardis & Calvi, 2001]. The strength of the devices is limited by the given strength of the

piers; the use of a safety factor is also recommended. Then, the devices should be

designed to limit the absolute and relative displacement of the deck. Assuming at first

stage a deformed shape for the deck, the combination of devices is checked, within an

iterative procedure, by means of a regularity index [Calvi & Pavese, 1996].

Seismic isolation can be applied to regularise the response of bridges with abrupt changes

in stiffness between adjacent piers. The combined use of bearings and hydraulic dampers

was proved successful in safely designing long viaducts, otherwise impossible to

construct [Isakovic et al., 2002]. Rubber or elastomeric bearings were used in order to

reduce the stiffness of the structure and the seismic forces, while dampers were used to

reduce the displacement of the deck and prevent impact with the abutments. Numerical

analyses performed with the aim to optimise the design and position of the devices,


15

highlighted the influence of the accelerogram characteristics, device properties, centering

capacity and SSI on the design forces and displacements.

The effects of various techniques on the seismic response of bridges were experimentally

and numerically investigated [DesRoches et al., 2003]. Simply supported and continuous

multi-span bridges with either steel or prestressed concrete girders, typical of Mid-

America were examined. It was found that continuity of the deck reduces the pounding

forces, while for simply supported bridges the critical elements are the columns.

Considering retrofit measures, numerical analyses pointed out that elastomeric bearings

result in about 50% decrease in ductility demand for the columns and in increase of the

displacement and pounding forces in the deck. Lead-rubber bearings had similar effect on

the ductility demand for columns and in addition decreased the displacements and forces

in the deck. Finally, when elastomeric bearings were combined with restrainer cables,

their results were reciprocally overpowered and the effectiveness was reduced.

Although various devices and techniques are available, and significant experience has

been gained from numerous past applications, there is still some uncertainty with regard

to the analysis method to be used and also concerning the damping characteristics of the

devices and the passage to the overall damping of the structure. For the above reasons, the

conceptual design of an isolated bridge is more art than science [Priestley et al., 1996].

2.5. DAMAGE ASSESSMENT

In the displacement-based procedures, demand-versus-capacity iterative verifications are

performed on the basis of different measures of deformation, such as drift [Calvi &

Kingsley, 1995], strain limit states related to top displacements [Priestley & Calvi, 1997;

Kowalsky, 2000; Paulay, 2002] and also chord rotation [Panagiotakos & Fardis, 1998].

For the quantification of structural damage, the most widely-used damage model is the

energy-based Park and Ang Damage Model [Park & Ang, 1985], that defines the damage

index by two parts, one taking into account the maximum deformations experienced and

the other accounting for the cycling effects. Concerning bridge structures and components

in particular, based on a database of experimental results, an attempt was made to

correlate different damage indices to performance levels and required repair [Hose et al.,


16

2000]. On the basis of cyclic tests on scaled circular bridge columns, a correlation of

damage limit states with visual observation has also been proposed [El-Bahy et al., 1999].

Cumulative damage, capacity and demand aspects and the influence of loading history are

to be taken into consideration [Krawinkler, 1996]. The effect of the loading history on the

failure mode and deformation capacity of members has been experimentally evaluated:

different failure modes and deformation capacities were observed, depending on the

loading history [Kunnath et al., 1997].

Assessment procedures exist in Europe, mainly for reinforced concrete and masonry

buildings [CNR, 1993; Grünthal, 1998] (for the USA see for example [FEMA, 1999]).

Alternative approaches have been proposed mainly in the USA, e.g. [Buckle & Friedland

1995; Taylor et al., 1997]. However, it has not yet been clarified which parameter is more

representative of deformations and which ultimate values correspond to each performance

level.

2.6. SEISMIC RETROFIT OF REINFORCED CONCRETE COLUMNS

Several techniques for seismic retrofit of structures exist, each one addressing a specific

seismic deficiency and requiring attention to details of the design and practical execution

[Fardis, 1998]. As far as bridges are concerned in particular, it is either desired to increase

the capacity, mainly by jacketing using concrete, steel or fibre-reinforced polymers (FRP)

or to decrease the seismic demand by isolation or dissipation devices. In certain cases it

might be desirable to improve the linkage between the bridge piers and the deck, e.g.

[Park et al., 1993]. It might be appropriate, instead, to add new members and rely on the

existing ones only for vertical load capacity, e.g. [Chua et al., 2001].

In this section the experimental verification of several retrofit techniques is presented.

The techniques comprise concrete, steel and FRP jacketing, which is aimed at increasing

the flexural and shear strength and the ductility capacity. The particular problem of

lapped splices is also discussed. Experimental results for retrofitted piers with hollow

cross-section are discussed in detail in a following chapter. The geometric and

mechanical properties of the specimens and the deformation capacities in terms of


17

displacement ductility and lateral drift are presented in Annex A and will be discussed in

the following chapter.

2.6.1. Retrofit by jacketing

Concrete jacketing is used to increase the ductility, as well as the shear and flexural

strength of components and is in general a low-cost intervention. Steel jacketing has the

same effects, but the cost varies depending on the amount of material used. FRP jackets

are effective in providing active or passive confinement, increasing the shear and flexural

strength and also the integrity of lapped splices. The materials are usually expensive, but

application is easier compared to the other techniques. The cost would increase for all

techniques in the case of low accessibility of the region in need of retrofit. An additional

advantage of FRP jackets is the limited change in stiffness, compared to concrete or steel

jackets [Priestley et al., 1996]. As a result, the dynamic characteristics of the structure are

not significantly altered and the retrofitted components do not attract higher seismic

loads.

Concrete jackets

Concrete jacketing was one of the first techniques used for seismic retrofit of columns. It

can be used to provide confinement, to increase the flexural or shear strength, or for a

combination of the above. Concrete jackets have been mainly used for rectangular

columns of buildings, but could also be applied on bridge piers.

Shotcrete jackets have been applied on repaired and strengthened short columns that

showed brittle failure due to shear [Bett et al., 1988]. Two different configurations were

considered for the jacket on the strengthened columns: additional vertical rebars only at

the corner, or distributed along the width of the pier. In all cases the vertical

reinforcement served only to support the additional horizontal reinforcement. The as-built

and repaired columns failed due to shear, whereas the strengthened columns failed due to

a combination of flexure and shear. The drift capacity was uδ = 2.0% and uδ = 2.5% for

the as-built and the retrofitted columns, respectively. The jackets did not have a

significant effect on the stiffness of the column, but almost doubled the strength. The

main effect of the jacket was to reduce the degradation of strength and stiffness with

cycling.


18

The effectiveness of concrete jackets with additional vertical and horizontal

reinforcement was experimentally assessed [Ersoy et al., 1993]. The vertical rebars of the

jacket were welded on the existing ones and on plates at the top and bottom of the

column. As-built, repaired and strengthened specimens were tested. Failure of all

specimens was due to crushing of concrete and buckling of vertical reinforcement. The

stiffness of the strengthened columns was similar to the one of the as-built column, while

the stiffness of the repaired columns was equal to 75% of the stiffness of the as-built

column.

Concrete-jacketed columns with different amounts of horizontal reinforcement and

vertical reinforcement either distributed or concentrated in the corners were

experimentally tested [Rodriguez & Park, 1994]. The effect of the jackets was to increase

by almost three times the strength and stiffness of the as-built piers, as well as to reduce

the strength degradation with cycling. The two configurations for vertical reinforcement

did not show a different effect on the performance of the retrofitted elements. The jackets

with large amounts of horizontal reinforcement did not proportionally improve the

behaviour of the columns.

Steel jackets

Steel jackets have been extensively used for seismic upgrading of columns and bridge

piers. They are used mainly to increase the confinement and shear strength of existing

elements, without increasing the flexural strength. Confinement is also expected to

improve the behaviour of lapped splices. Steel jackets are placed around the existing pier

within the plastic hinge region and a gap is left between the existing pier and the jacket

and later filled with normal or expansive grout. A gap is left between the steel casing and

the foundation in order not to increase the flexural strength. The dimensions of the gap

above the foundation condition the length of the equivalent plastic hinge length.

Large-scale models of circular bridge piers retrofitted with steel jackets were

experimentally tested [Chai et al., 1991]. The retrofitted specimen showed stable

hysteretic response until large values of displacement ductility, uµ = 8, and drift, uδ = 6%,

while the as-built specimen experienced brittle failure for ductility uµ = 4 and lateral drift

uδ = 3%. A small increase in strength was observed, as well as a 10% increase in

stiffness.


19

An extensive experimental campaign on as-built and retrofitted rectangular and circular

bridge piers was performed [Priestley et al., 1994c]. Elliptical and circular steel jackets

were applied with the aim to increase the shear strength and confinement. The retrofitted

columns exhibited stable hysteretic response, with displacement ductility capacity uµ = 8

and drift capacity uδ = 4%. The pattern of inelastic deformation changed from

predominantly shear deformation to predominantly flexural deformation for the retrofitted

specimens. Steel jackets increased the stiffness of the columns by 30% and 64% for

circular and rectangular cross-sections, respectively, and the energy-dissipation capacity

by 150 times, in comparison to the as-built piers.

Small-scale rectangular bridge piers were tested until failure and then repaired with

circular steel jackets [Yang et al., 2000]. The retrofit increased the strength by 40% to

110%, depending on the axial load and concrete strength, and also the displacement

ductility capacity from uµ = 3.7 to uµ = 6. The increase in stiffness was found to depend

on the length of the jacket, namely full-height or limited in the plastic hinge length.

Analytical studies have shown that the stiffness increases with increasing thickness of the

jacket, aspect ratio of the pier and bond strength between jacket and column [Chai, 1996].

For an extreme case of good bond between the jacket and the column, large aspect ratio

and large jacket thickness, an increase of stiffness in the order of 150% was estimated.

FRP jackets

FRP jackets are used to increase strength and/or ductility. They can be applied to either

circular or rectangular columns. FRP jackets present the advantages of low weight, easy

application and low maintenance, in comparison to concrete and steel jackets. The

effectiveness of FRP jackets for wall-type bridge piers is also reported [Uemura, 2000].

The effects of strap thickness, spacing and type of fibre, namely glass and carbon, were

analytically studied [Saadatmanesh et al., 1994]. It was found that the jackets increase the

ductility, without significantly increasing the resistance. The improvement increases with

the thickness of the strap and decreases with the spacing of the strap and the concrete

strength. Piers with carbon-fibre reinforced polymer (CFRP) jackets were found to have

larger capacity of energy dissipation than piers with glass-fibre reinforced polymer

(GFRP) jackets. A drawback of the adopted analytical procedure is that constant, and not


20

increasing, confining stress with lateral dilation was considered for the FRP jacket. This

aspect will be further discussed in the following.

The effectiveness of GFRP jackets on circular bridge piers was experimentally

investigated [Saadatmanesh et al., 1996]. Both passive and active retrofit solutions were

examined. Passive retrofit consists in simply wrapping the FRP straps around the pier,

while for active retrofit, a gap is left between the pier and the jacket and then filled with

pressurised grout infill. The jackets increased the ductility from uµ = 4 to uµ = 6, as well

as the strength and the energy-dissipation capacity of the as-built piers. No significant

difference was observed in the behaviour of the piers with active or passive retrofit.

Flared columns with GFRP and CFRP jackets were experimentally assessed [Saiidi et al.,

2000]. The effect of the jackets was to increase the stiffness, ductility (from uµ = 5.4 to

uµ = 7.4 or uµ = 7.9 for CFRP and GFRP jackets, respectively) and strength (by almost

40%). No significant difference was observed between the responses of the specimens

retrofitted with GFRP or CFRP jackets.

Small-scale models of rectangular bridge piers were tested using the pseudodynamic

testing method [Chang, 2002]. As-built models were first tested and then repaired using

CFRP jackets. The jackets were successful in restoring and slightly increasing the original

strength, but managed to restore only 70% to 75% of the original stiffness.

The effectiveness of CFRP and GFRP jackets for the improvement of the behaviour of

RC columns subjected to accelerated corrosion was experimentally investigated [Bousias

et al., 2002]. The as-built specimens failed due to a combined flexural-shear mode and

showed low drift capacity, uδ = 2.8%, while the retrofitted specimens failed in a flexural

mode. The deformation capacity of the retrofitted specimens was significantly increased

until uδ = 5.1% and uδ = 7.5% in the strong and the weak directions, respectively. It was

observed that increasing the number of FRP layers above a certain limit, does not

improve the performance of the specimens and also that the improvement is not

proportional to the amount of FRP. This is due to the fact that other failure modes, e.g.

fracture of steel rebars, precede the failure of the FRP material.


21

2.6.2. Retrofit for enhancement of lapped splices

For construction convenience, starter bars were often spliced just above the foundation,

within the potential plastic hinge region. In addition, in structures designed prior to

modern seismic codes, the overlapping length is short and the amount of transverse

reinforcement low. This may cause loss of bond between spliced rebars and consequently

premature failure of members. Experimental studies suggest that bond failure results in

degradation of resistance and also that lapped splices above the base force the

deformation demand to concentrate at a very thin slice [Paulay, 1982; Chai et al., 1991;

Lynn et al., 1996]. Therefore, it has been proposed to rely on the strength of lapped

splices only until low levels of displacement ductility, µ = 3 [Priestley & Park, 1987].

One technique for retrofitting bridge piers with lapped splices within the plastic hinge

region is by applying external prestressed reinforcement. This technique was applied on

flexure-dominated circular columns and assessed experimentally [Coffman et al., 1993].

The retrofit resulted in no change of the column stiffness and in slight increase of the

strength and of the energy-dissipation capacity. It mainly resulted in a significant increase

of the total number of cycles before failure. Yielding of the longitudinal reinforcement

occurred within a small length adjacent to the footing.

It has been proposed to retrofit circular columns with lapped splices using steel jackets.

Experimental results showed that columns with lapped splices at the base exhibit small

ductility, uµ = 1.5, drift, uδ = 1.4%, and dissipation capacities and that their behaviour is

significantly improved by applying steel jacket within the overlapping length [Chai et al.,

1991]. The ductility capacity of the retrofitted pier was uµ = 7 and the drift capacity was

uδ = 5.2%. The curvature demand of the jacketed specimen was concentrated in the gap

between the jacket and the foundation. The retrofitted pier had almost twice the lateral

strength of the as-built specimen.

Cyclic tests on scaled models of grooved rectangular bridge columns retrofitted with steel

jackets showed similar performance of the specimens with circular or elliptical jackets as

well as normal or expansive grout between the jacket and column [Daudey & Filiatrault,

2000]. The jackets slightly increased the strength of the column. They significantly

increased the energy-dissipation capacity and the displacement ductility from uµ = 1.5 for


22

the as-built specimen to uµ = 6 for the retrofitted ones. The curvature demand in all tested

specimens was concentrated in the gap between the steel jacket and the foundation.

Larger gap between the jacket and the foundation was found to reduce by 10% the

stiffness increase and to reduce the concentration of stress on the vertical rebars.

An alternative approach is the relocation of the plastic hinge. This retrofit strategy

involves adding a reinforced concrete footing block in order to move the location of the

plastic hinge from the base of the column to the top of the lapped splices [Griezic et al.,

1996]. The moment capacity at the base must exceed the applied moment when yielding

occurs at the top of the lapped splices. When first yielding occurs, it is expected that it

would spread above and below the critical cross-section and thus result in a significant

plastic hinge length in the retrofitted column. Experimental assessment of the proposed

technique was performed, applying a steel jacket at the part above the added concrete

block in order to increase confinement. The retrofit increased the flexural strength by

about 75% and the displacement ductility from uµ = 2.6 to uµ = 6.6. It also increased the

capacity of energy dissipation.

GFRP jackets applied on circular columns with lapped splices were assessed, considering

both passive and active retrofit [Saadatmanesh et al., 1996]. The jackets were found to

increase the strength and energy-dissipation capacity of the column. While the as-built

specimen failed at low ductility, uµ = 1.5, the retrofitted ones failed at uµ = 6. No

significant difference was observed between the performance of the specimens retrofitted

with the active and passive jacket.

The effectiveness of prefabricated FRP jackets for enhancement of lapped splices was

experimentally investigated [Xiao & Ma, 1997]. The failure of as-built circular columns

was brittle, for low displacement ductility, uµ ≈ 1, before reaching the design flexural

resistance. For the repaired and strengthened specimens, a significant increase in

displacement ductility ( uµ = 4 and uµ = 6, respectively) was achieved with prefabricated

jackets, although loss of bond initiated at high levels of displacement. The repaired

specimen managed to develop the nominal flexural strength, while the strength of the

strengthened specimen almost doubled, compared to the as-built specimen.


23

2.7. ANALYSIS AND MODELLING

Concerning the analysis of RC bridges, a comprehensive review of the various methods

can be found in [Priestley et al., 1996]. The effects of stiffness, damping, ductility,

regularity, simplified models, response spectrum or time-history analysis for the design of

RC bridges are discussed in [Flesch & Klatzer, 1995]. Assumptions related to material

constitutive laws, definition of limit states, mesh refinement, inclusion of the foundation,

soil and deck have been proved to significantly affect the analytical results of interest in

the design of new and the assessment of existing bridges [Elnashai & McClure, 1996].

Different modelling possibilities for the seismic analysis of bridge structures, namely:

elastic single-mode spectral method, elastic multi-mode spectral method and inelastic

time-history analysis, depending on the seismic hazard, the importance of the bridge and

the structural regularity were found to result in significant differences in terms of design

forces and displacements [Fishinger et al., 1997].

The standard method of analysis for normal bridges according to EC8-2 [CEN, 2002] is

the response spectrum method. When the dynamic behaviour of the bridge can be

sufficiently approximated by a SDOF model, the equivalent static seismic forces can be

derived from the inertia forces corresponding to the fundamental natural period of the

structure. Power spectrum and time series analysis are also permitted. Non-linear time

history analysis may be used in combination with the standard response spectrum analysis

and in general, with the exception of isolated or irregular bridges, it may not be used to

relax the demands calculated with the standard method. Specific objectives and

requirements are demanded for non-linear time history analysis. For irregular bridges, a

combination of pushover and equivalent linear analysis may be performed.

Similarly, linear response spectrum analysis, both single-mode and multi-mode, and non-

linear time history analysis is designated in the Japanese [JSCE, 1996], New Zealand

[SNZ, 1995] and USA [Caltrans, 1999] seismic codes, depending on the structural

configuration and simplicity of the bridge. More refined analysis methods are prescribed

with increasing complexity and importance of the bridge structure.

Modern seismic codes contain detailing provisions that protect the members against

undesirable failure modes. Capacity design procedures dictate a controlled failure mode,

with inelastic deformation (plastic hinges) developing at desired parts of the structure, by


24

designing the remaining sections for resistance calculated on the basis of the flexural

over-strength of the plastic hinge regions. Transverse reinforcement is detailed so that it

provides sufficient confinement of the concrete core and support of vertical reinforcement

bars against buckling, whereas the overlapping length is enough to ensure transfer of

stresses between spliced rebars. Lack of such provisions may instigate phenomena, such

as significant shear deformation, tension shift, loss of bond between steel and surrounding

concrete and premature buckling, which are difficult to model. As a result, simplified

models for the structural components, e.g. fibre models, are not always successful in

representing the whole range of phenomena that affect the failure mode, deformation

capacity and hysteretic behaviour of elements. For this reason, it is often unavoidable to

resort to modelling with the finite element method using extremely elaborated meshes and

constitutive laws for the materials (concrete, reinforcement bars and steel-concrete

interface). The performance of the aforementioned numerical approaches for the

modelling of as-built and retrofitted bridge piers will be discussed in a following chapter.

Existing bridge piers often have lapped splices within the critical zones, which affect the

structural response both in terms of strength and deformation. Therefore, the behaviour of

the steel to concrete interface should be appropriately considered in the analysis of these

elements. Extensive theoretical and experimental research work has been performed in

the past, before formulating constitutive laws for steel-to-concrete bond. The factors that

affect the bond strength are the steel stress, concrete strength, side and bottom cover, bar

spacing, amount of transverse reinforcement and bond condition [Tassios, 1979;

Eligehausen et al., 1983; Eligehausen & Balázs, 1993]. The stress history and level of

force are also important for the bond behaviour [Bresler & Bertero, 1968; Balázs, 1991].

Experiments showed the effect of the loading rate [Chung & Shah, 1989] and the effect of

repeated and reversed load [Balázs, 1991] on steel-to-concrete bond. Finally,

experimental results on members with noncontact splices [Sagan et al., 1991] verified the

effect of cycling, transverse reinforcement and concrete compression on the lap splice

length.

Similar difficulties, often to a greater extent, exist for the numerical modelling of

elements retrofitted with FRP jackets. A major concern is the confining effect of jacketing

on the properties of concrete. The existing models proposed for confinement provided by

steel stirrups are not applicable to FRP-confined concrete. The complication arises from


25

the fact that, while steel jackets apply constant confinement stress after yielding, FRP

jackets, due to the linear behaviour of the material until failure, provide increasing lateral

pressure with increasing dilation of the concrete core. Various empirical constitutive laws

have been proposed, based on experimental results, e.g. [Fardis & Khalili, 1981; Samaan

et al., 1998; Kawashima et al., 2000a]. These empirical laws do not perform well in cases

where the materials are significantly different from the ones used for the calibration of

each of them. A recently-proposed theoretical constitutive law for composite-confined

concrete [Spoelstra & Monti, 1999] overcomes this limitation. The same important is the

bond between FRP strips and concrete. Loss of adhesion may initiate premature failure of

the retrofitted member, e.g. [Arduini & Nanni, 1997]. The proposed models, their

inconsistencies and the implications on the modelling of retrofitted elements will be

discussed in depth in a following chapter.


26

EXPERIMENTAL ASSESSMENT OF HOLLOW BRIDGE PIERS WITH SEISMIC DEFICIENCIES

27

3. EXPERIMENTAL ASSESSMENT OF HOLLOW BRIDGE PIERS WITH

SEISMIC DEFICIENCIES

3.1. INTRODUCTION

When designing a bridge pier, rectangular, octagonal, circular or wall-type solid cross-

sections are often used. In the case of tall piers, it is desirable to reduce the mass of the

pier and consequently the seismic loads it has to resist. In the USA the trend is to use

solid sections and to reduce the cross-sectional dimensions with height, whereas only a

small percentage (in the order of 3%) of the existing bridge piers have hollow cross-

sections [Poston et al., 1986]. In contrast, piers with rectangular hollow cross-section are

commonly used in Japan and Europe for highway bridges that cross deep valleys [Hooks

et al., 1997]. As most of the existing bridges were designed before the modern seismic

codes came into practice, there is the need to assess the seismic performance of bridge

piers with hollow cross-section.

Modern codes do not distinguish between piers with solid and hollow cross-section,

probably because of limited knowledge. On the other hand, it is recognised that the

rational assessment of existing structures might require the revision of limit states and

methods of analysis [Calvi et al., 2000]. Indeed, recent research [Rasulo et al., 2002;

Hines et al., 2002a; Hines et al., 2002b] originates from the questions concerning the

shear resistance and the estimation of the deformation capacity of piers with hollow

cross-section and very large dimensions.

This chapter deals with the experimental results from cyclic quasi-static tests on large-

scale models of one short and one tall bridge pier performed at the ELSA laboratory of

the Joint Research Centre. The original piers belong to an existing highway bridge,

schematically shown in Figure 3.1. A view of the real structure is given in Figure C.1.

The bridge is situated in Austria and was designed in 1975. One tall pier, termed A40,

and one short pier, termed A70, were chosen in order to study components with different

aspect ratios and detailing. The main characteristics are the presence of lapped splices

with short overlapping length within the potential plastic hinge region of the short pier

and the premature termination of longitudinal reinforcement in the tall pier.


28

Figure 3.1. Talübergang Warth Bridge, Austria

The objective of the tests was twofold. The first scope was the assessment of the cyclic

behaviour of existing bridge piers with hollow cross-section. The second objective was

the calibration of non-linear numerical models for the substructured piers during the

pseudodynamic tests that followed. The pseudodynamic tests are presented in Chapter 4,

while the numerical modelling is further discussed in Chapter 5.

The design of the specimens is presented first, along with the instrumentation. The

experimental results are presented in terms of damage evolution, force-displacement

hysteretic curves and contribution of shear to the total displacement. The definition of

yield displacement is discussed in particular. A comparison to empirical expressions for

the prediction of yield and ultimate displacement highlights the importance of the

estimation of the equivalent plastic hinge length. The significance of seismic detailing is

evidenced through the comparison of the behaviour of the short pier to that of a squat pier

designed according to Eurocode 8 (EC8).

A literature review of experimental results on hollow bridge piers is also presented. An

attempt is made to qualitatively identify the effect of mechanical and geometrical

parameters on the deformation capacity of such piers. Finally, a preliminary estimation of

performance limits is based on the experimental results available in literature. This

highlights the differences between piers designed before and after the introduction of

modern seismic codes and also the effect of failure mode on the deformation capacity of

seismic-deficient piers.


29

3.2. BIBLIOGRAPHIC RESEARCH

3.2.1. Experimental assessment of piers with seismic design

Experimental assessment of scaled (1:2.5) models of bridge piers with square cross-

section was performed with the axial load and the hoop spacing as the main variables

[Mander, 1984]. The specimens with closely spaced stirrups showed stable hysteretic

response until displacement ductility uµ = 8 and drift uδ = 3.5% for low axial load,

cN / Afν = = 0.1, and uµ = 6 and uδ = 2.4% for medium axial load, ν = 0.3. The specimen

with large hoop spacing and high axial load, ν = 0.5, showed brittle failure for uµ = 4 and

uδ = 1.4%, whereas the one with medium axial load, ν = 0.3, presented significant loss of

resistance only for uµ = 8 and uδ = 3.3%.

Six piers with circular cross-section, representative of offshore concrete platform legs,

were tested in order to examine different configurations of transverse reinforcement

[Whittaker et al., 1987]. Transverse steel was designed to resist shear demand and various

configurations for confinement reinforcement were studied. The specimens with inner

and outer spirals and closed hoops showed stable response until drift uδ = 4.2%. The

specimens with closed hoops and only outer spirals showed brittle behaviour and smaller

drift capacity, uδ = 1.6%. Finally, the specimens with larger amount of confinement

reinforcement showed ductile behaviour and failed at drift uδ = 2.4%. These results

highlight the importance of correct detailing for the ductile behaviour of piers with

hollow cross-sections.

Six models of circular hollow piers with one layer of longitudinal and spiral

reinforcement placed near the outside face, were tested under cyclic loading [Zahn et al.,

1990]. The examined parameters were the axial load and the thickness of the walls. The

specimens failed in a brittle manner (displacement ductility uµ = 2.4) when the

compression zone comprised the internal face, which was not properly confined. When

the neutral axis was near the internal face, or inside the wall, stable ductile behaviour was

observed until ductility uµ = 7.5. It was concluded that, for this geometry of the cross-

section and reinforcement, ductile behaviour can be achieved for low axial load and for

low amounts of longitudinal reinforcement.


30

Within a large experimental campaign in support of EC8, seven large-scale (1:2.5)

models of rectangular hollow bridge piers were tested under cyclic and seismic loading

[Pinto et al., 1994; Pinto et al., 1996]. The piers were designed according to EC8-2 [CEN,

1994] and therefore conformed to seismic detailing. Piers with different aspect ratios and

tie configurations were tested. All the piers showed stable hysteretic behaviour until

ductility uµ > 5.5 and drift uδ > 2.3%, verifying the detailing criteria of EC8.

Three large-size circular hollow piers with vertical reinforcement only in the external face

were tested under cyclic loading in order to study flexural and shear failure modes and

also the effect of axial load [Ranzo & Priestley, 2000]. The pier with flexural failure

mode exhibited large capacities of displacement ductility, uµ = 6, and drift, uδ = 2.9%.

The specimen with shear-dominated response failed at ductility uµ = 3.5 and drift uδ =

2.5%, while the specimen with axial load ν = 0.15, failed after concrete spalled for

ductility uµ = 2.0 and drift uδ = 1.5%. A comparison of the experimental failure modes

and shear strength to theoretical expressions showed good agreement for the case of these

well-designed piers.

Small-scale models of hollow piers were tested in order to investigate the effect of the

aspect ratio and the amount of transverse reinforcement [Takahashi & Iemura, 2000]. The

tall specimens failed in flexure, whereas the short ones failed in shear. The tall specimen

with closely spaced horizontal reinforcement and crossties in the web, showed stable

behaviour and large drift capacity, uδ = 4.0%. The specimens with small amount of

transverse reinforcement showed rapid loss of resistance and drift uδ = 1.6% or uδ = 3.1%

for short (L/d = 2) and tall (L/d = 4) piers, respectively.

Two scaled specimens (1:3.5) of a rectangular hollow bridge pier were tested in order to

study the effect of lapped splices [Kim et al., 2001]. The specimen with lapped splices

showed stable response until uδ = 4.8%, when failure occurred due to loss of bond and

was associated with rapid loss of resistance. The specimen with continuous reinforcement

showed large deformation capacity, uδ = 7.8%. Failure was due to spalling of concrete

and buckling of steel.

A large number of square hollow bridge piers were tested with the aim of studying the

effect of the concrete compressive strength, axial load, aspect ratio and amount of shear


31

reinforcement [Mo et al., 2001; Mo & Nien; 2002; Yeh et al., 2002a; Yeh et al., 2002b].

All the specimens were detailed with crossties that provided protection against buckling

for all vertical rebars. The specimens with high-strength concrete had 20% higher

strength, but also 10% smaller deformation capacity. The effect of axial force was to

increase the strength and decrease the deformation capacity. On the other hand, larger

amount of horizontal reinforcement resulted in increase of both strength and ductility.

The maximum attained drift was uδ = 6.5% for a square pier with normal strength

concrete, low axial load, ν = 0.08, and adequate shear reinforcement. The smallest

attained drift was uδ = 2.1% for a pier with normal concrete, low axial load, ν = 0.08, and

inadequate shear reinforcement.

Three full-scale circular bridge piers with hollow cross-section were tested in order to

study the effect of shear and lapped splices [Yeh et al., 2001]. The piers were designed

according to modern codes, with the exception of one specimen that was provided with

insufficient horizontal reinforcement and a specimen that was detailed with lapped splices

at the base. The specimen with the lapped splices did not have crossties, in contrast to the

other two specimens. The specimen with seismic detailing showed stable hysteretic

curves until drift uδ = 5.9% and failed in flexure. The one with lapped splices failed

because of loss of bond at drift uδ = 1.6%. Only a few, relatively wide cracks were

observed and a plastic hinge did not fully develop. The pier with insufficient shear

reinforcement failed at uδ = 2.9% due to the combination of shear and flexure.

Eight specimens of rectangular hollow piers were tested with the aim to study the effect

of different tie configurations and concrete compressive strength [Mo et al., 2003]. All

specimens had sufficient shear reinforcement and failed after buckling or rupture of

longitudinal rebars at lateral drift ranging from uδ = 1.9% to uδ = 2.2%. The specimens

with different tie configurations showed similar performance. The spacing of stirrups

significantly affected the degradation after maximum load: specimens with double the tie

spacing had almost half the displacement ductility.

Scaled (1:4) bridge piers with hollow rectangular cross-section and highly confined

boundary element were tested [Hines et al., 2002a; b]. Based on the experimental data on

flexure-dominated specimens, an empirical expression for the calculation of the

equivalent plastic hinge length, that considers the effect of tension shift, was proposed.


32

Tests on shear-dominated specimens allowed updating the existing shear behaviour

models in order to incorporate the effect of flexure, which results in non-parallel shear

cracks. An empirical relation between flexural and shear deformation of piers with

elongated hollow cross-section was also proposed. It was concluded that the force-

deflection behaviour of such piers could be modelled with reasonable accuracy based on

moment-curvature analyses, with assumed plastic hinge lengths, conservative steel strain

limit states and assumed shear displacements that are proportional to the flexural

displacements.

3.2.2. Experimental assessment of piers without seismic design

Concerning existing bridge piers with hollow cross-section, small-scale specimens have

been mainly tested. The differences between bridge piers designed according to early and

modern seismic codes lay mainly in the amount of vertical and horizontal reinforcement,

the presence of confinement reinforcement in the form of closed hoops or crossties, the

splicing of rebars within the potential plastic hinge zone and the premature termination of

longitudinal rebars with insufficient development length.

Scaled (1:5) models of a bridge pier were tested considering different aspect ratios and

development length for the curtailed vertical reinforcement [Kawashima et al., 1990]. All

the specimens with aspect ratio L/d = 5.4 failed in flexure at the base, with the exception

of the one with termination of vertical rebars at mid-height, that failed in flexure at the

cut-off. The specimen with aspect ratio L/d = 9.9 and cut-off at mid-height showed

flexural damage above the critical cross-section and in the end failed in shear. The

specimens with L/d = 9.9 and anchorage of the terminated rebars equal to either the pier

width or half the pier width, both failed in flexure at the base.

A scaled (1:8) model of an existing bridge pier was tested under cyclic load [Huang et al.,

1997]. The model exhibited stable behaviour until ductility uµ = 4 and drift uδ = 1.8%,

after which failure occurred. The failure mode was flexure-dominated, indicated by

spalling of concrete, buckling and rupture of longitudinal reinforcement at the base.

The seismic behaviour of scaled (1:4) hollow piers, representative of existing Italian

bridge structures, was studied [Calvi et al., 2000; Rasulo et al., 2002]. The variables were

the collapse mode, the axial load and the geometry of the specimens, namely vertical


33

reinforcement in one or both of the faces of the cross-section. Specimens with lapped

splices at the base and with 50% reduction of vertical reinforcement at 1/3 of the height

were also tested. Because of the significant effect of shear on the response of the piers, all

specimens failed for low levels of lateral drift, ranging from uδ = 0.8% to uδ = 1.9%.

Comparing the experimental results to theoretical expressions for the strength of

elements, it was concluded that while the response of piers with flexure-dominated

behaviour can be predicted, further study is needed for the case of interaction between

shear and flexure.

From the above discussion some major conclusions are drawn. The presence of closed

stirrups provides adequate confinement to the concrete core and protection of vertical

reinforcement against buckling, resulting in stable response and large deformation

capacity. In addition, the premature termination of vertical reinforcement combined with

the tension shift phenomenon can be the cause of undesirable failure modes. Concerning

modelling, the combination of flexure and shear, as well as the spread of plasticity,

should be appropriately considered.

The mechanical and geometric properties of all the specimens are presented in Appendix

A, along with the deformation capacity in terms of displacement ductility and drift ratio.

Although quite a large scatter in the values of deformation capacity is observed, the

difference between seismic-deficient and retrofitted or code-designed specimens should

be highlighted. The deformation capacity of piers with hollow cross-section is further

discussed in a separate section at the end of the chapter.

3.3. DESIGN OF THE TEST MODELS

3.3.1. Scaling of the specimens

The scaling factor, λ = 2.5, was chosen in order to allow for testing within the capacity of

the laboratory, to facilitate the construction and to use normal concrete and bar diameters.

The similitude law dictates that the stresses in the model, Mσ , are equal to the stresses of

the prototype, Pσ . Then, the similitude relations for other quantities of interest are

presented in Table 3.1. The longitudinal reinforcement of the shaft of the mock-up was

detailed to obtain the flexural capacity corresponding to the scaling of the prototype,


34

while representing as best as possible the interaction between concrete and steel

reinforcing bars. The last condition (overlapping lenght) requires to keep the steel rebar

diameters close to those of the prototype, while at the same time keeping the spacing,

overlapping and anchorage lengths in correspondence to the steel reinforcement diameters

used in both the model and the prototype. Splicing of steel rebars was kept in the model

as close as possible to the prototype: the overlapping lengths were scaled in proportion to

the rebar diameters and the location and distribution of splicing was maintained

throughout the height of the shaft of the model. Transverse reinforcement was detailed in

the model to comply with both the shear capacity and proper spacing in relation to the

longitudinal reinforcement. Concerning shear capacity, the same percentage of transverse

reinforcement was maintained for both the prototype and the model.

3.3.2. Geometry of the specimens

The scaled specimens had a rectangular hollow cross-section with external dimensions

2.74x1.02 m, see Figure 3.2c. The width of the flange and the web was 0.21 m and 0.17

m, respectively. The concrete cover was chosen equal to 0.015 m for easiness of

construction. A rigid steel cap was attached on top of the concrete shafts in order to apply

the horizontal and vertical loads. The total height of the short pier was 6.5 m, L/d = 2.4,

and the total height of the tall pier was 14.00 m, L/d = 5.1. Each model had a foundation

block with dimensions 5.5x2.5x1.2 m, see Figure 3.2. The complete series of construction

drawings for the two piers is given in Appendix B.

Table 3.1. Similitude relationship between the full-scale prototype (P) and the constructed

model (M)

Quantity Label Relationship Quantity Label Relationship

Length L P ML L= λ Acceleration a 1P Ma a−= λ

Area A 2P MA A= λ Force F 2

P MF F= λ

Volume V 2P MV V= λ Time t P Mt t= λ

Mass M 2P MM M= λ Strain ε P Mε = ε

Velocity v P Mv v= λ Stress σ P Mσ = σ


35

Figure 3.2. Geometry of the scaled models of the short (a) and the tall (b) pier and typical

cross-section (c)

Concrete class C35/45 (nominal characteristic cylinder strength ckf = 35 MPa) and steel

class S500 (nominal characteristic yield strength o,2kf = 500 MPa) as defined in Eurocode

2 (EC2) [CEN, 2002], were assumed in accordance to the materials specified for the

prototype pier. Resulting from compression tests on cubic specimens, the average

concrete strength in compression was cf = 38.9 MPa for the short pier and cf = 51.6 MPa

for the tall pier. Standard tests on specimens of reinforcement bars resulted in yield stress

yf = 540.2 MPa, yf = 543.1 MPa and yf = 546.4 MPa, ultimate stress tf = 595.8 MPa, tf =

632.6 MPa and tf = 660.2 MPa and strain at maximum stress uε = 0.149, uε = 0.115 and

uε = 0.065 for F 6, F 10 and F 12 rebars, respectively. The material properties are grouped

in Table 3.2.

The longitudinal reinforcement of the short pier consisted of F 10 deformed bars with

volumetric ratio sρ = 0.4% and the transverse reinforcement consisted of one F 6 bar at

each face of the flange and the web with volumetric ratio wρ = 0.09%. The starter bars

were terminated above the base block and the vertical rebars of the pier shaft were spliced


36

just above the base cross-section and within the potential plastic hinge region. The

overlapping length was 38F , 43F and 50F for different groups of rebars. As seen in

Figure 3.2c and also in Appendix B, no stirrups or closed hoops were placed, according to

the original design of the pier.

The longitudinal reinforcement of the tall pier consisted of F 12 and F 16 bars with

volumetric ratio sρ = 0.7% at the base. The transverse reinforcement consisted of one F 6

bar at each face of the flange and the web with volumetric ratio wρ = 0.09%. The starter

bars were terminated above the base block and the rebars of the pier shaft were spliced

over a length equal to 38F , 47F , 63F and 100F for different groups of rebars. Another

important characteristic of the longitudinal reinforcement, common to piers designed in

the same period, is the bar cut-off, as a result of the linear design and of the absence of

capacity design. At the height of 3.5 m (25% of the total height) from the base of the

scaled specimen (3.5x2.5 = 8.75 m for the prototype) the total amount of longitudinal

reinforcement is reduced by almost 50%; the reduction is 30% for the flange

reinforcement. As a consequence and in combination with the tension shift phenomenon,

discussed further on, the moment capacity of this cross-section is reached before the

flexural resistance of the base cross-section. This resulted in location of the critical cross-

section above the bar cut-off.

Table 3.3 compares the properties of the tested specimens to the provisions of seismic

codes for new bridges in Europe [CEN, 2000; CEN, 2002], the USA [AASHTO, 1995;

ATC, 1996; Caltrans, 1999], New Zealand [SNZ, 1995] and Italy [Ordinanza 3274, 2003]

for the design values of the material properties. Although all codes forbid the splicing of

rebars within the plastic hinge zone, the minimum overlapping length, o,minl , is presented

for comparison. According to EC2 [CEN, 2002], the design lap length, ol , is

Table 3.2. Material properties of the specimens (average values)

Steel Concrete

F (mm) yf (MPa) tf (MPa) uε (%) cf (cubic) (MPa)

6 540.2 595.8 14.9 Short, A70 38.9

10 543.1 632.6 11.5 Tall, A40 51.6

12 546.4 660.2 6.5


37

Table 3.3. Mechanical properties of the specimens and seismic code requirements

mins s,minρ (%) w,minρ (%) o,minl uµ

Short pier 20F 0.4 0.09 38F -50F 3.2

Tall pier 20F 0.7 0.09 38F -100F 2.3

Europe 6F 0.2 0.4 44F 3.51/32

U.S.A. 6F 1.0 0.4 43F 4

N. Zealand 6F 0.8 0.3 45F 63/34

Italy 6F 0.2 0.4 44F 3.51/2.42

1 A40 (L/d = 5.1), 2 A70 (L/d = 2.4), 3 plastic hinge above ground level, 4 not easily

accessible plastic hinge

o 1 2 3 4 5 b s,req s,provl a a a a a l A / A= (3.1)

where 1a , 2a , 3a , 4a and 5a are coefficients considering the effect of confinement by the

concrete cover, non-welded and welded transverse reinforcement, transverse pressure and

percentage of lapped rebars at the same cross-section, s,reqA and s,provA are respectively

the areas of required and provided vertical reinforcement and bl is the basic anchorage

length

b yd bdl ( / 4)f / f= Φ (3.2)

where Φ is the bar diameter, ydf is the design yield stress of steel and bdf is the design

value of the ultimate bond stress. According to the ATC-32 Report [ATC, 1996] the lap

length is

'b yd cl 0.04 f / f= Φ (3.3)

where ydf is the yield stress of steel (in psi) and 'cf is the concrete stress (in psi). In the

New Zealand Standards a similar expression is used for the basic development length of

flexural reinforcement in tension

'b a y cl 0.5 f / f= α Φ (3.4)


38

where aα is a parameter considering the position of the rebar in the cross-section, yf and

'cf are measured in MPa. A different expression is used for diameters bigger than 32 mm.

All seismic codes demand the use of closed hoops or crossties for confinement of

concrete and protection of vertical reinforcement against buckling. Both piers fall short of

the requirements for seismic detailing. The most noteworthy difference concerns the

amount, wρ , and spacing, s, of transverse reinforcement that control the seismic

performance of members.

3.3.3. Test set-up and instrumentation

The horizontal displacement was applied by means of two hydraulic actuators of 1 MN

capacity each. The actuators were attached in one end to the laboratory reaction wall and

in the other to a rigid steel cap on top of the specimen. No torsion was allowed. Each

piston was equipped with a load cell and a displacement transducer. In addition,

displacement transducers mounted on an independent reference frame measured the

displacement of each horizontal actuator. The axial load was applied by means of 8 post-

tensioned rods anchored in the base block and attached to hydraulic actuators, positioned

on the steel cap, at the other end. The vertical actuators were controlled to apply constant

axial force during the test. A general view of the piers in the laboratory is given in Figure

C.2.

The instrumentation of the specimens consisted of a set of displacement transducers and

inclinometers, see Figure 3.3. The displacement transducers were arranged as a truss on

one face of the piers. Vertical displacement transducers placed in correspondence to the

flanges, shown in red in Figure 3.3, were used to measure the average slice rotation.

Diagonal displacement transducers, shown in green in Figure 3.3, were used to measure

the shear deformation of the slices. Additional horizontal displacement transducers were

used to form a statically indeterminate truss. Using the readings of the transducers,

relative displacements of the members of the truss, the absolute displacement of the nodes

of the truss can be calculated. More transducers were used in the lower part of the piers,

where significant deformation was expected, and less in the upper part, where elastic

behaviour was expected.

The vertical transducers were used to calculate the rotation, iΘ , of each slice


39

Figure 3.3. Instrumentation of the short (a) and the tall (b) pier

i l r i c( ) / LΘ = ∆ − ∆ (3.5)

where l∆ and r∆ are the vertical displacements measured at the ends of the slice and cL

is the horizontal distance between the transducers’ axes. Additional vertical displacement

transducers were placed within the first 1 m from the base of the pier on both flanges. The

average slice curvature was then computed by dividing the slice rotation by the slice

length, iL . The total rotation at the top of slice i was computed as the sum of the slice

rotations

i kθ = Θ∑ (3.6)

The flexural displacement at the top of each slice, ix , was then calculated as

i i 1 i ix x L−= + θ (3.7)


40

For the short pier, A70, the total absolute displacement at the top of each slice was

obtained using the measurements of the horizontal displacement transducers connected to

a rigid bar hinged at both the base and the top; the top followed the pier top displacement.

The shear displacement was finally computed as the difference between the total and

flexural displacement. The truss of horizontal, vertical and diagonal displacement

transducers placed on the web throughout the height of the specimens was also used to

calculate the absolute horizontal and vertical displacement of its nodes. As both systems

gave consistent results, only the truss of transducers was used for the tall pier, A40.

A set of inclinometers, shown as black squares in Figure 3.3, was provided along the

height of the bridge pier. Additional inclinometers were placed along the length of the

second slice to measure the deformation in the web.

3.4. CYCLIC TEST ON A MODEL OF A SHORT BRIDGE PIER

3.4.1. Experimental results

A constant axial load, N = 3820 kN, corresponding to a normalised axial load ν = 0.09,

was imposed on the top of the specimen. The displacement history consisted of one cycle

of 2 mm, one cycle of 9 mm, two cycles of 27 mm, two cycles of 56 mm and one cycle of

100 mm in the strong direction.

Force-displacement diagram and observed damage

The force-displacement diagram is presented in Figure 3.4. As explained in the following,

a trilinear skeleton curve is used to approximate the experimental curve. Based on the

trilinear approximation, the yield displacement is identified as y,tu = 0.025 m and the

displacement ductility is u,tµ =3.2. The drift capacity was uδ = 1.5%.

For the first cycles of displacement 27 mm, flexural cracks appeared in the flanges within

the first 0.5 m of the pier height. With increasing displacement a crack appeared at the

interface with the foundation block and extended throughout the flange. A horizontal

crack appeared above the lapped splices at 0.5 m from the base. For the following cycles

some diagonal cracks appeared and the existing flexural ones extended. Spalling of

concrete was observed at the corners within the first 0.1m from the base, corresponding to


41

the spacing of the horizontal reinforcement. Finally, failure of the specimen was attained

when the vertical rebars at the base collapsed after buckling in previous cycles. The

failure mode was due to flexure, with some evidence of loss of bond between concrete

and steel. Figures 3.5 and C.3 present the crack pattern after the end of the test: green

colour corresponds to the cycles with amplitude 27 mm, whereas red colour corresponds

to the cycles with amplitude 56 mm and 100 mm. In is noted that the direction of testing

was in the East-West direction (strong direction of the cross-section).

-1500

-1000

-500

0

500

1000

1500

-0.10 -0.05 0.00 0.05 0.10

Displacement (m)

Forc

e (k

N)

Figure 3.4. Cyclic test on the short pier: force-displacement curve

Figure 3.5. Cyclic test on the short pier: crack pattern at the end of the test


42

On the definition of yield displacement

Displacement ductility is often used as a measure of the deformation capacity of

structures and elements. The value of ductility strongly depends on the yield and ultimate

displacements, which, in turn, are difficult to define. Indeed, the term ‘nominal’ yield

seems more appropriate. According to EC8-1 [CEN, 2003a], the global force-

displacement curve for buildings can be approximated by an idealised elasto-plastic

relationship: the yield force is equal to the force at the formation of the plastic mechanism

and the areas below the idealised and actual force-displacement curves are equal. For the

case of bridges, EC8-2 [CEN, 2002] assumes a bilinear equivalent curve, which best

approximates the actual force-displacement curve, and has an elastic stiffness equal to the

secant stiffness at the theoretical yield point.

Several definitions have been proposed for the yield displacement based on experimental

results, considering always a bilinear equivalent system [Park, 1989]. The yield

displacement can be the displacement when yielding first occurs at the system, the yield

displacement of an elasto-plastic system with the same elastic stiffness and ultimate load

as the real system, the yield displacement of an equivalent system with the same energy

dissipation as the real system or the yield displacement of an equivalent system with

reduced elastic stiffness. Following a similar proposal [Priestley et al., 1996], the yield

displacement is defined by extrapolating the elastic response up to the strength of the

structure or component.

An alternative approach is given in the ATC Report on Seismic Evaluation and Retrofit of

Concrete Buildings [ATC, 1996]. The value of the post-elastic stiffness, sK , is

considered to be an average stiffness in the range in which the structure strength has

levelled off. The yield force, yF , is defined by the intersection of the sK and eK lines,

where eK is the elastic stiffness. Then, the effective stiffness is a secant line passing

through the point of the experimental curve corresponding to 0.6 yF . This procedure

requires trial and error iterations.

An equivalent elastic-perfectly plastic system can be considered, where the initial

stiffness is calculated at the point of intersection of the line from the origin to 75% of the


43

ultimate load with the actual force-displacement curve [Elnashai & McClure, 1995]. The

plastic load of the equivalent system is the ultimate load of the inelastic system.

Using experimental data, the yield displacement can be calculated by extrapolating a

straight line from the origin through the moment-displacement point at 0.75 iM to the

theoretical flexural strength, iM [Priestley & Park, 1987; Sommer, 2000].

Alternatively, the bilinear curve is determined by considering the same post-yielding

stiffness and equal energy to failure [Reinhorn, 1997]. The post-elastic stiffness is again

approximated as a line representative of the actual force-displacement curve.

The ultimate displacement is defined as the post-peak displacement when the load

carrying capacity is reduced by more than 20%, or when buckling or rupture of steel

occurs, whichever is smaller [Park, 1989].

Although it is recognised that the initial stiffness, the yielding level and the post-yielding

stiffness are the important parameters that characterise the inelastic behaviour, no precise

guidelines are given for the estimation of these parameters. A unique definition for the

yield displacement does not exist: the post-yield stiffness is approximated by judgment

and the yield force varies from 60% to 100% of the member strength. Values ranging

from 67% to 78% have been proposed for reinforced concrete (RC) shear wall elements,

depending on the geometry of the cross-section [Paulay, 2002].

The standard definition of ductility was found not to accurately describe the performance

of brittle members (namely coupling beams) and in certain cases to be misleading, while

an energy-based ductility was more appropriate. The energy-based ductility is the ratio of

the ‘ultimate’ to the ‘yield’ energy of the system. The ‘ultimate’ energy is equal to the

area of the last force-displacement semi-cycle at failure and the ‘yield’ energy is equal to

the area of the first semi-cycle at yielding. It was then proposed to describe the

performance of elements through a combination of ductility criteria [Tassios et al., 1996].

It is important to notice that the aforementioned definitions consider a priori an equivalent

bilinear system. In addition, these procedures are design-oriented and therefore, the

strongly non-linear response of elements from the onset of cracking until the development

of a mechanism is of little interest for the calculation of the design forces and

displacements. Looking at experimental data, a bilinear equivalent system is realistic for


44

specimens with low height-to-depth ratio, often d/b = 1, and vertical reinforcement

concentrated near the most stressed fibre. For the piers presented herein, with elongated

cross-section, d/b = 2.7, and distributed reinforcement in the web, see Figure 3.2c, a

trilinear envelope is more realistic.

Consider an elasto-plastic equivalent system for the short pier, A70. A low post-yield

stiffness results from the experimental curve, consequently elastic-perfectly plastic

behaviour can be assumed. maxF being the maximum force and considering the secant

stiffness at the point of the experimental curve corresponding to 0.75 maxF , the yield

displacement is calculated as y,bu =0.01 m and the displacement ductility is u,bµ =8 (the

index b stands for bilinear). The bilinear curve is plotted along with the experimental one

in Figure 3.6: the bilinear curve is a poor approximation of the experimental envelope in

the region between cracking and maximum resistance. Alternatively, by extrapolating the

linear behaviour until the maximum strength, the yield displacement is calculated as

y,bu =0.008 m and the displacement ductility is then u,bµ =10. Such high values of

ductility capacity are unrealistic. Following the definition of ductility given in EC8, one

obtains y,EC8u = 0.015 m and then u,EC8µ = 5.3 (the index EC8 stands for the definition

according to EC8).

The vertical reinforcement of the short pier A70 is almost equally distributed throughout

the web, similarly to shear wall elements. Therefore, the rebars of the web, and not only

those of the flange, contribute to the strength. The sequence of physical phenomena that

occur with increasing displacement is: cracking, yielding of the external series of vertical

rebars of the flange (first yielding - y1u ), yielding of the internal series of vertical rebars

of the flange, progressive yielding of the vertical rebars of the web, fluctuation of the

neutral axis until stabilization (total yielding - yu ), crushing of concrete and buckling of

reinforcement, rupture of vertical rebars, failure - uu .

A trilinear envelope curve, also shown in Figure 3.6, is a better approximation of the

experimental curve. The first branch is defined by the secant stiffness at 0.75 maxF and

corresponds to essentially linear behaviour before first yielding and initiation of cracking.

The third branch corresponds to the part after the resistance has levelled off, identified by

the stabilization of the tangent stiffness. Then, the second branch, which corresponds to


45

the progressive yielding and cracking, is a linear approximation of the experimental

curve. Following these rules, the yield displacement is identified as y,tu =0.025 m and the

displacement ductility is u,tµ =3.2 (the index t stands for the trilinear envelope).

The apparent large ductility capacity, u,bµ =8, is also due to the small number of cycles

the tested specimens experienced. Following EC8-2 [CEN, 2002], ductility is defined for

the ultimate displacement at which the structure can undergo five cycles without initiation

of failure of the confining reinforcement or loss of strength more than 30%. As observed

from the results of numerical simulations, see Chapter 5, the short pier shows a loss of

strength of almost 30% for the fourth cycle at u = 0.04 m, therefore the ductility should be

u,bµ < 4 and u,tµ < 1.6. These values are consistent with the low deformation capacity of

the pier, as defined by lateral drift. It seems, then, that ductility alone cannot fully

describe the deformation capacity of elements. For this reason, in the following

comparisons will be made mainly on the basis of lateral drift.

