Behaviour of Reinforced Concrete Slabs Strengthened ...

Behaviour of Reinforced Concrete Slabs

Strengthened Externally with Two-Way FRP

Sheets Subjected to Cyclic Loads

A thesis submitted to The University of Manchester for the

degree of Doctor of Philosophy in the Faculty of Engineering

and Physical Sciences

2015

Raid Ahmed Daud

SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL

ENGINEERING

1

PAPERS PRODUCED FROM THIS THESIS

1) Daud R, Cunningham L, Wang Y. C. Static and fatigue behaviour of the

bond interface between concrete and externally bonded CFRP in single shear.

Engineering Structures. 2015 August; 97: 54-67.

2) Daud R, Cunningham L, Wang Y. C. Non-linear FE Modelling of CFRP-

Strengthened RC Slabs under Cyclic Loading.Athens Journal of Technology

& Engineering. September 2015 (Volume 2, Issue 3)

3) Daud R., Cunningham L., Wang Y. C. Numerical Study of Effective Bond

Length for Externally Bonded CFRP Plate under Cyclic Loading.

Proceedings of the 23rd UK Conference of the Association for

Computational Mechanics in Engineering. Swansea: University of Swansea:

2015: 359-362.

The following papers are in preparation:

4) Daud R, Cunningham L, Wang Y. C. New model for post-fatigue behaviour

of CFRP to concrete bond interface in single shear. Submitted for publication

in ASCE.

5) Daud R, Cunningham L, Wang Y. C. Flexural behaviour CFRP-strengthened

RC two-way slabs under cyclic loading. . In preparation to be submitted for

publication in ACI.

2

List of Contents

List of Contents ............................................................................................................ 2

List of Figures .............................................................................................................. 9

List of Tables.............................................................................................................. 14

ABSTRACT ............................................................................................................... 15

Declaration ................................................................................................................. 17

Copyright Statement .................................................................................................. 18

Acknowledgements .................................................................................................... 19

Notation ...................................................................................................................... 20

Chapter One: Introduction

1.1 Introduction .............................................................................................. 22

1.2 Objectives and methodology of the research ........................................... 23

1.3 Layout of the thesis .................................................................................. 24

Chapter Two: Literature Review of Previous Work

2.1 Introduction .............................................................................................. 26

2.2 Properties of FRP materials used in strengthening, repair and retrofit of

reinforced concrete structural members ......................................................... 26

2.2.1 FRP composite materials and mechanical properties........................... 28

2.2.2 FRP- concrete bonding methods .......................................................... 32

2.2.3 Failure modes for FRP strengthened RC structural members .............. 33

2.3 Previous studies on FRP/concrete interface behaviour............................ 37

2.3.1 Bond behaviour under monotonic pull out loading.............................. 37

2.3.2 Bond behaviour under cyclic pull out loading ..................................... 39

2.3.3 Bond -slip analytical research studies .................................................. 43

2.4 Previous studies on flexural behaviour RC members strengthened with FRP

..................................................................................................................45

2.4.1 Flexural behaviour under monotonic loads .......................................... 46

2.4.2 Flexural behaviour under cyclic loads ................................................. 50

2.5 Numerical modelling ............................................................................... 52

2.5.1 Numerical modelling of FRP/concrete interface behaviour................. 53

3

2.5.2 Numerical modelling of flexural behaviour of RC slabs strengthened

with FRP .............................................................................................. 54

2.6 Review of exsiting design code approaches to FRP-concrete bond ........ 55

2.6.1 ACI Code ............................................................................................. 56

2.6.2 CEB-FIB Bulletin No.14 ...................................................................... 57

2.6.3 Concrete Society Technical Report 55 (TR55) .................................... 58

2.6.4 CNR- DT202 ........................................................................................ 59

2.6.5 JSCE ..................................................................................................... 59

2.7 Originality of research ............................................................................. 61

2.8 Summary .................................................................................................. 62

Chapter Three: Static and Cyclic Experimental

Investigation of CFRP/Concrete Interface in Single Shear

3.1 Introduction .............................................................................................. 63

3.2 Experimental programme ........................................................................ 63

3.3 Details of test specimens.......................................................................... 64

3.4 Test set-up ................................................................................................ 65

3.4.1 Surface preparation and bonding process ............................................ 67

3.5 Instrumentation and testing procedure ..................................................... 68

3.6 Material testing ........................................................................................ 68

3.6.1 Concrete ............................................................................................... 68

3.6.2 CFRP composite plate .......................................................................... 69

3.7 Test results and discussion ....................................................................... 71

3.7.1 Failure modes ....................................................................................... 71

3.7.2 Load- slip behaviour ............................................................................ 74

3.7.2.1 Monotonic tests ................................................................................ 74

3.7.2.2 Fatigue tests ...................................................................................... 75

3.7.2.3 Post-fatigue tests ............................................................................... 79

3.7.3 Tensile strain profiles ........................................................................... 81

3.7.3.1 Monotonic tests ................................................................................ 81


3.7.4 Interfacial shear stress distributions ..................................................... 84

3.7.4.1 Monotonic tests ................................................................................ 84

4


3.7.5 Interfacial bond stress- slip model ....................................................... 87

3.8 Summary .................................................................................................. 90

Chapter Four: Numerical Modelling and Validation of

CFRP/Concrete Interface in Single Shear

4.1 Introduction .............................................................................................. 92

4.2 Simulation model using ABAQUS .......................................................... 92

4.2.1 Finite element mesh ............................................................................. 92

4.2.2 Loading and boundary conditions ........................................................ 95

4.3 Approaches to model delamination ......................................................... 96

4.3.1 Cohesive elements approach ................................................................ 96

4.3.2 Cohesive surfaces approach ................................................................. 97

4.3.2.1 Linear elastic traction-separation behaviour .................................... 97

4.3.2.2 Damage modelling ........................................................................... 98

4.3.3 Virtual crack closure technique (VCCT) ........................................... 103

4.4 Sensitivity study ..................................................................................... 104

4.4.1 Description of pull out test specimen ................................................. 104

4.4.2 Finite element model .......................................................................... 105

4.4.3 Interfacial Bond Stress and Fracture Energy ..................................... 106

4.4.4 Effect of delamination approaches ..................................................... 108

4.4.5 Effect of interfacial bond stiffness ..................................................... 109

4.4.6 Effect of damage initiation criteria .................................................... 110

4.4.7 Effect of damage evolution response ................................................. 111

4.4.8 Effect of mesh size ............................................................................. 111

4.4.9 Summary ............................................................................................ 112

4.5 Validation against the author’s experimental results ............................. 113

4.5.1 Numerical simulation model .............................................................. 113

4.5.2 Comparison between simulation and experimental results for

monotonic and post-fatigue behaviour ............................................... 113

4.6 Numerical parametric study of post-fatigue behaviour ......................... 122

4.6.1 Effect of concrete compressive strength ............................................ 123

4.6.2 Effects of changing ratio of CFRP bonded plate width to concrete

substrate width ................................................................................................. 124

4.6.3 Effect of bond length .......................................................................... 127

5

4.7 Comparison between code provisions and numerical simulation results

................................................................................................................128

4.7.1 Debonding strain ................................................................................ 128

4.7.2 Effective length .................................................................................. 131

4.8 Proposed new model .............................................................................. 134

4.9 Summary ................................................................................................ 135

Chapter Five: Non-linear FE Modelling of CFRP-

Strengthened One- Way RC Slabs under Cyclic Loading

5.1 Introduction ............................................................................................ 138

5.2 Details of the numerical simulation model ............................................ 140

5.2.1 Material models .................................................................................. 140

5.2.1.1 Concrete .......................................................................................... 140

5.2.1.1.1 Principle of the concrete damaged plasticity formulation .......... 141

5.2.1.1.2 Plasticity parameters ................................................................... 142

5.2.1.1.3 Compressive behaviour............................................................... 145

5.2.1.1.4 Tensile behaviour ........................................................................ 147

5.2.1.1.4.1 Tension stiffening model ........................................................... 148

5.2.1.2 Steel reinforcement ......................................................................... 149

5.2.1.3 Carbon fibre reinforced polymer .................................................... 149

5.2.2 True stress and plastic strain .............................................................. 150

5.2.3 Main meshing elements...................................................................... 151

5.2.3.1 Truss element ................................................................................. 151

5.2.3.2 Shell element .................................................................................. 151

5.2.4 Boundary condition ............................................................................ 152

5.2.5 Loads .................................................................................................. 154

5.3 Validation of the simply supported CFRP-strengthened one-way RC slabs

(Type S) ........................................................................................................ 155

5.3.1 Model description............................................................................... 155


5.3.3 Investigation of numerical model parameters .................................... 158

5.3.3.1 Effect of mesh size ......................................................................... 158

5.3.3.2 Effect of tension stiffening curve ................................................... 159

5.3.3.3 Effect of the dilation angle ............................................................. 160

5.3.3.4 Effect of the Kc ............................................................................... 161

6

5.3.4 Discussion of computational results and comparison with experiments

............................................................................................................161

5.4 Effect of using modified FEMA 461 load protocol for (S-T1) slabs ..... 164

5.4.1 Interfacial slip profile ......................................................................... 166

5.4.2 Tensile strain profiles along CFRP .................................................... 169

5.5 Validation of the simply supported CFRP-strengthened one-way RC slabs

with an overhang at one extremity (Type C) ............................................... 170

5.5.1 Model description............................................................................... 170



............................................................................................................172

5.6 Effect of using modified FEMA 461 load protocol for (C-T1) slabs .... 175

5.6.1 Interfacial slip profile ......................................................................... 177

5.6.2 Tensile strain profiles along CFRP .................................................... 178

5.7 Summary ................................................................................................ 180

Chapter Six: Experimental Results of CFRP-Strengthened

Two-Way RC Slabs with Openings under Monotonic and

Cyclic Loading

6.1 Introduction ............................................................................................ 181

6.2 Experimental programme ...................................................................... 181

6.3 Details of test slabs ................................................................................ 182

6.4 Test Preparations.................................................................................... 184

6.5 Surface preparation and bonding process for CFRP .............................. 185

6.5.1 Evaluation of CFRP plate amount...................................................... 187

6.6 Test set-up .............................................................................................. 192

6.7 Instrumentation ............................................................................................ 195

6.8 Material testing ...................................................................................... 196

6.8.1 Concrete ............................................................................................. 196

6.8.2 Reinforcement steel bar...................................................................... 198

6.8.3 CFRP composite plate ........................................................................ 199

6.9 Test results and discussion ..................................................................... 200

6.9.1 Failure modes ..................................................................................... 200

7

6.9.2 Load- deflection behaviour ................................................................ 204

6.9.3 Steel reinforcement and concrete strain measurements ..................... 206

6.9.4 Tensile strain profiles along the CFRP plate...................................... 208

6.10 Validation of the numerical simulation model against the author’s

experimental results ............................................................................... 209

6.10.1 Finite element model ...................................................................... 210

6.10.2 Discussion of computational results and comparison with

experiments. ..................................................................................... 212

6.10.2.1 CFRP-strengthened two-way RC slabs with opening under monotonic

loading .............................................................................................. 212

6.10.2.2 CFRP-strengthened two-way RC slabs with opening under modified

FEMA cyclic loading ....................................................................... 216

6.10.2.3 Evolutions of crack pattern ......................................................... 219

6.11 Summary ................................................................................................ 220

Chapter Seven: A Parametric Study of the Bond Behaviour

of CFRP-Strengthened Two-Way RC Slabs with Openings

under Monotonic and Cyclic Loading

7.1 Introduction ............................................................................................ 222

7.2 Effect of concrete compressive strength ................................................ 223

7.3 Effect of the CFRP bonded plate width ................................................. 224

7.4 Effect of opening size ............................................................................ 226

7.5 Comparison of Code Provisions with numerical simulation results ...... 228

7.6 Summary ................................................................................................ 229

Chapter Eight: Conclusions and Recommendations for

Future Research

8.1 Introduction ............................................................................................ 232

8.2 Conclusions of this research .................................................................. 232

8.2.1 Experimental investigation of CFRP/concrete interface in single shear

under monotonic and cyclic loading .................................................. 232

8.2.2 Numerical investigation of post-fatigue behaviour of CFRP/concrete

interface in single shear ...................................................................... 233

8.2.3 Numerical investigation of CFRP-strengthened one- way RC slabs

under cyclic loading ........................................................................... 235

8

8.2.4 Experimental investigation of CFRP-strengthened two-way RC slabs

with openings under monotonic and cyclic loading ........................... 236

8.2.5 Numerical investigation of CFRP-strengthened two- way RC slabs

under cyclic loading ........................................................................... 237

8.3 Recommendations for future research works ........................................ 238

References ................................................................................................................ 239

Appendix A .............................................................................................................. 245

Appendix B .............................................................................................................. 253

Word count is 53,252 words.

9

List of Figures Figure 2- 1: stress –strain distribution on the composite element .............................. 31

Figure 2- 2: Installing FRP plates, using a roller to apply pressure. (TR55, 2012) ... 33

Figure 2- 3: Full composite action failure modes ...................................................... 34

Figure 2- 4: Debonding failure modes induced of flexural loading ........................... 36

Figure 2- 5: Debonding failure modes induced of the loss of adhesion between FRP

and concrete substrate ................................................................................................ 36

Figure 2- 6: Failure modes (a) Debonding at the adhesive–concrete interface. (b)

Concrete fracture (c) Debonding in concrete (Yao et al., 2005). ............................... 39

Figure 2- 7: Strain increments measured after 5 cycles loading for specimen (a) Plate

(b) sheet (Mazzotti and Savoia, 2009) ....................................................................... 40

Figure 2- 8: Schematics of the tested slab: (a) elevation view; (b) test setup; (c) steel

reinforcement and instrumentation; and (d) CFRP strengthening (bottom view) (Kim

et al., 2008) ................................................................................................................. 48

Figure 2- 9: Strengthening schemes for slabs with or without cut-out (a) Middle

strips, (b) Separated strip (c) Around the opening strip(Elsayed et al., 2009) ........... 49

Figure 2- 10: Characteristic bond failure force vs Anchorage length. (TR55, 2012) 58

Figure 3- 1: Test arrangement ............................................................................65

Figure 3- 2: Test setup................................................................................................ 66

Figure 3- 3: Bonding CFRP Plate to concrete substrate (a) ground the concrete

surface with a surface grinder, (b) applying adhesive layer to the concrete .............. 67

Figure 3- 4: Aluminium end-tabs at the grips ............................................................ 70

Figure 3- 5: Stress-strain curve for the 0.15 mm M46J CFRP plate .......................... 70

Figure 3- 6: Rupture failure of a CFRP plate in tension ............................................ 71

Figure 3- 7: Failure modes (a) Bond failure in the interfaces between concrete and

adhesive layer, (b) CFRP composite plate rupture, and (c) Concrete shearing beneath

adhesive layer ............................................................................................................. 72

Figure 3- 8: Monotonic load-slip curves .................................................................... 74

Figure 3- 9: Fatigue load-slip responses (the number above each curve indicates

cycle number) ............................................................................................................. 76

Figure 3- 10: Crack propagation ................................................................................ 76


cycle number) ............................................................................................................. 77

Figure 3- 12: CFRP stiffness- fatigue life relationship .............................................. 78

Figure 3- 13: Post-fatigue load-slip responses ........................................................... 80

Figure 3- 14: Strain distributions along CFRP plate in monotonic tests ................... 82

Figure 3- 15: Strain distributions along CFRP plate in post-fatigue tests ................. 83

Figure 3- 16: Shear stress as function of relative load level (M4) ............................. 85

Figure 3- 17: Shear stress as a function of relative load level for the post-fatigue tests

.................................................................................................................................... 86

Figure 3- 18: Interfacial bond stress-slip curves for single shear pull-out test in

monotonic test ............................................................................................................ 87

Figure 3- 19: Interfacial bond stress-slip curves for single shear pull-out test in post-

fatigue test .................................................................................................................. 88

Figure 3- 20: Interfacial bond stress-slip curves for single shear pull-out test (a)

fc=22.6 MPa (b) fc= 52.8 MPa .................................................................................. 89

Figure 3- 21: (a) Interfacial bond stress reduction CFRP stiffness relationship (b)

Fracture energy reduction CFRP stiffness relationship ............................................. 90

10

Figure 4- 1: Realistic behaviour of element subjected to pure bending (ABAQUS,

2011) ......................................................................................................................93

Figure 4- 2: Fully integrated linear brick elements subjected to pure bending

(ABAQUS, 2011) ....................................................................................................... 93

Figure 4- 3: Reduced- integration linear brick elements subjected to pure bending

(ABAQUS, 2011) ....................................................................................................... 94

Figure 4- 4: Four node shell element. (ABAQUS, 2011) .......................................... 94

Figure 4- 5: Eight node cohesive element (ABAQUS, 2011) .................................... 95

Figure 4- 6: Loading and boundary conditions for the single shear pull-out test. ..... 96

Figure 4- 7: Typical traction-separation response. ................................................... 100



Figure 4- 10: Experimental set up of (Yao et al., 2005) (top) and the numerical

model (bottom). ........................................................................................................ 106

Figure 4- 11: (a) Experimental results of interfacial bond stress reduction CFRP

stiffness relationship (b) Experimental fracture energy reduction CFRP stiffness

relationship ............................................................................................................... 108

Figure 4- 12: Load-slip curve of VI-6 for different three different delamination

approaches ................................................................................................................ 109

Figure 4- 13: Effect of interfacial bond stiffness on the load-deflection behaviour.110

Figure 4- 14: Load-slip curve of VI-6 for different damage initiation criteria

approaches ................................................................................................................ 110

Figure 4- 15: Load-slip curve of VI-6 for different damage evolution response ..... 111

Figure 4- 16: Sensitivity of the Load-slip behaviour to the mesh size of (A) the

concrete substrate; and (B) the CFRP plate ............................................................. 112

Figure 4- 17: Representative comparisons between numerical and experimental load-

slip relationships and stain distribution along CFRP plate (0.4 mm M46J) ............ 116


slip relationships and stain distribution along CFRP plate (0.3 mm T700) ............. 118

Figure 4- 19: Comparison of failure modes between experiment (bottom) and

numerical simulation (top); (a) CFRP composite plate rupture (M6), and (b)

Concrete shearing beneath adhesive layer (P-F1) [E11 is debonding strain] ............ 120

Figure 4- 20: Effects of concrete compressive strength (a) Bond ultimate Load; (b)

Debonding strain ...................................................................................................... 123

Figure 4- 21: Effects of CFRP plate/concrete width ratio (bf/bc): (a) Bond ultimate

Load; (b) Debonding strain ...................................................................................... 125

Figure 4- 22: Typical strain profile along the CFRP plate ....................................... 126

Figure 4- 23: Effect of bond width ratio (bf/bc) on the debonding strain profile for

specimen (0.3 mm T700) ......................................................................................... 126

Figure 4- 24: Effect of bonded CFRP plate length: (a) Bond ultimate load; (b)

Debonding strain ...................................................................................................... 127

Figure 4- 25: Comparison for effective bond length - CFRP plate stiffness

relationships between codes and simulation results. ................................................ 131

Figure 5- 1: Details of CFRP-strengthened RC slab specimen. (Arduini et al., 2004)

(a) Full-scale one-way RC slabs (Type S) (b) Full-scale one-way RC slabs with an

overhang at one extremity (Type C).......................................................................139

Figure 5- 2: Uniaxial load cycle (tension-compression-tension) (ABAQUS, 2011).

.................................................................................................................................. 141

11

Figure 5- 3: Concrete damage properties: (a) compression damage, (b) tension

damage ..................................................................................................................... 142

Figure 5- 4: Flow potentials in p-q plane (ABAQUS, 2011). .................................. 143

Figure 5- 5: Yield surface in plane stress(Carstensen, 2011). ................................. 144

Figure 5- 6: Yield surfaces in the deviatoric plane, corresponding to different values

of (ABAQUS, 2011)........................................................................................ 144

Figure 5- 7: Uniaxial compressive stress-strain behaviour of concrete ................... 145

Figure 5- 8: Post-failure tensile behaviour: (a) stress-strain approach; (b) fracture

energy approach ....................................................................................................... 147

Figure 5- 9: Uniaxial tensile stress-strain behaviour of concrete ............................. 148

Figure 5- 10: Truss element AB embedded in (3-D) continuum element; node A is

constrained to edge 1-4 and node B is constrained to face 2-6-7-3 ......................... 151

Figure 5- 11: A 3 node triangular facet thin shell .................................................... 152

Figure 5- 12: Finite element model for 3D analysis of on-way slabs (a) Quarter

model of the CFRP-strengthened RC slabs (Group S); (b) Half model of the CFRP-

strengthened RC slabs (Group C) ............................................................................ 153

Figure 5- 13: Load protocol: (a) FEMA461 (b) modified FEMA461 (FEMA 2007)

.................................................................................................................................. 154

Figure 5- 14: Finite element mesh of the quarter the CFRP-strengthened RC slabs

type (S) with a close-up view of the mesh ............................................................... 156

Figure 5- 15: Sensitivity of the S-T2L1 slab behaviour to the mesh size of (a) the

concrete; and (b) the steel reinforcement (c) the CFRP plate .................................. 159

Figure 5- 16: Load-deflection curve of slab S-T2L1 with different tension stiffening

models. ..................................................................................................................... 160

Figure 5- 17: Load-deflection curve of slab S-T2L1 with different dilation angle . 160

Figure 5- 18: Load-deflection curve of slab S-T2L1 with different Kc. .................. 161

Figure 5- 19: Comparison of predicted and experimental load-mid-span deflection

curves. (a) S-T2L0, (b) S-T2L1, (c) S-T2L2. .......................................................... 162

Figure 5- 20: Comparison of predicted and experimental load-strain curves at mid-

span, (a) Steel, (b) CFRP. ........................................................................................ 162

Figure 5- 21: Comparison monotonic and cyclic load-Mid-span deflection. (a) S-

T1L0 (b) S-T1L1, (c) S-T1L2. ................................................................................. 165

Figure 5- 22: Comparison of slip profile at monotonic and cyclic loading. (a)S-T1L1,

.................................................................................................................................. 167

Figure 5- 23: Contour plot of the damage initiation criterion at the CFRP/concrete

interface for slabs (a) S-T1L2 under monotonic loading & (b) S-T1L2 under cyclic

loading at failure. ..................................................................................................... 168

Figure 5- 24: Comparison of strain profile at monotonic and cyclic loading. (a)S-

T1L1, (b) S-T1L2 ..................................................................................................... 170


type (C) with a close-up view of the me .................................................................. 171


curves.(a) S-T2L0, (b) S-T2L1, (c) S-T2L2 ............................................................ 174

Figure 5- 27: Comparison of predicted and experimental load-strain curves at the top

of the support. (a) Steel, (b) CFRP ........................................................................... 174

Figure 5- 28: Comparison of monotonic and cyclic load-mid-span deflection. (a) C-

T1L0 (b) C-T1L1, (c) C-T1L2 ................................................................................. 176

Figure 5- 29: Comparison of slip profile at monotonic and cyclic loading. (a)C-

T1L1, (b) C-T1L2 .................................................................................................... 178

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Figure 5- 30: Strain profile in the CFRP for strengthened one-way slabs (a) C-T1L1

(b) C-T1L2 ............................................................................................................... 179

Figure 6- 1: Slab dimensions and reinforcement details (a) Top view (b) side

view.........................................................................................................................183

Figure 6- 2: Preparation process (steel reinforcement positioned in mould, casting

and cubes)................................................................................................................. 185

Figure 6- 3: Bonding CFRP plate to concrete substrate, profiling the concrete surface

with a surface grinder and applying adhesive layer to the concrete ........................ 187

Figure 6- 4: strain, stress, and internal forces at ultimate capacity .......................... 191

Figure 6- 5: Test setup for the RC slab (a) Laboratory photograph (b) Schematic

view .......................................................................................................................... 193

Figure 6- 6: Load frame (all dimensions in mm)...................................................... 194

Figure 6- 7: Typical strain gauge and linear variable differential transducers

(LVDTs) locations (concrete, steel, and CFRP plate).............................................. 196

Figure 6- 8: Test for concrete compressive modulus of elasticity ........................... 197

Figure 6- 9: Stress- strain curves for concrete cylinders .......................................... 198

Figure 6- 10: Tensile test of steel bar ...................................................................... 199

Figure 6- 11: Stress-strain curves for three representative steel bars....................... 199

Figure 6- 12: RC two-way slab during applied load ................................................ 200

Figure 6- 13: Debonding process (a) RC slab under monotonic (b) RC slab .......... 201

Figure 6- 14: Debonding near slab’s opening .......................................................... 202

Figure 6- 15: crack pattern for RC two-way slabs at failure load (a) RC slab under

monotonic loading (b) RC slab under cyclic loading............................................... 203

Figure 6- 16: Load-deflection for strengthened RC slab tested load (a) RC slab under

monotonic loading (b) RC slab under cyclic loading............................................... 205

Figure 6- 17: Load-strain relationships for steel reinforcement and concrete of CFRP

RC slab under (a) monotonic loading (b) cyclic loading ......................................... 207

Figure 6- 18: strain profile along CFRP plate (a) monotonic loading (b) cyclic

loading ...................................................................................................................... 209

Figure 6- 19: Finite element model for 3D analysis of quarter model of the CFRP-

strengthened two-way RC slab with opening .......................................................... 210

Figure 6- 20: Finite element mesh of the quarter the CFRP-strengthened two-way

RC slab with opening with a close-up view of the mesh ......................................... 212

Figure 6- 21: Comparison of numerical and experimental load- deflection curves for

RC two-way slab under monotonic loading ............................................................. 213

Figure 6- 22: Comparison of numerical and experimental load-strain curves in steel

and concrete for RC two-way slab under monotonic loading. ................................. 214


interface for RC two-way slab under monotonic loading. ....................................... 215

Figure 6- 24: Comparison of numerical and experimental strain profiles for RC two-

way slab under monotonic loading. ......................................................................... 215


RC two-way slab under cyclic loading. ................................................................... 216


and concrete for RC two-way slab under cyclic loading. ........................................ 217


way slab under cyclic loading. ................................................................................. 218


interface for RC two-way slab under cyclic loading. ............................................... 218

13

Figure 6- 29: Evolution of crack pattern of CFRP-strengthened two-way RC slabs

with opening under monotonic (a) 50.7 kN (b) 80.1 kN (c) 117 kN (d) 168.5 kN .. 220

Figure 7- 1: Comparison of strain profile at monotonic and cyclic loading. (a) fc = 33

MPa, (b) fc = 45 MPa........................................................................224

Figure 7- 2: Comparison of strain profile at monotonic and cyclic loading. (a) CFRP

plate width 75 mm, (b) CFRP plate width 100 mm, (c) CFRP plate width 125 mm

.................................................................................................................................. 226

Figure 7- 3: Comparison of strain profile at monotonic and cyclic loading. (a)

Opening size 750x750 mm, (b) Opening size 350x350 mm .................................... 227

14

List of Tables Table 2- 1: Mechanical properties of some fibres ((Enochsson, 2005)) .................... 28

Table 2- 2: Material properties of matrix materials, (Enochsson, 2005) ................... 29

Table 2- 3: Design code approaches for determining the effective strain in the FRP

laminate and anchorage length. .................................................................................. 60

Table 3- 1: Experimental programme .......................................................................64

Table 3- 2: Physical properties of the bonding adhesive (Weber Building Solution,

2014). ......................................................................................................................... 68

Table 3- 3: Concrete mix proportions (for 1m3 concrete). ........................................ 69

Table 3- 4: Monotonic and post-fatigue test failure loads and modes ....................... 73

Table 3- 5: Fatigue test results ................................................................................... 78

Table 4- 1: Material Properties of CFRP Plate.............................................. ......105

Table 4- 2: Material properties of adhesive layer .................................................... 106

Table 4- 3: Comparison between numerical and experimental results for all

monotonic and post-fatigue test failure loads .......................................................... 121

Table 4- 4: Main parameters investigated in numerical simulation ......................... 122

Table 4- 5: Comparison between numerical simulation results and code calculations

for debonding tensile strain ...................................................................................... 129

Table 4- 6: Summary of comparisons between numerical results and different code

calculation results for debonding tensile strain in CFRP plate, (ratio of calculation

result to simulation result, given in %) .................................................................... 130

Table 4- 7: Comparison between numerical simulation results and code calculation

results for effective bond length ............................................................................... 132

Table 4- 8: Summary of comparisons between numerical results and different code

calculation results for effective bond length in CFRP plate, ................................... 133

Table 4- 9: Calibration of constants C1, C2, C3 and C4 of the new proposal ........... 137

Table 4- 10: Calibration of constants C5, C6, C7 and C8 of the new proposal ......... 137

Table 5- 1: Strength and deformation characteristics for concrete (BSI (2004))

...................................................................................................................146

Table 5- 2: Details of materials used for slabs (S) &(C). ........................................ 156

Table 5- 3: Details of geometry used for Slabs Type (S) ......................................... 157

Table 5- 4: Comparison of the predicted and experimental results for one-way RC

slabs strengthened with CFRP type (S) .................................................................... 163

Table 5- 5: Comparison of the monotonic and cyclic loading results of slabs type (S)

.................................................................................................................................. 164

Table 5- 6: Specimen characteristics for slabs type (C) ........................................... 172

Table 5- 7: Comparison of the predicted and experimental results for one-way RC

slabs strengthened with CFRP type (C) ................................................................... 173

Table 5- 8: Comparison of the monotonic and cyclic loading results of slabs type (C)

.................................................................................................................................. 177

Table 6- 1: Concrete material properties ..........................................................198

Table 6- 2: Test results for two-way RC slabs ......................................................... 205

Table 7- 1 : Main parameters investigated in numerical simulation .....................223

Table 7- 2: Numerical simulation results and evaluated debonding tensile strain in

CFRP plates (Code) ................................................................................................. 231

15

ABSTRACT Behaviour of Reinforced Concrete Slabs Strengthened Externally

with Two-Way FRP Sheets Subjected to Cyclic Loads

Raid Ahmed Daud, 2015

For the degree of PhD/ Faculty of Engineering and Physical Sciences

The University of Manchester

The reliability of bond is crucial to the performance of concrete structures

strengthened with externally mounted carbon fibre reinforced polymer (CFRP) plate.

This thesis investigates the behaviour of the bond interface of reinforced concrete

slabs strengthened with CFRP under cyclic loading using both numerical modelling

and experimental methods. The main goals of this research are:

(1) To experimentally investigate the static and fatigue behaviour of the interfacial

bond between CFRP plate and the concrete substrate in single shear pull-out.

(2) To develop reliable numerical simulations in order to understand the post-fatigue

nonlinear behaviour of the adhesive interface for CFRP –concrete bonded joints.

(3) Using three dimensional finite element models, explore the nonlinear behaviour

of an adhesive layer connecting CFRP to reinforced concrete one-way slabs with

different levels of CFRP and different span scenarios under cyclic loading.

(4) Through both experimental and numerical modelling, explore the influence of

load protocol (i.e. monotonic and modified cyclic load protocol recommended by

FEMA 461) on the bond performance of the two-way RC slabs with openings

strengthened with CFRP plates.

To achieve the above goals, both experimental tests and numerical analysis were

conducted. In the experimental program, 28 single shear pull out tests were

conducted with variations in CFRP plate stiffness, concrete compressive strength and

loading hysteresis (static (monotonic), fatigue and fatigue following static). In all

specimens, the CFRP plate was 500 mm in length and 50 mm in width. The bonded

length was 300 mm. The plain concrete substrate had dimensions of 150 x 200 x 500

mm. From the tests, three failure modes were observed: (a) bond failure in the

interface between the concrete and the adhesive layer, (b) CFRP composite plate

rupture and (c) concrete shearing beneath the adhesive layer. The experimental

16

results indicate that when considering post-fatigue loading regimes, the strain

required to cause debonding of the CFRP and the ultimate load capacity of the

strengthening system is reduced by the previous cyclic loading. Based on the results

from these tests, a relationship between the CFRP plate stiffness with the ultimate

bond strength reduction and the fracture energy degradation is deduced.

Further to the pull-out tests, 2 two-way RC slabs with central openings strengthened

with CFRP plates were tested under cyclic loading. Results are presented in terms of

deflection, ultimate load capacity, crack patterns, strains and failure mode.

A detailed three Dimensional Finite Element (3D FE) model was developed using

ABAQUS /standard 6.10-1and was validated against the test results for both

monotonic and post-fatigue behaviour. The FE model accounted for the nonlinearity

of the concrete under cyclic loading by estimating the stiffness degradation in the

concrete for both compression and tension effects. The Bauschinger effect for steel

reinforcement was incorporated through the application of the kinematic hardening

model under cyclic loading. The ultimate bond strength reductions and fraction

energy degradations deduced from the cyclic loading history of single shear tests

were used as input for the interaction properties between the CFRP and the concrete

slab.

Using this model, a comprehensive study of the effect of variations in the bonded

CFRP plate length, concrete strength and bond width ratio was conducted. The

extensive numerical results have been used to assess the commonly used analytical

model proposed by (Chen and Teng, 2001) and the provisions in existing design

codes. The parametric study results show that the tensile strain limit is highly

overestimated in both ACI and fib-1design codes and it is underestimated for the fib-

2 and the CNR- DT202 codes. In contrast, the tensile strain limit proposed by TR55

and JSCE is generally acceptable; however, it is non-conservative with high CFRP

plate stiffness. The simulation results have been used to develop an alternative

analytical method to calculate the debonding strain and affective length for CFRP

plate bond to concrete and subject to single shear.

The developed numerical model was further validated by comparison against the

experimental results of the two-way RC slabs strengthened with CFRP plate.

17

Declaration No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.

18

Copyright Statement i. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and he has given The

University of Manchester certain rights to use such Copyright, including for

administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents Act

1988 (as amended) and regulations issued under it or, where appropriate, in

accordance with licensing agreements which the University has from time to time.

This page must form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trademarks and other

intellectual property (the “Intellectual Property”) and any reproductions of copyright

works in the thesis, for example graphs and tables (“Reproductions”), which may be

described in this thesis, may not be owned by the author and may be owned by third

parties. Such Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of the relevant

Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(seehttp://www.campus.manchester.ac.uk/medialibrary/policies/intellectualproperty.

pdf), in any relevant Thesis restriction declarations deposited in the University

Library, The University Library’s regulations (see

http://www.manchester.ac.uk/library/aboutus/ regulations) and in The University’s

policy on presentation of Theses.

19

Acknowledgements

First and foremost, I express my deepest thanks to almighty Allah for blessing me

with the health, wisdom, perseverance, patience, understanding and motivation

needed to successfully complete this work.

I would like to express my sincere appreciation and gratitude to my supervisors Dr.

Lee S. Cunningham and Prof. Yong C. Wang for their invaluable guidance and

advice, encouragement and support throughout this work.

Also, I wish to express my sincere thanks to the financial support given by The

Higher Committee for Education Development in Iraq for funding my

scholarship.

Many thanks also go to the technical staff at the School of Mechanical, Aerospace

and Civil Engineering, University of Manchester for their assistance during various

stages of the project.

My great gratitude and my sincere thanks are to be dedicated towards my late

father, who died on 25 June 2007. He and my mother have given all my academic

endeavours unwavering encouragement and in the pursuit of my study this support

substantially contributed to its completion.

My deepest appreciation goes to all members and friends at the School of

Mechanical, Aerospace and Civil Engineering, University of Manchester who

supported me in all respects during my PhD research.

20

Notation : The FRP plate area

: The steel reinforcement area

: The width of the concrete substrate beneath the FRP plate

: The width of the FRP plate

: The depth of the neutral axis

d: The effective slab depth

D: Degradation factor

cmE : The concrete modulus of elasticity

: Young’s modulus of FRP plate

: The Young’s modulus of the composite in fibre direction

: The Young’s modulus in the transverse direction to the fibre

: The concrete compressive strength

: The mean compressive strength of concrete

: The FRP plate stress

: The steel stress

: The concrete tensile strength

: The yield strength of steel

Ga : Shear modulus of adhesive layer

: The mixed mode fracture energy

Gf: The interfacial fracture energy

: The in-plane shear modulus

Gn , Gt , Gs : The work done in normal, first and second shear directions.

: Cracked moment of inertia

: Reduction factor

, , : The adhesive stiffness in normal, first and second shear directions

lb,max: Maximum anchorage length

: The effective bond length

: The nominal flexural capacity of the slab

: Moment due to dead load

nf: The number of FRP plate layers

[Q]: The stiffness matrix

21

[S]: The compliance matrix

: The slip at maximum shear stress

: The slip at debonding

ta: Thickness of adhesive layer

: Thickness of FRP plate

, and : The nominal stress components of the adhesive

: The volume of composite

: The fibre content by volume

: The volume of fibres

: The major poison’s ratio

: The bond length factor

: A width factor

: The effective slip

: The distance between strain gauge (i) and (i-1)

: The true strain

: Cracked strain

: Strain on the soffit

ck

t~ : The cracking strain of concrete

el

t0 : The elastic concrete strain

: Effective strain of the FRP

: Ultimate strain of the FRP

: The nominal strain

, and : The nominal strain components of the adhesive

t : Total concrete strain

, and : The strain of the FRP plate for three planes

µ: Fatigue reduction factor

: The true stress

: The nominal stress

: Tensile stress

, and : The stress of the FRP plate for three planes

: The mean shear

: The maximum shear stress at debonding initiation

22

Chapter One

Introduction

1.1 Introduction

At a practical level fatigue is a phenomenon which causes weakening of a material

due to repeatedly applied loads. More fundamentally, fatigue may be considered as

the propagation of damage. In the case of concrete externally strengthened with

polymer composites, this is usually associated with degradation in cohesive

behaviour of the adhesive and interfacial behaviour of the adhesive-concrete

interface. The main risk associated with fatigue is that repetitive loading may lead to

catastrophic failure at a much smaller load than that adopted for static design. In

order to prolong service life of existing structures and to accommodate potential

increases in cyclic loads various strengthening methods are adopted in practice. In

particular, there has been a growing interest over the past three decades in

strengthening concrete structures with externally bonded FRP. Bond behaviour is

considered the most critical issue in strengthening because the bond at the interface

between concrete and FRP is relatively weak compared with the constituent

materials in the strengthening system as a whole. Most of the previous research has

been concerned with the effect of fatigue of girders or beams involving the

strengthening techniques using composite materials. In contrast, the works

concerned with slabs under cyclic fatigue loading using strengthening techniques

have rarely been considered. In other words, the behaviour of strengthened slabs

with or without openings is not well understood yet. Given this, fatigue design

recommendations for slabs are needed to address the reduction in stiffness and

ultimate loading caused by fatigue cyclic loading.

Another issue that has been noticed from previous research is that the effect of

fatigue on bond behaviour has been neglected. This simplification was deemed

justified by previous researchers because the governing failure mode of strengthened

structural elements usually happens via excessive yield or rupture of internal

reinforcement. In special cases the effect of fatigue on bonding has to be considered

23

as bonding failure may govern in areas of stress concentration e.g. at flat slab

supports and corners of slab openings etc. In view of this, proper bond

considerations under fatigue conditions are required. These considerations have to be

reflected in the design equations which are used to address the bond failure in static

and cyclic conditions.

1.2 Objectives and methodology of the research

The objective of this study is to investigate the behaviour of reinforced concrete

slabs strengthened with externally bonded CFRP plate under cyclic loading using

both modelling and experimental methods; this study focuses mainly on slabs with

openings. Furthermore, this work seeks to investigate the interfacial bond behaviour

between the concrete and CFRP under fatigue loading. Through this investigation it

is possible to assess existing design equations which are used to address the bond

failure in static and cyclic conditions. Based on the aforementioned the following

more specific objectives are detailed:

1) To investigate, through experimental tests, the static and fatigue behaviour of

the interfacial bond between CFRP plate and the concrete substrate. These

tests explored the influence of both the stress range and CFRP stiffness on

fatigue life of the bond.

2) To investigate via numerical modeling of single shear pull-out tests, the

influence of bond length for different carbon fibre plate stiffness on the

ultimate load as well as the debonding strain for the post-fatigue analysis; and

produce a comparison with existing design codes.

3) Undertake parametric studies using the single shear numerical model to

investigate the effect of variations in thickness of FRP, type of FRP, concrete

strength and bond width ratio. The main objective of this numerical study is

to assess the existing design code approaches for FRP-concrete bond with

extensive data obtained from post-fatigue finite element analysis and propose

a model to predict the debonding strain and effective bond length

24

4) To develop optimum 3D FE models for simulation of slabs strengthened with

different levels of CFRP and different span scenarios, predicting the fatigue

response of flexural elements by using the modified cyclic load protocol

recommended by FEMA 461(after validation with relevant experiments). The

bond effect between the CFRP and concrete will be taken into consideration

during numerical analysis. The adopted model is capable of capturing the

failure mode, load capacity and strain profile along the middle of the bonded

CFRP sheets.

5) To investigate experimentally the influence of load protocol (i.e. monotonic

and modified cyclic load protocol recommended by FEMA 461) on the bond

performance of two-way RC slabs with openings strengthened with CFRP

plates.

6) Using the validated numerical model, investigate the influence of various

parameters on the nonlinear behaviour of an adhesive layer connecting CFRP

plates to RC two-way slabs under monotonic and cyclic loading. These

parameters are concrete compressive strength, CFRP bonded plate width and

opening size.

1.3 Layout of the thesis

Chapter Two gives a review of related experimental and numerical studies on the

behaviour of the adhesive interface between the FRP and the concrete surface under

monotonic and cyclic loading. In addition, the available previous experimental and

theoretical research dealing with flexural behaviour of strengthened concrete

members using FRP laminates under monotonic and cyclic loading were discussed.

Moreover, an overview of the most commonly used design codes for externally

bonded FRP strengthening system has been presented through this study.

Chapter Three presents a description of the experimental set up of single shear

specimens under static and fatigue loading, devices used and test procedures are

presented. From the result of the fatigue tests in terms of load slip and strain profile

of composite plate, it can be observed fracture energy degradation, ultimate bond

strength reduction, ultimate load reduction and reduction in the stain of the CFRP at

25

debonding loading due to the previous cyclic loading. Additionally, the CFRP

stiffness-fatigue life relationship for different load amplitude ranges is presented.

Chapter Four illustrates the finite element methods used to build the model that

simulates the post-fatigue interface behaviour between CFRP and concrete substrate

in single shear test. Three dimensional elements (solid, shell and cohesive) as well as

elastic and plastic behaviour of each material are described. Investigations of three

approaches for modelling the CFRP-to-concrete bonded joints (cohesive elements,

cohesive surfaces and virtual crack closure technique (VCCT)) are performed.

Parametric studies and assessment of the most common design codes are presented.

It proposes a simple and more accurate model for predicting debonding strain and

effective bond length of CFRP plate in single shear.

Chapter Five describes the validation of the adopted numerical model by simulating

the behaviour of one-way RC slabs strengthened with different levels of CFRP and

different span scenarios under cyclic loading. This section demonstrated a realistic

model for capturing the interface slip profile of CFRP with the concrete slab during

different cyclic stages that lead to good predictions of the actual slab failure mode.

Chapter Six gives a description of the experimental set up of two-way slabs with

opening strengthened with CFRP under different load protocol (i.e. monotonic and

modified FEMA cyclic load), instrumentation used and details of the test specimens

are discussed. The results of the test in terms of failure mode, deflection, ultimate

load and strain for concrete, steel, carbon fibre plate at critical locations will be

observed and compared with the numerical model.

Chapter Seven a parametric study and assessment of the most common design

codes, in the context of strengthening slabs with CFRP is presented.

Chapter Eight presents the summary and conclusions of the present research with

suggestions for possible future areas of interest.

26

Chapter Two

Literature Review of Previous Work

2.1 Introduction

The aim of this research is to investigate the behaviour of bond interface as well as

reinforced concrete slabs strengthened with CFRP under cyclic loading using both

modelling and experimental methods; this chapter presents detailed information of

five aspects of previous studies that are relevant to the current project.

1- Properties of FRP composite materials, including, failure modes for FRP

strengthened RC structural members.

2- Interface behaviour between the FRP and the concrete surface under monotonic

and cyclic loading.

3- Flexural behaviour of strengthened concrete members using FRP under

monotonic and cyclic loading.

4- Numerical modelling of FRP/concrete interface behaviour and reinforced

concrete slabs strengthening with FRP composite.

5- Current design methods.

2.2 Properties of FRP materials used in strengthening, repair and

retrofit of reinforced concrete structural members

The increased use of FRP as a means of strengthening existing structures is owing to

the inherent attractive characteristics of the material, in particular, good fatigue

resistance, excellent corrosion resistance, high strength-to-weight ratio and low

27

thermal conductivity, etc. Additionally, both the material and the geometrical

properties can be tailored to satisfy the required strength and stiffness for any desired

application.

Therefore, the FRP composite materials can be used for strengthening, repair and

retrofit. Strengthening is used to upgrade and improve performance of existing

structural buildings and to make the buildings more compatible with stringent design

requirements. The term repair is reserved for restoring an existing deteriorated

structure or building subjected to impact or blast in order to be capable to carry

design loads or return design ductility. Retrofit application is utilized to enhance the

structure performance subjected to cyclic loading or seismic (Du Beton (2006)). In

the current study, emphasis is placed on retrofit.

An extensive number of investigations to date have been performed on reinforced

concrete beams having FRP flexural retrofits subject to fatigue loading.

(Papakonstantinou et al., 2001, Gussenhoven and Brena, 2005, Aidoo et al., 2004,

Quattlebaum et al., 2005, Harries and Aidoo, 2006, Al-Saraj, 2007, Kim and

Heffernan, 2008). In most of the previous research, the governing failure mode of

strengthened structural beams usually happens in rupture of internal reinforcement;

so the effect of fatigue on bond behaviour has been neglected. In special cases the

effect of fatigue on bonding has to be considered as bonding failure may govern in

areas of stress concentration e.g. at flat slab supports and corners of slab openings

etc. In view of this, proper bond considerations under fatigue condition are required.

External bonded FRP system can be classified into two types which are FRP plates

and FRP sheets (Concrete Society (2012)). Plates are more desirable than sheets for

many reasons. Firstly, the flexibility of sheets makes handling and installation

significantly harder than plates. Plates contain more fibres than sheets of similar

cross-section, this property leads to plates having strength higher than sheets in some

cases. Furthermore, minor unevenness in the surface of the FRP plate can easily

addressed by the adhesive layer. Finally, less surface area of concrete needs to be

prepared in plate which leads to a significantly simpler and quicker strengthening

process than when using sheet. The following section presents a detailed review of

mechanical property models that are directly relevant to the present study and which

will be later used as background to defined numerical modelling.

28

2.2.1 FRP composite materials and mechanical properties

In civil engineering four types of fibres prevail. These are carbon, glass, aramid and

basalt fibres. Table 2-1 presents some mechanical properties of some common

fibres. Strength and stiffness are given for the longitudinal (principal) direction of

the fibres.

Table 2- 1: Mechanical properties of some fibres (Enochsson (2005))

Fibre type Elastic

modulus

[GPa]

Tensile strength

[MPa]

Failure strain

[%]

Carbon (HS/S) 160 – 250 1400 – 4930 0.8 – 1.9

Carbon (IM) 276 – 317 2300 – 7100 0.8 – 2.2

E glass 69 – 72 2400 – 3800 4.5 – 4.9

S-2 glass 86 – 90 4600 – 4800 5.4 – 5.8

Aramid (Kevlar 29) 83 2500 –

Aramid (Kevlar 49) 131 3600 – 4100 2.8

Basalt 78-90 4150-4800 4.1- 4.4

Carbon fibres have a high tensile stiffness (E). The ultimate elongation is 0.8 -

2.2%. Carbon fibres do not absorb water and have ability to resist many chemical

products. They withstand fatigue and impact excellently, do not suffer from stresses

erosion and do not show any creep or relaxation. Carbon fibre is electrically

conductive so it might produce galvanic corrosion in direct contact with steel.

Aramid fibres are prepared from aromatic polyamides. These have high fracture

energy and high modulus of elasticity. Aramid fibres have problems with stress

corrosion and relaxation. Moreover, aramid fibres are sensitive to high temperatures,

ultra violet radiation, and moisture. Therefore, they have not widely utilized in civil

engineering application.

Glass fibres are more popular compared with carbon and aramid as they are cheaper

than other type of fibres. Glass fibres are influenced to stress corrosion and may have

problems with relaxation at high stress levels. Furthermore, they are sensitive to

moisture. However, the fibres are protected with the correct choice of matrix

29

Basalt fibres are prepared from basalt rock by melting the rock at 1300-1700°C and

spinning it Young’s modulus of Basalt fibres varies between 78 and90 GPa for basalt

fibres from different sources. It has good thermal, electrical and sound insulating

properties. For example, basalt has much better chemical resistance than glass,

especially in strong alkalis and it has electrical insulating properties 10 times better

than glass (Parnas et al. (2007)). Carbon fibre shows better performance in terms of

withstanding fatigue, creep and relaxation compare to other fibre types. Therefore, it

can be adopted as a strengthening material for the research problem of the current

study.

From the aforementioned, the carbon fibre polymer plate has received more attention

than other type of fibre plate in strengthening structural members under the applied

mechanical fatigue loading. However, it still needs more research to predict the

remaining life for strengthened structural members under fatigue loading with

respect to various parameters. Therefore, the present study investigated the influence

of different carbon fibre plate types as well as the thicknesses on the fatigue life,

ultimate capacity, slip and failure mode for single shear pull out test specimens.

The matrix must keep the fibres in a desired location and orientation, protect the

fibre, transfer stress between fibres through shear and it is more ductile than the

fibres. It is also the source of composite toughness. The most common matrix

materials in civil engineering applications are vinyl ester, polyester and epoxy,

although epoxy is usually favoured above vinyl ester but is also more costly

(Lundqvist (2007)). Material properties are shown in Table 2-2.

Table 2- 2: Material properties of matrix materials, (Enochsson (2005))

Matrix/resin Elastic

modulus

(GPa)

Tensile strength

(MPa)

Failure

Strain

(%)

Polyester 3.1-4.6 50-75 1.0-6.5

Vinylester 3.1-3.3 70-81 3.0-8.0

Epoxy 2.6-3.8 60-85 1.5-8.0

30

FRP composite is an anisotropic material (i.e. material characteristics have different

aspects in different directions). A FRP composite with fibres in one direction is

designated as unidirectional. Whereas, the fibres are bonded or woven in many

directions is bi- or multidirectional. In strengthening applications, particularly in

beams, unidirectional composites are often utilized.

The mechanical characteristics of the composite are dependent on the matrix, fibres

type, fibre direction and fibre amount. The fibre content is defined by Equation (2.1).

(2.1)

Where and are the volume of fibres and the volume of composite respectively.

The fibre content by volume, is usually 30- 60% depending on the manufacturing

process, materials and required properties. The Young’s modulus of the composite in

fibre direction can be determined by the “rule of mixture” Equation (2.2)

(Carolin (2003)).

(2.2)

Where, subscript is utilized for fibre and for matrix. While the Young’s modulus

in the transverse direction to the fibre can be calculated according Equation (2.3)

(2.3)

The major poison’s ratio ( ) can be determined by the Equation (2.4)

(2.4)

The expression of the in-plane shear modulus of the composite lamina is shown as

Equation (2.5)

(2.5)

31

Figure 2- 1: stress –strain distribution on the composite element

Stresses can be transformed from one direction to the other direction using

expression in Equation (2.6), where L and T are subscripts for the fibres longitudinal

and transverse axes respectively. x and y are arbitrary perpendicular axes (see Figure

2-1)

(2.6)

Where is the transformation matrix which equal

(2.7)

With . For the strain the following relation is valid;

(2.8)

The following relationship is adequate for transforming principal strains in to

principal stresses:

(2.9)

Where is the matrix of stiffness and consists of

32

,

,

and

For transforming stresses into strains the relationship becomes

(2.10)

Where

,

,

,

, and

2.2.2 FRP- concrete bonding methods

With regard to the FRP installation, adhesively bonded joints between the FRP

system and the concrete substrate with a room-temperature curing are generally used.

The adhesively bonded joints offer certain advantages when compared with other

joints (i.e. bolted joints) and have, indeed, been extensively utilized in the procedures

for installing FRP systems. The main advantages are that adhesively bonded joints

include less stress concentration, superior fatigue resistance, excellent electrical and

thermal insulation properties, high strength-weight ratio, improved visual

appearance, corrosion prevention, low fabrication cost etc. (Pandey et al.(1999)).

The performance of structural members strengthened or retrofitted with FRP can be

effectively influenced on a surface preparation of the concrete and the quality of the

concrete substrate itself. Chajes et al. (1996) examined three different surface

preparations which are as-formed surface (i.e. untreated), ground surface and

mechanically abraded surface; it was found that the as-formed surface gives weaker

average stress at failure. Therefore, to achieve the best possible bond, the concrete

surface was first ground with a surface grinder before sandblasting and then cleaned

to remove dust and loose particles by vacuum cleaner. Moreover, the two part epoxy

system (i.e. Epoxy resin and Epoxy hardener) should be mixed in the correct ratio

based on the recommendations of the manufacturer until there is a uniform and

complete mixing of components within prescribed mixing time and visually

inspected for uniformity of colour. Following the application of the adhesive, the

CFRP plate was adhered to the glued concrete surface and pressed by roller to ensure

no air voids and squeeze the resin was squeezed from both sides of the plate edge

33

(see Figure 2-2) (ACI 440 (2008)). This method of surface preparation is adopted in

the present study for all experimental tests (i.e single shear and strengthened RC

two-way slabs).

Figure 2- 2: Installing FRP plates, using a roller to apply pressure. (Concrete

Society, 2012)

2.2.3 Failure modes for FRP strengthened RC structural members

A significant amount of previous research has reported the common modes of failure

of reinforced concrete (RC) members externally strengthened with FRP (Toutanji et

al., 2006, Esfahani et al., 2007, Mofidi et al., 2013). From this observation, the

failure modes can be classified into two main modes which are full composite action

failure modes and loss of composite action failure modes (Abdullah (2011)).

Full composite action also has the following three sub-categories, schematically

represented in Figure 2-3.

34

Mode 1: Steel yielding followed by concrete crushing; flexural failure may

occur with yield of the steel reinforcement in tension side followed by

crushing of the concrete in the compression region. In contrast, there is no

damage in FRP.

Mode 2: Steel yielding followed by FRP rupture; this failure mode may occur

for low ratios of both steel and FRP.

Mode 3: Concrete crushing; the RC members may fail by the crushing of the

concrete in the compression region, while both reinforcement steel and the

FRP are intact

Figure 2- 3: Full composite action failure modes

The possible failure modes for RC members that fail by loss of composite action are

categorized as follows (Pin, T., B. (2004)). Schematically represented in Figure 2-4

Steel yielding

Concrete crushing

Mode 1

Steel yielding

FRP rupture

Mode 2

Concrete crushing

Mode 3

35

1) Debonding failure modes induced by flexural loading.

Mode 1: FRP peeling- off at the outermost crack in the anchorage zone; when

the shear stress in the concrete exceeds its shear strength and the outermost

crack initiates, FRP separation in the anchorage zone will start.

Mode 2: FRP plate-end shear failure; this failure type may occur as a result of

shearing fracture through the concrete at the end of the FRP. The failure

mechanism begins with initiation of a vertical crack in the concrete at the

externally bonded plate end near to the support and then propagates as an

inclined shear crack (see Figure 2-4).

Mode 3: FRP peeling – off at flexural cracks; peeling- off of the FRP causes

in high moment regions far from the anchorage zone by flexural cracks in the

concrete which will propagate and become wider. Thus, the shear stresses

generated between the FRP and concrete surface lead to separation starting

from the mid-span and propagate towards the FRP plate end

Mode 4: FRP peeling-off occurred by shear cracking; inclined cracks in

concrete created horizontal and vertical opening displacements (see Figure 2-

4) due to dowel action effect and aggregate interlock. The horizontal opening

displacement causes debonding initiation between FRP plate and concrete

substrate. However, vertical open displacement may cause debonding

propagation towards the end of FRP plate resulting from tensile stresses in

the concrete layer underneath the FRP

Mode 5: FRP peeling-off due to unevenness of the concrete surface; localized

debonding of the FRP may increase and lead to FRP peeling off due to the

roughness and unevenness of the concrete surface. Therefore, quality control

needs to be particularly high during installation of FRP plate in order to

minimise this type of failure. The Concrete Society (2013) suggested a

maximum unevenness in the concrete surface ranges between 3- 5 mm in 1 m

depend on FRP system (i.e. plate or sheet).

36

Figure 2- 4: Debonding failure modes induced of flexural loading

2) Debonding failure modes induced of the loss of adhesion between FRP and

concrete substrate. Shown in Figure 2-5

Mode 1: Bond failure in the adhesive; the bonding failure which denotes as

debonding through the FRP adhesive will occur when the strength in the

adhesive is lower than the strength of concrete. However, the shear and

tensile strengths of adhesive layer usually exceed those of concrete. In some

cases a dramatic increase of temperature causes a pronounced drop in

adhesive strength compared with concrete strength or very high tensile

concrete strength.

Mode 2: Bond failure in the interfaces between concrete FRP and adhesive;

in the relatively rare case where the surface conditions during the FRP

application are inadequate, bond failure may occur through the adhesive-

concrete interface or FRP- adhesive. This failure type can easily be avoided

by proper surface preparation for concrete and FRP.

Figure 2- 5: Debonding failure modes induced of the loss of adhesion between FRP

and concrete substrate

Mode 4

Mode 1 Mode 2 Mode 3 Mode 5

Concrete

Adhesive

FRP

Mode 1

Mode 2

37

2.3 Previous studies on FRP/concrete interface behaviour

Fatigue is a phenomenon which causes the weakening of a material due to repeatedly

applied loads. The main risk associated with fatigue is that the repetitive loading may

lead to catastrophic failure at a much smaller load than that adopted for design.

Fatigue conditions are important in structures subject to cyclic loads e.g. traffic

loading on structures such as car parks and bridges. In order to prolong service life of

existing structures and accommodate potential increases in cyclic loads various post-

strengthening methods are adopted in industry. To that end, there has been a growing

interest over the past three decades in strengthening with FRP. Bonding is

considered a critical issue of any strengthening because the bond at the interface

between concrete and FRP is relatively weak as compared with the constituent

materials in the strengthening system as a whole. The following sub-sections will

present a comprehensive study of bond interface behaviour under monotonic as well

as cyclic loading and a detailed review of a number of selected analytical researches

which will be used to compare with the numerical modelling of the present research

study.

2.3.1 Bond behaviour under monotonic pull out loading

An extensive number of studies have been performed on the experimental

investigation of the behaviour and failure modes of bond tests for the FRP composite

–concrete interfaces. In particular, bond behaviour and load transfer between FRP

composite plate and concrete under monotonic loading. (Mazzotti et al., 2003, Yao et

al., 2005, Guo et al., 2005, Ali-Ahmad et al., 2006, Carloni and Subramaniam, 2010,

Subramaniam et al., 2011).

The influence of different parameters on the bond behaviour between the FRP and

concrete has been investigated through experimental studies, such as the influence of

concrete surface preparations (De Lorenzis et al., 2001, Chajes et al., 1996). It was

found that different surface preparation approaches give the same failure mode

which is shear cracking in the concrete just beneath the adhesive. However, surface

preparation of the concrete can influence the ultimate bond strength (i.e. the

mechanical abrasion surface gives the highest average stress at failure). Adhesive

38

types (Chajes et al., 1996, Dai et al., 2005). It was concluded that the adhesive types

were determined to have similar average shear stresses.

The common failure modes were shearing of the concrete directly beneath the bond

and FRP rupture. FRP stiffness (i.e. FRP thickness & FRP type) (Bizindavyi and

Neale, 1999, Dai et al., 2005, Pellegrino et al., 2008). It was determined that the

material stiffness has a significant influence on the ultimate interfacial load carrying

capacity and the bond stress slip relationship. The common failure mode is that

debonding at adhesive-concrete interface, shearing of the concrete directly beneath

the bond and FRP and concrete prism failure. Concrete strength (Chajes et al., 1996,

De Lorenzis et al., 2001, Yao et al., 2005, Guo et al., 2005) it was deduced that the

concrete strength did not affect the failure load while it has a significant effect on

bond stress. The debonding at adhesive-concrete interface is a governed mode of

failure. FRP bond length (Chajes et al., 1996, Bizindavyi and Neale, 1999, De

Lorenzis et al., 2001, Mazzotti et al., 2003, Yao et al., 2005, Guo et al., 2005,

Hosseini and Mostofinejad, 2014). It was concluded that both the Chen and Teng

model 2001 and FIB code are overestimated to predict effective length. In addition,

no further increases in failure load beyond the effective length. This is due to stress

transformation is not generated beyond an effective bond length. FRP/ concrete

width (De Lorenzis et al., 2001, Yao et al., 2005, Subramaniam et al., 2007,

Subramaniam et al., 2011). It was determined that Chen and Teng’s bond strength

model is slightly conservative when the FRP/concrete width ratios are at the two

extremes. Moreover, the nominal stress at debonding increases with the FRP-to-

concrete width ratio. Furthermore, the strain across width of the edge region was

found to be relatively constant during the debonding process. Finally, the fracture

energy is independent on the width of the FRP sheet. Types of bonding test (Yao et

al., 2005, Pellegrino et al., 2008, Carloni and Subramaniam, 2010). It was

recommended that the single shear test is considered a standard bond test.

Based on these investigations, it is understandable as the stress transfer mechanism is

mainly reliant on the bond quality between the FRP and concrete as well as the bond

strength. In addition, relative slip has a linear relationship with the concrete tensile

strength, while the fracture energy is an important parameter for the bond

characteristics and usually expresses a linear relationship with the square root of the

39

concrete tensile strength. The bond strength will not increase when the bond length

of FRP sheet–concrete interfaces exceeds the effective bond length. On the other

hand, the dominant failure mode observed by the aforementioned research is

debonding within a few millimetres of the concrete layer beneath the adhesive.

However, two more failure modes might be identified during the tests, the formation

of a fracture plane in the concrete substrate and debonding at the adhesive-concrete

interface. Figure 2-6 shows three failure modes resulting from a standard single

shear pull-out test.

Figure 2- 6: Failure modes (a) Debonding at the adhesive–concrete interface. (b)

Concrete fracture (c) Debonding in concrete (Yao et al. (2005)).

2.3.2 Bond behaviour under cyclic pull out loading

Few of the previous research studies have investigated the bond behaviour in a single

shear pull out test under fatigue loading (a single shear pull out test is accomplished

by exerting tensile pressure (pull-out force) in the transverse plane of the supporting

conditions until debonding failure occurs. Pull-out force causes FRP plate sliding

parallel to the contact plane with the concrete substrate). A few number of relevant

pieces of research, Bizindavyi et al. (2003) have investigated experimentally the

influence of bond length, bond width and cyclic bond stress levels on bond

characteristics between FRP laminates and concrete under cyclic loading and they

have proposed a stress level–fatigue life relationship. Yun et al. (2008) observed the

fatigue behaviour of the bond between FRP and concrete by comparing five different

bonding systems [externally bonded FRP (EB-FRP), near-surface mounted FRP

(NSM-FRP), fibre anchored FRP (FB-FRP) and a newly developed hybrid bonded

FRP system (HB-FRP) with tight or loose mechanical fastener] and they identified

(c) (b) (a)

40

that the fatigue endurance of the hybrid-bonded FRP (HB-FRP) system with a tight

mechanical fastener was the highest among all of the tested systems.