-1500

-1000

-500

0

500

1000

1500

-0.10 -0.05 0.00 0.05 0.10

Displacement (m)

For

ce (k

N)

experimentalbilineartrilinear

Figure 3.6. Cyclic test on the short pier: experimental and envelop force-displacement

curves


46

0

1

2

3

4

5

6

7

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Hei

ght (

m)

shear flexure 0.1% drift

0

1

2

3

4

5

6

7

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Hei

ght (

m)


0

1

2

3

4

5

6

7

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Hei

ght (

m)


0

1

2

3

4

5

6

7

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Hei

ght (

m)


Figure 3.7. Cyclic test on the short pier: flexural and shear displacement

Flexural and shear deformation

The flexural and shear deformation was computed from the measurements of the

displacement transducers, as explained before. Figure 3.7 presents the shear and flexural

deformation along the height of the pier model for increasing values of lateral drift.

Although the pier had a relatively small aspect ratio, L/d = 2.4, it showed a prevailing

flexural response. This is consistent with the observed damage (few diagonal cracks,

concentration of deformation demand at the base, failure due to rupture of vertical

reinforcement) and was due to the small amount of longitudinal reinforcement and to the

presence of lapped splices at the base of the pier. In fact, this resulted in a weak interface

between the pier and foundation, with most of the rotation concentrated there.

The ratio of shear to flexural displacement at the maximum positive and negative

displacement excursions ranges from 0.3 to 0.4. In agreement with the observed damage

and experimental plastic hinge length, the ratio is in the order of 0.5 within the first 1.0 m

from the base of the specimen and reduces to about 0.1 in the upper part of the specimen.


47

The average value for all cycles is 0.35. This value is in quite good agreement with the

values 0.25 and 0.3 experimentally measured from tests on scaled models of rectangular

hollow bridge piers with highly confined boundary elements [Hines et al., 2002a]. It

points out that shear has a significant contribution to the total displacement of piers with

elongated hollow cross-section.

Equivalent plastic hinge length

Before a member reaches the yield deformation, the distribution of curvature is linear

along its length. With increasing displacement, plastic deformation is concentrated in a

small portion of the element, the plastic hinge, and the curvature follows a parabolic

distribution along the height of the element. For reasons of simplicity, it can be assumed

that the maximum curvature remains constant within an equivalent plastic hinge length,

and then the curvature follows a linear distribution. Among the expressions proposed for

the length of the equivalent plastic hinge, hL , EC8-2 [CEN, 2002] suggests

d)6.04.0(Lh −= (3.8)

and

h ykL 0.08L 0.022 f= + Φ (3.9)

Considering a cantilever of length L with a triangular distribution of moments, it writes

sysuhyu f/f)LL/(LM/M ≈−= , where uM and yM are, respectively, the maximum and

yield moments of the cross-section. For the commonly-used value sysu f/f = 1.15, it

follows that L13.0Lh = , which is similar to the first term at the right part of Equation

3.9.

A modification of Equation 3.9 is introduced in EC8-3 [CEN, 2003b] for the estimation

of the equivalent plastic hinge length of columns and beams in existing buildings

h sl y

1L 0.08L f

60= + α Φ (3.10)

where slα is equal to 1 if there is slippage of vertical reinforcement and 0 otherwise and

yf is the estimated yield strength of steel.


48

A widely used expression for the estimation of the equivalent plastic hinge length is

[Pauley & Priestley, 1992]

hL 0.08L 6= + Φ (3.11)

Based on experimental observations of ductile columns with hollow cross-section, it has

been proposed to estimate the equivalent plastic hinge length as [Mander, 1984]

hL 0.4d= (3.12)

Piers with hollow cross-section and distributed reinforcement can be considered similar to

wall elements. For this case, the expressions

h wL 0.2l 0.044L= + (3.13)

and

Wh l)8.03.0(L −= (3.14)

have been proposed [Paulay & Priestley, 1992]. Also for wall-type elements, an

estimation of the plastic hinge length is [Wallace and Moehle, 1992]

Wh l)0.15.0(L −= (3.15)

In the above expressions wl is the length of the wall, L is the length of the pier, Φ is the

diameter of the longitudinal rebars, yf is the yield stress of steel and d is the section

depth.

Based on numerical parametric analyses, a formulation for the plastic hinge length has

been proposed, that considers the contribution of plastic rotation, IhL , and the

contribution of fixed end rotation, IIhL , according to the equations [Ceroni et al., 2003]

83.132/65.0yt

43.0Ih )1()1f/f()H/L(1.6L −− ν+ε−= (3.16)

II 0.2h b t yL 5d (f / f 1)= − (3.17)


49

where yf and tf are the yield and maximum stress of steel, e is the ultimate deformation

of steel, ? is the normalised axial load and db is the diameter of the longitudinal rebars.

These expressions were developed for rectangular columns and incorporate the effect of

plasticity spreading through the ratio of ultimate and yield stress of steel.

A modification of Equation 3.9 has been introduced [Hines et al., 2002b] to account for

the effect of tension shift in deep beams. The proposed equation was calibrated on

experimental results on large-scale specimens of bridge piers with rectangular hollow

cross-section and highly confined boundary elements. It takes the form

ykh f022.0d3.0L08.0L Φ++= (3.18)

Based on experimental results, the plastic hinge length, hL , can be calculated using the

expression [Paulay & Priestley, 1992]

p m u h hu ( )L (L 0.5L )= ϕ − ϕ − (3.19)

where pu is the measured plastic displacement, equal to the difference between the

maximum displacement and the yield displacement, mϕ and uϕ are respectively the

values of curvature measured at yield and at maximum displacement.

Table 3.4. Experimental and empirical values of plastic hinge length for the short pier Empirical Experimental

ykf022.0L08.0 Φ+ 0.65 uδ = 0.4% 0.05

(0.4~0.6)d 1.09~1.63 uδ = 0.9% 0.30

0.08L 6+ Φ 0.58 uδ = 1.5% 0.18

sl y

10.08L f

60+ α Φ 0.61

0.4 h 1.10

w0.2l 0.044L+ 0.83

(0.3~0.8) wl 0.80~2.20

I IIh hL L+ 4.71

ykf022.0d3.0L08.0 Φ++ 1.47


50

The values obtained from the empirical expressions are compared to those obtained from

Equation 3.19 for different levels of displacement ductility in Table 3.4. The yield

displacement was defined considering the trilinear equivalent curve. The experimental

values are smaller than the empirical ones for all levels of displacement ductility. The

extremely limited plastic hinge results from the presence of the lapped splices at the base.

The experimental equivalent plastic hinge length was smaller than the overlapping length

and smaller than the empirical values. Note the very large value predicted by Equations

3.16 and 3.17. It is recalled that the design plastic hinge length is used for detailing

purposes (e.g. extent of the critical region) and therefore should be larger than the

experimental value for reasons of safety.

Distribution of curvature

The evolution of average curvature, as measured from the instrumentation, along the

height of the pier for increasing values of drift is presented in Figure 3.8. Until 0.4%

lateral drift, the curvature demand was concentrated at the base of the pier, whereas for

higher values of drift, a significant demand was also observed above the lapped splices, in

accordance with the evolution of cracking pattern observed during the tests. In both cases,

the deformation demand was concentrated in a very thin slice with height in the order of

0.25 m. As stated before, such a small plastic hinge length was due to the presence of

lapped splices just above the base block that did not allow for the development of the

yield stress throughout the whole length of the overlapping bars.

Using the vertical displacement transducers placed on the flange of the specimen, one can

follow the average vertical deformation of the slices along the height of the pier model, as

shown in Figure 3.9 for the first four slices from the base. The first two slices are 0.25 m

high, whereas the next two are 0.5 m high. Note that the overlapping length is 0.50 m and

corresponds to the first two slices. In Figure 3.9 is plotted also the line at ε = 0.0025,

corresponding to the yield deformation of the steel rebars. The rebars near the external

face of the flange at the base reached the yield limit for displacement around y1u = 0.008

m during the first cycle with amplitude 0.009 m, whereas the ones of the third slice

reached the yield limit for displacement around u = 0.04 m during the first cycle with

amplitude 0.056 m. It should be highlighted that the rebars of the second and the fourth

slices did not seem to reach the yield strain. This leads to the conclusion that the


51

longitudinal reinforcement was not allowed to develop the yield stress through the whole

overlapping length.

Damage assessment

Several models have been proposed for the quantification of damage. One of the most

popular, the Park and Ang model [Park & Ang, 1985], defines the damage index by two

parts, one taking into account the maximum deformations experienced and the other

accounting for the cyclic effects. The damage index, DI, is defined as

m u,m y u,mDI u / u dE(F u )= + β∫ (3.20)

where mu is the maximum response deformation, u,mu is the ultimate deformation

capacity in monotonic loading, dE is the incremental dissipated hysteretic energy, yF is

the yield strength and β is a non-negative constant; β = 0.05 for reinforced concrete

components [Park et al., 1987].

0.1% drift

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Curvature (rad/m)

Hei

ght (

m)

0.4% drift

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Curvature (rad/m)

Hei

ght (

m)

0.9% drift

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Curvature (rad/m)

Hei

ght (

m)

1.5% drift

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Curvature (rad/m)

Hei

ght (

m)

Figure 3.8. Cyclic test on the short pier: distribution of average curvature along the height


52

h = 0.125 m

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000Loading step

Stra

in

h = 0.375 m

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000Loading step

Stra

in

h = 0.625

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000Loading step

Stra

in

h = 1.125

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 500 1000 1500 2000Loading step

Stra

in

Figure 3.9. Cyclic test on the short pier: evolution of vertical deformation

Table 3.5. Park & Ang Damage Index [Park & Ang, 1985]

DI Damage Physical appearance

> 1 Collapse Total or partial collapse

0.8 - 1 Severe Extensive crushing of concrete, disclosure of buckled reinforcement

0.3 - 0.5 Moderate Extensive large cracks, spalling of concrete

0.2 – 0.3 Minor Minor cracks, partial crushing of concrete

< 0.2 Slight Sporadic occurrence of cracking

Equation 3.20 yields unity for failure of the component or structure. Five degrees of

damage are associated with different values of DI, as seen in Table 3.5. The evolution of

the Park and Ang Damage Index for the short pier is shown in Figure 3.10, where the

observed damage is also indicated: good agreement between the structural damage and

the calculated values of the damage index is observed.


53

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 500 1000 1500 2000

Loading step

Par

k &

Ang

Dam

age

Inde

x

cracking

rupture of 1st rebar

rupture of rebars

buckling, crushing

Figure 3.10. Cyclic test on the short pier: Park & Ang Damage Index

Table 3.6. Bridge damage and performance assessment [Hose et al., 2000]

Level Damage Repair Performance level Socio-economic

description

I No No Cracking Fully operational

II Minor Possible Yielding Operational

III Moderate Minimum Initialisation of local

mechanism Life safety

IV Major Repair Full development of

local mechanism Near collapse

V Local failure/collapse Replacement Strength degradation Collapse

An attempt was made [Hose et al., 2000] to correlate different values of several damage

indices to different damage levels, see Table 3.6. The relation depends on the behaviour

mode of the structure or component, namely brittle (sudden drop of resistance after the

maximum value), strength-degrading (gradual drop of resistance for increasing

displacement after yielding), and ductile (almost constant resistance for increasing

displacement after yielding). For the test presented herein the behaviour is identified as

ductile.


54

The residual deformation index, RDI, is a function of the inelastic behaviour of the

structure and can be used to estimate damage. It is a non-dimensional index equal to the

ratio of the permanent residual displacement, pu , to the yield displacement, yu ,

according to the expression

p yRDI u / u= (3.21)

The normalised stiffness, kn , quantifies the stiffness degradation. It is equal to the ratio

of the effective stiffness, effK , to the initial stiffness at yielding, oK , according to the

expression

k eff on K / K= (3.22)

where the effective stiffness defines the slope of the equivalent elastic system (secant

stiffness) and can be calculated from the maximum force, F, and the corresponding

displacement, u,

effK F / u= (3.23)

and the initial stiffness can be calculated by the yield force and the yield displacement

o y yK F / u= (3.24)

The plastic rotation, pθ , is defined as the plastic displacement, at a given level divided by

the length of the member

p pu / Lθ = (3.25)

Equivalent damping, eqξ , can be seen as an index of the energy-dissipation capacity and

is defined as the ratio of the dissipated energy in one cycle, ED, to the strain energy of an

equivalent linearly elastic system. It can be calculated using the expression, e.g. [Clough

& Penzien, 1975]

Deq

max max

E2 F u

ξ =π

(3.26)


55

where maxF is the maximum force and maxu is the maximum displacement reached for the

cycle.

Table 3.7 presents the values of the previously defined damage indices for different levels

of displacement ductility. The stiffness degradation, as measured by the normalised

stiffness, increases rapidly for ductility µ > 2; the same applies for the residual

displacement index that measures the inelastic displacement. The values of equivalent

damping do not change significantly with increasing values of displacement ductility:

quite stable, but limited, resources of energy-dissipation capacity are available after

yielding. In general the different damage indices are able to follow the evolution of the

damage state of the specimen.

3.4.2. Comparison to empirical predictions

A comparison is made, in terms of yield displacement and displacement ductility

capacity, between the experimental data and the values predicted using empirical

expressions. Based on the theory of elasticity, we obtain [Paulay & Priestley, 1992]

2y yu L / 3= ϕ (3.27)

u y pu u u= + (3.28)

p u y h hu ( )L (L 0.5L )= ϕ − ϕ − (3.29)

where yϕ and uϕ is the curvature at yield and ultimate capacity respectively, yu and uu

are the yield and ultimate displacement respectively and hL is the plastic hinge length, as

calculated from Equation 3.9, are used to predict the values of displacement at yielding

and failure. The yield curvature can be estimated as [Park & Paulay, 1975]

Table 3.7. Damage assessment of the short pier

tµ bµ δ eqξ kn RDI DI pθ

1.1 2.7 0.4% 11.6% 0.30 0.12 0.30 0.0003

2.3 5.6 0.9% 13.1% 0.15 0.22 0.65 0.0048

3.2 8.0 1.2% 14.8% 0.10 0.42 1.15 0.0089


56

yy (1 k)d

εϕ =

− (3.30)

( ) ( ) ( )y

'tt

2

y

'tct2

y

2'tt 2

14

14

1k

αρ+ρ−

αρβ+ρ+

αρ+ρ= (3.31)

t yt

c

A f

bdfρ = ; c y'

tc

A f

bdfρ = ; y

yo

εα =

ε;

ddc

c =β (3.32)

where y y sf Eε = is the yield strain of steel, tρ and 'tρ are respectively the volumetric

ratios of the tension and the compression reinforcement, oε is the strain at maximum

strength of concrete and cd is the concrete cover. The ultimate curvature is

cmu

ucε

ϕ = (3.33)

where cmε is the ultimate strain of concrete in compression and uc is the height of the

neutral axis at the ultimate curvature. Hollow cross-sections with elongated web, d/b =

2.72/1.02 = 2.7, and longitudinal reinforcement almost equally distributed along the

length of the web can be considered similar to shear wall elements. EC8-1 [CEN, 2003a]

proposes the following expression for the depth of the neutral axis of wall elements at

ultimate curvature

u d v c c oc ( )h b / b= ν + ω (3.34)

d c c cdN / h b fν = ; v sv c c yd cd(A / h b )(f / f )ω = (3.35)

where the axial force, N, and the vertical reinforcement ratio are normalised to the area of

the flange, ch b .

For wall elements the following expression has been proposed for the yield curvature

[Paulay & Priestley, 1992]

y w0.0033 / lϕ = (3.36)

where wl is the length of the wall.


57

Alternative expressions have been proposed for the yield curvature, yield displacement,

equivalent plastic hinge length, plastic displacement and ultimate curvature of shear wall

elements [Wallace & Moehle, 1992]

y w0.0025 / lϕ = (3.37)

2y yu 11 L / 40= ϕ (3.38)

p u y wu 0.5( )Ll= ϕ − ϕ (3.39)

y1 cm

cu w

y2

c w w c

f(0.85 3 '' )

fl

f N[1.50 ( '')-1.25 ']

f l t f

β + ρ εφ =

ρ + ρ ρ + (3.40)

where wt is the width of the wall and lb is a factor defined by ACI-318-89; Figure 3.11

plots the relation between the wall parameters and the available ultimate curvature. The

equivalent plastic hinge length is calculated by Equation 3.15, considering the lower

limit, because closer to the experimental value.

Figure 3.11. Relation between wall parameters and ultimate curvature [Wallace &

Moehle, 1992]


58

Table 3.8. Experimental and empirical displacement for the short pier

Empirical

Experimental Columns1 Walls1 Walls2

cu (mm) 3

y1u (mm) 8

yu (mm) 253/104 14 17 10

pl (m) 0.48 0.64 0.83 1.36

uu (mm) 82.5 207 263 60

µ 3.33/8.04 14.8 15.5 6

δ (%) 1.3 3.2 4.1 0.9

1 [Paulay & Priestley, 1996], 2 [Wallace & Moehle, 1992], 3 trilinear envelope, 4 bilinear

envelope

The results are compared to the experimental values in Table 3.8. While the empirical

expressions predict relatively well the yield displacement, they significantly overestimate

the plastic hinge length, which is conditioned by the lapped splices, and therefore also the

ultimate displacement. The empirical equations do not successfully predict the

deformation capacity of the pier, mainly in terms of the plastic displacement.

3.4.3. Comparison to a squat pier designed according to EC8

General

A comparison is made to a squat pier designed according to EC8 and tested within the

PREC8 research programme [Pinto et al., 1995; Calvi & Pinto, 1996]. The pier had a

rectangular hollow cross-section with external dimensions 1.60x0.80 m and thickness

0.16 m for both the flange and the web. The height of the scaled pier was 2.8 m, which

corresponds to aspect ratio L/d = 1.75. The longitudinal reinforcement was continuous

and the transverse reinforcement consisted of closed hoops. The reinforcement ratio was

sρ = 0.9% and wρ = 0.4% for the vertical and horizontal steel, respectively. Although

shear had a considerable contribution to the deformation of the pier, significant capacity

of ductility, uµ = 6, and drift, uδ = 2.6%, was observed.


59

-1500

-1000

-500

0

500

1000

1500

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

Drift (%)

For

ce (k

N)

A70 PREC8

Figure 3.12. Force-drift diagrams for the short, A70, and the squat, PREC8, piers

The force-drift diagrams for the short and the squat piers are presented in Figure 3.12.

The squat pier had larger drift, ductility and energy-dissipation capacity compared to the

short pier. This was due to the absence of lapped splices from the plastic hinge zone, the

larger reinforcement ratios and the seismic detailing of the transverse reinforcement.

Equivalent damping

The values of equivalent damping are plotted against drift in Figure 3.13 along with trend

lines of the form eq [(1 ( ) ] 5γξ = α + βδ + . For small levels of drift, both piers had similar

dissipation capacities, but the maximum value for the PREC8 pier, eq,PREC8ξ = 19%, was

higher than the one for the short pier A70, eq,A70ξ = 15%. Note that the capacity of pier

A70 was exhausted at drift u,A70δ = 1.5%, while the PREC8 pier exhibited stable capacity

of energy dissipation until almost twice this value, u,PREC8δ = 2.6%.

Several theoretical relations have been proposed for the estimation of equivalent damping

as a function of displacement ductility. These expressions correlate the equivalent

damping, eqξ , of a linear singe degree-of-freedom (SDOF) oscillator to the displacement

ductility, µ. Following an early proposal [Gulkan & Sozen, 1974]. the equivalent

damping, can be calculated as


60

eq 0.02 0.02( 1) /ξ = + µ − µ (3.41)

A large number of theoretical expressions for the estimation of the equivalent damping

can be found in [Iwan & Gates, 1979]. Two methods are used for the determination of the

equivalent damping, either based on harmonic response or based on random response. A

theoretical expression is

eq 2

1 ( -1)(1- )( - 0.5) 0.5 ( -1)

µ αξ =

π µ + α µ (3.42)

for a = 5%.

Based on analysis of column experimental data, the ratio of the dissipated hysteretic

energy to that of an elastic-perfectly plastic hysteretic loop was found to be 0.35

[Priestley, 1993]. By expressing this ratio as a function of displacement ductility, the

equivalent damping is

eq 0.2228(1 1/ )ξ = − µ (3.43) Considering the Takeda model for the

hysteretic behaviour of SDOF RC structures the equivalent damping can be calculated as

[Kowalsky et al., 1994]

eq

0.95(1- - 0.05 )

0.05µ

µξ = +

π (3.44)

A different set of empirical expressions is drawn from experimental data. An empirical

expression, resulting from test data and considering P-d effects for the calculation of the

equivalent damping is [Kowalsky et al., 1994]

eq 0.05 0.39372(1 1/ )ξ = + − µ (3.45)

Alternatively, the equivalent damping of reinforced concrete buildings can be estimated

as [Shimazaki, 2000]

eq 0.05 (1 1/ )ξ = + β − µ (3.46)


61

where the viscous damping index, β , is equal to 0.01 for shear-failure type RC structures,

0.1 for frame type RC structures with shear wall, 0.15 for frame type RC structures with

slippage of reinforcing bar at beam-column joint, 0.2 for frame type RC structures and

0.25 for frame type steel structure.

0

5

10

15

20

0 0.5 1 1.5 2 2.5 3

Drift (%)

Equ

ival

ent d

ampi

ng (%

)

A70 PREC8

Figure 3.13. Equivalent damping – drift for the PREC8 and A70 piers

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12Displacement ductility

Equ

ival

ent d

ampi

ng (%

)

Gulkan & Sozen, 1974Iwan & Gates, 1979Priestley, 1993Kowalsky et al., 1994Kowalsky et al., 1994 Takeda modelShimazaki, 2000A70,experimentalPREC8, experimental

Figure 3.14. Equivalent damping – displacement ductility: theoretical expressions and

experimental values for the PREC8 and A70 piers


62

Figure 3.14 plots the experimental values of equivalent damping for the short, A70, and

the squat, PREC8, piers along with the empirical expressions described above. Ductility

is defined assuming the bilinear envelope. The empirical curves based on the Takeda

model [Kowalsky et al., 1994] and on the elastic-perfectly plastic behaviour [Priestley,

1993] fit well the experimental values for the PREC8 pier, which showed an almost

elastic-perfectly plastic response. On the other hand, the relations that consider pinched

hysteretic response [Shibata & Sozen, 1976; Shimazaki, 2000] are closer to the

experimental values for pier A70, which actually exhibited pinched hysteretic curves, as

seen Figure 3.4. This leads to the conclusion that it is possible to obtain a credible

estimation of the relation between equivalent damping and displacement ductility,

provided that the behaviour of the element is known. In assessment of existing structures

such behaviour is not known, unless detailed analyses are performed.

Damage assessment

A quantitative comparison of the behaviour of the two piers is made in Table 3.9, which

presents several indices of damage corresponding to the final cycles for both piers. The

energy-dissipation capacity, as quantified by the equivalent damping, of the squat pier

increased until eq,PREC8ξ = 18.6% for PREC8δ = 1.3% and remained quite stable until

u,PREC8δ = 2.6%. On the other hand, the energy-dissipation capacity of the short pier

increased until eq,A70ξ = 14.8% for lateral drift u,A70δ = 1.5%, where failure occurred.

Despite the larger stiffness degradation, partly due to the larger number of cycles

sustained by the specimen, the squat pier showed wider hysteretic cycles, as evinced by

the larger values of RDI and pϑ , and almost double the drift capacity of the short pier.

Table 3.9. Comparison of the two piers (values at ultimate displacement) sρ (%) wρ (%) uµ uδ (%) eqξ (%) kn RDI

A70 0.40 0.09 3.20a/8.0b 1.54 14.8c 0.10a/0.16b 2.2a/7.0b

PREC8 0.90 0.40 6.0 2.57 18.6d 0.16 4.4

a trilinear envelope, b bilinear envelope, c d = 1.5%, d d = 1.3%


63

-1000

-750

-500

-250

0

250

500

750

1000

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

Displacement (m)

Forc

e (k

N)

Figure 3.15. Cyclic test on the tall pier: force-displacement curve

Observing the values of Table 3.9, better cyclic behaviour is indicated for the PREC8 pier

by all indices for ductility defined by the trilinear diagram. The damage indices for

ductility defined by the bilinear diagram imply similar or even better performance of pier

A70. This supports the idea that the bilinear envelope might guide to misleading results

and that the trilinear diagram describes better the performance of pier A70.

3.5. CYCLIC TEST ON A MODEL OF A TALL BRIDGE PIER


A constant axial load, N = 4050 kN, corresponding to a normalised axial load ν = 0.10,

was imposed on the top of the specimen. The displacement history consisted of one cycle

of 6 mm, two cycles of 30 mm, two cycles of 70 mm, two cycles of 140 mm and one

cycle of 250 mm in the strong direction.

Force-displacement diagram and observed damage

The force displacement diagram is presented in Figure 3.15. Based on a trilinear envelop

curve, the yield displacement is identified as y,tu = 0.10 m and the displacement ductility


64

is u,tµ = 2.3. For the bilinear skeleton curve, the corresponding values are y,bu = 0.06 m

and u,bµ = 3.7. Following the EC8 definition, the yield displacement is identified as

y,EC8u = 0.07 m and the displacement ductility is then u,EC8µ = 3.3. The drift capacity was

δ = 1.6%, with respect to the base.

The crack pattern at the end of the test is shown in Figures 3.16 and C.4, where green

colour corresponds to the cracks developed during the cycles of 30 mm and 70 mm, while

red colour corresponds to the cracks developed during the cycles of 140 mm and 250 mm.

For the cycles of 30 mm flexural cracks appeared within the first 1.0 m from the base of

the pier. For the cycles of 70 mm the flexural cracking extended up to the height of 3.0 m

from the base. A large horizontal crack at the height of 1.5 m, corresponding to the top of

the lapped splices, was also observed. With increasing amplitude of displacement, cracks

appeared throughout the first 4.0 m of the pier. For the cycles of 140 mm a large

horizontal crack appeared at the critical cross-section at 3.5 m. With further cycling, the

flexural cracking above the critical cross-section increased and diagonal cracks appeared

in the lower part. For the final cycle of 250 mm spalling of concrete occurred at the

corners of the pier at 3.5 m and failure was caused by rupture of vertical rebars at the

flange after buckling. Failure was due to a combination of flexure and shear.

Figure 3.16. Cyclic test on the tall pier: crack pattern at the end of the test


65

The buckling length was equal to almost twice the transverse reinforcement spacing, see

Figure C.8, implying that the horizontal reinforcement, which was not properly anchored,

did not provide sufficient lateral support for the vertical rebars.

For the prototype pier the critical cross-section is at about 9.0 m from the base, not

conforming to the requirement of EC8-3 for accessibility of the plastic hinge region for

inspection and eventual repair and/or strengthening. Similar failure mode has been

reported for rectangular pier models with termination of the longitudinal reinforcement at

mid-height [Kawashima et al., 1990; Ogata & Osada, 2000; Calvi et al., 2000]. Premature

termination of vertical rebars was common practice in Japan before the introduction of

modern seismic codes. Actually, it is reported that failure of the Hanshin Expressway was

triggered by this deficiency [Kawashima, 2000a].

The location of failure can be explained with reference to Figure 3.17. Considering the

equilibrium of a diagonally cracked element with shear reinforcement, one can define the

following forces acting on a cross-section: cF is the compressive force on concrete, tF is

the tension force on longitudinal steel and in addition one can consider the uniformly

distributed inclined forces of the transverse steel (tension forces), wF , and the concrete

strut (compression forces), dF . From equilibrium of these forces and the external axial

load, N, shear force, V, and bending moment, M, we obtain

)cot(cotV5.0z/MN5.0z/)cot(cotVyz/MN5.0F ww1sc α−θ−+−≈α−θ−+−= (3.47)

and

)cot(cotV5.0z/MN5.0z/)cot(cotVyz/MN5.0F ww1st α−θ++≈α−θ++= (3.48)

where w wV F= ∑ is the contribution of the transverse reinforcement to the shear

strength, ϑ is the inclination of the cracks with respect to the element axis, α is the angle

of the transverse reinforcement, s1y is the distance between the reinforcement centreline

and the cross-section centroid and z is the internal lever arm. The last term in the previous

expressions is due to the diagonal shear cracking and is additive to the forces due to pure

bending. It is evident that after the development of diagonal cracks, the tension force

acting on the longitudinal reinforcement is greater than that required to resist the bending

moment alone. This phenomenon is termed tension shift. In EC2 tension shift is taken


66

into consideration by shifting the design moment curve in the unfavourable direction by a

distance 1a

1a z(cot cot ) / 2= ϑ − α (3.49)

which is in agreement with the previous theoretical expressions.

Figure 3.17. Equilibrium of internal forces in diagonally cracked element with shear

reinforcement

02468

10121416

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30Displacement (m)

Hei

ght (

m)


02468

10121416

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30Displacement (m)

Hei

ght (

m)


02468

10121416

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30Displacement (m)

Hei

ght (

m)


02468

10121416

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30Displacement (m)

Hei

ght (

m)


Figure 3.18. Cyclic test on the tall pier: flexural and shear displacement

α θ


67

Flexural and shear deformation

The flexural and shear deformations were computed from the measurements of the

displacement transducers, as explained before. Figure 3.18 presents the shear and flexural

deformation along the height of the scaled model for the maximum displacement of each

cycle. The contribution of shear to the total displacement was consistent with the

observed damage. Throughout the height of the pier and for all levels of lateral drift, the

displacement due to flexure was more than 80% of the total displacement. Note a

difference in the slice above the first lapped splices at 0.75 m from the base, where the

total displacement results from equally shared shear and flexural components. These

values support the need to further study the contribution of shear to the total deformation

of hollow piers, which is not included in simple models.

The mean values, over the height of the specimen, of the ratio of shear to flexural

displacement increase with the amplitude of imposed displacement, namely from 0.16

through 0.19 and 0.33 until 0.51. In accordance with the observed damage, for the cycles

with amplitude 3 mm and 7 mm, the ratio assumes large values, in the order of 0.5, within

the first 1.5 m from the base cross-section. For the cycles with larger amplitude, large

values of the ratio are observed in the part of the pier from the base until the height of 4.5

m. The mean value for all cycles with different amplitudes, 0.3, is in agreement with the

value experimentally measured for piers with highly confined boundary elements [Hines

et al., 2002a]. Nevertheless, it does not seem appropriate to use the mean value for a

magnitude that keeps increasing with displacement. Further studies are needed in order to

provide safe and comprehensive rules.

Distribution of curvature

The evolution of average curvature, as measured from the instrumentation, along the

height of the pier is presented in Figure 3.19 for increasing values of drift. Until 0.5%

drift, the curvature demand was evenly distributed within the first 3 m from the base of

the pier specimen. For increasing levels of lateral drift, the deformation demand was

shifted to the cross-section above the cut-off; a significant curvature demand was also

observed above the first lapped splices.


68

0.2% drift

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

0.5% drift

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

1.0% drift

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

1.6% drift

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

Figure 3.19. Cyclic test on the tall pier: distribution of average curvature along the height

The evolution of vertical deformation of the slices of the tall pier is presented in Figure

3.20, along with the value ε = 0.0025 that corresponds to the yield deformation of steel.

The first two graphs correspond to the lower 0.5 m of the tall pier. The vertical rebars at

the base, close to the external face of the flange, exceeded the yield deformation for the

cycles with amplitude 70 mm. The third graph plots the vertical deformation of the slice

just above the first lapped splices. The vertical rebars reached the yield deformation for

the cycles with amplitude 140 mm, as observed by the deformation demand evident in

Figure 3.19. The last three graphs present the vertical deformation of the pier within a

distance of 1.5 m from the critical cross-section. The longitudinal rebars above the critical

cross-section exceeded the yield deformation for the cycles with amplitude 140 mm and

failed during the cycle of amplitude 250 mm, as they reached deformation above 20%. As

seen in the last graph of Figure 3.20, yielding occurred in the rebars within 1.0 m from the

critical cross-section. This is in agreement with the experimental value of the plastic

hinge length, hL = 0.90 m.


69

h = 0.125 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Stra

in

h = 0.375 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Str

ain

h = 1.25 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Str

ain

h = 3.75 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Str

ain

h = 4.25 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Str

ain

h = 4.75 m

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1000 2000 3000Loading step

Str

ain

Figure 3.20. Cyclic test on the tall pier: evolution of vertical deformation

Equivalent plastic hinge length

The empirical predictions, Equations 3.8-3.18, for the equivalent plastic hinge length are

compared to the values calculated using the instrumentation measurements, Equation

3.19, in Table 3.10. The values predicted by the empirical expressions are in fair

agreement with the experimental ones. Note that, contrary to what was observed on the

short pier, spread of plasticity was allowed above and below the critical cross-section of

the tall pier. Note again the unrealistic value predicted by Equations 3.16 and 3.17.


70

Table 3.10. Experimental and empirical values of plastic hinge length for the tall pier

Empirical Experimental

ykf022.0L08.0 Φ+ 0.92 µ = 1.4 0.95

(0.4~0.6)d 1.09~1.63 µ = 2.3 0.90

0.08L 6+ Φ 0.91

y

10.08L f

60+ Φ 0.95

0.4 h 1.10

w0.2l 0.044L+ 1.16

(0.3~0.8) wl 0.80~2.20

I IIh hL L+ 6.44

ykf022.0d3.0L08.0 Φ++ 1.74

Table 3.11. Damage assessment of the tall pier

tµ bµ δ eqξ kn RDI DI pθ

1.4 2.2 1.0% 9.60% 0.76 0.070 0.6 <<

2.3 3.7 1.6% 13.7% 0.43 0.365 1.2 0.01

Table 3.12. Experimental and empirical displacement for the tall pier

Empirical

Experimental Columns1 Walls1 Walls2

cu (mm) 15

y1u (mm) 20

yu (mm) 1003/624 40 44 30

pl (m) 0.90 0.98 1.0 1.36

uu (mm) 230 520 532 110

uµ 2.33/3.74 13 12.1 3.7

uδ (%) 1.6 3.7 3.8 0.8

1 [Paulay & Priestley, 1996], 2 [Wallace & Moehle, 1992], 3 trilinear, 4 bilinear


71

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 500 1000 1500 2000 2500 3000 3500

Loading step

Par

k &

Ang

Dam

age

Inde

x

cracking

extended cracking

spallingrupture of rebars

Figure 3.21. Cyclic test on the tall pier: Park & Ang Damage Index

Damage assessment

The evolution of the Park and Ang Damage Index is presented in Figure 3.21, where the

observed damage is also indicated. As for the short pier, the Park and Ang Damage Index

follows well the evolution of damage: cracking was indicated at an early stage of the test,

then cracking extended without significant inelastic deformation and only near the end of

the test the element failed after spalling of concrete and rupture of vertical rebars.

The one-parameter damage indicators, defined previously, are presented in Table 3.11 for

the tall pier. All damage indicators follow the evolution of damage of the specimens, but

the limited amount of experimental data prohibits an insightful assessment of the

examined damage indicators.

3.5.2. Comparison to empirical predictions

The experimental results are compared to the results of the empirical expressions of

Equations 3.25-3.36 for the prediction of the yield and ultimate displacement. The

empirical values of displacement are calculated considering only the plastic hinge above

the bar cut-off. As seen in Figures 3.18 and 3.19, inelastic deformation of steel rebars is

indicated also at the base of the pier and at the cross-section above the first lapped splices.


72

The empirical formulae underestimate the yield displacement also because they do not

take into consideration the deformation due to the rotation of the part below the critical

cross-section. The empirical formulae predict a smaller ultimate curvature than the one

developed during the test and consequently a lower ultimate displacement. As discussed

before, they predict fairly well the length of the equivalent plastic hinge. It is important to

remind that these empirical formulae refer mainly to elements with dominating flexural

response. When shear has a significant contribution to the total displacement, it becomes

difficult to estimate the displacement at collapse, as the interaction between flexure and

shear is not fully understood [Calvi & Pavese, 2003].

3.6. PERFORMANCE OF HOLLOW CROSS-SECTION BRIDGE PIERS

3.6.1. Effect of mechanical and geometrical parameters

The experimental data discussed in this chapter constitute a database that can be used for

parametric studies. The database consists of tests on 112 specimens, among which 75%

have rectangular cross-section and the remaining 25% have circular cross-section. 27% of

the specimens in the database are classified as seismic-deficient, while 73% of the

specimens are code-designed. Seismic-deficient piers reflect design procedures without

seismic provisions. Code-designed piers are detailed according to modern seismic codes,

or correspond to retrofitted piers. The complete list of the properties and the deformation

capacities of the piers is given in Appendix A. The population of the examined piers is

certainly not extensive, but the maximum effort was dedicated to collect all the published

material. The limited amount of available data, particularly for seismic-deficient piers,

adds to the importance of the experimental campaign described in this thesis and calls for

further investigation. Anyhow, the amount of available information is a restriction to the

generalisation of the observations made in the following.

The examined parameters are the aspect ratio, amount of transverse reinforcement,

overlapping length and axial load. The deformation capacity is quantified by the lateral

drift ratio, because of the problems related with the definition of displacement ductility.

Figure 3.22 presents the drift capacities of the piers versus the aforementioned parameters

for both seismic-deficient and code-designed bridge piers with hollow cross-section.

Although large scatter is observed in all cases, general trends can be identified.


73

The deformation capacity of bridge piers with hollow cross-section increases with aspect

ratio and transverse steel ratio. As seen in Figures 3.22a and c, the increase is more

pronounced for seismic-deficient piers. This could be due to the fact that existing piers

are susceptible to shear failure, which is controlled by these two parameters. On the other

hand, code-designed piers are detailed in order to develop their full flexural capacity and

sustain large deformations before shear damage occurs. This is visually verified by linear

trend lines and lines defining a lower bound of drift capacity (bold and dotted lines,

respectively, in Figure 3.22).

It is interesting to note that in the presence of lapped splices, the drift capacity is

uδ < 2.0%, almost independently of the overlapping length, Figure 3.22e. As seen also in

Chapter 2 for piers with solid cross-section, it is possible to improve the deformation

capacity of hollow piers with lapped splices by jacketing, but failure will be always due to

loss of bond and the performance would only slightly improve, Figure 3.22f. Therefore,

alternative objectives, e.g. shifting of the critical cross-section, should be examined. As

expected, the deformation capacity decreases with axial load, for both groups of piers,

Figures 3.22g and h. The decrease seems to be more rapid for seismic-deficient piers,

probably because of the inadequate confinement.

To highlight the complexity of interaction between the parameters that affect the

deformation capacity of RC members, an empirical expression is recalled. This

expression was fitted to the results of more than 1000 experimental tests on beams,

columns and walls with flexure-dominated behaviour [Panagiotakos & Fardis, 2001]. The

mean value of the ultimate chord rotation, uθ , of an RC member under cyclic loading is

sx yw c

0.2 0.425f / fs

u st,w c

Lmax(0.01, ')0.3 f 25

max(0.01, ) hαρν ω θ = α ω

(3.50)

where st,wα is a coefficient for the steel of longitudinal rebars, ν is the normalized axial

load, ω and 'ω are, respectively, the mechanical reinforcement ratios of the tension and

compression longitudinal reinforcement, cf is the concrete strength, sL / h is the shear

span, α is a confinement effectiveness factor, sxρ is the transverse steel ratio and ywf is

the yield stress of steel. The coefficient of variation of the ratio of experimental values to

predictions of the empirical relation was 46%.


74

0

2

4

6

8

0 5 10 15

Aspect ratio

Drif

t rat

io (

%)

(a)

0

2

4

6

8

0 5 10 15

Aspect ratio

Drif

t rat

io (

%)

(b)

0

2

4

6

8

0.0 0.5 1.0 1.5 2.0 2.5

Transverse reinforcement ratio (%)

Drif

t rat

io (

%)

(c)

0

2

4

6

8

0.0 0.5 1.0 1.5 2.0 2.5


Drif

t rat

io (

%)

(d)

0

2

4

6

8

0 10 20 30 40

Overlapping length (db)

Drif

t rat

io (

%)

(e)

0

2

4

6

8

0 10 20 30 40

Overlapping lenght (db)

Drif

t rat

io (

%)

(f)

0

2

4

6

8

0.0 0.2 0.4 0.6

Normalised axial load

Drif

t rat

io (

%)

(g)

0

2

4

6

8

0.0 0.2 0.4 0.6


Drif

t rat

io (

%)

(h)

Figure 3.22. Performance of seismic-deficient (left column) and code-designed (right

column) bridge piers with hollow cross-section


75

A general form of this expression is adopted in EC8-3 [CEN, 2003b] and takes the form

sx yw c d

0.2

slu st,w cyc wall c

0.425f / f 100s

max(0.01, ')(1 0.38 )(1 )(1 0.37 )0.3 f

1.7 max(0.01, )

L25 1.45

h

ν

αρ ρ

α ωθ = α − α + − α ⋅ ω

⋅

(3.51)

where cycα is equal to 0 for monotonic and 1 for cyclic loading, slα is equal to 1 if there

is slippage of the longitudinal rebars and 0 if there is not, wallα is equal to 1 for walls and

0 for beams and columns and dρ is the diagonal steel ratio.

3.6.2. Estimation of deformation limits

An attempt is made in this section to exploit the collected experimental data in order to

identify deformation limits for piers with hollow cross-section. The drift ratio is chosen as

the deformation indicator. The drift capacity is presented in Table 3.13 for different

failure modes and two groups of piers, namely seismic-deficient and code-designed.

Failure due to flexure is evidenced by concrete crushing, buckling or failure of

longitudinal rebars, fracture of longitudinal rebars or a combination of the above. Shear

failure is identified by diagonal concrete cracking, loss of bond at the region of lapped

splices and in extreme cases by failure of stirrups. Combined flexural/shear failure mode

corresponds to crushing of concrete and/or buckling of steel with significant shear

damage. The minimum, u,minδ , and mean, uδ , values of drift are presented along with the

number of piers in each group.

Table 3.13. Drift capacity of piers with hollow cross-section

Seismic-deficient Code-designed

No of

specimens u,minδ (%) uδ (%)

No of

specimens u,minδ (%) uδ (%)

Flexure 16 0.9 2.9 57 1.3 3.6

Shear 8 0.8 1.9 10 2.1 3.7

Flexure/Shear 6 1.0 2.1 4 2.4 3.7

All

specimens 30 0.8 2.5 71 1.3 3.6


76

Seismic-deficient hollow piers are shown to have limited deformation capacity, ud =

2.5%. Among them, piers with flexure-dominated failure mode have a somehow

acceptable deformation capacity, uδ = 2.9%, while shear-deficient piers and piers with

combined failure mode have very limited deformation capacity, uδ = 1.9% and uδ = 2.1%,

respectively. These differences are not the same pronounced for the case of code-

designed piers. The mean value of drift capacity is in the order of uδ = 3.6%,

independently of the failure mode. This is because code-designed and retrofitted piers are

able to develop their full flexural capacity and are detailed in order to sustain large

deformations before experiencing shear damage.

As a conclusion, failure of hollow bridge piers without seismic design is expected at uδ =

2.9% or uδ = 1.9% for flexural or shear failure mode, respectively. This demonstrates the

limited deformation capacity and the need to study appropriate retrofit solutions. On the

other hand, code-designed hollow piers are expected to have sufficient deformation

capacity in the order of uδ = 3.6%. This can be used as target value when designing the

retrofit of a deficient pier.

A number of experimental tests on bridge piers with solid cross-section were examined,

as described in Chapter 2. The geometrical and mechanical properties of these piers are

presented in Appendix A, along with their displacement ductility and drift capacities.

Seismic-deficient piers with solid cross-section show limited deformation capacity, uδ =

2.8%, similar to piers with hollow cross-section. Failure in seismic-deficient piers is most

of the times due to limited shear resistance and/or inadequate confinement. These

phenomena result in similar deformation capacities independently of the type of cross-

section (hollow or solid).

On the other hand, code-designed piers with solid cross-section have larger deformation

capacity, uδ = 4.8%. This value is more than 30% higher than the corresponding value for

code-designed piers with hollow cross-section. The database of piers with solid cross-

section contains a number of specimens with large drift capacity, uδ > 7, which contribute

to the higher mean value. These specimens correspond to piers with circular cross-section

designed according to American seismic codes. Apart from a few specimens with heavy


77

retrofit or special concrete, they have mechanical and geometrical properties that are

uniformly distributed in the whole range of values. On the contrary, most of the code-

designed piers with hollow cross-section have low values of aspect ratio and transverse

reinforcement ratio, which possibly explains the smaller deformation capacity.

In addition, confinement plays an important role. Circular hoops or spirals provide very

good confinement for the concrete core in solid circular piers. The effectiveness of

confinement is reduced for hollow piers with rectangular hoops or crossties and even

more for circular hollow piers with confinement reinforcement only on the external face.

In the latter case and when the position of the neutral axis is within the less confined part

of the cross-section, limited deformation capacity and brittle failure are expected. This

behaviour has been experimentally observed [Zahn et al., 1990; Ranzo & Priestley, 2000].

Other factors, such as the mechanical properties of steel, should be considered. Compared

to steel used in Europe, steel used in the USA results in better performance in terms of

plasticity spreading and resistance to buckling [Priestley et al., 1996].

In conclusion, seismic-deficient piers with solid and hollow cross-sections seem to have

similar deformation capacities because of the shear flexural mode. Solid piers with

seismic design seem to have slightly better deformation capacity than their hollow

counterparts. It is however possible, as proved by experimental testing, to obtain very

good seismic performance of hollow piers when sufficient confinement reinforcement is

provided for the whole compression zone in the form of closed hoops.

3.7. CONCLUDING REMARKS

The failure mode of the tested specimens deserves further discussion. Both piers were

designed with neither capacity design considerations nor seismic detailing. As a result,

they failed due to a complex combination of phenomena. Observing the distribution of

curvature demand along the height of the pier models, Figures 3.8 and 3.18, a collapse

mechanism with multiple hinges is evidenced. One plastic hinge forms at the base of the

piers, another initiates above the first lapped splices, and for the tall pier, a third plastic

hinge fully develops above the bar cut-off. Then, flexure, shear (tension shift) and steel-

to-concrete bond phenomena interact in different parts of the piers and at different

magnitudes of lateral displacement and all contribute to the failure mode. The failure


78

mode is flexure-dominated with limited deformation capacity, because of the small

amount of vertical reinforcement and the concentration of deformation in thin slices that

impose large strain on the rebars and lead them to premature failure. In addition, the lack

of protection against buckling results in collapse of the vertical rebars due to low-cycle

fatigue. Due to the large number of existing bridges with the same characteristics, the

response of bridges with multiple hinges has been recognised as a problem that has to be

addressed [Kawashima, 2000a].

The previous observations point to a complex behaviour that will probably obscure

numerical modelling, as well as eventual repair and/or strengthening interventions. With

reference to numerical modelling, the contribution of different phenomena to the failure

mode might prove simplified models to be inadequate, as will be discussed in a following

chapter. As far as retrofit is concerned, the initiation of different failure modes at distinct

levels of lateral displacement calls for the need for a global study that takes into account

possible failure modes that did not appear during the tests. For example, because of the

small amount and inadequate anchorage of horizontal reinforcement and should the

vertical reinforcement ratio have been higher, say equal to the minimum requirements of

modern seismic codes, a more pronounced contribution of shear would have been

expected. Retrofit considerations will also be further discussed in a dedicated chapter.

The comparison between experimental and empirical values for the yield and ultimate

displacement, as well as the equivalent plastic hinge length, is useful for the validation of

the empirical formulae for the case of elements with elongated hollow cross-sections,

distributed reinforcement and lapped splices within the potential plastic hinge region. As

far as yield displacement is concerned, the predictions are in fair agreement with the

experimental values. On the other hand, the ultimate displacement strongly depends on

the equivalent plastic hinge length. For the tall pier and considering the critical cross-

section above the cut-off, the empirical value of the equivalent plastic hinge length was

close enough to the experimental one. For the short pier, where an extremely limited

plastic hinge length was observed, due to the lapped splices that did not allow the yield

stress to develop in the whole overlapping length, the empirical formulae proved

inadequate. For piers with multiple hinges, the contribution of all of them (possibly not

fully developed) must be considered and this further complicates the estimation of the

deformation capacity.


79

These empirical formulae seem valid for hollow cross-sections, but not for members with

lapped splices: they failed to predict the plastic hinge length of the short pier not because

of some phenomenon related to the geometry of the cross-section, but because of the

presence of lapped splices. For members with lapped splices without sufficient

development length and/or confining reinforcement within the plastic hinge zone, the

equivalent plastic hinge length is much smaller than the predicted values.

The contribution of shear to deformation is not taken into consideration by simplified

empirical procedures for the calculation of strength and deformation capacity, with the

exception of a recent proposal [Hines et al., 2002a]. Shear displacement is actually

expected to be an important fraction of the total displacement for piers with elongated

hollow cross-section. For the short pier, A70, which showed a predominantly flexural

behaviour, the ratio of shear to flexural deformation was in the order of 0.3. In the case of

the tall pier, A40, for which shear phenomena were marked and appeared on various parts

of the element, the ratio increased with top displacement and therefore a constant value

cannot be considered.

Figure 3.14 shows that different theoretical or empirical expressions result in significantly

different estimations of damping for significant ductility demand, bµ > 2. The relations

that assume elastic-perfectly plastic response were accurate for the well-designed PREC8

pier, whereas the expressions that assumed pinched hysteretic curves were more suitable

for the short pier, A70, that did not have proper seismic detailing. In innovative

displacement-based design and assessment procedures and also in the design of isolation

systems for existing bridges, an overestimation of the equivalent damping would lead to

unsafe estimate of the spectral displacement, at least in the low period range. The

implication is that the hysteretic behaviour of the pier should be known a priori for the

assessment of existing structures, or should be guaranteed by proper detailing for the

design of new structures.

The importance of seismic detailing, principally of the minimum requirements for the

longitudinal and vertical reinforcement (see Appendix B) is verified by comparing the

behaviour of the existing short pier, A70, to that of the PREC8 pier, designed according

to EC8. As observed also in previous experimental campaigns, the amount of

confinement reinforcement plays a key role in the deformation and energy-dissipation

capacities of piers with hollow cross-sections: lack of adequate confinement results in


80

pinched hysteretic curves. The short pier, A70, had smaller ductility capacity and almost

half the drift capacity of the PREC8 pier.

Considering the definition of displacement ductility, it is concluded that the conventional

procedure based on a bilinear approximation of the envelope force-displacement diagram

leads to very high values of ductility capacity for pier A70, u,bµ = 8.0, which contrasts

with the value u,EC8µ = 5.3 and the limited ductility value, u,tµ = 3.2, calculated from the

yielding displacement corresponding to the stabilization of strength (‘total yielding’). It is

noted that the ductility capacity of the PREC8 pier was µu,PREC8 = 6.0, which, compared to

the values for the short pier, confirms that ductility per se can be misleading or

contradictory as a meaningful parameter of the deformation capacity of elements. On the

contrary, drift and energy-dissipation capacities can fully characterize the cyclic

behaviour of these bridge piers.

The quantification of damage is an important issue when assessing the available capacity

and when deciding on the target capacity for the retrofit of as-built elements. Depending

on the choice of the damage indicator, one might have an incomplete, or unrealistic,

estimation of the deformation capacity of the structure. Actually, the damage indicators

related to a single behaviour parameter, such as stiffness degradation or plastic

displacement, provide information only on the single parameter and not a complete

picture of the damage state of the element. Among the ones examined in this work, the

drift ratio better describes the performance of the piers. A combination of performance

parameters seems more appropriate. In fact, the Park and Ang Damage Index better

correlates with the observed damage, as it takes into consideration both maximum

displacement and dissipated energy. Nevertheless, either experimental or non-linear

numerical investigation is required in order to calculate this damage index.

A database of experimental results on specimens of bridge piers with hollow cross-section

has been built. The limited available information on piers with this geometry adds to the

significance of the research presented in this thesis. Based on the collected information, it

is concluded that hollow piers without seismic design are expected to have limited

deformation capacity, mean values of drift uδ = 2.9% for flexural failure mode and uδ =

1.9% for shear failure mode. These values show that existing bridge piers need upgrading.

On the other hand, hollow piers with sufficient confinement of the compression zone, as


81

guaranteed by modern seismic design, are expected to have stable behaviour and large

deformation capacity, uδ > 3.6%.

These considerations give also a hint on the objectives of retrofit. The first seismic

deficiency that has to be addressed is the limited shear resistance. This can be easily

improved (by additional shear reinforcement) and then failure would be due to flexure

alone. Also in that case, a relatively limited deformation capacity is expected, uδ = 2.9%.

Better performance is expected for piers designed according to modern seismic codes,

due to the effective confinement of the compression zone. Therefore, confinement should

be a target when designing a retrofit intervention. The effectiveness and limitations of

confinement provided by fibre-reinforced polymer jackets will be studied through

extensive numerical studies in Chapter 6.


82

SEISMIC ASSESSMENT OF AN EXISTING HIGHWAY BRIDGE

83

4. SEISMIC ASSESSMENT OF AN EXISTING HIGHWAY BRIDGE

4.1. INTRODUCTION

Severe earthquake-induced damage on bridges, apart from the possible human victims,

results in economic losses in the form of significant repair or replacement costs and

disruption of traffic and transportation. For the above reasons, important bridges, which

are components of lifelines, are required to suffer only minor, repairable damage and to

maintain immediate functionality during the post-earthquake emergency. However, the

greatest part of existing bridges in Europe and other economically advanced areas has

been designed before their seismic response had been fully understood and modern codes

introduced. Consequently, they are expected to show unsatisfactory earthquake

performance because of limited deformation capacity, as well as poor hysteretic

behaviour and to represent a source of risk in earthquake-prone regions. This is verified

by field observations during all the recent destructive earthquakes, such as the 1987

Whittier Narrows earthquake [Gates et al., 1988], the 1989 Loma Prieta earthquake

[Housner & Thiels, 1990], the 1994 Northridge earthquake [Housner & Thiels, 1995] and

the 1995 Hyogo-Ken Nambu (Kobe) earthquake [Seible et al., 1995a; Kawashima &

Unjoh, 1997].