Mazzotti and Savoia (2009) have studied experimentally typical seismic excitations

behaviour for both a CFRP plate and CFRP sheet bonded to concrete substrate. The

load protocol that has been applied before the debonding consists of four load levels

and five loading – unloading cycles which have been repeated for each one of the

load levels. Their findings showed that debonding load is not affected by cyclic

loadings. However, a deterioration of maximum shear stress occurred after the

debonding onset induced by a small degradation of stiffness. Finally, the effects of

cyclic loadings in terms of strain increments can be found at a larger distance in FRP

plates as a compared with FRP sheets as illustrated in Figure 2-7.

Figure 2- 7: Strain increments measured after 5 cycles loading for specimen (a) Plate

(b) Sheet (Mazzotti and Savoia (2009))

(a)

(b)

41

Nigro et al. (2010) conducted an experimental study on the effect of three different

cyclic load paths in addition to monotonic load path on concrete prismatic specimens

reinforced with carbon FRP (CFRP) sheets or plates. The first two cyclic load paths

used in these tests were adopted to simulate a seismic event while the third one was

adopted to find the extent of the influence of cycle number on bond behaviour. It was

found that the value of ultimate slip achieved by plate is less than that achieved by

sheet because the strain recorded in plate is lower than the strain distribution

recorded in sheet and both cyclic and monotonic tests give approximately equal

ultimate slip. The failure modes for all tested specimens were observed at shear

crack in the concrete just beneath the adhesive layer. Moreover, a few load -unload

cycles up to 90% of ultimate load caused shear-stress shifting along the CFRP

composite and reduced the cracking load by about 10%. However, they did find that

the influence of cycles up to 70% was negligible. Finally, the design equations

provided by the international codes (ACI 2008; CNR 2004; fib 2001) to estimate the

effective bond lengths were in good agreement with experimental results for sheets

and more conservative for plates.

Carloni et al. (2012) have performed seven direct shear tests of FRP composite –

concrete interface debonding under fatigue and monotonic quasi-static. The strain

field on the surface of the specimens which is obtained from optical technique,

digital image correlation (DIC), during testing the interfacial crack propagation in

both fatigue and monotonic quasi-static loading conditions was monitored. They

found fatigue loading with high stress amplitude causing crack initiation while

fatigue loading with low stress amplitude was causing the crack propagation. Finally,

they have illustrated that the critical loads in the monotonic post-fatigue tests were

not influenced by the fatigue if the stress transfer zone is less than the bonded length.

To date, few studies have investigated the fatigue behaviour of adhesive joints.

Among the relevant studies, Ferreira et al. (2002) performed an experimental

investigation for evaluating the effect of layer orientation, lap joint length and water

immersion on adhesive lap joints produced from bi-directional woven E-glass fibres

and polypropylene. The adhesive used was Bostik 7452-Super Glue 4, Rubber &

Plastics Grade ethyl cyanoacrylate type, while the primer was Bostik 7480-Super

Glue 4 based on n-heptane. The tests results suggest that the fatigue behaviour is not

42

significantly influenced by the adhesive thickness. The fatigue strength was also

shown to improve when using stiffer laminate adherent. Azari et al (2011) also

studied the fatigue performance of adhesive joints. The main parameters examined in

this fatigue experiment were surface treatment, surface roughness and adhesive layer

thickness. The results of this study indicate that surface treatment can change the

failure mode. However, the surface roughness had no effect on the fatigue life

threshold. It was also found that a thinner adhesive layer would lead to a shorter

fatigue life. Furthermore, the adhesive thickness had more pronounced influence on

the crack growth rate than the fatigue life threshold. The fatigue behaviour of a FRP

strengthened concrete structure is complex and is affected by many parameters. The

aim of this study is to obtain basic properties of one of the important structural

components: the interfacial bond under shear. More research is required to better

understand the debonding mechanism and to develop detailed design approaches for

strengthened structural members subjected to cyclic loads. Specifically, none of the

aforementioned research has considered the effect of CFRP type or CFRP thickness

on fatigue and post-fatigue behaviour.

The current study intended to address degradation of the bond which may be induced

by fatigue loading. Guidance for addressing fatigue debonding failure of externally

bonded FRP composites applied to the tension side of concrete has been evaluated

by Harries and Aidoo (2006). However, this evaluation is based on data obtained

from a small number of bridge girders retrofitted with CFRP. A further limitation of

the previous study is that the common failure mode in flexural FRP-strengthened RC

members is intermediate crack debonding (IC debonding) which in turn gives

different failure mechanisms from that observed in a pull-out test. As is well known,

the IC debonding mechanism has a highly brittle descending branch of the bond-slip

response as described by Lu et al. (2007), which causes a high level of dispersion in

predicting strain at debonding. Yao et al. (2005) proved a single shear test to be more

reliable and robust in determining the debonding strain for strengthened RC

members that fail by loss of composite action.

43

2.3.3 Bond -slip analytical research studies

A significant amount of analytical research has been undertaken to develop a bond

slip model that described the interfacial bond behaviour up to failure. These models

categorized in accuracy and simplicity based on the number of parameters involved

in each model.(Chen and Teng, 2001, Yuan et al., 2004, Niu and Wu, 2005, Lu et al.,

2005a, Dai et al., 2005, Faella et al., 2007, Zhou et al., 2010). However, in the

experimental investigation, most of these studies have all focused on the

strengthening system under monotonic load conditions. Among other relevant

research studies Dai et al. (2005) performed an experimental and analytical

investigate on different on FRP composite laminates stiffness, FRP materials (carbon

FRP, aramid FRP and glass FRP) and different adhesives (CN-100, SX-325, FR-

E3P, FP-NS (primer)). An analytical model, have been given as follows, need only

interfacial fracture energy (Gf ) and interfacial ductility index (B) which were

obtained through regressing.

(2.11)

(2.12)

(2.13)

(2.14)

(2.15)

Ga =shear modulus of adhesive layer; ta =thickness of adhesive layer. This model

cannot produce accurate bond-slip relationship because it only depends on a few

bond parameters and did not focus on the ascending and descending branches of the

analytical bond slip model.

Lu et al. (2005a) have assessed several existing bond strength models with 253

single and double shear pull test results from the literature. Then three different new

bond slip models, namely, Precise model, Simplified model, bilinear model were

44

proposed. The three bond-slip proposed models showed better agreement with the

test results in terms of both bond strength and strain distributions in the FRP plate

than the existing bond strength models. However, Chen and Teng (2001) model’s is

almost the same as the proposed model. Therefore, the Chen and Teng model was

used in a comparison with the current experimental bond slip model for single shear

pull out test under monotonic loading due to its accuracy and simplicity. The bond -

slip model and effective bond length is given by equations below.

(2.16)

(2.17)

(2.18)

(2.19)

is the maximum shear stress in MPa

(2.20)

Where f

b and c

b are the widths in mm of the FRP and concrete slab, respectively.

(2.21)

the corresponding slip at maximum shear stress

(2.22)

The ultimate carrying load capacity of the FRP-concrete bonded system in terms of

interfacial fracture energy is given by:

(2.23)

45

(2.24)

The analytical solution for the effective bond length e

L with the bilinear bond–slip

model is given by:

(2.25)

Where

(2.26)

It has been suggested that the bond strength model depends on the ultimate tensile

strength because test results showed that the main failure mode is few millimetres

within the layer of concrete beneath the adhesive layer. In addition, the FRP-to-

concrete member width ratio is taken into consideration because it was observed that

the ratio has a significant effect on the overall bond strength behaviour.

2.4 Previous studies on flexural behaviour RC members

strengthened with FRP

This section reviews the research study to date in the field of external FRP

strengthening technique. Although strengthening members with FRP laminates, in

terms of fundamental understanding and characterization of the bond behaviour has

reached an advanced stage, there are still some areas requiring further research. In

particular, understanding the post-fatigue nonlinear behaviour of the adhesive

interface. This is vital for appropriate design of FRP-strengthened flexural members

subject to cyclic loads. To that end, the reliability of the bond is crucial to the

performance of reinforced concrete (RC) members externally strengthened with fibre

reinforced polymers (FRP) under monotonic and cyclic loading. The force transfer

mechanism at the interface between the FRP composite plate and concrete is

dependent on the quality of the adhesive layer. The adhesive layer connecting the

46

FRP-concrete composite consists of an effective mechanism for resisting the shear

force at the interface between FRP and the concrete slab. Hence, enhancing the bond

promotes the extension of service fatigue life of FRP-strengthened RC elements, as

well as increasing their load bearing capacity.

2.4.1 Flexural behaviour under monotonic loads

Many studies have experimentally investigated the nonlinear behaviour of RC

members, strengthened with FRP under monotonic loading. Among these studies,

Seim (2001) investigated the effect of externally bonded fibre-reinforced polymer

composite strips and fabric to the tension side of scaled slabs on load and deflection

capacities. Thirteen scaled slab panels were tested in flexure. The main parameters in

the study were adhesive thickness, bond length, strip length and the type of FRP

strengthening. From the research, it was concluded that load capacity can be

increased by up to 370%. However, overall response of the specimen changes from

the ductile failure followed with the yielding of steel reinforcement, to a more

sudden failure followed with separation of the FRP composite from the concrete. It

was also observed that, only about 50% of the capacity of the strip is used, at best,

with performance being constrained by a 0.65% strain limitation in the adhesive.

Mosallam and Mosalam (2003) performed an experimental investigation for

evaluating the ultimate capacity of two-way slab strengthened with flexible FRP

composite strip. They tested ten full-scale unreinforced and reinforced concrete

slabs repaired and retrofitted with FRP composite strips with dimension

(2670X2670X76 mm). All tested slabs were simply supported on all four sides

undergoing two-way action. Both carbon epoxy and E-glass epoxy composite

systems were utilised in this study. Furthermore, two more samples were tested to

85% of the expected ultimate load for subsequent repair. The research concluded that

the FRP strengthening systems have succeeded in enhancement of the structural

capacity of both two-way unreinforced and reinforced concrete slabs. For repair

applications of unreinforced concrete slabs, test results noted that the composite

system restored not only the original capacity of the damaged slabs but also resulted

in a significant increase of the strength of the repaired slabs to an average increase of

more than 540% of the original capacity of the control slabs. For retrofitting

47

applications, the use of FRP systems resulted in appreciable upgrade of the structural

capacity of the as-built slabs up to 500% for unreinforced specimens and 200% for

steel reinforced slabs. In all cases, the failure was preceded by obviously large

deformations (more than 1/45 of the clear span length) which provided enough visual

warning before ultimate failure.

Ebead and Marzouk (2004) assessed the use of FRP to strengthen two-way slabs

experimentally. Both carbon FRP strips and glass FRP laminates were evaluated. Six

slab specimens of size 1900 mm x1900 mm x150 mm were strengthened in flexure.

There were two steel reinforcement ratios: 0.35 and 0.5% (two unstrengthened as

reference specimens, two specimens strengthened with CFRP and two specimens

strengthened with GFRP). All specimens were simply supported along the four

edges, corners were free to lift and were centrally loaded through the square column

stub 250 mm side dimension. The study concluded that flexural strengthening slabs

using CFRP strips and GFRP laminates showed an average gain in the load capacity

of approximately 40%, 31% over that of the reference slabs, respectively. A decrease

in ductility and energy absorption was also recorded.

Rusinowski (2005) tested full scale two-way slabs with an opening under simply

supported conditions. The uniformly distributed load was applied by means of

pneumatic pressure bags. Three main variables were investigated; the opening size,

strengthening type (i.e. steel bars or CFRP) and strengthening schemes. From this

test, it was concluded that the applying CFRP in the corners of the opening is more

sufficient rather than adding extra embedded steel reinforcement in the corner in

terms of crack propagation in the tension side, stable performance after cracking and

higher carrying loading.

Kim et al.(2008) presented the flexural behaviour of two-way reinforced concrete

slabs strengthened with prestressed or non-prestressed CFRP sheets. The

experimental program included one slab with nonprestressed CFRP sheets, two slabs

with prestressed CFRP sheets and one unstrengthed slab. All large scale two-way

slabs had the same measurement of (3000 mm x 3000 mm x 90 mm). Each of them

was simply supported (2700 mm span) and subjected to a monotonic patch load with

an 800 mm x 800 mm square loading frame at the centre span, as shown in Figure 2-

8

48

Figure 2- 8: Schematics of the tested slab: (a) elevation view; (b) test setup; (c) steel

reinforcement and instrumentation; and (d) CFRP strengthening (bottom view) (Kim

et al. (2008))

From the research work investigation, it was concluded that an increase in the

flexural load-carrying capacities was achieved for the slab strengthened with

nonprestressed and prestressed CFRP sheets of up 25% and 72%, respectively, as

compared to the un-strengthened reference slab. However, the prestressed CFRP

sheets do not show effectiveness in reducing computed crack mouth opening

displacements, as they provided a notable load sharing mechanism with the steel

reinforcement that induced in higher yield loads with respect to the reference slab.

Elsayed et al.(2009)assessed experimentally the performance of use the mechanically

fastened (MF) FRP technique of external bonded system for flexure strength of nine

two-way concrete slabs; five slabs without a cut-out and a further four slabs with a

central square cut-out of a side length of 800 mm. Two different schemes were used

for the strengthening of slabs without a cut-out; The FRP strips were either attached

to the slab centre or separately attached with a centre-to- centre spacing of 500 mm.

For both schemes, six FRP strips were used. For slabs with a cut-out only one

49

strengthening scheme was used. Four FRP strips of the same dimensions were

attached to the concrete surface around the cut-out Figure 2-9.

Figure 2- 9: Strengthening schemes for slabs with or without cut-out (a) Middle

strips, (b) Separated strip (c) Around the opening strip Elsayed et al.(2009)

In these previous studies, it is observed that different parameters of one-way or two-

way slab tests under monotonic load condition were studied, such as the shape of the

loading surface (i.e. point load, line load and uniformly distributed load), FRP

arrangements, FRP type and FRP installation purpose (i.e. strengthening, repair and

retrofit). These differences influence the ability of bending action occurring and are

also believed to affect the failure behaviour. The test conducted in the present Ph.D.

study for monotonic loading condition is confined to strengthened two-way slab with

central opening to quantify and compare the strains in CFRP plates around the

opening and failure mode with those results obtained from the slab with opening

under cyclic loading.

(c) Around the opening strips

50

2.4.2 Flexural behaviour under cyclic loads

Several studies have also investigated the behaviour of RC members strengthened by

FRP under cyclic loading.

Shahawy and Beitelman (1999) studied the fatigue performance of reinforced

concrete beams strengthened with externally bonded CFRP sheets. The main

parameter in the accelerated fatigue testing was performed to investigate various

amounts of the CFRP lamination system (partially wrapped and fully wrapped). A

control beam was provided in order to establish the behaviour of control response.

The study illustrated the feasibility of using CFRP fabric in the repairing and

strengthening of RC structures with respect to fatigue performance. It was found

from the testing results that strengthening with fully wrapped systems is preferable

to partially wrapped systems.

Arduini et al. (2004) presented experimental research carried out twenty six full-

scale one-way reinforced concrete (RC) slabs with and without an overhang at one

extremity (with and without externally bonded unidirectional CFRP) under simply

supported conditions. They were subjected to two cycles. For fourteen samples, the

research focused on simply supported conditions. For the twelve remaining samples,

they were simply supported with an overhang. Additionally to the amount of FRP,

the steel reinforcement ratio was the second variable in the experimental program.

Based on the work investigated, it was concluded that the load-carrying capacity can

be increased up to 122% in comparison with the reference slabs. The percentage for

slabs with low steel reinforcement ratio is more obvious than that of those with high

steel reinforcement ratio. Moreover, different failure modes of slabs with external

CFRP laminates were observed (namely concrete shear, concrete crushing, CFRP

rupture and CFRP peeling).

Aidoo et al.(2004) observed the flexural fatigue performance of reinforced concrete

bridge girders that had been repaired using one-dimensional FRP composite systems.

Two different CFRP systems were used (strip retrofit system and fabric system).

Three stress levels were investigated for fatigue testing (80%, 63% and 46% of

observed general yield value of reference beam). Observations have shown that the

fatigue performance of such retrofit beams is controlled by the fatigue performance

of the reinforcing steel and the quality of the bond between the CFRP and the

51

concrete substrate. On the other hand, the application of an FRP retrofit increased

fatigue life of a reinforced concrete beam. It was also found that the strip retrofit

showed a better response under fatigue conditions than the fabric system.

Rosenboom and Rizkalla (2005) investigated the fatigue performance of CFRP

strengthening systems for pre-stressed concrete bridge girders. Two girders were

subjected to fatigue loading conditions: one strengthened with externally bonded

CFRP strips and the other with wet lay-up sheets. The study concluded that pre-

stressed concrete girders strengthened with externally bonded CFRP sheets can

withstand over one million cycles of loading equivalent to a 60 percent increase in

live load. Moreover, the specimen strengthened with the externally bonded sheet

strengthened systems performed better under fatigue loading conditions than

externally CFRP strips.

Harries and Aidoo (2006) evaluated guidance for addressing debonding failure of

externally bonded FRP composites applied to tension side of concrete by using data

obtained from large- and full-scale experimental works. It has demonstrated that the

ACI committee 440 proposed limits to address the debonding by implementing

reduction factor to reduce the ultimate strain was found to be non-conservative.

Kotynia et al.(2010) presented the experimental results of reinforced concrete slabs

strengthened with pre-stressed and gradually anchored carbon fibre–reinforced

polymer (CFRP) strips under cyclic loading. The purpose of cyclic tests was to

identify the fatigue behaviour of the new pre-stressing technique on strengthened

slabs and to demonstrate the influence of long-term cyclic loading on the bond

properties of the pre-stressed CFRP laminates, ductility and flexural strength of the

strengthened slabs. From this research, it was noticed that the failure of all tested

slabs was initiated by the fatigue fracture of several longitudinal tensile steel bars

and then the CFRP strip debonded from the concrete surface.

Al-Rousan and Issa (2011) investigated the fatigue responses of RC beams

externally strengthened with a different number and configuration of CFRP sheets.

Four different stress ranges were used in this study (0.25fy– 0.35fy, 0.45fy–0.65fy,

0.65fy–0.90fy and 0.45fy–0.90fy). Form this study, it was concluded that a reduction

in the stiffness due to cyclic loading induced severe serviceability problems (i.e.

52

excessive permanent deflection). Additionally, failure modes, stiffness and ultimate

load capacity can be influenced by the stress ranges.

It is clear from the above-mentioned discussions in Section 2.4 that no further

research needs to be done on strengthened slab specimens with or without opening

under monotonic loading and strengthened one-way flexural members. However,

more research is needed to understand the effect of cyclic loading on bond behaviour

in critical cases where there is stress concentration for instance, the corners of slab

openings and at the flat slab support. In addition, none of the above research studies

have quantified the allowable tensile strain in CFRP plates at debonding initiation in

strengthened two-way slab under monotonic or cyclic loading. The main objective of

the experiment is to assess the existing design code approaches for FRP-concrete

bond with data obtained from an experimental programme. Moreover, the

experimental tests will be used to validate the numerical simulation of strengthened

two-way slabs under cyclic loading in order to recognize the reliability of the

suggested post-fatigue bond slip model in capturing the correct failure mode.

2.5 Numerical modelling

It is well-known that several finite element models have been developed to

investigate CFRP-strengthened RC members subjected to monotonic loading by

imposing the interface behaviour. However, the need to understand the actual

interface behaviour in CFRP-strengthened RC slabs under cyclic loading still exists.

The study of the nonlinear behaviour of RC members strengthened with CFRP, using

the finite element method (FEM) often entails some fundamental assumptions

ABAQUS (2011). One of these assumptions is the insertion of both the tension and

compression damage parameter for estimating the stiffness degradation in the

concrete for both compression and tension, due to cyclic effects. Another important

assumption is to impose the Bauschinger effect for steel reinforcement bars through

the application of the kinematic hardening model. In addition, the traction-separation

based model is another assumption that defines the material properties of the

adhesive layer with a degraded cohesive stiffness, when the stresses at the contact

point satisfy maximum nominal stress criterion.

53

2.5.1 Numerical modelling of FRP/concrete interface behaviour

Due to lack of information about the expected FRP/ concrete interface behaviour

under cyclic loading, numerical simulation is a substantial tool to generate extensive

data to assess the existing design code methods. Thus it is necessary to review the

different numerical techniques which were adopted by other researhers and then

used as a starting point to develop the present detailed numerical FRP/concrete

interface model under cyclic loading. Several numerical analyses have been

performed to model the FRP/concrete interface under monotonic loading in recent

years. In essence two common techniques have been implemented. In the first

technique, it is assumed that the FRP and the concrete are connected directly without

interface elements. Using this approach, Lu et al. (2005b) studied the debonding

process in pull-out tests using a meso-mechanical model for the concrete.

Subsequently Lu et al.(2007) investigated the debonding process using the smeared

crack approach, due to intermediate cracking (IC). This type of debonding is caused

by flexural cracks in the concrete and occurs at a critical section in the high moment

region and propagates to the FRP plate ends. Lundqvist (2007) conducted three

dimensional nonlinear FE analyses for beams in four-point bending strengthened

with FRP plate or sheet to determine the critical anchorage length. The failure mode

for the beam was debonding within a few millimetres of the concrete layer beneath

the adhesive. The second technique uses an interface element to define the interface

between the FRP and the concrete. For example, Wong and Vecchio (2003) carried

out two dimensional FE analyses to model the debonding phenomena in three large-

scale RC concrete beams strengthened with externally bonded FRP plates. Perera et

al. (2004) made a two dimensional adherence analysis of RC beams strengthened

externally with FRP by incorporating a damage model for the concrete. Camata et al.

(2004) investigated end peeling failure and mid-span debonding of RC beams

accounting for distributed concrete crack damage. The second technique is preferred

because it is able to accurately find the locations of interfacial slip concentration near

the cracks without numerical convergence problem.

Finally, limited numbers of studies have been undertaken to investigate the

feasibility of using finite element modelling to simulate the single shear pull-out

tests under cyclic loading. Khomwan et al.(2010) developed two dimension

nonlinear FE model to capture debonding failure between the FRP and concrete due

54

to cyclic loading. Loo et al.(2012) conducted two dimension FE analyses to model

FRP-to-concrete bond for fatigue loading. These studies were confined to 2

dimensional elements. In the current study, three dimensional single shear pull-out

tests was presented and then extended to numerical investigation of the nonlinear

behaviour of an adhesive layer connecting (CFRP) to reinforced concrete one-way

slabs under cyclic loading.

2.5.2 Numerical modelling of flexural behaviour of RC slabs strengthened

with FRP

Initially, Seim (2001) modelled the behaviour of scaled slabs strengthened with FRP

numerically using the moment-curvature relationship and a hypothetical three-stage

load displacement curve where these three stages are defined by the un-cracked

response The response before the yielding of steel, the yielding of steel and failure of

either concrete or the FRP composite showed reasonable agreement between

experimental and analytically predicted response.

Hörmann et al.(2002) proposed two different nonlinear finite element models to

study the flexural behaviour of RC scaled slabs strengthened with FRP. In the first

model, two-dimensional (2D) design space assumed a plane stress condition for the

concrete and the fibre reinforced polymer. It was found that the 2D model is

sufficient in cases where the slabs are strengthened with uniformly distributed FRP

along the entire width of the slab. In the second model, the slabs were represented by

a three-dimensional (3D) design space with multi-layered shell elements. The second

model showed that the (3D) model is applicable to capture the complex stress state.

Perfect bond between the FRP and concrete is assumed for both two models.

Both (Limam et al., 2003, Mosallam and Mosalam, 2003) introduced a numerical

study of FRP-strengthened two-way RC slabs using a layered approach with shell

elements (i.e. the concrete, the reinforcement steel and the FRP composite as

constituent layers in the shell element). In this approach full bond was assumed

between the different layers where the debonding failure mode cannot be captured.

Comparisons of the computational model with experimental results indicated the

55

validity of the computational models in capturing the experimental results for both

the reference and the retrofitted specimens.

Enochsson (2005) studied numerically the CFRP strengthening of concrete slabs

with openings. The commercial finite element programme ABAQUS was used to

analysis this model. Concrete is modelled by eight-node brick elements with reduced

integration, steel reinforcement is represented by discrete truss elements and the

CFRP sheets as membrane elements. The interaction between CFRP and concrete is

assumed to be complete and there is no slip. Therefore, this model cannot capture the

debonding failure mode which is usually governed failure mode of slabs with

opening. A similar approach was proposed by Kim et al.(2008) who performed

numerical analysis to model two-way reinforced concrete slabs strengthened with

prestressed or nonprestressed CFRP using FEA software ANSYS (2004). In the

model, a composite solid element, eight nodes with three translational degrees of

freedom per node, was used to represent the concrete. The steel reinforcement was

modelled using three-dimensional spar elements having two nodes per element. The

unidirectional CFRP were simplified to three dimensional spar elements for

computational convenience. A full bond between materials was also assumed.

Both (Elsayed et al., 2009, Abdullah, 2011) modelled two-way concrete slabs using

3D brick elements; truss elements to model reinforcement bars and 2D shell

elements to represent the FRP laminates. The FRP/concrete interface was then

modelled using a spring element. This model was used load slip response to

represent the damage evolution behaviour. Thus, it cannot estimate the

unloading/reloading relationship in the spring element, while, it is common approach

to modelling unloading/reloading in cohesive technique. Therefore, this technique

was adopted to simulate the bonding in the current research in order to get more

accuracy in predicting the nonlinear behaviours of the strengthened slab specimens.

2.6 Review of exsiting design code approaches to FRP-concrete

bond

In design practice, the approach of limiting the tensile strain in the FRP sheets or

plates is often suggested for the most externally bonded FRP systems design codes to

prevent the debonding failure in strengthened/ retro-fitted RC members. The

56

prevalent code provisions for determining the permissible tensile strain in FRP are

described as follows.

2.6.1 ACI Code

The design approach outlined by ACI 440.2R-08 (2008) proposes a limit to address

debonding via a reduction factor (Km) to reduce the ultimate strain in FRP ( ) in

the static case (see Equation (2.27)).

fumfek

(2.27)

where m

k should not exceed 0.90 and is defined as follows:

(2.28)

In Equation (2.28), (n) represents the number of FRP plate layers; (Ef ) is tensile

modulus of elasticity of FRP in (MPa), (tf )is the nominal thickness of one ply of

FRP (mm) and fu) is the ultimate rupture strain of FRP (mm/mm). The computation

of the reduction factor (km) as suggested by ACI440.2R-02 (Equation (2.28)) was

based on a combination of general investigation and engineering experience on FRP

bonded system design. Equation (2.28) recognizes that the severity of the strain

limitation increases with an increase in the stiffness of the FRP plates. In addition,

there is still no accurate method to estimate bond failure due to fatigue. For example,

ACI 440.2R-02, takes account of fatigue on the FRP composite behaviour by

imposing stress limits of 0.2, 0.3 and 0.55 times the ultimate strength for Glass,

Aramid and Carbon FRP, respectively. This limitation does not address degradation

of the bond which may be induced by cyclic loading. The anchorage length relies on

the type of flexural member and for simply supported members the FRP plate have

to terminate a distance (d) past the point along the span corresponding to the

cracking moment. For continuous members, the FRP plate should be extended (d/2)

or 150 mm beyond the inflection point where there is zero moment resulting from

factored load.

000,180for 9.0)000,90

(60

1

000,180for 9.0)000,360

1(60

1

ff

fffu

ff

ff

fu

m

tnEtnE

tnEtnE

k

57

2.6.2 CEB-FIB Bulletin No.14

FIB (2001)presents three alternative approaches to mitigate debonding failure. The

first approach is restricting the ultimate tensile strain by limiting the maximum

allowable axial load in the FRP sheets or plates and anchorage length. FIB (2001)

recommendations go on to acknowledge that “A global strain limit may not be

suitable to represent the whole range of applications”. Therefore the strain limitation

in some cases could lead to a non-economical use of the FRP externally bonded

reinforcement, especially when strengthening large spans”

(2.29)

(2.30)

Where = 0.9, = 1, is the geometry factor relies on the width of FRP sheets and

RC beam, and in Equation (2.29) and Equation (2.30), respectively, obtained

through calibration of test results. The second approach calculates the maximum

possible increase in tensile stress within FRP sheets or plates. This approach presents

the bond stresses between two subsequent flexural cracks which are obtained by

critical crack pattern. The allowable tensile strain and anchorage length equations

derived from this approach is that

(2.31)

(2.32)

Where, and in Equation (2.31) and Equation (2.32) are 0.23 and 1.44,

respectively. The last approach assumes that no additional limitation should apply on

the FRP tensile strain if the flexural cracks only produce stable micro-cracking at the

FRP-concrete interface, which will not cause bond failure. This latter approach is

deemed very complex to derive allowable tensile strain equations for FRP sheets or

plates. Therefore, it is not appropriate for engineering applications.

58

2.6.3 Concrete Society Technical Report 55 (TR55)

The United Kingdom’s Concrete Society, (2012) the technical report 55 (TR55) –

Design Guidance for Strengthening Concrete Structures Using Fibre Composite

Materials– addresses the potential for debonding failures of externally bonded

systems by presenting an approach which is similar to the first approach of CEB-FIB

Bulletin No.14 (i.e. restricting the ultimate tensile strain by limiting the maximum

ultimate bond force (TK,max) in the FRP sheets or plates and the corresponding

maximum anchorage length(lb,max) ). Figure 2-10 illustrates the relationship between

the characteristic bond failure force with anchorage length. It is clear from this figure

that there is an optimal anchorage length, above which no increase in the force is

transferred between concrete and FRP.

Figure 2- 10: Characteristic bond failure force vs Anchorage length. Concrete

Society (2012)

The allowable tensile strain in FRP sheets or plates and the corresponding anchorage

length can be calculated using the following expressions:

(2.33)

(2.34)

Anchorage length

Char

acte

rist

ic b

ond f

ailu

re

forc

e

TK,max

lb,max

59

2.6.4 CNR- DT202

CNR-DT202 (2005)issued by the Italian National Research Council (Guidelines for

The Design and Construction of Externally Bonded FRP Systems for Strengthening

Existing Structures), proposes a simplified approach which depends on the fracture

energy concept to estimate the allowable stress level. However, the CNR-DT202

recommendations recognise that “no accurate and reliable model (such as the S-N

curve) is currently available for the evaluation of the fatigue resistance of the

adhesive joint” CNR-DT202 (2005). If no experimental data on the fatigue resistance

are available, the fatigue limit can be assumed, approximately, equal to 20 - 30 % of

the static failure strength” CNR-DT200 (2004)proposes the allowable tensile strain

in FRP sheets or plates and the corresponding anchorage length to address sheets or

plates end debonding in static case

(2.35)

(2.36)

where, is the partial factor for concrete and is the partial factor for FRP

ranges between (1.2-1.5).

2.6.5 JSCE

The JSCE guide published by the Japanese Society of Civil Engineers (JSCE(2001))

–Recommendation for Upgrading of Concrete Structures with Use of Continuous

Fibre sheets- addresses the interfacial peeling fatigue failure between the continuous

fibre sheet and concrete. This is based on limiting the tensile stress acting on the

fibre sheets or plates. From this concept the debonding strain equation is driven (See

Equation (2.37)). It also recommends a reduction factor (µ) on the interfacial fracture

energy Gf subjected to fatigue loading which is equal (0.7) to mitigate the debonding

failure. However, JSCE goes on to acknowledge that “Methods for accurate

calculation of the flexural capacity fatigue resistance of members upgraded with

continuous fibre sheets have not yet been established”. As well as this, the Gf which

accounts for several factors is solely determined by experimental results, which may

increase the complexity and reduce accuracy of the design process.

60

(2.37)

Table 2- 3: Design code approaches for determining the effective strain in the FRP

laminate and anchorage length.

Code Effective strain Anchorage length

ACI fumfe

k

for simply supported member

FIB1

FIB2

TR55

CNR

JSCE

-

Based on the above review of design practice, it can be concluded that the interface

fatigue behaviour between FRP composite and concrete substrates is still poorly

understood with the design code provisions giving fairly rudimentary

approximations. Further research studies are clearly necessary. The objectives of this

study are to investigate the influences of a wide range of design parameters on the

fatigue failure condition at the CFRP composite and concrete interface. The

investigated parameters include the FRP plate to concrete substrate width ratio, the

61

concrete compressive strength, bond length and the CFRP composite plate stiffness.

The simulation results will then be used to develop an alternative analytical method

to calculate the debonding strain and affective length for CFRP plate bond to

concrete and subject to single shear.

2.7 Originality of research

In this chapter, the review of previous studies have been presented and discussed in

order to identify the gaps in knowledge that are summarized as follows:

1. No study was found to simulate the one-way slab strengthening with FRP

composite under fatigue loading

2. No experimental investigation of two-way slabs with or without openings under

fatigue loading has been done yet.

3. Some of the finite element models used to simulate slabs strengthened with FRP

composites assume full bond between the FRP composite and concrete.

However, other studies took into consideration the actual performance of

adhesive layer in monotonic conditions only.

4. The experimental study of the interface behaviour between FRP composite and

concrete substrates as represented by single shear tests under monotonic loading

is mostly utilized in order to find the bond-slip curve and the ultimate load

carrying capacity of adhesive bond.

5. Very little published research dealing with the interface behaviour between FRP

composite and concrete substrates under fatigue loading exist. In view of this,

practical design equations to address the bonding failure are based on monotonic

loading

6. There is no accurate fatigue life prediction of the interface failure between the

FRP composite and concrete substrate.

62

2.8 Summary

The researcher has confirmed that FRP composites are effective for strengthening a

wide variety of concrete structural members. To date, no work has been performed

on the behaviour of strengthened two-way slabs with opening under cyclic loading.

Furthermore, there were few numerical and experimental studies done on the

FRP/concrete interfacial behaviour under cyclic loading. The aim of this study is to

investigate numerically as well as experimentally (on strengthened slabs with or

without opening) the influence of cyclic loading. Furthermore, the interface

behaviour between the CFRP and concrete substrate under monotonic and cyclic is

investigated experimentally by considering various parameters; i.e., CFRP type,

CFRP thickness, load cycle amplitude and concrete strength. Thus, interfacial post-

fatigue models which describe the interface behaviour were introduced and

implemented numerically to assess the existing design approaches for predicting the

effective tensile strain of the CFRP at debonding initiation. These models are

exploited in finite element analyses of strengthened one-way slabs as well as

strengthened two-way slabs.

Currently, most numerical simulations to date of strengthened slabs usually

represented the FRP/concrete interface either with full bond or using a spring

element as an interface element. In this Ph.D. work, a cohesive technique has been

used to model FRP/concrete interface in a nonlinear finite analysis of slabs under

cyclic loading. Appropriate bond- slip models for the interface are employed for a

better understanding of the debonding phenomenon and to capture the realistic

failure modes.

63

Chapter Three

Static and Cyclic Experimental Investigation of


3.1 Introduction

In a FRP strengthened reinforced concrete structure, the bond interface between the

concrete and FRP is relatively weak compared with the constituent materials. In

addition, fatigue increases this weakness due to repeatedly applied loads. Therefore,

it is necessary to understand and quantify the influence of load amplitude as well as

FRP stiffness on the fatigue life of the bonding system. This chapter reports the

results of an experimental investigation into the static and fatigue behaviour of the

interfacial bond between (CFRP) composite and the concrete substrate. Twenty four

single-shear pull-out tests with two different types of CFRP and different composite

plate thicknesses have been carried out. Four additional specimens were tested using

different concrete compressive strengths for the sake of comparison. Modes of

failure, load- slip relationships, strain profiles of CFRP, interfacial shear stress

distributions and interfacial bond stress- slip for monotonic, fatigue and post-fatigue

loading have been obtained. The experimental results were used to examine the

CFRP stiffness-fatigue life relationship and CFRP stiffness level – debonding strain

relationship.

3.2 Experimental programme

Twenty four single shear pull-out tests were conducted by changing the following

three experimental variables: (1) two types of CFRP composite (T700, M46J); (2)

CFRP plate thickness which ranged between 1 mm to 0.15 mm; (3) loading

hysteresis (static (monotonic), fatigue and fatigue following static). The

experimental programme consisted of four groups: the first group tested six

specimens subjected to monotonic loading with a loading rate of 0.0005 mm/s; the

second and third groups tested six specimens each subjected to fatigue loading at a

64

frequency of 1 Hz with loading ranges of (70%-15%) and (80%-15%) of the ultimate

load obtained from monotonic loading respectively; the fourth group tested six

specimens subjected to fatigue loading with a loading range of 70% -15% at a

frequency of 1 Hz until a slip of 0.4 mm was reached followed by monotonic loading

at rate of 0.0005 mm/s until failure. Also, four additional specimens were tested

using different concrete compressive strengths for the sake of comparison. Table 3-1

summarises the experimental programme.

Table 3- 1: Experimental programme

Test Type Static

(Monotonic)

Fatigue

(70% -15%)

Pult*.

Fatigue

(80% -15%)

Pult.

(Post-fatigue

Test)

[(70% -15%)

Pult*. +

Monotonic]

Loading Rate mm/s

0.0005

1 Hz

1 Hz

1 Hz+0.0005

CFRP

Type

CFRP

Thickness

(mm)

Concrete

compressive

strength

(MPa)

Specimen ID

Specimen ID

Specimen ID

Specimen ID

T700

1 52.8 M2 F2 F9 P-F2

0.3 52.8 M4 F4 F11 P-F4

0.2 52.8 M5 F5 F12 P-F5

0.3 22.6 M7

F7

F14

P-F7

M46J

1 52.8 M1 F1 F8 P-F1

0.4 52.8 M3 F3 F10 P-F3

0.15 52.8 M6 F6 F13 P-F6

* Pult.: ultimate load capacity in monotonic loading.

3.3 Details of test specimens

Figure 3-1 shows the single shear test arrangement. In all tests, the CFRP composite

plate was 500 mm in length and 50 mm in width. The bonded length was 300 mm.

The plain concrete substrate had dimensions of 150 x 200 x 500 mm. A notch of 40

mm was introduced at the interface between the CFRP plate and the concrete by

leaving an un-bonded area of the CFRP plate near to the top edge of the concrete

substrate (Figure 3-1(a)) to facilitate crack growth and to avoid undesirable concrete

failure. Two types of CFRP were used (T700 and M46J). The CFRP plates were

provided by (Reverie Ltd., 2014).

65

Figure 3- 1: Test arrangement

3.4 Test set-up

Figure 3-2 shows the test set-up. All specimens were tested by applying a tensile

force to the loaded end of the CFRP composite plate. The concrete substrate facing

was restricted in the same direction of loading to prevent it from moving so that a

direct shear force was applied at the CFRP-to-concrete interface. The specimen was

inserted into a conventional loading steel rig for single-shear pull-out test. This rig

consisted of three plates (bottom plate, top plate and spacer plate). The bottom plate

CFRP plate length = 500 mm

50 mm 70 mm 70 mm 70 mm

Bonded length = 300 mm

(c) Strain gauges

detail

(a) Front view (b) Side view

66

was securely mounted to the bottom crosshead of a 100 kN capacity hydraulic

testing machine with 12 mm thick steel plates and four 12.5 mm diameter threaded

steel at the corners of the bottom and top steel plates. As can be seen from (Figure 3-

1(b)), an additional plate, the spacer plate, was used to separate the concrete

substrate from the rig top plate, so as to allow shearing fracture (i.e. when shear

stress in the concrete exceeds its shear strength) through the concrete. The loaded

end of the CFRP composite plate was clamped in a grip at the top of the crosshead of

the hydraulic testing machine. The current set-up is similar to that adopted by other

researchers such as (Bizindavyi and Neale, 1999, Carloni et al., 2012)

Figure 3- 2: Test setup

Lower

crosshead

Upper

crosshead

Testing

specimen

Load cell

Hydraulic testing machine

67

3.4.1 Surface preparation and bonding process

Surface preparation has an effect on bond behaviour. A mechanically sound and

clean surface is required prior to adhering the CFRP composite plate in order to

achieve full bond with the plain concrete substrate. To achieve this, the concrete

surface was first ground with a surface grinder and then cleaned to remove dust and

loose particles by vacuum cleaner. During preparation of the specimens, the adhesive

layer was placed to both the concrete and CFRP surfaces with uniform thickness of

1-1.5 mm within its pot life (cure time). The adhesive thickness range achieved in

testing is in-line with the adhesive thickness range suggested by The UK’s Concrete

Society Technical Report 55 (Concrete Society (2012)). This adhesive layer was

made of approximately 2/3 Epoxy resin and 1/3 Epoxy hardener which was provided

by Weber Building Solution (2014). The physical properties of the bonding adhesive

are listed in Table 3-2. The CFRP plate was then applied to the glued concrete

surface and kept in place with weight to ensure there was no air voids and to squeeze

the glued components from both sides of the plate edges. Figure 3-3 shows the

procedure of grinding and applying the adhesive layer on concrete surface.

Figure 3- 3: Bonding CFRP Plate to concrete substrate (a) grind the concrete surface

with a surface grinder, (b) applying adhesive layer to the concrete

(a) (b)

68

Table 3- 2: Physical properties of the bonding adhesive (Weber Building Solution

(2014)).

Colour White, transparent

Density 1.3 kg/litre

Application viscosity 650 mPa s

Shear strength* ≥12 N/mm2

* BSI (2004).

3.5 Instrumentation and testing procedure

External instrumentations were placed on all test specimens. For the monotonic tests,

five strain gauges were mounted along the bonded length of the CFRP plate (Figure

3-1(c)) to measure the strain; and linear potentiometers (pots) were used to measure

slip. For the post-fatigue tests, the same instrumentations were used during the

monotonic loading phase. In addition, linear variable differential transducers

(LVDTs) were used to measure slip in the fatigue loading phase. Only LVDTs were

used in the fatigue tests. The strain gauges utilized for CFRP composite plates were

foil-type, three-wired temperature-compensating, with a resistance of 120 ohm,

gauge length of 6 mm and base material dimensions of 3.4×10 mm. They were

installed at the centre line of the surface of the composite plate in the fibre direction.

The strain gauges were covered by specialized silicon to protect them from any

external connection or damage.The data was recorded every 5 s. by the data

acquisition system. The fatigue loading was applied under load control at a

frequency of 1 Hz. The cyclic reading data was saved at every 50 cycles. All the

tested data were monitored graphically in real-time and were collected digitally by

the laboratory computer.

3.6 Material testing

3.6.1 Concrete

The concrete mix for the twenty four specimens was designed to give a 28-day cube

compressive strength of 35 MPa. Four concrete substrates were designed to achieve

an average compressive strength of 24 MPa after 28 days. The maximum crushed

aggregate size was 10 mm and the cement used was Ordinary Portland cement

69

content. Three concrete cylinders and three concrete cubes measuring 100 x 200

mm and 100 x 100 x 100 mm, respectively, were cast for subsequent compressive

and tensile strength testing for each of the eight concrete substrates. For the twenty

four concrete substrates, the average measured cube compressive strength and the

mean tensile strength from the standard spilt tensile test on the day of testing was

52.8 N/mm2 and 4.5 N/mm

2 with a standard deviation of 2.4 N/mm

2 and 0.43

N/mm2, respectively. For four additional lower strength concrete substrates, the

average measured cube compressive strength was 22.6 N/mm2

with a standard

deviation of 0.55 N/mm2 and the mean tensile strength from the standard spilt tensile

test was 3.02 N/mm2 with a standard deviation of 0.37 N/mm

2 on the day of single

shear pull-out test. Table 3-3 presents the mix proportions to produce 1 m3 of the

concrete, the target 28 day cube strengths and the measured cube strength on the

actual day of testing which varied from 28 to 90 days.

Table 3- 3: Concrete mix proportions (for 1m3 concrete).

3.6.2 CFRP composite plate

The CFRP plates (T700 UD and M46J UD) used in the single shear pull-out tests

were provided by Reverie Ltd. (2014). This type of CFRP product is high

performance as well as having high tensile strength. To establish the mechanical

properties, tensile tests on three specimens for each type of CFRP plate as well as

thickness were conducted. Both load and tensile strain were recorded during the test

to evaluate the ultimate strain and modulus of elasticity (see Table 3-4). Aluminium

plates were applied to both sides of the CFRP plate at the grips of the tension

machine (see figure 3-4) to avoid damage that may occur on the CFRP plate due to

transverse pressure of the grips.

Target 28 day

compressive

strength(MPa)

compressive

strength at

time of test

(MPa)

Cement

(kg)

Water

(kg or litres)

Fine aggregate

(kg)

Coarse

aggregate (kg)

35 52.8 450 250 580 1078

24 22.6 389 230 651 1110

70

Figure 3- 4: Aluminium end-tabs at the grips

Figure 3-5 shows that the stress-strain relationships are always linear up to fracture

failure. For the CFRP T700 composite plate, the mean modulus of elasticity was

127.2 GPa with a standard deviation of 11.7 GPa and mean tensile strength was

2160.4 MPa with a standard deviation of 166 MPa. The CFRP M46J composite plate

had a mean Young’s modulus of 229.6 GPa with a standard deviation of 31.6 GPa, a

mean tensile strength in the longitudinal direction of 1639.2 MPa with a standard

deviation of 108.3 MPa. Figure 3-6 shows typical tension rupture of CFRP plates.

Figure 3- 5: Stress-strain curve for the 0.15 mm M46J CFRP plate

71

Figure 3- 6: Rupture failure of a CFRP plate in tension

3.7 Test results and discussion

3.7.1 Failure modes

Figure 3-7 shows the three failure modes observed during the monotonic and post-

fatigue tests, (a) Bond failure in the interface between the concrete and the adhesive

layer where there was little concrete attached to the FRP strip after failure( denoted

as C-S-I), (b) CFRP composite plate rupture ( denoted as P-R) and (c) concrete

shearing beneath the adhesive layer in which a thin layer of concrete was attached to

the FRP strip after separation (denoted as C-S). All the specimens that failed by

CFRP rupture had comparatively thin CFRP plates. This failure mode started with

crack initiation between the CFRP and concrete surface followed by crack

propagation in the CFRP until rupture. The third failure mode was more dominant

than the other two failure modes. This type of failure commenced with visible cracks

in the concrete at the loaded end of the concrete substrate and then the crack

propagated towards the far end of the CFRP composite plate. Three specimens

experienced adhesive failure (first failure mode). This may have been the result of

inadequate surface preparation at the beginning of the test series, a problem duly

72

rectified in the subsequent samples. The fatigue tests always displayed concrete

shearing beneath the adhesive layer; due to susceptibility of the concrete to fatigue

failure at load amplitudes far lower than those that would cause the CFRP plate to

rupture. Table (3-4) lists the failure modes for all the tested specimens.

Figure 3- 7: Failure modes (a) Bond failure in the interfaces between concrete and

adhesive layer, (b) CFRP composite plate rupture and (c) Concrete shearing beneath

adhesive layer

73

Table 3- 4: Monotonic and post-fatigue test failure loads and modes

* Compressive strength of the concrete substrate was (22.6) MPa

P-R: CFRP composite plate rupture, C-S: Concrete shearing beneath the adhesive layer, C-S-I: Bond failure in the interface between

concrete and adhesive layer

ID Test Type

CFRP Elastic

Modulus

GPa

CFRP

Thickness

(mm)

CFRP

Stiffness

(kN/mm)

CFRP

Ultimate

Strain

(Microstrain)

Test

Failure

Mode

Number

of cycles

N

N/Nf Debonding

Strain

(Microstrain)

Ultimate

Load

(kN)

M1 Monotonic 203.59 1 203.59 7810 C-S-I - - 3926.47 35.32

M2 Monotonic 114.90 1 114.9 20130 C-S-I - - 4154.21 25.52

M3 Monotonic 264.86 0.4 105.94 6414 C-S - - 5395.91 22.01

M4 Monotonic 128.46 0.3 38.53 18168 C-S - - 8064.63 14.33

M5 Monotonic 138.35 0.2 27.67 17660 C-S - - 9213.24 12

M6 Monotonic 220.60 0.15 33 7980 C-S&P-R - - 7988.69 13.14

M7* Monotonic 128.46 0.3 38.53 18168 C-S - - 6489.64 11.71

P-F1 Post-fatigue 203.59 1 203.59 7810 C-S-I 1485 0.6 2662 25.62

P-F2 Post-fatigue 114.90 1 114.93 20130 C-S 3750 0.344 3224.82 20.16

P-F3 Post-fatigue 264.86 0.4 105.94 6414 C-S 4150 0.275 4134.91 16.41

P-F4 Post-fatigue 128.46 0.3 38.53 18168 C-S 5600 0.268 6729 11.73

P-F5 Post-fatigue 138.35 0.2 27.67 17660 C-S 9900 0.319 8361 10.44

P-F6 Post-fatigue 220.60 0.15 33 7980 C-S 7800 0.398 7303 10.92

P-F7* Post-fatigue 128.46 0.3 38.53 18168 C-S 3900 0.253 5795.32 9.97

74

3.7.2 Load- slip behaviour

The behaviour of the bond between the CFRP plate and the concrete substrate can be

described by the load-slip relationship. The following describes the experimental

load-slip relationship for each of the loading regimes adopted.

3.7.2.1 Monotonic tests

Figure 3-8 presents the recorded load-relative slip relationships for the monotonic

single shear pull out tests. The relative slip refers to the relative movement of point

(A) on the concrete substrate and (B) on the CFRP plate shown as in Figure 3-1 (a).

It can be noted that all the specimens have similar load –slip curves: an initial linear

relationship, followed by a nonlinear portion before maintaining the maximum load

with increasing slip. This load-slip relationship is typical of monotonic tests.

Furthermore, specimens with lower CFRP stiffness also have lower ultimate load,

but higher slip after reaching the maximum strength. This is a result of the shorter

active bond zone required to transfer tension from the CFRP plate to the concrete

surface at lower CFRP plate stiffness based on the analytical model of (Chen and

Teng (2001)). A shorter active bond zone also leads to a longer slip process, hence

the increased slip after reaching the maximum strength. Higher ductility is desirable

because it avoids sudden failure.

Figure 3- 8: Monotonic load-slip curves

0

10

20

30

40

0 0.5 1 1.5 2

Load

(KN

)

Slip (mm)

M1 M2 M3 M4 M5 M6

75

3.7.2.2 Fatigue tests

Figure 3-9 (a and b) presents the experimental load-slip relationships for two

specimens with the same CFRP plate thickness of 0.3 mm, but different applied

fatigue load ranges of 0.7Pult.-0.15Pult. (Specimen F4) and 0.8Pult.-0.15Pult. (Specimen

F11), respectively, at 1 Hz frequency, where Pult. is the ultimate load from the

corresponding monotonic test. In general, the ultimate slip of the specimen during

the fatigue test was lower than from the monotonic test. As the number of cycles

increased, the separation between the CFRP plate and the concrete substrate became

visible to the eye along the side edges of the CFRP composite plates (Figure 3-

10).For high stiffness CFRP, failure occurred at or just after crack initiation, while

for low stiffness CFRP failure occurred after significant crack propagation. The

reloading path did not coincide with the unloading path due to fracture energy

release during the load cycle. The amount of energy released during one cycle did

not change significantly, indicating steady fracture energy release rate. It is also

noticeable that cyclic loading caused minor, but steady reduction in the bond secant

stiffness (i.e. the upper load versus slip in a specific cycle). As a result, cumulative

steady fracture energy release which further led to reductions in both the ultimate

load and the debonding strain of the specimen. The reduction in secant bond stiffness

was much more modest in specimens with higher CFRP plate thicknesses (see

Figure3-11).

76


cycle number)

Figure 3- 10: Crack propagation

(b) F11

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Loa

d (

KN

)

Slip (mm)

[1] [1600] [3200] [4800] [6400] [12600

]

[9600] [8000] [11200]

(a) F4

[1] [2800] [5600] [8400] [11200] [14000]

[16000] [19600] [20839]

Visible crack

77


cycle number)

The results in Table 3-5 show that using CFRP plate with lower stiffness gave a

higher fatigue life under the same load amplitude range. Furthermore, the load

amplitude range had a significant effect on the fatigue life. Figure 3-12 plots the

CFRP plate stiffness versus fatigue life Nf relationship for both loading ranges

0.8Pult.-0.15Pult. and 0.7Pult.-0.15Pult. with coefficient of correlation 0.8595 and

0.8987, respectively.

[15050] [1] [1000] [3000] [5000] [7000] [9000] [11000] [13000]

(a) F3

(b) F10

[5100] [1] [500] [1000] [1500] [2000] [2500] [3000] [3500] [4000] [4500]

78

Table 3- 5: Fatigue test results

ID

Fatigue Test

Thickness

(mm)

Elastic

modulus

(GPa)

Stiffness

(kN/mm)

Failure

mode

Fatigue

life (Nf)

F1 (0.7-0.15) Pult. 1 203.59 203.6 C-S 2475

F2 (0.7-0.15) Pult. 1 114.9 114.9 C-S 10900

F3 (0.7-0.15) Pult. 0.4 264.86 105.9 C-S 15050

F4 (0.7-0.15) Pult. 0.3 128.46 38.5 C-S 20839

F5 (0.7-0.15) Pult. 0.2 138.35 27.6 C-S 31000

F6 (0.7-0.15) Pult. 0.15 220.6 33 C-S 19550

F7* (0.7-0.15) Pult. 0.3 128.4 38.5 C-S 15400

F8 (0.8-0.15) Pult. 1 203.59 203.6 C-S 450

F9 (0.8-0.15) Pult. 1 114.9 114.9 C-S 2900

F10 (0.8-0.15) Pult. 0.4 264.86 105.9 C-S 5100

F11 (0.8-0.15) Pult. 0.3 128.46 38.5 C-S 12600

F12 (0.8-0.15) Pult. 0.2 138.35 27.6 C-S 19200

F13 (0.8-0.15) Pult. 0.15 220.6 33 C-S 9050

F14* (0.8-0.15) Pult. 0.3 128.46 38.5 C-S 9600

* Compressive strength of the concrete substrate was (22.6) MPa

Figure 3- 12: CFRP stiffness- fatigue life relationship

0

50

100

150

200

250

0 5000 10000 15000 20000 25000 30000 35000

N.E

f.tf

(K

N/m

m)

fatigue life, Nf

Load range: 0.7Pult.-0.15Pult. Load range: 0.8Pult.-0.15Pult.

79

3.7.2.3 Post-fatigue tests

Figure 3-13 shows the load-slip relationships from the post-fatigue tests (see Table

3-1 for details of the loading sequence). Comparing the results in Figure 3-8 for the

monotonic tests, it can be seen that after cyclic loading, the ultimate load capacity

was reduced for all six specimens. The ultimate load capacity reduction ranged from

27.5% for the 1 mm M46J CFRP plate to 13.3% for the 0.2 mm T700 CFRP plate.

This reflects the steady fracture energy release under cyclic loading prior to

monotonic loading to failure. These results are contradictory to the conclusions of

Carloni et al. (2012) who reported that the ultimate load of their composite system

did not change much after applying cyclic loading between 15% and 80% until a

threshold global slip equal to 0.4 mm was reached. This is due to the fact they tested

in the post-fatigue situation only a very limited number of specimens (precisely one

specimen) for a single thickness of 0.167 mm. The effect of this small thickness on

the ultimate bond strength reduction and the fracture energy degradation is

insignificant. As an indication of the level of system utilisation, a comparison of the

number of cycles (N) required to achieve 0.4 mm slip in the post-fatigue (P-series)

tests against the number of cycles at failure (Nf) in the corresponding fatigue (F-

series) tests is given in Table3-4. Across the number of specimens, the N/Nf ratio

ranged from a minimum of 0.25 to a maximum 0.6.

80

Figure 3- 13: Post-fatigue load-slip responses

P-F1 P-F2

0

3

6

9

12

15

18

21

0 0.2 0.4 0.6 0.8 1 1.2

Lo

ad

(K

N)

Slip(mm)

pre-fatigue post-fatigue

P-F4

0

3

6

9

12

15

0 0.5 1 1.5 2 2.5

Lo

ad

(K

N)

Slip (mm)

pre-fatigue post-fatigue

P-F3

P-F6 P-F5

81

3.7.3 Tensile strain profiles


Figure 3-14 presents the recorded strain profile curves along the CFRP plate for the

six monotonic test specimens at 5 different load levels. The profiles are nonlinear at

low load levels, but attained a linear shape for a period at higher load levels.

Debonding (when the strain reached the maximum) marked the start of the linear

strain shape. Figure 3-14 shows that the CFRP composite stiffness had a pronounced

effect on the debonding strain. The debonding strain ranged from 3926.5 microstrain

for the 1 mm M46J CFRP plate (M1) to 9213.2 microstrain for 0.2 mm T700 CFRP

plate (M5). The M46J specimen with a CFRP plate thickness of 0.15 mm shows

nonlinear behaviour through all loading levels because the failure mode of this

specimen was rupture in the CFRP plate at the beginning of the debonding process.


Figure 3-15 presents the strain profiles for the post-fatigue tests. Pre-failure cyclic

loading had significant effects on the strain distributions in the CFRP composite

plate during the monotonic loading phase. The reduction in the maximum strain,

compared to the results in Figure 3-14 for monotonic loading, was caused by fracture

energy release. Application of a pre-failure cyclic load caused reduction in the

debonding strain ranging from 35% for the 1 mm M46J CFRP plate (M1) to 5.6%

for the 0.2 mm T700 CFRP plate (M5). Moreover, the strain profiles indicate a

steady level of debonding strain in the initial 50 mm of the bonded length in the

earlier stages of loading. This is due to crack initiation induced by the previous

cyclic loading.

82

Figure 3- 14: Strain distributions along CFRP plate in monotonic tests

M1

M2

M4 M3

M5 M6

83

Figure 3- 15: Strain distributions along CFRP plate in post-fatigue tests

P-F2 P-F1

P-F4 P-F3

P-F6 P-F5

84

3.7.4 Interfacial shear stress distributions

Based on the strain distribution on the bonded length of the CFRP composite plate,

recorded from the tested specimen in the monotonic as well as the post-fatigue tests,

the mean experimental shear stress between the two strain gauges mounted on the

centre line of the CFRP plate were calculated using the following relationship

(3.1)

where, is the distance between strain gauge (i) and (i-1); and are the strain

in the CFRP plate at strain gauge (i) and (i-1); and and are the Young’s

modulus and thickness of the CFRP plate respectively. It is clear from Equation (3.1)

that the shear stress mainly depends on the CFRP plate stiffness. However, both the

adhesive and concrete stiffness also implicitly affect the estimate of shear stress

given by Equation 3.1.


Figure 3-16 shows the evolutions of the mean interfacial shear stress at four different

locations [(0-50) mm, (50-120) mm, (120-190) mm, (190-260) mm] (see Figure 3-1

(c)) as the relative load level (P/Pult) is increased. Herein, (P) denotes the applied

load level and (Pult) is the ultimate load. This figure is for test specimen M4 and is

typical of other test specimens. In the first region [(0-50) mm] of the bonded CFRP

plate, a gradual increase of the shear stress was observed until reaching a value of

8.2 MPa which represents the bond strength. As the relative load level was increased

further, the shear stress decreased abruptly and eventually reached zero.

Simultaneously, increases in the mean shear stress in the adjacent region started to

occur. This explains the process of debonding during different stages of loading.

This phenomenon was observed progressively from one region to another until total

failure of the bond interface occurred.

85

Figure 3- 16: Shear stress as function of relative load level (M4)


Figure 3-17 shows the corresponding mean shear stress distribution- relative load

level relationships at different regions along the bonded CFRP plate for all the six

post-fatigue tests. Due to debonding from the concrete substrate resulting from the

previous cyclic loading, the shear stress for the first region [(0-50)] for most of test

specimens (P-F2, P-F4, P-F5) are equal to zero for the whole static loading stage.

Furthermore, for the 0.15 mm M46J test specimen (P-F6) the last region [(190-260)

mm] of the specimen has zero mean shear stress due to fracture failure mode of this

specimen.

Figure 3-17 indicates that the peak mean shear stress varied from one specimen to

another when the CFRP stiffness is 27.67 kN/mm (specimen P-F5), the mean shear

stress is 6.3 MPa and there is minor peak shear stress variations found between the

four different regions. When the CFRP stiffness is increased to 203.592 kN/mm

(specimen P-F1), the peak shear stress decreases to 2.75 MPa. The peak shear stress

progressively moved from one region to the adjacent region as the relative load level

increases until complete debonding of the interface similar to the observation from

the monotonic tests.

86

Figure 3- 17: Shear stress as a function of relative load level for the post-fatigue tests

P-F1

P-F4 P-F3

P-F6 P-F5

P-F2

87

3.7.5 Interfacial bond stress- slip model

Based on Equation (3.1), the interfacial bond stress between the first two consecutive

strain gauges in the bonded region was computed. In this section, firstly the static

results of interfacial bond stress-slip curves are compared with Chen and Teng

(2001) model that was described in Chapter 2. This model was developed based on

the fracture energy concept with rational simplification. Moreover, it is suitable to

predict bond strength for single-shear or double-shear pull tests for two failure

modes either shearing of the concrete directly beneath the bond or debonding at

adhesive-concrete interface. The experimental results of the tested specimens under

monotonic loading showed that the interfacial bond stress-slip relationship does not

vary for those six specimens that have approximately the same tensile concrete

strength (4.5 MPa). The bond –slip curves are very close to the analytical bond –slip

model proposed by Chen and Teng (2001) in terms of the maximum value of shear

stress and the slip at debonding, which underlines the capability of their model.

However, the analytical model of Chen and Teng (2001) shows a softer response

during the descending branch (i.e. between the maximum shear stress and

debonding, see Figure 3-18).

Figure 3- 18: Interfacial bond stress-slip curves for single shear pull-out test in

monotonic test

0

2

4

6

8

10

0 0.05 0.1 0.15 0.2 0.25 0.3

Shea

r St

ess

(MPa

)

Slip (mm)

M1 M2 M3 M4 M5 M6 Chen and Teng model,2001

88

Secondly, for the post-fatigue results of interfacial bond stress-slip curves are

compared with analytical interfacial bond stress-slip (i.e. M1 was chosen as

representative of the static specimens). Figure 3-19 presents the estimated interfacial

bond stress –slip relationships based on measured tensile strain profile along the

bonded CFRP plate. It can be observed that both the ultimate bond strength and

fracture energy for two different types of CFRP (T700 & M46J) is reduced with

increase in CFRP plate thickness. However, these six specimens were subjected to

cyclic loading until reaching 0.4 mm slip. This experimental observation for bond

slip curves had the same response as reported by other researchers. For example,

Turon et al.(2007) reported a decrease both stiffness as well as interfacial bond

strength of the bonding system with an increasing number of cycles. Turon Travesa

(2006) reported that the fracture energy release rate increased as fatigue loading

amplitude ratio increased.

Figure 3- 19: Interfacial bond stress-slip curves for single shear pull-out test in post-

fatigue test

Figure 3-20 shows the experimental bond –slip curve compared with the analytical

model as well as the bond-slip curve after applied cyclic loading until reaching 0.4

mm slip to the bond system in the concrete with compressive strength equal 22.6

MPa and CFRP stiffness 38.538 kN/mm. The fracture energy can be estimated by

measuring the area under the bond-slip curve.

Based on this calculation method, the ultimate bond strength reduction and fracture

energy degradation ratios are 0.48 (from a value of 5.2 to 2.7) and 0.28 (from a value

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4

Sh

ea

r S

tre

ss (

MP

a)

Slip (mm)

Chen and Teng model,2001 P-F1 P-F3 P-F6

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4

Sh

ea

r S

tre

ss (

MP

a)

Slip (mm)

Chen and Teng model,2001 P-F2 P-F4 P-F5

89

of 0.71 to 0.51), respectively. These reduction values are approximately equal to the

reductions when concrete compressive strength is equal to 52.8 MPa and the CFRP

stiffness is 38.53 kN/mm, being 0.42 (from 8.3 to 4.8) and 0.21 (from 0.9 to 0.71).