The need to assess the seismic capacity of existing bridge structures has been recognised

[Calvi & Pinto, 1996] and various research documents that contain overall considerations,

e.g. [Priestley et al., 1996; Pinto & Monti, 2000], or propose simplified methods, e.g.

[Fajfar & Gašperšic, 1996; Priestley & Calvi, 1997], have been produced. In the USA the

results of the research have been codified in normative documents, such as the FHWA

Seismic Retrofit Manual [Buckle & Friedland, 1995] and the HAZUS probabilistic

method for earthquake risk assessment [FEMA, 1999]. European codes, namely EC8,

lack such provisions, with the exception of EC8-3 [CEN, 2003b] that refers to building

structures. A possible reason for this is the number of parameters that should be

considered (the most important of which were discussed in Chapter 2) and the scarce

verification of simplified procedures for the assessment of complex bridge structures. For

these reasons, in practice each case is considered separately and general guidelines,

similar to those for the design of new structures, are followed.


84

Figure 4.1. Talübergang Warth Bridge, Austria

As a contribution to the assessment of existing bridge structures, the results of an

experimental campaign are presented in this chapter. Within the VAB research

programme, a series of pseudodynamic (PSD) tests were performed on a large-scale

(1:2.5) model of an existing highway bridge. The project was focused on the Talübergang

Warth Bridge, schematically shown in Figure 4.1, which is considered representative of

European highway bridges. Three PSD tests were performed for input motions with

increasing amplitude.

The objective of the research was, on one hand, to develop and implement the

substructuring technique with non-linear models for the numerical substructure in PSD

testing, referred to in the following as non-linear substructuring. This advance in PSD

testing at the ELSA laboratory allowed for testing of the complete bridge system using

the existing laboratory capacity and reducing considerably the costs of the testing

campaign and set-up (two piers instead of six). On the other hand, the aim was the

seismic assessment of a reinforced concrete (RC) bridge, that presents characteristics

(such as hollow cross-section piers, lapped splices within the potential plastic hinge

region, bar cut-off with insufficient development length of the terminated reinforcement

at not easily accessible heights, low percentage of reinforcement, short overlapping

length, inadequate detailing of horizontal reinforcement and lack of appropriate

confinement reinforcement) commonly found in existing bridges in Europe and Japan

[Hooks et al., 1997]. The contribution of the author to the experimental campaign was

focused on the numerical modelling and exploitation of the test results, therefore these

aspects will be discussed in detail, while the implementation aspects of the testing method

will be briefly recalled.

The PSD testing method is presented first, considering the particular cases of

asynchronous input motion, non-linear substructuring and continuous PSD testing. The


85

pre-test numerical simulations of the PSD tests are presented next and the analytical

results are compared to the experimental ones, as well as to in-situ measurements of the

dynamic properties. The results of three earthquake tests are presented in terms of

hysteretic curves, dissipated energy and deformation demands. Then, the seismic

performance of the bridge is assessed for the different amplitudes of the earthquake

motion and a preliminary estimation of vulnerability curves for the bridge is performed.

The distribution of damage is discussed along with various definitions for irregularity of

bridges. In the last section simplified assessment procedures, both probabilistic and

deterministic, are checked against the experimental results. Introducing a correction for

the given structure, the simplified procedures are applied for the assessment of the bridge

for earthquake demand compatible with the EC8 spectrum for a high-seismicity zone.

4.2. THE PSEUDODYNAMIC TESTING METHOD

4.2.1. The pseudodynamic testing method

A PSD test [Shing & Mahin, 1985; Nakashima et al., 1992; Donéa et al., 1996] is one,

which, although carried out quasi-statically, uses on-line computer calculation and control

together with experimental measurement of the actual properties of the structure to

provide a realistic simulation of the dynamic response. For simulating the earthquake

response of a structure, a record of a real or artificially generated earthquake ground

acceleration history is given as input data to the computer running the PSD algorithm.

The horizontal displacements of the controlled degrees of freedom (DOFs), where the

mass of the structure can be considered to be concentrated, are calculated for a small time

step using a suitable time-integration algorithm. These displacements are then applied to

the tested structure by servo-controlled hydraulic actuators fixed to the reaction wall.

Load cells on the actuators measure the forces necessary to achieve the required

displacements and these structural restoring forces are returned to the computer for use in

the next time step calculation. Because the inertia forces are modelled, there is no need to

perform the test on the real time-scale, thus allowing very large models of structures to be

tested with only a relatively modest hydraulic power requirement.


86

4.2.2. The a-Operator Splitting scheme

Consider the following system of semi-discrete differential equations

Ma Cv r(d) f+ + = (4.1)

which describe the motion of a structure, where a, v and d represent the acceleration,

velocity and displacement vectors, r and f the structural internal and external force

vectors, M and C the mass and damping matrices, respectively. In the case of

synchronous seismic loading, a, v and d represent the motion of the structure in a

reference frame which is relative to the uniform ground motion. The seismic action is

taken into account by means of an inertial contribution to the external force vector

baseMIaf −= (4.2)

where basea is the intensity of the base acceleration and I is a vector that accounts for the

direction of earthquake loading. To solve the system given by Equation 4.1, a numerical

step-by-step integration technique is adopted: in this work it is the so-called α method

implemented by means of an Operator Splitting (OS) technique. This scheme is

unconditionally stable and does not require iterations.

According to the α method [Hilber et al., 1977], the displacement and velocity vectors at

step n + 1 can be written in terms of both the acceleration vector and the previous step

values

n 1 n 1 2 n 1d d t a+ + += + ∆ β% (4.3)

n 1 n n 2 nd d tv 0.5 t (1 2 )a+ = + ∆ + ∆ − β% (4.4)

n 1 n 1 n 1v v t a+ + += + ∆ γ% (4.5)

n 1 n nv v t(1 )a+ = + ∆ − γ% (4.6)

with

2(1 ) / 4β = − α (4.7)


87

(1 2 ) / 2γ = − α (4.8)

for 1 3 0≤ α ≤ and then introduced into the following time discrete system of equilibrium

equations

n 1 n 2 n n 1 n n 1 nMa (1 )Cv Cv (1 )r r (1 )f f+ + + ++ + α − α + + α − α = + α − α (4.9)

This scheme is implicit since n 1d + depends on n 1a + , related to n 1r + , which is a function of n 1d + , and then it implies an iterative procedure. It is however possible to implement the

method without iterating by using an OS method [Combescure & Pegon, 1997], based on

the following approximation of the restoring force n 1r +

)d~

K)d~

(r~(dK)d(r 1nI1n1n1nI1n1n ++++++ −+≈ (4.10)

where IK is a stiffness matrix, generally chosen as close as possible to the elastic one, EK , and in any case, for stability reasons, higher or equal to the current tangent stiffness, TK (d) , of the structure. Note that the digital PSD experimental set-up clearly offers all

what is needed for an accurate measurement of the elastic characteristics of the structure

to be tested or of its current stiffness at the beginning of any test.

All useful quantities being known at time nt , the step-wise operations for reaching the

time n 1 nt t t+ = + ∆ are

(i) Compute (prediction phase) n 1d +% and n 1v +% .

(ii) Apply (control phase) the displacement n 1d +% to the tested (and eventually the

numerical) structure in order to get (measuring phase) the restoring force n 1r +% .

(iii) Solve for an+1 the system of linear equations

n 1 n 1ˆM̂a f+ + +α= (4.11)

where the pseudo-mass matrix M̂ and the pseudo-force vector n 1f̂ + +α are given by

2 IM̂ M t(1 )C t (1 )K= + γ∆ + α + β∆ + α (4.12)


88

and

n 1 a n 1 n n 1 n 2 I nˆ ˆf (1 a)f af ar aCv (1 a)Cfa(?? tC ß? t K )a+ + + += + − + + − + +% % (4.13)

(iv) Compute (correction phase) n 1d + and n 1v + .

Note that the computation, and possibly the factorisation of M̂ , which usually does not

depend on the time, may be performed during the initialisation phase of the algorithm,

before entering the time stepping loop.

4.2.3. The substructuring technique

It is generally not feasible to test structures as large as bridges or offshore platforms.

However, earthquake loading often generates severe damage only in parts of the structure

and the rest of the structure could be modelled via finite elements. Therefore, it is useful

to combine PSD testing of only a part of the structure, the tested substructure, together

with an adequate time-integration of the equations of motion for the model of the rest of

the structure, the modelled substructure. To this purpose a substructuring technique is

proposed [Dermitzakis & Mahin, 1985], considering either synchronous or asynchronous

base motion. The modelled substructure must be approximated by an adequate numerical

model and the time-integration scheme must be applied to its spatially discrete equations

of motion.

The strategy adopted in the past [Pegon & Pinto, 2000] was to run two processes in

parallel. The one responsible for the PSD algorithm applied to the tested structure,

running in the master PSD computer and the other, responsible for the modelled structure,

running in a remote workstation. The communication between these two processes used

standard network capabilities. In the meantime, the experimental side was updated to run

the continuous PSD method, where the motion of the structure is controlled every 1 msec

(10-3 sec).

4.2.4. Substructuring in the case of asynchronous motion

For the PSD tests with asynchronous input motion [Pegon, 1996a], special attention has

been devoted to the mathematical and implementation aspects, which is the object of this


89

section. In fact, the PSD testing with substructuring for asynchronous motion is not a

trivial extension of the case with synchronous motion. The main difficulty at the

mathematical level comes out from the fact that the structure in the laboratory can only be

tested in a reference frame relative to the earthquake motion because its base is always

fixed to the floor. Then, in order to realize a meaningful test on a structure (tested and

modelled substructures) undergoing an asynchronous motion, only physically

unconnected parts of the tested structure can be submitted to different base accelerations.

This condition is easily verified for bridges: the tested substructure consists of a set of

different piers, which do not interact one with the others, apart through the modelled

deck.

Equation 4.1 may describe a relative or an absolute motion. The description with a

relative motion is the most widely used in earthquake engineering. The base of the

structure of interest is considered to be subjected to a uniform base acceleration field

basea . The basic principle of dynamics is expressed in a reference frame, which follows

this ground motion. The motion of the structure is originated by the inertial forces

considered as being part of the external force vector f, see Equation 4.2. The relative

motion description is quite natural since it expresses directly the contribution of the

structure response to the overall motion.

The description with an absolute motion is scarcely used, only when the other approach is

impossible. This is the case of an asynchronous ground motion where the base

acceleration field changes spatially from point to point. The motion of the structure is

now originated by the motion of some of its internal points. In consequence, provision

should be made while performing the discretisation of the structure not to eliminate the

ground connecting DOFs and to subject them to the convenient base acceleration basea .

Clearly, in the case of synchronous motion, both descriptions lead to the same results in

terms of intensive variables (internal stress state, for instance).

4.2.5. The continuous pseudodynamic testing with non-linear substructuring

In the conventional PSD test procedure, the actuator motion (S-ramp phase) is stopped

when the test specimen reaches the target displacement (hold period), so that the reaction

force can be measured and the next target displacement computed. On the contrary, in


90

continuous PSD testing, the servo-controller moves the actuator continuously. The

continuous PSD testing avoids the load relaxation problem and improves the quality of

the results. It allows a considerable reduction of the test duration.

The continuous PSD method is implemented by means of a synchronous process (in

electronics terms: communication to the outside is clock-governed) with short control

period and small time step. This introduces some difficulties for the implementation of

the substructuring technique. First, if the numerical part is complex, the analytical process

is unable to perform even an elastic computation during a control period of the

experimental process. In addition, it is not evident that using the same explicit scheme for

both the experimental and analytical processes would allow to obtain stable results.

Finally, the exchange of information between the two processes should not add a too

large overhead.

The experimental process of the continuous PSD method is synchronous and then unable

to wait for information coming from the analytical process. Thus, a parallel inter-field

procedure should be used. For the simple inter-field procedure, see Figure 4.2a, the

analytical part is advanced with a large time step, t∆ , using, possibly, at each new step

the acceleration, velocity and displacement of the connection points obtained through the

experimental process at the end of the previous large step. On the contrary, the

experimental part uses at each subcycle, tδ , as an additional external force, what was

generated in the analytical part at the end of the previous large time step.

The main drawback of this approach is that the force coming from the numerical part is

not well synchronized with the external loading of the physical model. This delay

introduces damping when the experimental and analytical processes are strongly coupled,

i.e. have similar mass. For the case of the numerical part having bigger mass than the

experimental (representative of bridges with experimental piers and numerical deck),

slowly increasing oscillations, associated with higher frequencies, were observed.

Introducing subcycling in the experimental part does not significantly improve the results

[Pegon & Magonette, 1999].


91

Figure 4.2. Parallel procedures: simple inter-field procedure (a), improved inter-field

procedure (b) and intra-field procedure (c)

An improved scheme is introduced, in which the modelled structure is integrated with a

time step 2? T, see Figure 4.2b. This allows to know the kinematics of the numerical


92

structure one large time step in advance with respect to the tested part. Then, an

approximation of the additional force n 1r + at time n 1t + is known before starting the

subcycling between nt and n 1t + . It is thus possible to drive the experimental structure

with more updated information than with the basic scheme. The force n m / Mr + that is used

in the experimental process at each subcycle level can be simply

n m / M n 1r r+ += (4.14)

However, since nr is also known, it is possible to use both quantities to improve the time-

integration accuracy. The additional force that enters the algorithm for the experimental

substructure can be interpolated as

n m / M n 1 n 1 nr r (1 m / M)( r r )+ + += − − − (4.15)

Using this scheme, improved results are obtained, compared to those obtained with the

simple scheme. However, the method is conditionally stable, depending on the

distribution of mass on the connecting DOFs and on the time step. The error is reduced

when reducing the time step, but convergence is slow. The number of subcycles does not

seem to significantly improve the results [Pegon & Magonette, 2002].

Considering the time-integration schemes for non-linear substructuring, it was found that

explicit schemes can be used for the analytical part only when a small number of DOFs is

involved, whereas implicit schemes depend strongly on the local nature of the problem

and could result in significant local deviations from the medium time step duration

[Pegon & Magonette, 2002].

4.2.6. Implementation for the Talübergang Warth Bridge tests

At the time of testing the inter-field procedures were not yet robust enough to be applied

in large-scale testing of bridge structures. In fact, there was evidence of the instability of

the global problem, which could not be solved within the time frame for the bridge tests.

The instability issue was subsequently tackled using an intra-field partitioned scheme

with different time steps and assuming a kinematic continuity between the subdomains

(numerical and experimental) expressed in terms of velocity [Gravouil & Combescure,

2001; Pegon & Magonette, 2002]. The problem was solved using an intra-field procedure


93

(a unique main process delegating all the tasks to numerical and experimental processes)

rather than an inter-field procedure (two or more processes running in parallel), see

Figure 4.2c. The experimental and numerical parts are advanced in time (subcycling is

introduced in both) and exchange information at the end of the time step, through the

Modelling Master workstation.

The implementation of the substructuring technique for the Talübergang Warth Bridge

PSD tests is schematically presented in Figure 4.3, which includes three main workstation

groups, namely: the Experimental Master, the Physical models and the Numerical models.

The Numerical models group includes the Modelling Master workstation (holding the

linear model of the deck and the lateral DOFs of the piers), which performs the time-

integration of the motion of the whole bridge, using the a-OS scheme. Each pier, either

modelled or tested, is condensed on two DOFs, namely the base and the top displacement.

Obviously, it is the difference of the displacement of these two DOFs that is transmitted

as target to the controller of the pier. The force, which is measured and transferred back to

the numerical process, is then associated to the two DOFs.

As soon as the predicted displacement, d% , see Equation 4.3, is computed, the

displacements to impose to the analytical piers are sent to two other computers

(Modelling Slaves) holding the non-linear model of the piers and using an iterative

process to equilibrate the internal nodes of the discrete model. The displacements to

impose to the experimental piers are sent to the Experimental Master, which in turns

generates the appropriate curve (S-shaped displacement ramp and elongated sustain-level

plateau) to be reached by two controllers, each of them responsible for one experimental

pier.

The communication is implemented in such a way that if the numerical piers require a

large number of iterations at the interior of one step, the controllers of the physical piers

can wait (further small time steps are performed) for the input of the next time step.

Actually, the time required to perform the numerical integration for the substructured

piers was always inferior to that value during the pre-test calculations. When the

analytical piers are equilibrated and the experimental piers attain the target displacement,

the force levels reached at the ends of each pier are transmitted back to the Modelling

Master in order to compute the next displacement. The communication between the

workstations was done via the laboratory local network.


94

Figure 4.3. PSD test with substructuring of the Warth Bridge at the ELSA laboratory

4.3. PRE-TEST NUMERICAL SIMULATION

4.3.1. Numerical models for the substructured piers

In order to reduce the computational demand for the PSD tests and to increase the

robustness of the numerical models and procedures, a simple, yet accurate numerical

model should be used for the substructured piers. The most accurate choice is a refined

tri-dimensional finite element model with realistic constitutive laws for the materials and

the steel-to-concrete interface. Such a model, though, would demand exaggerated

computation time. For this reason, it was decided to use a fibre/Timoshenko beam

element [Guedes et al., 1994] implemented in the finite element code Cast3m [Millard,

1994], as a compromise between accuracy and simplicity. Taking into account the

symmetry of the geometry and the loading, a bi-dimensional (2D) beam element was

used. The constitutive law for concrete fibres was cyclic non-linear, while for the steel

fibres an elasto-plastic model with hardening was considered.


95

The vertical rebars in the specimen were uniformly distributed along the web and were

expected to be under tension gradually as the neutral axis fluctuates. Accordingly, in

order to enable a more realistic representation of the distribution of reinforcement, to

avoid eventual numerical problems and to reduce the computation time during the PSD

tests, the mesh for the cross-section was refined and new elements, with less integration

points, were implemented.

The experimental results discussed in the previous chapter, as well as the results of

numerical simulations using a 2D damage model [Faria et al., 2001; Pouca, 2001], were

used to calibrate the models for the substructured piers. The fibre model was adequate for

the case of the short pier, A70, that had a prevailing flexural behaviour; pier A20 was

expected to show similar behaviour. Concerning the tall pier, A40, the damage model

gave results similar to the experimental ones, while the fibre model was unable to

accurately represent the shear deformation in the lower part of the specimen. Diagonal

cracking caused tension shift that, combined with the bar cut-off and the inadequate

development length of the terminated rebars, dictated that the resisting moment of the

critical cross-section was surpassed before the base cross-section developed its full

strength. Piers A30, A50 and A60 had curtailment of the longitudinal reinforcement and

were therefore expected to show a similar failure mode. In the end, it was decided to use a

fibre model with reduced area of longitudinal reinforcement in the flange above the

critical cross-section for the substructured piers A30, A50 and A60. The amount of

vertical reinforcement for the piers is presented in Table 4.1.

Table 4.1. Longitudinal reinforcement steel ratio and characteristic values of

displacement for the scaled bridge piers

A-A B-B C-C

h (m) sρ (%) h (m) sρ (%) h (m) sρ (%) cu (m) yu (m) uu (m)

A20 2.76 0.9 7.04 0.6 2.12 0.3 0.006 0.065 0.187

A30 3.52 0.7 7.08 0.3 4.96 0.2 0.016 0.038 0.372

A40 1.20 1.0 2.30 0.7 10.5 0.2 0.013 0.081 0.230

A50 1.60 0.7 7.24 0.3 5.56 0.3 0.009 0.044 0.326

A60 1.48 0.8 2.68 0.4 7.84 0.3 0.007 0.043 0.179

A70 6.50 0.4 0.003 0.011 0.100


96

Table 4.1 presents also the displacement at characteristic points, namely cracking ( cu ),

yielding ( yu ) and ultimate capacity ( uu ), as resulting from numerical pushover analysis.

These values will be later used to identify the damage of the numerical piers. The yield

displacement, yu , is identified by assuming an elastic-perfectly plastic equivalent system,

where the initial stiffness is the tangent stiffness at 75% of the maximum force. The

ultimate displacement is the displacement at which the resistance drops by more than

20% or the steel fibres collapse [Park, 1989]. Numerical modelling considerations for the

bridge piers will be further discussed in the following chapter.

4.3.2. Numerical model of the bridge structure

Description of the model

Pre-test dynamic analyses were performed with the aim of predicting the earthquake

response of the bridge. The results of the dynamic analyses were compared to the results

of the numerical simulation of the PSD test in order to assess the ability of the latter to

represent a real earthquake test. In order to better represent the PSD test, the numerical

model of the bridge was accordingly simplified in comparison to the real structure.

The deck was modelled using a Fibre/Timoshenko beam element with the cross-section

schematically shown in Figure 4.4. The height of the scaled model was 2.00 m and the

width of the top and bottom flanges was 5.00 m and 2.48 m, respectively. The area of the

cross-section was A = 1.57 m2. The moments of inertia were yyI = 3.35 m4 and xxI = 3.18

m4 by the vertical and horizontal axes, respectively, and the rotational moment of inertia

was J = 2.72 m4. The deck was considered to remain elastic, in accordance with the

requirements of modern codes [CEN, 2002; Caltrans, 1999] for new bridges and

assumptions commonly used in the design and retrofit of bridges [Priestley et al., 1996].

All 6 DOFs by node have been kept in order to better describe the coupling between

translation, bending and torsion of the deck. Nine elements were used along each span.

A 2D beam model with 3 DOFs by node was adopted for the piers, as discussed in detail

in the next chapter. Each pier was divided into an adequate number of elements along its

height; more elements were used in the region where damage was expected and less

elements near the top of the pier, where the behaviour was expected to be essentially


97

elastic. The number and distribution of the elements was chosen such to obtain reliable

results with the minimum computational demand. The foundation blocks of the piers were

considered to remain elastic and to be fixed along all 3 DOFs. The assumption of

perfectly fixed base was exact for the physical models tested in the lab, but may not be

the case for the real structure due to soil-structure interaction. As stated before, all 6

DOFs per node were considered for the deck, whereas only 3 DOFs per node were

considered for the piers; an adequate connection between the corresponding DOFs of the

deck and the top of the piers was established.

Only the vertical and horizontal forces in the direction of testing, in the transverse bridge

direction, were transmitted between the piers and the deck. The abutments constrained the

displacement in all three axes and the rotation by the bridge axis.

During the PSD test only the DOF at the top of the piers (where the mass of the pier is

considered to be lumped) was controlled, therefore a concentrated external load was

applied on the top of the piers to take into consideration the vertical static forces

transmitted by the deck and the pier self-weight. During the test constant vertical forces

were applied on the physical models of the two piers.

Figure 4.4. Cross-section of the deck


98

The vertical loading can be considered comprising two parts. The first part results from

the mass of the deck. This is the reaction force at the top of the pier computed by an

elastic analysis. The second part results from the self-weight of the piers. Following the

similitude relations in Table 3.1, the stress at the base cross-section of the prototype and

the model should be equal. This means that the stress applied on the model should be

p p M MM g / A 2.5M g / A= =σ , where M denotes the mass of the pier and A the area of the

base cross-section. However, the mass of the pier, corresponding to a stress equal to

M MM g / A , is already present. Then, the vertical force on the physical piers is calculated

based on the mass of the model multiplied by 2.5 – 1 = 1.5.

Damping matrix

The damping matrix was formulated by considering only the contribution of the deck and

assuming a truncated modal damping [Pegon, 1996b] in order to avoid problems related

to rigid body motion in the case of asynchronous loading. This expression of damping is

based on the commonly used Rayleigh damping, see for example [Clough & Penzien,

1993], that consists of two parts, one proportional to the mass of the structure and the

other proportional to the stiffness

o 1C M K= +α α (4.16)

In the modal space, Rayleigh damping takes the form

R RM RK o 1 ii i i

i2 2α α ω

ξ = ξ + ξ = +ω

(4.17)

where iω is the angular frequency of the i-th mode. The proportionality

coefficients oα and 1α are calculated by setting known values of damping to two modes.

Then the values of modal damping for the significant eigenmodes can be calculated from

Equation 4.17. In fact, this simple expression for the damping matrix leads to different

results whether its computation is performed in the absolute or in the relative space,

because the mass matrix in not rank-deficient. In order to overcome this problem, it was

proposed [Pegon, 1996b] to reproduce the Rayleigh damping by means of a truncated

sum of the modal damping, expressed in the physical space using the stiffness matrix. In

this way, the same results are obtained independently from the absolute or relative frame.


99

For the truncated modal damping, the mass-proportional damping is distributed to the n

first modes and then added to the stiffness-proportional damping. In matrix form it writes

n

ii 1

C C−

= ∑ (4.18)

The mass-proportional damping matrix is

Ti i i iC K b K= ψ ψ (4.19)

where ψ contains the eigenvectors and the terms of the diagonal matrix Mb are

i i i ib 2 / k= ξ ω ; i = 1…n (4.20)

In the previous equations, iξ stands for the modal damping ratio, iω denotes the

eigenfrequency and ik represents the modal stiffness corresponding to the i-th mode.

Modal analysis

The numerical model was used to calculate the eigenfrequencies of the bridge structure.

Experimental measurement of the natural frequencies of the bridge structure has been

performed [Flesch et al., 1999; Flesch et al., 2002] by dynamic in-situ tests. The results

are reported in Table 4.2, along with the numerical values. It is reminded that the scaling

factor λ = 2.5 applies to the eigenfrequencies: the values for the model are obtained by

the values for the prototype multiplied by the scaling factor. Since the analytical values

were similar to the experimental ones, the numerical model for the bridge seemed capable

of representing the modal properties of the bridge structure. Figure 4.5 presents the first

eigenmodes of the bridge in the transverse direction.


100

mode 1

mode 2

mode 3

mode 4

mode 5

mode 6

Figure 4.5. Mode shapes of the bridge

Table 4.2. Eigenfrequencies of Warth Bridge

Mode Measured (Hz) Measured (Hz) Calculated (Hz)

1 0.796 0.80 0.9988

2 1.095 1.10 1.2093

3 1.584 1.62 1.6978

4 2.194 2.23 2.2861

5 2.907 2.98 2.7052

6 3.709 3.77 3.1592


101

4.3.3. Input motion

According to modern seismic codes for bridge structures, e.g. EC8-2 [CEN, 2002] and the

Caltrans Seismic Design Criteria [Caltrans, 1999], the spatial variability of the ground

motion must be taken into consideration in the design of long bridges in the presence of

geological discontinuities or marked topographical features. As discussed in Chapter 2,

analytical studies of regular bridges subjected to asynchronous excitation suggest that the

internal forces are in general reduced, in comparison to synchronous input, but in certain

cases, e.g. stiff structures and significant soil amplification, an increase was observed.

Experimental results show the reduction of internal forces and increase in displacements

for an irregular bridge [Calvi & Pinto, 1996; Pinto et al., 1996].

Various models for asynchronous motion, considering the accelerations as samples of a

stochastic process, have been proposed. For the present study, the input motion was

defined by artificial accelerograms, shown in Figure 4.6. Based on the local soil

conditions, different focal depths, distance and source mechanisms, displacement,

velocity and acceleration time histories were calculated [Panza et al., 2001]. Different

accelerograms at the bases of the piers and the abutments were provided for the case of

asynchronous motion. Some treatment of these accelerograms was performed in order to

have a uniform distribution of the time step, null final displacement and velocity, null

average velocity and correct scaling. Loading in the bridge transverse direction alone was

considered. Figure 4.7 presents the elastic response spectra of the input accelerograms,

considering 5% of critical damping.

4.3.4. Numerical simulation of the pseudodynamic tests

The PSD test was numerically simulated in order to validate its representativeness of an

earthquake test. The same model and assumptions considered for the dynamic analysis

were used for the numerical simulation of the PSD tests, with the difference that only the

horizontal forces in the direction of loading were transmitted between the deck and the

piers, since the substructuring method would be applied. In addition, both an implicit

iterative and the a-OS explicit schemes were used for the integration of the equation of

motion. The results of the numerical simulation of the PSD tests were compared to the

results of the dynamic analysis. The same input motion used for the dynamic analysis was


102

used for the numerical simulation of the PSD tests for both the explicit and implicit

iteration schemes.

Abutment Wien

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A50

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A20

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A60

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A30

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A70

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Pier A40

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Abutment Graz

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Time (sec)

Acc

eler

atio

n (g

)

Figure 4.6. Input accelerograms for the abutments and the pier bases (see Figure 4.3 for

abutment and pier labels)


103

Abutment Wien

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)Pier A50

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Pier A20

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Pier A60

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Pier A30

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Pier A70

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Pier A40

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Abutment Graz

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3

Period (sec)

Acc

eler

atio

n (g

)

Figure 4.7. Response spectra of the accelerograms for the nominal earthquake


104

Pier A20

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Pier A50

-0.04-0.03-0.02-0.010.000.010.020.030.04

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Pier A30

-0.050

-0.025

0.000

0.025

0.050

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Pier A60

-0.02

-0.01

0.00

0.01

0.02

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Pier A40

-0.05

-0.03

-0.01

0.01

0.03

0.05

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Pier A70

-0.002

-0.001

0.000

0.001

0.002

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Dynamic OS Implicit

Figure 4.8. Displacement histories for the 0.4xNE test, pre-test numerical analysis

The results of the numerical simulation of the PSD test using the implicit and explicit

schemes for the numerical integration of the equation of motion were similar, see Figure

4.8. There was only a small difference in amplitude at certain time steps that can be

attributed to the numerical approximations of the residual in the a-OS method. In

addition, the results of these numerical simulations were in good agreement with the

results of the dynamic analysis, considered as the reference. Note, however, that the

results of the dynamic analysis were affected by the vertical modes. This was partly due


105

to the concrete constitutive model itself that does not represent perfectly the re-opening

and closing of cracks and to the assumption that the base is infinitely rigid.

The numerical simulation for the nominal earthquake indicated low level of damage for

the bridge piers. In detail, the short pier, A70, remained essentially in the elastic range

and the tall pier, A40, suffered only cracking. This was due to the amplitude and the

frequency content of the generated accelerograms that did not excite too much the

significant modes of the structure. For this reason, it was decided to perform a PSD test

with the given input motion, followed by a test with the input motion multiplied by a

factor equal to 2. The dynamic analyses showed that piers A40 and A70 would be more

heavily damaged. Therefore, it was decided to test physical models of these two and

numerically simulate the remaining piers.

4.4. PSEUDODYNAMIC TESTING OF THE BRIDGE MODEL

4.4.1. Testing programme

Before the main PSD test campaign, small-amplitude static and PSD tests were

performed. The objectives were to verify the communication between the different

workstations used for the control and data acquisition and to check the robustness of the

overall procedure. The amplitude of displacement was controlled not to produce inelastic

deformation of the structure. The check tests are described elsewhere [Pinto et al., 2002].

Three effective earthquake tests were performed. A low-level earthquake (0.4xNE) test

with amplitude 40% of the nominal earthquake was performed first. According to EC8-1,

the seismic action associated with the damage limitation criterion, in other words with the

Serviceability Limit State (SLS), is 0.4 or 0.5 of the design seismic action, depending on

the importance of the structure. Then followed a test for the nominal earthquake

(1.0xNE), corresponding to the Ultimate Limit State (ULS) and defined by the

accelerograms shown in Figure 4.6. Finally, a high-level earthquake (2.0xNE) test,

corresponding to twice the nominal earthquake was performed. After the completion of

the PSD tests a cyclic capacity test was performed on the model of the tall pier, A40; the

short pier, A70, collapsed during the 2.0xNE test. ULS and SLS are used in the sense of

EC8-2 [CEN, 2002], where the ULS is associated to the “non-collapse” requirement for


106

an earthquake with approximately 475 years return period and the SLS is associated to the

“minimisation of damage” requirement for a more frequent earthquake.

At the end of each PSD test the physical piers were brought at zero force; obviously a

residual displacement remained in the piers. The same was applied for the numerical

piers: at the end of the test they were brought at zero force and the residual displacement

was used as initial displacement for the following test. Since for the bilinear constitutive

law for steel no ultimate deformation was provided, at every time step the maximum

plastic deformation of the steel fibres at every cross-section of the numerical piers was

extracted from the results so that a warning would come into view in case failure of a

rebar in a numerical pier should occur. The bilinear constitutive law was adopted in order

to ensure the stability of the iterative processes; it was verified that this simplification did

not significantly affect the response of the structure. The calibration of the numerical

models is further discussed in the following chapter.

4.4.2. Low-level earthquake test

The first effective PSD test was performed for an earthquake input corresponding to the

given accelerograms scaled by 0.4. This scaling factor was chosen so that the effect of the

SLS earthquake could be studied. The force-drift curves are given in Figure 4.9.

For this amplitude of the input earthquake only minor damage, namely cracking, was

observed in the numerical piers. The damage of the numerical piers was estimated on the

basis of the displacement corresponding to cracking and yielding as results from the pre-

test numerical simulation, see Table 4.1. On the other hand, visual inspection of the

physical piers showed slight horizontal cracking within the first 2.5 m of the tall pier,

A40, and no damage in the short pier, A70. The damage pattern of the tall pier after the

end of the test is shown in Figures 4.10 and C.5. It is reminded that displacement was

imposed in the East-West direction.

The amount of energy dissipated by each pier was calculated: for the 0.4xNE test the

largest percentage corresponds to the physical tall pier and the smallest to the physical

short pier that remained essentially elastic during the test. The Park and Ang Damage

Index was calculated, based on the experimental data. The small values of the index

indicate slight damage for all the physical and numerical piers. In accordance with the


107

experimental observations, a very small Damage Index was calculated for the short

physical pier, A70.

The experimental displacement histories are compared to the ones obtained from the pre-

test calculations in Figure 4.11, where good agreement is observed. Only for the short

physical pier, A70, the experimental displacement was of inferior amplitude compared to

the numerical simulation. This was due to the fact that the stiffness of the physical piers

A40 and A70 used in the pre-test numerical simulation corresponded to the numerical

model of the piers and not to the physical models. After performing the first test, the

actual stiffness of the piers could be measured and resulted equal to about 2/3 of the

calculated stiffness. The numerical models were accordingly updated.

Pier A20

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A50

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A30

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A50

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A40

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A70

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Figure 4.9. Force-drift diagrams for the 0.4xNE test


108

Figure 4.10. Damage pattern of the tall pier for the 0.4xNE test

4.4.3. Nominal earthquake test

The following test was performed for the nominal earthquake, always considering

asynchronous motion for each pier and abutment. The residual displacement from the

0.4xNE test was considered as the initial condition for the numerical piers, in order to

represent the damage suffered in the previous earthquake test; residual displacement was

anyway present on the physical piers. The force-drift curves for the physical and

numerical piers are shown in Figure 4.12.

The experimental displacement histories are compared to those calculated from the pre-

test analysis in Figure 4.13: the difference due to the stiffness for this earthquake intensity

was less evident. The displacement histories are in agreement for the first and most

significant part of the accelerogram; near the end of the test, a phase difference is

observed in some piers.


109

Pier A20

-0.050

-0.025

0.000

0.025

0.050

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)Pier A50

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A30

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A60

-0.05

-0.03

0.00

0.03

0.05

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A40

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A70

-0.02

-0.01

0.00

0.01

0.02

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)


numerical (thin line) results

The Park and Ang damage index for the physical and numerical piers was calculated for

the 1.0xNE test. Minor damage, described as cracking, was indicated for all piers. The

distribution of dissipated energy was similar to that for the 0.4xNE test: the largest

percentage corresponds to the tall physical pier, A40, whereas equal percentages are

allocated to the substructured piers. A small percentage was assigned to the short physical

pier, A70, that showed limited damage.


110

Pier A20

-1500

-1000

-500

0

500

1000

1500

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

Drift (%)

For

ce (

kN)

Pier A50

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A30

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A60

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A40

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A70

-1500

-1000

-500

0

500

1000

1500

-1 -0.8 -0.5 -0.3 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Figure 4.12. Force-drift diagrams for the 1.0xNE test

For the 1.0xNE test, the existing cracks of the tall physical pier, A40, extended and new

cracks appeared up to the height of 4 m. A horizontal crack initiated at the height of 3.5 m

where the bar cut-off takes place, see Figure 4.14. For the short physical pier, A70, only

slight horizontal cracks near the base were observed. Based on the force-drift curves and

the pre-test numerical analysis, the damage of the numerical piers was identified as

extended cracking. Only the numerical piers A30 and A50 had maximum displacements

above the values that correspond to the conventional yielding displacement, yu .


111

Pier A20

-0.050

-0.025

0.000

0.025

0.050

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A50

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A30

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A60

-0.050

-0.025

0.000

0.025

0.050

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A40

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A70

-0.01

-0.01

0.00

0.01

0.01

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)



4.4.4. High-level earthquake test

The final PSD test was performed for the input accelerograms times 2. The objective of

this test was to investigate the resistance of the bridge system subjected to a strong

earthquake after having suffered damage due to the ULS earthquake. The force-drift

experimental curves for the physical and numerical piers are presented in Figure 4.15. In

Figure 4.15 significant non-linear deformation and energy dissipation is observed mainly


112

in the physical piers, as predicted by the pre-test analyses. The limited energy dissipation

observed in the substructured piers is not due to some inadequacy of the numerical

models, which were calibrated to simulate as best as possible the cyclic behaviour, but to

the small amplitude of imposed displacement that induced limited inelastic deformation.

This will be further discussed in the following chapter.

The experimental displacement histories are presented in Figure 4.16 along with the

values resulting from the pre-test analysis. The fit in this case is not so good: there is a

phase difference after the first second of the input accelerograms. It is reminded that the

PSD tests were performed one after the other and at the beginning of each test the damage

suffered in the previous one was present. This was not considered in the pre-test

numerical analyses: for each level of the input earthquake the undamaged structure was

analysed.

Figure 4.14. Damage pattern of the tall pier for the 1.0xNE test


113

Pier A20

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A50

-1500

-1000

-500

0

500

1000

1500

-1 -0.8 -0.5 -0.3 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A30

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A60

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1Drift (%)

For

ce (

kN)

Pier A40

-1500

-1000

-500

0

500

1000

1500

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Pier A70

-1500

-1000

-500

0

500

1000

1500

-1 -0.8 -0.5 -0.3 0 0.25 0.5 0.75 1

Drift (%)

For

ce (

kN)

Figure 4.15. Force-drift diagrams for the 2.0xNE earthquake test

For the 2.0xNE test the numerical piers, as well as the tall physical pier, A40, were

already damaged and were able to further deform, without significant additional damage.

Regarding the tall physical pier, A40, the cracks at the lower part extended with a slight

inclination and remained open, while the crack at the height of 3.5 m extended through

the web and spalling of concrete was observed at that cross-section. All the numerical

piers were beyond the yield limit.


114

Pier A20

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A50

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A30

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A60

-0.10

-0.05

0.00

0.05

0.10

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A40

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)

Pier A70

-0.08

-0.04

0.00

0.04

0.08

0 1 2 3 4 5Time (sec)

Dis

plac

emen

t (m

)



Figure 4.17. Damage pattern of the short pier for the 2.0xNE test


115

The short physical pier, A70, was the most heavily strained for this earthquake amplitude:

it had to undergo a large number of cycles at significant levels of displacement. As a

result, a considerable loss of resistance was observed. A horizontal crack developed at the

base (interface with the foundation block) throughout the whole length of the pier. At the

corners the concrete crushed and two vertical rebars collapsed, showing evidence of

buckling. Vertical cracks were observed in the web in correspondence to the lapped

splices. The damage pattern of the short physical pier, A70, after the end of the 2.0xNE

test is presented in Figures 4.17 and C.6.

For the 2.0xNE test the short physical pier, A70, dissipated the largest percentage of

energy; this was consistent with the heavy damage suffered by this pier. Observing the

values of the Park and Ang Damage Index for the 2.0xNE test, the most heavily damaged

piers were the physical A40 and A70. Moderate damage was attributed to pier A40,

corresponding to extensive large cracks and spalling of concrete. For the numerical piers

the damage level was also moderate. For the short pier, A70, the damage level was

identified as severe, corresponding to crushing of concrete and disclosure of buckled

reinforcement. The calculated damage indices were in fair agreement with the observed

damage.

4.4.5. Final collapse test

After the end of the PSD tests, a cyclic test with increasing imposed displacement until

failure was performed on the tall physical pier, A40. The short pier, A70, also physically

present in the lab had already failed, as evidenced by the significant drop of resistance

and by the rupture of vertical reinforcement bars. The objective of the test was to assess

the ultimate capacity of the pier after a number of cycles at significant levels of

displacement.

The displacement history consisted of increasing monotonic displacement, in the presence

of vertical load, until failure. Then, the specimen was unloaded and as some residual

displacement was observed, it was pushed in the opposite direction in order to minimize

the residual displacement once the horizontal loads had been removed. The experimental

force-displacement curve for the final capacity test on the tall pier, A40, is presented in

Figure 4.18.


116

-800

-600

-400

-200

0

200

400

600

800

1000

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Displacement (m)

For

ce (k

N)

Figure 4.18. Final collapse test on the tall pier: force-displacement diagram

Figure 4.19. Damage pattern of the tall pier for the final collapse test

The failure mode of the tall physical pier was as observed for the cyclic test that was

discussed in detail in the previous chapter. Figures 4.19 and C.7 present the crack pattern

after the end of the final capacity test. Green colour corresponds to the cracks observed


117

after the 1.0xNE test, red colour is for the cracks that appeared during the 2.0xNE test,

while black stands for the cracks that developed during the final capacity test. A

horizontal crack had already appeared at the critical cross-section at the bar cut-off during

the 2.0xNE test. During the final capacity test, the existing cracks extended with

significant inclination and a few new ones appeared in the region from 3.0 m until 4.0 m

from the base of the pier. Crushing of concrete and buckling of vertical reinforcement

bars was observed at the corners of the cross-section for both directions of imposed

displacement. Vertical cracking, indicating bar slippage, was observed in the flange above

and below the critical cross-section.

4.5. SEISMIC ASSESSMENT OF THE BRIDGE

4.5.1. Deformation and curvature distribution in the physical piers

The measurements of the instrumentation on the two physical piers were used to split the

flexural and shear deformations, using the procedure outlined in the previous chapter. The

results for the three earthquake tests are presented in Figures 4.20 and 4.21. For the short

pier and the 2.0xNE test, the ratio of shear to flexural displacement is 0.3, which is very

close to the value measured during the quasi-static cyclic test, see 3.4.1. The small

amplitude of displacement and limited damage, the piers remained essentially elastic or

suffered slight cracking, during the previous two tests does not allow a reliable

comparison of flexural and shear displacement.

To what concerns the tall pier, increasing values of the shear to flexural displacement

ratio were measured for the four tests. In detail the ratio was 0.2 for the 0.4xNE and

1.0xNE tests, 0.25 for the 2.0xNE test and 0.6 for the final cyclic capacity test. In

accordance with the damage observed during the PSD tests, shear deformation was a

significant portion of total deformation within the lower part of the pier. Only for the final

capacity test, in which severe damage was observed above the cut-off, shear deformation

was significant also above the critical cross-section.


118

0.4xNE

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Displacement (m)

Hei

ght (

m)

shear flexure

1.0xNE

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Displacement (m)

Hei

ght (

m)

shear flexure

2.0xNE

0

1

2

3

4

5

6

7

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Displacement (m)

Hei

ght (

m)

shear flexure

Figure 4.20. Flexural and shear deformation of the short pier

0.4xNE

02468

10121416

-0.2 -0.1 0.0 0.1 0.2Displacement (m)

Hei

ght (

m)

shear flexure 1.0xNE

02468

10121416

-0.2 -0.1 0.0 0.1 0.2Displacement (m)

Hei

ght (

m)

shear flexure

2.0xNE

02468

10121416

-0.2 -0.1 0.0 0.1 0.2Displacement (m)

Hei

ght (

m)

shear flexure Final cyclic

02468

10121416

-0.2 -0.1 0.0 0.1 0.2Displacement (m)

Hei

ght (

m)

shear flexure

Figure 4.21. Flexural and shear deformation of the tall pier


119

The evolution of average curvature along the height of the short physical pier, A70, is

presented in Figure 4.22 for the three earthquake tests. The curvature demand was

concentrated at the base, where failure was observed. For the 2.0xNE test, that caused

extended damage and collapse of the pier, a notable curvature demand was also observed

at the cross-section just above the first lap-splice. Similar distribution of deformation

demand (concentration at the base) was observed during the cyclic test performed on a

specimen of the same pier, discussed in the previous chapter, and also in previous

experiments on columns with lapped splices [Paulay, 1982; Chai et al., 1991; Park et al.,

1993; Lynn et al., 1996; Xiao & Ma, 1997].

Regarding the tall pier A40, the distribution of curvature varies for the different

amplitudes of the input motion, as seen in Figure 4.23. For the 0.4xNE and 1.0xNE tests,

the curvature demand was quite uniformly distributed within the region up to the height

of about 3.5 m, where the vertical reinforcement was curtailed. For the 2.0xNE and the

final cyclic test the demand was shifted to the critical cross-section above the bar cut-off.

Similar evolution of curvature with increasing displacement was observed during the

cyclic tests on the tall pier, presented in the previous chapter.

4.5.2. Damage assessment

Comparing the maximum attained displacement for each earthquake test to the

characteristic values of Table 4.1, the damage of the bridge piers can be identified, as

reported in Table 4.3. For the SLS earthquake, 0.4xNE test, the bridge suffered only

minor damage: the short pier remained elastic and only slight cracks were observed in the

rest of the piers. At this level of damage no repair is required. For the ULS earthquake,

1.0xNE test, the imposed displacement caused yielding, without significant inelastic

deformation, of the numerical piers A30 and A50. At this level of damage the cracks need

repair. For the high-level and less frequent earthquake, 2.0xNE test, significant damage

was observed in most of the piers that were beyond the yield limit. For the 2.0xNE test,

failure of the vertical reinforcement in the short pier occurred, without causing global

instability problems. The short pier reached its capacity: for consecutive cycles its

resistance dropped and in the end the vertical rebars in the flange failed. The cracks in the

numerical and tall physical piers need repair.


120

0.4xNE

0

1

2

3

4

5

6

7

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

1.0xNE

0

1

2

3

4

5

6

7

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

2.0xNE

0

1

2

3

4

5

6

7

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03Curvature (rad/m)

Hei

ght (

m)

Figure 4.22. Distribution of average curvature along the height of the short pier

0.4xNE

0

2

4

6

8

10

12

14

-0.02 -0.01 0.00 0.01 0.02

Curvature (rad/m)

Hei

ght (

m)

1.0xNE

0

2

4

6

8

10

12

14

-0.02 -0.01 0.00 0.01 0.02

Curvature (rad/m)

Hei

ght (

m)

2.0xNE

0

2

4

6

8

10

12

14

-0.02 -0.01 0.00 0.01 0.02Curvature (rad/m)

Hei

ght (

m)

Final cyclic

0

2

4

6

8

10

12

14

-0.02 -0.01 0.00 0.01 0.02

Curvature (rad/m)

Hei

ght (

m)

Figure 4.23. Distribution of average curvature along the height of the tall pier


121

Table 4.3. Damage of the bridge piers

A20 A30 A40 A50 A60 A70

0.4xNE cracking cracking cracking cracking cracking -

1.0xNE cracking yielding cracking yielding cracking cracking

2.0xNE cracking yielding yielding yielding yielding failure

Table 4.4. Maximum drift and ductility demand for the piers

d (%) µ

A20 A30 A40 A50 A60 A70 A20 A30 A40 A50 A60 A70

0.4xNE 0.16 0.28 0.25 0.20 0.12 0.03 0.3 0.9 0.4 0.7 0.4 0.2 1.0xNE 0.37 0.57 0.44 0.41 0.30 0.13 0.7 1.9 0.8 1.4 0.9 0.7 2.0xNE 0.58 0.88 0.87 0.55 0.41 0.69 1.1 2.9 1.5 1.8 1.1 3.9 Capacity 1.57 2.39 1.43 2.26 1.49 0.69 2.9 9.8 2.5 7.4 4.1 3.9

Table 4.5. Dissipated energy and Damage Index

Dissipated energy (% of total) Park & Ang Damage Index

A20 A30 A40 A50 A60 A70 A20 A30 A40 A50 A60 A70

0.4xNE 7.0 8.2 62.2 13.3 7.4 1.8 0.11 0.10 0.16 0.09 0.09 0.02

1.0xNE 5.8 6.8 57.7 5.8 7.7 16.1 0.24 0.20 0.28 0.19 0.21 0.09

2.0xNE 1.2 1.3 26.2 4.8 2.7 63.8 0.39 0.31 0.56 0.25 0.29 1.00

Table 4.4 presents the maximum drift and ductility demands in the piers for the different

earthquake amplitudes. It is reminded that displacement ductility is defined assuming a

bilinear equivalent system. The first branch is defined by the tangent stiffness at 75% of

the maximum force and zero post-yield stiffness is assumed. For the numerical piers the

monotonic curves resulting from the numerical analyses are used. For the physical piers

the envelop curves of the 2.0xNE and the final collapse test for the short, A70, and the

tall, A40, piers, respectively are used to identify the yielding point and the displacement

capacity. It is interesting to note that for all the numerical piers and the physical tall pier,

the deformation demand/capacity ratio increases almost linearly with the earthquake

intensity, whereas for the short pier, A70, very low values correspond to the 0.4xNE and

1.0xNE tests and the capacity is reached for the 2.0xNE test.

The drift capacities of the piers are extremely limited and significantly lower that the

commonly adopted limit u,minδ = 3%. On the other hand, the values of displacement


122

ductility capacity range between uµ = 2.9 and uµ = 9.8 and then imply a desirable ductile

behaviour. This is inconsistent with the experimental observations and the drift capacities.

In addition, the ratio of maximum attained drift to the drift capacity correlates well with

the observed damage for increasing amplitude of the seismic input, while the same ratio

based on displacement ductility seems misleading. This originates from the conventional

definition of displacement ductility and supports the remark made in the previous chapter

that drift describes better the performance of the tested piers.

The distribution of dissipated energy is presented in Table 4.5. For the 0.4xNE test the

greatest part of the total energy was dissipated by the tall physical and the numerical

piers. The short pier remained almost elastic and dissipated only a small fraction of the

total energy. Similar distribution was observed also for the 1.0xNE test, with the

difference that the short physical pier dissipated a significant part of the total energy. The

distribution changed for the 2.0xNE test: the short pier dissipated the largest percentage

of energy. It is reminded that the short pier suffered the heaviest damage during the

2.0xNE test and in the end collapsed.

The Park and Ang Damage Index is also presented in Table 4.5 for all the piers and the

different earthquake amplitudes. For the 0.4xNE test slight damage (sporadic cracking) is

identified for all the piers. For the 1.0xNE test slight damage is predicted for piers A50

and A70 and minor damage (minor cracks and partial crushing of concrete) for the

remaining piers. Finally, for the 2.0xNE test minor damage corresponds to piers A50 and

A60, moderate damage (large cracks and concrete spalling) to piers A20 and A30, severe

damage (concrete crushing and steel buckling) to pier A40 and collapse to pier A70. The

calculated damage level is in general confirmed by the observations on the physical and

numerical piers after the end of each PSD test.

4.5.3. Overall damage index

Having established different damage indices for the substructures (bridge piers), an

extension to the whole structure (bridge) would provide a quantitative assessment of the

overall damage level. A number of alternative procedures for the estimation of overall

damage indices for buildings exist, e.g. [Powell & Allahabadi, 1988]. These procedures

apply provided that the distribution of damage is uniform throughout the structure; this


123

was not the case for the tested bridge. When the damage index is computed for the

substructures, an adequate combination can provide an overall damage index, tDI . The

latter is estimated as a weighted mean of the damage indices of the substructures

according to the expression

i it

i

w DIDI

w= ∑

∑ (4.21)

where iDI is the damage index and iw is the weight assigned to the i-th substructure.

The weight, iw , is a measure of the importance of the substructure for the structural

integrity. For the case of bridges, all piers are of the same importance for the structural

integrity. Due to the low statical indeterminacy, collapse of any single pier corresponds to

total or partial collapse of the bridge structure. Nevertheless, equal weight cannot be

attributed to the piers. The implication is that for the 2.0xNE test that caused collapse of

the short pier, and consequently failure of the bridge system, the overall damage index

would be smaller than the value that indicates collapse, as affected by the slightly

damaged remaining five piers. It seems, therefore, more realistic to use a weighting factor

proportional to the damage index of each substructure [Park et al., 1987]. The overall

damage index is then

2i

ti

DIDI

DI= ∑

∑ (4.22)

Alternatively, the Park and Ang damage index [Park & Ang, 1985] for buildings defines

the overall damage index as the weighted sum of the indices for each substructure

(storey), according to the expression

t i iDI w DI= ∑ (4.23)

where the weighting factor is calculated on the basis of the dissipated energy of each

substructure, iE , and is given by the expression

i i iw E E= ∑ (4.24)


124

Table 4.6. Overall Park and Ang Damage Index

Damage-based weight Energy-based weight

0.4xNE 0.11 0.13

1.0xNE 0.22 0.23

2.0xNE 0.61 0.81

The same procedures can be applied using the experimental results for the bridge

structure and considering the piers as the substructures. The deck being considered

elastic, does not suffer any damage and therefore does not contribute to the estimation of

the damage of the whole structure. The values of the overall damage index according to

Equations 4.22-4.24 are presented in Table 4.6. The damage-weighted index

underestimates the overall damage of the structure, compared to the energy-weighted

sum. In fact, the energy-based weight is able to better reflect the distribution of damage

among the piers for each earthquake test.