Therefore, it can be said both the ultimate bond strength reduction and fracture

energy reduction due to cyclic loading is dependent on the stiffness of the CFRP

plate in the bond system, not the concrete strength, for the range of the concrete

strength tested.

Figure 3- 20: Interfacial bond stress-slip curves for single shear pull-out test (a)

fc=22.6 MPa (b) fc= 52.8 MPa

The relationship between the CFRP plate stiffness with the ultimate bond strength

reduction and the fracture energy degradation are shown in Figure 3-21 (a) and 3-21

(b), respectively. The fracture energy degradation is calculated as a difference

between the monotonic and post-fatigue fracture energy. Also, the fracture energy

was estimated by measuring the area under the bond-slip curve. Numerical

simulations were implemented to validate the current interfacial bond stress- slip

model, as will be discussed in Chapter 4.

(a) (b)

0

1

2

3

4

5

6

7

8

9

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Sh

ea

r str

ess (

MP

a)

Slip (mm)

M4 P-F4 Chen and Teng model,2001

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5

Sh

ea

r S

tre

ss (

Mp

a)

Slip (mm)

M7* P-F7* Chen and Teng model,2001

90

Figure 3- 21: (a) Interfacial bond stress reduction CFRP stiffness relationship (b)

Fracture energy reduction CFRP stiffness relationship

3.8 Summary

In this chapter, single shear pull-out tests were undertaken to investigate the

behaviour of the bond interface between concrete and externally bonded CFRP under

different loading hysteresis (static (monotonic), fatigue and fatigue followed by

static (monotonic)). The following conclusions may be drawn:

Three different failures (CFRP rupture, concrete shearing and concrete-

adhesive interface failure) were observed in both monotonic and post-fatigue

tests while the fatigue tests exhibited one predominant type of failure, that of

concrete shearing.

The analytical model of Chen and Teng (2001) gives an accurate prediction

of the static test bond load slip relationships.

(a) (b)

91

The load amplitude ranges have been shown to have a significant effect on

fatigue life of the bonding system for the same CFRP stiffness. The reduction

in the secant bond stiffness in fatigue tests resulting from steady fracture

energy release with repeated fatigue cycles, leads to a decrease in the

ultimate load capacity as well as in debonding strain of the single shear pull-

out specimens. These reductions in both the ultimate load capacity and

debonding strain of the bonding system due to fatigue have to be considered

in practice.

The cyclic load prior to the static load caused reductions in debonding strain

ranging from 35% for the 1 mm M46J CFRP plate (M1) to 5.6% for the 0.2

mm T700 CFRP plate (M5). At the same time, the reduction in ultimate load

carrying capacity ranged from 27.5% for the 1 mm M46J CFRP plate to

13.3% for the 0.2 mm T700 CFRP plate.

The concrete compressive strength had little effect on the ultimate bond

strength and fracture energy degradation induced during fatigue loading.

These reductions are predominantly dependent on the stiffness of the CFRP

plates.

Following on from this, the suggested bond-slip model will be validated by

comparing the ABAQUS simulation results with experimental results in term

of load-slip behaviour as well as strain profile along the bonded CFRP plate

in post-fatigue tests and then it will be used for further numerical modelling

in the next chapter.

92

Chapter Four

Numerical Modelling and Validation of


4.1 Introduction

This chapter presents a detailed description of the finite element model, constructed

using ABAQUS 6.10-1, to simulate the behaviour of FRP to concrete bonded joint in

single shear pull out tests. Three dimensional elements (solid, shell, cohesive) are

used and the model takes into consideration elastic and plastic behaviour of the

materials. Three different approaches (cohesive elements, cohesive surfaces and

virtual crack closure technique (VCCT)) will be investigated for modelling the

contact and to decide which approach is the most suitable. Validation of the model

will be demonstrated by comparison against the test results in Chapter 3. Afterwards,

parametric studies will be carried out to investigate the effect of variations in bond

length, thickness of FRP, type of FRP, concrete strength and bond width ratio. The

simulation results will then be used to assess the various existing design code

approaches for predicting the FRP concrete bond behaviour. This chapter will then

propose an alternative analytical method to calculate the debonding strain and

effective length for CFRP plate bond to concrete and subject to single shear.

4.2 Simulation model using ABAQUS

4.2.1 Finite element mesh

The simulation model will be built up using the general finite element software

ABAQUS. Three different element types (solid, shell, cohesive) have been used to

model different geometry. For the solid part (i.e. concrete), it was decided to use the

three dimensional eight-node linear brick element with reduced integration and

hourglass control (C3D8R). However, several types of three-dimensional (3D)

93

continuum elements are available in ABAQUS. The reason for selecting linear brick

elments is that they can be used with contact in contrast to quadratic brick elements

which take longer to calculate the consistent nodal loads over the slave surface.

While the purpose of choosing reduced integration rather than full integration is that

full integration gives poor results due to shear locking phenomenon. This

phenomenon can be demonstrated by the realistic behaviour of the element subjected

to pure bending is shown in Figure 4-1.

Figure 4- 1: Realistic behaviour of element subjected to pure bending (ABAQUS

(2011))

The horizontal break lines distort with constant curvature and increase their length

while the vertical break lines have the same length in the deformed element. It can be

concluded that only the normal stress is non zero. Moreover, the shear stress

is zero. The finite element approximation shows realistic behaviour based on number

of integrated points of the first-order (linear) brick elements. Fully integrated linear

brick elements (C3D8) which consist of eight integration points, 2 on each side, are

subjected to pure bending and the upper and lower sides change their length but they

cannot curve, see Figure 4-2. Vertical break lines pass through integration points,

resulting in distortion and changing angle towards the horizontal break lines.

Inaccurate results can be obtained due to the shear stress generated in this type of

element subjected to pure bending. In this case more shear distortion than bending

distortion is created by the strain energy and this phenomenon is called shear

locking.

Figure 4- 2: Fully integrated linear brick elements subjected to pure bending

ABAQUS (2011)

94

Reduced integration is used in the linear solid elements to reduce the problem of

shear locking. This method has only 4 integration points, one on each side as shown

in Figure 4-3; no shear stress is generated and the vertical and horizontal break line

passing through integration points are always perpendicular to each other with

relatively fine mesh so it is similar to the real structure (Rusinowski (2005)).

Figure 4- 3: Reduced- integration linear brick elements subjected to pure bending

ABAQUS (2011)

For the CFRP plate, linear three dimensional four-node doubly curved general

purpose shell elements with reduced integration and hourglass control (S4R5) are

used (see Figure 4-4). The thickness of this type of a conventional shell element is

defined through the section properties since the nodes of a conventional shell

element are located on defined planer dimensions. Conventional shell elements are

considered more accurate in contact modelling than continuum shell elements

because they are capable of measuring strain or slip without having an effect on the

thickness of FRP composite plate. Moreover, conventional shell elements offer

superior performance in term of computational efficiency.

Figure 4- 4: Four node shell element. ABAQUS (2011)

95

A cohesive element was chosen to model adhesion between two different

components. This element was only used in the cohesive element approach which

will be described later in Section 4.3.1. The adhesive layer should be represented in a

single layer of cohesive elements through the thickness to avoid the distortion during

the debonding process. The cohesive element in three dimensional problems assumes

connectivity between two nodes or two surfaces through three components; one

normal to the interface and two parallel to it so it is capable of determining the stress

directly through the thickness (S33) and two transverse stresses (S13, S23). The

adopted cohesive element in ABAQUS is named as COH3D8 (an 8- node –three

dimensional cohesive element with three degree of freedom at each node) as shown

in Figure 4-5.

Figure 4- 5: Eight node cohesive element ABAQUS (2011)

4.2.2 Loading and boundary conditions

Figure 4-6 shows the support conditions in the single shear pull out test. The

concrete substrate facing was restricted in the X, Y, Z directions to prevent

movement in the direction of loading to simulate the real case. The width of the

CFRP composite plate at the loading end is prevented from moving in Y and Z

directions to avoid offset in the load position. A traction load is applied at the edge

of the CFRP plate (see Figure 4-6). This load is applied using the static general

method available in the ABAQUS. This method can be used to trace the entire

behaviour and non-linear collapse of the structure.

96

Figure 4- 6: Loading and boundary conditions for the single shear pull-out test.

4.3 Approaches to model delamination

ABAQUS offers three techniques to model the behaviour of adhesive joints or

interfaces in composite layers. The three approaches which are cohesive elements,

cohesive surfaces and virtual crack closure technique (VCCT) will be investigated in

the current finite element analysis and then it will be decided which approach is

more appropriate.

4.3.1 Cohesive elements approach

The first approach to study the bond interface behaviour between FRP composite

plate and concrete substrate is available in ABAQUS/standard using cohesive

elements. The top and bottom surfaces of the cohesive element have to be tied with

the concrete and CFRP plate by using tie constraint. The debonding growth occurs

along the layer of cohesive elements and without deformation into the adjacent parts.

Thus, the cohesive element approach can predict the bond behaviour from the initial

loading, to the initiation of damage and then the damage propagation. However, this

approach undergoes convergence difficulties in a solution procedure. The main

aspect of this approach is that constitutive thickness has a noticeable effect on the

interface behaviour because the nodal coordinates of the cohesive elements are

Bond Length

Concrete Substrate C3D8R Element

CFRP Composite Plate

S4R5 Element

Adhesive Layer

U: 1, 2, 3 = Translation in X, Y and Z directions respectively

Fixed Face B.C U1=U2=U3=0

Fixed Face B.C U1=U2=U3=0

Traction Load

97

calculated based on the initial thickness. Thus, if the adhesive layer is not thick and

properties such as stiffness and strength of the adhesive material are available, it may

be more appropriate to model the interface using conventional cohesive elements.

Furthermore, the cohesive constraints of cohesive elements are determined at the

material points. Therefore, the damage has to be defined as part of the material

properties.

4.3.2 Cohesive surfaces approach

ABAQUS/Standard offers an alternative approach to define adhesive joints that are

very similar to cohesive elements in terms of constitutive response. This approach is

named surface- based cohesive approach which is represented by the surface

interaction properties that are assigned to a contact pair using the finite-sliding,

node-to-surface formulation. Cohesive surface is more desirable to begin the analysis

with the surfaces just touching each other. Consequently, cohesive surfaces are never

affected by interface thickness ABAQUS (2011). So the surface-based cohesive

approach is widely used in cases in which the adhesive thickness is negligibly small.

Moreover, the cohesive constraint of cohesive surfaces is enforced at each slave

node. Therefore, to improve constraint satisfaction and gain more accurate results in

cohesive surfaces the slave surface needs to be refined as compared to the master

surface. Finally, damage in the surface based cohesive approach is always defined in

the interaction property

4.3.2.1 Linear elastic traction-separation behaviour

For both the aforementioned approaches, a traction-separation model represents the

constitutive response. This model shows initially linear elastic behaviour followed

by the initiation and evolution of damage. The elastic behaviour before the damage

initiation is written in terms of an elastic constitutive matrix which makes the

relationship between the nominal stresses to the nominal strains across the interface.

(4.1)

98

The nominal traction stress vector, t, consists of three components in 3D FE analysis

tn, ts and tt , which represent the normal to the interface plane and the two shear

traction stresses along the local first and second directions, respectively. The

nominal strains can be defined as the corresponding separations which are denoted

by δn, δs and δt divided by initial constitutive thickness as denoted by T0. The initial

constitutive thickness T0 was assumed equal to unity. Therefore, the nominal strain

components are equal to the respective components of the relative displacement.

(4.2)

4.3.2.2 Damage modelling

ABAQUS/Standard allows modelling of the initiation and evolution failure in

cohesive elements or cohesive surfaces where response is defined in terms of

traction-separation. Once the damage initiation criterion is met, damage is initiated

according to a user-defined damage evolution law. If the damage initiation criterion

is specified without a corresponding damage evolution model, ABAQUS finds the

damage initiation criterion for output purposes only and so no damage will occur on

cohesive surfaces or cohesive elements. The degradation in penalty stiffness of the

cohesive surfaces and cohesive elements occurs under application of tensile and

shear loading but does not undergo degradation under application of pure

compressive loading. ABAQUS (2011)

A. Damage initiation

Damage initiation indicates the start of degradation of the constitutive response at the

bonding joint. The procedure of degradation commences when the stresses and/or

separations at contact points satisfy particular damage initiation criteria. Several

damage initiation criteria are available such as

99

1. Maximum nominal stress criterion: when the maximum nominal stress

ratio (as explained in the function below) equals one, damage initiates. This

criterion can be represented as

(4.3)

2. Maximum nominal separation criterion: when the maximum nominal

strain ratio (as explained in the function below) equals one, damage initiates.

This criterion can be represented as

(4.4)

3. Quadratic nominal stress criterion: when a quadratic interaction function

involving the nominal stress ratios (as explained in the function below) is

equal of unity, damage initiates. This criterion can be represented as

(4.5)

4. Quadratic nominal separation criterion: when a quadratic interaction

function involving the nominal strain ratios (as explained in the function

below) is equal of unity, Damage initiates. This criterion can be represented

as

(4.6)

B. Damage evolution

Once the initiation damage criterion is reached the damage evolution law

commences. This means the rate of cohesive stiffness starts to degrade. (D) is

defined as a scalar damage variable which represents the overall damage at the

contact surfaces. It should have a value from 0 if there is no damage to 1 as the

100

element has completely lost its strength. The evolution response is defined based on

the following:

Evolution based on effective displacement

This evolution is defined by specifying the difference in the effective displacement at

complete failure , relative to the effective displacement at damage initiation

.

Three methods can be used to represent the degradation in penalty stiffness during

the damage evolution.

Linear damage evolution: For linear softening (see Figure 4-7) ABAQUS applies an

evolution of the damage variable, D, that reduces to the equation proposed by

Camanho and Dávila (2002)

(4.7)

where, is the maximum value of the effective slip attained during the loading

history in the pull-out load direction.

Figure 4- 7: Typical traction-separation response.

Separation

A

B

Unloading/ Reloading path

Traction

ko

km

101

Exponential damage evolution: For exponential softening (see Figure 4-8) ABAQUS

uses an evolution of the damage variable, D, that reduces to

(4.8)

In the expression above is a non-dimensional material parameter that defines the rate

of damage evolution


Tabular damage evolution: the damage evolution is defined directly in tabular

function which shows the difference between the effective displacement relative to

the effective displacement at initiation. The damage variable D is estimated as

shown in the (Figure 4-9) as follows;

(4.9)

Traction

Separation

A

B


Exponential damage response

K0

Km

102


Evolution based on energy

This evolution is defined by specifying the energy that is dissipated as a result of the

damage process, also called fracture energy. This was estimated by measuring the

area under the traction-separation curve. It can be specified in ABAQUS either as a

linear or an exponential softening behaviour depending on mechanical material

properties.

Linear damage evolution: for a linear softening, ABAQUS uses the damage

evolution variable that is used in linear softening based on effective displacement

(Equation 4.10). However, is determined by this expression

(4.10)

where, is the mixed-mode fracture energy, . , and

refers to the work done by the traction and its conjugate relative displacement in

the normal, the first and the second shear directions. is the effective traction at

damage initiation in the first direction.

Traction

Separation

A

B


Exponential damage response Linear damage response

K0

Km

Effective response if damage was not defined

Damage

initiation

103

Exponential damage evolution: For exponential softening ABAQUS uses an

evolution of the damage variable based on the following expression

(4.11)

In the expression above and are the effective traction and elastic energy at

damage initiation, respectively. The unloading/reloading stiffness is determined as

. The contact stress components in the normal, first and second

directions between points A and B (Figure 4-9) are affected by the damage according

to the following functions.

(4.12)

(4.13)

(4.14)

4.3.3 Virtual crack closure technique (VCCT)

The virtual crack closure technique (VCCT) is considered as a new method for

modelling the delamination between two composite layers under static and fatigue

loading. The constitutive response of this approach is based on the linear elastic

fracture mechanics by computing energy release rates to supply debonding required

when using the mixed-mode fracture criterion in three dimensional finite element

analyses. However, the virtual crack closure approach is more appropriate for brittle

fracture problems.

The surface- based cohesive approach cannot be combined with the VCCT approach.

In spite of this, the VCCT fracture criterion and cohesive elements approach can be

linked with each other in the same simulation because the cohesive elements

approach can model some features of the bonded interface like stitches, while VCCT

can model other features such as brittle failure.

The most significant advantage of Virtual Crack Closure Technique (VCCT) is that

it is capable of evaluating the debonding when a structure is subjected to fatigue

104

loading, in which case the damage to the material is called fatigue failure.

Debonding under the static and fatigue loading basically has the same micro

mechanisms and processes, which means that there is also an initiation and evolution

process of the debonding due to the fatigue loading. Carloni and Subramaniam

(2010). While, the disadvantage of the VCCT is that crack propagation problems are

numerically complex and require small time increments. Matched meshes between

the slave and master surfaces of the debonding contact pair, also add a small

clearance to the initially un-bonded portion. Nevertheless, it might cause

unnecessary severe discontinuity in iterations during the running of the programme

the crack begins to progress and leads to a convergence problem.

4.4 Sensitivity study

The numerical simulation model detailed in the previous section requires decisions

to be made for the values of numerical parameters. In order to ensure suitable

selection of these parameters, sensitivity studies have been carried out to examine

the effects of changing these values. The parameters to be decided include: effect of

delamination approaches, effect of interfacial bond stiffness, effect of damage

initiation criteria, effect of damage evolution response and effect of mesh size.

4.4.1 Description of pull out test specimen

The pull-out specimen is prepared and tested horizontally in a similar way to the

tests conducted by Yao et al.(2005). The test set up is shown in Figure 4-10 together

with the present ABAQUS model. It consists of a concrete prism (150 mm wide x

150 mm high x 350 mm long) and short length of FRP plate (250 mm length x 25

mm width x 0.165 mm thickness). The plate was then applied to the concrete prism

with 190 mm bond length beyond the edge of the concrete prism. The concrete

compressive strength is 27.7 MPa and the associated modulus of elasticity calculated

from Euro-code 2, BSI (2004) is 29865 MPa.

105

4.4.2 Finite element model

In this simulation, the concrete prism is idealised using three dimensional eight-node

linear brick element with reduced integration and hourglass control (C3D8R). while,

linear three dimensional four-node doubly curved general purpose shell elements

with reduced integration and hourglass control that account for the finite membrane

strains with five degree of freedom per node (S4R5) have been chosen to model FRP

plate.

The damage plasticity model available in ABAQUS which will be described in detail

in next chapter was used for the concrete substrate, in conjunction with the uniaxial

compression stress-strain model of BSI (2004). The stress-strain relationship of

concrete in tension was assumed to consist of a linear ascending branch with slope

equal to the modulus of elasticity of concrete and exponential descending based on

Wang and Hsu (2001).The CFRP plate was modelled as an orthotropic elastic

material. Elastic modulus in the direction of fibre was taken according to the

experimentally measured values, with the other two elastic moduli taken as 10% of

the elastic modulus in the fibre direction of fibre), while other material properties

were taken according to those given by (Reddy, 2004). The CFRP material

properties are given in Table 4-1. The adhesive material properties are summarized

in Table 4-2.

Table 4- 1: Material Properties of CFRP Plate

*: according to (Reddy, 2004)

Material Description CFRP Plate

Yao. J. et

al (2005)

T700 M46J

CFRP

Longitudinal modulus (E1), Gpa 256 114.9-

138.3

220.6-

264.8

*Transverse in-plane modulus(E2), GPa 25.6 8.273 20.684

*Transverse out-plane modulus(E3), GPa 25.6 8.273 20.684

*In- plane shear modulus (G12), GPa 6.894 4.136 6.894

*out- of-plane shear modulus (G23), GPa 4.136 3.447 4.136

*out- of-plane shear modulus(G13),GPa 6.894 4.136 6.894

*Major in -plane Passion’s ratio, ν12 0.3 0.26 0.3

*Out-of-plane Passion’s ratio, ν23 0.25 0.34 0.25

*Out-of-plane Passion’s ratio, ν13 0.25 0.26 0.25

106

Table 4- 2: Material properties of adhesive layer Interfacial bond strength in the first tangential direction ( ), MPa 6.4-2.5

*

Interfacial bond stiffness in the first tangential direction ( ), MPa/mm 300

Interfacial fracture energy (Gs), MPa/mm 0.78-0.49*

*: (Daud et al., 2015)

Figure 4- 10: Experimental set up of Yao et al. (2005) (top) and the numerical model

(bottom).

4.4.3 Interfacial bond stress and fracture energy

An earlier experimental study conducted by the authors Daud et al. (2015) already

established the post-fatigue interfacial bond stress-slip relationship, where it was

shown that both the ultimate bond strength ( ) and fracture energy (Gs) decrease as

the CFRP plate stiffness for the tested range of concrete compressive strengths (22.6

Support block

Traction load

CFRP plate (S4R5)

Adhesive layer

(COH3D8)

Fixed B.C U1=U2=U3=0

Fixed B.C U1=U2=U3=0

Concrete prism

(C3D8R)

107

MPa – 52.8 MPa) rises. The study also indicated that the sensitivity of the post-

fatigue bond stress-slip relationship to plate stiffness is greater than it is to the

concrete compressive strength. The cause of the reductions is mainly due to the

cyclic loading of each single shear pull-out test. Figure 4-11 (a) shows the

relationship between interfacial bond stress reduction (IBSR) and CFRP plate

stiffness, while Figure 4-11 (b) shows the relationship between the fracture energy

degradation (FER) and CFRP plate stiffness. The fracture energy degradation is

equivalent to the difference between the monotonic and post-fatigue fracture energy.

The estimation of the fracture energy was achieved through the measurement of the

area under the bond-slip curve. These experimental findings on the interfacial bond

stress-slip relationship were required in the cohesive surface approach to define

accurately the traction-separation based model as depicted in Figure4-7.

Consequently, the mechanical post-fatigue behaviour of the CFRP/concrete interface

is modelled as follows.

(4.15-a)

(4.15-b)

(4.15-c)

(4.15-d)

(4.15-e)

Both and were obtained from the analytical model

proposed by Chen and Teng (2001). is the tensile concrete strength, bf is the

CFRP plate width and bc is the concrete substrate width

108

Figure 4- 11: (a) Experimental results of interfacial bond stress reduction CFRP

stiffness relationship (b) Experimental fracture energy reduction CFRP stiffness

relationship

4.4.4 Effect of delamination approaches

Figure 4-12 shows the comparison of the results obtained using VCCT, cohesive

elements and cohesive surfaces in terms of load slip behaviour for the test specimen

(VI-6). The convergence study implies that both the cohesive elements and cohesive

surfaces converge to the experimental results. On the other hand the VCCT approach

appears to display precisely linear behaviour before debond onset as well as

unsmooth response after cracking and experiences numerical problems. This is due

to the fact that the nodes in the slave surface for the both approaches (cohesive

elements or cohesive surface) debond altogether. Whereas, the slave nodes in the

surface for the VCCT approach are released one after another. Therefore, it was

decided to adopt the cohesive surface approach for the rest of the analysis.

IBSR= -2E-05(Ef.tf)2 + 0.0078 (Ef.tf) + 0.0862

0

0.2

0.4

0.6

0.8

0 50 100 150 200 250

Inte

rfa

cia

l B

on

d S

tre

ss R

ed

ucti

on

CFRP Stiffness [n.Ef. tf *10^3 (N/mm)]

FER = -9E-06 (Ef.tf)2 + 0.0041(Ef.tf) + 0.047

0

0.2

0.4

0.6

0 50 100 150 200 250

Fra

ctu

re E

ne

rgy

Re

du

cti

on

CFRP Stiffness [n.Ef. tf *10^3 (N/mm)]

(a) (b)

109

Figure 4- 12: Load-slip curve of VI-6 for different three different delamination

approaches

4.4.5 Effect of interfacial bond stiffness

This study aims to clarify the effect of interface bond stiffness [ which formed an

elastic constitutive matrix of the traction-separation model (see Equation 4.1). The

interface bond stiffness ranges between 30 and 340 MPa/mm depending on the type

of the adhesive. From Figure 4-13, it was found that Interfacial bond stiffness has

nearly no effect on load-slip relationship. These numerical results are in a close

agreement with the experimental observations Chajes et al.(1996). This is based on

the fact that the type of adhesive displayed only excellent workability for transfer

shear stress from the concrete surface to the CFRP plate and has minimal effect on

the load-slip behaviour and ultimate capacity. It was decided to use the 300 MPa/mm

as interface bond stiffness for the rest of the analysis.

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Load

(K

N)

Slip (mm)

VI-6 VI-6 (Cohesive surface) VI-6(Cohesive element) VI-6 (VCCT)

110

Figure 4- 13: Effect of interfacial bond stiffness on the load-deflection behaviour.

4.4.6 Effect of damage initiation criteria

Damage initiation criteria have a visible effect on the bond behaviour prior to the

cracking onset as shown in Figure 4-14. This is due to the fact that each damage

initiation criterion has an output variable associated with it to indicate whether the

criterion is satisfied. Furthermore, the load slip relationships are approximately

similar during the debonding propagation stage with a good agreement with

experimental load-slip curve of specimen (VI-6). In this study, the maximum

nominal stress criterion was used in the rest of FE analysis of single shear to

determine the damage initiation.

Figure 4- 14: Load-slip curve of VI-6 for different damage initiation criteria

approaches

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Loa

d (

KN

)

Slip (mm)

VI-6 VI-6 (K=35 Mpa/mm) VI-6 (K=80 Mpa/mm)

VI-6 (K=180 Mpa/mm) VI-6 (K= 340 Mpa/mm)

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Loa

d (

KN

)

Slip (mm)

VI-6 VI-6 ( Maximum nominal stress criterion)

VI-6 (Quadratic nominal stress criterion) VI-6 (Quadratic nominal separation criterion)

VI-6 (Maximum nominal separation criterion)

111

4.4.7 Effect of damage evolution response

Figure 4-15 shows the load-slip curve of the single shear test using different damage

evolution response. The damage evolution response based on displacement shows

lower bond strength performance leads to early debonding cracks. The results start to

converge with damage evolution response based on energy. However the exponential

softening requires more computational time compare with linear softening.

Therefore, it was decided to adopt the linear softening based on energy current FE

analysis.

Figure 4- 15: Load-slip curve of VI-6 for different damage evolution response

4.4.8 Effect of mesh size

The effect of mesh size of the concrete substrate and along the CFRP plate length on

single shear pull-out behaviour was tested by changing the mesh size for each part

and plotting the corresponding load –slip behaviour. However, during verifying the

mesh size it should be considered that the slave surface (CFRP) has to have a finer

mesh in the contact pair to prevent penetration master node to the slave surface.

Figure 4-16 (A and B) illustrates the convergence of the result for each mesh size.

The load-slip behaviour is more mesh size sensitive for the CFRP plate than the

concrete substrate. For CFRP plate, 5 mm mesh size gives reasonable results

compared to 10 and 15 mm mesh size. On the other hand, the 3 mm converge with 5

mm. For concrete substrate, 10 gives similar behaviour with 15, 20 and 25 mm.

Furthermore, both 20 and 25 mm mesh size appears to have experience numerical

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Lo

ad

(K

N)

Slip (mm)

VI-6 VI-6 (Linear softening-based on energy)

VI-6 (Exponential sofrening-based on energy) VI-6 (Linear softening-based on displacement)

VI-6 (Exponential softening-based on displacement) VI-6 (Tabular softening-based on displacement)

112

problems. Therefore, it was decided to use 5 mm and 15 mm as a minimum mesh

size for the CFRP plate and concrete substrate, respectively.

Figure 4- 16: Sensitivity of the Load-slip behaviour to the mesh size of (A) the

concrete substrate; and (B) the CFRP plate

4.4.9 Summary

Different numerical parameters have been investigated to simulate the correct

interface behaviour of single shear pull-out tests. The current sensitivity analysis has

been compared with Yao. J. et al (2005) experimental works. It was concluded that

the cohesive surface approach is to be adopted to simulate the interface behaviour. It

has been proven through numerical analysis that the interfacial bond stiffness has

(a)

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Load

(K

N)

Slip (mm)

VI-6 VI-6 Mesh-10 mm VI-6 Mesh-15 mm

VI-6 Mesh-20 mm VI-6 Mesh-25 mm

(b)

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Loa

d (

KN

)

Slip (mm)

VI-6 VI6 Mesh-3 VI-6 Mesh-5 VI-6 Mesh-10 VI-6 Mesh-15

113

negligible effect on the load-slip behaviour. It was also found that the maximum

nominal stress criterion and the linear softening based on energy give good

agreement with experimental load-slip curve. Therefore, these two criteria were

adopted for damage initiation criteria and damage evolution response, respectively.

Finally, the appropriate element size for CFRP plate and concrete were 5 mm and 15

mm. respectively.

4.5 Validation against the author’s experimental results

This section describes the comparison between the numerical results with

experimental results previously discussed in Chapter 3. The comparison includes

verifications of load-slip curves and strain profile for both monotonic and post-

fatigue tests. The aim of these comparisons is to validate the proposed bond-slip

models for the post-fatigue tests, see Section 4.4.3 and to check the accuracy and

efficiency of the numerical models.

4.5.1 Numerical simulation model

The general finite element software package ABAQUS was used to develop the

simulation model which is shown in Figure 4-6. The simulation analysis was

terminated when full debonding occurred between the CFRP plate and concrete

substrate. The CFRP material properties are given in Table 4-1. The concrete

compressive and tensile strengths were 52.8 N/mm2 and 4.5 N/mm

2, respectively,

based on the authors’ experimental results (Chapter 3).

4.5.2 Comparison between simulation and experimental results for monotonic

and post-fatigue behaviour

Figure 4-17 and 4-18 present detailed comparisons between the numerical and the

experimental results for two representative specimens (CFRP thickness equal 0.4

114

mm, CFRP type equal M46J) and (CFRP thickness equal 0.3 mm CFRP type equal

T700), respectively. Results for the other tests are presented in Appendix A.

The quantities being compared are strain profile in the loading direction along the

centre of the bonded CFRP plate and load slip curves. These comparisons show that

the simulation model is able to capture the behaviour of the test specimens for both

the monotonic and the post-fatigue tests cases throughout the entire period of testing.

Table 4-3 compares the debonding strain, the ultimate load and failure mode

between the simulation and the experimental results for all the tests. It can be seen

that the agreement is excellent. This confirms that it is suitable to use the numerical

model to conduct further numerical simulations to extend the applicability of the

experiments to obtain the necessary data for the development of a design calculation

method to calculate the CFRP strain limit in post-fatigue failure. Also, the simulation

model is able to predict the failure modes (i.e. (a) CFRP composite plate rupture and

(b) Concrete shearing beneath adhesive layer) as shown in Figure 4-19. However,

specimens (M1, M2, P-F1) had different failure modes (i.e. Bond failure in the

interfaces between concrete and adhesive layer) than that observed in numerical

simulations. This is due to inadequate surface preparation in these specimens giving

an unrepresentative failure mode.

115

(a) Monotonic test (M3)

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1 1.2

Lo

ad

(K

N)

Slip (mm)

0.4mm (M465)EXP. 0.4mm (M465) FEM

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)

Distance in longitudinal direction (mm)

20.5 KN (EXP) 20.5 KN (FEM) 19.8 KN (EXP.)20.2 KN (FEM) 20 KN (EXP.) 20 KN (FEM)12.8 KN (EXP.) 12.8 KN (FEM)

Debonding stain at ultimate load

116

(b) Post-fatigue test (P-F3)


slip relationships and stain distribution along CFRP plate (0.4 mm M46J)

0

3

6

9

12

15

18

0 0.2 0.4 0.6 0.8 1 1.2

Loa

d (

KN

)

Slip (mm)

pre-fatigue (EXP) post-fatigue (EXP)

Pre-fatigue (FEM) Post-fatigue (FEM)

0

1000

2000

3000

4000

5000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)

Distance alone the longitudinal direction (mm)

15.7 (EXP.) 15.7 (FEM) 15.48 KN (EXP.)

15.48 KN (FEM) 12.98 KN (EXP.) 12.98 KN (FEM)

6.45 KN (EXP.) 6.45 KN (FEM)

Debonding strain at ultimate load

117

(a) Monotonic test (M4)

0

2

4

6

8

10

12

14

16

0 0.4 0.8 1.2 1.6 2 2.4

Lo

ad

(K

N)

Slip (mm)

0.3 mm (T700) EXP. 0.3 mm (T700) FEM

0

1500

3000

4500

6000

7500

9000

0 50 100 150 200 250 300

De

bo

nd

ing

stra

in (

Mic

ron

)


14 KN (EXP) 14 KN (FEM) 13.9 KN (EXP) 13.9 KN (FEM)

12 KN (EXP) 12 KN (FEM) 1.5KN (EXP) 1.5 KN (FEM)


118

(b) Post-fatigue test (P-F4)


slip relationships and stain distribution along CFRP plate (0.3 mm T700)

0

2

4

6

8

10

12

14

0 0.4 0.8 1.2 1.6 2 2.4

Lo

ad

(K

N)

Slip (mm)

prefatigue (EXP) postfatigue (EXP)

Prefatigue (FEM) postfatigue (FEM)

0

1500

3000

4500

6000

7500

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)


11.7 KN (EXP) 11.7 KN (FEM) 10 KN (EXP)

10 KN (FEM) 8 KN (EXP) 8 KN (FEM)

6.3 KN (EXP) 6.3 KN (FEM)


119

(a)

CFRP rupture

CFRP rupture

120

Figure 4- 19: Comparison of failure modes between experiment (bottom) and

numerical simulation (top); (a) CFRP composite plate rupture (M6) and (b) Concrete

shearing beneath adhesive layer (P-F1) [E11 is debonding strain]

Concrete shearing

(b)

Concrete shearing

121

Table 4- 3: Comparison between numerical and experimental results for all monotonic and post-fatigue test failure loads

* Compressive strength of concrete substrate = 22.6 Mpa.

ID

Test Type

Elastic

Modulus

GPa

Thickness

(mm)

Stiffness

(kN/mm)

Ultimate

Strain

(Micro-

strain)

Failure mode Debonding Strain

(Microstrain)

Ultimate Load (kN)

EXP FEM EXP FEM FEM/

EXP

EXP FEM FEM/

EXP

M1 Monotonic 203.5 1 203.5 7810 C-S-I C-S 3926.4 3491 0.88 35.3 35.5 1.1

M2 Monotonic 114.9 1 114.9 20130 C-S-I C-S 4154.2 4103 0.98 25.5 24.8 0.97

M3 Monotonic 264.8 0.4 105.9 6414 C-S C-S 5395.9 5388 0.99 22.01 22.04 1.02

M4 Monotonic 128.4 0.3 38.5 18168 C-S C-S 8064.6 7419 0.92 14.3 14.1 0.98

M5 Monotonic 138.3 0.2 27.6 17660 C-S C-S 9213.2 9500 1.03 12 11.2 0.93

M6 Monotonic 220.6 0.15 33 7980 C-S&P-R P-R 7988.6 7816 0.97 13.1 12.1 0.92

M7* Monotonic 128.4* 0.3 38.5 18168 C-S C-S 6489.6 6707 1.03 11.7 11.9 1.02

P-F1 Post-fatigue 203.5 1 203.5 7810 C-S-I C-S 2662 2427 0.91 25.6 24.1 0.94

P-F2 Post-fatigue 114.9 1 114.9 20130 C-S C-S 3224.8 3268.3 1.05 20.1 19 0.94

P-F3 Post-fatigue 264.8 0.4 105.9 6414 C-S C-S 4134.9 4606.3 1.11 16.4 16.8 1.02

P-F4 Post-fatigue 128.4 0.3 38.5 18168 C-S C-S 6729 7005 1.04 11.7 11.6 0.99

P-F5 Post-fatigue 138.3 0.2 27.6 17660 C-S C-S 8361 8657 1.03 10.4 10.3 0.99

P-F6 Post-fatigue 220.6 0.15 33 7980 C-S C-S 7303 8220 1.2 10.9 10.18 1.07

P-F7* Post-fatigue 128.4* 0.3 38.5 18168 C-S C-S 5795.3 5857 1.01 9.97 10.2 1.02

122

4.6 Numerical parametric study of post-fatigue behaviour

In order to develop a simplified analytical method to calculate the debonding strain

and the effective bond length of CFRP bonded concrete due to post-fatigue loading,

the numerical simulation model developed and validated in the previous section has

been used to investigate the effects of changing the different design parameters,

including concrete strength, CFRP plate to concrete width ratio, bond length and

CFRP plate stiffness. Table 4-4 lists the ranges of the parameters. The concrete

width was 200 mm in all cases.

Table 4- 4: Main parameters investigated in numerical simulation

Material

parameters

Concrete

compressive

strength

(MPa)

Bond

width

ratio

Bond length

(mm)

CFRP plate stiffness

(kN/mm)

35

0.25

300

27.6

33

38.5

105.9

114.9

203.5 40

45

52.8

52.8

0.125

300

27.6

33

38.5

105.9

114.9

203.5 0.25

0.375

0.5

52.8

0.25

100

27.6

33

38.5

105.9

114.9

203.5

120

140

160

180

200

220

240

260

280

300

123

4.6.1 Effect of concrete compressive strength

Figures 4-20 (a) and (b) show the effects of changing the concrete compressive

strength on bond ultimate load and debonding strain for CFRP plate stiffness of

27.67 kN/mm (T700, 0.2 mm thick), 33 kN/mm (M46J, 0.15 mm thick), 38.5

kN/mm (T700, 0.3 mm thick) and 105.9 kN/mm (M46J, 0.4 mm thick), 114.9

kN/mm (T700, 1 mm thick), 203.5 kN/mm (M46J, 1mm thick), respectively.

Figure 4- 20: Effects of concrete compressive strength (a) Bond ultimate Load; (b)

Debonding strain

(a)

6

9

12

15

18

21

24

30 35 40 45 50 55

Bo

nd

ult

imat

e lo

ad (

kN)

Concrete compressive strength (MPa)

1 mm M46J 1 mm T700 0.4 mm M46J

0.3mm T700 0.15 mm M46J 0.2 mm T700

(b)

0

2000

4000

6000

8000

10000

30 35 40 45 50 55

Deb

on

din

g st

rain

(M

icro

n)

Concrete compressive strength (MPa)

1 mm M46J 1 mm T700 0.4 mm M46J

0.3 mm T700 0.15 mm M46J 0.2 mm T700

124

Depending on the relative FRP strength and concrete strength, the failure mode

changes from FRP fracture ( kN/mm, MPa) to concrete

shearing failure ( kN/mm, MPa). If the failure mode is FRP

fracture, changing the concrete strength has little effect, as clearly shown in Figure

4-20 (b) (specimen 0.2 mm T700).

If the failure mode is concrete shearing, the results in Figure 4-20 show that

increasing the concrete strength results in increase in the ultimate bond strength and

debonding strain. The rates of these increases are small at lower concrete strengths

than at higher concrete strengths. This is because the bond strength depends on the

fracture energy of concrete which mainly depends on the tensile strength of concrete

(Chen and Teng, 2001). For the four concrete compressive strengths (35, 40, 45 and

52.8) MPa, the tensile strengths of (2.9, 3.2 and 3.4 MPa) using BSI (2004) do not

change very much for the lower concrete strengths 35, 40, 45 MPa. For the high

concrete compressive strength of 52.8 MPa, the tensile strength of 4.5 MPa from the

authors’ was used.

The results in Figure 4-20(a) show more drastic changes of bond strength for

specimens 1 mm T700 & 1 mm M46J at high concrete strengths. This is due to the

fact that the fracture energy reduction (FER) induced by previous cyclic loading is

relatively high for both specimens 1 mm T700 & 1 mm M46J see Figure 4-11 (b)

and approximately equal to the total fracture energy of the specimens with concrete

compressive strength less than 52.8 MPa (i.e. total fracture energy reduced with

decrease concrete compressive strength). In both these specimens, debonding failure

occurred prior to the ultimate load being reached.

4.6.2 Effects of changing ratio of CFRP bonded plate width to concrete

substrate width

Figure 4-21 shows the effects of changing the CFRP to concrete width ratio on the

bond ultimate load and debonding strain, for different CFRP plate stiffness.

Based on the FE analysis it was found that the effect of change in bond width ratio

generally follows expected trends: increasing the bond width ratio increases the bond

ultimate load carrying capacity and decreases the debonding. Similar to the results

observed in monotonic tests of Kamel et al. (2004).

125

The exceptions are specimens 1 mm T700 and 1mm M46J. At the low bond width

ratio of 0.125, these two specimens experienced CFRP plate rupture unlike the other

samples. Increasing the CFRP plate width ratio to 0.25, 0.375 and 0.5 changes the

failure mode to the desirable failure mode of concrete shearing beneath the CFRP

plate. However for these two specimens increasing the bond width ratio to 0.375 and

0.5 caused a shift in the effective bond length and the actual bond length is no longer

sufficient to generate full stress in the transfer zone. In order to highlight this effect,

the same model was rerun with an increased bonded length of 400 mm. The new

simulation results agree with the trend for the rest of the CFRP plate stiffnesses as

shown in Figure4-21.

Figure 4- 21: Effects of CFRP plate/concrete width ratio (bf/bc): (a) Bond ultimate

Load; (b) Debonding strain

0

5

10

15

20

25

30

35

40

45

0 0.125 0.25 0.375 0.5 0.625

Bond

ult

imat

e lo

ad (k

N)

Width ratio (bf/bc)

1 mm M46J (400 mm) 1 mm T700 (400 mm)

0.4 mm M46J 0.3mm T700

0.15 mm M46J 0.2 mm T700

1 mm M46J (300 mm) 1 mm T700 (300 mm)

(a)

(b)

0

2000

4000

6000

8000

10000

0 0.125 0.25 0.375 0.5 0.625

Deb

ondi

ng s

trai

n (M

icro

n)

width ratio (bf/bc)

1 mm M46J (400 mm) 1 mm T700 (400 mm)

0.4 mm M46J 0.3 mm T700

0.15 mm M46J 0.2 mm T700

1 mm M46J (300 mm) 1 mm T700 (300 mm)

126

This phenomenon (i.e. the shift in the effective bond length with increasing bond

width) becomes apparent when observing the strain distributions in the FRP and the

debonding strain, shown in Figures 4-22 and 4-23 respectively, for specimen 0.3 mm

T700. The FRP strain profile in Figure 4-22 shows three distinct zones (a) the stress

free zone, (b) the stress transfer zone and (c) the fully debonded zone. Figure 4-23

shows that as the bond width ratio increases from 0.125 to 0.5, the stress free zone is

decreased from 120 mm to 80 mm due to the stress transfer zone of a constant length

is shifted with increase bond width ratio.

Figure 4- 22: Typical strain profile along the CFRP plate

Figure 4- 23: Effect of bond width ratio (bf/bc) on the debonding strain profile for

specimen (0.3 mm T700)

0

0.002

0.004

0.006

0.008

0 50 100 150 200 250 300

Stra

in

y

Fully Debonding CFRP

Stress Transfer Zone

Stress Free CFRP

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250 300

De

bo

nd

ing

stra

in (

Mic

ron

)


(bf/bc) =0.125 (bf/bc) =0.25 (bf/bc)=0.375 (bf/bc)=0.5

127

4.6.3 Effect of bond length

Figure 4-24 shows the influence of changing the bond length on the ultimate load

and debonding strain for the six different CFRP plate stiffnesses (Eftf) with a

concrete compressive strength of 52.8 N/mm2

and a bond width ratio of 0.25.

The results show expected trends: increasing the bond length leads to increased bond

ultimate load and debonding strain. The increases are initially governed by the bond

length until an effective bond length (Le) is reached. Once the bond length is

sufficiently higher than effective bond length and capable of carrying shear,

increasing the bond length has no effect.

Figure 4- 24: Effect of bonded CFRP plate length: (a) Bond ultimate load; (b)

Debonding strain

(a)

0

5

10

15

20

25

30

0 50 100 150 200 250 300

Bon

d ul

tim

ate

load

(kN

)

bonded CFRP plate length (mm)

0.2 mm T700 0.15 mm M46J 0.3 mm T7000.4 mm M46J 1 mm T700 1 mm M46J

(b)

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300

Deb

on

din

g st

rain

(M

icro

n)

bonded CFRP plate length (mm)

0.2mm T700 0.15 mm M46J 0.3 mm T7000.4 mm M46J 1 mm T700 1 mm M46J

128

4.7 Comparison between code provisions and numerical simulation

results

4.7.1 Debonding strain

Table 4-5 compares all the numerical simulation results and the calculation results

using the different code methods reviewed in Section 2.6 of Chapter 2, for the

debonding strain. Table 4-6 summarises the comparison. The first impression is that

none of the existing code calculation methods is wholly accurate, with very large

standard deviation values.

Among the different methods, the TR55 and JSCE methods have similar accuracy

and give the best results, with the standard deviation and average close to 40% and

100%, respectively. The ACI calculation method gives the worst correlation with the

numerical simulation results. This is mainly because the ACI design code only

considers the effect of the CFRP stiffness. Between the two FIB methods, fib-2 gives

better results than fib-1 and should be preferred. DT-202 gives the lowest standard

deviation with the numerical simulation. However, the average ratio is quite low.

Overall, a more accurate method should be developed.

129

Table 4- 5: Comparison between numerical simulation results and code calculations for debonding tensile strain

E

(GPa)

tf

(mm)

(MPa)

Bond

length

(mm)

FE

(Microstrain)

ACI fib-1 fib-2 TR55 CNR-DT

202

JSCE ACI

fib-1

fib-2

TR55

CNR-DT

202

JSCE

203.6 1 52.8 0.25 300 2427 7029 5277.29 2001.2 2931.8 1983.9 2447.5 2.93 2.20 0.83 1.22 0.82 1.02

114.9 1 52.8 0.25 300 3268.3 11347 7024.6 2663.93 3902.5 2640.9 3257.9 3.47 2.14 0.81 1.19 0.80 0.99

264.8 0.4 52.8 0.25 300 4606.3 5772.6 7315.5 2774.25 4064.2 2750.2 3392.8 1.25 1.58 0.60 0.88 0.59 0.73

128.46 0.3 52.8 0.25 300 7005 14882.5 12129.6 4599.8 6738.6 4560. 5625.5 2.20 1.79 0.68 0.99 0.67 0.83

138.3 0.2 52.8 0.25 300 8657 15385.6 14314.6 5428.5 7952.6 5381.5 6638.9 1.82 1.69 0.64 0.94 0.63 0.78

220.6 0.15 52.8 0.25 300 8220 7182 13090.0 4964.0 7272.2 4921.1 6071 0.87 1.59 0.60 0.88 0.59 0.73

203.6 1 45 0.25 300 975.407 7029 4519.20 1779.42 2510.6 1764.0 2264.9 7.24 4.63 1.82 2.57 1.81 2.32

114.9 1 45 0.25 300 2372.1 11347 6015.5 2368.6 3341.9 2348.1 3014.8 4.78 2.53 0.99 1.40 0.98 1.27

264.8 0.4 45 0.25 300 3790 5772.6 6264.6 2466.70 3480.3 2445.3 3139.7 1.52 1.65 0.65 0.91 0.64 0.82

128.46 0.3 45 0.25 300 6300 14882.5 10387.1 4089.9 5770.6 4054.5 5205.8 2.36 1.64 0.64 0.91 0.64 0.82

138.3 0.2 45 0.25 300 8730 15385.6 12258.3 4826.6 6810.2 4784.9 6143.6 1.76 1.40 0.55 0.78 0.54 0.70

220.6 0.15 45 0.25 300 7820 7182 11209.6 4413.7 6227.5 4375.5 5618 0.91 1.43 0.56 0.79 0.55 0.71

203.6 1 40 0.25 300 892.11 7029 4308.8 1687.10 2393.8 1672.5 2211.6 7.93 4.83 1.89 2.68 1.87 2.48

114.9 1 40 0.25 300 2293.83 11347 5735.61 2245.7 3186.4 2226.3 2943.9 4.95 2.50 0.97 1.39 0.97 1.28

264.8 0.4 40 0.25 300 3730 5772.6 5973.14 2338.72 3318.4 2318.5 3065.8 1.54 1.60 0.62 0.88 0.62 0.82

128.4 0.3 40 0.25 300 6200 14882.5 9903.7 3877.73 5502.1 3844.2 5083.2 2.40 1.59 0.62 0.88 0.62 0.82

138.3 0.2 40 0.25 300 8650 15385.6 11687.9 4576.29 6493.2 4536.7 5999. 1.77 1.35 0.53 0.75 0.52 0.69

220.6 0.15 40 0.25 300 7750 7182 10687.9 4184.78 5937.7 4148.5 5485. 0.92 1.37 0.53 0.76 0.53 0.70

264.8 0.4 35 0.25 300 3450 5772.6 5718.84 2213.2 3177.1 2194.1 2999.8 1.67 1.65 0.64 0.92 0.63 0.86

128.46 0.3 35 0.25 300 6030 14882.5 9482.15 3669.72 5267.8 3637.9 4973.9 2.46 1.57 0.60 0.87 0.60 0.82

138.3 0.2 35 0.25 300 8450 15385.6 11190.3 4330.8 6216.8 4293.3 5869.9 1.82 1.32 0.51 0.73 0.50 0.69

220.6 0.15 35 0.25 300 7600 7182 10232.9 3960.2 5684.9 3926.0 5367.7 0.94 1.34 0.52 0.74 0.51 0.70

203.6 1 52.8 0.125 300 2797.3 7029 4394.04 1769.4 2441.1 1810.3 2329.8 5.05 3.14 1.26 1.74 1.29 1.66

114.9 1 52.8 0.125 300 3295.77 11347 7482.02 2663.9 4156.6 2725.5 3507.5 3.44 2.27 0.80 1.26 0.82 1.06

264.8 0.4 52.8 0.125 300 4752.72 5772.6 7791.87 2774.2 4328.8 2838.3 3652.8 1.21 1.63 0.58 0.91 0.59 0.76

128.4 0.3 52.8 0.125 300 7564.74 14882.5 12919.3 4599.8 7177.4 4706.1 6056.5 1.96 1.70 0.60 0.94 0.62 0.80

130

Table 4- 6: Summary of comparisons between numerical results and different code calculation results for debonding tensile strain in CFRP plate,

(ratio of calculation result to simulation result, given in %)

Code Max. ratio Min. ratio Average STD.

ACI 7.93 0.80 2.49 1.73

fib-1 4.83 1.32 1.97 0.83

fib-2 1.89 0.51 0.77 0.33

TR55 2.68 0.73 1.09 0.46

CNR-DT202 1.87 0.50 0.76 0.32

JSCE 2.48 0.68 0.96 0.42

138.3 0.2 52.8 0.125 300 9372.54 15385.6 15246.6 5428.5 8470.3 5553.9 7147.6 1.64 1.62 0.57 0.90 0.59 0.76

220.6 0.15 52.8 0.125 300 8966.83 7182 13942.3 4964.08 7745.7 5078.8 6536. 0.80 1.55 0.55 0.86 0.56 0.72

203.5 1 52.8 0.375 300 1218.38 7029 4949.6 2001.2 2749.8 1921.4 2276.8 5.77 4.06 1.64 2.25 1.57 1.86

114.9 1 52.8 0.375 300 2847.76 11347 6588.5 2663.93 3660.3 2557.6 3030.7 3.98 2.31 0.93 1.28 0.89 1.06

264.8 0.4 52.8 0.375 300 3934.46 5772.6 6861.4 2774.2 3811.9 2663.5 3156.2 1.46 1.74 0.70 0.96 0.67 0.80

128.4 0.3 52.8 0.375 300 6416.91 14882.5 11376.6 4599.86 6320.3 4416.2 5233.2 2.31 1.77 0.71 0.98 0.68 0.81

138.3 0.2 52.8 0.375 300 8253.48 15385.6 13426.0 5428.50 7458.9 5211.8 6175.9 1.86 1.62 0.65 0.90 0.63 0.74

220.6 0.15 52.8 0.375 300 7867.08 7182 12277.4 4964.0 6820.8 4765.9 5647.6 0.91 1.56 0.63 0.86 0.60 0.71

264.8 0.4 52.8 0.5 300 3803.56 5772.6 6425.34 2774.2 3569.6 2577.4 2938.3 1.51 1.68 0.72 0.93 0.67 0.77

128.4 0.3 52.8 0.5 300 6096 14882.5 10653.5 4599.8 5918.6 4273.6 4871.8 2.44 1.74 0.75 0.97 0.70 0.79

138.3 0.2 52.8 0.5 300 7903.87 15385.6 12572.7 5428.5 6984.8 5043.5 5749.5 1.99 1.63 0.70 0.90 0.65 0.74

220.6 0.15 52.8 0.5 300 7709.53 7182 11497.1 4964.0 6387.2 4612.0 5257.6 0.93 1.49 64 0.82 0.59 0.68

Average 2.49 1.97 0.77 1.09 0.76 0.96

STD. 1.73 0.83 0.33 0.46 0.32 0.42

131

4.7.2 Effective length

Figure 4-25 shows a comparison of the effective bond length (Le) against CFRP plate

stiffness between the different code methods and the present post-fatigue numerical

simulation. It can be seen that the post-fatigue simulation results have behaviour

similar to that predicted by different code methods. However, the values predicted by

these methods are significantly different from the simulation results. In general, the

code calculation equations give lower effective lengths, meaning that short bond

length is required. This is because the code equations are based on monotonic

results. These methods are potentially unsafe for post-fatigue applications because

they always give underestimate predications. Therefore, a vital practical design

consideration for anchorage of externally bonded FRP plate is the Le limit in the

fatigue and post-fatigue regimes, so as to mobilise full tensile strength of the CFRP

plate.

Figure 4- 25: Comparison for effective bond length - CFRP plate stiffness

relationships between codes and simulation results.

Table 4-7 compares the simulation and code calculation results for effective bond

length. And Table 4-8 summarises the comparison. All the design code methods

show underestimates with average code calculation/ numerical simulation ratios

being 0.47, 0.51, 0.47 and 0.47 for fib-1, fib-2, TR55 and D202, respectively.

However, these existing design code methods all have similar results among

themselves, reflecting the fact that they were derived using similar monotonic test

results.

0

50

100

150

200

250

300

0 50 100 150 200 250

Effe

ctiv

e bo

nd le

ngth

(m

m)

(Ef.tf) (kN/mm)

FE model FIB1 FIB2 TR55 DT202

132

Table 4- 7: Comparison between numerical simulation results and code calculation results for effective bond length

ft

(MPa)

fc

(MPa)

Ef.tf

kN/mm

bf/bc Le

(FE)

(mm)

Effective length Le

(mm)

Le/Le(FE)

fib-1 fib-2 TR55 CNR-DT202 fib-1 fib-2 TR55 CNR-DT202%

3.8 52.8 27.67 0.125 135 60.3 63.8 59.7 60.3 0.446 0.473 0.442 0.446

3.8 52.8 33 0.125 150 65.8 69.7 65.2 65.8 0.439 0.465 0.434 0.439

3.8 52.8 38.54 0.125 165 71.2 75.3 70.4 71.2 0.431 0.456 0.427 0.431

3.8 52.8 105.9 0.125 205 118. 124.9 116.8 118. 0.575 0.609 0.57 0.575

3.8 52.8 114.9 0.125 240 122.9 130.1 121.7 122.9 0.512 0.542 0.507 0.512

3.8 52.8 203.6 0.125 280 163.6 173.2 162. 163.6 0.584 0.578 0.584

3.8 52.8 27.6 0.25 140 60.3 63.8 59.7 60.3 0.43 0.456 0.426 0.43

3.8 52.8 33 0.25 160 65.8 69.7 65.2 65.8 0.411 0.436 0.407 0.411

3.8 52.8 38.5 0.25 170 71.2 75.3 70.4 71.2 0.418 0.443 0.414 0.418

3.8 52.8 105.9 0.25 220 118. 124.9 116.8 118. 0.536 0.568 0.531 0.536

3.8 52.8 114.9 0.25 240 122.9 130.1 121.7 122.9 0.512 0.542 0.507 0.512

3.8 52.8 203.6 0.25 280 163.6 173.2 162. 163.6 0.584 0.618 0.578 0.584

3.8 52.8 27.6 0.375 145 60.3 63.8 59.7 60.3 0.416 0.44 0.411 0.416

3.8 52.8 33 0.375 165 65.8 69.7 65.2 65.8 0.399 0.422 0.395 0.399

3.8 52.8 38.5 0.375 170 71.2 75.3 70.4 71.2 0.418 0.443 0.414 0.418

3.8 52.8 105.9 0.375 225 118. 124.9 116.8 118. 0.524 0.555 0.519 0.524

3.8 52.8 114.9 0.375 250 122.9 130.1 121.7 122.9 0.491 0.52 0.486 0.491

3.8 52.8 203.6 0.375 290 163.6 173.2 162. 163.6 0.564 0.597 0.558 0.564

3.8 52.8 27.67 0.5 150 60.3 63.8 59.7 60.3 0.402 0.425 0.398 0.402

3.8 52.8 33 0.5 170 65.8 69.7 65.2 65.8 0.387 0.41 0.383 0.387

3.8 52.8 38.5 0.5 175 71.2 75.3 70.4 71.2 0.406 0.43 0.402 0.406

3.8 52.8 105.9 0.5

235 118. 124.9 116.8 118 0.502 0.531 0.497 0.502

133

Table 4- 8: Summary of comparisons between numerical results and different code calculation results for effective bond length in CFRP plate,

(ratio of calculation result to simulation result, given in %)

Code Max. ratio Min. ratio Average STD.

fib-1 0.59 0.38 0.47 0.063

fib-2 0.63 0.41 0.50 0.067

TR55 0.58 0.38 0.46 0.062

CNR-DT202 0.59 0.38 0.47 0.063

3.4 45 27.6 0.25 145 63.7 68.1 63.1 63.7 0.439 0.469 0.435 0.439

3.4 45 33 0.25 165 69.6 74.3 68.9 69.6 0.422 0.45 0.417 0.422

3.4 45 38.5 0.25 175 75.2 80.3 74.5 75.2 0.43 0.459 0.425 0.43

3.4 45 105.9 0.25 225 124.7 133.2 123.5 124.7 0.554 0.592 0.549 0.554

3 40 27.6 0.25 150 67.9 72.3 67.2 67.9 0.452 0.482 0.448 0.452

3 40 33 0.25 170 74.1 79. 73.4 74.1 0.436 0.464 0.431 0.436

3 40 38.5 0.25 180 80.1 85.4 79.3 80.1 0.445 0.474 0.44 0.445

3 40 105.9 0.25 230 132.8 141.5 131.5 132.8 0.577 0.615 0.571 0.577

2.7 35 27.6 0.25 155 71.5 76.8 70.8 71.5 0.461 0.495 0.457 0.461

2.7 35 33 0.25 175 78.1 83.8 77.3 78.1 0.446 0.479 0.442 0.446

2.7 35 38.5 0.25 185 84.4 90.6 83.6 84.4 0.456 0.49 0.452 0.456

2.7 35 105.9 0.25 235 140. 150.2 138.6 140. 0.595 0.639 0.589 0.595

Average 0.474 0.503 0.468 0.474

STD. 0.063 0.067 0.062 0.063

134

4.8 Proposed new model

The previous section has revealed inaccuracy of all the prevalent code methods to

calculate the debonding strain and effective bond length for application under post-

fatigue loading. An attempt has been made to derive new analytical equations with

improved accuracy. The new proposal follows a similar format to the equations

developed by Said and Wu (2008), shown as follows:

(4.16)

(4.17)

(4.18)

The coefficients C1-C8 were obtained through calibration against the numerical

simulation results. The coefficients were determined by using the non-linear

regression analysis function in the commercially available software Wolfram

Mathematica 7. The procedure is as follows:

The constant C3 (reflecting the influence of concrete strength) is the most important

value that controls the accuracy of the analytical equation. Therefore, for the

debonding strain, a value of C3 is assumed and the optimised values for the other

three constants (C1, C2 and C4) are found by using an iterative subroutine. The value

of C3 is determined when changing C3 would worsen the overall accuracy of the

analytical equation, as measured by the average ratio of the regression equation

result to the simulation result. Table 4-9 summarises results of the iterative

regression analysis. This table indicates that the best accuracy is achieved when

135

using C3= 0.9, giving the maximum, minimum, average ratios and standard deviation

184.1%, 65.2%, 100.8% and 29.6% respectively.

The accuracy of the analytical equation is reasonable. The largest occurrence of

inaccuracy of the analytical equation is from samples 1 mm M46J and 1 mm T700 at

concrete compressive strengths less than 52.8 N/mm2. These samples behaved

differently from other samples, as explained previously in Section 4.6. These two

samples also have comparatively high CFRP stiffness (>115 kN/mm). If these two

samples are excluded from the statistical analysis, the maximum, minimum, average

ratios and the standard deviation would be 107%, 76%, 95.4% and 12.2 %

respectively. Therefore, it can be said the proposed analytical model is more suitable

for CFRP plate stiffness less than 115 kN/mm and instances where plate rupture do

not govern ultimate loads. Further limitation is that the analytical model was

developed based on a loading range of 70% - 15% and concrete compressive

strength range of 22.6-52.8 MPa. Further investigation is necessary to test the

applicability/ sensitivity of the model to other loading ranges and concrete strengths.

To determine the regression equation coefficients (C5, C6, C7 and C8) for effective

bond length, the same procedure as above was used. The optimising procedure

sought to obtain the values of C5, C7 and C8 while assuming a value for C6 (which

determines influence of the concrete strength). Table 4-10 summarises the optimising

results. The final values of the four constants are C5= 5.9, C6=0.03, C7= 0.31 and

C8=0.27, with the corresponding regression equation giving an average ratio of 99.9

% and standard deviation of 4.7%.

4.9 Summary

This chapter has presented a model for post-fatigue behaviour of the bond interface

between concrete and externally bonded CFRP plate. The following conclusions may

be drawn:

The finite element model presented is capable to capture the actual failure

mode, load-slip relationship as well as strain profiles under monotonic and

post-fatigue loading.

The convergence study for the three numerical FE bonding approaches

(VCCT, cohesive elements and surface cohesive based model) implies that

136

the surface cohesive based model can adequately describe the bond between

the CFRP plate and the concrete.

The failure modes of the single shear specimens with low CFRP plate

stiffness changed from concrete shearing to CFRP plate rupture with the

increase in concrete compressive strength.

The bond ultimate load and ultimate strain increases to a certain value

depending on the bond length until an effective bond length (Le) is reached,

beyond which an extension of the bond length cannot increase the ultimate

load and debonding strain, but this certain value depends on the CFRP plate

stiffness.

A comparison between the simulation results and calculation results using the

currently available design methods has shown that both the ACI and fib-1

methods highly overestimated the debonding strain limit, but this limit was

underestimated by the fib-2 and the CNR- DT202 methods. The calculation

results for the debonding strain limit are generally acceptable when using

TR55 and JSCE. However, if the CFRP plate stiffness is high, predictions of

these two codes are non-conservative.

The numerical simulation results have revealed strongly dependency of both

debonding strain limit and the effective bond length on concrete compressive

strength , width ratio and CFRP plate stiffness . This

section has proposed new regression equations between the debonding strain

limit, the effective bond length with these three variables. The constants of

these regression equations were determined using an optimisation procedure.

For the series of specimens investigated, the new regression equations predict

the simulation results with an average analysis result/ simulation result ratio

of 0.1008 and standard deviation of 0.296 for the debonding strain; the

respective values for the effective bond length are 0.999 and 0.047

respectively.