4.5.4. Vulnerability functions

Vulnerability functions represent an important part of studies aimed at risk assessment

and various procedures are available, e.g. [Corsanego, 1991]. Vulnerability functions

correlate the damage (quantified using an appropriate damage index) observed in the

structure, to a parameter that defines the earthquake input (often macroseismic intensity

or ground acceleration). Data obtained from field investigations after a significant

earthquake are commonly used for the development of vulnerability functions. An

attempt is made in this section to perform a preliminary estimation of such functions on

the basis of the experimental results. The seismic motion was characterised by the peak

ground acceleration normalised to the value for the 1.0xNE test and different damage

indices were examined, namely the Park and Ang Damage Index, the drift demand and

the displacement ductility (defined by the bilinear envelope curve). The results are

presented in Figure 4.24. Concerning piers A20 to A60, damage increases almost linearly

with the earthquake intensity, but remains always at low levels. For the short physical

pier, A70, damage increases rapidly from the 1.0xNE level to the 2.0xNE level, for which

the pier failed. All damage indices give consistent results.


125

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.5 1 1.5 2 2.5a/anom

Par

k &

Ang

Dam

age

Inde

x A20 A30A40 A50A60 A70

(a)

0.0

0.2

0.4

0.6

0.8

1.0

0 0.5 1 1.5 2 2.5a/anom

Drif

t (%

)

A20 A30A40 A50A60 A70

(b)

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5a/anom

Dis

plac

emen

t duc

tility

A20 A30A40 A50A60 A70

(c)

0.0

0.2

0.4

0.6

0.8

1.0

0 0.5 1 1.5 2 2.5

a/anom

Ove

rall

Dam

age

Inde

x

(d)

Figure 4.24. Vulnerability functions: Park and Ang Damage Index (a), drift ratio (b),

displacement ductility (c) and overall Park and Ang Damage Index (d)

Observing Figure 4.24, it is obvious that the vulnerability function cannot in general be

considered a linear one, as commonly assumed in the past. An exponential or higher-

order polynomial in the form suggested by [Powell and Allahabadi, 1988]

m

c ts

t

d dDI

d d −

= − (4.25)

seems more appropriate. An exponential or 3rd order polynomial fit the experimental

results better than a linear relation. It should be underlined, though, that the small number

of experimental results allows only a preliminary evaluation of the vulnerability

functions. Further numerical simulations could be used for a more reliable estimate of the

vulnerability functions.


126

4.5.5. Effect of cycling

Seismic detailing, as required by modern seismic codes, guarantees ductility and

dissipation capacity of members and structures, in other words it allows for stable

response without significant loss of resistance and stiffness with cycling. Members

without seismic detailing are expected to be more sensitive to cycling, in terms of

strength and stiffness degradation. Cycling is also considered significant for the behaviour

of lapped splices [Balázs, 1991], which was a weak point of the tested bridge piers.

The relation between the ultimate displacement and the number of cycles has been

experimentally investigated for well-confined circular columns with flexural failure mode

[El-Bahy et al., 1999]. It was found that for a small number of cycles at significant levels

of displacement, similar to the static cyclic tests, failure is usually due to rupture of

reinforcement, whereas in the case of more cycles at smaller displacement levels, similar

to the PSD earthquake tests, failure is usually due to crushing of concrete. The cyclic

effects have been proved significant even in the case of well-confined circular columns:

for ductility demand in the order of µ = 2 the piers sustained a number of cycles without

significant structural damage, but for ductility close to µ = 4, moderate to severe damage

was more probable, depending on the number of cycles [Taylor et al., 1997]. Because of

cumulative damage, it has been suggested that in evaluating the seismic performance of

structures the capacity is dependent on the demand (in terms of number and amplitude of

inelastic excursions). This holds mainly for ductile steel structures and might not

completely apply to RC structures [Krawinkler, 1996].

The performance of the tall pier, A40, during the PSD tests is first compared to the

behaviour of the same pier subjected to cyclic loading until collapse. As seen in Table

4.7, the deformation capacity, as described by displacement ductility (defined by the

bilinear envelope) and lateral drift, was respectively 45% and 12% lower for the

earthquake tests, compared to the cyclic tests. The failure mode was in both cases due to

collapse of vertical reinforcement at the critical cross-section at 3.5 m from the base. The

smaller value of ultimate displacement was due to the structural degradation of the pier

during the large number of cycles of the three earthquake tests. The maximum drift

demand was ud = 1.5%, half of 3%, which is commonly set as the target value for new


127

bridges [Priestley et al., 1996]. No significant difference in the maximum strength was

observed between the cyclic and the PSD tests.

Also for the short physical pier, A70, the displacement ductility capacity was smaller for

the earthquake tests in comparison to the cyclic test, see Table 4.7. The maximum drift

demand was d= 0.7% for the PSD tests and d= 1.3% for the cyclic test. The

displacement ductility capacity was also reduced by 50%. This difference can be

attributed to cyclic effects, since for the PSD tests the pier had to undergo a significant

number of cycles at high levels of displacement. Again, no significant difference in the

maximum strength was observed.

4.5.6. Irregularity issues

The irregular distribution of damage among the bridge piers is evidenced in Figure 4.25,

which presents the distribution of displacement ductility, drift, Park and Ang damage

index and dissipated energy in the bridge piers for the different earthquake tests. The

displacement ductility and drift demands were calculated for the maximum displacement

of each pier that, in general, was reached at different time steps. For the 0.4xNE and the

1.0xNE tests, the ductility demand, drift demand, as well as the damage, are quite

regularly distributed among the piers. For the 2.0xNE test, though, the demand is shifted

to the short pier that remained practically undamaged for the previous tests. The

percentage of dissipated energy follows an irregular distribution for all three earthquake

tests.

This irregular distribution of damage is attributed to higher mode effects. For the 0.4xNE

and the 1.0xNE tests the bridge followed mainly the first two eigenmodes. Higher

eigenmodes (see Figure 4.5) impose on the short pier displacement similar to those

imposed on the other piers. Given the smaller height, larger drift and more severe damage

are expected for the short pier. The effect of higher modes is verified in Figure 4.26 that

plots the Fast Fourier Transforms of the displacement histories at the top of the piers for

the three earthquake tests. For the 0.4xNE test one peak at frequency 1.95 Hz is observed,

for the 1.0xNE tests there are two peaks at 1.75 Hz and 2.20 Hz, while for the 2.0xNE test

there are three peaks at 1.46 Hz, 2.20 Hz and 2.93 Hz.


128

0

1

2

3

4

5

6

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t duc

tility

dem

and

0.4xNE NE 2.0xNE (a)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A30 A40 A50 A60 A70

Drif

t dem

and

(%)

0.4xNE NE 2.0xNE(b)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

A20 A30 A40 A50 A60 A70

Par

k &

Ang

Dam

age

Inde

x

0.4xNE NE 2.0xNE(c)

0

20

40

60

80

100

A20 A30 A40 A50 A60 A70

Dis

sipa

ted

ener

gy (

% o

f tot

al)

0.4xNE NE 2.0xNE (d)

Figure 4.25. Distribution of ductility demand (a), drift demand (b), Park and Ang Damage

Index (c) and percentage of dissipated energy (d) among the piers

0.00

0.02

0.04

0.06

0.08

0.10

0 1 2 3 4Frequency (Hz)

Dis

plac

emen

t (m

)

A20A30A40A50A60A70

0.4xNE

0.00

0.02

0.04

0.06

0.08

0.10


Dis

plac

emen

t (m

)

A20A30A40A50A60A70

1.0xNE

0.00

0.02

0.04

0.06

0.08

0.10


Dis

plac

emen

t (m

)

A20A30A40A50A60A70

2.0xNE

Figure 4.26. Fast Fourier Transforms of the pier top displacement


129

Table 4.7. Displacement ductility and drift capacities for the cyclic and PSD tests

µ d (%)

Cyclic PSD Cyclic PSD

A40 3.7 2.4 1.7 1.5

A70 8.0 3.9 1.3 0.7

At seismic code level, regularity is related to the selection of analysis methods and of the

values of the behaviour factor. When a bridge is of regular geometry, equivalent static

analysis for lateral forces that follow a distribution similar to the first eigenmode is

allowed; otherwise more elaborate methods (usually multi-modal spectral analysis) are

required. Concerning the definition of regularity for bridge structures, several criteria

have been proposed. According to EC8-2 [CEN, 2002], a bridge is defined as regular

when

omin,d

max,d

qq

ρ≤=ρ (4.26)

where

Ed,id,i

Rd,i

Mq q

M= (4.27)

In the above expressions q is the behaviour factor, EdM is the design moment for the

seismic action and RdM is the resisting moment. The value o? = 2 is recommended. One

or more piers can be excluded from the criterion if the sum of their shear force is inferior

to 20% of the total shear force.

The criterion of Equation 4.26 can be interpreted as a requirement that the maximum

value of ductility must not be higher than o? times the minimum value for a bridge to be

regular. For the tested bridge and the 0.4xNE test the maximum value of ductility was

d,maxq = 0.9 and the minimum d,mind = 0.2. Therefore, ? = 4.5 and the bridge is classified as

irregular. Also for the 1.0xNE test, ? = 2, and for the 2.0xNE test, ? = 3.6, the bridge is

classified as irregular.


130

0

100

200

300

400

500

600

A20 A30 A40 A50 A60 A70

Stif

fnes

s ch

ange

(%)

Figure 4.27. Change in stiffness between adjacent piers and distribution of stiffness

According to the AASHTO Bridge Design Specifications [AASHTO, 1995], a bridge is

classified as irregular when changes in stiffness or mass from one pier to the adjacent

exceed 25%. Figure 4.27, plots the change of stiffness between adjacent piers, along with

the AASHTO limit. Following this criterion, the bridge is considered highly irregular.

The ratio of the maximum column stiffness, pk , to the deck stiffness, dk , has been also

proposed as a regularity index [Fishinger et al., 1997]. The stiffness ratio, kr , is defined as

k p dr k / k= (4.28)

where 3d d dk 48EI / L= is the stiffness of the deck and dL is the total length of the deck. A

bridge is regular if kr < 15. Qualitatively, a bridge is defined as regular when the columns

do not govern the response and consequently the influence of higher modes is not

important. For the Talübergang Warth Bridge the stiffness ratio is calculated as kr » 15:

this value indicates that the bridge is highly irregular.

The recent Italian seismic code [Ordinanza 3274, 2003] adopts the EC8 regularity

criterion for what concerns the selection of the behaviour factor. If a bridge is regular, the

nominal behaviour factor, q, is used for each pier. In the opposite case, it is multiplied by

2 / ? . For the selection of the analysis method, a different regularity criterion is adopted.

A bridge is regular in the longitudinal direction if the total effective mass of the piers,


131

corresponding to half the pier height, is less than 1/5 of the deck mass. In the transverse

direction a bridge is regular if the eccentricity, defined as the distance between the mass

centre and the stiffness centre, is less than 5% of the deck length. Following this criterion,

the Talübergang Warth Bridge is regular in the longitudinal direction and irregular in the

transverse direction.

4.6. APPLICATION OF SIMPLIFIED ASSESSMENT METHODS

4.6.1. General

After the serious damage suffered by bridges during recent destructive earthquakes and

the consequent losses, much research has been performed on the development of

simplified assessment methods. The simplest method follows the traditional force-based

design procedures: the structural forces of a linear model of the structure are determined

for an earthquake loading that is described by a response spectrum. Then, a

capacity/demand check is performed. In this area, much effort was dedicated towards the

assessment of the shear capacity of existing members, including the effect of splice

failure and different types of cross-section, e.g. [Ascheim & Moehle, 1992; Ascheim et

al., 1997; Priestley et al., 1994a; Kowalsky & Priestley, 2000; Rasulo et al., 2002]. The

force capacity/demand approach has several drawbacks [Priestley et al., 1996] and for this

reason, performance-based methods have been developed.

Performance-based methods can be divided in two categories. Probabilistic methods use

fragility curves to estimate the possibility of exceeding a certain damage level for a given

earthquake. Fragility curves result either from field observations or from numerical

analyses. The HAZUS methodology is briefly described in the following and then applied

for the assessment of the tested bridge.

For the detailed assessment of a single structure, deterministic methods are more

appropriate. Simplified methodologies make use of an equivalent linear structure and

displacement spectra. The structural response is obtained through non-linear incremental

analysis, which involves some sophistication without at the same time requiring much

effort and experience. The capacity spectrum (CS) and N2 methods, which belong to the

family of performance-based procedures, are discussed in the following.


132

4.6.2. HAZUS method

HAZUS [FEMA, 1999] is a methodology for earthquake risk assessment developed by

the Federal Emergency Management Agency. Using information on the ground shaking

and structural type, loss estimates are performed. An integral part of the methodology is

the fragility curves for the various structural types. The method is probabilistic and many

uncertainties are inherent in the definition of the input parameters. It is anticipated that it

provides reliable results for damage estimates in extended regions and not for single

structures.

Elastic response spectra with 5% damping are used to characterize the ground-shaking

demand. These spectra have a standard format, see Figure 4.28, consisting of three parts:

a region of constant spectral acceleration, a region of constant spectral velocity and a

region of constant spectral displacement. The region of constant spectral acceleration is

defined by spectral acceleration at the period of 0.3 sec. The constant spectral velocity

region has spectral acceleration proportional to 1/T and is anchored to the spectral

acceleration at the period of 1 sec. The transition period, AVT , defines the intersection of

the regions of constant spectral acceleration and constant spectral velocity and varies

depending on the values of spectral acceleration that define these regions. The constant

spectral displacement region has spectral acceleration proportional to 21/ T and is

anchored to the spectral acceleration at period VDT , where constant spectral velocity

transitions to constant spectral displacement. VDT is considered a function of moment

magnitude.

Figure 4.28. Response spectrum used in HAZUS [FEMA, 1999]


133

Damage functions, or fragility curves, for bridges are modelled as log-normally

distributed functions that provide the probability of reaching or exceeding different

damage states for a given level of ground motion or ground failure. Each fragility curve is

characterized by a median value of ground acceleration or displacement and an associated

dispersion factor. Ground motion is quantified in terms of peak ground acceleration and

ground failure is quantified in terms of permanent ground displacement.

Bridges in particular are classified based on the following characteristics: seismic design,

number of spans (single or multi-span bridges), structure type (concrete, steel, others),

pier type (multiple column or single column bents and pier walls), abutment type

(monolithic or non-monolithic), bearing type and span continuity (continuous,

discontinuous or simply supported). Following this classification, 28 types are identified.

A total of five damage states are defined for highway system components. These are: No

damage, Slight, Moderate, Extensive and Complete Damage. No Damage is defined by

minor cracking and spalling of the abutments, cracks in shear keys at abutments, minor

spalling and cracks at hinges, minor spalling at columns (only cosmetic repair is required)

or minor cracking to the deck. Moderate Damage is defined by any column experiencing

moderate cracking (shear cracks) and spalling (the column is structurally still sound),

moderate movement of the abutments (< 5 cm), extensive cracking and spalling of shear

keys, any connection having cracked shear keys or bent bolts, keeper bar failure without

unseating, rocker bearing failure or moderate settlement of the approaches. Extensive

Damage is defined by any column degrading without collapse (shear failure, the column

is structurally unsafe), significant residual movement at connections, major settlement of

the approaches, vertical offset of the abutments, differential settlement at connections and

shear key failure at abutments. Complete Damage is defined by any column collapsing

and connection losing all bearing support, which may lead to imminent deck collapse or

tilting of the substructure due to foundation failure.

For each damage state damage ratios are provided, as shown in Table 4.9. Damage ratios

are defined as a fraction of the component replacement cost. Damage ratios are useful in

cost estimation and in the decision and prioritisation of action when a large population of

structures is screened.


134

Table 4.9. Damage ratios for highway bridges [FEMA, 1999]

Damage ratio

Damage state Best estimate Range

Slight 0.03 0.01-0.03

Moderate 0.08 0.02-0.15

Extensive 0.25 0.10-0.40

Complete 1.00 0.30-1.00

Table 4.10. Discrete values of restoration functions for highway bridges [FEMA, 1999]

Functional percentage

Restoration period Slight Moderate Extensive Complete

1 day 70 30 2 0

3 days 100 60 5 2

7 days 100 95 6 2

30 days 100 100 15 4

90 days 100 100 65 10

In addition, restoration curves have been elaborated. Restoration curves give the

functional percentage at different periods of time after the occurrence of an earthquake

that produces a given damage state on the structure. They follow a normal distribution

characterised by a mean and a standard deviation. Table 4.10 gives values of the

restoration curves for highway bridges. A bridge with slight damage will be fully

functional (functional percentage 100%) in 3 days, while one with moderate damage in 30

days. After 90 days, bridges with extensive and complete damage will be only 65% and

10% functional, respectively.

The procedure for the estimation of shaking-related damage states for bridges is

summarized in the following. The first step comprises the classification of the bridge and

the identification of the geometric properties of interest (number of spans, skew angle,

span width, bridge length, and maximum span length). Then, the peak ground

acceleration and spectral accelerations are evaluated considering eventually the

amplification due to soil conditions. In the following step three modification factors

(taking into account the skew of the bridge, skewK , spectral ordinates, shapeK , and tri-

dimensional arch action in the deck, 3DK ) are evaluated and the medians for the standard


135

fragility curves are appropriately modified. Finally, the fragility curves are calculated for

the corrected medians and the given values of dispersion.

For a complete evaluation of the functionality of a bridge structure, the probability of

exceeding ground-shaking related damage states should be combined with the probability

of exceeding damage states related to ground failure. Since ground failure was not

considered in the experiments, only the former source of damage is examined in the

following.

4.6.3. The substitute structure methods

The basis of this family of methods is the substitution of the real MDOF structure with an

equivalent SDOF one [Shibata & Sozen, 1976], following the concepts developed for the

direct displacement-based design, e.g. [Priestley & Calvi, 1997]. The most difficult task is

the definition of the effective properties of the equivalent structure, namely: deformed

shape, stiffness/period and damping. Using the equivalent damping and effective period,

the displacement is estimated from a displacement spectrum.

Following the CS method [Freeman, 1998], the seismic demand is obtained through an

acceleration-displacement response spectrum (ADRS) that is a plot of spectral

acceleration versus spectral displacement. The capacity curve of the structure, obtained

by means of pushover analysis, is superimposed on the ADRS. Then, the performance

point is defined at the intersection of the capacity and demand curves. The performance

point gives the displacement that the substitute structure will experience for the given

earthquake. Iterations are necessary to define the performance point for the correct value

of structural damping, since damping is considered a function of displacement. Several

expressions of this relation have been proposed for different structural systems, e.g. [Iwan

& Gates, 1979]. The CS method is adopted in the FHWA Seismic Retrofitting Manual for

highway bridges [Buckle & Friedland, 1995].

Various alternatives have been proposed, such as the N2 method [Fajfar & Gašperšic,

1996], which was adopted by EC8-1 [CEN, 2003a] for the design of new structures. The

first step of the N2 method is the non-linear analysis of a MDOF model of the structure.

Pushover analysis is performed for a distribution of forces that corresponds to the

distribution of inertia forces due to an assumed time-invariant displacement shape. The


136

deformed shape can be the one corresponding to the first eigenmode. This choice is valid

for the case of single bridge piers [Kowalsky et al., 1995] and regular bridges [Calvi &

Kingsley, 1995; Fajfar et al., 1997]. For the case of irregular bridges the contribution of

higher modes is expected to be significant and therefore, a different deformed shape must

be adopted. It is believed that, within rational limits, different assumptions will produce

similar results [Fajfar et al., 1997]. Suggested displacement shapes for different types of

bridges are presented in Figure 4.29.

Based on the computed response, a bilinear force-displacement curve is determined for

the equivalent SDOF system. The force is the sum of the reactions at the pier bases, while

the displacement corresponds to the control point, which depends on the structural

system. It is proposed to consider the point of the deck where the maximum displacement

is expected [Fajfar et al., 1997], or the top of the critical pier where failure occurs first

[Panagiotakos et al., 2003]. Both definitions require an a priori knowledge of the dynamic

structural response. In the case of a regular bridge these points will probably coincide, but

it might not be so in an irregular bridge. The stiffness of the equivalent structure is

*y yK F / u= (4.29)

where yF is the yield force and yu is the yield displacement of the bilinear curve. EC8-2

[CEN, 2002] adopts a bilinear curve where the yield force is equal to the force at the

formation of the mechanism. The yield displacement is such that the area under the actual

curve, mE , is the same as the area under the bilinear curve

y m m yu 2(u E / F )= − (4.30)

Figure 4.29. Suggested displacement shapes, adapted from [Fajfar et al., 1997]


137

where mu is the displacement at the formation of the mechanism. The effective period is

then calculated according to the expression

* * *T 2 m / K= π (4.31)

The mass, *m , of the SDOF structure is [Fajfar & Gašperšic, 1996]

*i im m= Φ∑ (4.32)

where im is the mass of each DOF and iΦ is the assumed displacement.

The seismic demand for the SDOF structure is defined by inelastic displacement spectra.

The inelastic displacement spectrum, dS , is obtained from the elastic one, deS , following

the relation

d deS SRµ

µ= (4.33)

where µ is the displacement ductility factor and Rµ is a reduction factor due to ductility.

A simple expression for Rµ may be adopted [Fajfar, 2000]

c

TR ( 1) 1

Tµ = µ − + ; cT T< (4.34a)

Rµ = µ ; cT T≥ (4.34b)

where cT is the period that defines the transition from the constant acceleration to the

constant velocity part of the spectrum. From Equations 4.33 and 4.34b, it is shown that

the equal displacement rule holds for structures with long periods. The local demand is

obtained by imposing the spectral displacement on the control point of the MDOF system.


138

4.6.4. Application to the Talübergang Warth Bridge tests

HAZUS

For the damage probability assessment according to HAZUS, the geometric data of the

bridge are first needed for the classification of the structural type. The bridge has single

column bents, the deck is made up by a prestressed continuous box girder and the design

is identified as conventional (as opposed to seismic). Then, the bridge is classified as type

HWB20. The seismic input is defined by the mean acceleration response spectrum for 5%

damping, shown in Figure 4.30a.

The correction factors can now be estimated for the structural type and spectral

accelerations, as reported in Table 4.11. For the given structural type, the median values

for each damage state are also given in Table 4.11. The modified medians and the

dispersion β = 0.4 are used for the estimation of the probability of exceeding each

damage state for the three earthquake tests. The fragility curves are plotted in Figure 4.31.

The control period and the spectral accelerations for the tested model of the bridge have

been modified following the similitude law. For the prototype bridge the control period

for the ground acceleration is PT = 1.0 sec, while for the model it is 1M PT T−= λ = 0.4 sec.

Accordingly, the spectral acceleration for the prototype is 1P Ma a−= λ . According to this,

the acceleration at MT = 0.4 sec is read from the spectra of Figure 4.30a, it is divided by

2.5 to obtain the acceleration of the prototype and this value is entered in the fragility

curves of Figure 4.31. As seen in Table 4.12, no damage is predicted for the 0.4xNE test,

which corresponds to minor cracking and need for cosmetic repair only. This is consistent

with the observed damage, as described in section 4.4.2. After the low-level earthquake

the bridge is expected to be fully functional and only a small repair cost (less than 10% of

the replacement cost) will be required. For the 1.0xNE test the probabilities of exceeding

all damage states are similar, therefore no judgement can be made. Finally, complete

damage is predicted for the 2.0xNE test. This is in agreement with the experimental

observations that indicate collapse of one pier and complete damage of the bridge.

Table 4.12 presents also the probabilities of exceeding each damage level for earthquake

input described by the EC8 response spectrum Type 1 for ground type B, damping 5% of

critical and PGA = 0.36 g, see Figure 4.30b. For the 0.4xNE test no damage or slight


139

damage is predicted. For the 1.0xNE similar probabilities of exceeding all damage states

are predicted, with slightly higher probabilities for moderate or more severe damage.

Finally, for the 2.0xNE test, complete damage is predicted, with higher probability

compared to the prediction for the PSD tests of the same amplitude. The expected repair

cost ranges between 30% and 100% percent of the replacement cost. The bridge would be

fully functional after more than 1.5 years from the date of the event.

The HAZUS methodology underestimates the damage observed during the 1.0xNE and

2.0xNE PSD test and predicts serious damage for the EC8 spectrum. This is due to the

characteristics of the accelerograms used in the PSD tests: the spectral accelerations at 1.0

sec are relatively low. On the contrary, the spectral accelerations at the same period for

the EC8 spectrum are higher by about 30 % (see Table 4.12). The vulnerability of the

bridge is verified, since the bridge would suffer severe damage for the EC8 design

earthquake and would most probably collapse for the 2.0xNE input.

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5Period (sec)

Acc

eler

atio

n (g

)

0.4xNE

2.0xNE1.0xNE

(a)

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4

Period (sec)

Acc

eler

atio

n (g

)

0.4xNE

2.0xNE1.0xNE

(b)

Figure 4.30. Acceleration response spectra for 5% damping: mean experimental (a) and

EC8 Type 1, Soil Class B and PGA = 0.36 g (b)

Table 4.11. Parameters for estimation of damage probability

Median aS (g)

Damage level Original Modified

skewK 1.00 Light 0.35 0.35

shapeK 2.19 Moderate 0.42 0.44

3DK 1.05 Extensive 0.50 0.53

shapeI 0.00 Complete 0.74 0.78


140

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5

Spectral acceleration at 1.0 sec (g)

Pro

babi

lity

of e

xcee

ding

dam

age

stat

e

SlightModerateExtensiveComplete

Figure 4.31. Fragility curves for the Talübergang Warth Bridge

Table 4.12. Assessment of the Talübergang Warth Bridge according to HAZUS

Probability of exceeding damage level

Sa(1.0) No Slight Moderate Extensive Complete

Exp. 0.17 1.0 0.0 0.0 0.0 0.0 0.4xNE

EC8 0.22 0.9 0.1 0.0 0.0 0.0

Exp. 0.42 0.3 0.2 0.2 0.2 0.1 1.0xNE

EC8 0.54 0.1 0.2 0.2 0.3 0.2

Exp. 0.84 0.0 0.0 0.1 0.3 0.6 2.0xNE

EC8 1.08 0.0 0.0 0.0 0.2 0.8

Capacity Spectrum method

The performance-based assessment methods discussed before were applied to the tested

bridge structure. For the CS and N2 methods, a non-linear model of the complete

structure was subjected to incremental lateral loading. The forces followed either a

trapezoidal, or triangular distribution, shown in Figure 4.32. Two alternatives were

considered for the control point. The first is the top of pier A30, which had the maximum

displacement in all the PSD tests and the second is the top of pier A70, which collapsed

during the 2.0xNE test.


141

Figure 4.32. Distribution of lateral forces

0

500

1000

1500

2000

2500

3000

3500

0.00 0.05 0.10 0.15 0.20 0.25

Displacement (m)

For

ce (k

N)

Pier A30Pier A70

Figure 4.33. Force-displacement curves from pushover analysis

Table 4.13. Equivalent damping (%)

A20 A30 A40 A50 A60 A70 Total

0.4xNE 2.42 1.04 2.88 0.33 0.71 2.85 2.19

1.0xNE 1.04 0.96 4.46 0.69 0.06 2.85 3.20

2.0xNE 0.87 0.59 8.27 0.45 0.08 12.24 10.0

The force-displacement curves from the pushover analysis for trapezoidal distribution of

lateral forces are presented in Figure 4.33, along with the bilinear approximation

according to EC8. As expected, if the control point is the top of pier A70, a much stiffer


142

response is obtained. The curves are similar for triangular distribution of the lateral

forces.

The value of equivalent damping for the complete structure is calculated as a weighted

sum of the experimental values for each pier. The weight is the percentage of dissipated

energy for each earthquake test. The equivalent damping, eqξ , for each pier is estimated

for the cycle with maximum displacement for each test, according to the expression

Deq

max max

E2 F u

ξ =π

(4.35)

In the previous expression DE is the dissipated energy in the cycle, maxF and maxu are

respectively the mean values of maximum force and displacement in positive and

negative directions. The resulting values are reported in Table 4.13, where it is seen that

low values of damping correspond to the small and nominal-amplitude tests.

At this point, both the capacity and demand curves can be estimated. The capacity curve

is obtained by dividing the force of the bilinear curve by the mass of the equivalent

structure, see Equation 4.32. In Figure 4.34 the capacity curves are superimposed on the

mean ADRS of the accelerograms used in the PSD tests. For each earthquake intensity

the equivalent damping reported in Table 4.13 was used for the calculation of the ADRS

and hence, no iterations are required. The displacements of the control points for each

earthquake intensity are reported in Table 4.14. The displacements of the pier tops for

each earthquake intensity and the different control points and distributions of lateral

forces are compared to the maximum experimental displacements in Figure 4.35.

0.0

0.5

1.0

1.5

2.0

0.00 0.02 0.04 0.06 0.08Displacement (m)

Acc

eler

atio

n (g

)

A30 A70 (a)

0.0

0.5

1.0

1.5

2.0

0.00 0.02 0.04 0.06 0.08Displacement (m)

Acc

eler

atio

n (g

)

A30 A70 (b)

Figure 4.34. Evaluation of performance point for mean experimental ADRS: trapezoidal

(a) and triangular distribution of forces (b)


143

0.00

0.01

0.02

0.03

0.04

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)

Triangular

Trapezoidal

Experimental

0.4xNE

0.00

0.01

0.02

0.03

0.04

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)

TriangularTrapezoidalExperimental

0.4xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


1.0xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


1.0xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


2.0xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


2.0xNE

Figure 4.35. Maximum displacement of the piers: experimental values and CS method for

control at top of pier A30 (left column) and control at top of pier A70 (right column)

0

1

2

3

4

5

0.00 0.05 0.10 0.15 0.20Displacement (m)

Acc

eler

atio

n (g

)

A30 A70 (a)

0

1

2

3

4

5

0.00 0.05 0.10 0.15 0.20Displacement (m)

Acc

eler

atio

n (g

)

A30 A70 (b)

Figure 4.36. Evaluation of performance point for EC8-compatible ADRS: trapezoidal (a)

and triangular distribution of forces (b)


144

Table 4.14. Displacement of control point (m) for mean ADRS

Trapezoidal distribution of forces

0.4xNE 1.0xNE 2.0xNE

CS N2 CS N2 CS N2

A30 0.019 0.008 0.031 0.020 0.050 0.035

A70 0.024 0.009 0.038 0.022 0.054 0.042

Triangular distribution of forces


CS N2 CS N2 CS N2

A30 0.024 0.008 0.039 0.020 0.056 0.035

A70 0.003 0.010 0.049 0.025 0.061 0.047

Table 4.15. Displacement of control point (m) for EC8 ADRS and triangular distribution

of lateral forces


CS N2 CS N2 CS N2

A30 0.035 0.042 0.119 0.105 0.175 0.210

A70 0.025 0.043 - 0.108 - 0.215

Table 4.16. Characteristic values of the equivalent bilinear structures

Trapezoidal Triangular

A30 3440 3406 yF (kN)

A70 3440 3406

A30 0.08 0.08 yu (m)

A70 0.02 0.02

A30 43000 42575 *K (kN/m)

A70 172000 170300

A30 2.66 2.03 *T (sec)

A70 1.33 1.02

The trapezoidal distribution of forces provides a very poor approximation of the

experimental response of the bridge. The triangular distribution of forces for control point

at the top of pier A30 gives better results for the 0.4xNE and the 1.0xNE, for which the

dynamic response followed mainly the first two eigenmodes, although in some cases the


145

displacements are underestimated by as much as 2.5 times. On the other hand, the

triangular distribution for control point at the top of pier A70 significantly overestimates,

by about two times, the experimental displacements. The 0.4xNE test is an exception

because of the small demand that is defined by the ADRS spectrum, see Figure 4.34b.

In Figure 4.36 the capacity curves are superimposed on the ADRS spectra according to

EC8. The ADRS spectra are calculated considering the values of damping in Table 4.13

for each test. It is reminded that the similitude law was applied in the construction of the

spectra of Figure 4.36 The acceleration, displacement and period of the prototype, given

in EC8, were appropriately scaled to obtain the values for the tested model. It is seen that

the bridge cannot meet the seismic demand for the 1.0xNE and 2.0xNE intensities when

the control point is considered at the top of pier A70.

The predicted displacements of the control points are presented in Table 4.15. Only the

results for triangular distribution of lateral forces are presented. The displacements

predicted for the EC8 spectrum are 1.5 times or 3 times, for the 0.4xNE or the 1.0xNE

and 2.0xNE tests respectively, the displacements predicted for the mean experimental

ADRS. These values correspond to moderate damage for the 0.4xNE test, severe damage

for the 1.0xNE test and imminent collapse for the 2.0xNE test. It is reminded that this

method underestimated the experimental displacements and therefore more damage

would be actually expected. Qualitatively, these results are in agreement with the damage

predicted by the HAZUS methodology and once again verify the high seismic

vulnerability of the bridge.

N2 method

For the N2 method, the mean displacement spectra for 5% damping are presented in

Figure 4.37a for the three earthquake tests. Following Equations 4.29 to 4.32, the

characteristic properties are estimated and reported in Table 4.16. As observed before,

stiffer response is obtained if the control point is the top of the critical pier, A70.

Comparing the trapezoidal and triangular distributions of forces, no major differences are

observed in terms of stiffness, but different periods are calculated. This is because the

effective mass is different for the two assumed displacement shapes, as shown in

Equation 4.32. Then, different periods correspond to different spectral displacements. As

shown in Figure 4.37a, the stiffer equivalent structure has higher displacement for the


146

accelerograms used in the PSD tests. For the EC8 displacement spectrum the periods of

the equivalent structure, appropriately scaled from the model to the prototype, fall within

the plateau of maximum displacement or within the descending branch, as seen in Figure

4.37b. All the periods are higher than CT , therefore the equal displacement rule applies

and the inelastic displacement is equal to the elastic displacement (see Equation 4.34).

Table 4.14 compares the displacement of the control point, as results from the two

alternative methods. The displacements predicted by the N2 method are 3, 2 and 1.6 times

smaller than the displacements predicted by the CS method, for the 0.4xNE, 1.0xNE and

the 2.0xNE tests respectively. This difference is of the same order independently of the

control point and the distribution of lateral forces.

The last step in the assessment procedure is the application of the target displacement,

shown in Table 4.14, to the control point, following the assumed deformed shape. The left

column of Figure 4.38 presents the results of the N2 method for control at the top of pier

A30 and the right column presents the results for control at the top of pier A70. The

trapezoidal distribution of forces produces results in poor agreement with the

experimental data, both in terms of absolute values of displacement and in terms of

deformed shape. It is concluded that this deformed shape cannot sufficiently describe the

dynamic response of the bridge. On the other hand, the triangular distribution of forces

better approximates the actual deformed shape of the bridge. Nevertheless, the predicted

displacements diverge from the experimental values. When considering the top of pier

A30 as the control point, the predictions underestimate the displacements by more than

4.5 times in the worst case. For the control point at the top of pier A70 the prediction

gives a better approximation of the distribution of the maximum experimental

displacements. Considering the absolute values, the prediction underestimates some

displacements by as much as 70 %.

Table 4.15 presents the values of displacement of the control points for the two methods,

following the triangular distribution of forces, and the EC8 (Type 1 and Soil Class B)

ADRS spectra. As for the CS method, the predicted displacements are significantly higher

than the displacements for the mean experimental displacement spectra. The N2 method

predicts moderate damage for the SLS earthquake, severe damage for the ULS earthquake

and imminent collapse for the 2.0xNE.


147

0.00

0.02

0.04

0.06

0.08

0.0 0.5 1.0 1.5 2.0 2.5Period (sec)

Dis

plac

emen

t (m

)

0.4xNE

2.0xNE

1.0xNE

(a)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12

Period (sec)

Dis

plac

emen

t (m

)

0.4xNE1.0xNE

2.0xNE

(b)

Figure 4.37. Mean displacement spectra for use in N2 method: experiment (a) and EC8

Type 1 for Soil Class B (b)

0.00

0.01

0.02

0.03

0.04

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)

Triangular

Trapezoidal

Experimental

0.4xNE

0.00

0.01

0.02

0.03

0.04

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


0.4xNE

0.00

0.02

0.04

0.06

0.08

0.10

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


1.0xNE

0.00

0.02

0.04

0.06

0.08

0.10

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


1.0xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


2.0xNE

0.00

0.05

0.10

0.15

0.20

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)


2.0xNE

Figure 4.38. Maximum displacement of the piers: experimental values and N2 method for

control at top of pier A30 (left column) and control at top of pier A70 (right column)


148

0.0

0.1

0.2

0.3

0.4

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)N2 methodN2 correctedYieldingUltimate

0.4xNE

0.0

0.1

0.2

0.3

0.4

A20 A30 A40 A50 A60 A70

Dis

plac

emen

t (m

)

N2 methodN2 correctedYieldingUltimate

1.0xNE

Figure 4.39. Assessment of the bridge for the EC8 spectrum and N2 method

Among the examined solutions, the N2 method for triangular distribution of forces and

control point at the top of pier A70 gives the best approximation of the experimental

behaviour. Figure 4.39 plots the results of the N2 method for the EC8 spectrum with peak

ground acceleration ga = 0.36 g and control point at the top of pier A70. The yield and

ultimate displacements of the piers are also plotted. It is expected that displacements (and

damage) might be underestimated in certain cases. For the 0.4xNE input, yielding of all

the piers with the exception of A20 is predicted. The highest ductility demand, µ = 2.4,

corresponds to pier A50. For the 1.0xNE input all piers are beyond the yield point and

piers A40, A50, A60 and A70 reach their capacity. The highest ductility demand, µ =

10.8, corresponds to the short pier A70. For this input, which corresponds to the SLS, the

bridge is considered to fail and then the no-collapse criterion is not met.

The predicted response shown in Figure 4.39 could be unrealistic due to the difference

between the assumed and the experimentally observed deformed shapes of the bridge.

Therefore, an attempt is made to correct the results of the N2 method in order to follow

the effective deformed shape. The pier top displacements are multiplied by a correction

factor, which is the ratio of the experimental displacement and the value predicted by the

N2 method for triangular distribution of forces and control at the top of pier A70. This is

an interpretation of the proposal [Fajfar & Gašperšic, 1996] to apply appropriate dynamic

amplification (or de-amplification) factors to selected design quantities when the effects

of higher modes are significant. It is reminded that the deformed shape changes for each

earthquake test and this can be attributed to the change of the dynamic properties of the

piers due to the damage suffered in the previous tests. Although cumulative damage is not

considered in the simplest version of the method, the correction seems more meaningful if


149

the damage pattern predicted for the EC8 spectrum is similar to the damage observed in

the PSD tests. This will be verified in the following.

The displacements of the piers according to the corrected N2 method are also plotted in

Figure 4.39. For the 0.4xNE input all the piers are beyond the yield displacement, while

only the short pier A70 is at incipient yielding. The distribution of damage is similar to

the pattern observed in the PSD tests, therefore the correction is considered reliable. The

maximum ductility demand, µ = 3.2, corresponds to pier A30. The values of drift and

ductility indicate that most of the piers develop almost half their deformation capacity,

which means that they suffer heavy damage and require significant repair. For the 1.0xNE

input all the piers have yielded and piers A20 and A40 have exceeded their deformation

capacity. The maximum ductility demand, µ = 7.5, corresponds again to pier A30. The

damage of all piers, as defined by the drift and ductility demands, is severe because they

either collapse, or develop more that 70% of their deformation capacity. At this level of

damage, repair might not be economically feasible and replacement of the bridge would

be required. This again verifies the seismic vulnerability of the bridge.

It should be kept in mind that the simple procedures used in the substitute structure

method do not account for cycling effects. In the case of poorly designed bridge piers

(lack of confinement reinforcement) this results in rapid strength and stiffness

degradation. Then, the displacement capacity of the monotonic curves is higher than the

actual capacity during an earthquake and the damage is underestimated. Certain

modifications have been proposed [Fajfar, 2000]. One possibility is to apply an equivalent

ductility factor that reduces the monotonic deformation capacity as a consequence of

cumulative damage. Alternatively, the seismic demand may be increased.

In addition, the method predicts the performance of the bridge subjected to an earthquake

without previous damage. This was not the case of the tested bridge, particularly for the

2.0xNE test. The previous tests had caused cracking and yielding of the piers and then the

stiffness and dynamic properties of the bridge were altered.

Comparing the examined methods, the HAZUS method results superior to the CS and the

N2 methods in terms of simplicity. Very few input data are required by the HAZUS

methodology and all the parameters are clearly defined and quantified. On the other hand,

the deterministic methods require more detailed information on the structure (not always


150

available) and the earthquake input and demand relatively refined analyses. In addition,

uncertainties related to the deformed shape, control point and the relation between

equivalent damping and lateral displacement require analyses of alternative cases. When

damage and changes in dynamic properties significantly influence the results of

simplified analysis methods, these results can only be used for qualitative comparisons.

This does not justify the demanded effort and in such case, probabilistic methods are

advantageous. It emerges from this application that, apart from the need for engineering

judgement and experience, non-linear dynamic analysis is the best available tool for the

reliable assessment of irregular structures.


A few words should be spent on the implementation aspects of the PSD tests, and

rightfully so, because these tests were the first at world-level to have been performed

considering non-linear behaviour for the substructured part and asynchronous input

motion. The tests were performed with two physical piers tested in the lab and the rest of

the piers, abutments and the deck modelled in the computer. The implemented

substructuring technique was proved to be representative of an earthquake test: the

experimental results were in fair agreement with pre-test results of dynamic analyses,

applying two alternative time integration schemes. The simplified numerical models

guaranteed reasonably short computation time and reliable results. It is interesting to note

that the testing part has been completely controlled remotely and that the connection

between the various processes used standard internet features. Thus, this test campaign

showed that the tele-operation of experimental facilities, further combined with

sophisticated numerical algorithms running on decentralised hardware, is already a

working reality [Pinto et al., 2004].

From the engineering point of view, as far as seismic assessment of existing bridges is

concerned, the results from the tests represent a data set, which allowed to calibrate

numerical models and to assess the performance of a typical European bridge (highway

bridge with rectangular hollow cross-section and with many seismic deficiencies such as

short overlapping and development lengths, lack of transversal reinforcement to prevent

buckling, tension shift effect, absence of capacity design requirements, etc). The PSD


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tests demonstrated that these infrastructures represent a great source of risk in seismic

regions.

It is important to note that the damage patterns change with the intensity of the input

motion. In fact, the 0.4xNE PSD test, hypothetically corresponding to the SLS, caused

only minor damage (cracking) in almost all piers but the physical short pier that remained

elastic. Then, damage concentrated at the tall physical pier, A40, for the 1.0xNE test,

hypothetically corresponding to the ULS, whereas the numerical piers A30 and A50 were

also beyond yielding. However, the non collapse criterion was satisfied. Finally, collapse

was reached at the short pier, A70, for the 2.0xNE test. Such behaviour is termed

sequential yielding in EC8-2 [CEN, 2002], while the optimal behaviour is characterised

by simultaneous yielding of the piers. Sequential yielding of piers is expected to cause

deviations between the results of simplified linear analysis and the actual non-linear

response of the bridge. In particular, it can induce additional horizontal eccentricity and

also increase the transverse bending of the deck. For these reasons, non-linear time-

history analysis is demanded by EC8-2 in such cases.

Note also that for the tall physical pier, A40, and the numerical piers A30, A50 and A60

the most heavily damaged region was above the bar cut-off at about one third of the total

height of the scaled specimen (8.75 m for the real physical pier A40), further

complicating the eventual repair works. The above reflect the absence of design

strategies, which are presently included in the design codes for new structures.

The drift and displacement ductility capacities of the bridge piers do not meet the

requirements of modern codes for new bridge structures. A limited capacity of hysteretic

energy dissipation is also observed for all piers due to the lack of detailing for seismic

resistance.

Concerning the quantification of damage, the difficulty in defining an overall damage

index for the whole bridge structure was discussed. Because of the irregular distribution

of damage among the bridge components-substructures, a weighted sum of their damage

indices was used to estimate the overall damage index. Among the damage-weighted and

the energy-weighted sums, the latter described better the performance of the tested bridge

structure.


152

The cyclic effects were evident since they resulted in a significant reduction of the

resistance of the bridge components and smaller displacement capacity, compared to the

same components tested under quasi-static conditions for a few cycles of increasing

displacement. For the short physical pier, A70, the larger number of cycles initiated

failure of the lapped splices, as indicated by the vertical cracks near the corner of the pier

in Figure C.6b.

The observed damage was compared to the predictions of simplified assessment methods.

The simplicity of the probabilistic methods was highlighted against the uncertainties

(concerning the deformed shape, control point, relation between equivalent damping and

lateral displacement, cycling effects and cumulative damage) encountered during the

application of deterministic methods that make use of a substitute structure. Due to the

differences between the assumed and the actual deformed shapes, the deterministic

methods were unable to predict the damage distribution observed during the tests and

their results could be used only for qualitative comparisons. Several improvements are

needed in these simplified methods in order to account for the aforementioned problems.

It was possible to introduce a correction of the N2 method in order to account for the

correct deformed shape. Nevertheless, this correction requires the knowledge of the actual

structural behaviour, in other words a complete non-linear dynamic analysis. Among the

available tools, dynamic non-linear analysis is the most appropriate for the detailed and

reliable assessment of existing structures with irregular configuration.

It is underlined that this bridge was considered in a low-seismicity zone (the prototype

was a viaduct in Austria) with near-field earthquakes, i.e. energy content only at high

frequency ranges. However, similar bridges exist in medium and high-seismicity zones in

Europe and with different earthquake scenarios, e.g. Italy, Greece, and Portugal. In this

last situation, it is felt that the structure would reach collapse for earthquake intensities

even below the nominal ones. This was qualitatively confirmed by the results of the

simplified assessment methods. Indeed, for the SLS earthquake significant inelastic

deformation demand, and consequently retrofit cost, is expected for all piers. For the ULS

earthquake collapse of two piers and severe damage (close to collapse) for the remaining

piers is expected. At the event of the ULS earthquake, repair might be economically

unfeasible and the solution would be the replacement of the bridge structure.

NUMERICAL MODELLING OF AS-BUILT AND RETROFITTED BRIDGE PIERS

153

5. NUMERICAL MODELLING OF AS-BUILT AND RETROFITTED

BRIDGE PIERS

5.1. INTRODUCTION

Numerical analysis is a procedure complementary to experimental testing. While test

results serve to validate numerical models, numerical analysis is used to generalise the

experimental findings. Considering reinforced concrete (RC) structures, either detailed or

simplified models may be employed. Detailed models make use of the Finite Element

Method (FEM) with appropriate mesh and constitutive laws for concrete, steel

reinforcement and contact interfaces. Reliable results are not easy to achieve and one has

to consider the computation time. Fibre-type models, which describe the behaviour at the

cross-section level, belong to this category. On the other hand, simplified models aim at

representing the global behaviour of structural elements such as columns, beams and

walls.

An attractive combination of the previous approaches is the use of fibre models for the

description at the cross-section level and the use of beam models for the description of the

flexural response at the element level. This combination offers a reliable and practical

solution for the non-linear analysis of RC elements, especially in the case of bending

combined with axial load. Non-linear cyclic constitutive laws can be used for both

concrete and steel and the results of the calculations include information on the stress and

strain distribution within the cross-section.

The use of macro-level models for reinforced concrete seen as a composite material has

been proposed also [CEB, 1996]. These models consider the smeared properties of the

composite material as an average of the effect of discrete rebars (contribution of steel)

and cracks (contribution of concrete). They have been mainly used for plate elements

with uniformly distributed reinforcement in plane stress conditions under both monotonic

and cyclic loading. Such models will not be examined in this work.

A fibre/Timoshenko beam model is described first, along with the cyclic constitutive laws

for concrete and steel. This modelling approach is adopted to simulate the response of the

two piers tested under static cyclic loading, as described in Chapter 3. The advantages and


154

limitations of this type of modelling are highlighted. In the following, appropriate models

are elaborated for the piers that were numerically simulated during the PSD tests

presented in Chapter 4. To overcome the problems related to shear deformation and

account for slippage between steel rebars and the surrounding concrete, the response of

the two piers is simulated using the FEM method. The constitutive laws for the materials

and interfaces are discussed and the results of the numerical simulation are compared to

the experimental data from the cyclic tests.

It is verified that the FEM is appropriate for studies where detailed information is needed

at local level, while fibre/Timoshenko beam (FTB) models are useful for parametric

studies where global behaviour is of interest. Both approaches are used for the numerical

analysis of piers with rectangular hollow cross-section retrofitted with fibre-reinforced

polymer (FRP) jackets. The FEM is applied for the study of the effect of confinement on

the concrete properties in piers with this particular geometry. The FTB model is then used

to study the global behaviour of retrofitted piers. The results of the FEM analyses are

used to define the material properties for concrete in the analyses with the FTB model.

This approach is validated against experimental data and will be used for parametric

analyses discussed in the following chapter.

5.2. FIBRE/TIMOSHENKO BEAM MODELLING

In support of the PSD tests on the bridge structure, presented in the previous chapter,

numerical pre-test analyses have been performed using a fibre/Timoshenko beam element

implemented in the finite element code Cast3m [Millard, 1993]. In this section a general

description of the model and constitutive laws for concrete and steel is given. Then,

alternative modelling configurations for the bridge piers are discussed and the results of

the FTB model are compared to the experimental data presented in Chapter 3 and to the

results of more refined analyses.

5.2.1. The Fibre/Timoshenko Beam element in Cast3m

A two level approach is adopted for this model: the first is the description of the section

(fibre elements) and the second is the description of the Timoshenko beam. At the section

level, the usual fibre modelling is adopted, which accounts only for interaction between


155

normal force and bending moment. The section is described by a model with various sub-

zones that correspond to different materials, namely steel and concrete. Linear bi-

dimensional (2D) elements, namely triangular with three nodes or quadrangular with four

nodes, may be used to construct the cross-section mesh. The components of interest at the

cross-section level are the normal, x xf ( ,...)σ = ε , and shear, xyτ and xzτ , stresses. Only

elastic shear is considered. At the element level, the Timoshenko beam theory is adopted,

assuming that plane sections remain plane after deformation, but not necessarily normal

to the beam axis.

The evaluation of the stress resultant for each beam element proceeds as follows

(i) Evaluation of the generalized strain E at the integration point of each beam element,

from the nodal generalized displacement ( 1U , 1Θ , 2U , 2Θ ).

(ii) Use of the beam model in order to evaluate the strain tensor ε and in particular its

normal component, xε , at the level of each fibre, located at the Gauss integration points

of the elements describing the section.

(iii) Use of the constitutive relationship in order to evaluate the stress tensor σ at the

level of each fibre, in particular its normal component, xσ .

(iv) Integration over the section of the relevant stress components in order to compute the

generalized stress F for the section.

(v) Computation of the stress resultant ( 1F , 1M , 2F , 2M ) for the beam element.

5.2.2. Constitutive laws

Concrete

Concrete behaviour is represented by a parabolic curve up to the peak stress point

followed by a straight line in the softening zone. Confinement is taken into account by the

modification of the plain concrete curve and including an additional plateau zone at the

residual strength. Cyclic behaviour accounts for stiffness degradation and crack closing

phenomena. Tensile resistance is also considered.


156

Strain

Str

ess

unconfinedconfined

(a)

Strain

Str

ess

(b)

Figure 5.1. Monotonic constitutive law for in compression (a) and tension (b)

The constitutive law for unconfined concrete in compression consists of two branches, as

shown in Figure 5.1a. The first branch, which is a parabolic function, describes the

ascending branch of the curve from zero stress to the maximum compression strength

co co co

2 σ ε ε

= − σ ε ε (5.1)

where coσ and coε are respectively the compressive strength and the corresponding strain.

The second branch is linear and describes the softening behaviour after maximum stress

and until failure

( )coco

1.0 Zσ

= + ε − εσ

(5.2)

where Z is the slope of the descending branch and depends on the degree of confinement.

The maximum stress and corresponding strain can be modified to account for

confinement, as shown in Figure 5.1a. For confined concrete, a third branch is considered

after the softening branch. This describes a compression plateau with constant value equal

to a residual strength, ptσ . The value pt co0.2σ = σ has been proposed [Park & Priestley,

1982].

In tension, a bilinear stress-strain curve has been adopted, as shown in Figure 5.1b. From

zero stress to the maximum tensile strength, tσ , the model presents a linear elastic

behaviour with a slope equal to the initial compression Young modulus, oE

ptσ

coσ

coε

tσ

tε

tmε


157

oEσ = ε (5.3)

The second branch describes the softening behaviour after cracking and follows a straight

line

tt

r ( / )r 1

− ε εσ = σ

− (5.4)

where

tm tr /= ε ε (5.4)

In the above expressions tσ is the tension strength and tmε is the deformation at zero

stress.

The compression monotonic curve is the envelope of the concrete behaviour under cyclic

compressive loading. Unloading from the envelope follows a straight line with a slope

depending on the maximum strain, maxε , ever reached during the loading history

( )

( ) ( )

2max co

d o 2max co max co

/E E 1

1 / /

ε ε= −

+ ε ε + ε ε (5.5)

The decrease of the slope with increasing maximum strain accounts for the degradation of

stiffness due to cycling. The reloading compression curve is also a straight line from zero

stress at the plastic strain, plε , until the last point reached on the envelop. No strength

degradation is considered.

Strain

Str

ess

Strain

Str

ess

Figure 5.2. Cyclic constitutive law for concrete in compression (a) and tension (b)

dE

maxεplε tmε

coε

tσ

plε


158

Strain

Str

ess

Strain

Str

ess

Figure 5.3. Monotonic (a) and cyclic (b) constitutive law for steel

Concerning tensile stresses, an envelope going from zero stress at coε to the tensile

strength is considered, as shown in Figure 5.2b. The envelope comprises a second linear

branch from the maximum tensile strength to the point of zero stress and strain tm trε = ε .

An appropriate value for tmε is the yield strain of the longitudinal reinforcing bars

[Barzegar-Jamshidi & Schnobrich, 1986]. Unloading after tr2 pl tmε = ε + ε follows a zero

stress path. When the maximum tensile strength is reached, no more tensile stresses can

be supported from the concrete in subsequent cycles. If no tensile stresses are considered

in the model, the plastic strain is determined by the zero stress point from the

compression unloading curve.

Steel

The monotonic constitutive law for steel is a five-parameter model. The first zone is

elastic and is defined by the Young modulus, E, and the yield strain, syε ,

syEσ = ε (5.6)

Then follows the yield plateau at the yield stress, syσ , until the hardening strain, shε ,

syσ = σ (5.7)

Finally, the hardening curve until the maximum stress, suσ , and corresponding strain, suε ,

follows a fourth-degree polynomial

suε

shε

syε

suσ syσ

oσ

rσ

rε

oε

o r( )ξ ε − ε

oE


159

4

susu su sy

su sh

( ) ε − ε

σ = σ − σ − σ ε − ε (5.8)

The same law is used also for compressive loading, if no buckling is considered for the

longitudinal rebars. Otherwise, some modifications are introduced.

A modified Menegotto-Pinto model is adopted for cyclic loading. If small unloading

cycles are imposed to the bars, no hysteretic effect is evidenced and a straight line with

slope equal to the initial Young modulus is adopted for both loading and unloading.

Otherwise, if the strain satisfies the condition

symax 3

εε − ε < (5.9)

where maxε is the maximum attained strain in the loading history, the behaviour of steel is

described by the relation

( )

* * *1 RR*

1 bb

1

−σ = ε + ε

+ ε

(5.10)

where

* s r

o r

σ − σσ =

σ − σ (5.11a)

* s r

o r

ε − εε =

ε − ε (5.11b)

1o

2

R Rα ξ

= −α + ξ

(5.11c)

In the previous expressions rσ and rε describe the last reversal point, b is the ratio

between the hardening slope, hE , and the initial slope, oE , and R is a parameter that

defines the shape of the transition branch of the curve. Parameters oσ , oε , and ξ are

defined in Figure 5.3b. Parameters oR , 1α and 2α should be obtained from experimental


160

data; the values oR = 20.0, 1α = 18.5 and 2α = 0.15 are proposed [Menegotto & Pinto,

1973].

Based on experimental results, buckling is considered important when the ratio between

the unsupported length, L, and diameter, D, of the rebars is greater than 5 [Monti & Nuti,

1992]. In that case, the unloading curve from tensile stresses and the reloading curve after

reversal from compression must be modified. The post-yield compression zone has a

softening behaviour and the b factor is accordingly modified. On the other hand, during

reloading after reversal from compression, also the Young modulus is reduced. Further

details on the implementation of the model can be found elsewhere [Guedes et al., 1994].

5.2.3. Alternative configurations for the cross-section and the beam element

In order to reduce the computational demand for the PSD tests and to increase the

robustness of the numerical models and procedures, a simple, yet accurate numerical

model should be used for the substructured piers. The most accurate choice is a refined

tri-dimensional (3D) finite element model with realistic constitutive laws for the materials

and the steel-to-concrete interface. It will be shown in the following that such a model

would demand exaggerated computation time. For this reason, it was decided to use a

fibre/Timoshenko beam element implemented in the finite element code Cast3m, as a

compromise between accuracy and simplicity.

Taking into account the symmetry of the geometry and the loading, a 2D beam element

was used. Different simplified configurations at the cross-section level have been

examined, as explained in detail in the following. Non-linear behaviour was assumed for

the concrete and elastic-perfectly plastic behaviour for the reinforcement steel. Numerical

analysis showed no significant difference between the results obtained using this bilinear

model for steel and those obtained with a, more realistic, modified Menegotto-Pinto

model. Table 5.1 presents the material properties used in the numerical model. Since no

closed stirrups or crossties were present in the tested piers, no confinement effect was

considered for the concrete.

Different configurations have been examined for the discretisation of the cross-section of

the piers. The results of each alternative configuration were compared and the adopted


161

numerical models were calibrated on the basis of the cyclic tests performed on scaled

models of the piers described in Chapter 3.

The bridge piers have a rectangular hollow cross-section. The corresponding fibre model

for the cross-section is presented in Figure 5.4a. The elements shown in blue correspond

to the (unconfined) concrete, whereas those shown in red correspond to the vertical

reinforcement steel. Each element used to model the reinforcement has four integration

points and an area equal to the area of the reinforcement of each face of the cross-section.

This configuration was initially chosen in order to be close to the geometry of the

specimens. Keeping in mind that the displacement was imposed in the strong direction of

the cross-section, the discretisation adopted for the steel elements was considered

adequate for the flanges, but not for the web. The vertical rebars of the specimen are

uniformly distributed along the two faces of the web and are expected to be under tension

gradually as the neutral axis moves along the web. This cannot be accurately modelled

with the initial configuration and could cause problems during the iterations for the PSD

tests with substructuring. The mesh for the cross-section was therefore modified in order

to avoid such eventual numerical problems.

Since the cross-section was symmetric and the loading would be applied along an axis of

symmetry, an alternative model at the cross-section level was examined, shown in Figure

5.4b. An equivalent I cross-section was considered with web width equal to the total

width of the two webs of the original cross-section. Rectangular elements with four

integration points each, better distributed along the web, were used for the steel

reinforcement. This configuration enabled a more realistic representation of the actual

distribution of vertical reinforcement along the web of the pier model, with similar

computational demand as for the original box cross-section.

Figure 5.4. Discretisation of alternative models for the cross-section

(a)

(d) (b)

(c)


162

Table 5.1. Material properties used in the numerical models of the piers

Concrete Steel

cE (GPa) 33.5 cE (GPa) 200

Pν 0.2 Pν 0.3

cf (MPa) 43 yf (MPa) 545

tf (MPa) 3 uf (MPa) 611

coε (%) 0.257 syε (%) 0.5

Table 5.2. Characteristics of different models

Cross-section Concrete Steel Beam

A20 Hollow Section Section 3D

A20I I Section Section 3D

A20Ip I Section Point 3D

A20Ip_2D I Section Point 2D

A20s Line Segment Point 2D

0

200

400

600

800

1000

1200

1400

0.00 0.05 0.10 0.15 0.20

Displacement (m)

For

ce (k

N)

3D

3D

3D

2D

2D

Figure 5.5. Pier A20: force-displacement monotonic curves for different models

In an attempt to further simplify the model, a new element was implemented for the

reinforcement steel bars. The element originally used is a linear quadrilateral element


163

with four nodes. In order to reduce to minimum the integration points, an element with

one integration point was implemented. The geometrical support is a point, thus there is

one integration point instead of four. This enabled the use of more elements better

distributed to model the vertical rebars. The corresponding model of the cross-section is

shown in Figure 5.4c. The rebars of the flanges and the webs were lumped at elements

with equivalent area, positioned along the longitudinal axis of symmetry of the cross-

section. This configuration made it possible to reproduce the exact distribution of the steel

rebars of the tested model, without increasing, but actually decreasing, the computational

demand. In fact, the number of nodes for the steel elements was reduced from 40 (for the

discretisation shown in Figure 5.4b) to 25 (for the discretisation shown in Figure 5.4c).

Furthermore, a new element was implemented for the concrete fibres in order to meliorate

the speed of computation for the substructured models during the PSD tests. The new

element has only two integration points, since the geometrical support is a segment. The

corresponding model at the cross-section level is shown in Figure 5.4d. Also in this case

the number of nodes for the concrete elements was reduced from 112 (for rectangular

elements shown in Figure 5.4c) to 44 (for linear elements show in Figure 5.4d).

The original FTB model was used to perform 3D analysis, and then six degrees of

freedom (DOFs) were considered for each node of the beam element. The calculated

reactions were the forces along the three axes, namely xR , yR and zR , and the moments

by the three axes, namely xM , yM and zM . Considering the symmetry of the geometry

and the loading, only three DOFs were significant in the present case for the tested piers:

displacements along the vertical and longitudinal axes and rotation by the transversal

axis. A 2D beam model was used considering the cross-section shown in Figure 5.4d. The

results of all alternative models at the cross-section level are compared in Figure 5.5 for

pier A20. All alternative models gave consistent results. Therefore it was decided to

proceed with the simplest one.

Table 5.2 recapitulates the types of cross-sections and elements used for every alternative

model. Passing from the original hollow cross-section to the equivalent I cross-section, a

slightly larger resistance is observed, due to the larger lever arm of the steel fibres of the

web. The use of point elements for the steel fibres of the equivalent I cross-section results

in larger resistance, compared to the original configuration. This also can be attributed to


164

the discretisation of the vertical reinforcement fibres. Passing from the 3D beam element

to a 2D beam element, almost identical response is observed. Finally, for the 2D beam

element and using line elements for the concrete fibres the strength does not change

significantly.

5.2.4. Validation of the numerical models

Before the PSD tests, two scaled models of the piers A40 and A70 were tested under

cyclic loading. The results of the cyclic tests were used to calibrate the numerical models

for the substructured piers. The results of numerical simulations using a damage model

[Faria et al., 2001; Pouca, 2001] were also compared to the experimental values. The

main objective of the numerical simulation was the preparation of accurate models for the

numerical piers during the PSD tests. The fibre model was adequate for the case of the

short pier A70, whose failure mode was flexure-dominated. Pier A20 was expected to

have a similar failure mode. Concerning the tall pier A40, the fibre model resulted in

larger resistance and different failure location, whereas the damage model gave results

similar to the experimental values. The fibre model was unable to accurately represent the

shear effects in the lower part of the specimen. The same failure mode and overall

behaviour was expected also for piers A30, A50 and A60.

Piers with flexure-dominated behaviour

The experimental and numerical force-displacement curves for the short pier A70 are

compared in Figure 5.6. Very good agreement is observed in terms of strength and cyclic

behaviour. The numerical simulation was terminated at the displacement at which a

sudden drop of resistance is evidenced in the numerical curve. This was due to failure of a

steel fibre and occurred for a displacement similar to the experimental displacement that

corresponds to failure of the first vertical reinforcement bar. Although the effect of lapped

splices was not considered and perfect contact was assumed between concrete and steel

elements, the fibre model was successful in simulating the global behaviour of the short

pier.

Damage was observed at the lower part of the pier only. The numerical model indicated

yielding of steel within the first 1.5 m from the base cross-section. This is contrary to the

experimental observations that showed evidence of yielding at a limited zone just above


165

the foundation and at the end of the lapped splices. It is reminded that continuous

reinforcement and perfect bond between steel rebars and surrounding concrete was

assumed in the numerical analysis. This, combined with the assumption of elastic

behaviour of the base block (yield penetration in the foundation was not allowed in the

numerical model), may explain the aforementioned difference.

Figure 5.7 compares the experimental and numerical moment-curvature diagrams. The

experimental curvature was calculated from the instrumentation readings, while the

moment was obtained by dividing the measured force by the pier height. The numerical

moment-curvature curve was extracted from the results of the analysis. Also in this case

good agreement is observed, although the numerical model results in smaller dissipation

capacity and exhibits more pinched response, compared to the experimental behaviour.

The cumulative dissipated energy versus the lateral displacement is plotted in Figure 5.8.

The dissipated energy is equal to the area within the force-displacement loops, as results

from the numerical analysis and the experimental data. It is seen that for the cycles with

small amplitude (0.027 m), the numerical model results in smaller dissipation capacity,

compared to the experimental data. This shows the inability of the numerical model to

fully capture the damage (small horizontal cracks in the flanges within the lower part of

the pier) induced in the pier during the small-amplitude cycles. For the cycles with higher

amplitude the numerical model slightly overestimates the dissipated energy. The total

energy dissipated by the numerical model is only 6.4% higher than the experimental

value.

From the above considerations it is concluded the FTB formulation accurately reproduces

the experimental behaviour of the short pier in terms of resistance, damage location and

hysteretic response. It is reminded that certain simplifications were introduced, namely

elastic behaviour of the base, continuous reinforcement and no steel-concrete slip. It is

important to note that, as regards the tested specimen, predominant flexural response was

observed.


166

-1500

-1000

-500

0

500

1000

1500

-0.10 -0.05 0.00 0.05 0.10

Displacement (m)

For

ce (k

N)

experimental

numerical

Figure 5.6. Short pier A70: experimental and numerical force-displacement curves

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05

Curvature (1/rad)

Mom

ent (

kNm

)

experimental

numerical

Figure 5.7. Short pier A70: experimental and numerical moment-curvature curves


167

0

50

100

150

200

250

-0.10 -0.05 0.00 0.05 0.10

Displacement (m)

Dis

sipa

ted

ener

gy (k

Nm

)

experimental

numerical

Figure 5.8. Short pier A70: experimental and numerical dissipated energy versus top

displacement

Piers with combined flexural and shear behaviour

In this section the results of a FTB model are compared to the experimental data from a

cyclic test on a scaled specimen of a bridge pier [Peloso, 2003]. The objective of this

simulation is to highlight the limitations of the classic FTB modelling when studying

elements with significant shear deformation and to validate the model for further studies

of a retrofitted pier (see section 5.4.3).

The scaled specimen had a rectangular hollow cross-section with external dimensions

0.45x0.45 m and internal dimensions 0.35x0.35 m. A foundation block 1.20x1.20 in plan

and 0.60 m high was used to anchor the specimen on the laboratory floor. The horizontal

load was applied at 1.35 m from the base cross-section of the specimen, corresponding to

aspect ratio L/d = 3. The longitudinal reinforcement consisted of 40 Φ 8 bars uniformly

distributed along the internal and external faces of the pier, corresponding to

reinforcement ratio sρ = 0.025. The horizontal reinforcement consisted of one rectangular

stirrup for each wall of the specimen, vertically spaced at 0.075 m. The stirrups were

made of Φ 3 smooth bars. The compressive strength of concrete was cf = 30.3 MPa. The

yield stress of steel was yf = 550 MPa, while the ultimate stress was uf = 660 MPa.


168

Cyclic displacement with increasing amplitude was applied at the top of the pier in the

presence of constant axial load equal to 250 kN ( ν = 0.1). During the first cycles,

horizontal cracks appeared near the base and then within 1.0 m from the foundation. With

increasing displacement, diagonal cracks appeared and the existing ones opened further.

Finally, at drift δ = 3.6 % a sudden reduction of strength, associated with crushing of

concrete, was observed. The specimen was able to sustain further cycling with limited

resistance. The experimental force-displacement curve is shown in Figure 5.9. At the end

of the test, large diagonal cracks and disintegration of concrete at the webs and crushing

of concrete at the base of the flanges were observed. This points to a combined flexural-

shear response.

A FTB model of the tested pier was built. The constitutive laws for concrete and steel

presented in section 5.2.2 were adopted with properties as for the tested specimen.

Because of the configuration of the stirrups, no confinement effect was considered and

the residual strength of concrete was set to zero. At the cross-section level, rectangular

elements with four integration points each were used for the concrete fibres and point

elements were used for the steel fibres. In this way, a detailed discretisation of the section

was obtained and the exact position of all rebars was reproduced. For the beam element, 6

elements 0.15m-high were used for the lower part, where damage was observed during

the tests, and 2 elements were used for the remaining part. The foundation block was

considered to be fully fixed at the base and elastic behaviour was assumed.

The experimental and numerical force-displacement curves are compared in Figure 5.9.

The agreement is not as good as for the previous case. The numerical model reproduces

well the experimental behaviour for the cycles of small amplitude, but not for the cycles

of large amplitude. This can be attributed to the contribution of shear phenomena that are

not appropriately modelled in the numerical simulation. In fact, during the large cycles,

diagonal shear cracks developed in the tested specimen and are responsible for the

pinching observed in the experimental force-displacement curves for these cycles. The

numerical model accounts only for elastic shear and therefore does not succeed in

predicting the cyclic behaviour of the specimen at large deformations.

The experimental and numerical cumulative dissipated energy is plotted in Figure 5.10

against the top displacement. It is seen that for the cycles with small displacement, the

numerical model results in lower capacity of energy dissipation. This shows that it does


169

not capture the small damage observed in these cycles and some tuning of the material

parameters is needed to obtain better agreement. On the contrary, for the cycles with large

deformation, the numerical model results in larger dissipation capacity. This is a

consequence of the problems related to shear phenomena, as explained before.

-250

-200

-150

-100

-50

0

50

100

150

200

250

-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05

Displacement (m)

For

ce (k

N)

ExperimentalNumerical

Figure 5.9. Tall pier T250: experimental and numerical force-displacement curves

0

5

10

15

20

25

30

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

Displacement (m)

Dis

sipa

ted

ener

gy (k

Nm

)

experimentalnumerical

Figure 5.10. Tall pier T250: experimental and numerical dissipated energy versus top

displacement


170

In conclusion, it is shown that the adopted fibre/Timoshenko beam model is fully valid

for the case of piers with pure flexural behaviour, while presents several limitations in the

case that shear phenomena have a significant contribution in the structural response.

Piers with tension shift

In this section the experimental data from the cyclic test on the tall bridge pier, A40, are

compared to the results of numerical analyses using the FTB modelling. The original

formulation of the FTB model for the tall pier resulted in higher resistance and ultimate

displacement, as well as different height-wise distribution of curvature, compared to the

experimental results. The experimental and numerical distributions of curvature at

maximum displacement are compared in Figure 5.11. This model predicted failure of the

pier above the cross-section at 1.20 m from the base, where the first reduction of

longitudinal reinforcement takes place. It is reminded that the reinforcement at the base

cross-section of the scaled specimen consists of 80 Φ 16 rebars, it is reduced to almost

half (76 Φ 12) at the height of 1.20 m and then to almost one quarter (40 Φ 12) at the

height of 3.5 m. Looking at bending capacity alone, the critical cross-section is identified

at 2.5 m from the base, as predicted by the original numerical model. Due to shear

cracking and to the tension shift phenomenon, as discussed in Chapter 3, the critical

cross-section was shifted above the bar cut-off at 3.5 m from the base.

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Curvature (rad/m)

Hei

ght (

m)

numericalexperimental

Figure 5.11. Tall pier A40: distribution of average curvature along the height of the pier

for the original model


171

As only elastic shear deformation is considered in the FTB model, this phenomenon could

not be captured. The same failure mode and overall behaviour was expected also for the

piers A30, A50 and A60. These piers were part of the numerical substructure of the PSD

tests and therefore an adequate numerical model that predicts correct failure mode,

resistance and hysteretic behaviour was needed in order to perform the PSD tests.

In order to obtain the correct failure location, and then the correct resistance and

deformation capacity, alternative configurations were considered. So as to artificially

increase the tension in the rebars above the cut-off, an alternative model with an external

moment, proportional to the applied force, applied at the critical cross-section was

studied; this model yielded results close to the experimental ones. Since for the PSD tests

the input at each time step would be the top displacement, while the restoring force would

be measured, or calculated, this configuration was complicated. An alternative solution

was to reduce the area of reinforcement in the flange above the critical cross-section. The

force-displacement monotonic curves for the two alternative solutions are compared to

the experimental envelope curve for the tall physical pier, A40, in Figure 5.12. Both

models yielded a good approximation of the experimental envelope. Because of the

complications related to the PSD testing procedures, it was decided to proceed along the

line of modifying the area of steel in the model, rather than apply an external moment.

0

200

400

600

800

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Displacement (m)

For

ce (k

N)

experimental

external moment

reduced steel area

Figure 5.12. Tall pier A40: force-displacement curves for alternative models


172

Alternative modifications were also considered. For the first alternative, elastic behaviour

was adopted for the part of the pier below the critical cross-section and thus, the correct

failure location was obtained. Looking at the cyclic behaviour, see Figure 5.13a, the post-

crack stiffness is not sufficiently reproduced. This is because cracking in the tested

specimen first occurred at the lower part, then extended along the height and only at

relatively large levels of top displacement damage concentrated above the bar cut-off,

while damage below the critical cross-section of the numerical model was not allowed.

For the same reasons, the energy-dissipation capacity is not correctly represented, see

Figure 5.13b. During the PSD tests, the post-crack behaviour of the numerical piers was

significant, because they were expected to respond mainly in this region for all three

earthquake amplitudes. Then, this configuration was not satisfactory.

Alternatively, the steel area below the critical cross-section was artificially increased.

This forced damage to concentrate above the critical cross-section and the objective of

getting the correct failure location was met. Nevertheless, the cyclic response, Figure

5.14a, indicates that also this model does not accurately follow the post-crack behaviour.

Looking at the dissipation capacity, it is seen that this model shows smaller capacity,

compared to the tested pier, see Figure 5.14b. This could be due to the fact that in the

lower part of the pier, the larger amount of steel results in smaller crack widths and

smaller strains in the rebars and consequently in smaller inelastic deformation and energy

dissipation. For the above reasons, also this solution was judged unsatisfactory.

-800

-400

0

400

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3


(a)

0

100

200

300

400

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


(b)

Figure 5.13. Numerical model with elastic base for the tall pier A40: force-displacement

curves (a) and dissipated energy (b)


173

-800

-400

0

400

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3


(a)

0

100

200

300

400

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)

Experimental

Numerical

(b)

Figure 5.14. Numerical model with increased steel at the base for the tall pier A40: force-

displacement curves (a) and dissipated energy (b)

-800

-400

0

400

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Forc

e (k

N)


(a)

0

100

200

300

400

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)ExperimentalNumerical

(b)

0

2

4

6

8

10

12

14

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Curvature (rad/m)

Hei

ght (

m)

numericalexperimental

(c)

Figure 5.15. Numerical model with reduced steel at the critical cross-section for the tall

pier A40: force-displacement curves (a), dissipated energy (b) and distribution of

curvature along the height (c)

The last examined alternative was to reduce the amount of steel above the critical cross-

section. This solution enabled to approximate the damage observed within the lower part


174

of the pier during the cycles of small amplitude and also to approximate the post-crack

stiffness. The reduction was such that the correct resistance is obtained, as seen in Figure

5.15a. The dissipation capacity was fairly well estimated for the small-amplitude cycles.

Worse agreement is observed, though, for the large-amplitude cycles, see Figure 5.15b.

This can be attributed to the smaller amount of steel, compared to the actual amount

present in the physical model. The numerical model predicts the correct failure location,

as expected, but does not perfectly account for the damage in the lower part of the pier,

see Figure 5.15c. Despite the shortcomings, among the available solutions, this last one

was the one that better satisfied the requirements of correct failure location, correct

resistance and best possible approximation of cyclic behaviour and dissipated capacity.

Therefore, it was decided to proceed with this modification for the numerical models of

the substructured piers.

From the examples presented previously the FTB model can be validated for elements

with different behaviour modes, namely flexure-dominated, combined flexural and shear

and flexural response with tension shift. For the first case, the numerical model was able

to reproduce the experimental behaviour, even though continuous reinforcement and

perfect bond between concrete and steel was considered. For the second case, some

differences appeared in the cyclic behaviour because of the inability of the model to

account for inelastic shear damage. It is reminded that this was observed only at large

displacements. For the last case, the numerical model was able to predict the correct

failure location and resistance and to approximate the cyclic behaviour only after certain

modifications were introduced.

Numerical models for the Talübergang Warth Bridge PSD tests

In this section the numerical models for the substructured piers A20, A30, A50 and A60

are presented. It was decided to use fibre/Timoshenko beam elements with the cross-

section and material laws presented previously, appropriately modified to account for the

relocation of the critical cross-section due to the tension shift phenomenon. With this

scope, the results of refined FEM analysis using a damage model [Faria et al., 2001;

Pouca, 2001] were used as reference. It is reminded that this modification was necessary

for the numerical pier A30, A50 and A60. For these piers the area of reinforcement in the

flange above the bar cut-off was artificially reduced in order to obtain the correct

resistance. The “correct resistance” was taken from the results of the damage model


175

analyses. Table 5.3 shows the amount of longitudinal reinforcement for the scaled piers as

well as the values assumed in the numerical simulation to achieve the “correct

resistance”.

Figure 5.16 presents the force-displacement curves for all the piers and the two alternative

modelling approaches. For the short physical pier A70 also the experimental curve is

shown. Figure 5.17 presents the cumulative dissipated energy against the lateral

displacement for the two alternative models. It is seen that the difference between the

results lays mainly in the cyclic hysteretic behaviour. In Figure 5.16 it is observed that all

piers exhibit a pinched response for the damage model and much less for the fibre model.

The latter is in better agreement with the experimental evidence.

The difference in hysteretic response results in lower dissipation capacity for the damage

model with comparison to the fibre model, as seen in Figure 5.17 and Table 5.4. For the

physical piers A40 and A70 the numerical results can be compared to the experimental

results presented in Chapter 3. It is seen that the fibre model results in slightly higher total

dissipated energy than the experimental value, by 2.4% and 3.5% for the tall and short

pier, respectively. On the other hand, the damage model underestimates the experimental

total dissipated energy by 17% and 7.7% for the tall and short pier, respectively. In this

respect, the fibre model seems advantageous, compared to the damage model.

Table 5.3. Longitudinal reinforcement steel ratio for the scaled bridge piers

A-A B-B C-C

Height (m) sρ Height (m) sρ Height (m) sρ

A20 2.76 0.9 7.04 0.6 2.12 0.3

A30 3.52 0.7 7.08 0.4/0.3a 4.96 0.2

A40 1.20 1.0 2.30 0.7 9.75 0.4/03a

A50 1.60 0.7 7.24 0.4/0.3a 5.56 0.3

A60 1.48 0.8 2.68 0.5/0.4a 7.84 0.3

A70 6.50 0.4 a original/modified


176

Pier A20

-1500

-1000

-500

0

500

1000

1500

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Forc

e (k

N)

damage model

fibre model

Pier A50

-800

-400

0

400

800

-0.2 -0.1 0.0 0.1 0.2Displacement (m)

Forc

e (k

N)

damage modelfibre model

Pier A30

-800

-400

0

400

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Forc

e (k

N)

damage model

fibre model

Pier A60

-800

-400

0

400

800

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15Displacement (m)

Forc

e (k

N)

damage modelfibre model

Pier A40

-800

-400

0

400

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Forc

e (k

N)

damage model

fibre model

Pier A70

-1500

-1000

-500

0

500

1000

1500

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15Displacement (m)

Forc

e (k

N)

damage modelfibre modelexperimental

Figure 5.16. Talübergang Warth Bridge piers: force-displacement curves for the fibre

model and the damage model

Table 5.4. Values of dissipated energy (kNm) for the bridge piers

A20 A30 A40 A50 A60 A70

Damage model 27.7 126 227 97 79 296

Fibre model 34.4 223 280 162 145 332

Experimental - - 273.5 - - 320.8


177

0

20

40

60

80

100

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)

fibre modeldamage model

Pier A20

0

50

100

150

200

250

-0.20 -0.10 0.00 0.10 0.20Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


Pier A50

0

50

100

150

200

250

300

350

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


Pier A30

0

50

100

150

200

250

-0.20 -0.10 0.00 0.10 0.20Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


Pier A60

0

50

100

150

200

250

300

350

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


Pier A40

0

50

100

150

200

250

300

350

-0.10 -0.05 0.00 0.05 0.10Displacement (m)

Dis

sipa

ted

ener

gy (

kNm

)


Pier A70

Figure 5.17. Talübergang Warth Bridge piers: dissipated energy versus lateral

displacement for the fibre model and the damage model

In conclusion, the modified fibre models are considered to represent the actual behaviour

of the numerical piers with sufficient accuracy, for what concerns the failure location,

resistance, post-cracking stiffness and cyclic behaviour.

Finally, the numerical models developed in this section are used for monotonic analyses

in order to define the displacement ductility capacity of the piers. Ductility capacity, uµ ,


178

is defined as the ratio of the ultimate displacement, uu , to the yield displacement, yu . An

elastic-perfectly plastic approximation of the monotonic numerical curve is considered;

both curves are shown in Figure 5.18 for all the piers. The yield displacement is defined

at the intersection of the line from the origin passing from the numerical curve at max0.75F

and the horizontal branch of the bilinear curve. Ultimate displacement is defined at the

point after the attainment of maximum force, maxF , where the resistance is reduced to

max0.8F . Following this definition, the values of displacement and force at yielding and

ultimate are presented in Table 5.5, along with the values of displacement ductility. Table

5.5 presents also the values of displacement at cracking of the first concrete fibre, cu ,

which are identified at the attainment of the tensile concrete strength. These values of

cracking displacement, yield displacement and displacement ductility were used in the

previous chapter to define the damage suffered by the numerical piers during the PSD

tests and to evaluate the performance of the bridge structure, following the simplified

assessment procedures.

5.3. FEM MODELLING

To overcome the limitations of the FTB models, related to shear deformation and slippage

between steel rebars and concrete, the response of the two piers is simulated using the

FEM method. The constitutive laws for concrete and steel-concrete bond are presented

and the results of the numerical simulation are compared to the experimental data. It will

be shown that this modelling approach allows to obtain the correct evolution of damage,

failure location and resistance, at the expense of significant computational demand.

Table 5.5. Characteristic values of force and displacement for the bridge piers

A20 A30 A40 A50 A60 A70

cu (m) 0.006 0.016 0.013 0.011 0.007 0.003

yu (m) 0.065 0.038 0.081 0.044 0.043 0.011

uu (m) 0.187 0.372 0.230 0.326 0.179 0.100

uµ 2.9 9.8 2.8 7.4 4.1 9.1


179

Pier A20

0

200

400

600

800

1000

1200

0.00 0.05 0.10 0.15 0.20

Displacement (m)

Forc

e (k

N)

Pier A50

0

200

400

600

800

0.0 0.1 0.2 0.3 0.4

Displacement (m)

Forc

e (k

N)

Pier A30

0

200

400

600

800

0.0 0.1 0.2 0.3 0.4

Displacement (m)

Forc

e (k

N)

Pier A60

0

200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20

Displacement (m)

Forc

e (k

N)

Pier A40

0

200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20

Displacement (m)

Forc

e (k

N)

Pier A70

0

500

1000

1500

0.00 0.02 0.04 0.06

Displacement (m)

Forc

e (k

N)

Figure 5.18. Talübergang Warth Bridge piers: force-displacement curves from pushover

analysis and bilinear envelope

5.3.1. Constitutive laws

Concrete

A constitutive law that accounts for non-linear behaviour in tension and for linear elastic

behaviour in compression is presented in this section. To describe tension cracking, either

discrete or smeared cracks are considered. Discrete cracking allows cracks to form at the


180

boundaries of elements and for a more realistic representation, double joints have to be

declared from the beginning, or new elements have to be introduced after cracking. This

approach is best suited for structures where a single crack forms and offers detailed

results at the local level of the crack, at the expense of large memory and computational

demand. Following the smeared crack approach, cracks are assumed to be distributed

over a concrete element. This requires less computational demand and is best suited for

elements where distributed cracking is expected [CEB, 1996]. A smeared cracking model

[Dahlblom & Ottosen, 1990] is described in the following.

Considering an isotropic and homogeneous bar, it is assumed that two regions exist: one

region that exhibits strain softening and another region in elastic unloading. Following a

fictitious crack model [Hillerborg et al., 1976], the post-peak behaviour is described by an

undamaged, elastic, region, which occupies the whole length, L, of the bar, and an

infinitely thin damaged, softening, region, in which additional elongation, w, occurs in

the post-peak region. The fictitious crack model describes the behaviour of the cracked

zone in terms of normal stress, σ , and elongation normal to the crack plane, nw . For

simplicity, the stress-elongation behaviour of the second region, shown in Figure 5.19a, is

described by a straight line

n t

1w ( )

N= σ − σ (5.12)

where N is the slope of the curve and tσ is the uniaxial tensile strength. Then, the bar

elongation in the post-peak region is

Crack opening

Str

ess

Crack opening

Str

ess

(a) (b)

Figure 5.19. Concrete constitutive law: loading (a) and unloading (b) of a crack

0=β 1=β

5.0=β


181

t

1u L ( )

E Nσ

= + σ − σ (5.13)

where E is the Young modulus and the slope of the softening branch is obtained by

equating the fracture energy, fG , to the energy dissipated by the whole bar

f

2t

G2N

σ= (5.14)

At this point, the material characteristic length, λ , is introduced

2t

f EG2σ

=λ (5.15)

In order to consider the fact that the cracks are subjected to shear, it is assumed that the

tangential crack displacement, tw , occurs within the infinitely thin cracked zone and that

it depends on the shear stress, τ . A simple expression is adopted

τ=s

nt G

ww (5.16)

where sG is a material constant, called slip modulus.

In the general three-dimensional case it is assumed that three cracks may develop. The

crack planes are considered to be perpendicular to each other. The first crack initiates

when the maximum principle stress, 1σ , exceeds the tension strength, tσ , and the first

crack is taken normal to the principal direction of 1σ . A possible second crack develops if

the normal stress in some perpendicular direction exceeds the tensile strength. Finally, a

possible third crack develops if the stress perpendicular to the plane of the first two cracks

exceeds tσ . When a crack has been created, its direction is considered fixed.

For the particular case of plane stress formulation, and without repeating the intermediate

steps given in [Dahlblom & Ottosen, 1990], the constitutive relation in matrix form is

σ−

σσσ

++ν−

ν−+=

εεε

oJJ

K)G/1(000J)E/1(E/0E/J)E/1(

2y

x

t

xy

yy

xx

xy

yP

Px

xy

yy

xx

(5.17)


182

x

x NL1

J = ; y

y NL1

J = ;

−=

y

yy

x

xx

sxy L

wLw

G1

K (5.18)

In the previous equations G is the shear modulus, xL and yL are respectively the

equivalent lengths related to the cracks in the x and y directions, while xxw and yyw are

the crack openings.

Introducing the aspect of mesh sensitivity, the equivalent length is in general the

maximum length of the cracked element region in the direction normal to the crack plane.

For example, for an element with three nodes the region of interest is the whole region of

the element, while for an element with eight nodes, the region of interest is the tributary

region of the Gauss point where cracking occurs. For general loading and with the

condition of keeping the slope of the stress-strain curve negative in the post-peak region,

the following restriction to the equivalent length applies

P

x 1L

ν+λ

< (5.19)

For normal concrete λ varies between 0.4 m and 0.8 m. The issue of mesh sensitivity is of

practical interest when elements are very lightly reinforced, while results will vary

insignificantly with mesh size for moderately and heavily reinforced elements [CEB,

1996].

For unloading-closing of a crack a linear relation between normal stress, xxσ , and crack

width, xxw , is adopted, as shown in Figure 5.19b. When the normal stress arrives at zero

value, a fraction β of the developed crack width is considered to remain open. The value

β = 0.2 provides results that are in good agreement with experimental data. If

compressive normal stress develops, no change of crack width occurs. Reloading follows

the unloading path until the previously obtained crack width, max,xxw , is regained.

Steel-to-concrete interface

When the global response of members is of interest, perfect contact is often considered

between steel and concrete elements and the interaction between the two materials

(namely slip and dowel action) is accounted for by appropriate modification of the


183

parameters of the constitutive relations of steel and/or concrete. It is however possible to

introduce contact elements between the nodes of the two materials. The simplest type is

the dimensionless link element, which connects the corresponding nodes of concrete and

steel. These elements are able to model the slip in the direction of the rebar by one spring

and the dowel effect by another spring in the direction normal to the rebar. Continuous

contact elements, which connect the corresponding faces of steel and concrete elements,

are also available. With these elements it is possible to model the effect of lateral pressure

on the behaviour of the interface [CEB, 1996].

Steel-to-concrete bond has been of interest for many years and extensive research has

been performed in this field. Among the aspects investigated with experimental testing

was the bond deterioration with repeated loads [Bresler & Bertero, 1968], crack pattern

[Goto, 1971], effect of loading rate [Chung & Shah, 1989], role of stirrups [Giuriani et

al., 1991; Soroushian et al., 1991] and fatigue [Balázs, 1991]. An early shear-slip relation

has been formulated [Tassios, 1979] and then several constitutive laws have been

proposed on these grounds [Eligehausen et al., 1983; Filippou, 1986; Hawkins et al.,

1987; Alsiwat & Saatcioglu, 1992].

The stress-slip constitutive model used in this work [Eligehausen & Balázs, 1993] is

shown in Figure 5.20. The model consists of an initial non-linear relationship

max 1(s / s )ατ = τ ; 10 s s≤ ≤ (5.20)

that corresponds to the mechanical interaction between the bar lugs and the surrounding

concrete. It is followed by a plateau

maxτ = τ ; 1 2s s s≤ ≤ (5.21)

that describes the advanced micro-cracking and the initiation of shearing of the concrete

between the lugs. Then comes a linearly decreasing branch

max max f 2 3 2( )(s s ) /(s s )τ = τ − τ − τ − − ; 2 3s s s≤ ≤ (5.22)

that refers to the reduction of bond resistance due to partly sheared off concrete between

the lugs. The final branch is a constant line


184

Slip

Bon

d st

ress

Figure 5.20. Steel-to-concrete bond constitutive law: Eligehausen- Balázs model

fτ = τ ; 3s s≥ (5.23)

that represents the residual bond capacity after the concrete between the lugs is

completely sheared off. The unloading branch is linear and valid for all parts of the

diagram. The same relationship is assumed regardless of whether the bar is pushed or

pulled. Values of 1s , 2s and 3s , as well as maxτ and fτ as a function of the concrete

compressive strength, have been proposed for confined and unconfined concrete, good

and bad bond conditions [Eligehausen & Balázs, 1993].

5.3.2. Validation of the numerical model

Piers with tension shift

To overcome the inadequacy of the fibre/beam model to simulate the experimental

behaviour of the tall pier, a 2D finite element model in plane stress formulation was

implemented. The pier shaft was modelled using quadrangular elements with four

integration points. Equivalent thickness was considered for the web and flanges. The

horizontal and vertical steel bars were modelled using linear elements with two

integration points.

Non-linear behaviour, based on the model described previously, was assumed for the

concrete elements of the pier, while the foundation block was considered elastic. Because

the model follows elastic behaviour in compression, it was necessary to reduce by 30 %

3s 2s 1s

maxτ

fτ


185

the nominal values of the elastic properties of concrete, so as to obtain the correct

stiffness and strength. In order to reduce the computation time, the part of the pier above

the height of 5.0 m, where damage was not observed during the quasi-static cyclic tests,

was considered to remain elastic. Elastoplastic behaviour with hardening was assumed for

the longitudinal steel elements. The horizontal steel elements were considered to have

linear elastic behaviour. The material properties are given in Table 5.6, where hE is the

hardening stiffness.

Figure 5.21 compares the evolution of damage resulting from the analysis to the

experimental observations. Figure 5.21a shows snapshots of the distribution of concrete

inelastic deformation at displacement that corresponds to the amplitude of the cycles

during the quasi-static tests. It is seen that damage is restricted to the lower part of the

pier shaft for small amplitude of the lateral displacement. Then, extended damage is

observed in that region and concentration of inelastic deformation at the critical cross-

section above the bar cut-off.

The crack pattern resulting from the numerical analysis shows distinct horizontal cracks

within the first 1.0 m from the base for top displacement 25 mm. The cracks extend

through approximately half the length of the web. For a lateral displacement of 30 mm,

corresponding to the first large cycle of the test, more horizontal cracks are observed at

the same zone and another appears at the critical cross-section at 3.5 m. With increasing

amplitude of displacement, namely 70 mm, cracking extends through three quarters of the

web length. Diagonal cracks appear above the height of 2.5 m. For top displacement

equal to 140 mm, cracking extends through the whole length of the web and new

horizontal cracks appear above the cross-section at 4.0 m. Finally, for top displacement

250 mm, diagonal cracks appear within the first 3.0 m from the foundation and new

horizontal cracks form above the critical cross-section.

Recalling the experimental observations, for the cycles of 30 mm horizontal cracks

appeared within the first 1.0 m from the base of the pier and extended up to the height of

3.0 m for the cycles of 70 mm. For the cycles of 140 mm a large horizontal crack

appeared at the critical cross-section at 3.5 m and with further cycling, the flexural

cracking above the critical cross-section increased and diagonal cracks appeared in the

lower part. The damage predicted by the numerical analysis is in fair agreement with

these experimental observations.


186

(b)

u =

250

mm

u =

140

mm

u =

70 m

m

u =

30 m

m

u =

25 m

m

(a)

Figu

re 5

.21.

Evo

lutio

n of

dam

age

for p

ier A

40: n

umer

ical

(a) a

nd e

xper

imen

tal (

b) re

sults


187

u =

250

mm

u =

140

mm

u =

70 m

m

u =

30 m

m

u =

25 m

m

Figu

re 5

.22.

Def

orm

ed s

hape

for p

ier A

40, n

umer

ical

resu

lts (d

ispl

acem

ents

mag

nifi

ed x

15)


188

Table 5.6. Material properties for the tall pier A40

Concrete Steel

cE (GPa) * 33.5 sE (GPa) 200

Pν * 0.2 Pν 0.3

ctf (MPa) 3.5 syf (MPa) 545

fG (MPa) 0.00014 sh E/E 0.003

sG (MPa) 4.2

β 0.2

*nominal values

0

200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20 0.25

Displacement (m)

For

ce (k

N)


Figure 5.23. Tall pier A40: experimental and numerical force-displacement curves

Figure 5.22 shows the deformed shape of the pier, as results from the numerical

simulation. The displacements are magnified to allow a better illustration of the results. It

is seen that until top displacement equal to 70 mm, the deformation is uniformly

distributed within the lower part of the pier shaft and shear seems to have an important

contribution. The behaviour changes for larger amplitude of lateral displacement, after the

concentration of deformation demand at the cross-section above the bar cut-off. While


189

shear continues to be significant in the lower part of the pier, the upper part seems to

rotate like a rigid body by the compressed flange of the critical cross-section.

Considering global results, it is verified in Figure 5.23 that the numerical force-

displacement curve provides a good approximation of the experimental envelope. Very

satisfactory fit is observed in the elastic region. The agreement is good also in the post-

cracking and yielding range.

Piers with lapped splices

For the numerical simulation of the cyclic test on the short pier with lapped splices, a

more refined 2D mesh was used. Quadrangular elements with four integration points were

used for the concrete of the foundation block and the pier shaft. In order to introduce the

joint elements, it was necessary to use quadrangular elements also for the longitudinal

steel. Then, it was decided to consider the vertical reinforcement concentrated at the

flanges. At each flange two rebars, with equivalent area, embedded in the foundation

block extended above the foundation until the height of 0.5 m (equal to the overlapping

length). Adjacent to each of them was positioned a steel bar that extends from the top face

of the foundation through the whole height of the pier. Uni-dimensional joint elements

were introduced between these two steel bars, as well as between the steel elements and

concrete both within the foundation block and the pier shaft. The horizontal

reinforcement was modelled with linear elements with two integration points.

Figure 5.24 presents the mesh of the numerical model. In Figure 5.24a the concrete

elements of the foundation block are shown in light blue. The concrete elements of the

flange are shown in blue and the concrete elements of the web are shown in green. Figure

5.24b presents the mesh for the longitudinal steel, where the starter bars are shown in blue

and the rebars of the pier shaft are shown in red. Finally, Figure 5.24c presents the mesh

for the horizontal steel bars. A close-up of the pier flange around the foundation is shown

in Figure 5.25, where the concrete elements are shown in blue and the steel elements are

shown in red. The overlapping length is also indicated.

Elastic behaviour was considered for the concrete elements of the foundation, while the

constitutive law described in 5.3.1 was used for the pier shaft. It is reminded that this

model considers non-linear behaviour only in tension, while it follows elastic behaviour

in compression. Because of this it was necessary to reduce by 50 % the nominal values of


190

the elastic properties of concrete so as to obtain the correct stiffness and strength. In order

to reduce the computational demand, elastic-perfectly plastic and elastic behaviour was

assumed for the longitudinal and horizontal steel elements, respectively. It was verified

that the strain in horizontal steel did not exceed the yield limit. The constitutive model

described in 5.3.1 was used for the joint elements. The material properties are listed in

Table 5.7, where sK denotes the elastic stiffness along the joint and nK stands for the

stiffness in the direction normal to the joint, for which a high value was considered.

(a) (b) (c)

Figure 5.24. Mesh of the numerical model: concrete (a), longitudinal steel (b), and

transverse steel (c) elements

Figure 5.25. Close-up at the base of the mesh: concrete and steel elements

Overlapping length

Starter bars


191

Table 5.7. Material properties for the short pier A70

Concrete Steel Joint

cE (GPa)* 33.5 sE (GPa) 200 sK ( 3m/N ) 710x2.2

Pν * 0.2 Pν 0.3 nK ( 3m/N ) 1010

ctf (MPa) 3.5 syf (MPa) 550 maxτ (MPa) 3.35

fG (MPa) 0.00014 fτ (MPa) 0.5

sG (MPa) 6.0 1s (mm) 0.6

β 0.2 2s (mm) 0.6

3s (mm) 1.0 *nominal values α 0.4

0

500

1000

1500

0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

For

ce (k

N)

experimental

numerical

Figure 5.26. Short pier A70: experimental and numerical force-displacement curves

As seen in Figure 5.26, the numerical force-displacement curve is in good agreement with

the experimental envelope curve. After first cracking, the numerical curve shows a stiffer

response, compared to the experimental envelop. This is because of the concentration of

steel at the flanges and also because of the modification of the elastic properties of

concrete that results in higher strain at tensile cracking. Looking at the numerical results

at local level, it is observed that stresses are first concentrated on the starter bars around


192

the base cross-section and do not exceed the yield limit. For displacement equal to 6 mm,

the stress concentration is shifted to the steel elements of the pier shaft, around the cross-

section where the starter bars are terminated. At top displacement equal to 8 mm, the

stress on the outermost steel elements reaches the yield limit. This is reflected on the

global force-displacement curve that shows a stabilisation of resistance after this point. It

is reminded that the analysis was performed for monotonically increasing displacement

and therefore the degradation due to cycling was not included in the numerical curve.

The distribution of damage predicted by the numerical analysis is compared to the

experimental data in Figure 5.27 (displacement at the top is applied from left to right).

Figure 5.27a shows the crack pattern resulting from numerical analysis considering

continuous reinforcement and perfect contact between concrete and steel: distributed

horizontal cracks are predicted in the lower part of the pier until the height of 2.5 m.

Some diagonal cracks pointing to the compressed flange develop. The crack pattern

predicted by the numerical model that considers the lapped splices and joint elements at

the contact surfaces is shown in Figure 5.27b. It comprises two distinct horizontal cracks:

one appears at the base of the pier shaft and the second one just above the cross-section

where the starter bars are terminated. This is in agreement with the experimental damage

pattern, schematically shown in Figure 5.27c. Effectively, the experimental behaviour

was between the two cases considered in the numerical analysis: two large cracks

developed at the base and above the splices and secondary cracks formed in the lower

part of the pier.

The previous results show that is possible to obtain qualitative, at least, agreement with

experimental data in terms of damage evolution, failure mode and global force-

displacement curves. However, obtaining high accuracy at the local level for structural

elements with complicated configuration is not a trivial task. It is imperative to include in

the numerical model all materials and interfaces and to adopt a detailed discretisation in

order to avoid deviations from the experimental results. Furthermore, appropriate

constitutive laws, which consider cyclic non-linear behaviour both in tension and

compression (in the general case in three dimensions), require the calibration of a large

number of material parameters, which are not readily available.


193

(a) (b) (c) Figure 5.27. Crack pattern of the short pier A70: numerical analysis for continuous

reinforcement (a), numerical analysis with joint elements (b) and experimental data (c)

5.4. NUMERICAL MODELLING OF PIERS WITH HOLLOW CROSS-

SECTION AND FRP JACKETS

In this section a combination of the numerical tools described previously is employed

with the aim to study the behaviour of bridge piers with hollow cross-section wrapped

with FRP jackets. First, the experimental results concerning a small-scale specimen of a

bridge pier retrofitted with an FRP jacket are briefly presented. In the following, FEM

analysis of a hollow concrete cross-section wrapped with an FRP jacket is performed.

This study allows to investigate on the effect of confinement provided by the jacket.

Effectively, regions of the cross-section are identified, where the confinement effect is

qualitatively and quantitatively different. Finally, an FTB model is studied, in which the

effect of confinement is taken care of by modifying the concrete properties according to

the results of the FEM analysis.


The experimental results of a retrofitted pier, termed T250-FRP, recently tested at the

University of Pavia in Italy [Peloso, 2003] are briefly presented in the following. The

geometry of the specimen was identical to specimen T250, described in 5.2.4. The retrofit


194

intervention consisted in applying longitudinal and transversal GFRP strips. Two

longitudinal layers of 0.1 m-wide strips were applied on both faces orthogonal to the

loading direction. The longitudinal strips were anchored by means of a CFRP bar

embedded in the foundation block; additional steel collars were used to resist the large

tensile forces. The transversal strips had the same width and the spacing was 0.2 m from

centre to centre. The thickness of each strip was 0.23 mm. The nominal values, as

provided by the manufacturer, of the Young modulus and the ultimate stress in the fibre

direction were fE = 65000 MPa and ff = 1700 MPa, respectively.

Constant axial load of 250 kN ( ν = 0.1) was applied and cyclic displacement with

increasing amplitude was imposed on the top. At drift δ = 2.4% some problems with the

anchorage system were encountered. Concrete crushing was observed at δ = 3.6%, as for

the as-built pier, T250. Nevertheless, the specimen was able to sustain further cycling and

at δ = 4.8% crushing of concrete and buckling of steel was observed, without significant

loss of resistance. Finally, the pier failed at uδ = 6.0% by rupture of the transversal GFRP

strips at the base. The force-displacement curves of the as-built and retrofitted specimens

are plotted in Figure 5.28. Compared to the as-built specimen, the retrofitted specimen

had higher resistance, thanks to the additional longitudinal reinforcement. More

important, the retrofitted specimen showed larger deformation capacity, stable response

and larger capacity of energy dissipation. This clearly demonstrates the improvement

provided by the retrofit intervention.

5.4.2. FEM modelling of the confinement effect

As will be further discussed in the following chapter, the existing models for FRP-

confined concrete cannot be simply extrapolated to the case of hollow cross-section.

Apart from the inconsistencies concerning the predicted values of strength and ultimate

deformation of FRP-confined concrete, most of the empirical models have been calibrated

on the basis of tests on cylindrical specimens. In addition, recent experimental and

numerical studies suggest that differences exist between circular and rectangular cross-

sections [Tan, 2001; Karabinis & Rousakis, 2003; Monti, 2003]. Furthermore, no

verification of the confinement effect on rectangular hollow cross-sections is available.

For these reasons, it was decided to study the cross-section of pier T250-FRP by means

FEM analysis.


195

-300

-200

-100

0

100

200

300

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

For

ce (k

N)

as-builtretrofitted

Figure 5.28. Tall pier T250: force-displacement curves of the as-built and retrofitted

specimens [Peloso, 2003]

A 3D plasticity-based constitutive law, implemented in Cast3m [Millard, 1993], was used

for the concrete elements. It follows a failure function )k,J,J,I(FF 321= that depends on

the three stress invariants, 1I , ,J2 and 3J , and on a hardening parameter, k. The total

strain pe ddd ε+ε=ε is the sum of an elastic, edε , and a plastic, pdε , component. The

elastic part is calculated following Hooke’s law, while the plastic deformation is

described by the flow rule

σ∂

∂λ=ε

Gdd p (5.24)

where )k,J,J,I(GG 321= is the plastic potential function.

To illustrate the ability of the model to account for confinement, stress-strain curves for

unconfined concrete and concrete confined with steel and FRP are plotted in Figure 5.29.

The results refer to a concrete cylinder of 0.15 m diameter under uniaxial compression

( cE = 33.5 GPa, Pν = 0.2, cf = 36 MPa for monotonic loading). Shell elements with

orthotropic behaviour were used for the steel and FRP jackets. Steel was considered to


196

follow an elastic-perfectly plastic constitutive law ( sE = 200 GPa, Pν = 0.3, yf = 500

MPa), while linear elastic behaviour was adopted for FRP ( fE = 52 GPa, Pν = 0.2). The

thickness of the FRP jacket was 2 mm, while the thickness of the continuous steel jacket

was 0.1 mm. The curve for unconfined concrete follows a parabola until maximum

strength and then comes a softening branch. The curve for concrete confined with a

continuous steel jacket shows larger resistance and smoother softening stiffness,

compared to plain concrete. Finally, FRP-confined concrete shows a bilinear response

with increasing strength for the second branch. These curves are in agreement with

experimental evidence and commonly adopted laws for concrete.

For the analysis of pier T250-FRP only one corner of the cross-section was modelled.

Cubic elements with eight integration points were used for concrete, while shell elements

with four integration points were used for the FRP strips. The FRP elements followed an

orthotropic linear stress-strain relation. The nominal value of Young modulus, 1fE , was

used in the fibre direction, while in the other direction, 2fE , the properties were estimated

considering only the contribution of the resin. The material properties are given in Table

5.8.

The thickness of the FRP strips was modified in order to take into consideration the effect

of partial wrapping. While continuous jackets exert a constant lateral pressure along the

height of the element, partial wrapping is less efficient as parts of the concrete remain

unconfined. A confinement effectiveness coefficient, ek , is introduced, based on the

assumption that the unconfined zone between two consecutive strips is enclosed by a

parabola with initial slope of 45o [fib, 2001]. The effectiveness coefficient takes the form

Strain

Str

ess

unconfinedsteel-confinedFRP-confined

Figure 5.29. Numerical stress-strain curves for concrete under uniform compression


197

Table 5.8. Material properties for concrete and FRP

Concrete FRP

E (GPa) 32.0 1fE (GPa) 65.0

Pν 0.2 2fE (GPa) 5.0

cf (MPa) 30.0 Pν 0.2

tf (MPa) 3.0

cmε (%) 0.2

cuε (%) 0.6

2

e

s 'k 1 1

2D ≈ − ≤

(5.25)

where s ' is the clear spacing between the FRP strips and D is the width of the cross-

section. Considering the values s ' = 0.1 m and D = 0.45 m, an effectiveness coefficient

ek = 0.8 is estimated. In the numerical simulation, the nominal thickness of the transverse

FRP strips is multiplied by this coefficient.

The results of the numerical model are presented in Figure 5.30 in terms of axial stress

and axial strain, where the curve for unconfined concrete is also plotted for comparison.

The axial stress is normalised to the nominal strength of unconfined concrete, cuf . The

global stress is obtained by dividing the axial resistance by the area of the cross-section.