137

Table 4- 9: Calibration of constants C1, C2, C3 and C4 of the new proposal

Table 4- 10: Calibration of constants C5, C6, C7 and C8 of the new proposal

0.84

0.76

Average 1.163 1.151 1.117 1.11 1.089 1.07 1.056 1.037 1.027 1.008 1.119

STD 0.402 0.388 0.367 0.357 0.343 0.33 0.321 0.311 0.305 0.296 0.33

Max. ratio 2.717 2.621 2.477 2.397 2.288 2.187 2.099 2.004 1.929 1.841 2.005

Min. ratio 0.721 0.725 0.714 0.719 0.716 0.713 0.713 0.709 0.711 0.652 0.706

Range ratio 1.997 1.896 1.763 1.677 1.572 1.474 1.387 1.294 1.218 1.189 1.299

0.31

0.04

Average 0.97 0.98 0.98 0.996 0.999 0.988

STD 0.043 0.044 0.044 0.045 0.047 0.048

Max. ratio 1.05 1.06 1.07 1.09 1.09 1.08

Min. ratio 0.87 0.88 0.88 0.896 0.895 0.884

Range ratio 0.179 0.183 0.187 0.194 0.199 0.202

138

Chapter Five

Non-linear FE Modelling of CFRP-

Strengthened One- Way RC Slabs under Cyclic

Loading

5.1 Introduction

This chapter presents a numerical model to simulate the nonlinear behaviour of an

adhesive layer connecting CFRP sheet to reinforced concrete (RC) one-way slabs.

The simulation model will be compared with the earlier experimental results of

Arduini et al.(2004). In this experiment, a series of full-scale one-way RC slabs with

and without an overhang at one extremity (with and without externally bonded

unidirectional CFRP) under simply supported conditions were subjected to two load

cycles. For the first cycle, the load reached 1/3 of the nominal capacity of the

specimen. In the second cycle, the specimen was taken to failure. Figure 5-1 shows

the test specimen characteristics and the test configuration. This chapter presents the

details of the numerical model.

139

Figure 5- 1: Details of CFRP-strengthened RC slab specimen. (Arduini et al., 2004)

(a) Full-scale one-way RC slabs (Type S) (b) Full-scale one-way RC slabs with an

overhang at one extremity (Type C)

30m

m

1500 mm 1500mm 1500mm

5000mm

RC slab

CFRP sheet

P/2 P/2

240 (b)

(a)

1500mm

2P/3 P/3

Top plan view

Bottom plan view

6500mm

2000mm 2000mm 2000mm

CFRP sheet

(b)

1500mm

140

5.2 Details of the numerical simulation model

The main components of a one-way RC slab strengthened by CFRP are the concrete,

the steel reinforcement bars embedded inside the concrete, the external CFRP sheet

and the adhesive layer connecting CFRP to RC one-way slabs. In order to introduce

a realistic model of CFRP-strengthened one- way RC slabs under cyclic loading, it is

necessary to simulate the actual material behaviour of each component. The

ABAQUS material library offers effective material models that can simulate the

actual behaviour of each component with acceptable accuracy.

5.2.1 Material models

5.2.1.1 Concrete

ABAQUS/ Standard has two approaches to model concrete behaviour; smeared

cracking and damaged plasticity. The smeared crack concrete model offers a general

ability for modelling concrete in different types of structures including trusses,

beams, shells and solids. This model does not track individual macro-cracks during

the analysis. Constitutive calculations are attributed to an integration point that is

translated into a deterioration of the current stiffness and strength at that integration

point. Only three cracks can occur at any integration point (two in a plane stress

case, one in a uniaxial stress case).The crack affects the constitutive calculations

because oriented damaged elasticity concepts. These concepts are implemented to

describe the reversible part of the material’s response after cracking failure

(Chaudhari and Chakrabarti (2012)). However, it has difficulty making the model

suitable in 3D applications due to the convergence problems which are caused by

nonexistence of cyclic/unloading response or the damage in the elastic stiffness

resulting from plastic straining. Otherwise, the damaged plasticity model is mostly

used in structures subjected to cyclic or dynamic loading because it is capable to

anticipate the behaviour of the test up to failure, (Rusinowski (2005)). For the reason

outlined above, the damage plasticity model has been chosen for analysis each slab.

141

5.2.1.1.1 Principle of the concrete damaged plasticity formulation

The most significant aspects of the damaged plasticity model can be defined as

compression and tension degradation. When the element plasticizes, the elastic

stiffness becomes lowered by damaged properties, thus it is unable to recover its

initial elastic stiffness. This is substantial for cyclic loading, as the two damage

parameters, , which are assumed to be functions of the plastic strains,

temperature and field variables represent degradation of the elastic stiffness.

(5.1)

(5.2)

Where the subscripts t and c refer to tension and compression respectively;

and

are the equivalent plastic strains; is the temperature; and

are other predefined field variables (ABAQUS (2011)). The damage

parameters can take values ranging from zero (characterizing the undamaged

material), to one (characterizes total loss of strength). The default of damage

plasticity can be illustrated using Figure 5-2.

Figure 5- 2: Uniaxial load cycle (tension-compression-tension) ABAQUS (2011).

WC=

0 W

c=1

σto

σt

ε

Wt=1 W

t=0

Eo

Eo

(1-dt)E

0

(1-dt)(1-d

c) E0 (1-d

c)E

0

142

Figure 5-2 shows the basic tension and compression stress –strain curve as a dotted a

line, while the solid line represents a high damage cyclic loading curve when the

element is subjected to tension exceeding its tensile strength (Tyau (2009)). Cracking

however leads to partial damage of the material and can be denoted by the

variable . The elastic behaviour of the element after unloading can be determined

by . When the element is compressed, the parameter determines its

elastic behaviour and presents the modulus of elasticity in

compression. It is necessary to note that the stiffness in compression is not

influenced by cracks (i.e. parameter equals unity). On the other hand, when full

degradation and compression stiffness become equal to the stiffness in tension, then

the parameter equals zero. Similarly, the damage in compression can be described

by the parameter (which defines loses in initial properties that occur in the

crushing section), while the parameter defines initial properties in tension. Hence,

Figure 5-3 shows both the tension and compression damage parameter curves for

estimating stiffness degradation during cyclic loading for the one-way RC slabs.

Figure 5- 3: Concrete damage properties: (a) compression damage, (b) tension

damage

5.2.1.1.2 Plasticity parameters

The Drucker- Prager flow potential yield surface proposed by Lubliner et al. (1989)

with the modifications proposed by Lee and Fenves (1998) can be solved by defining

five parameters. To find exact value of these parameters, a lot of tests would have to

(a)

0

0.2

0.4

0.6

0.8

1

0 0.001 0.002 0.003 0.004 0.005

Co

mp

ress

ion

Da

ma

ge

Strain

(b)

0

0.2

0.4

0.6

0.8

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Te

nsio

n D

am

ag

e

Strain

143

be conducted for the different material used in the experimental model; the proposed

numerical parameters investigations or default parameters in ABAQUS have been

used. The five parameters that need to be defined are:

Ψ is the dilation angle which represents the ratio of the volume change to

shear strain, determined in the plane at high confining pressure

where

and

are hydrostatic pressure stress

and Misses equivalent effective stress respectively and are

maximum and minimum principal stresses in a triaxial test. Most of the

published research take the dilation angle for concrete between 12 0

to 37 0

Lundqvist (2007) and ABAQUS (2011).

is a parameter referred to as the eccentricity that defines as the eccentricity

tends to zero the flow potential tends to a straight line, see Figure 5-4

(0.1 the default value of eccentricity is used).

Figure 5- 4: Flow potentials in p-q plane (ABAQUS (2011)).

is the ratio of initial equibiaxial compressive strength to initial

uniaxial compressive strength (the default value is used in analysis 1.16) as

shown in Figure 5-5

144

Figure 5- 5: Yield surface in plane stress (Carstensen (2011)).

is the viscosity parameter which representing the relaxation time of the

viscoplastic system and usually helps improve the rate of convergence of the

slab model in the softening region, the viscosity parameter is assumed to be

zero because the slab model did not cause the severe convergence difficulty.

Thus, no viscoplastic regularization is performed in the current analysis.

is the ratio of the second stress invariant on the tensile meridian (T.M.) to

that on the compressive meridian (C.M.) and it represents the yield surface in

deviatoric plane, see Figure 5-6 and it should satisfy the condition

(the default value is 2/3).

Figure 5- 6: Yield surfaces in the deviatoric plane, corresponding to different values

of (ABAQUS (2011))

145

5.2.1.1.3 Compressive behaviour

The uniaxial compressive stress-strain relationship for plain concrete after the elastic

regime needs to be defined. According to ABAQUS, both hardening and strain-

softening ranges are defined in terms of compressive stress,c

and inelastic strain,

in

c~ which is given as follows:

el

cc

in

c 0

~ (5.3)

where cmc

el

cE/

0 and

cmE is the initial modulus of elasticity

The FE analyses described in this work were conducted based on the uniaxial

compressive concrete model of (BSI (2004)) Euro code 2 Design of concrete

structures as shown in Figure 5-7, is described by the expression

nk

nkn

fcm

c

)2(1

2

(5.4)

1c

cn

(5.5)

k = 1.05 cm

E × |εc1| / cmf (5.6)

It should be noted that the expression in Equation (5.4) is valid for 0 < |εc1| < |εcu1|

where εcu1 is the nominal ultimate strain (0.0035); εc1 is the strain at peak stress (see

Table 5-1); and cm

f is mean compressive strength.

Figure 5- 7: Uniaxial compressive stress-strain behaviour of concrete

0

10

20

30

40

0 0.001 0.002 0.003 0.004 0.005

Stre

ss (M

Pa)

Strain

146

Table 5- 1: Strength and deformation characteristics for concrete (BSI (2004))

Strength classes for concrete Analytical relation/ Explanation

(MPa)

12 16 20 25 30 35 40 45 50 55 60 70 80 90

(MPa)

15 20 25 30 37 45 50 55 60 67 75 85 95 105

(MPa)

20 24 28 33 38 43 48 53 58 63 68 78 88 98

(MPa)

1,6

1,9

2,2

2,6

2,9

3,2

3,5

3,8

4,1

4,2

4,4

4,6

4,8

5,0

(MPa)

1,1 1,3 1,5 1,8 2,0 2,2 2,5 2,7 2,9 3,0 3,1 3,2 3,4 3,5

(MPa)

2,0 2,5 2,9 3,3 3,8 4,2 4,6 4,9 5,3 5,5 5,7 6,0 6,3 6,6

(GPa)

27 29 30 31 33 34 35 36 37 38 39 41 42 44

1,8 1,9 2,0 2,1 2,2 2,25 2,3 2,4 2,45 2,5 2,6 2,7 2,8 2,8

3,5

3,2

3,0

2,8

2,8

2,8

147

5.2.1.1.4 Tensile behaviour

Three approaches to describe the post cracking tension softening curve are available

in ABAQUS/standard, by defining strain, crack opening (displacement)or fracture

energy as shown in Figure 5-8. The tensile stress-strain softening relationship, based

on strength criterion, might introduce mesh sensitivity in the results in plain

concrete, Abdullah, A. (2010), meaning that the finite element predictions do not

converge to a unique solution as the mesh is refined, because mesh refinement

results in narrower crack bands rather than formation of additional cracks. Therefore,

adopting the strain approach is not recommended with structural members that have

little or no reinforcement because the failure occurs at localized regions in the

structure. The softening data are defined as tabular yield stress- cracking strain data.

Where cracking strain equal the total strain minus the elastic strain corresponding to

the undamaged material, el

tt

ck

t 0

~ where

cmt

el

tE/

0 as shown in Figure 5-8 (a)

,and tensile stress (t

)

Figure 5- 8: Post-failure tensile behaviour: (a) stress-strain approach; (b) fracture

energy approach

On the other hand, the fracture energy and stress- displacement can be used

alternatively to describe the concrete tensile behaviour because they are connected to

each other crack. These two approaches based on a fracture energy cracking

criterion, developed by Hillerborg et al (1976), overcome the deficiencies of the

previous way by reducing the mesh dependency problem. The brittle behaviour of

148

concrete was described by a tensile stress-displacement curve rather than a stress-

strain curve as shown in Figure 5-8 (b). The technique relies on brittle fracture

concepts; the concrete fracture energy is defined as the energy required to open a

unit area of crack as a material parameter. The fracture energy can be illustrated as

the area under the stress-displacement curve which represents physically the work

done by the tensile stress and its conjugate opening displacement.

5.2.1.1.4.1 Tension stiffening model

The tension stiffening effect is considered owing to the fact that the cracked concrete

will initially carry some tensile stresses in the direction normal to the crack due to

concrete and steel reinforcement interaction. This can be performed by assuming a

gradual release of the concrete stress component normal to the cracked plane.

Tension stiffening models based on strength criteria have been represented by three

curves which are linear, bilinear and exponential curves in the current analysis. The

exponential curve shown in Figure 5-9 was obtained from Wang and Hsu (2001).

While, the bilinear curve was obtained by Peterson (1996)

(5.7)

Figure 5- 9: Uniaxial tensile stress-strain behaviour of concrete

(0.33 fctk, 0.22 )

0

0.5

1

1.5

2

2.5

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Str

ess

(M

Pa

)

Strain

Wang and Hsu linear bi-linear

149

5.2.1.2 Steel reinforcement

The elastic-plastic bilinear kinematic hardening model was utilized for steel

reinforcement. This model adequately accounts for the Bauschinger effect. This is

defined as a reduced yield stress upon cyclic loading, after plastic strain has been

reach during the initial loading. This Bauschinger effect decreases with continued

cycling. The true stress and true strain values, which will be described in section

5.2.2, were then inserted in the plastic option input of the ABAQUS software.

5.2.1.3 Carbon fibre reinforced polymer

The CFRP composite strip was modelled as an orthotropic elastic material and it has

linear behaviour up to failure. The stress-strain relationships can be expressed thus;

(5.8)

where the stiffness matrix consists of nine independent elastic stiffness parameters

( ), which were defined as shown in Equations (5.9)-(5.16)(ABAQUS, 2011);

(5.9)

(5.10)

(5.11)

(5.12)

(5.13)

(5.14)

, (5.15)

(5.16)

150

5.2.2 True stress and plastic strain

Nominal stress and strain should be converted to their true values and plastic strain

should be calculated as shown in following equations, According ABAQUS/standard

User manual.

l

dld (5.17)

)ln(

o

l

l l

l

l

dl

o

(5.18)

Where:

l = The current length, o

l = the original length and = the true strain

The stress that is accompanied to this strain called true stress and calculated as

follow.

A

F (5.19)

Where F the force in the material and A is the current area.

The relations between nominal and true strain can be written as follow.

1

0

o

o

nom

l

l

l

ll (5.20)

)1ln(nom

(5.21)

By considering the incompressible nature of the plastic deformation and assuming

the elasticity is also the incompressible; the relationship between true stress and

nominal stress is formed as follow.

lAAloo (5.22)

)(

o

nom

ool

l

l

l

A

F

A

F (5.23)

ol

l can be substituted as

nom1

)1(nom

(5.24)

151

5.2.3 Main meshing elements

In this section, a description is presented of the additional elements which have been

used in the one-way RC slabs analysis; 3D solid elements used for the concrete

components have already been described in Chapter 4.

5.2.3.1 Truss element

In ABAQUS/ standard a linear 3D two node truss element with three degrees of

freedom at each node (T3D2) was used to represent the discrete reinforcement bars

in reinforced concrete slab examples. Figure 5-10 shows truss elements are

embedded into “host” three – dimensional (3-D) continuum brick elements.

Embedding means that the translational degrees of freedom at the nodes of the

embedded element are restrained and become limited to the corresponding

interpolated values (shape function) in the host continuum element.

Figure 5- 10: Truss element AB embedded in (3-D) continuum element; node A is

constrained to edge 1-4 and node B is constrained to face 2-6-7-3

5.2.3.2 Shell element

Conventional shell elements (STRI3: A 3 node triangular facet thin shell, with six

degree of freedom at each node, faceted element means initial curvature is ignored).

This element has been decided to use to model CFRP in the one-way reinforced

concrete slab in ABAQUS/ standard after a convergence investigation was

152

undertaken. A dense mesh of this element type may be required in order to obtain

accurate results during the analysis. Figure 5-11shows the (STRI3) element.

Moreover, the STRI3 element has the same aspects of a conventional shell element

(S4R5). However, the STRI3 element cannot be used with thick shell problems.

Therefore, the transverse shear stiffness to enforce the Kirchhoff constraints

numerically is not applicable for this element.

Figure 5- 11: A 3 node triangular facet thin shell

5.2.4 Boundary condition

The proper modelling of boundary conditions in ABAQUS/ Standard is considered

one of the most complicated parts of the model. The supporting condition has been

modelled in the one-way slabs as simply supported without any horizontal restraint.

Due to symmetry of the support and loading conditions, only a quarter of the simply

supported one-way slabs and half of the one-way slab with an overhang at one

extremity have been considered. The degrees of freedom of all nodes along the

middle of one-way slab (surface 1) are restricted to move in Y-direction due to

symmetry. All concrete nodes, CFRP nodes and steel reinforcement nodes, which lie

on the other symmetry surface (surface 2), are restricted to move in x-direction

because of symmetry as shown in Figure 5-12. Where axes 1, 2 and 3 represent the

three coordinate axes x, y and z respectively.

1

3

2 1

3

2

153

Figure 5- 12: Finite element model for 3D analysis of on-way slabs (a) Quarter

model of the CFRP-strengthened RC slabs (Group S); (b) Half model of the CFRP-

strengthened RC slabs (Group C)

Mid-span

(Surface 2) X-symmetry plane & B.C

U1=UR2=UR3=0

(Surface 1) Y-symmetry plane & B.C

U2=UR1=UR3=0

Pressure

Loading

Load plate

Support B.C U3=UR3=UR1=0


U2=UR1=UR3=0



(2P/3) Load plate

(P/3) Load plate at a

cantilevered overhang

CFRP Sheet

(b) U: 1, 2, 3 = Translation in X, Y and Z directions respectively UR: 1, 2, 3 =Rotation about X, Y and Z directions respectively

154

5.2.5 Loads

The line loading (Figure 5-12) has been applied as an equivalent pressure on the top

surface of the load plate over a concrete contact width of 2.5mm. The cyclic load

was modeled using a modified load protocol recommended by FEMA (2007). The

load protocol has been amended to use only the positive loading scenario, i.e. load

reversal does not occur (Figure 5-13). This is more characteristic of imposed floor

loads on buildings or traffic loads on bridges (i.e. on/off loading as opposed to load

reversal which is more associated with wind and seismic actions). This protocol is

appropriate to low cycle fatigue where the maximum load amplitude of the cycle is

greater than 50% of the member’s ultimate load and where typically less than one

million cycles are needed to induce failure of the member. In this load protocol, the

first stage of the low fatigue cycle applies ten cycles of deformation amplitude i.e.

= 0.1 of the ultimate deformation in the monotonic case, this is followed by three

further cycles of amplitude 1.2 times the deformation amplitude in the first stage i.

e. . In each of the subsequent stages, the deformation amplitude is

increased by 0.2 (i.e. , ,.. , etc.), while subjecting the

specimen to three cycles until complete damage.

Figure 5- 13: Load protocol: (a) FEMA461 (b) modified FEMA461 (FEMA (2007))

(a) (b)

155

5.3 Validation of the simply supported CFRP-strengthened one-

way RC slabs (Type S)

5.3.1 Model description

Arduini et al. (2004) tested full- scale one- way reinforced concrete slabs with and

without unidirectional CFRP under simply supported conditions. The group of slabs

was loaded symmetrically by two line loads and it was identified as type (S). Which

consisted of three sets (T1 to T3) based on different a mounts of internal steel

reinforcement in tension and compression. Each slab set has two different levels of

CFRP strengthening (L1 to L2).


Figure 5-12 (a) shows the FE model of the simply supported CFRP-strengthened RC

one-way slab with a clear span of 4.5 m as modelled using the ABAQUS software.

The test load was applied as a uniform pressure on the top surface of the steel

bearing plate (2.5 mm width and 1500 mm length, which is equivalent to the full

width of the slab, so as to uniformly distribute the load across the concrete surface).

In order to minimise computational burden, only a quarter of the slab has been

modelled in the 3DFE analysis, although, all conditions (loading, boundary

conditions and geometry symmetry) were properly accounted, as shown in Figure 5-

14. The restrained degrees of freedom at the symmetrical edge boundary conditions

are also shown in Figure 5-12. The element type is decided to use at each instance,

namely; concrete, reinforcement bars, CFRP as shown in a close-up view of the

mesh in Figure 5-14. and explained as follows, a 3D eight-node linear brick element

with reduced integration and hourglass control (C3D8R) for modelling the concrete

was most appropriate. For the embedded reinforcement bars, a linear 3D two node

truss element with three degrees of freedom at each node (T3D2) was used. The

CFRP composite plate was modelled using linear 3D three-node triangular facet thin

shell element (STRI3). The cohesive contact was applied between the CFRP and

concrete slab using the cohesive surface technique, which is represented as part of

the surface interaction properties that were assigned to a contact pair (adhesive

thickness was negligibly small). A nonlinear static, general step was performed to

analyse the current model. The basic algorithm of this analysis is the Full Newton

156

method, where the numerical solution is defined as a series of increments with

iterations to achieve equilibrium within each increment. Material and geometrical

details of the RC slab strengthened with CFRP are provided in Tables 5-2 and 5-3

respectively.


type (S) with a close-up view of the mesh

Table 5- 2: Details of materials used for slabs (S) &(C).

Material Description Value

Concrete

Elastic modulus, GPa 33

Poisson’s ratio 0.15

Characteristic compressive strength(fc), MPa 33

Characteristic tensile strength(ft), MPa 2.2

Reinforcement bars

Elastic modulus, GPa 200

Poisson’s ratio 0.3

Yield strength of reinforcing bar (fy), MPa 512

Longitudinal modulus (E1), Gpa 230

*Transverse in-plane modulus(E2), GPa 23

Truss element (Steel) 3-D Solid element (concrete)

Cohesive surface interaction

Shell element (FRP)

Applied load

157

CFRP

*Transverse out-plane modulus(E3), GPa 23

*In- plane shear modulus (G12), GPa 6.894

*out- of-plane shear modulus (G23), GPa 4.136

*out- of-plane shear modulus(G13),GPa 6.894

*Major in -plane Possion’s ratio, ν12 0.3

*Out-of-plane Possion’s ratio, ν23 0.25

*Out-of-plane Possion’s ratio, ν13 0.25

Characteristic tensile strength(ft), MPa 3400

*: material properties are taken according to the reference (Reddy, 2004).

Table 5- 3: Details of geometry used for Slabs Type (S)

code

Dimension(m)

Tension steel

Compression

steel

CFRP

Span

L(m)

Ns* ϕ

(mm)

ρs

Ns’*

ϕ

(mm)

ρ's wf

(mm)

Nf Af

(mm2)

Lf

(m)

4.5

S-T1L0

5.0 x 1.5 x 0.24

8 ϕ 12

0.0027

8 ϕ 12

0.0027

0 0 0 0

S-T1L1

800 1 132

4.4

S-T1L2

1500 1 247

S-T2L0

11 ϕ 18

0.0085

11 ϕ 18

0.0085

0 0 0 0

S-T2L1

1500

1 247

4.4

S-T2L2

4.33 1072

S-T3L0

8 ϕ 14

0.0037

6 ϕ 10

0.0014

0 0 0 0

S-T3L1

900 1 148

4.4

S-T3L2

1500 1 247

Ns* ϕ(mm): number and reinforcing bar diameter, that is 8 ϕ 12 means 8 reinforcing bars 12 mm in

diameter.

158

5.3.3 Investigation of numerical model parameters

In this section, various numerical model parameters which may affect the prediction

of ultimate load and slab stiffness were investigated. Firstly, a mesh sensitive study

was performed to select the optimum mesh sizes. Then, the influence of different

tension stiffening curves on the performance of one-way slabs was observed.

Moreover, the concrete plasticity parameters such as the dilation angle Ψ and Kc

were also investigated in the current study. For the numerical model parameters

investigation purpose, strengthened one-way RC slab S-T2L2 was selected.

5.3.3.1 Effect of mesh size

The mesh size sensitivity for each instance (namely; concrete, reinforcement bars,

CFRP) of the strengthened one-way RC slab (S-T2L1) was verified. The load mid-

span deflection behaviour was considered as a reference in determining the

appropriate mesh size. Figure 5-15 (a, b and c) shows the comparison between

numerical results with experiments for different mesh size of concrete, steel and

CFRP, respectively. It was found that there is no effect of mesh size along the length

and width of the concrete slab on the load deflection behaviour. While, it has

noticeable affect over the thickness of concrete slab since the stresses due to flexural

load throughout the thickness of concrete slab can be analysed correctly with

increase layer numbers.

Moreover, it can be seen from this figure that the load deflection behaviour of the

strengthened RC slab is more sensitive to the concrete mesh size than to the two

other instance (steel & CFRP) because the line load and boundary conditions applied

at the concrete part. Brilliant matching can be obtained between the FE simulation

results experimental results corresponding to the mesh sizes shown in Figure 5-15 (4

layers, 80 and 100 mm for concrete, steel and CFRP respectively). The accuracy in

this mesh size case in terms of FE predictions to experimental ultimate load was

93.4%. Therefore, it was decided to use this mesh size for the rest of slabs.

159

Figure 5- 15: Sensitivity of the S-T2L1 slab behaviour to the mesh size of (a) the

concrete; and (b) the steel reinforcement (c) the CFRP plate

5.3.3.2 Effect of tension stiffening curve

Figure 5-16 shows the comparison of numerical and experimental load-deflection

responses of the slab (S-T2L2) for the three different tension stiffening curves. In

both linear and bi-linear models, the direct influence of tension stiffening after the

occurrence of flexural cracking gradually disappeared and this resulted to the

abortion of the run. The exponential model on the other hand, retained the flexural

stiffness up to the failure load. This due to the fact that the exponential curve is

characterized by gentle loss of the tensile strength, which introduces a realistic

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1, Concrete-2 layers

S-T2L1, Concrete-3 layers S-T2L1, Concrete-4 layers

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1, Steel mesh -30 mm

S-T2L1, Steel mesh -50 mm S-T2L1, Steel mesh -80 mm

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1, CFRP mesh-80 mmS-T2L1, CFRP mesh-100 mm S-T2L1, CFRP mesh-130 mm

(a) (b)

(c)

©

160

representation of the interaction between embedded steel reinforcement and

concrete. Thus, the exponential curve has been proposed to model tension stiffening

for strengthened RC slabs analysis.

Figure 5- 16: Load-deflection curve of slab S-T2L1 with different tension stiffening

models.

5.3.3.3 Effect of the dilation angle

Figure 5-17 demonstrates the effect of the dilation angle of concrete (Ψ) on the load

deflection behaviour of the strengthened one-way RC slab (S-T2L1). It can be seen

that a dilation angle of concrete equal 370

gives the best performance of the slab S-

T2L1 compare to other values of dilation angle. In fact this value was used already

by Coulomb’s work which has been described by Heyman. Changing the dilation

angle causes convergence problems and the numerical model terminates because this

angle affected principal stresses of concrete generated due to external loading

according to the dilation angle definition in Section 5.2.1.1.2.

Figure 5- 17: Load-deflection curve of slab S-T2L1 with different dilation angle

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1 (exponential softening)

S-T2L1 (bilinear softening) S-T2L1 (linear softening)

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1 (dilation angle =12)

S-T2L1 (dilation angle = 20) S-T2L1 (dilation angle =30)

S-T2L1 (dilation angle =37)

161

5.3.3.4 Effect of the Kc

Figure 5-18 demonstrates the effect of the ratio of the second stress invariant on the

tensile meridian (T.M.) to that on the compressive meridian (C.M.) (Kc) on the load

deflection behaviour of the strengthened one-way RC slab (S-T2L2). Three different

values for Kc (i.e. Kc=0.5, 0.667 and 1). It is found that the variation of Kc value

does not influence the entire behaviour of the load deflection but slightly changes the

value of ultimate load. It is also noticed when Kc=0.5, some convergence problem

occurred, leading to termination in the nonlinear stage. It was decided to use the

default value which has been suggested by ABAQUS, (2011).

Figure 5- 18: Load-deflection curve of slab S-T2L1 with different Kc.


The validation of the present FE predictions in terms of ultimate load, mid-span

deflection and ultimate strain in steel and CFRP are compared with the experimental

results (Table 5-4). Table 5-4 indicates that the ratio of FE predictions to

experimental ultimate load ranges from 0.873 to 1.052 with a standard deviation of

0.063. The predicted failure mode for all one-way RC slabs was agreement with

experimental observations as illustrated in Table 5-4. Figure 5-19 and Figure 5-20

shows the experimental and FE prediction results in terms of load to mid-span

deflection curves as well as load-strain curves in steel and CFRP obtained at the mid-

span of selected slabs, respectively, where it can be observed that the experimental

results and FE predictions are in good agreement throughout the entire loading

range.

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)

S-T2L1 S-T2L1 (Kc=0.5) S-T2L1 (Kc=0.667) S-T2L1(Kc=1)

162


curves. (a) S-T2L0, (b) S-T2L1, (c) S-T2L2.

Figure 5- 20: Comparison of predicted and experimental load-strain curves at mid-

span, (a) Steel, (b) CFRP.

0

100

200

300

400

500

0 20 40 60 80 100

Lo

ad

(K

N)

Deflection (mm)

S-T2L0-Exp. S-T2L0-Num.

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Lo

ad

(K

N)

Deflection (mm)


0

200

400

600

800

1000

0 20 40 60 80

Lo

ad

(K

N)

Deflection (mm)


0

200

400

600

800

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Lo

ad

(K

N)

strain (Microstrain)

S-T2L2-Exp. (Steel) S-T2L2 Num. (Steel)

0

200

400

600

800

0 1000 2000 3000 4000 5000

Lo

ad

(K

N)

strain (Microstrain)

S-T2L2 Exp. (CFRP) S-T2L2 Num. (CFRP)

(a) (b)

(c)

(a) (b)

163

Table 5- 4: Comparison of the predicted and experimental results for one-way RC slabs strengthened with CFRP type (S)

*: Strain gages not working, NA: Not applicable

Code

Experimental Numerical Accuracy

Ultimate

load

(kN)

Midspan

deflection

f (mm)

Ultimate

strain in

steel

bars

%

Ultimate

strain in

CFRP

%

Failure

mode Ultimate

load

(kN)

Midspan

deflection

f (mm)

Ultimate

strain in

steel

bars

%

Ultimate

strain in

CFRP

%

Failure

mode

S-T1L0 136 110 > 0.1 NA Steel yielding

136.2 114.7 4.1 NA Steel

yielding 1

S-T1L1 210 68 0.2 0.8 Fibre rupture

184.6 63.7 2.4 0.84 Fibre

rupture 0.88

S-T1L2 302 86.2 0.7 * FRP peeling

273.5 89 1.6 0.6 FRP

peeling 0.91

S-T2L0 380 84 > 0.3 NA Steel yielding

399.9 84.6 2.4 NA Steel

yielding 1.05

S-T2L1 560 `110 0.3 0.9 Fibre rupture

522.9 110.2 1.4 1 Fibre

rupture 0.94

S-T2L2 715 65 0.4 0.6 Concrete shear

& FRP peeling 684.9 65.9 0.7 0.4 FRP

peeling 0.96

S-T3L0 176 120 0.1*

NA Steel yielding

180.5 123.9 4.5 NA Steel

yielding 1.03

S-T3L1 285 91 0.5 0.8 Fibre rupture

262.2 89.4 3 1.2 Fibre

rupture 0.92

S-T3L2 340 78 > 1 0.9 FRP peeling

296.7 78.7 1.5 0.9 FRP

peeling 0.80

164

5.4 Effect of using modified FEMA 461 load protocol for (S-T1) slabs

In order to assess the damage accumulation due to the effect of cyclic loading, the

numerical results in terms of load versus mid span deflection curves were recorded

under monotonic loading and under cyclic fatigue loading using the FEMA 461

modified load protocol (Figure 5-21). All through the discussion, the predictable

behavioural aspects and practice of slab series (S-T1) are used as a reference. The

ultimate load in the monotonic response of slab S-T1L0 is significantly higher than

the ultimate load in the fatigue response when compared with the other two slabs

(i.e. S-T1L1 & S-T1L2). This is because the effect of repeated load cycles on the

slabs’ stiffness is less than the effect of added CFRP. Hence, Figure 5-21 shows that

the mid-span deflection of the unstrengthened slab (S-T1L0) exhibits a higher

deflection than the slabs strengthened with 800 mm (S-T1L1) and 1500 mm (S-

T1L2) width of CFRP respectively (i.e. increase in CFRP contact area with concrete

reduces the ductility of the specimen). The ultimate load reduction percentage

spanned from 4.70% (S-T1L0) to 0.1% (S-T1L2). . Table 5-5 summarized the

comparison of the monotonic and cyclic loading results of slabs type (S).