The effect of wrapping is to increase the maximum strength, by no more than 10%, and

the corresponding deformation. The increase is expected to be more significant for larger

amount of FRP, as will be discussed in the following chapter.

The most important improvement concerns the post-peak behaviour. The proposed

empirical models for FRP-confined concrete contain a “hardening” branch after

attainment of the unconfined concrete strength. On the contrary, the numerical results

indicate that for the examined case a softening branch, with smoother slope compared to

unconfined concrete, follows the point of maximum compressive stress, until a residual

strength. While plain concrete is considered to have nil residual strength, the values for

FRP-confined concrete range from 0.3 cuf to 0.8 cuf in the different zones of the cross-


198

section. Confinement results also in increase of the concrete pseudo-ductility, as seen by

the deformation capacity of FRP-confined concrete, compared to unconfined concrete.

Figure 5.31 presents the distribution of maximum axial stress within the cross-section. It

is clearly seen that the effect of confinement is restricted to the corner of the cross-

section. Apart from a stress concentration at the external part of the corner, consistent

with experimental observations, the cross-section may be divided into three regions, as

shown in Figure 5.30a. One comprises the flange, termed Zone 1, where the maximum

strength is not increased, but the residual strength is r,1 cuf 0.2f= . The second part, termed

Zone 2, corresponds to the external part of the corner, where the maximum strength is

increased by 10% and the residual strength is r,2 cuf 0.75f= . In Zone 2 an ascending

branch initiates at strain levels of about 0.7%. This is reminiscent of the “hardening”

branch of the empirical constitutive laws for FRP-confined concrete. In the following this

branch will be ignored and constant residual stress, r,2f , will be considered. One reason is

related to the difficulties in incorporating this behaviour in the concrete constitutive law

used in the fibre modelling. More important, this behaviour is observed at a rather limited

zone and its effects on the global results are not visible, see Figure 5.30. Finally, Zone 3

comprises the remaining part of the corner, where the maximum strength remains

unchanged and the residual strength is r,3 cuf 0.5f= . The stress-strain curves for the three

zones are seen in Figure 5.30. These values hold for the particular geometry and

materials; more general considerations will be developed in the following chapter.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

Axial strain (%)

Nor

mal

ised

axi

al s

tress

unconfinedglobalzone 1zone 2zone 3

(a) (b) Figure 5.30. Tall pier T250-FRP: numerical stress-strain curves for FRP-confined

concrete (a) and definition of zones (b)

1

3

2


199

Figure 5.31. Tall pier T250-FRP: distribution of maximum axial stress within the cross-

section

5.4.3. Global behaviour of retrofitted pier

To study the global behaviour of the retrofitted pier, a fibre/beam model, similar to the

one used for the as-built specimen, was studied. The effect of confinement is not directly

taken into consideration. In lieu, the concrete properties are modified according to the

observations reported in the previous section. The concrete cross-section is shown in

Figure 5.32. Blue colour corresponds to zone 1, where only the residual strength is

increased. Green colour corresponds to zone 2, in which both the maximum strength and

residual strength are increased. Finally, zone 3, where an intermediate increase of the

residual strength is observed, is shown in red colour. The values of the concrete properties

used in the model are reported in Table 5.9. The steel rebars were modelled as for the as-

built specimen, see 5.2.4.

The longitudinal FRP strips were modelled using quadrangular elements with equivalent

area, positioned on the two faces of the cross-section. The constitutive law for the

longitudinal strips was considered elastic-perfectly plastic, although the actual behaviour

is elastic until failure. This behaviour was adopted in order to impose a limit,

corresponding to the nominal maximum stress ff = 1700 MPa, on the strength of the

longitudinal strips. Numerical simulation considering elastic behaviour of the longitudinal


200

strips showed that the strength constantly increased with displacement, even after many

concrete fibres had collapsed.

Figure 5.32. Tall pier T250-FRP: different zones of concrete in the cross-section mesh

0

100

200

300

0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

For

ce (k

N)

As-built

Longitudinal FRP

FRP jacket

concrete crushing steel fracture

Figure 5.33. Tall pier T250-FRP: numerical force-displacement monotonic curves


201

Table 5.9. Concrete properties for different zones of the cross-section

cof (MPa) coε (%) rf (MPa) crε (%)

Unconfined 32.0 0.25 0.0 1.25

Zone 1 32.0 0.25 6.4 0.75

Zone 2 35.2 0.35 24.0 0.67

Zone 3 32.0 0.30 16.0 0.72

The results of monotonic numerical analyses are plotted in Figure 5.33. The numerical

force-displacement curve for the as-built specimen follows accurately the experimental

envelop. The loss of strength at lateral displacement 0.03 m is associated with crushing of

concrete, as observed during the test. Figure 5.33 plots also the monotonic curve of a pier

retrofitted only with the longitudinal FRP strips, i.e. without modifying the concrete

properties to account for confinement. Also in this case, crushing of concrete occurs at

lateral displacement around 0.03 m, after which some residual strength is provided by the

FRP strips and the undamaged concrete fibres, until rupture of the longitudinal steel

occurs for lateral displacement around 0.08 m. This shows that the improved performance

of the retrofitted pier cannot be attributed solely to the additional shear and flexural

resistance provided respectively by the horizontal and vertical strips. The numerical

force-displacement curve for the pier where both the longitudinal and transverse FRP

strips are considered, indicate that a small loss of strength occurs when some concrete

fibres (those of zone 1) reach their residual strength. Then, the pier can sustain further

deformation without loosing its load-carrying capacity, until failure occurs due to rupture

of steel rebars.

The complete model was used to simulate the cyclic test on the retrofitted specimen. The

numerical and experimental force-displacement curves are compared in Figure 5.34,

where good agreement is observed. The resistance and degradation predicted by the

numerical model are close to the experimental values. Some differences are observed in

the reloading branches of the cycles of large amplitude. As discussed before, the response

of the tested pier can be attributed to the opening and closing of cracks in the concrete

and also to inelastic shear deformation, both of which are not perfectly considered in the

numerical analysis. These differences result in higher energy dissipation in the numerical

model, as shown in Figure 5.35. The difference is localised on the cycles with large


202

displacement, δ = 4.8%, where relatively important shear deformation and big crack

openings are expected.

-300

-200

-100

0

100

200

300

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

For

ce (k

N)


Figure 5.34. Tall pier T250-FRP: experimental and numerical force-displacement curves

0

50

100

150

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

For

ce (k

N)


Figure 5.35. Tall pier T250-FRP: experimental and numerical dissipated energy versus

lateral displacement


203

5.5. FINAL REMARKS ON THE ASSESSMENT OF MODELLING TOOLS

The fibre\beam model was successful in simulating the response of the short pier, whose

behaviour was flexure-dominated, but failed to capture the tension shift phenomenon, that

dictated the failure mode of the tall pier, and predicted different failure location and

resistance. Nevertheless, for the sake of simplicity and stability of the numerical

processes during the PSD tests, it was possible to obtain the correct failure location and

resistance, as well as similar dissipation capacity, by modifying the steel properties.

The 2D FEM models were able to simulate the physical phenomena that were significant

for the behaviour of the tested specimens and consequently predict the correct damage

evolution, resistance and failure location. This allows to conclude that this numerical

approach can be adopted for the analysis of structural elements similar to those studied in

this work, without necessarily performing experimental tests on large-scale specimens.

However, it was shown that it is not a trivial task to produce results of high accuracy at

the local level of complex elements, such as the ones examined in this study. The large

computational demand, due to the refined meshes used to describe the cross-section and

the distribution of horizontal and vertical reinforcement, as well as the joints (steel-

concrete interface) and also due to the constitutive laws for the materials and contact

surfaces, should be highlighted. Such onerous numerical tools appear useful for refined

studies on retrofit solutions, but would be prohibitive for use within the PSD testing

scheme.

Considering the case of piers retrofitted with FRP strips, the comparison between the

numerical and experimental results serves as a validation procedure for the numerical

tools and their combination. The adopted approach consists of FEM analyses used to

study the confinement effect provided by FRP strips, combined with simplified modelling

of the global behaviour. The numerical simulation yields rational results, which are able

to interpret the experimental behaviour of the tested specimen. The agreement between

the numerical and experimental global results provides confidence in the numerical tools

and procedure. This combined approach will be used in the following chapter for

parametric analyses in order to study the effect of various parameters (namely:

dimensions of the cross-section and of the jacket, amount of longitudinal reinforcement

and axial load) on the effectiveness of this retrofit technique and to identify eventual

limitations.


204

SEISMIC RETROFIT OF EXISTING HOLLOW BRIDGE PIERS

205

6. SEISMIC RETROFIT OF EXISTING HOLLOW BRIDGE PIERS

6.1. INTRODUCTION

It has become clear from the material presented in the previous chapters that existing

bridge piers are vulnerable to earthquakes and therefore appropriate retrofit solutions

should be studied. This need is further accentuated by the significant economic loss

related to collapse, or even serious damage, of a major bridge and by the importance of

bridge structures within complex transportation and communication systems. Particular

attention is devoted in this work to bridge piers with hollow cross-section. Although this

structural type is common in highway bridges across Europe and other seismic-prone

regions, it has been the object of research only recently.

While various alternatives exist for the seismic upgrading of buildings [Fardis, 1998], the

practical solutions for bridges are rather limited. It is either desired to reduce the seismic

demand by modifying the structural response using isolation/dissipation devices, or to

increase the available strength and deformation capacity of the substructure. Considering

the last objective, jacketing has seen numerous practical applications. Concrete jackets

have not been used extensively and in recent years fibre reinforced polymers (FRP) are

becoming much more attractive than steel. Apart from the undisputed advantages of high

strength-to-weight ratio, fast application and corrosion resistance, this preference follows

the general popularity of FRP materials. This trend to indiscriminately use FRP

reinforcement is not justified and only very recently it has been recognised that this

material is not a panacea. This provided the motivation to investigate on the performance

and eventual limitations of the use of FRP reinforcement for the seismic retrofit of hollow

piers with large dimensions.

The present chapter deals with the design of retrofit solutions for seismic-deficient bridge

piers with hollow cross-section using external FRP reinforcement. The first part of the

chapter is dedicated to a literature review on the experimental assessment of bridge piers

with hollow cross-section retrofitted with FRP reinforcement. The experimental results on

one hand provide confidence in the effectiveness of various retrofit techniques,

considering in particular FRP jackets for confinement of hollow piers [Peloso, 2003]. On

the other hand, they highlight the need for rational design rules, as some times FRP

reinforcement is over-designed [Ogata & Osada, 2000]. Then follows a review of the


206

available design procedures and equations for retrofit of bridge piers using FRP strips.

This is all examined within the framework of a global retrofit procedure that accounts for

all possible failure modes and for the desired sequence of them. While a sound

background and experimental verification exist for the calculation of flexural and shear

strength [Seible et al., 1995b; fib, 2001], there is scarce confidence with respect to design

for confinement [De Lorenzis, 2001].

The particular problem of confinement for rectangular hollow cross-sections with large

dimensions constitutes the core of the chapter and is addressed following a two-level

numerical analysis approach. The effect on the concrete properties in different parts of the

cross-section is studied with Finite Element Method (FEM) analyses. The empirical

constitutive laws for FRP-confined concrete are found inadequate for the case of

rectangular hollow cross-sections with large dimensions. The results of the previous

analyses are integrated in moment-curvature analyses performed with the aim to study the

effect of jacket geometry, amount of reinforcement and axial load on the ductility

capacity of the cross-section. The values of the previous parameters, above which there is

no further improvement, are identified. Finally, a preliminary design equation is

formulated on the basis of more than 1000 analyses.

6.2. SEISMIC RETROFIT OF REINFORCED CONCRETE BRIDGE PIERS

WITH HOLLOW CROSS-SECTION

6.2.1. Retrofit with steel jackets

The effectiveness of steel jackets for the seismic retrofit of bridge piers with hollow

cross-section has been experimentally investigated in two cases. One experimental

campaign dealt with the problem of premature termination of the longitudinal

reinforcement [Kawashima et al., 1990], while the second dealt with the problem of

limited deformation capacity [Huang et al., 1997].

Four scaled specimens of bridge piers with square hollow cross-section were tested in

order to study the effectiveness of steel jackets [Kawashima et al., 1990]. The specimens

had high aspect ratio, L/d = 5.2, and axial load ν = 0.3. The longitudinal reinforcement,

sρ = 1.3%, was reduced to almost half at 35% of the pier height. Steel jackets were


207

applied in that region. The examined parameters were the jacket length, equal to 1.0 or

1.5 times the cross-section width, and the material injected between the jacket and the

pier, namely concrete mortar or epoxy resin.

The retrofitted piers showed stable response until displacement ductility uµ = 7. For the

jackets with length equal to the pier width, damage was observed at the base of the pier

and failure was due to flexure. A small crack was observed at the bar cut-off cross-section

after removing the steel jacket. For the jacket with length 1.5 times the pier width and

epoxy resin, similar performance and damage pattern was observed. For the specimen

with mortar injected between the jacket and the pier, shear cracks developed at the lower

part of the pier and failure was due to a combination of flexure and shear. From this

experimental campaign it was shown that steel jackets were effective in addressing the

problem of rebar curtailment. No major difference was observed for the examined lengths

of the jacket and the injection materials.

Two small-scaled (1:8) specimens of bridge piers with rectangular cross-section

retrofitted with steel jackets were tested [Huang et al., 1997]. The specimens had high

aspect ratio, L/d = 5.9, medium axial load, ν = 0.2, and longitudinal reinforcement

sρ =1.3%. Normal concrete and steel were used. The as-built specimen showed limited

deformation capacity, uµ = 4 and uδ = 1.9%. Steel jackets were applied at the base of the

retrofitted specimens. In the first specimen a gap was left between the jacket and the pier

foundation, while in the second specimen the jacket was anchored in the foundation. Both

retrofitted specimens showed improved stability and larger energy dissipation and

deformation capacities, uµ = 6 and uδ = 2.8%. Nevertheless, the inelastic deformation

demand in the retrofitted specimens was concentrated at the gap between the jacket and

the foundation and failure was because of buckling and rupture of the steel rebars in that

region.

In conclusion, this experimental campaign verified the effectiveness of steel jackets for

the enhancement of the deformation and energy-dissipation capacities of piers with

hollow cross-section. It is noted that the effectiveness was limited, compared to steel-

jacketed piers with full circular cross-section. Finally, the small scale of the specimens

does not allow a reliable verification of the effectiveness of steel jackets for the full-scale

piers, which have much larger dimensions.


208

6.2.2. Retrofit with FRP jackets

Limited experimental data from piers with hollow cross-sections retrofitted with FRP

jackets are available in literature. A few recent experimental campaigns performed in

Japan, Taiwan and Italy are discussed in detail in the following.

Five small-scale (1:20) models of existing bridge piers with hollow circular cross-section

were tested as-built and retrofitted with FRP strips [Ogata & Osada, 2000]. The internal

diameter of the cross-section increased with height and the amount of longitudinal

reinforcement decreased. The former characteristic resulted in shear failure at the top part

of an as-built specimen with small width: at that region the contribution of concrete to

shear strength was small and the amount of transverse reinforcement was not sufficient to

resist the shear demand. The decrease of longitudinal reinforcement caused yielding of

longitudinal rebars at all cross-sections above cut-off, although failure was due to shear.

The drift capacities for the first and second specimens were uδ = 2.3% and uδ = 3.1%,

respectively. The concrete strength of the second specimen was 1.8 times the strength of

the first.

Three retrofit solutions were experimentally evaluated. The first solution (CF) consisted

of longitudinal FRP strips in order to shift the critical cross-section to the base. A small

amount of transverse FRP strips was also used, mainly to ensure the transfer of stresses

between the longitudinal strips. For the second alternative (CF2), the amount of

longitudinal FRP was reduced to half and the amount of transverse FRP was increased 5

times. The third solution (CF3) comprised only transverse strips. Pier CF presented

flexural damage only above the foundation, while failure was due to shear at drift uδ =

3.0%. Pier CF2 presented stable response with flexural damage at the base, without

collapse, until drift uδ = 5.4%. Finally, pier CF3, without longitudinal FRP, showed stable

response until uδ = 5.3%. Horizontal flexural cracks at all cut-off cross-sections were

observed at the end of the test after the jacket was removed.

The failure mode of the retrofitted specimens calls for a comprehensive and rational

retrofit procedure. External FRP reinforcement is often over-designed: half of the FRP

longitudinal reinforcement used in pier CF was successful in shifting the critical cross-

section at the base of pier CF2. The overall retrofit procedure must also consider the fact


209

that upgrading for the most critical failure mode (e.g. flexure at rebar cut-off) might

initiate the second most critical one (e.g. shear). The above observations are particularly

important in cases of real structures that present a variety of seismic deficiencies that

come into light for different levels of loading, as was observed during the experimental

tests described in Chapters 3 and 4.

Scaled specimens of bridge piers with rectangular and circular cross-section were tested

until failure, repaired and strengthened with FRP jackets and tested again [Cheng et al.,

2003]. Different collapse modes were observed, namely: flexural failure (specimen PS1-

C), loss of bond (PI1-C), shear failure (PI2) and combination of flexure and shear (PI2-

C). After testing, the cracks were repaired and FRP jackets, following design equations

that are presented in a following section [Seible et al., 1995b], were applied. All the

retrofitted specimens showed the same failure mode as the as-built ones. Drift capacities

were moderate, ranging from uδ = 2.1% to uδ = 4.5%. Drift capacities were higher than

the corresponding values for the as-built specimens, with the exception of pier PS1-C that

was heavily damaged before retrofit. Note that the comparison of the seismic

performance of the specimens based in displacement ductility is misleading. Indeed, the

reported values of ductility for all the retrofitted specimens are lower than those for the

as-built piers, which would lead to the conclusion that retrofit was detrimental for the

deformation capacity of the specimen.

The experimental data verify the effectiveness of FRP jackets for shear retrofitting of

seismic-deficient bridge piers with hollow cross-sections, either rectangular or circular.

The proposed design equations were successfully applied to change shear-dominated

failure mode to flexure-dominated (specimens PI2 and PI2-C). Due to the fracture and

repair of longitudinal rebars, it is not clear whether, and more important how much, the

jacket was effective in improving the behaviour of lapped splices (specimen PI1-C). Also,

no indication can be drawn on the confinement effect alone: the deformation and energy-

dissipation capacities were improved, but it is believed that this was mainly due to

shifting to a ductile flexural failure mode. Unfortunately, the specimen that failed due to

flexure at the as-build condition was severely damaged and the consequent poor

behaviour after repair does not allow to validate the confinement by the jacket.

Five small-scale specimens of square hollow piers were tested as-built and retrofitted with

FRP strips [Peloso, 2003]. The two short specimens failed in shear and were retrofitted


210

with horizontal aramid-FRP (AFRP) strips. For the two tall specimens that failed due to a

combination of flexure and shear, it was decided to apply longitudinal GFRP strips in

order to increase the flexural capacity. Horizontal GFRP strips were also applied in order

to meet the increased shear demands. For the specimen with lapped splices at the base

(overlapping length equal to 20 rebar diameters) it was decided to relocate the critical

cross-section above the lapped splices and for this, longitudinal CFRP strips were applied

near the base. Due to problems with the anchorage system for the longitudinal strips, the

retrofit technique was not successful in relocating the plastic hinge and therefore, the

experimental results for this specimen are not further discussed.

The as-built shear-deficient short piers failed at low values of drift, uδ = 2.4%,

independently of the axial load. For these piers the retrofit was successful in changing the

failure mode to flexure-dominated. This resulted in increased energy-dissipation capacity.

The drift capacities of the retrofitted piers were uδ = 4.8%, which is double the capacity

of the as-built piers.

The as-built tall piers failed due to a combination of flexure and shear at uδ = 2.4%. For

the retrofitted specimens, shear damage was avoided and failure was due to buckling of

longitudinal reinforcement. Compared to the as-built specimens, higher strength and

deformation capacity, uδ = 6.0% or uδ = 3.6% for low and high axial load respectively,

were achieved. A problem concerning anchorage was encountered. The anchorage system

comprised an FRP bar, around which the longitudinal strips were wrapped, embedded in

the foundation and steel angles positioned above the FRP bar and bolted at the foundation

block. This system was not sufficient to resist the forces from the longitudinal strips and

uplifting of the steel angles was observed after a certain level of displacement. In

addition, buckling of longitudinal rebars was observed above the steel angles and not

directly over the base cross-section.

A final remark concerns the effectiveness of FRP strips for the retrofit of piers with

hollow cross-section. Although they do not completely preclude buckling of longitudinal

rebars, they can delay it and consequently increase the deformation and energy-

dissipation capacities. FRP jackets seem actually to have confining action. Therefore, the

improved performance, in terms of strength and deformation, can be attributed partly to


211

the longitudinal FRP reinforcement and partly to the confinement offered by the

horizontal strips.

6.2.3. Performance of retrofitted bridge piers

A total of 289 experimental tests on as-built and retrofitted bridge piers are discussed in

this section. Both as-built and retrofitted specimens are examined. The main parameters

of the test campaigns were the cross-section type (full or hollow; circular, oval,

rectangular or wall-type), concrete properties (normal-strength or high-strength), presence

of lapped splices, premature termination of longitudinal reinforcement, amount and

detailing of transverse reinforcement and retrofit technique. The retrofit techniques

comprise mainly jacketing (rectangular, oval or circular; steel or FRP) and application of

external stirrups. The tested piers can be divided in two categories based on seismic

detailing. Seismic-deficient piers have inadequate detailing and are expected to have poor

performance. Retrofitted piers and piers designed according to seismic codes have proper

detailing and are expected to perform in a desired manner. The latter two types of piers

are referred to in the following as code-designed piers. Table 6.1 shows the general

characteristics of the cross-sections and the percentage of each pier type within the

database. The geometric and mechanical properties, as well as the deformation capacities

of all specimens are presented in Appendix A.

Figure 6.1 plots the drift ratio versus different geometrical and mechanical properties of

the piers, namely: aspect ratio, transverse reinforcement ratio, splicing length and

normalised axial load. The first column presents the results for seismic-deficient piers,

while the second presents the results for code-designed piers. Although large scatter is

observed with respect to all examined parameters, general trends may be identified. For

seismic-deficient piers, drift capacity increases with aspect ratio and transverse

reinforcement ratio (squat piers with low amount of horizontal reinforcement exhibit

brittle failure at low levels of drift) and decreases with axial load. For code-designed piers

similar trends are observed. Considering in particular piers with lapped splices, drift

capacity remains in the range uδ = 1% ~ 4%, independently of the overlapping length.

Retrofitting for enhancement of the behaviour of lapped splices can be successful, as

specimens can develop values of lateral drift up to uδ = 8%.


212

02468

10121416

0 2 4 6 8 10 12

Aspect ratio

Drif

t rat

io (

%)

(a)

02468

10121416

0 5 10 15

Aspect ratio

Drif

t rat

io (

%)

(b)

02468

10121416

0 1 2 3 4 5


Drif

t rat

io (

%)

(c)

02468

10121416

0.0 1.0 2.0 3.0 4.0 5.0


Drif

t rat

io (

%)

(d)

02468

10121416

0 10 20 30 40

Splicing length (db)

Drif

t rat

io (

%)

(e)

02468

10121416

0 10 20 30 40


Drif

t rat

io (

%)

(f)

02468

10121416

0.0 0.2 0.4 0.6


Drif

t rat

io (

%)

(g)

02468

10121416

0.0 0.2 0.4 0.6


Drif

t rat

io (

%)

(h)

Figure 6.1. Drift capacity versus aspect ratio, transverse reinforcement ratio, splicing

length and normalised axial load for seismic-deficient (left) and code-designed (right)

piers

)(Φ )(Φ


213

0

2

4

6

8

10

0 2 4 6 8

Aspect ratio

Drif

t rat

io (

retr

ofitt

ed/a

s-bu

ilt)

(a)

0

2

4

6

8

10

0.0 0.2 0.4 0.6 0.8 1.0


Drif

t rat

io (

retr

ofitt

ed/a

s-bu

ilt)

(b)

0

2

4

6

8

10

0 10 20 30 40


Drif

t rat

io (

retr

ofitt

ed/a

s-bu

ilt)

(c)

0

2

4

6

8

10

0.0 0.1 0.2 0.3 0.4


Drif

t rat

io (

retr

ofitt

ed/a

s-bu

ilt)

(d)

Figure 6.2. Increase in drift capacity versus aspect ratio (a), transverse reinforcement ratio

(b), splicing length (c) and normalised axial load (d)

Table 6.1. Bridge pier test database

Cross-section

geometry No %

Cross-section

type No % Detailing No %

Rectangular 157 54 Full 187 65 Seismic-

deficient 77 27

Circular 119 41 Hollow 102 35 Code-

designed 212 73

Oval 10 3

Wall-type 3 1

The drift capacity of the retrofitted specimen divided by the drift capacity of the as-built

specimen can be considered as an index of the effectiveness of the retrofit technique. This

ratio is plotted in Figure 6.2 for all the parameters considered. Although large scatter is

observed, qualitative observations may be made. The effectiveness decreases with

increasing aspect ratio and increasing transverse reinforcement ratio. This is due to the

fact that most retrofit interventions aim at improving the shear performance of existing


214

bridge piers, which is more critical for squat piers and/or for piers with low amount of

transverse reinforcement. The effectiveness of the retrofit decreases with the axial load

and with the splicing length of longitudinal rebars. The same trends are observed when

one considers displacement ductility capacity.

6.3. DESIGN OF RETROFIT OF BRIDGE PIERS WITH FRP

6.3.1. Global retrofit procedure

A global retrofit procedure is proposed in this section and the existing design guidelines

and equations are discussed. The term global refers to the consideration of all possible

failure modes. The first step of the retrofit procedure is the assessment of the as-built

structure and the identification of all possible failure modes. Considering RC bridge piers,

the main seismic deficiencies, which have been reported from field observations and

laboratory testing, are

• premature termination of vertical reinforcement

• lapped splices within the potential plastic hinge region

• inadequate confinement (small drift, ductility and dissipation capacities)

• inadequate shear capacity

• small amount of longitudinal reinforcement

Existing bridge piers are usually found to possess adequate flexural strength. However,

they might not be able to develop this nominal strength, because of shear failure or failure

of lapped splices.

Quite often, existing bridge piers present a combination of the aforementioned seismic

deficiencies. Nevertheless, only one of them, the weakest, is the main cause of failure

during an earthquake or a laboratory test, while the contribution of others is difficult to

quantify. It is obvious that if the objective of the retrofit intervention is to provide

resistance against the weakest mechanism only, then most probably failure will be due to

the second weakest mode. For this reason, a global retrofit procedure, that takes into

consideration all possible failure modes, is proposed in Figure 6.3.


215

Seismic Deficiency Objective of Retrofit Method of Retrofit

• tension shift

• lapped splices in the

plastic hinge region

relocation of critical cross-

section

additional longitudinal

reinforcement

?

• small length of

plastic hinge

• development of full

plastic hinge

• increase concrete

strength and deformation

jacketing

?

• limited shear

capacity • increase shear capacity

additional transverse

reinforcement

Capacity Design

Figure 6.3. Global retrofit procedure for seismic-deficient bridge piers

The procedure outlined in Figure 6.3 presents three retrofit methods, namely additional

longitudinal reinforcement, jacketing and additional transverse reinforcement. Each

method is related to specific seismic deficiencies and retrofit objectives. Apparently,

certain steps can be omitted if the single deficiency does not exist. The arrows indicate

the sequence of the objectives to be sought: the critical cross-section is chosen and

provided with sufficient confinement and then the remaining sections are protected

against shear failure, following Capacity Design philosophy.

Jacketing is not proposed as a means to avoid failure of lapped splices, because it is felt

that, in the case of cross-sections with large dimensions and even more for hollow piers, it

cannot provide the required confinement for enhancement of lapped splices. However,

jackets can provide some degree of confinement that is effective for the increase of

concrete strength and deformation.


216

6.3.2. Relocation of critical cross-section

Piers with curtailment of vertical reinforcement

Many existing bridge piers present premature termination of vertical reinforcement and

insufficient development length, resulting from elastic design methods and relaxed

detailing rules. This, combined with shear cracking and tension shift, can cause failure

above the bar cut-off, which results in low resistance and deformation capacity. This has

been observed during the tests described in Chapters 3 and 4 and also during previous

experimental campaigns [Kawashima et al., 1990; Calvi et al., 2000; Ogata & Osada,

2000]. Premature termination of vertical rebars was common practice in Japan. Actually,

it is reported that failure of the Hanshin Expressway was triggered by this deficiency

[Kawashima, 2000]. Failure above the cut-off might not conform to the requirements of

EC8-2 [CEN, 2002] for accessibility of the plastic hinge region for inspection and

eventual repair after an earthquake. This problem can be solved relatively easy by

increasing the flexural strength of the cross-section at the cut-off and thus relocating the

critical cross-section at the base. External FRP reinforcement, designed according to the

procedure outlined in a following section, can be applied. The effectiveness of this

method was experimentally verified [Ogata & Osada, 2000].

Piers with lapped splices

In case of bridge piers with lapped splices within the potential plastic hinge zone, two

solutions exist. Either a jacket is applied to provide confinement, or it is decided to

relocate the critical cross-section. Sufficient confinement of large rectangular cross-

sections might require jackets with extremely large dimensions. This would prove

impractical and the alternative of relocation of the critical cross-section should be

examined.

Considering the relocation of the critical cross-section, the solution will depend on the

location and detailing of the longitudinal reinforcement. If all vertical rebars are spliced at

the base, the critical cross-section can be shifted just above the lapped splices. In the case

of a more complex scheme of vertical reinforcement, the choice of the new critical cross-

section might not be straightforward.


217

Attention must be paid not to force failure to happen at a cross-section far from the base.

This would decrease the shear span of the pier and consequently increase the shear force

it has to resist. Since existing bridge piers are often found to have low shear strength,

increase of the shear demand would further complicate the design of the retrofit and

increase the cost. Decrease of the shear span would also increase the demand on the

foundation. It is felt that the actual solution will result as a compromise between the

above restrictions.

Once the new critical cross-section is chosen, its moment capacity can be estimated from

moment-curvature analysis with assumed, or, if possible, measured, values of the material

properties. Then, the resisting moment of the critical cross-section of the as-built pier

should be increased to the moment that corresponds to failure of the new critical cross-

section, applying an appropriate safety factor to account for material overstrength.

Capacity Design considerations apply for the verification in shear. The design shear force,

SdV , of the retrofitted pier can be estimated based on the resisting moment, RdM , as

Sd CD RdV M / L= γ (6.1)

where L is the height of the pier and CDγ is a Capacity Design safety factor. Values of

CDγ = 1.35 and CDγ = 1.2 are proposed for bridges [CEN, 2002] and buildings [CEN,

2003a], respectively. The recent Italian seismic code [PCM, 2003] provides a relation

between the safety factor and behaviour factor, CD 0.7 0.2qγ = + , which yields CDγ = 1.4

for q = 3.5. The eventual additional shear reinforcement can be dimensioned following

the procedure described in a following section. The effectiveness of this method has been

verified for circular columns retrofitted with concrete jackets [Griezic et al., 1996.] for the

case of square hollow piers retrofitted with FRP strips [Peloso, 2003] failure of the

anchorage conditioned the effectiveness of the retrofit system.

6.3.3. Anchorage

A major concern is the anchorage of FRP strips or rods in order to guarantee safe transfer

of forces from the FRP to concrete. Debonding of FRP is recognised as a possible failure

mode that can condition the design of FRP reinforcement and limit its effectiveness. In


218

the following, three different methods of anchorage, namely overlaying, mechanical

anchorage and U-anchors, are presented.

Overlaying

The most common way of anchoring FRP strips is by overlaying. In the fib Bulletin 14 -

Externally Bonded FRP Reinforcement for RC Structures (fib Bulletin) [fib, 2001] three

alternative procedures are proposed for the design of anchorage. The simplest one,

presented in the following, consists in anchorage verification and FRP strain limitation. A

second procedure consists in the calculation of the envelope line of tensile stress, while

for the third procedure the force transfer between FRP and concrete is verified.

According to the first approach, to prevent peeling-off, the ultimate tensile strain εfu

(ranging from 0.005 to 0.015) at Ultimate Limit State (ULS) is restricted to a certain

value. In addition to this, the end anchorage has to be verified using methods mainly

based on fracture mechanics and bond stress-slip relationships. Recent test results have

demonstrated that the FRP tensile strain when peeling-off occurs depends on a broad

range of parameters, such as the properties of FRP and concrete, the loading pattern, the

crack spacing, etc.

The model proposed by [Holzenkämpfer, 1994], as modified by [Neubauer & Rostásy,

1997], is adopted. It gives the maximum FRP force that can be anchored, fa,maxN

fa,max 1 c b f f ctN c k k b E t f= α (6.2)

and the maximum anchorage length, b,maxl , equal to

f fb,max

2 ct

E tl

c f= (6.3)

In the above expressions α is a reduction factor, approximately equal to 0.9, to account

for the influence of inclined cracks on the bond strength, ck is a factor accounting for the

state of compaction of concrete (for FRP bonded to concrete faces with low compaction,

e.g. faces not in contact with the formwork during casting, ck = 0.67, otherwise ck = 1.0)

and bk is a geometry factor


219

fb

f

2 b / bk 1.06 1.0

1 b / 400−

= ≥+

(6.4)

with fb / b ≥ 0.33. In the above expressions b is the width of the element, fE , ft and fb

are respectively the Young modulus, thickness and width of the FRP strip and ctf is the

tensile strength of concrete. Note that b, fb and ft are measured in mm, and fE , ctf are

measured in MPa. c1 and c2 in Equations 6.2 and 6.3 may be obtained through calibration

with test results; for CFRP strips they are equal to 0.64 and 2.

For bond length b b,maxl l< , the ultimate bond force can be calculated as [Holzenkämpfer,

1994]

b bfa fa,max

b,max b,max

l lN N 2

l l

= −

(6.5)

Mechanical anchorage

For FRP strips used for increase in flexural strength, it is recommended to improve the

anchorage by mechanical means. One technique is to externally confine the ends of the

FRP strip using additional reinforcement in the orthogonal direction (Figure 6.4). This

type of anchorage is considered effective and avoids plate-end shear failure.

FRP strips used for shear strengthening can be anchored following the scheme shown in

Figure 6.5. It is desirable to anchor the FRP in the compression zone by fully wrapping it

around the member in order to guarantee sufficient anchorage. When this is not feasible,

U-shaped strips can be anchored using bolts (Figure 6.5b). This solution is easier to apply

and satisfies the requirement for anchorage in the compression zone. For the case of

insufficient anchorage in the compression zone, the usable height (inner lever arm) of the

cross-section has to be reduced, so that the member has a fictitious lower ultimate

bending resistance [fib, 2001].


220

Figure 6.4. Anchorage of flexural FRP reinforcement with external confinement

reinforcement

Figure 6.5. Anchorage of shear FRP reinforcement in the compression zone by

embedment in concrete (a) and using bolts (b)

With respect to bolted systems, it is not adequate to drill through the strengthening strip

omitting special provisions and merely fixing with a bolt, as drilling holes through

unsupported composites severs the unidirectional fibres. As compressive forces can

further weaken the strip and as it is not possible for the forces in the strip to be

transmitted into the bolt, the end tabs should be designed to take the full force to be

anchored. Bolted systems should be positioned at suitable spacing and anchored in the

concrete to a depth beyond the steel reinforcement. The bolts should be supplied with

large washers and tightened up to a specified torque to prevent crushing of the composite

materials. At holes that are necessary when bolts are applied, interlaminar shear failure or

splitting of the strip may initiate. Moreover, holes reduce the cross-section of the strip. In

general, anchoring devices that may influence the integrity of the strengthening system

are not recommended [fib, 2001].


221

A special mechanical anchorage system is shown in Figure 6.6 [Zehetmaier, 2000]. With

this mechanical anchorage a significant increase in anchored tensile force can be

obtained. This system can be applied in case where no wrapping is possible, for local

strengthening and as an anchorage for prestressed strips. A minimum concrete cover of

about 20 mm is required for practical reasons.

Special anchorage heads exist for pre-stressed FRP rods. The systems vary with each

single manufacturer.

U-anchor

The U-anchor [Khalifa et al., 1999] can be used with FRP strips and pre-cured laminates

that are unbonded or fully bonded to concrete. It is based on the idea of embedding a bent

portion of the end of the FRP reinforcement into a groove in the concrete. The U-anchor

is expected to avoid high stress concentration and durability concerns. Three possible

uses of the U-anchor are proposed, namely surface anchorage of strips, after-corner and

before-corner U-anchors.

Anchoring of the FRP reinforcement is attained by grooving the concrete near the end of

the FRP strip, perpendicular to the fibre direction. In the case where the groove is before a

corner or on a plane surface, the edges of the groove should be rounded off (for CFRP a

minimum radius of 10 mm is suggested). This is intended to reduce stress concentration

and prevent premature failure of the FRP strip. The FRP reinforcement is bonded to the

concrete surface and to the walls of the groove. After the saturant has set, the groove is

filled half way with a high-viscosity binder. An FRP bar is then placed into the groove

and is pressed in place. The bar can be held in place using wedges at appropriate spacing.

The groove is then filled with the same paste and the surface is levelled. A cross-section

showing details of an after corner type U-anchor is shown in Figure 6.7. The system can

be applied with or without an FRP bar and can be used to anchor continuous, as well as

discontinuous strips. If the U-anchor is not specifically designed for the intended

application, a recommended FRP bar diameter is 10 mm and groove dimensions can be

taken as 1.5 times the bar diameter.


222

CFRP-strip

Adhesive

40 mm

L-section length: 100 - 300 mm

Concrete

slits

30 mm

Figure 6.6. Anchorage of CFRP strips [Zehetmaier, 2000]

Figure 6.7. Cross-section of an after-corner U-anchor [Khalifa et al., 1999]

Experimental verification of the method was performed. For a beam strengthened in shear

with CFRP strips without U-anchor, the strength increased by 72% in comparison to the

control beam, but failure was governed by debonding of the CFRP. The maximum strain

in the CFRP strip was 28% of the ultimate value. In the specimen where the U-anchor

was used, the shear capacity increased by 145% and no FRP debonding was observed at

failure. The maximum strain in the CFRP strip was 40% of the ultimate value. The failure

mode was flexure-dominated. This resulted in a ductile failure mode, uµ ≈ 3, compared

to the brittle failure due to shear observed in the control beam and the one reinforced with

CFPR without U-anchor. Based on experimental observations [Peloso, 2003], there seem

to be some limitations on the effectiveness of this technique, when relatively large tensile

forces develop in the FRP strips.


223

6.3.4. Retrofit for flexural strength enhancement

Reinforced concrete elements can be strengthened in flexure using FRP reinforcement

externally bonded to the tension zones, with the direction of the fibres parallel to that of

tensile stresses. In design for bending, the following assumptions are made: Bernoulli’s

hypothesis is valid, which means that the strain is linearly distributed over the cross-

section and implies complete composite action between the materials; cracked concrete

has no tensile strength; the FRP is linear elastic until failure. Concerning concrete and

steel, the stress-strain curves used in design of RC members apply, e.g. from Eurocode 2

(EC2) [CEN, 2002].

The possible failure modes can be divided in two groups: failure where full composite

action is maintained until concrete crushes or steel yields and failure where composite

action is lost before failure of concrete or steel. In general six primary failure modes are

considered, namely concrete crushing, yielding of reinforcement, laminate failure,

anchorage failure, peeling-off and delamination [Täljsten, 2003]. Yielding of the tensile

reinforcement in the ULS is assumed, while yielding of the reinforcement in the

Serviceability Limit State (SLS) is not permitted. In the following, only the ULS is

considered, as the SLS is not expected to be critical for seismic retrofitting of structures.

The SLS can be critical in case a small amount of FRP is enough to increase the strength

to the desired level the strength for ULS, but might not be enough for deformation control

at SLS.

For the design in bending the actual strain distribution over the member is calculated,

following the previous assumptions. According to the fib Bulletin [fib, 2001], the initial

stress state of the element, usually cracked under service loads, must be considered for the

design of the strengthening. The failure criterion for concrete is c cue e< = 3.5‰ and for

the FRP f fue 0.6e< .

The stress and strain distributions of a RC beam considering full composite action and

failure due to yielding of steel and crushing of concrete, which is the most desirable

failure mode, is shown in Figure 6.8. The neutral axis depth, ? , can be calculated from

equilibrium of internal forces

cd s2 s s2 s1 yd f f f0.85? f b? A E e A f A E e+ = + (6.6)


224

where ? = 0.8 and

2s2 cu

? de e

?−

= ; s s2 ydE e f≤ (6.7)

f cu o

h ?e e e

?−

= − (6.8)

In the above expressions cdf is the design value of the concrete compressive strength, sE

is the Young modulus of steel, s1A and s2A are respectively the areas of tension and

compression steel, s2e is the strain of the compression steel, oe is the initial deformation

of concrete in the tension zone before the application of the FRP strip, cue and fue are the

ultimate deformations of concrete and FRP, respectively, fA is the area of the FRP, d and

2d are respectively the distance of the tension and compression reinforcement from the

most compressed concrete fibre.

The design bending moment capacity is

Rd s1 yd G f f f G s2 s s2 G 2M A f (d d ?) A E e (h d ?) A E e (d ? d )= − + − + − (6.9)

where Gd = 0.4. The required amount of FRP, fA , can be then calculated from Equations

6.6 to 6.9.

Figure 6.8. Cross-section analysis: (a) geometry, (b) strain distribution and (c) stress

distribution

s1e

c cue e=

cd0.85? f

s1 ydA f

f f fA E e

s2 s s2A E e

oe fe

s2e

d


225

For the equations given above to be valid, the following assumptions should be checked:

yielding of tensile steel reinforcement and FRP strain is limited to the ultimate maximum

strain, fude

yds1 cu

s

fdE

− χε = ε ≥

χ (6.10)

f cu o fud

h − χε = ε − ε ≤ ε

χ (6.11)

Other failure modes, due to loss of composite action should be considered. These are

peeling-off caused by shear cracks, peeling-off at the end anchorage and at flexural

cracks, end shear failure and peeling-off caused by the unevenness of the concrete surface

[fib, 2001]. Several parameters, such as the crack opening displacement, flexural and

shear rigidity of the FRP and tensile strength of concrete influence the resistance against

peeling-off. Design for these failure modes requires verification of the anchorage and

might result in additional shear reinforcement.

6.3.5. Retrofit for shear strength enhancement

According to the fib Bulletin [fib, 2001], the external FRP reinforcement may be treated

in analogy to the internal steel (assuming that the FRP carries only normal stresses in the

principal FRP material direction), assuming that at the ULS in shear the FRP develops an

effective strain in the principal material direction, fee . The effective strain, fee , is in

general less than the tensile failure strain, fue . Hence, the design shear resistance, RdV , of

a strengthened element may be calculated according to the EC2 [CEN, 2002] format as

Rd cd wd fdV V V V= + + (6.12)

where cdV is the shear strength of concrete and wdV is the shear strength provided by the

transverse steel reinforcement. The FRP contribution to shear capacity, fdV , can be

written in the following form

fd fd,e f f wV 0.9e E ? b h(cot ? cot a ) sin a= + (6.13)


226

where fd,ee is the design value of effective FRP strain, wb is the minimum width of the

cross-section over the effective depth, h is the depth of the cross-section, f? is the FRP

reinforcement ratio, ? is the angle of diagonal cracks with respect to the member axis

(usually assumed equal to 45o) and a is the angle between the principal fibre orientation

and the longitudinal member axis. The same equation with ? = 45o is adopted in EC8-3

[CEN, 2003b].

The design value of the effective FRP strain, fd,ee , equals the characteristic value, fk,ee ,

divided by the partial safety factor, f? . Given the lack of sufficient data, fk,ee may be

approximated by multiplying the mean value of the effective FRP strain, f ,ee , by a

reduction factor. Yet, fk,ee should be limited to fue , in order to ensure that the shear

integrity of concrete is maintained sufficiently, so that other mechanisms, such as

aggregate interlock, may be activated. In other words

fk,e f ,e fue ke e= ≤ (6.14)

where k = 0.8 and fue ≈ 0.006.

A more elaborated expression for the reduction factor, k, is available [Duthinh &Starnes,

2001] in the form

f fnE tk 1 0.9

428= − ≤ ; f fnE t ≤ 210 kN/mm (6.15a)

f f

105k 0.9

nE t= ≤ ; f fnE t > 210 kN/mm (6.15b)

where n is the number of plies applied.

The partial safety factor is taken from Table 6.2 if failure involves FRP fracture

(combined with, or following diagonal tension), or f? = fd? = 1.3 if debonding leading to

peeling-off dominates. Application types A and B in Table 6.2 refer to the quality control

of the system and the application procedure. Type A stands for good quality control,

while type B stands for bad quality control.


227

Table 6.2. FRP material safety factors f? [fib, 2001]

Application type A Application type B

CFRP 1.20 1.35

AFRP 1.25 1.45

GFRP 1.30 1.50

It is recommended to consider a design strain limit of fde = 0.004 for a CFRP jacket

[Seible et al., 1995b]. This value is below the ultimate strain of CFRP, fue = 0.01, but

higher than the yield strain of steel reinforcement. This in turn, ensures that the

contribution of steel reinforcement, wdV , can be fully activated.

EC8-3 [CEN, 2003b] provides design formulae for the estimation of the effective FRP

strain depending on the material. For well-anchored CFRP jackets it writes

0.302 3

cfd,e fu

f f

fe 0.17 e 0.006

E ?

= ≤

(6.16)

For U-shaped CFRP jackets the ultimate strain is

0.56 0.302 3 2 3

3 c cfd,e fu

f f f f

f fe min 0.65 10 ;0.17 e 0.006

E ? E ?−

= × ≤

(6.17)

Finally, for properly anchored AFRP jackets

0.472 3

cfd,e fu

f f

fe 0.048 e 0.006

E ?

= ≤

(6.18)

In the previous equations cf (in MPa) is the estimated value of concrete compressive

strength.

A similar approach is adopted by the Japanese Society of Civil Engineering. The

contribution of FRP to the shear strength is added to that of concrete and steel

reinforcement. The FRP shear strength is estimated as [JSCE, 2001]

fd f f fV KA f z(sin a cosa) / s= + (6.19)


228

where K is an effectiveness coefficient, ff is the tensile strength, z is the internal lever-

arm, a is the angle of fibres to the longitudinal direction and fs is the spacing of the

strips. Based on experimental results, the effectiveness coefficient is estimated as

0.4 K 1.68 0.67R 0.8≤ = − ≤ (6.20)

where

( )12

331fud4

f f 'f cd

f 1R E

E f

= ρ

; 0.5 R 2.0≤ ≤ (6.21)

The material presented above refers to RC members of rectangular cross-section. If the

cross-section is circular, the contribution of FRP (wrapped around the column) to shear

capacity is controlled by the tensile strength of the FRP jacket, but is limited to a

maximum value corresponding to excessive dilation of the concrete due to aggregate

interlock at inclined cracks [fib, 2001]. By limiting the concrete dilation, that is the radial

strain, to a maximum value, maxe , one may easily show that for inclined cracks forming

an angle ? with the column axis, the FRP contribution to shear capacity is

2

maxfd f f

f

DV E 0.5 cot

4ε π

= ρ ϑγ

(6.22)

where D is the column diameter. The derivation of Equation 6.22 is easily understood if

one assumes that at shear failure all the FRP material crossing an inclined crack is

strained uniformly at fue .

The above discussion concerns retrofit by applying externally bonded FRP strips. In case

an FRP jacket is applied, its contribution to shear strength, fdV , can be calculated for

circular jackets as

fd f fd fV 0.5 E t h cot= π ε ϑ (6.23)

and for rectangular jackets as

fd f fd fV 2E t h cot= ε ϑ (6.24)


229

where h is the length of the cross-section in the direction of loading and ϑ is the shear

crack inclination (conservatively it can be considered ϑ = 45o).

The Japan Building Disaster Prevention Association Guidelines provides a different

expression for the estimation of shear strength of elements retrofitted with FRP strips

[JBDPA, 1999]

0.23t c

Sd w wy o

0.053 (17.6 f )V 0.845 f 0.1 bj

M / Vd 0.12 ρ +

= + ρ + σ + ∑ (6.25)

where

w wy ws wys wf fdf f f 10ρ = ρ + ρ ≤∑ MPa (6.26)

oσ is the axial stress ( oσ < 7.84 MPa) and j is the internal lever-arm (j = 0.8d for

columns). Equation 6.25 expresses the shear strength as the square root of the summation

of the steel and FRP contribution and is similar to the one used for the design of steel

shear reinforcement for new buildings. The effective ultimate strain of FRP is fue = 0.007.

Experimental studies suggest that elements strengthened with FRP sheets fail in shear

mainly in one of the two modes: tensile rupture of the FRP and debonding of the FRP

from the sides of the RC element. Common methods of strengthening include side

bonding, U-jacketing and wrapping. Available experimental data indicate that almost all

beams strengthened by wrapping failed due to FRP rupture. In contrast, almost all beams

strengthened by side bonding only, and most strengthened by U jacketing, failed due to

FRP debonding. For the case of debonding failure mode, it has been proposed to limit the

strain in the FRP to an effective strain, which is obtained from regression of experimental

data [Triantafillou & Antonopoulos, 2000]. A reduction factor 0.8 is proposed [fib, 2001].

When failure is due to debonding, the contribution of FRP to the shear strength can be

calculated as [Chen & Teng, 2003]

f ffd f f

b f

f h (sin cos )V 2 t w

sβ + β

=γ

(6.27)


230

where bγ = 1.25 is the partial safety factor, fw , fh and fs are the width, effective height

and spacing of the FRP strips, respectively, and β is the angle of fibre orientation. The

design effective FRP stress, ff, is defined as

f f f ,max,df D= σ (6.28)

The maximum design stress in FRP, f ,max,dσ , can be obtained by using the 95-percentile

characteristic value of the bond strength

ff ,max,d w L c f

f

E0.315 f f

tσ = β β ≤ (6.29)

where wβ and Lβ are coefficients that reflect the effect of FRP-to-concrete width ratio

and the effect of bond length, respectively. They are calculated as

Lβ = 1; λ ≥ 1 (6.30a)

L sin( / 2)β = πλ ; λ < 1 (6.30b)

max eL / Lλ = (6.30c)

f fe

c

E tL

f= (6.30d)

f fw

f f

2 w /(s sin )1 w /(s sin )

− ββ =

+ β (6.30e)

where maxL is the bond length.

In the design of a shear strengthening scheme using U jacketing or side-bonding with

strips, an iterative procedure is required because the coefficient wβ is related to the ratio

of strip width to strip spacing f fw /(s sin )β . An initial value of wβ = 1 may be used. The

iterative process will converge very quickly, with three iterations being usually sufficient

[Chen & Teng, 2003].


231

6.3.6. Retrofit for confinement

General

The objective of confinement is to provide lateral support of the longitudinal

reinforcement, to enhance the ultimate compression strain of concrete and consequently

the deformation capacity of the member and to prevent premature spalling of concrete. In

general, confinement by circular hoops or circular jackets would be most beneficial. In

rectangular columns either circular or oval jackets can provide confinement along the

entire column perimeter, while rectangular jackets provide only inward forces at the

corners and therefore significant jacket thickness needs to be provided between corners to

restrain the lateral dilation of concrete and the buckling of vertical rebars. In the presence

of lapped splices, jackets with elliptical shape are more advantageous to provide

continuous lateral pressure along the entire perimeter of the column.

Considering different FRP materials, it seems more appropriate to use GFRP jackets that

also increase deformation capacity, while maintaining the same effectiveness of CFRP

jackets with respect to strength enhancement. CFRP should be used to provide concrete

with higher strength increase and moderate deformation capacity, whereas GFRP should

be used to provide higher deformation capacity and moderate strength increase [Pinto &

Monti, 2000].

FRP-confined concrete

The effect of confinement due to FRP jacketing on the ultimate stress and strain of

concrete is different from the effect due to steel jacketing. The difference originates from

the elastic behaviour of FPR jackets that apply increasing pressure on the concrete with

lateral dilation. On the contrary, a steel jacket applies constant pressure after yielding.

Based on experimental evidence, a number of bilinear constitutive models, as seen in

Figure 6.9, for FRP-confined concrete have been proposed. FRP-confined concrete

displays a distinct bilinear response with a sharp softening and a transition zone at the

level of the unconfined strength, cmf , after which the tangent stiffness stabilises at a

constant value, until reaching the ultimate strength, cuf .


232

Strain

Str

ess

Figure 6.9. Bilinear constitutive model for FRP-confined concrete

Following the proposal of [Samaan et al., 1998], the stress-strain relation of concrete is

written as

1 2 cc 2 c1/

1 2 c

o

(E E )f E

(E E )1

f

ηη

− ε= + ε

− ε +

(6.31)

The parameters to define the model (Figure 6.9) are defined as

1 coE 3950 f= (6.32a)

0.22 co f fE 245.61f 1.3456E t / D= + (6.32b)

o co lf 245.61f 0.371f 6.258= + + (6.32c)

In the previous expressions cof is the compressive strength of unconfined concrete and lf

is the pressure provided by the jacket. The first slope of the model, 1E , depends solely on

concrete, while the second slope, 2E , is a function of the stiffness of the confining jacket

and of the strength of unconfined concrete. η is a parameter that controls the curvature of

the transition zone; a constant value η= 1.5 is recommended [Samaan et al., 1998].

1E

2E cof

cuf

cuε


233

The strength of confined concrete, cuf , can be estimated as

0.2cu ocu co l

2

f ff f 6f

E−

= + (6.33)

The ultimate concrete strain, cuε , is defined by the geometry of the bilinear curve

cu ocu

2

f fE−

ε = (6.34)

An alternative empirical bilinear stress-strain relationship for FRP-confined concrete,

considering the effect of both steel stirrups and FRP jackets has been proposed

[Kawashima et al., 2000]. For the first branch the proposed law takes the form

n 1

c2c c c

c o

E1f E 1 1

n E

− ε = ε − − ε

(6.35a)

and for the second

c t 2 c of f E ( )= ε − ε (6.35b)

The strain at the intersection of the two branches, oε , is defined as

o f f f co sh yh co0.003 0.00939 E / f 0.0107 f / fε = + ρ ε + ρ (6.36)

The stress at the intersection of the two branches, tf , is calculated as

t co f f f sh yhf f 1.93 E 2.2 f= + ρ ε + ρ (6.37)

and the stiffness of the second branch, 2E , is defined as

2co

2 f ff f f sh yh

fE 0.658 0.078 E

E 0.098 f= − + ρ

ρ ε + ρ (6.38)

where shρ and yhf are the volumetric ratio and yield stress of steel stirrups, respectively.

Finally, η is calculated as


234

C 2 co

c co t

(E E )E f

− εη =

ε − (6.39)

The empirical bilinear models have been fitted on experimental results performed mainly

on cylindrical specimens applying a relatively large number of FRP layers. Experimental

results from specimens wrapped with a few layers and/or specimens with rectangular

cross-section, indicate that the stress-strain relation for FRP-confined concrete comprises

a softening post-peak branch with higher ultimate strain and residual strength, compared

to plain concrete. The bilinear empirical models cannot capture this behaviour and the

need for a theoretical approach emerges. According a proposed theoretical model

[Spoelstra & Monti, 1999], the lateral strain of concrete is related to the axial strain and

then an iterative procedure is followed until attainment of a given ultimate deformation of

the FRP. Based on regression analysis, the following simplified formulae have been

proposed for the maximum strength of confined concrete

( )cu co lf f 0.2 3 f= + (6.40)

and for the ultimate strain

( )cu co c fu l2 1.25E fε = ε + ε (6.41)

where coε is the ultimate strain for unconfined concrete, c c coE E / f= is the concrete

elastic modulus and l l cof f / f= is the maximum confining stress, both normalised to the

maximum strength of unconfined concrete, cof .

Exact formulae for the estimation of strength and strain of FRP-confined concrete have

also been proposed. The ultimate strength of confined concrete is

l lcu co

co co

f ff f 2.254 1 7.94 2 1.254

f f

= + − −

(6.42)

and the ultimate stress is

cucu co

co

f1 5 1

f

ε = ε + −

(6.43)


235

A large number of constitutive models for FRP-confined concrete have been collected

and examined with the objective to systematically assess their performance [De Lorenzis,

2001]. The performance is compared on the basis of the predicted values of the properties

of interest, namely compressive strength and ultimate deformation of concrete and

ultimate strain in the FRP. Figure 6.10 plots the average absolute errors for the ultimate

strength and deformation of concrete. Considering the compressive strength, errors

ranging from 10% to 60% are observed, often on the unconservative side. The predictions

of the ultimate deformation overestimate the experimental data and the errors are higher

(ranging from 20% to 140%) than for the compressive strength.

Experimental data on the ultimate FRP strain were also examined. For FRP-encased

specimens the experimental values were very close to the theoretical values. On the

contrary, for wrapped specimens, the effective ultimate strain was significantly lower

than the theoretical value. The most important parameters that affect this reduction were

identified as the quality of execution, size effects and the radius of curvature. A tentative

equation was proposed and takes the form

1.8271

f f8.7375D E ntR (1.25 0.0063D)e−−= − (6.44)

where R is the ratio of the measured hoop strain in the confining FRP at tensile failure to

the FRP ultimate strain in uniaxial tension, D is the diameter of the specimen (in mm), ft

is the thickness of the FRP (in mm) and n is the number of plies.

The discrepancies of constitutive laws for FRP-confined concrete are reflected on the

global response of elements, as highlighted in a comparative study [Yuan et al., 2001]. A

circular cross-section (diameter 1.5 m and longitudinal reinforcement ratio sρ = 2.3%)

wrapped with ten layers of CFRP ( ff = 3483 MPa) was analysed. Figure 6.11a presents

the moment – axial force interaction diagrams following different constitutive laws for

FRP-confined concrete. All the models show similar trend of moment with axial load, but

a variation of the actual values is observed. Considering moment-curvature analysis of the

same cross-section (for axial load ν = 0.4), the results in Figure 6.11b indicate significant

differences in the predicted values of strength and ultimate curvature. While moment

capacity is influenced mainly by concrete strength, curvature capacity directly depends on

the ultimate deformation of concrete. This explains why larger scatter is observed in the


236

predicted values of maximum curvature, than in the values of maximum moment.

Concrete ultimate strain and cross-section curvature are of great importance in seismic

retrofit and hence it is unfortunate that no reliable model is yet available.

The material presented above refers mainly to FRP-wrapped columns with circular cross-

section. In an experimental campaign, the effectiveness of confinement of a rectangular

jacket on a rectangular column was found to decrease with increase in the aspect ratio,

b/h, of the cross-section [Cole & Belarbi, 2001]. This will be discussed with reference to

Figure 6.12, where a rectangular cross-section with dimensions b and d is shown. A

rectangular jacket is applied after rounding-of the corners at a radius r. The hatched area

shows the part of the cross-section that is not effectively confined.

Ave

rage

abs

olut

e er

ror

Ave

rage

abs

olut

e er

ror

Theoretical model Theoretical model (a) (b)

Figure 6.10. Average absolute error: prediction of strength (a) and ultimate deformation

(b) of FRP-confined concrete [De Lorenzis, 2001]

(a)

(b)

Figure 6.11. Moment – axial force interaction diagrams (a) and moment – curvature

monotonic curves (b) for different constitutive laws for FRP-confined concrete [Yuan et

al., 2001]


237

Figure 6.12. Effectiveness of confinement for rectangular jacket

Considering a parabolic shape for the unconfined areas, the total unconfined area is

2 2

u

(b 2r) (d 2r)A

3− + −

= (6.45)

A confinement effectiveness coefficient, ek , is introduced [fib, 2001]

2 2

es

(b 2r) (d 2r)k 1

3bd(1 )− + −

= −− ρ

(6.46)

where sρ is the longitudinal reinforcement ratio. The effectiveness coefficient multiplies

the lateral pressure calculated for a fully confined cross-section, i.e. circular cross-section

with circular jacket.

Design based on ultimate curvature

The basis for the design of a FRP jacket for confinement is the volumetric reinforcement

ratio, fρ , required to satisfy a performance criterion, quite often a target value of

curvature ductility. Ultimate curvature is defined at the maximum strain of concrete. A

conservative expression for the concrete ultimate compression strain, cuε , in circular piers

confined with circular jackets is [Priestley et al., 1996]

f fu fucu

cd

2.5 f0.004

fρ ε

ε = + (6.47)

For a circular column retrofitted with a circular jacket of diameter D (Figure 6.13), the

volumetric ratio is


238

f f4t / Dρ = (6.48)

From Equations 6.44 and 6.45 the required thickness of the jacket, ft , can be calculated

cu cdf

fu fu

0.1( 0.004)Dft

fε −

=ε

(6.49)

A similar approach is adopted in the technique proposed in the FHWA Seismic Retrofit

Manual for Highway Bridge [Buckle & Friedland, 1995]. A layer of thickness at stressed

to provide an active confinement stress, af , is combined with a layer of thickness pt that

provides passive confinement. Assuming that the ultimate stress of FRP is fuε = 0.004 and

on the condition that lf ≥ 2 MPa, the minimum required jacket thickness is

a a p p at E t E 125D(2 f )+ = − (6.50)

where aE and pE are respectively the elastic moduli of the active and passive layers.

Experimental evidence suggests that, under the previous limitations, piers retrofitted

according to Equation 6.50 will be capable to sustain drift uδ = 4% with an adequate

reserve of displacement capacity. The jacket needs to extend until the cross-section where

the moment decreases to 75% of the maximum moment and not less that half the column

diameter.

For columns with rectangular cross-section, either rectangular or elliptical jackets can be

considered. For the case of rectangular columns with rectangular jackets (Figure 6.14a), a

modification of the aforementioned design equations is proposed in order to consider the

reduced effectiveness of the jacket [Priestley et al., 1996]. According to this proposal,

Equation 6.47 becomes

f fu fucu

cd

1.25 f0.004

fρ ε

ε = + (6.51)

Considering that the volumetric ratio of confinement, fρ , can be written as

f f2t (b h) / bhρ = + (6.52)


239

where b and h are the dimensions of the cross-section, the required thickness of the

jacket, ft , is calculated as

It is reminded that experimental evidence shows that the circumferential failure mostly

occurs at strains lower than the ultimate strain, fuε , obtained by standard tensile testing of

the FRP strip. This reduction is due to the triaxial state of stress of the wrapping

reinforcement, the quality of the execution, the curved shape of the wrapping

reinforcement and the size effects when applying multiple layers. Proper design values

for the effective ultimate circumferential strain, fuε , justified by experimental evidence,

should be taken into account.

cu cdf

fu fu

( 0.004)f bht 1.6

f (b h)ε −

=ε +

(6.53)

Figure 6.13. Confinement of circular column with circular jacket

Figure 6.14. Confinement of rectangular column with rectangular (a) and oval (b) jacket


240

For rectangular columns, elliptical jackets are expected to be more effective, as they

provide more uniform compression stresses. Design guidelines for rectangular jackets

applied on rectangular columns have been proposed [Seible et al., 1995b]. The rules are

limited to cross-sections with aspect ratio h/b < 1.5, otherwise it is recommended to

design a circular or oval jacket. Following these rules, the corners of the cross-section

should be rounded to a radius r > 50 mm and the thickness of the jacket should be twice

the one calculated for a column with the equivalent diameter eD , as defined in the

following. Some limitations for the application of rectangular FRP jackets on rectangular

columns are also proposed [Priestley et al., 1996]. These limitations concern the axial

load ( maxν = 0.15), longitudinal reinforcement ratio ( l,maxρ = 3%) and aspect ratio

( maxh / b = 3).

For the design of oval FRP jackets applied on rectangular columns, an equivalent column

diameter, eD , is defined as

e 1 2D R R= + (6.54)

where the jacket radii are

21R b / a= ; 2

2R a / b= (6.55)

In the above expressions a and b are the dimensions of the oval jacket (Figure 6.14b).

The jacket dimensions that minimise the total length of the principal axes are

a = k b (6.56a)

2 2A B

b2k 2

= +

(6.56b)

23A

kB

=

(6.56c)

where A and B are the dimensions of the original rectangular cross-section.


241

Then, the equivalent diameter, eD , can be used in Equation 6.49 to calculate the required

thickness of the oval jacket. It is expected that for rectangular cross-sections with high

aspect ratio the radius of the jacket will be extremely large and will result in ineffectual

confinement.

Design based on upgrade index

An alternative design procedure, developed for circular columns and based on an upgrade

index has been proposed [Monti et al., 1998]. The upgrade index, I, is defined as the ratio

of target and available values of strength, F, and displacement ductility, uµ , of the

member

tar u,tar

av u,av

FI

Fµ

=µ

(6.57)

The available strength and ductility are estimated from the geometry of the cross-section

and the material properties. The target values are calculated for a given loading. If a

strength-only intervention is decided, then u,tar u,avµ = µ . Similarly, if the objective is to

increase ductility only, then tar avF F= .

Based on regression analysis, the upgrade index, I, is written as

cu cul

co co

fI 1 k(1 ) 1

f

γ

α β ε= + + ην ρ − ε

(6.58)

where lρ is the percentage of longitudinal reinforcement.

The confined concrete strength, cuf , is estimated as

f f fu f f fucu co

co co

0.5 E 0.5 Ef f 2.254 1 7.94 2 1.254

f f

ρ ε ρ ε= + − −

(6.59)

and the ultimate strain of concrete is

c f f fucu co fu

co co

E 0.5 E2 1.25

f f

ρ εε = ε + ε

(6.60)


242

The maximum strain, fuε , for GFRP and CFRP is respectively 0.02 and 0.01. The

parameters k, α , β , γ and η are estimated through parametric analyses and are

presented in Table 6.3.

The same authors proposed a simplified upgrade index for circular columns, considering

only the increase in curvature ductility, ϕµ , in the form

,tar

,av

I ϕ

ϕ

µ=

µ (6.61)

Following some simplifying assumptions [Monti et al., 2001] the required thickness of

the jacket is

2

cu,av cu,av2f 3

fu fu

ft 0.175DI

f

ε=

ε (6.62)

This design equation has been adopted in EC8-3 [CEN, 2003b] for the design of

strengthening for building elements. The design procedure begins with the estimation of

the available curvature ductility, based on the analysis of the cross-section with known

geometry and material properties. For given loads, the target curvature ductility is defined

and then the upgrade index is calculated from Equation 6.61. Finally, the jacket of the

thickness is calculated from Equation 6.62 for a given FRP material. No specific

limitations are given for the maximum strain of the FRP, fuε .

Table 6.3. Parameters k, α , β , γ and η from regression analysis [Monti et al., 1998]

GFRP CFRP k 1.0/0.7* 0.8/0.5* α 0.6 0.6 β 0.2 0.2 γ 0.8 0.7 η 125 125

*optimal value/minimum value


243

Detailing

To prevent buckling of longitudinal reinforcement for rectangular columns with shear

span L/D > 4, it is recommended [Seible et al., 1995b] to apply a jacket with minimum

thickness

f ft 6.9nD / E= (6.63)

where n is the number of longitudinal rebars.

The jacket must be extended beyond the expected plastic hinge region. For bridge

columns with typical axial loads ν < 0.3, the confinement length, fl , should be [Seible et

al., 1995b]

fl L / 8≥ (6.64a)

fl 0.5D≥ (6.64b)

measured from the cross-section of maximum moment. In the previous expressions L is

the length of the member and D is the (equivalent) diameter of the cross-section.

Moreover, a jacket with reduced thickness, 0.5 ft , should be extended for a length for a

distance equal to 2 fl from the cross-section of maximum moment.

When the jacket increases significantly the cross-section, a similar increase in strength

and stiffness of adjacent members should be avoided. For that purpose, a gap should be

provided between that jacket and adjacent members. A minimum gap length of 50 mm is

recommended [Seible et al., 1995b], while more exact calculations can be performed

considering the maximum expected plastic hinge rotation.

When applying an FRP jacket it is important to round the corners of the as-built cross-

section. The effect of curvature radius was experimentally investigated [Yang et al.,

2001]. Depending on the curvature radius, two different failure positions were identified

for the FRP strips: at the corner (for radii smaller than 19 mm) and at the flat portion (for

larger radii). When using large radius, a smaller difference in the strains measured at

different positions along the perimeter was observed. The test results indicate that only

67% of the nominal ultimate strength can be developed when the FRP is wrapped around


244

a circular section. As the corner radius decreases, the efficiency of the wrapping

decreases.

6.3.7. Retrofit for enhancement of lapped splices

It was common practice in bridge piers designed according to early seismic codes to

splice the longitudinal rebars just after the foundation, i.e. within the potential plastic

hinge zone. This can be the cause of brittle failure, before reaching the nominal flexural

strength, associated with limited deformation capacity. The use of FRP jackets has been

proposed for enhancement of lapped splices through confinement.

Before presenting the design guidelines, a simple model for failure of lapped splices

[Priestley et al., 1996] is introduced. Failure of lapped splices requires the formation of a

series of fracture surfaces orthogonal to the column surface to allow the rebars to slide

relative one to the other and a further fracture surface parallel to the column surface to

allow the radial cracks to dilate and to permit the bars to slide relative to the concrete core

(Figure 6.15).

A characteristic block of concrete can be identified, whose length is equal to the

overlapping length, bld , and the perimeter, p, for rectangular columns is

bl bl

sp 2(d c) 2 2(d c)

2= + + ≤ + (6.65a)

and for circular columns

bl bl

Dp 2(d c) 2 2(d c)

2nπ

= + + ≤ + (6.65b)

Figure 6.15. Failure of lapped splices


245

In the above equations s is the spacing between pairs of spliced rebars, c is the concrete

cover and n is the number of longitudinal rebars evenly distributed in the cross-section.

A jacket can be designed to provide adequate lateral compression that will not allow the

development of the aforementioned crack surfaces. The confining stress required to

inhibit failure of lapped splices can be estimated using the expression [Priestley et al.,

1996]

2bl s

ls

0.8d ff

pl= (6.66)

where sf is the stress to be transferred between the spliced rebars, sl is the overlapping

length and p is the perimeter of the characteristic block of concrete. For jackets within the

plastic hinge region, the stress to be transferred between the lapped rebars should

correspond to hardening and consider material overstrength. It is recommended [Priestley

et al., 1996] to consider s yf 1.7f= , where yf is the nominal yield stress of steel. More

relaxed criteria, suggest s yf 1.4f= [Seible et al., 1995b]. The more conservative

overstrength factor, s yf 1.7f= , can be used on the safe side. Then, Equation 6.66 becomes

2bl y

ls

1.21d ff

pl= (6.67)

Based on the simplified model of a circular jacket shown in Figure 6.16 [Seible et al.,

1995b], the jacket tensile force, fT , developed by the jacket stress, ff , acting over the

jacket thickness, ft , is calculated as

f f fT t f= (6.68)

From equilibrium of forces (Figure 6.16) we obtain

f f l2t f f D= (6.69)

and the required jacket thickness is

lf

f

Dft

2f= (6.70)


246

Figure 6.16. Confinement of circular column with circular jacket, equilibrium of internal

forces

where the lateral pressure, lf , to avoid failure of lapped splices is obtained from Equation

6.67.

Following the approach proposed by the FHWA Seismic Retrofit Manual for Highway

Bridges [Buckle & Friedland, 1995], the minimum required jacket thickness of active, at ,

and passive, pt , FRP reinforcement for enhancement of lapped splices is obtained from

the expression

a a p p at E t E 500D(2 f )+ = − (6.71)

The jacket needs to be provided only over the length of the lapped splices.

Based on experimental results, it is suggested to limit the strain of the FRP below fuε =

0.001 [Seible et al., 1995b]. Then, the stress on the jacket is f ff 0.001E= . However, due

to the low modulus of elasticity of certain composite materials, particularly GFRP

composites, the stress developed at that level of strain, fuε = 0.001, will be low and a very

large jacket thickness will be required. For that reason, it has been proposed to provide

active confinement of the column, either by winding the FRP under tension, or by

prestressing the jacket by pressure grouting between the jacket and column [Priestley et

al., 1996]. In that case, the required jacket thickness is estimated as


247

2bl f

as

ff

0.56d ff

plt 0.5D

0.0015E

−= (6.72)

where af is the active confinement stress after losses, and the maximum FRP strain is

considered equal to fuε = 0.0015.

The contribution of existing horizontal reinforcement can be considered in the design of

the jacket for enhancement of lap splice behaviour. When the horizontal reinforcement

ratio is low, it can be omitted, but the contribution of circular hoops or spirals can be

estimated considering the same limit for lateral dilation, suε = 0.001, as [Seible et al.,

1995b]

sh shh

0.002A Ef

Ds= (6.73)

where shA , shE and s are the area, elastic modulus and spacing of horizontal

reinforcement. The jacket should extend in the region recommended for the jacket for

confinement according to Equation 6.64 [Seible et al., 1995b].

The above are valid for circular jackets applied on circular cross-section. Since the lateral

pressure to prevent failure of lapped splices in piers with rectangular cross-section can be

quite high, a curved jacket is required to provide such force. Therefore, no rectangular

jackets are recommended. However, if controlled debonding is allowed, rectangular

jackets can prevent cover concrete from spalling and preserve the vertical load carrying

capacity of the column. A design rule for twice the jacket thickness of a circular jacket is

recommended, with the same restrictions for the geometry and dimensions as before

[Seible et al., 1995b]. The concept of equivalent diameter can be applied for the design of

circular or oval jackets for rectangular cross-sections.


248

6.4. DESIGN OF FRP JACKETS FOR PIERS WITH RECTANGULAR

HOLLOW CROSS-SECTION

6.4.1. General

Up to this point, the seismic deficiencies of existing bridge piers have been identified, as

discussed in Chapters 3 and 4. In addition, in the first part of the present chapter the

available retrofit techniques have been reviewed. It emerges that while design guidelines

exist to remedy most seismic deficiencies, there is a lack for the particular problem of

confinement of piers with hollow cross-section. Experimental evidence [Peloso, 2003]

suggests that FRP jackets provide effective confinement for piers with this particular

geometry. Nevertheless, because of the small scale of the specimens and the limited

number of tests, further studies are needed to verify the effectiveness of this technique for

hollow piers with large dimensions.

Towards this direction, numerical analyses have been performed in order to identify the

effect of various parameters. A two-level approach was adopted. First, the effect of the

FRP jacket on the properties of concrete was examined by FEM analyses. This was

necessary because of the inconsistencies of existing constitutive laws for FRP-confined

concrete (see 6.3.6) and of the limited confidence in their applicability to large hollow

cross-sections. Then, moment-curvature analysis of a hollow cross-section was performed

considering different configurations. The effect of confinement was modelled by

appropriately modifying the properties of concrete. The proposed approach was verified

against experimental results in the previous chapter and only the parametric analyses are

discussed in the following.

6.4.2. Numerical analysis - effect on concrete properties

Description of the numerical model

In order to verify the actual effect of concrete jacketing and wrapping with FRP on the

properties of concrete, FEM analyses were performed using the computer code Cast3m

[Millard, 1993]. The basic dimensions of the cross-section are defined in Figure 6.17,

while Figure 6.18 shows the concrete (in blue) and FRP (in red) elements for a parabolic

jacket with height jh = 0.10 m. The width of the pier cross-section was b = 1.0 m and the


249

depth d = 3.0b. The thickness of both the web and the flange was pt = 0.2b. For reasons of

symmetry, only a fourth of the cross-section was analysed. Cubic elements with 8 or 6

integration points were used for the concrete cross-section, while shell elements with 4

integration points were employed for the FRP jacket. Five values were considered for the

height of the concrete jacket, namely jh = 0.0 (no concrete jacket), jh = 0.05 m, jh = 0.10

m, jh = 0.15 m and jh = 0.20 m. The thickness of the FRP jacket was jt = 1 mm, jt = 3

mm and jt = 5 mm. In this way a total number of 15 different cases were studied. The

corner of the concrete cross-section was rounded at a radius in the order of 5 cm, as

recommended for practical applications.

A plasticity-based 3D constitutive model was used for the concrete elements; the stress-

strain curves for uniaxial compression are given in Figure 6.19. Elastic behaviour was

considered for the FPR jacket. Orthotropic material behaviour was used to account for the

presence of fibres only in one direction (at the plane of the cross-section). The material

properties in the other direction (normal to the cross-section plane) were estimated

considering the contribution of the matrix resin only. The material properties for concrete

and FRP are listed in Table 6.4. It was decided to study a GFRP jacket, which is

considered more effective for the enhancement of deformation capacity [Pinto & Monti,

2000]. Perfect bond was considered between the two materials.

Figure 6.17. Definition of cross-section geometry


250

Figure 6.18. Concrete (blue) and FRP (red) jacket mesh

Strain (%)

Stre

ss (M

Pa)

unconfinedFRP-confined

Figure 6.19. Stress-strain curve of concrete for uniaxial compression

Table 6.4. Material properties

cE (GPa) Pν cf (MPa) oε

33.5 0.2 36.3 0.00254

f1E (GPa) f 2E (GPa) Pν G (GPa)

52 5.0 0.2 2.0

The analyses were performed for increasing compressive axial load. At this stage, the

vertical steel rebars were omitted. In the following the results of the analyses are

discussed in terms of general stress-strain behaviour, increase in compressive strength and

distribution of the confinement effect along the cross-section.


251

Effect of confinement within the cross-section

The distribution of the effect of confinement within the cross-section is discussed with

reference to Figure 6.20 in which the areas with the same compressive strength have the

same colour. Compressive strength is normalised to the compressive strength of

unconfined concrete. Blue colour corresponds to the smallest increase and changes to

green, yellow and red for the areas with the highest increase. The first row presents the

results for a rectangular FRP jacket applied directly on the as-built cross-section. The

second, third, fourth and fifth rows correspond to the analyses for concrete jacket with

height jh = 0.05 m, jh = 0.10 m, jh = 0.15 m and jh = 0.20 m, respectively. The thickness

of the FRP jacket increases when moving from left to right in Figure 6.20 from jt = 1 mm

through jt = 3 mm until jt = 5 mm for the last line.

A general observation from Figure 6.20 is that the effect of confinement is not

homogeneous throughout the cross-section. Zones with different extent of confinement

may be identified within the cross-section; in certain cases the boundaries between the

zones are not clearly defined. In order to avoid the analysis of a prohibitive number of

cases, the cross-section is divided as follows. Zone 1 comprises the corner of the cross-

section, without the external rounded part. As will be seen in the following, a moderate

increase in compressive and residual strength is observed in this zone. The external part

of the corner, where the biggest increase is observed is termed Zone 2. Zone 3 coincides

with the flange, where a small increase in compressive and residual strength is observed.

Finally, Zone 4 encompasses the additional concrete for the parabolic jacket. In this zone

a small increase in strength is observed. The web is not considered to benefit from the

jacket.

A similar stress pattern was identified for full rectangular sections wrapped with FRP

strips [Monti, 2003]. Resulting from FEM analysis of a rectangular concrete cross-section

under uniaxial compression, the circular core of the cross-section shows a bilinear stress-

strain curve, in accordance to the empirical constitutive models discussed previously. A

strut originating from the corner and expanding towards the core shows a smaller

enhancement of concrete properties, while the remaining parts of the cross-section are

practically unaffected.


252

jt = 1 mm jt = 3 mm jt = 5 mm

h =

0.00

m

h =

0.05

m

h =

0.10

m

h =

0.15

m

h =0

.20

m

Figure 6.20. Effect of jacket height and thickness on the compressive strength of concrete


253

Effect of confinement on the concrete properties

The effect of the FRP jacket on the concrete properties is discussed in this section.

Figures 6.21 to 6.25 plot the stress-strain curves of concrete in the four zones of the cross-

section for the examined values of jacket height and thickness. The stress is obtained as

the sum of the nodal reactions at each zone, divided by the area of the zone. The stress is

normalised to the compressive strength of unconfined concrete. The stress-strain curve for

unconfined concrete is included in all graphs for comparison.

It is clearly seen in Figures 6.21 to 6.25 that the behaviour of concrete (softening after

peak strength) does not follow the empirical constitutive relations proposed for FRP-

confined concrete (bilinear relation with increasing strength for the second branch). In

fact, the effect of confinement is to increase the compressive and residual strength of

concrete. This is reminiscent of the behaviour of full cross-sections confined with steel

stirrups or jackets. A bilinear stress-strain curve with increasing stiffness for the second

branch was observed only for extremely high values of the FRP jacket thickness, jt ≈ 20

mm, that do not have practical application. Such behaviour was also observed in a few

elements close to the rounded corner. Nevertheless, it is not reflected in the global stress-

strain curves for each zone. Similar behaviour was shown in experimental tests on

rectangular concrete specimens wrapped with small amounts of FRP ( sρ =0.23% and

sρ =0.83% for CFRP and GFRP, respectively) [Karabinis & Rousakis, 2003]. The

specimens showed softening after maximum strength, while increasing strength in the

second branch was observed for higher amounts of FRP.

In some of the examined cases, namely cross-sections with small jacket thickness and/or

large jacket height, the numerical analysis was terminated before reaching a residual

strength. This was because of collapse of some elements in zone 5, where no confinement

effect was observed. The softening stiffness was calculated from the global stress-strain

curves for each zone and the residual strength was estimated by analysing a similar model

with higher ultimate deformation for the elements in zone 5.


254

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

stj = 1 mm tj = 3 mm tj = 5 mm

zone 1

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s

tj = 1 mm tj = 3 mm tj = 5 mmzone 2

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


Figure 6.21. Stress-strain curves for confined concrete ( jh = 0.00 m)

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s

tj = 1 mm tj = 3 mm tj = 5 mm

zone 2

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


zone 3

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s




255

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

stj = 1 mm tj = 3 mm tj = 5 mm

zone 1

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


zone 2

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


zone 3

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s



0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s




256

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

Axial strain (%)

Nor

mal

ised

axi

al s

tres

s


0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

Axial strain (%)

Nor

mal

ised

axi

al s

tres

s



Elastic behaviour was considered for the FRP elements and thus it was not possible to

introduce an ultimate deformation. This is a limitation of the analyses, as failure due to

tensile fracture of the FRP strips (and “explosive” collapse of concrete) was not

considered. Looking at the global behaviour of the cross-section in bending, the above

phenomena will happen at large deformations and close to collapse. Then, the inadequacy

of the model to capture the failure of the FRP strips is not expected to affect the global

results at failure. In all the examined cases, the FRP strain was not greater than 1.2%,

which is below the typical values of ultimate strain obtained from tensile tests. Typical

values of ultimate strain can be even higher than uε =3% [fib, 2003]. Experimental results

indicate failure of FRP strips for smaller strains and then a safety factor in the order of 0.6

has been proposed. This design value was not surpassed in the analyses.

The analytical results are further discussed with focus on characteristic values of the

stress-strain curves. The properties of interest are the compressive strength, the residual

strength and the softening stiffness. These parameters, on one hand, give a qualitative

view of the improvement of the concrete properties due to confinement. On the other


257

hand, they are the material parameters used for the moment-curvature analysis described

in the following section.

The effect of the jacket on the concrete compressive strength is discussed in more detail

with reference to Figure 6.26. For all cases the concrete compressive strength increases

with the jacket thickness, jt . In Zones 1 and 3 the compressive strength is increased by

40% and 20%, respectively, for jt = 5 mm. In Zone 2 the compressive strength is

increased by more than 80% for jt = 5 mm. The compressive strength enhancement

increases until jh = 0.10 m and then remains constant. Finally, it is interesting to note that

concerning Zone 4, the compressive strength decreases with the jacket height. The above

observations suggest that a parabolic jacket of limited height is beneficial for the concrete

properties, but when the jacket becomes relatively large, no further beneficial effect is

obtained, or even a detrimental effect is observed. The value jh = 0.10 m can be

considered as an upper limit for the examined case.

Figure 6.27 plots the change of the concrete residual strength for different values of the

jacket height and thickness. The residual strength is normalised to the compressive

strength of unconfined concrete. The residual strength increases with the jacket thickness.

The area that benefits more is again the region near the rounded corner, where in most

cases a bilinear response is obtained. Moderate improvement is observed in Zones 1 and

4, while in Zone 3 the residual strength remains at less that 0.6 cf . An interesting feature is

that for small amount of FRP, jt = 1 mm, the improvement does not increase with the

jacket height. For what concerns the residual strength, no further improvement is obtained

for jackets with height larger than jh = 0.10 m.

The softening stiffness of concrete, normalised to the compressive strength of unconfined

concrete, is presented in Figure 6.28 for the examined values of jacket thickness and

height. The softening stiffness is obtained as the difference of the maximum and residual

strength, divided by the difference of the corresponding strains. It is observed in Figure

6.28 that the softening stiffness (absolute values) decreases with the jacket height. The

decrease is faster until jh = 0.10 m and then no change, or slow decrease is observed. The


258

jacket height does not seem to significantly affect the softening stiffness, with the

exception of Zone 4, where smaller stiffness corresponds to larger jacket height, jh .

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Com

pres

sive

str

engt

h


zone 1

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Com

pres

sive

str

engt

h


1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Com

pres

sive

str

engt

h


1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Com

pres

sive

str

engt

h


Figure 6.26. Effect of jacket on the compressive strength of concrete

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Res

idua

l str

engt

h


0.0

0.5

1.0

1.5

2.0

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Res

idua

l str

engt

h


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Res

idua

l str

engt

h


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Res

idua

l str

engt

h


Figure 6.27. Effect of jacket on the residual strength of concrete


259

0

50

100

150

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Sof

teni

ng s

tiffn

ess


0

50

100

150

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Sof

teni

ng s

tiffn

ess


0

50

100

150

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Sof

teni

ng s

tiffn

ess


0

50

100

150

0.00 0.05 0.10 0.15 0.20Jacket height (m)

Sof

teni

ng s

tiffn

ess


Figure 6.28. Effect of jacket on the softening stiffness of concrete

6.4.3. Numerical analysis - effect on cross-section ductility

Description of the numerical model

Moment-curvature analyses were performed using the finite element code Cast3m

[Millard, 1993] with the aim to study the effect of axial load and reinforcement ratio on

the effectiveness of the retrofit. The cross-section of the numerical model is shown in

Figure 6.29. An equivalent I cross-section was analysed, instead of the original

rectangular hollow cross-section. This geometry of the cross-section was proved to

provide results in agreement with experimental data, as discussed in Chapter 5. The steel

elements (shown as red points in Figure 6.29) were distributed at the external and internal

faces of the flanges, as well as through the web: 20% of vertical reinforcement was

concentrated at the external face of the flange, 10% was concentrated at the internal face

of the flanges and the remaining 70% was distributed along the web.

Non-linear cyclic behaviour was considered for the concrete fibres and a modified

Menegotto-Pinto constitutive law for the steel fibres [Guedes et al., 1994]. The


260

constitutive laws were described in the previous chapter and only the monotonic stress-

strain curves for concrete and steel are presented in Figure 6.30 for reasons of

completence. The effect of confinement was considered by modifying the concrete

properties in accordance to the results of the previous FEM analyses. The cross-section

was divided in the five distinct zones described in the previous section and shown with

different colours in Figure 6.29.

Moment-curvature analysis of the cross-section described above was performed.

Monotonically increasing curvature was imposed at the presence of constant axial load.

Different values of axial load (ranging from ν = 0.0 to ν = 0.3) and longitudinal

reinforcement ratios (namely: sρ = 0.17%, sρ = 0.34%, sρ = 0.68% and sρ = 1.02%) were

considered. The normalised axial load, c cP / A fν = , and the ratio of longitudinal

reinforcement, s s cA / Aρ = , are defined for the original rectangular cross-section without

the jacket, cA . P is the axial force, cf is the nominal compressive strength of concrete

( cf = 35 MPa) and sA is the area of steel rebars.

Curvature ductility capacity

Curvature ductility is defined considering a bilinear envelop of the moment-curvature

diagram (Figure 6.31a). The yield moment is considered equal to the maximum moment,

maxM . The yield curvature, yϕ , is defined at the intersection of a line from the origin

passing through the numerical curve at 0.75 maxM and a horizontal line at maxM . The

ultimate curvature, uϕ , is defined at the point where the resistance reduces to uM =

0.8 maxM , or at the point where there is a sudden drop of resisting moment, whichever

occurs first. Finally, curvature ductility, ϕµ , is calculated as

u y/ϕµ = ϕ ϕ (6.74)

This definition follows the most common procedures for the estimation of ductility from

experimental data [Park, 1989] and the standard definitions given in seismic codes for the

design of structures, e.g. EC8 [CEN, 2002].


261

Figure 6.29. Concrete and steel mesh for the moment-curvature analysis ( jh = 0.05 m)

Strain

Str

ess

unconfinedconfined

(a)

Strain

Str

ess

(b)

Figure 6.30. Material constitutive laws: concrete (a) and steel (b)

Curvature

Mom

ent

(a)

Curvature

Mom

ent

(b)

Figure 6.31. Definition of failure criteria and curvature ductility: at maximum moment (a)

and at 20% loss of strength (b)

The results in terms of curvature ductility are presented in Figures 6.32 to 6.37. The

parameter that mostly affects the curvature ductility capacity is the axial load. In

qualitative terms, axial load dictates the failure mode, either due to tensile fracture of steel

or due to crashing of concrete in compression. For both the as-built and retrofitted cross-

sections, increase of axial load initially increases the curvature ductility. This range of

max0.75M

maxM

max0.2M

yϕ yϕuϕuϕ

maxM

max0.75M


262

axial load corresponds to failure of the cross-section due to collapse of steel, as indicated

by rapid loss of resistance in the moment-curvature diagrams. After a certain value,

further increase of axial load causes decrease of curvature ductility. This range of axial

load corresponds to failure of the cross-section due to crushing of concrete, as indicated

by smooth decrease of resistance after the peak in the moment-curvature diagrams. The

limit value of axial load ranges from ν = 0 to ν = 0.1 for the as-built cross-section and

from ν = 0.05 to ν = 0.20 for the jacketed cross-section. This limit value decreases with

the reinforcement ratio. This point of transition is also responsible for the peculiar shape

and discontinuities of some curves shown in the following figures, e.g. Figure 6.35 for

jt = 3 mm and jt = 5 mm.

Axial load somehow influences also the effect of the jacket thickness, jt , on the curvature

ductility of the cross-section. Keeping all other parameters constant, curvature ductility

does not significantly increase with jacket thickness. As seen in the following figures, the

actual effect of jacket thickness is to move the transition point of the curves to higher

values of axial load. On the other hand, the effect of jacket height, jh , seems to be

independent of the level of axial load. Similarly to what was observed previously for the

enhancement of the properties of concrete, the curvature ductility capacity increases with

the jacket height until the value jh = 0.10 m, after which no further improvement is

obtained. As expected, curvature ductility decreases with increasing amount of

longitudinal reinforcement.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad

p hor = 0.17%p hor = 0.34%p hor = 0.68%p hor = 1.02%


(as-built cross-section)


263

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

adp hor = 0.17%p hor = 0.34%p hor = 0.68%p hor = 1.02%

tj = 5 mm


( jh = 0.00 m)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.05 m)


264

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.10 m)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.15 m)


265

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60 70

Curvature ductility

Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.20 m)

Selected moment-curvature diagrams are presented in Figures 6.38 to 6.41 in order to

illustrate the effect of the examined geometrical and mechanical characteristics. The

curves shown in Figure 6.38 highlight the effect of reinforcement ratio. The curves

correspond to jacket height jh = 0.10 m, axial load ν = 0.1, and jacket thickness jt = 5

mm. As expected, higher resistance corresponds to larger amount of longitudinal

reinforcement. This increase in strength affects the conventional yield curvature and

although all cross-sections fail at almost the same curvature (which corresponds to

attainment of the ultimate strain in the outermost steel element), smaller ductility

corresponds to the cross-sections with higher axial load.

The effect of axial load is shown in Figure 6.39 that plots the moment-curvature diagrams

for jacket height jh = 0.10 m, jacket thickness jt = 5 mm and longitudinal reinforcement

ratio sρ = 1.02%. The resisting moment increases and the ultimate curvature decreases

with increasing values of axial load. This in turn leads to drastic decrease of curvature

ductility for high axial load. Figure 6.39 is very illustrative also on what concerns the


266

effect of axial load on the failure mode of the cross-section: collapse of reinforcement for

ν = 0.1 and concrete crushing for ν = 0.2 and ν = 0.3.

0

5000

10000

15000

20000

0.000 0.010 0.020 0.030 0.040

Curvature (1/m)

Mom

ent (

kNm

)

Figure 6.38. Effect of reinforcement ratio ( jh = 0.10 m, jt = 5 mm, ν = 0.1)

0

5000

10000

15000

20000

25000

0.00 0.01 0.02 0.03 0.04

Curvature (1/m)

Mom

ent (

kNm

)

Figure 6.39. Effect of axial load ( jh = 0.10 m, jt = 5 mm, sρ = 1.02%)

8.17,1.0 =µ=ν ϕ

0.9%, 21.3ρ = µ =

6.14,2.0 =µ=ν ϕ

ρ = µ =

8.5,3.0 =µ=ν ϕ

0.9%, 21.3ρ = µ =

8.17%,02.1s =µ=ρ ϕ

6.19%,68.0s =µ=ρ ϕ

4.24%,34.0s =µ=ρ ϕ

7.39%,17.0s =µ=ρ ϕ


267

0

5000

10000

15000

20000

0.00 0.01 0.02 0.03 0.04 0.05

Curvature (1/m)

Mom

ent (

kNm

)

Figure 6.40. Effect of jacket thickness ( jh = 0.10 m, sρ = 1.02%, ν = 0.1)

0

2000

4000

6000

8000

10000

0.00 0.01 0.02 0.03 0.04

Curvature (1/m)

Mom

ent (

kNm

)

Figure 6.41. Effect of jacket height ( jt = 5 mm, sρ = 0.17%, ν = 0.1)

The effect of jacket thickness for a cross-section with axial load ν = 0.1, longitudinal

reinforcement sρ = 1.02% and jacket thickness jt = 5 mm is shown in Figure 6.40. The

resisting moment is not significantly affected by the jacket thickness. The ultimate

curvature and curvature ductility increase with jt . Note that in this example and for the

highest value of jacket thickness, jt = 5 mm, curvature ductility decreases. This is due to

9.12,mm1t j =µ= ϕ

2.20,mm3t j =µ= ϕ

0.9%, 21.3ρ = µ =

8.17,mm5t j =µ= φ

0.39,m15.0h j =µ= ϕ 7.39,m10.0h j =µ= ϕ 6.37,m05.0h j =µ= ϕ 4.35,m00.0h j =µ= ϕ

4.38,m20.0h j =µ= ϕ


268

the change of failure mode, which is due to steel, while failure was determined by

concrete for the smaller values of jacket height.

Finally, the effect of jacket height is discussed with reference to Figure 6.41, in which the

curves for ν = 0.1, jt = 5mm and sρ = 0.045 are plotted. The effect of the jacket height is

slightly beneficial until = 0.10 m, but after this value, a slow decrease of curvature

ductility is observed. This is similar to the observation made on the effect of the jacket

height on the concrete properties and supports the suggestion to consider an upper limit in

the jacket height for practical applications.

Effectiveness index

The ratio of the curvature ductility of the jacketed cross-section to the curvature ductility

of the as-built cross-section can be used as an effectiveness index. The effectiveness

index is plotted in Figures 6.42 to 6.46 for different values of the examined parameters.

The effect of axial load is to initially increase the effectiveness of the retrofit (increase of

the effectiveness index until ≈µµ −φφ builtas,dretrofitte, / 7) and then to decrease the

effectiveness, similarly to the effect on the ductility capacity of the cross-section.

Furthermore, the effectiveness index increases with the jacket thickness and jacket height.

The effect of longitudinal reinforcement ratio is related to the axial load. In fact, as seen

in the following figures, the effectiveness index increases with axial load before the limit

value and then decreases. This inversion of the trend is again related to the change in

failure mode, which depends on the applied axial load.

The limit value of the axial load ranges from ν = 0.05 to ν = 0.25, depending on the

amount of longitudinal reinforcement, jacket thickness and jacket height. For low to

medium amounts of vertical reinforcement (from sρ = 0.17% to sρ = 0.68%) jacketing is

not effective for piers with axial load ν < 0.10. In these cases, large tension strains

develop in the steel before significant compression on the concrete and failure is due to

collapse of steel. For higher amounts of longitudinal reinforcement jacketing is effective

even for low values of axial load. The effectiveness, though, is reduced, compared to the

cases of lower reinforcement ratios.


269

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7

Curvature ductility (confined/as-built)

Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo


tj = 5 mm


( jh = 0.00 m)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.05 m)


270

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.10 m)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.15 m)


271

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 1 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 3 mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7


Nor

mal

ised

axi

al lo

ad


tj = 5 mm


( jh = 0.20 m)

Enhancement of moment capacity

For the given range of axial load, the ratio of moment capacity of the retrofitted cross-

section to the moment capacity of the as-built cross-section is constantly increasing. As

expected, the increase is higher for higher axial load. The maximum increase of moment

capacity, for the cases examined in this study, is about 20% and in few cases reaches

30%. This corresponds to an increase in shear demand that might exhaust the as-built

shear capacity of the pier. In that case, retrofit for shear strength enhancement will be

required in order to avoid brittle failure, following Capacity Design philosophy. Also,

retrofit of the foundation might be needed. When increasing the dimensions of the cross-

section an increase of stiffness is expected. A member with increased stiffness will attract

higher seismic forces and this fact has to be taken into consideration when designing the

global retrofit. This increase will also affect the dynamic properties, which are significant

for bridge structures. Jacketing will decrease the usually high periods of bridge piers and

then most probably will increase the spectral ordinates and accordingly the seismic

demand.


272

-25000

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

Curvature (1/m)

Mom

ent (

kNm

)

as-builtretrofitted (h = 0.2 m)retrofitted (h = 0.0 m)

Figure 6.47. Cyclic behaviour: moment-curvature diagrams for the as-built and jacketed

cross-section ( ν =0.2, jt = 5 mm, sρ = 1.02%).

Cyclic behaviour and energy-dissipation capacity

The effect of the addition of concrete and the wrapping with FRP on the energy-

dissipation capacity is verified in Figure 6.47 that plots the moment-curvature numerical

curves for the favourable case of ν = 0.2, sρ = 1.02% and jt = 5 mm and the two extreme

values of the jacket height. For no concrete jacket and the same values of curvature, no

difference is observed between the as-built and the retrofitted cross-sections.

Nevertheless, the retrofitted cross-section has a much higher curvature ductility, which

can be exploited also under cyclic loading. For higher values of the concrete jacket, both

strength and ultimate curvature increase and then a more pronounced dissipation capacity

is evidenced by the wider cycles shown in Figure 6.47.

6.4.4. Design equations and recommendations

Curvature ductility

The objective of this section is to derive empirical design equations based on the

numerical results presented previously. First, an expression of curvature ductility as a

function of the examined geometrical and mechanical parameters (namely axial load,


273

longitudinal reinforcement ratio, height and thickness of the jacket) is sought. These

parameters are grouped in a single design parameter, termed j j sS f ( ,h , t , )= ν ρ in the

following, and then an expression in the form f (S)ϕµ = is fitted to the numerical results.

Observing Figures 6.32 to 6.37, there seems to be a limit value of normalised axial load

until which the values of curvature ductility increase and after which they decrease.

Although in general this limit value is not an independent parameter, the value ν = 0.1

was chosen. The results of the numerical analyses were divided in two groups according

to the limit value of axial load. This choice is arbitrary and based on a visual

interpretation of the obtained results, but simplifies the derivation of the empirical

formulae. In fact, it was not possible to obtain an empirical fit with high correlation,

without introducing this grouping. For each group different forms of the functions

j j sS f ( ,h , t , )= ν ρ and f (S)ϕµ = were studied. Figure 6.48 plots the values of curvature

ductility versus the design parameter, S, for the two groups. A linear relation fits the

numerical results for ν ≤ 0.1 (Figure 6.48a), while a power expression fits the results for

ν > 0.1 (Figure 6.48b).

The empirical formulae for ν ≤ 0.1 are

63.10S42.57 1m, +=µϕ (6.75a)

23.7S94.45 105.0, +=µϕ (6.75b)

8 0.03

j j1

s

(1 ) (1 h )(1 t )S

10.045

+ ν + +=

ρ+

(6.75c)

and for ν > 0.1

78.12m, S63.0 −

ϕ =µ (6.76a)

74.1205.0, S35.0 −

ϕ =µ (6.76b)

0.7 0.08 0.3

j s2 0.3

j

(1 h )S

(1 t )

ν + ρ=

+ (6.76b)


274

In the previous equations ν is the normalised axial load, jh is the jacket height (in m), jt

is the jacket thickness (in mm) and sρ is the longitudinal reinforcement ratio (in %). m,ϕµ

is the mean value of curvature ductility, while 05.0,ϕµ is the 5% characteristic value (95% of the

empirical values are lower than the corresponding numerical values). The numerical values are

plotted in Figure 6.48, along with Equations 6.75 and 6.76. The correlation factor for Equation

6.75a is 2R = 0.82 and for Equation 6.76a it is 2R = 0.70.

0

10

20

30

40

50

60

70

0.0 0.1 0.2 0.3 0.4 0.5 0.6

S1

Cur

vatu

re d

uctil

ity

Equation 6.75aEquation 6.75b

(a)

0

10

20

30

40

50

60

70

0.0 0.1 0.2 0.3 0.4 0.5 0.6

S2

Cur

vatu

re d

uctil

ity


(b)

Figure 6.48. Empirical fit to the numerical values of curvature ductility: ν ≤ 0.1 (a) and

ν > 0.1 (b)


275

Figure 6.49 plots the empirical values according to Equations 6.75b and 6.76b versus the

numerical values. A straight line passing from the origin with a 45o slope is also plotted in

Figure 6.49. It is seen that conservative results are obtained, as most of the empirical

values are lower than the numerical values. It should be highlighted that the large scatter

imposed a large safety factor and then the jacket may be over-designed in many cases.

Effectiveness index

The ratio of curvature ductility of the retrofitted cross-section to the ductility of the as-

built cross-section is used as an effectiveness index. With the aim to derive an empirical

expression for the design of FRP jackets, the numerical results are studied in the two

groups defined previously. Using Equation 6.75b, the effectiveness index for ≤ν 0.1

takes the form

045.023.7)1(94.45

045.023.7)t1)(h1()1(94.45

81.0I 3.0s8

3.0s03.0

jj8

05.0,builtas,

05.0,dretrofitte,05.0 ρ

+ν+

ρ+++ν+

=µµ

=−ϕ

ϕ (6.77)

For ν > 0.1 and using Equation 6.76b, the effectiveness index is written as

14.0j

52.0j

05.0,builtas,

05.0,dretrofitte,05.0 )h1(

)t1(6.0I

++

=µµ

=−ϕ

ϕ (6.78)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Curvature ductility (empirical)

Cur

vatu

re d

uctil

ity (

num

eric

al) (a)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Curvature ductility (empiricall)

Cur

vatu

re d

uctil

ity (

num

eric

al) (b)

Figure 6.49. Comparison between empirical and numerical values of curvature ductility:

ν ≤ 0.1 (a) and ν > 0.1 (b)


276

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Effectiveness index (empirical)

Effe

ctiv

enes

s in

dex

(num

eric

al) (a)

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Effectiveness index (empiricall)

Effe

ctiv

enes

s in

dex

(num

eric

al) (b)

Figure 6.50. Comparison between empirical and numerical values of effectiveness index:

ν ≤ 0.1 (a) and ν > 0.1 (b)

Because of the scatter in the numerical results, a safety factor is introduced in Equations

6.77 and 6.78, so that 95% of the empirical values are higher than the numerical values.

The comparison between the empirical and numerical values is given in Figure 6.50,

where a line with 45o inclination is also shown.

Alternative definition of curvature ductility

It is seen in the previous section that a complex relation holds between the geometric and

mechanical characteristics of the cross-section and the curvature ductility capacity. This

made it necessary to introduce an artificial grouping of the numerical results and even in

this way an unsatisfactory correlation between the empirical and numerical results was

obtained. To make things easier, an alternative definition of curvature ductility is

introduced in this section. Moment and curvature at yield are defined as before and

ultimate curvature is conservatively defined at maxM , see Figure 6.31b. Although this

might lead in over-dimensioning at certain cases, the results remain on the safe side. It is

reminded that values of the effectiveness index as high as builtas,dretrofitte, / −ϕϕ µµ = 6.8 are

obtained if ultimate curvature is defined at the point of the moment-curvature diagram

where there is a 20% loss of strength. This definition is more realistic and demonstrates

the actual effectiveness of the retrofit method.

Following the alternative definition of ductility introduced in this section, a single

expression fits all the numerical results and takes the form


277

+ρ+ν+−

=µϕ 2.0j

3.0s

1.0j

7.0

m, )t1()h1()1.0(86.6

exp94.52 (6.79a)

+ρ+ν+−

=µϕ 2.0j

3.0s

1.0j

7.0

05.0, )t1()h1()1.0(10.8

exp35.42 (6.79b)

2.0j

3.0s

1.0j

7.0

)t1()h1()1.0(

S+

ρ+ν+= (6.79c)

The numerical values are plotted in Figure 6.51, along with Equations 6.77a and 6.77b.

The correlation factor for Equation 6.77a is 2R = 0.81.

Using Equation 6.77b it is possible to obtain also a single empirical expression of the

effectiveness index as a function of the examined geometrical and mechanical parameters.

This expression takes the form

++

−ρν+=µµ

=−ϕ

ϕ2.0

j

1.0j3.0

s7.0

05.0,builtas,

05.0,dretrofitte,05.0 )t1(

)h1(1)1.0(1.8exp6.0I (6.80)

Due to the relatively poor correlation, a modification is included in Equation 6.78 to

obtain the 5% characteristic value of the effectiveness index (95% of the empirical values

are lower than the numerical values). The empirical and numerical values are compared in

Figure 6.52, where a straight line with 45o inclination is also shown.

Recommendations

In Equations 6.75 to 6.80 there are two unknown design parameters, namely jacket

height, jh , and jacket thickness, jt . This means that the designer has to select one of

them and then enter the design formulae, or the graphs presented previously, with this

value and the desired value of curvature ductility, or effectiveness index, in order to

calculate the other. It might be preferable to limit the jacket height so as not to increase

the strength and stiffness of the retrofitted member. The limit jh = 0.10 m, identified in

this study, may be considered. Alternatively, it might be desired to limit the jacket

thickness in order to avoid practical problems related to the superposition of many FRP

layers. The above imply an iterative procedure and require some engineering judgement.


278

0

10

20

30

40

0.0 0.1 0.2 0.3 0.4 0.5 0.6

S = f(v, hj,tj,p)

Cur

vatu

re d

uctil

ity


Figure 6.51. Empirical fit to the numerical values of curvature ductility

0

1

2

3

4

0 1 2 3 4

Effectiveness index (empirical)

Effe

ctiv

enes

s in

dex

(num

eric

al)

Figure 6.52. Empirical (5% characteristic) and numerical values of the effectiveness

index

The equations derived in this section can be used when the geometrical and mechanical

characteristics of the piers fall within the limits examined in the present study.

Considering axial load, longitudinal reinforcement ratio, jacket height and thickness it is

believed that the whole range of interest has been examined. For piers with dimensions

smaller than those examined in this study, the jacket dimensions may be scaled down and


279

conservative results will be obtained. The formulae should not be used for piers with

larger dimensions because it is expected that confinement will not be the same effective

and the proposed empirical equations might provide unsafe results.

Two groups of design formulae have been elaborated, namely Equations 6.75 to 6.78 and

Equations 6.79 and 6.80. For the first group a failure criterion, considering failure due to

concrete crushing or rupture of steel, was used to define ultimate curvature. Then, a limit

value of the normalised axial load was set and different formulae were elaborated for the

two sub-groups of the numerical results. To avoid this artificial grouping, an alternative

definition of ultimate curvature was considered and a single equation was found to fit the

numerical values. The alternative definition of ultimate curvature simplifies the

procedure, because the failure mode does not influence the ultimate curvature.

Conservative results are obtained because maximum moment occurs always at curvature

lower or equal to the curvature that corresponds to failure of concrete or steel fibres. For

reasons of simplicity, it seems preferable to use Equations 6.79 and 6.80.


Several methods have been proposed for the retrofit of seismic-deficient bridge piers

using FRP reinforcement. External reinforcement is applied for the enhancement of

flexural or shear strength, while jackets are wrapped around the piers for the improvement

of ductility capacity and behaviour of lapped splices. Design equations, which take into

consideration all possible failure modes, have been proposed for flexural and shear FRP

reinforcement. Regarding FRP jackets, noteworthy deviations are observed in the

predictions of different models for the properties of confined concrete. The semi-

empirical rules proposed for the design of FRP jackets for rectangular or circular solid

cross-sections cannot be simply extrapolated to the case of hollow cross-sections with

large dimensions.

Numerical analyses of a concrete cross-section wrapped with an FRP jacket suggest that

for the case of hollow piers with large dimensions, the existing empirical laws for FRP-

confined concrete are not suitable. The effect of lateral pressure provided by the jacket is

to increase the maximum and residual stress, as well as the ultimate deformation of

concrete, similarly to concrete confined by steel stirrups or jackets. A softening branch,

with a slope less steep than the one for unconfined concrete, follows the peak strength. A


280

bilinear stress-strain curve with increasing stress in the second branch, as proposed for

full cross-sections, is only observed for unrealistic values of the jacket thickness.

The effect of confinement is mainly concentrated in the corners and its extent depends on

the dimensions of the jacket. For rectangular jackets, the confined zone is limited to the

corners, even for large amounts of FRP. For oval jackets, the confined area comprises

also part of the flange and added concrete. In this case, the confined area increases with

increasing thickness of the FRP jacket. A limit value of the concrete jacket, after which

no further enhancement of the concrete properties was obtained, was identified.

The effectiveness of jacketing for the enhancement of the deformation capacity of cross-

sections is conditioned by the axial load, amount of longitudinal reinforcement and

dimensions of the concrete jacket. The jackets are most effective in the range of ν = 0.1 to

ν = 0.3, which, luckily, corresponds to the axial loads bridge piers usually carry. The

effectiveness reduces with increasing amount of longitudinal reinforcement. Parabolic

jackets are found to be more effective for enhancement of ductility capacity than

rectangular jackets. Indicatively, it is noted that the curvature ductility of the jacketed

cross-section can be up to 7 times the ductility of the as-built cross-section, provided a

significant amount of FRP and the corresponding oval concrete jacket are provided. For

the simplest solution of a rectangular jacket, i.e. application of the FRP strips directly

around the original cross-section without adding new concrete, the curvature ductility can

be increased up to 3 times, as seen in Figure 6.42. This demonstrates that this fast and

economic intervention can effectively improve the deformation capacity of seismic-

deficient bridge piers with rectangular hollow cross-section.

Parabolic jackets increase the stiffness of the cross-section. This might result in higher

design shear forces. On the other hand, the moment capacity of the cross-section is

slightly increased (about 20%). Upgrade of adjacent members might then be required.

Based on the results of numerical analyses, FRP jackets are effective in improving the

cyclic behaviour and the energy-dissipation capacity of retrofitted cross-sections,

particularly for the case of cross-sections with medium to high amount of longitudinal

reinforcement. In case a very small amount of longitudinal reinforcement is present,

failure will be due to steel rupture and then the enhancement of the concrete properties

will not affect the global behaviour of the cross-section. Therefore, more intrusive


281

interventions (e.g. additional steel reinforcement) will be required in order to increase the

dissipation capacity.

On the grounds of limited experimental observations and extended parametric numerical

analyses, it is concluded that parabolic FRP jackets constitute an effective method for

improving the seismic response of poorly-detailed hollow bridge piers, keeping in mind

the limitations in terms of axial load and reinforcement ratio, highlighted in this study. To

assist in the design procedure, empirical design equations have been elaborated on the

basis of more than 1000 numerical analyses.


282

CONCLUSIONS AND FUTURE RESEARCH

283

7. CONCLUSIONS AND FUTURE RESEARCH

In this final chapter the salient aspects of the research presented in the thesis are

summarised and the principal conclusions are put forward. The chapter is organised in

sections that recapitulate the main findings of each chapter of the thesis. In closure, a

number of suggestions for future research are given.

7.1. SUMMARY AND CONCLUSIONS

7.1.1. Performance of existing bridge piers with hollow cross-section

Cyclic tests were performed on large-scale (1:2.5) specimens of existing bridge piers with

rectangular hollow cross-section. A short pier with lapped splices at the base and a tall

pier with premature termination of the longitudinal reinforcement were tested. Given the

scale and geometry of the specimens, the test results constitute an important contribution

to the assessment of the seismic performance of existing highway bridge piers.

In both piers a collapse mechanism with multiple hinges (above the base, lapped splices

and bar cut-off) was observed. The failure mode of the short pier was flexure-dominated

with limited spread of plasticity, while a combination of flexure and shear dictated the

failure mode of the tall pier. Limited deformation capacity, because of the small amount

of horizontal and vertical reinforcement, was observed in both specimens. The lack of

protection against buckling resulted in collapse of the vertical rebars due to low-cycle

fatigue. The initiation of different failure mechanisms at distinct levels of lateral

displacement and various regions of the piers calls for a global retrofit procedure that

takes into account and addresses the whole range of possible failure modes.

The importance of seismic detailing, principally of the minimum requirements for

horizontal reinforcement, was verified by comparing the short pier to one designed

according to EC8. The first pier had smaller ductility and energy-dissipation capacity and

almost half the drift capacity of the second.

The conventional definition of ductility, based on a bilinear approximation of the force-

displacement diagram, can be misleading or contradictory as a meaningful parameter of


284

the deformation capacity. On the contrary, drift and energy-dissipation capacities can

fully characterize the cyclic behaviour of these bridge piers.

The predictions of empirical formulae were in fair agreement with the experimental

values, as far as yield displacement is concerned. On the other hand, ultimate

displacement strongly depends on the equivalent plastic hinge length. For piers with

multiple hinges, the contribution of all hinges (possibly not fully developed) must be

considered. The empirical formulae were found to be valid for hollow cross-sections, but

not for members with lapped splices, for which the equivalent plastic hinge length was

much smaller than the predicted values.

For these piers with elongated hollow cross-section deformation due to shear was found

to constitute a significant fraction of the total displacement. For the short pier the ratio of

shear to flexural displacement was 0.3, while for the tall pier this ratio increased with

imposed top displacement from 0.2 to 0.5.

A database of experimental results on specimens of bridge piers with hollow cross-section

has been compiled. On this basis, it is concluded that hollow piers without seismic design

are expected to have limited deformation capacity with mean values of drift uδ = 2.9% for

flexural failure mode and uδ = 1.9% for shear failure mode. These values show that

existing bridge piers need upgrading. Hollow piers with sufficient confinement of the

compression zone are expected to have stable behaviour and large deformation capacity,

uδ > 3.6%. The previous considerations give also a hint on the objectives of retrofit: the

main seismic deficiencies that have to be addressed are the limited shear resistance and

poor confinement.

7.1.2. Performance of existing bridge structures

A series of pseudodynamic tests on a large-scale (1:2.5) model of a highway bridge were

successfully performed. The substructuring technique, considering non-linear behaviour

for parts of the numerical substructure, was implemented for the first time at world level.

The representativeness of the testing method was checked against the results of dynamic

non-linear numerical analyses. This represents an advance in experimental techniques and

demonstrates the effectiveness of this hybrid method. It constitutes a step forward in the


285

tele-operation of experimental facilities and distributed testing, as the tests were carried

out with a distributed computer and testing system with communication via standard

internet connection.

As far as seismic assessment of existing bridges is concerned, the results from the tests

allowed to assess the performance of a typical European bridge (highway bridge with

rectangular hollow cross-section piers and with many seismic deficiencies such as short

overlapping length, lack of transversal reinforcement, tension shift, absence of capacity

design, etc). The PSD tests demonstrated that these infrastructures represent a source of

risk in seismic regions. In fact, the test corresponding to the SLS caused minor damage.

Damage concentrated at the tall physical pier for the test that corresponds to the ULS,

whereas two numerical piers were beyond yielding. This corresponds to significant

damage, although the non collapse criterion was satisfied. Collapse was reached for the

2.0xNE test. Note that damage increased disproportionally to the seismic intensity and

that the damage pattern changed for each earthquake test.

The cycling effects resulted in a marked reduction of the resistance and displacement

capacity of the bridge piers, compared to the same components tested under a few cycles

of increasing displacement. The larger number of cycles initiated failure of the lapped

splices at the base of the short pier. It is reminded that cycling effects are not expected to

significantly influence the performance of bridge piers with proper seismic detailing.

The observed damage was compared to the predictions of simplified assessment methods.

The simplicity of probabilistic methods was highlighted against the uncertainties

encountered during the application of deterministic methods that make use of a substitute

structure. Due to the differences between the assumed and the actual deformed shapes,

the deterministic methods were unable to predict the damage distribution observed during

the tests and their results could be used only for qualitative comparisons. It was possible

to introduce a correction of the N2 method in order to account for the correct deformed

shape. Nevertheless, this correction requires the a priori knowledge of the structural

behaviour. It is concluded that among the available tools, dynamic non-linear analysis

remains the most appropriate for the detailed and reliable assessment of existing

structures with irregular configuration.


286

The tested bridge was considered in a low-seismicity zone. The higher expected damage

in medium and high-seismicity zones was confirmed by the results of the modified N2

method. For the SLS earthquake at a high-seismicity region, significant inelastic

deformation demand was estimated for all piers, while collapse of two piers and severe

damage (close to collapse) for the remaining piers was predicted for the ULS earthquake.

At this level of damage, repair might be economically unfeasible and the solution would

be the replacement of the bridge structure. Therefore, appropriate retrofit is a necessity.

7.1.3. Assessment of numerical tools for existing bridge piers

The simple fibre/beam model was successful in simulating the response of the short pier,

whose behaviour was flexure-dominated, but failed to capture the tension shift

phenomenon, that dictated the failure mode of the tall pier, and predicted different failure

location and resistance. For the sake of simplicity and stability of the numerical processes

during the PSD tests, it was possible to obtain the correct failure location and similar

resistance and dissipation capacity, by modifying the properties of steel in the numerical

model. This modelling approach provided reliable and detailed results both at global and

local level. Keeping in mind the small computational demand, it seems appropriate for

extensive parametric studies that require a large number of analyses.

The 2D FEM analyses were able to simulate the whole range of physical phenomena that

were significant for the response of the tested specimens. However, the large

computational demand, because of the refined meshes used to describe the cross-section

and the distribution of horizontal and vertical reinforcement, as well as the steel to

concrete interface, and also because of the constitutive laws for the materials and contact

surfaces, should be highlighted. Such numerical tools appear useful for refined studies on

retrofit solutions.

A combination of the previous numerical approaches was used to study the behaviour of

bridge piers with hollow cross-section wrapped with FRP strips. The finite element

method was used to study the effect of the jacket on the concrete properties. The

observations of these analyses were then used to modify the material properties for

concrete in a fibre/beam model of a retrofitted pier. Based on the comparison between

experimental and numerical results, it is concluded that this combination of modelling

tools is valid and therefore it was used for further parametric analyses.


287

7.1.4. Retrofit of bridge piers with hollow cross-section using FRP strips

Several methods have been proposed for the retrofit of seismic-deficient bridge piers

using FRP strips. Design equations, which take into consideration all possible failure

modes, have been proposed for flexural and shear FRP reinforcement. Regarding FRP

jackets, inconsistencies and limitations are observed in the predictions of different models

for the properties of confined concrete. Experimental evidence calls for a global retrofit

procedure that considers all possible failure modes (not only the weakest one) and also

rational design rules, as sometimes retrofit interventions are over-designed.

FEM analyses of a concrete cross-section wrapped with an FRP jacket showed that the

existing empirical laws for FRP-confined concrete are not suitable for hollow piers with

large dimensions. The effect of lateral containment provided by the jacket is to increase

the maximum and residual stress of concrete. A softening branch, with a slope less steep

than the one for unconfined concrete, follows the peak strength. A bilinear stress-strain

curve with increasing stress in the second branch, as proposed for full cross-sections, was

only observed for unrealistic values of the jacket thickness.

The effect of confinement is mainly concentrated in the corners and its extent depends on

the dimensions of the jacket. For rectangular jackets, the confined zone is limited to the

corners, while for oval jackets it comprises also part of the flange and added concrete. A

limit value of the jacket height, jh = 0.10 m, after which no further enhancement of the

concrete properties is obtained, was identified. The limit value corresponds to 10% of the

flange width.

The effectiveness of jacketing for the enhancement of the deformation capacity of cross-

sections is conditioned by the axial load and amount of longitudinal reinforcement. The

jackets are most effective in the range of ν = 0.1 to ν = 0.3, which, luckily, corresponds

to the axial loads bridge piers usually carry. The effectiveness is reduced with the amount

of longitudinal reinforcement. Indicatively, it is reminded that the curvature ductility of

the jacketed cross-section can be up to 7 times the ductility of the as-built cross-section,

provided a significant amount of FRP and the corresponding oval concrete jacket are

provided. For the simplest solution of a rectangular jacket, the curvature ductility can be

increased up to 3 times. This demonstrates that this fast and economic intervention can


288

effectively improve the deformation capacity of seismic-deficient bridge piers with

rectangular hollow cross-section.

Parabolic jackets increase the stiffness of the cross-section. The moment capacity of the

cross-section is increased by not more than 20%. Therefore, upgrade of adjacent members

might be required.

On the grounds of limited experimental observations and extended numerical analyses, it

is concluded that, keeping in mind the aforementioned limitations, FRP jackets constitute

an effective method for improving the seismic performance of poorly detailed hollow

bridge piers. To assist in the design procedure, empirical design equations were

elaborated on the basis of more than 1000 numerical analyses.

7.2. SUGGESTIONS FOR FUTURE RESEARCH

The work performed within the framework of this thesis offered an overview of the issues

that are important in seismic design, assessment and retrofit of bridges. These issues were

discussed in Chapter 2 and several research needs were identified. It is felt that the

statement “in the whole field of assessing the safety of existing bridges, designing

strengthening intervention and re-assessing the safety of strengthened bridges, more

research is needed” [Calvi & Pinto, 1996] still holds. With respect to the problems that

were the object of this work, namely assessment of as-built piers with hollow cross-

section, assessment of existing highway bridges and retrofit of hollow bridge piers using

FRP strips, some aspects that require further investigation are suggested in the following.

Considering the assessment of bridge piers with hollow cross-section, it is reminded that

only 30 specimens of seismic-deficient hollow bridge piers have been tested world-wide

(the first 4 with elongated rectangular cross-section are presented in this work), while

experimental results for a much larger population of solid bridge piers are available.

Therefore, further experimental testing involving large-scale, and hopefully full-scale,

specimens would be most interesting. The interpretation of additional experimental

results should aim at the systematic assessment of the deformation capacity of these

structures and at the identification of a relation between damage indicators and

performance levels. Furthermore, it will be possible to further validate the empirical


289

formulae used for the assessment of their strength and deformation capacities, considering

the significant contribution of shear to the total displacement. With reference to the last

issue, an interesting experimental campaign, involving large-scale specimens of hollow

piers with modern seismic design, has been recently concluded [Hines & Seible, 2003].

The above will also contribute to the calibration of numerical models for these bridge

piers.

Laboratory testing of complete bridge structures is a most challenging task. The

successful completion of the pseudodynamic tests with non-linear substructuring provides

confidence in advanced experimental techniques. A further improvement is the practical

application of continuous pseudodynamic testing combined with the non-linear

substructuring technique, already sufficiently studied at theoretical level [Pegon &

Magonette, 2002]. With the same objective, an ambitious and promising project is

undertaken in the USA [Elnashai, 2002].

A large number of highway bridges designed and constructed without provisions for

seismic resistance, whose seismic vulnerability is verified by field observations as well as

experimental and numerical studies, are present in seismic-prone regions around the

world. As retrofit of all is not economically feasible, prioritization of interventions

requires fast and at the same time reliable assessment tools. It was shown in this study

that the existing simlpified assessment procedures need further refinement with attention

on bridges with irregular configuration. An interesting proposal is the estimation of

dynamic correction factors [Fajfar & Gašperšic, 1996].

While FRP strips have been used successfully for the seismic retrofit of many structural

types in the past years, their application on large bridge piers with elongated hollow

cross-section has not been studied to a satisfactory degree. This problem is of particular

importance in Europe and other seismic region around the world, where many existing

bridges comprise piers with this geometry. The most important issue is the effect of

confinement on the concrete properties and the distribution of this effect within the cross-

section. Dedicated studies should aim at the development of an appropriate mechanical

model. For full rectangular cross-sections, such a model has been recently developed on

the basis of numerical studies [Monti, 2003].


290

Considering design tools, the empirical formulae elaborated in Chapter 6 need further

refinement. The effect of concrete, steel and FRP properties needs to be studied, although

it is expected that no significant corrections will be needed. On the other hand, the

consideration of bond between FRP and concrete and larger cross-sectional dimensions

will provide safer design and extend the applicability of the proposed equations.

Finally, it is necessary to experimentally verify the effectiveness of the proposed

technique and design tools for the case of large and full-scale piers. The most important

parameters that should be examined are the cross-section and jacket dimensions.

REFERENCES

291

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APPENDIX A – EXPERIMENTAL DATA FOR BRIDGE PIERS

309


Table A.1. Seismic-deficient piers with solid cross-section: geometrical and mechanical

properties and deformation capacity

Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Chai et al., 1991 C 0.61 0.61 6.00 2.53 0.17 20 0.177 1.4 1.5 C 0.61 0.61 6.00 2.53 0.17 0.177 3.8 5.0 Coffman et al., 1993 R 0.46 0.46 6.6 1.20 0.10 35 0.150 2.0 Park et al., 1993 R 0.46 0.46 6.5 1.30 0.20 0.085 3.0 7.0 Priestley et al., 1994 C 0.61 0.61 2.0 2.50 0.08 0.065 1.1 2.5 C 0.61 0.61 2.0 2.50 0.08 0.177 0.9 3.0 C 0.61 0.61 2.0 2.50 0.08 0.056 0.7 1.0 C 0.61 0.61 1.5 2.50 0.08 0.066 0.8 1.0 R 0.41 0.41 2.0 2.50 0.08 0.054 1.4 3.0 R 0.41 0.41 2.0 2.50 0.08 0.059 1.0 1.4 R 0.41 0.41 1.5 2.50 0.08 0.063 0.7 0.8 Saadatmanesh et al., 1996 C 0.31 5.6 2.48 0.07 20 0.167 2.4 1.5 C 0.31 5.6 2.48 0.07 0.166 5.2 4.0 Saadatmanesh et al., 1997 R 0.24 0.24 4.9 2.70 0.11 16 0.150 1.5 R 0.24 0.24 4.9 5.45 0.11 0.150 2.0 Xiao & Ma, 1997 C 0.61 4.0 2.00 0.08 20 0.050 1.8 Daudey & Filiatrault, 2000 R 0.36 0.36 2.4 3.20 0.42 26 0.040 2.0 Fujikura et al., 2000 O 0.40 0.9 2.8 0.74 0.56 0.022 2.4 O 0.40 0.9 2.8 0.74 0.91 0.023 3.2 O 0.40 0.9 2.8 0.83 0.90 0.023 4.1 Saiidi et al., 2000 R 0.14 0.14 2.5 0.80 5.4 Sakai & Kawashima, 2000 R 0.40 0.4 3.4 1.58 0.79 0.131 2.4 R 0.40 0.4 3.4 1.58 0.79 0.043 4.0 R 0.40 0.4 3.4 1.58 0.79 0.087 4.0 R 0.40 0.4 3.4 1.58 0.79 0.117 3.0 Yang et al., 2000 R 0.20 0.2 5.0 2.40 1.13 0.360 5.5 R 0.20 0.2 5.0 3.40 0.81 0.150 4.0 R 0.20 0.2 5.0 2.40 1.22 0.150 4.0 R 0.20 0.2 5.0 2.40 0.81 0.150 3.7 Kim et al., 2001 C 1.00 5.0 0.9 0.2 0.05 0.8 1.5 Bousias et al., 2002 R 0.25 0.5 6.4 0.8 0.2 0.38 2.5 R 0.25 0.5 6.4 0.8 0.2 0.38 2.8 R 0.50 0.25 3.2 0.8 0.1 0.38 4.1 R 0.50 0.25 3.2 0.8 0.1 0.35 4.4 Chang, 2002 R 0.60 0.6 5.4 2.00 0.50 0.100 2.1 R 0.60 0.6 5.4 2.00 0.50 0.100 2.2 Chung et al., 2003 C 1.20 4.0 1.0 0.1 31.6 0.1 1.7 2.3 C 1.20 4.0 1.0 0.2 31.6 0.1 2.2 3.0 C 1.20 4.0 1.0 0.1 31.6 0.1 1.1 1.9 C 1.20 4.0 1.0 0.2 31.6 0.1 2.4 3.2 Kawashima, 2003 (webpage) C 0.40 3.4 2.02 0.75 0.067 5.0


310

Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Kawashima, 2003 (webpage) C 0.40 3.4 2.02 0.75 0.067 5.0 C 0.40 3.4 2.02 0.75 0.064 5.1 C 0.40 3.4 2.02 0.75 0.065 1.9 C 0.40 3.4 2.02 1.49 0.057 3.5 C 0.40 3.4 2.02 0.75 0.057 C 0.40 3.4 2.02 0.75 0.054 4.5 C 0.40 3.4 2.02 1.49 0.054 4.5 Kawashima, 2003 (webpage) R 0.40 0.4 4.0 0.95 0.77 15 0.044 3.3 R 0.40 0.4 4.0 0.95 0.77 30 0.043 3.3 R 0.40 0.4 4.0 0.95 0.77 15 0.044 3.7 Kawashima, 2003 (webpage) C 0.40 3.4 1.89 0.26 0.049 3.4 C 0.40 3.4 1.89 0.13 0.049 3.0

R: Rectangular cross-section, C: circular cross-section, O: oval cross-section


311

Table A.2. Code-designed piers with solid cross-section: geometrical and mechanical


Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Munro et al., 1976 O 0.50 5.5 3.28 1.26 0.003 4.7 Ng et al., 1978 O 0.25 5.4 3.28 1.87 0.009 4.8 O 0.25 3.7 3.28 2.48 0.333 4.4 Ang et al., 1981 R 0.40 0.4 4.0 1.51 2.83 0.380 0.3 R 0.40 0.4 4.0 1.51 2.22 0.210 3.6 Petrovski & Ristic, 1984 C 0.31 6.2 1.83 0.63 0.051 2.6 C 0.31 6.2 1.83 0.63 0.095 1.8 C 0.31 2.9 1.83 0.63 0.055 3.5 C 0.31 2.9 1.83 0.63 0.100 2.5 Zahn et al., 1986 R 0.40 0.4 4.0 1.51 1.56 0.223 4.4 R 0.40 0.4 4.0 1.51 1.99 0.390 0.3 Stone &Cheok, 1989 C 1.52 3.0 1.99 1.49 0.071 6.2 C 0.25 3.0 1.98 1.41 0.102 1.3 C 0.25 3.0 1.98 1.41 0.212 6.0 C 0.25 6.0 1.98 0.68 0.097 5.1 C 0.25 3.0 1.98 1.41 0.101 7.2 C 0.25 3.0 1.98 1.41 0.202 6.4 C 0.25 6.0 1.98 0.68 0.106 4.5 Kawashima et al., 1990 W 1.60 0.40 6.5 1.31 0.08 0.028 2.7 5.0 W 1.60 0.40 6.5 1.31 0.08 0.030 3.5 7.0 W 1.60 0.40 6.5 1.31 0.08 0.023 2.3 7.0 Lim et al., 1990 C 0.15 7.5 5.57 1.45 0.240 7.9 C 0.15 3.8 5.57 1.45 0.240 8.0 C 0.15 3.8 5.57 1.45 0.350 8.0 Park and Paulay, 1990 R 0.40 0.6 3.0 1.88 2.17 0.100 4.8 Wong et al., 1990 C 0.40 2.0 3.20 1.42 0.190 5.0 C 0.40 2.0 3.20 0.47 0.390 2.0 C 0.40 2.0 3.20 1.42 0.390 3.2 Chai et al., 1991 C 0.61 0.61 6.00 2.53 0.17 20 0.177 2.5 3.0 C 0.61 0.61 6.00 2.53 0.17 0.177 6.0 8.0 C 0.61 0.61 6.00 2.53 0.17 20 0.177 C 0.61 0.61 6.00 2.53 0.17 20 0.177 5.3 7.0 Coffman et al., 1993 R 0.46 0.46 6.6 1.20 0.10 35 0.150 4.0 R 0.46 0.46 6.6 1.20 0.10 35 0.150 4.0 R 0.46 0.46 6.6 1.20 0.10 35 0.150 4.0 Park et al., 1993 0.46 0.46 6.5 1.30 0.20 0.085 3.0 7.0 0.46 0.46 6.5 1.30 0.20 0.085 4.0 10.0 Priestley et al., 1994a 0.61 0.61 2.0 2.50 0.08 0.059 4.4 10.0 0.61 0.61 2.0 2.50 0.08 0.173 4.1 10.0 0.61 0.61 2.0 2.50 0.08 0.051 5.5 10.0 0.61 0.61 1.5 2.50 0.08 0.065 5.2 8.0 Priestley et al., 1994b R 0.41 0.41 2.0 2.50 0.08 0.053 3.6 11.0


312

Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Priestley et al., 1994b R 0.41 0.41 2.0 2.50 0.08 0.057 3.8 8.0 R 0.41 0.41 1.5 2.50 0.08 0.062 3.7 7.0 Saadatmanesh et al., 1996 C 0.31 5.6 2.48 0.07 20 0.159 8.2 7.0 C 0.31 5.6 2.48 0.07 20 0.158 7.1 6.0 C 0.31 5.6 2.48 0.07 0.167 7.1 6.0 Hose et al., 1997 C 0.61 6.0 2.66 0.89 0.148 8.7 Kunnath et al., 1997 C 0.31 4.5 2.04 0.94 0.094 5.0 C 0.31 4.5 2.04 0.94 0.094 11.5 C 0.31 4.5 2.04 0.94 0.086 4.2 C 0.31 4.5 2.04 0.94 0.086 5.5 C 0.31 4.5 2.04 0.94 0.086 5.5 C 0.31 4.5 2.04 0.94 0.093 5.8 C 0.31 4.5 2.04 0.94 0.093 5.8 C 0.31 4.5 2.04 0.94 0.093 4.6 C 0.31 4.5 2.04 0.94 0.101 6.0 C 0.31 4.5 2.04 0.94 0.101 7.7 C 0.31 4.5 2.04 0.94 0.101 5.9 Saadatmanesh et al., 1997 R 0.24 0.24 4.9 2.70 0.11 16 0.150 6.0 R 0.24 0.24 4.9 5.45 0.11 0.150 6.0 R 0.24 0.24 4.9 5.45 0.11 0.150 6.0 Takemura & Kawashima, 1997 R 0.40 0.4 3.5 1.58 0.57 0.027 1.5 R 0.40 0.4 3.5 1.58 0.57 0.027 1.4 R 0.40 0.4 3.5 1.58 0.57 0.029 1.9 R 0.40 0.4 3.5 1.58 0.57 0.030 3.1 R 0.40 0.4 3.5 1.58 0.57 0.027 2.4 R 0.40 0.4 3.5 1.58 0.57 0.027 3.1 Xiao & Ma, 1997 C 0.61 4.0 2.00 0.08 20 0.050 4.0 C 0.61 4.0 2.00 0.08 20 0.050 6.0 C 0.61 4.0 2.00 0.08 20 0.050 6.0 Wehbe et al., 1998 R 0.38 0.61 3.8 2.22 0.37 0.098 0.5 R 0.38 0.61 3.8 2.22 0.37 0.239 5.9 R 0.38 0.61 3.8 2.22 0.48 0.092 5.5 R 0.38 0.61 3.8 2.22 0.48 0.232 0.1 Henry & Mahin, 1999 C 0.61 4.0 1.49 0.70 0.120 5.3 C 0.61 4.0 1.49 0.35 0.060 5.3 Kowalsky et al., 1999 C 0.46 8.0 3.62 0.92 0.296 9.9 C 0.46 8.0 3.62 0.60 0.271 5.7 C 0.46 8.0 3.62 0.92 0.281 9.3 Calderone et al., 2000 C 0.61 3.0 2.73 0.89 0.091 6.8 C 0.61 8.0 2.73 0.89 0.091 12.3 C 0.61 10.0 2.73 0.89 0.091 14.6 Daudey & Filiatrault, 2000 R 0.36 0.36 2.4 3.20 0.42 26 0.040 6.0 R 0.36 0.36 2.4 3.20 0.42 26 0.040 7.0 R 0.36 0.36 2.4 3.20 0.42 26 0.040 8.0 R 0.36 0.36 2.4 3.20 0.42 26 0.040 6.0 Kawashima et al., 2000 R 0.40 0.4 4.0 1.07 0.77 0.050 3.1


313

Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Kawashima et al., 2000 R 0.40 0.4 4.0 0.95 0.77 0.051 2.7 R 0.40 0.4 4.0 0.99 0.77 0.052 3.1 R 0.40 0.4 4.0 0.95 0.77 0.050 3.3 Lehman & Moehle, 2000 C 0.61 4.0 1.49 0.70 0.072 5.3 C 0.61 8.0 1.49 0.70 0.072 9.1 C 0.61 10.0 1.49 0.70 0.072 1.4 C 0.61 4.0 0.75 0.70 0.072 5.3 C 0.61 4.0 2.98 0.70 0.072 7.3 Saiidi et al., 2000 R 0.14 0.14 2.5 0.80 7.4 R 0.14 0.14 2.5 0.80 7.9 Yang et al., 2000 R 0.20 0.2 5.0 2.40 1.13 0.360 6.0 R 0.20 0.2 5.0 3.40 0.81 0.150 6.0 R 0.20 0.2 5.0 2.40 1.22 0.150 6.0 R 0.20 0.2 5.0 2.40 0.81 0.150 6.0 Kim et al., 2001 C 1.00 5.0 0.9 0.2 0.05 3.5 4.5 Nagaya & Kawashima, 2001 R 0.40 0.4 2.4 1.58 0.79 0.033 4.5 R 0.40 0.4 2.9 1.58 0.79 0.032 4.5 R 0.40 0.4 3.4 1.58 0.79 0.034 4.0 R 0.40 0.4 3.4 1.49 0.79 0.032 4.0 Chang, 2002 R 0.60 0.6 5.4 2.00 0.50 0.100 4.6 R 0.60 0.6 5.4 2.00 0.50 0.100 4.6 Moyer & Kowalsky, 2002 O 0.46 5.3 2.08 0.92 0.043 6.1 O 0.46 5.3 2.08 0.92 0.041 5.8 O 0.46 5.3 2.08 0.92 0.044 7.6 O 0.46 5.3 2.08 0.92 0.042 6.2 Bousias et al., 2002 R 0.25 0.5 6.4 0.8 0.2 0.37 4.1 R 0.25 0.5 6.4 0.8 0.2 0.38 5.1 R 0.25 0.5 6.4 0.8 0.2 0.34 3.8 R 0.25 0.5 6.4 0.8 0.2 0.37 4.1 R 0.50 0.25 3.2 0.8 0.1 0.35 7.2 R 0.50 0.25 3.2 0.8 0.1 0.37 7.2 R 0.50 0.25 3.2 0.8 0.1 0.37 7.5 R 0.50 0.25 3.2 0.8 0.1 0.34 7.5 Chung et al., 2003 C 1.20 4.0 1.0 0.2 0.1 5.1 6.1 C 1.20 4.0 1.0 0.2 0.1 4.7 6.6 Kawashima, 2003 (webpage) R 0.40 0.4 3.4 1.35 0.99 0.041 4.5 R 0.40 0.4 3.4 1.35 0.99 0.041 2.8 R 0.40 0.4 3.4 1.35 0.99 0.037 3.0 R 0.40 0.4 3.4 1.90 1.19 0.042 3.8 R 0.40 0.4 3.4 1.90 1.19 0.040 2.2 R 0.40 0.4 3.4 1.90 1.19 0.039 2.5 Kawashima, 2003 (webpage) R 0.40 0.4 3.4 1.27 0.79 0.034 4.0 R 0.40 0.4 3.4 1.27 0.79 0.033 3.9 R 0.40 0.4 3.4 1.27 0.79 0.034 3.5 R 0.40 0.4 3.4 1.27 0.79 0.032 3.5 R 0.40 0.4 3.4 1.27 0.79 0.038 2.8


314

Reference b (m)

d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%)

uµ

Kawashima, 2003 (webpage) R 0.40 0.4 3.4 1.27 0.79 0.037 3.5 Kawashima, 2003 (webpage) C 0.40 3.4 1.89 0.26 0.049 5.0 C 0.40 3.4 1.89 0.26 0.053 3.6 C 0.40 3.4 1.89 0.13 0.049 4.5 C 0.40 3.4 1.89 0.13 0.053 4.5

R: Rectangular cross-section, C: circular cross-section, O: oval cross-section, W: wall-type cross-section


315

Table A.3. Retrofitted piers with solid cross-section: geometrical and mechanical


Reference b (m) d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν uδ 1 uµ 1

Chai et al., 1991 C 0.61 0.61 0.61 2.53 0.17 20 0.177 C 0.61 0.61 0.61 2.53 0.17 20 0.177 1.8 2.0 C 0.61 0.61 0.61 2.53 0.17 0.177 C 0.61 0.61 0.61 2.53 0.17 0.177 1.7 1.6 C 0.61 0.61 0.61 2.53 0.17 20 0.177 C 0.61 0.61 0.61 2.53 0.17 20 0.177 1.4 1.4 Coffman et al., 1993 R 0.46 0.46 6.6 1.20 0.10 35 0.150 R 0.46 0.46 6.6 1.20 0.10 35 0.150 2.0 R 0.46 0.46 6.6 1.20 0.10 35 0.150 2.0 R 0.46 0.46 6.6 1.20 0.10 35 0.150 2.0 Park et al., 1993 R 0.46 0.46 6.5 1.30 0.20 0.085 R 0.46 0.46 6.5 1.30 0.20 0.085 1.0 1.0 R 0.46 0.46 6.5 1.30 0.20 0.085 1.3 Priestley et al., 1994 C 0.61 0.61 2.0 2.50 0.08 0.065 C 0.61 0.61 2.0 2.50 0.08 0.059 4.0 C 0.61 0.61 2.0 2.50 0.08 0.177 C 0.61 0.61 2.0 2.50 0.08 0.173 4.6 C 0.61 0.61 2.0 2.50 0.08 0.056 C 0.61 0.61 2.0 2.50 0.08 0.051 7.9 1.0 C 0.61 0.61 1.5 2.50 0.08 0.066 C 0.61 0.61 1.5 2.50 0.08 0.065 6.5 8.0 R 0.41 0.41 2.0 2.50 0.08 0.054 R 0.41 0.41 2.0 2.50 0.08 0.053 2.6 3.7 R 0.41 0.41 2.0 2.50 0.08 0.059 R 0.41 0.41 2.0 2.50 0.08 0.057 3.8 5.7 R 0.41 0.41 1.5 2.50 0.08 0.063 R 0.41 0.41 1.5 2.50 0.08 0.062 5.3 8.8 Saadatmanesh et al., 1996 C 0.31 5.6 2.48 0.07 20 0.167 C 0.31 5.6 2.48 0.07 20 0.159 3.5 4.7 C 0.31 5.6 2.48 0.07 20 0.158 3.2 4.0 C 0.31 5.6 2.48 0.07 0.166 C 0.31 5.6 2.48 0.07 0.167 1.5 1.5 Saadatmanesh et al., 1997 R 0.24 0.24 4.9 2.70 0.11 16 0.150 R 0.24 0.24 4.9 2.70 0.11 16 0.150 4.0 R 0.24 0.24 4.9 5.45 0.11 0.150 R 0.24 0.24 4.9 5.45 0.11 0.150 3.0 R 0.24 0.24 4.9 5.45 0.11 0.150 3.0 Xiao & Ma, 1997 C 0.61 4.0 2.00 0.08 20 0.050 C 0.61 4.0 2.00 0.08 20 0.050 2.2 C 0.61 4.0 2.00 0.08 20 0.050 3.3 C 0.61 4.0 2.00 0.08 20 0.050 3.3 Daudey & Filiatrault, 2000 R 0.36 0.36 2.4 3.20 0.42 26 0.040 R 0.36 0.36 2.4 3.20 0.42 26 0.040 3.0


316

Reference b (m) d (m) L/b sρ

(%) wρ

(%) sl

( bd ) ν uδ 1 uµ 1

Daudey & Filiatrault, 2000 R 0.36 0.36 2.4 3.20 0.42 26 0.040 3.5 R 0.36 0.36 2.4 3.20 0.42 26 0.040 4.0 R 0.36 0.36 2.4 3.20 0.42 26 0.040 3.0 Saiidi et al., 2000 R 0.14 0.14 2.5 0.80 R 0.14 0.14 2.5 0.80 1.4 R 0.14 0.14 2.5 0.80 1.5 Yang et al., 2000 R 0.20 0.2 5.0 2.40 1.13 0.360 R 0.20 0.2 5.0 3.40 0.81 0.150 R 0.20 0.2 5.0 2.40 1.22 0.150 R 0.20 0.2 5.0 2.40 0.81 0.150 R 0.20 0.2 5.0 2.40 1.13 0.360 1.1 R 0.20 0.2 5.0 3.40 0.81 0.150 1.5 R 0.20 0.2 5.0 2.40 1.22 0.150 1.5 R 0.20 0.2 5.0 2.40 0.81 0.150 1.6 Bousias et al., 2002 R 0.25 0.5 6.4 0.8 0.2 0.38 R 0.25 0.5 6.4 0.8 0.2 0.38 R 0.25 0.5 6.4 0.8 0.2 0.37 1.5 R 0.25 0.5 6.4 0.8 0.2 0.38 1.8 R 0.25 0.5 6.4 0.8 0.2 0.34 1.3 R 0.25 0.5 6.4 0.8 0.2 0.37 1.5 R 0.50 0.25 3.2 0.8 0.1 0.38 R 0.50 0.25 3.2 0.8 0.1 0.35 R 0.50 0.25 3.2 0.8 0.1 0.35 1.6 R 0.50 0.25 3.2 0.8 0.1 0.37 1.6 R 0.50 0.25 3.2 0.8 0.1 0.37 1.7 R 0.50 0.25 3.2 0.8 0.1 0.34 1.7 Chang, 2002 R 0.60 0.6 5.4 2.00 0.50 0.100 R 0.60 0.6 5.4 2.00 0.50 0.100 2.2 R 0.60 0.6 5.4 2.00 0.50 0.100 R 0.60 0.6 5.4 2.00 0.50 0.100 2.1 Kawashima, 2003 (webpage) C 0.40 3.4 1.89 0.26 0.049 C 0.40 3.4 1.89 0.26 0.049 1.4 C 0.40 3.4 1.89 0.26 0.053 1.1 C 0.40 3.4 1.89 0.13 0.049 C 0.40 3.4 1.89 0.13 0.049 C 0.40 3.4 1.89 0.13 0.053

R: Rectangular cross-section, C: circular cross-section, 1 retrofitted / as-built


317

Table A.4. Seismic-deficient piers with hollow cross-section: geometrical and mechanical


Reference b (m)

d (m)

ft (m)

wt (m)

L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%) uµ b

(m)

Kawashima et al., 1990 RH 0.50 0.50 5.0 2.03 0.10 0.005 2.4 8.0 0.50 0.50 5.0 2.03 0.10 0.005 2.0 6.5 0.50 0.50 5.0 2.03 0.10 0.005 2.8 8.5 0.50 0.50 5.0 2.03 0.10 0.004 2.8 8.0 0.50 0.50 9.2 2.03 0.10 0.023 3.9 4.0 0.50 0.50 9.2 2.03 0.10 0.024 2.6 6.0 0.50 0.50 9.2 2.03 0.10 0.026 2.6 6.0 Huang et al., 1997 RH 0.94 0.64 0.139 0.125 5.9 1.30 0.15 0.019 1.3 4.0 Calvi et al., 2000 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 20 0.07 1.2 0.45 0.45 0.075 0.075 3.0 1.8 0.3 20 0.15 1.2 Takahashi & Iemura, 2000 RH 0.32 0.32 0.085 4.0 1.96 0.34 0.000 5.5 0.32 0.32 0.085 4.0 1.96 0.17 0.100 3.1 0.32 0.32 0.085 4.0 1.96 0.17 0.100 3.1 0.32 0.32 0.085 4.0 1.96 0.34 0.100 3.9 0.32 0.32 0.085 4.0 1.96 0.34 0.100 3.9 0.32 0.32 0.085 2.0 1.96 0.17 0.100 1.6 0.32 0.32 0.085 2.0 1.96 0.34 0.100 3.1 Kim et al., 2001 RH 0.60 1.04 0.150 0.150 8.3 1.1 0.5 0.05 4.8 6.0 Yeh et al., 2001 CH 1.50 0.300 3.7 2.15 0.29 23 0.094 1.6 2.8 Pinto et al., 2001a R 1.02 2.74 0.21 0.170 2.4 0.40 0.09 38 0.090 1.3 3.2 Pinto et al., 2001b R 1.02 2.74 0.21 0.170 5.1 0.70 0.09 38 0.100 1.6 2.3 Pinto et al., 2002a R 1.02 2.74 0.210 0.170 2.4 0.4 0.1 38 0.09 0.9 2.3 Pinto et al., 2002b R 1.02 2.74 0.210 0.170 5.1 0.7 0.1 38 0.10 1.5 2.0 Pinto et al. 2003 Pinto & Tsionis, 2003 Rasulo et al., 2002 RH 0.45 0.45 0.075 2.0 1.10 0.13 0.150 0.8 0.45 0.45 0.075 3.0 1.80 0.25 0.150 1.0 0.45 0.45 0.075 3.0 1.10 0.13 0.150 1.1 0.45 0.45 0.075 3.0 1.10 0.13 0.075 1.9 0.45 0.45 0.075 3.0 1.10 0.13 0.150 1.2 Cheng et al., 2003 CH 1.50 0.300 3.7 2.2 0.9 0.10 6.5 9.7 CH 1.50 0.300 2.3 2.2 0.3 0.10 2.9 4.9

RH: Rectangular hollow cross-section, CH: circular hollow cross-section


318

Table A.5. Code-designed piers with hollow cross-section: geometrical and mechanical


Reference b (m)

d (m)

ft (m)

wt (m)

L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%) uµ

Mander, 1984 RH 0.75 0.75 0.120 0.120 4.3 1.6 0.8 0.10 3.5 8.0 RH 0.75 0.75 0.120 0.120 4.3 1.6 1.6 0.50 1.4 4.0 RH 0.75 0.75 0.120 0.120 4.3 1.6 1.2 0.30 3.3 8.0 RH 0.75 0.75 0.120 0.120 4.3 1.6 0.8 0.30 2.4 6.0 Whittaker et al., 1987 CH 0.80 0.100 4.0 2.3 1.1 0.13 4.2 8.0 CH 0.80 0.100 4.0 2.3 1.4 0.30 4.5 12.0 CH 0.80 0.050 4.0 2.9 1.0 0.30 1.6 3.0 CH 0.80 0.050 4.0 2.9 0.8 0.30 1.3 3.0 CH 0.80 0.050 4.0 2.9 1.0 0.30 2.0 5.0 CH 0.80 0.050 4.0 2.9 0.6 0.30 2.4 6.0 Kawashima et al., 1990 RH 0.50 0.50 5.2 1.3 0.1 0.03 7.0 RH 0.50 0.50 5.2 1.3 0.1 0.03 7.0 RH 0.50 0.50 5.2 1.3 0.1 0.03 8.0 RH 0.50 0.50 5.2 1.3 0.1 0.03 7.0 RH 0.50 0.50 5.2 1.3 0.1 0.03 8.0 Zahn et al., 1990 CH 0.40 0.094 4.5 3.6 1.1 0.08 12.4 CH 0.40 0.094 4.5 3.6 1.3 0.40 2.4 CH 0.40 0.075 4.5 4.2 1.4 0.10 7.5 CH 0.40 0.075 4.5 4.2 1.7 0.22 4.9 CH 0.40 0.055 4.5 5.4 1.9 0.12 6.6 CH 0.40 0.055 4.5 5.4 2.3 0.12 3.0 Pinto et al., 1996 RH 0.80 1.6 0.160 0.160 7.0 1.2 0.4 0.03 3.8 6.6 RH 0.80 1.6 0.160 0.160 10.5 0.6 0.5 0.02 2.5 6.0 RH 0.80 1.6 0.160 0.160 3.5 0.9 0.4 0.03 3.3 7.6 RH 0.80 1.6 0.160 0.160 3.5 1.7 0.5 0.03 5.0 9.4 RH 0.80 1.6 0.160 0.160 7.0 1.2 0.4 0.03 3.5 6.3 RH 0.80 1.6 0.160 0.160 3.5 0.5 0.5 0.03 2.3 13.1 RH 0.80 1.6 0.160 0.160 6.8 1.2 0.4 0.02 6.2 5.5 Huang et al., 1997 RH 0.94 0.64 0.139 0.125 5.9 1.3 0.2 0.02 1.8 6.0 RH 0.94 0.64 0.139 0.125 5.9 1.3 0.2 0.02 1.8 6.0 Ogata & Osada, 2000 CH 0.35 0.100 5.1 4.3 0.7 0.03 2.3 2.0 CH 0.35 0.100 5.1 4.3 0.7 0.02 3.1 3.0 CH 0.35 0.100 5.1 4.3 0.7 0.03 3.0 3.0 CH 0.35 0.100 5.1 4.3 0.7 0.03 5.4 5.0 CH 0.35 0.100 5.1 4.3 0.7 0.03 5.3 5.0 Ranzo & Priestley, 2000 CH 1.60 0.152 2.5 1.4 0.3 0.05 2.9 6.0 CH 1.52 0.139 2.5 2.2 0.3 0.05 2.5 3.5 CH 1.52 0.136 2.5 2.2 0.3 0.15 1.5 2.0 Mo et al., 2001 RH 0.50 0.50 0.120 3.6 1.9 0.3 0.09 4.9 5.3 RH 0.50 0.50 0.120 3.6 1.9 0.3 0.18 4.7 4.9 RH 0.50 0.50 0.120 3.6 1.9 0.1 0.09 4.7 4.6 RH 0.50 0.50 0.120 3.6 1.9 0.1 0.19 4.3 4.4 RH 0.50 0.50 0.120 3.0 1.9 0.1 0.14 4.2 4.2


319

RH 0.50 0.50 0.120 3.0 1.9 0.1 0.26 3.4 3.7

Reference b (m)

d (m)

ft (m)

wt (m)

L/b sρ

(%) wρ

(%) sl

( bd ) ν

uδ (%) uµ

Mo et al., 2001 RH 0.50 0.50 0.120 3.6 1.9 0.3 0.09 4.6 4.6 RH 0.50 0.50 0.120 3.6 1.9 0.3 0.13 4.3 4.3 RH 0.50 0.50 0.120 3.6 1.9 0.2 0.08 4.8 4.5 RH 0.50 0.50 0.120 3.6 1.9 0.2 0.13 4.1 3.9 RH 0.50 0.50 0.120 3.0 1.9 0.2 0.11 4.6 4.4 RH 0.50 0.50 0.120 3.0 1.9 0.2 0.05 4.8 4.7 Kawashima et al., 2001 RH 0.40 0.4 0.100 0.100 3.38 2.5 1.1 0.08 4.1 RH 0.40 0.4 0.100 0.100 3.38 2.5 1.2 0.07 4.5 RH 0.40 0.4 0.100 0.100 3.38 2.5 1.1 0.15 3.5 RH 0.40 0.4 0.100 0.100 3.38 2.5 1.2 0.14 3.5 Kim et al., 2001 RH 0.60 1.04 0.150 0.150 8.3 1.1 0.5 0.05 7.5 8.5 Yeh et al., 2001 CH 1.50 0.300 3.7 2.2 0.9 0.10 5.9 9.0 CH 1.50 0.300 2.3 2.2 0.3 0.10 2.9 4.9 Yeh et al., 2002a RH 1.50 1.5 0.300 2.3 1.7 1.1 0.08 6.5 1.3 RH 1.50 1.5 0.300 3.0 1.7 0.4 0.08 4.4 8.7 RH 1.50 1.50 0.300 4.3 1.7 0.3 0.08 2.1 4.1 Yeh et al., 2002b RH 1.50 1.50 0.300 4.3 1.7 0.3 0.08 6.5 11.1 RH 1.50 1.50 0.300 3.0 1.7 0.1 0.08 4.4 8.6 RH 0.50 0.50 0.120 10.8 1.9 0.4 0.09 5.1 5.5 RH 0.50 0.50 0.120 10.8 1.9 0.4 0.18 4.9 5.3 RH 0.50 0.50 0.120 10.8 1.9 0.2 0.09 4.7 4.3 RH 0.50 0.50 0.120 10.8 1.9 0.2 0.19 4.3 3.5 Cheng et al., 2003 CH 1.50 0.300 3.7 2.2 0.9 0.10 2.7 2.1 CH 1.50 0.300 3.7 2.2 0.3 22.7 0.09 2.1 2.4 RH 1.50 0.300 2.3 1.7 0.3 0.08 2.5 4.9 CH 1.50 0.300 2.3 2.2 0.3 0.10 4.5 3.6 Mo et al., 2003 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.6 0.19 2.0 3.7 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.6 0.09 2.2 6.3 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.3 0.11 2.2 6.6 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.3 0.11 2.0 6.3 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.6 0.11 1.9 5.6 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.6 0.06 2.0 7.1 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.3 0.08 2.0 7.2 RH 0.50 0.5 0.100 0.100 4.0 5.5 0.3 0.08 2.1 7.1 Peloso, 2003 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.10 4.8 8.0 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.19 4.8 8.0 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.08 6.0 6.0 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.15 3.6 4.0

RH: Rectangular hollow cross-section, CH: circular hollow cross-section


320

Table A.6. Retrofitted piers with hollow cross-section: geometrical and mechanical


Reference b (m)

d (m)

ft (m)

wt (m)

L/b sρ

(%) wρ

(%) sl

( bd ) ν uδ 1 uµ 1

Huang et al., 1997 RH 0.94 0.64 0.139 0.125 5.9 1.30 0.15 0.019 RH 0.94 0.64 0.139 0.125 5.9 1.30 0.15 0.018 1.4 1.5 RH 0.94 0.64 0.139 0.125 5.9 1.30 0.15 0.016 1.4 1.5 Cheng et al., 2003 CH 1.50 0.300 3.7 2.2 0.9 0.10 CH 1.50 0.300 3.7 2.2 0.3 22.7 0.09 RH 1.50 0.300 2.3 1.7 0.3 0.08 CH 1.50 0.300 2.3 2.2 0.3 0.10 CH 1.50 0.300 3.7 2.2 0.9 0.10 0.4 0.2 CH 1.50 0.300 3.7 2.2 0.3 22.7 0.09 1.3 0.9 RH 1.50 0.300 2.3 1.7 0.3 0.08 1.3 1.4 CH 1.50 0.300 2.3 2.2 0.3 0.10 1.6 0.7 Peloso, 2003 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.10 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.10 2.0 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.19 RH 0.45 0.45 0.075 0.075 2.0 1.1 0.1 0.19 4.4 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.08 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.08 2.5 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.15 RH 0.45 0.45 0.075 0.075 3.0 1.8 0.3 0.15 1.5

RH: Rectangular hollow cross-section, CH: circular hollow cross-section, 1 retrofitted / as-built

APPENDIX B – CONSTRUCTION DRAWINGS

321


Figure B.1. Vertical reinforcement of pier A70 (side view)

Figure B.2. Horizontal reinforcement of pier A70


322

Figure B.3. Vertical reinforcement of pier A70 (sections A-A, B-B)


323

Figure B.4. Vertical reinforcement of pier A70 (sections C-C, D-D)


324

Figure B.5. Vertical reinforcement of pier A40 (side view)


325

Figure B.6. Horizontal reinforcement of pier A40


326

Figure B.7. Vertical reinforcement of pier A40 (sections A-A, B-B)


327

Figure B.8. Vertical reinforcement of pier A40 (sections C-C, D-D)


328

APPENDIX C – PHOTOGRAPHIC DOCUMENTATION

329


Figure C.1. Talübergang Warth Bridge in Austria (both independent lanes are shown)

Figure C.2. General view of the tested piers A40 and A70 inside the laboratory


330

(a)

(b) Figure C.3. Cyclic test on the short pier A70: crack pattern of the flange (a) and the web

(b) at the end of the test

(a)

(b) Figure C.4. Cyclic test on the short pier A60: crack pattern of the flange (a) and the web

(b) at the end of the test


331

(a)

(b)

Figure C.5. 0.4xNE test: crack pattern of the flange (a) and the web (b) of pier A40

(a)

(b) Figure C.6. 2.0xNE test: crack pattern of the flange (a) and the web (b) of pier A70


332

Figure C.7. Final collapse test on the tall pier A40: crack pattern of the web

Figure C.8. Pier A40: buckling of longitudinal reinforcement at 3.5m


333

(a)

(b)

Figure C.9. 1.0xNE test: hysteresis loops for substructured piers A20 and A30 (a) and on-

line comparison of experimental and pre-test displacement histories (b)


334

seismic assessment and retrofit of existing …

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