Table 5- 5: Comparison of the monotonic and cyclic loading results of slabs type (S)

Code Monotonic loading Cyclic loading

Ultimate

load

(kN)

Ultimate

strain in

CFRP

%

Failure

mode

Ultimate

load

(kN)

Ultimate

strain in

CFRP

%

Failure

mode

1 S-T1L0 136.2 NA Steel yielding 130.4 NA Steel yielding

2 S-T1L1 184.6 0.84 Fibre rupture 180.9 0.83 FRP peeling

3 S-T1L2 273.5 0.7 FRP peeling 273.1 0.6 FRP peeling



6 S-T2L2 684.9 0.4 FRP peeling 683.2 0.25 FRP peeling



9 S-T3L2 296.7 0.95 FRP peeling 293 0.88 FRP peeling

165

Figure 5- 21: Comparison monotonic and cyclic load-Mid-span deflection. (a) S-

T1L0 (b) S-T1L1, (c) S-T1L2.

0

30

60

90

120

150

0 20 40 60 80 100 120

Loa

d (

KN

)

Deflection (mm)

FE analysis (FEMA 461 Load Protocol)FE analysis (experment Load protocol)

0

50

100

150

200

0 20 40 60 80

Load

(K

N)

Deflection (mm)

FE analysis (FEMA461 Load Protocol)

FE analysis (experment Load Protocol)

(a)

(b)

0

50

100

150

200

250

300

0 20 40 60 80

Loa

d (

KN

)

Deflection (mm)

FE analysis (FEMA461 Load Protocol)FE analysis (experment Load Protocol)

(c)

166

5.4.1 Interfacial slip profile

In this section, the determined interfacial slip profiles between the CFRP sheets and

concrete surface for (S-T1) slabs series are discussed. The interface behaviour

between the concrete surface and CFRP sheet was modelled using the Chen and

Teng (2001) bond-slip model for the static case. While, applying the post fatigue

bond slip curve as described in Chapter 3 and validated in Chapter 4 in a

strengthened RC slab subjected to modified FEMA 461 load protocol. Figure 5-22

shows the predicted relative slip distributions at the CFRP - concrete interface at four

different load levels for the specimens strengthened with CFRP. The interface slip is

estimated as the difference in horizontal displacement (i.e. in the longitudinal

direction) between the adjacent FE nodes in the tension side of the concrete slab and

the CFRP layer.

This comparison illustrates that the predicted interfacial slip values for the slabs

tested under the modified FEMA461 load protocol are higher than those of the

specimens tested under the monotonic load protocol. It has also been shown that the

difference between the interfacial slip profiles of two different load protocols are

increased significantly with increased load levels. This is due to the fact that there is

a gradual loss of stiffness for concrete, steel and interface bond resulting from cyclic

loading. In these interfacial slip profiles, slip was observed to vary from the centre of

the slab to the end support (Figure 5-22). This corresponds to the areas of maximum

tensile plastic strain in the concrete (i.e. point of line load application) and the region

of increasing interfacial slip. The strengthened one-way RC slab (S-T1L2) under

static load as well as under modified FEMA cyclic load has the FRP/concrete

interface slip higher than the slip value at peak shear stress (S0), these being equal to

0.042 mm and 0.032 mm, respectively, for S-T1L1 and S-T1L2 respectively. This

means that the debonding initiation which occurred at a point on the FRP/concrete

interface is the governing failure mode of slab S-T1L2 in both load regimes,

whereas, S-T1L1 suffered failure associated with separation of CFRP sheet from the

concrete when only subjected to the modified FEMA cyclic load protocol. This

observation suggests that separation should be initiated in the region between two

line loads and then propagates towards the ends of the support, which is in

agreement with a contour plot (Figure 5-23) for the damage initiation criterion at the

CFRP/concrete interface at failure.

167

Figure 5- 22: Comparison of slip profile at monotonic and cyclic loading. (a)S-T1L1,

(b) S-T1L2

(a)

(b)

(b)

168


interface for slabs (a) S-T1L2 under monotonic loading & (b) S-T1L2 under cyclic

loading at failure.

From figure 5-23, according to the legend; the red colour shows that the maximum

nominal stress criterion has been satisfied and transfer of stress among CFRP and

concrete has started to gradually reduce until debonding occurs, whereas the blue

colour shows that the CFRP sheet is still bonded to the tension side of the concrete

slab. (CSMAXCR) is maximum traction damage initiation criteria for cohesive

surface.

(a)

(b)

169

5.4.2 Tensile strain profiles along CFRP

Figure 5-24 (a) and (b) depict predicted tensile strain distribution along CFRP at four

different load levels for the S-T1L1 and S-T1L2, respectively. From these figures, it

can be seen that the tensile strain profiles along CFRP sheet have almost the same

trend as those of the interfacial slip profiles which means that the strain values at the

point of line load application near to the centre of the slab are significantly higher

than those near to the end support. Strengthened one-way slabs (S-T1L1) have a

CFRP rupture failure mode in the middle of slab’s span due to the strain reaching the

same value of the strain in experimental case. On the other hand, the figures clearly

indicate that during early load levels, the strain profiles are linear. Upon increasing

the load levels, the strain profiles then begin to fluctuate due to flexural cracks that

occurred in the tension side of the RC one-way slabs. As earlier mentioned (Figure

5-24), when the load levels increase, the predicted tensile strains in the longitudinal

direction of CFRP (corresponding to the specimens subjected to modified FEMA461

load protocol) become much smaller than the specimens subjected to monotonic

loading. Also, the strain profiles show that the negligible strains near the end support

indicate that the CFRP is adequately anchored (i.e. effectively no slip at its end).

(a)

170

Figure 5- 24: Comparison of strain profile at monotonic and cyclic loading. (a)S-

T1L1, (b) S-T1L2

5.5 Validation of the simply supported CFRP-strengthened one-

way RC slabs with an overhang at one extremity (Type C)

5.5.1 Model description

Arduini et al.(2004) tested full- scale one- way reinforced concrete slabs with a

cantilevered overhang under simply supported conditions. This series of slabs was

strengthened with unidirectional CFRP. It was loaded by two line loads one at the

extremity, an overhang edge (one-third of total load) and another line load at the

middle distance between two supports (two-thirds of total load) and it was identified

as type (C). Which consisted of two sets (T1 and T2) based on different a mounts of

internal steel reinforcement in tension and compression. Each slab set has two

different levels of CFRP strengthening (L1 to L2).

(b)

171


Figure 5-12 (b) shows the FE model of the simply supported slab over 4 m with a

2.25 m overhang at one extremity CFRP-strengthened RC one-way slab using the

commercially available software ABAQUS. It has a rectangular cross section 1.5 m

in wide and 0.24 m in depth. The test load was applied as a uniform pressure on the

top surface of the steel bearing plate similar to the simply supported slabs as

described in Section 5.3. By making use of geometric and loading symmetry, a

segment which represents a half of slab type (C), was used for the finite element

analysis to reduced computational time. Figure 5-25 show the finite element

idealization of the half slab type (C). Eight –node (3D) solid elements are

implemented to represent the concrete with three degrees of freedom at each node

(C3D8R), two node truss elements with three translational degrees of freedom at

each node (T3D2) are used for steel reinforcement and three node triangular thin

shell element with six degrees of freedom (STRI3) are employed to represent the

CFRP. The material properties of concrete, steel and FRP geometrical details of the

RC slab strengthened with CFRP type (C) are mentioned in Tables 5-2 and 5-6

respectively.


type (C) with a close-up view of the me

Truss element (Steel)

3-D Solid element (concrete)


Shell element (FRP)

172

Table 5- 6: Specimen characteristics for slabs type (C)

Code

Dimension(m)

Tension steel

Compression

steel

CFRP Span L(m)

Ns* ϕ

(mm)

ρs

Ns’*

ϕ

(mm)

ρ's wf

(mm)

Nf Af

(mm2)

Lf

(m)

4.0

C-T1L0

6.5 x 1.5 x 0.24

8 ϕ 12

0.0027

8 ϕ 12

0.002

7

0 0 0 0

C-T1L1

800 1 132 3.5

+

3.5

C-T1L2

1500 1 247

C-T2L0

11 ϕ

18

0.0085

11 ϕ

18

0.0085

0 0 0 0

C-T2L1

1500

1 247 3.5

+

3.5

C-T2L2

5 4.33 6 1072

Ns* ϕ(mm): number and reinforcing bar diameter, that is 8 ϕ 12 means 8 reinforcing bars 12 mm in

diameter


Based on the numerical model parameters investigation performed in the previous

simply supported one-way RC slab type (S), it was found that a mesh with four

layers, 80 and 100 mm for concrete, steel and CFRP respectively is adequate mesh

size. An exponential curve based on Wang and Hsu (2001) was used to model

tension stiffening of concrete. Furthermore, the concrete plasticity parameters each

of the dilation angle (Ψ) and Kc were 370 and 0.667, respectively was used in the

current simulation. Numerical predictions will be compared with reported

experimental data for slabs type (C). The experimental results of six specimens of a

cantilevered overhang under simply supported conditions are used to validate the

results of the finite element analyses. Figure 5-26 and 5-27 show the graphical

comparison of the experimental and numerical results in terms of total load –

deflection curves as well as total load versus strain for steel and CFRP sheet at the

top of the support for selected slabs(C-T2). The deflection was measured under the

line load at the extremity of the overhang similar to experiment. Table 5-7 presented

a comparison between ultimate load capacities, deflection, ultimate strain in steel

bars ( ), ultimate strain in CFRP ( ) and mode of failure.

173

Table 5- 7: Comparison of the predicted and experimental results for one-way RC slabs strengthened with CFRP type (C)

*: Strain gauges not working, NA: Not applicable.

Code

Experimental Numerical Accuracy

Ultimate

load

(kN)

Deflection

f (mm)

Ultimate

strain in

steel

bars

%

Ultimate

strain in

CFRP

%

Failure

mode

Ultimate

load

(kN)

Deflection

f (mm)

Ultimate

strain in

steel

bars

%

Ultimate

strain in

CFRP

%

Failure

mode

C-T1L0 135 27 > 0.3 NA Steel yielding

162.9 97.6 2.56 NA Steel yielding +

concrete crshing 1.2

C-T1L1 204 75 * 0.4 Top FRP rupture

on support 237.6 76.2 1.37 0.4

Top FRP rupture

on support 1.16

C-T1L2 282 60 0.3 0.6 Top FRP rupture

on support 279.3 63.3 0.63 0.39

Peeling 0.99

C-T2L0 450 37 * NA

Steel yielding

464.3 100. 2.85 NA

Steel yielding +

concrete

crushing

1.03

C-T2L1 630 75 > 0.3 0.6 Concrete

crushing 611.8 72.4 0.82 0.4

Concrete

crushing+peeling 0.97

C-T2L2 750 46 0.3 0.4 Concrete

crushing+peeling 769.4 47. 0.37 0.29

Concrete

crushing+peeling 1.03

174

Figure 5- 26: Comparison of predicted and experimental load-mid-span deflection curves.(a)

S-T2L0, (b) S-T2L1, (c) S-T2L2

Figure 5- 27: Comparison of predicted and experimental load-strain curves at the top of the

support. (a) Steel, (b) CFRP

0

100

200

300

400

500

600

0 30 60 90 120

Lo

ad

(K

N)

Deflection (mm)

C-T2L0 Exp. C-T2L0 Num.

0

100

200

300

400

500

600

700

0 20 40 60 80

Lo

ad

(K

N)

Deflection (mm)


0

200

400

600

800

1000

0 20 40 60 80

Lo

ad

(K

N)

Deflection (mm)


0

200

400

600

800

1000

0 500 1000 1500 2000 2500 3000 3500 4000

Lo

ad

(K

N)

Microstrain (mm/mm)

C-T2L2 Exp. (STEEL) C-T2L2 Num. (STEEL)

0

100

200

300

400

500

600

700

800

900

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Lo

ad

(K

N)

Microstrain (mm/mm)

C-T2L2 Exp. (CFRP) C-T2L2 Num. (CFRP)

(a) (b)

(c)

(a) (b)

175

5.6 Effect of using modified FEMA 461 load protocol for (C-T1) slabs

Figure 5-28 shows the numerical results in terms of load versus mid span deflection

curves which were recorded under monotonic loading and under cyclic fatigue

loading using the FEMA 461 modified load protocol for (C-T1) slabs series. The

numerical load deflection curve does not show pronounced degradation. This is

because the interfacial bond stress and fracture energy for the cyclic case is limited

for the specific chosen load protocol (i.e loading range70%-15%). For the slab (C-

T1L0), the ultimate load in monotonic response was 162.86 kN compared with 152.8

kN ultimate load obtained from fatigue response. The numerical monotonic failure

load is greater than that load obtained from numerical cyclic load protocol by 6.2 %.

In this test slab, the failure modes for both responses are combined failure which is

steel yielding followed by concrete crushing near to the cantilever support. For the

strengthened slab (C-T1L1) and (C-T1L2), the ultimate load in monotonic response

were 237.6 and 279.3 kN respectively compared with 235.1 and 278.2 kN obtained

from the fatigue response. The numerical monotonic failure loads are greater than

that ultimate failure load obtained from fatigue response by 1.1% and 0.4 % for

strengthened slab (C-T1L1) and (C-T1L2) respectively. Based on the monotonic

load protocol, the top CFRP sheet rupture near the cantilever support is the mode of

failure for C-T1L1 specimen and CFRP sheet separation for C-T1L2. While based

on the fatigue load protocol, the failure mode is separation of the top CFRP sheet

near to the cantilever support. Thus, the monotonic and fatigue responses lead to

different failure mode predictions; this is due to the fact that, the bond-slip model

considered the post-fatigue bond slip model with lower fracture energy and interface

bond stress was used to model the bonding between the CFRP sheet and concrete

surface. Table 5-8 summarized the comparison of the monotonic and cyclic loading

results of slabs type (C).

176

Figure 5- 28: Comparison of monotonic and cyclic load-mid-span deflection. (a) C-

T1L0 (b) C-T1L1, (c) C-T1L2

0

30

60

90

120

150

180

0 20 40 60 80 100

Load

(KN

)

Deflection (mm)

FE analysis (FEMA461 load protocol)

FE analysis (experment load protocol)

0

50

100

150

200

250

300

0 20 40 60 80 100

Load

(K

N)

Deflection (mm)



0

50

100

150

200

250

300

0 10 20 30 40 50 60

Load

(KN

)

Deflection (mm)



(a)

(b)

(c)

177

Table 5- 8: Comparison of the monotonic and cyclic loading results of slabs type (C)

5.6.1 Interfacial slip profile

Figure 5-29 (a) and (b) shows the interfacial slip profile comparisons between

monotonic load and modified fatigue load at three different load levels for the

strengthened RC slabs C-T1L1 and C-T1L2, respectively. For both RC slabs, it is

obvious that the maximum slip values occurred near to the support for the top CFRP

sheets and at the middle distance between two supports for the bottom CFRP sheets.

This indicated the separation between the CFRP sheet and the concrete surface might

occur at the mid- span between to support or at the support from the cantilever side.

Also noticeable is that a negative slip variation can be seen near to the left support

because the cantilever edge causes this region to lift up and making the bottom side

the compression side. The strengthened one-way RC slabs (C-T1L1) and (C-T1L2)

under modified FEMA cyclic load have the FRP/concrete interface slip at the bottom

CFRP sheets higher than the slip value at peak shear stress (S0) for `C-T1L1 and C-

T1L2 which are equal 0.042 mm and 0.032 mm, respectively, which means that the

debonding initiation occurring at a point on the bottom CFRP sheet/concrete

interface is the governing failure mode of slab C-T1L1 and C-T1L2.

Code Monotonic loading Cyclic loading

Ultimate

load

(kN)

Ultimate

strain in

CFRP

%

Failure mode Ultimate

load

(kN)

Ultimate

strain in

CFRP

%

Failure mode

C-T1L0 162.9 NA

Steel yielding +

concrete crushing 152.8 NA

Steel yielding +

concrete crushing

C-T1L1 237.6 0.4

Top FRP rupture

on support 235.1 0.37

peeling

C-T1L2 279.3 0.38

Peeling

278.2 0.35

Peeling

C-T2L0 464.3 NA

Steel yielding +

concrete crushing 431.8 NA

Steel yielding +

concrete crushing

C-T2L1 611.84 0.41

Concrete

crushing+

peeling

598.8 0.35

peeling

C-T2L2 769.4 0.29

Concrete

crushing+

peeling

765.5 0.2

Concrete

crushing+

peeling

178

Figure 5- 29: Comparison of slip profile at monotonic and cyclic loading. (a)C-

T1L1, (b) C-T1L2

5.6.2 Tensile strain profiles along CFRP

Figure 5-30 (a) and (b) depict predicted tensile strain distribution along the CFRP at

three different load levels for the C-T1L1 and C-T1L2, respectively, in terms of

monotonic response as well as modified fatigue load. It was found that the prediction

strains of the top CFRP sheet at the distance (2000 mm) from the line load of the

-0.03

-0.02

-0.01

0

0.01

0.02

0 500 1000 1500 2000 2500 3000 3500

In

te

rfa

cia

l s

lip

(m

m)

Distance along the CFRP sheet (mm)

110 KN 160 KN 230.3 KN110 KN -Static 160 KN -Static 237.6 KN -Static

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0 500 1000 1500 2000 2500 3000 3500Inte

rfa

cia

l sli

p (

mm

)


154 KN 256 KN 279.2 KN

154 KN -Static 256 KN -Static 279.3 KN -Static

0

0.01

0.02

0.03

0.04

0.05

0 500 1000 1500 2000 2500 3000 3500

Inte

rfa

cia

l sli

p (

mm

)

Distance from the line load to the end of CFRP sheet (mm)

110 KN 160 KN 230 KN

110 Kn -Static 160 KN -Static 237.6 KN -Static

De-bonding

(I) along cantilever edge (II) along span between

supports (a) C-T1L1

0

0.01

0.02

0.03

0.04

0.05

0 500 1000 1500 2000 2500 3000 3500

In

te

rfa

cia

l slip

(m

m)


154 KN 256 KN 279.2 KN


De-bonding

(I) along cantilever edge (II) along span between

supports

(b) C-T1L2

179

cantilever edge is much higher than those of other region, since the major crack

region occurs in the top surface of the concrete near to support in the side of

cantilever. Strengthened one-way slabs (C-T1L1) has top CFRP rupture failure

mode near to the support that was also observed in the experimental test. Whereas,

(C-T1L1) has a top CFRP sheet peeling failure mode contrary what observed in

experimental test this is due to the presence of lifting hooks which caused rupture in

top CFRP sheet.

Figure 5- 30: Strain profile in the CFRP for strengthened one-way slabs (a) C-T1L1

(b) C-T1L2

(I) along cantilever edge (II) along span between supports

(a) C-T1L1

(I) along cantilever edge (II) along span between supports

(b) C-T1L2

-1500

-1000

-500

0

500

1000

1500

0 500 1000 1500 2000 2500 3000 3500S

tra

in (

Mic

ro

stra

in)



110 KN 160 KN 230.3 KN

0

1000

2000

3000

4000

0 500 1000 1500 2000 2500 3000 3500

Stra

in (

Mic

ro

stra

in)



110 KN 160 KN 230.3 KN

-2000

-1000

0

1000

2000

3000

0 500 1000 1500 2000 2500 3000 3500Mic

ro

stra

in


154 KN-static 256 KN-static 279.3 KN-static

154 KN 256 KN 279.2 KN

0

1000

2000

3000

4000

0 500 1000 1500 2000 2500 3000 3500

Mic

ro

stra

in


154 KN-static 256 KN-static 279.3 KN-static

154 KN 256 KN 279.2 KN

180

5.7 Summary

In this chapter, the development of a three-dimensional finite element model of

CFRP-strengthened RC slabs under cyclic loading has been described. A non-linear

damage plasticity model is adopted for modelling the concrete and the FE model

accounted for the nonlinearity of the concrete under cyclic loading by estimating the

stiffness degradation in the concrete for both compression and tension effects. A

surface cohesive based model was used to describe the interaction between the CFRP

and the concrete slab. The nonlinear bond-slip relationship of the bonding interface

is taken from numerical modelling of post-fatigue pull-out test, as explained in

Chapter 4. For the reinforcement bars, the Bauschinger effect was incorporated

through the application of the kinematic hardening model under cyclic loading. The

model was also validated with the findings from an earlier experimental study in

terms of ultimate load, mid-span deflection, ultimate strain in steel and CFRP and

failure mode. The validation results show the model has an acceptable level of

accuracy in terms of predicting the overall behaviour. From this basis, the suggested

3-dimensional finite element model introduces a more realistic model for capturing

the interface slip profile of composite sheets with the concrete slab during different

cyclic stages of loading (which is difficult, if not impossible to obtain

experimentally). It was observed that always the strengthened one-way reinforced

concrete slabs have debonding of the CFRP sheet from the concrete as a failure

mode for the modified FEMA 461 cyclic load protocol which is sometimes different

from the failure mode was observed in experimental load protocol (i.e. rupture in

CFRP sheet)

181

Chapter Six

Experimental Results of CFRP-Strengthened

Two-Way RC Slabs with Openings under

Monotonic and Cyclic Loading

6.1 Introduction

This chapter presents the experimental results of full scale two-way RC slabs

strengthened with CFRP plates and further validation of the numerical simulation

model presented in Chapter 5. The main objectives of these tests are to detect the

reduction in the strain at debonding induced by the modified FEMA cyclic load

protocol. However, the strain reduction due to cyclic loading history was observed in

single shear pull out tests previously (i.e. Chapter 3 and 4). Herein, the bond

behaviour in real structural elements (slabs), involving cracking, nonlinear multi-

axial material properties and damage effect for both steel and concrete is explored.

Flexural behaviour (up to the point of failure) of the strengthened two-way RC slabs

with a central opening under monotonic and cyclic load will be investigated by

monitoring the deflection, ultimate load capacity, crack patterns, strains and failure

mode.

6.2 Experimental programme

Two full scale CFRP-strengthened two-way RC slabs, simply supported on four

sides with a central opening, characterised by different loading hysteresis (static

(monotonic) and modified FEMA cyclic load protocol which has been described in

Chapter 5) were tested, so as to obtain the strain limit in CFRP plate at specimens’

failure. These two tests will be used as control tests, prior to conducting of the

parametric study using a finite element (FE) model.

182

6.3 Details of test slabs

Figure 6-1 shows a schematic representation of the test set-up. The dimensions of the

two-way RC slab are 1750 (length) x 1750 (width) x 90 (thickness) mm with central

square opening of 550 mm (length = width). The type of CFRP plate used is the

T700, with nominal thickness of 2 mm, length 1500 mm and 50 mm width, which

was bonded to the tension face of the concrete slab. The slabs were reinforced with

ten 10 mm diameter standard ribbed bars in each direction. The adhesive was

provided by Weber Building Solution (UK), while the CFRP plates were provided

by Reverie Ltd., (UK). The quantity of CFRP was estimated based on the quantity of

steel reinforcement in the opening, so as to keep the capacity of the section before

the opening equal. Figure 6-1 (a) shows the CFRP plate configurations. Details of

the estimations of the quantity of CFRP plates required to replace the steel

reinforcements in the opening are provided in Section 6.5.1.

183

Figure 6- 1: Slab dimensions and reinforcement details (a) Top view (b) side view

1750 m

m

1750

mm

55

0

mm

550

mm

125 mm

600 mm

(a)

(b)

25 mm

Applied load

Loading frame D 10 mm @ 185

mm

560 mm

550 mm 560 mm

750 mm

90 mm

184

6.4 Test Preparations

Firstly, a mould for casting the concrete slabs was constructed using 20 mm thick

plywood. All the contact edges of the specimen formwork were sealed with silicon.

The internal surface of the framework was also oiled prior to the positioning of the

steel reinforcement cage, so as to ease the process of de-moulding. Secondly, the

steel reinforcement cage was prepared in the laboratory, using deformed steel bars

with an appropriate length of 1800 mm. The steel bars were then cut using an

electrically powered hacksaw and then bent upwards at the slab ends, so as to

achieve a better confinement core for the concrete. The steel reinforcements in the

transverse and longitudinal directions were then connected to each other by

uniformly spaced (185 mm) spring steel reinforcement ties. Steel spacer bars, tied

using wires to the bottom of the steel reinforcement cage, were used to maintain the

correct bottom and side cover for the two slabs. Four lifting anchors (R12 mm) were

installed at the opposite sides of the slab’s formwork to enable safe lifting of the

slabs. Figure 6-2 (a) shows a photograph of the completed reinforcing cage

positioned in the mould. The final stage of the test preparations involves the casting

and curing of the concrete slabs. The concrete was mixed by a concrete mixer with a

maximum capacity of 400 kg. Each of the fresh concrete slabs was vibrated for

approximately 60 seconds, using a poker vibrator, prior to the levelling of the

concrete surface with a hand towel (see Figure 6-2). For each slab, additional 10

cubes and 6 cylinders of fresh concrete were taken during casting and then vibrated

on a shake table. The slab was then left to cure for approximately 24 hours and then

de-moulded. After de-moulding, the concrete slab was then covered with black

nylon sheets and then left to cure for a week. Three control cubes were tested after

seven days to measure the concrete compressive strength development, which was

found to be satisfactory. The curing process of the concrete slab was halted by the

removal of the black nylon sheet and surface preparation commenced as will be

further explained in Section 6.5.

185

Figure 6- 2: Preparation process (steel reinforcement positioned in mould, casting

and cubes)

6.5 Surface preparation and bonding process for CFRP

The bonded method applied in the current reinforced concrete slabs involved the

external strengthened with CFRP plates, as suggested by the following design

guides;

In order to remove the layer of pure cement (owing to the fact that the tensile

strength of pure cement alone is very low compared to the tensile strength of

concrete) from the concrete surface around the opening in the tension side, a

surface grinder was used to remove approximately 5 mm until the aggregate

became visible (see Figure 6-3).

(b)

(c)

(d)

(a)

186

The loose particles and dust were removed from the concrete surface using a

vacuum cleaner and then washed with water to improve the bond between the

concrete and CFRP plates.

The CFRP plates were sized to 1500 mm lengths in the laboratory, using an

electric cutter.

In order to improve the appearance of the CFRP surface as well as enhance

adhesion, acetone was used to clean the CFRP surface. Full descriptions of

the adhesive components (i.e. epoxy and hardener) have been provided in

Section 3.4.1.

A layer of the adhesive was applied onto the ground concrete and CFRP

surfaces (see Figure 6-3) and then brushed out using a paint brush. The

thickness of the adhesive layer applied to both surfaces (i.e. concrete and

CFRP) was uniform and ranged between 1-1.5 mm.

Adequate pressure was applied to the CFRP plate, so as to expel the excess

resin as well as eliminate bubbles from the joint. The bonded reinforced

concrete slabs were then allowed to cure inside the laboratory for seven days.

187

Figure 6- 3: Bonding CFRP plate to concrete substrate, profiling the concrete surface

with a surface grinder and applying adhesive layer to the concrete

6.5.1 Evaluation of CFRP plate amount

The ACI 318 code (1995) that specifies the guidelines for creating openings in slabs

under static case was adopted in the current experiment. According to this standard,

the amount of steel reinforcement from the opening shall be distributed around the

opening. Consequently, this amount steel reinforcement will then be used to estimate

the quantity of CFRP plates to be bonded around the opening. Hence, the current

experiment considered the following assumptions during the estimations.

188

Strains in the reinforcement (i.e. CFRP and steel) and concrete are directly

proportional to the distance from the neutral axis (assuming that the plane

sections before loading remain plane after loading).

Full composite action between the concrete and external CFRP plates.

The shear deformation within the adhesive layer is ignored.

The maximum usable compressive strain in the concrete is 0.003.

The tensile resistance of the concrete is ignored.

The CFRP material has a linear elastic stress-strain relationship until failure.

Let us assume that the steel reinforcement area in the opening is As1, the remaining

steel reinforcement area in slab section is As2 and the CFRP plate area is Af (see

Figure 6-4).

For the section without opening, the nominal flexural capacity can be calculated

based on the equilibrium of forces and strain compatibility as illustrated in Figure 6-

4 (a)

(6.1)

The nominal flexural capacity of the section which its opening was strengthened

with CFRP can be obtained by calculating as shown in Equation (6.1), which is

also illustrated by Figure 6-4 (b).

(6.2)

In order to keep same nominal flexural capacity for the section without opening and

the section with its opening strengthened with CFRP plate, and must be

equal.

(6.3)

During the elastic range, Hook’s law can be used to obtain the strains in steel and

CFRP, as shown in Equation (6.4).

189

(6.4)

Applying strain compatibility,

(6.5)

Substituting Equations (6.4) and (6.5) into Equation (6.3), yields the following

relationship

(6.6)

Where;

Number of steel bars equal 10, steel reinforcement area in the opening, As1 equals

157.1 mm2, section height (h) equals 90 mm, section width (b) equals1750 mm,

depth of bottom steel reinforcement to the top surface of slab section (d) equals 65

mm, steel elastic modulus equals 200000 MPa, concrete elastic modulus equals

23700 MPa, steel yield stress equals 550 MPa, concrete compressive strength equals

37.5 MPa.

Calculate the CFRP-system design material properties

The existing state of strain on the soffit

Determine the bond-dependent coefficient of the CFRP system

Ef . tf = 115600 X 2 = 231200 >180000. Therefore,

Estimate Cb, the depth to the neutral axis

190

Assume Cb = 12 mm

Determine the effective level of strain in the CFRP reinforcement

Calculate the strain in the internal reinforcing steel

Calculate the stress level in the reinforcing steel and FRP

Calculate the required CFRP plate area (See Equation (6.6))

=129 mm2

Calculate the internal force resultants and check equilibrium

191

Cb = 11.8 mm OK

The value of c selected for the first iteration is correct.

Once the area of the CFRP needed across the entire slab section has been

determined, then the thickness (2 mm) and width (50 mm) for each CFRP strip was

also determined.

Figure 6- 4: strain, stress and internal forces at ultimate capacity

d

h

b

(b) Section with opening strengthened with CFRP plate

N.A

Cb

As2

Af

d

h

b

(a) Section without opening

N.A

Cb

As1

+As2

192

6.6 Test set-up

Figure 6-5 shows photographic and schematic representations of the test

experimental setup. The steel testing frame consists of four channel section columns

300 x 100 x 46, bolted to strong points on the floor via 32 mm threaded rods. The

load was applied through 500kN cyclic hydraulic jacks, bracketed onto the steel

universal I-section beam 610 x 305 x 179. The manner in which the load was applied

to the slabs is similar to that described by Elsayed (2009). A special loading frame

on a perimeter of 750 x 750 mm (see Figure 6-6) was used to distribute the actuator

load around the opening as a line load. The 1750 x 1750 x 90 mm concrete slabs

were supported by steel beams to provide a line support distance of 75 mm from the

slab edges. Steel plates of 40 mm thickness of and threaded steel rods of 20 mm

diameter were set at each slabs’ corner, which were fixed with supporting frame in

order to prevent up-lift movement. The first slab was subjected to monotonic loading

with a loading rate of 0.02 mm/s, while the second slab was subjected to cyclic

loading at a frequency of 1 Hz. The applied loads were measured directly from the

hydraulic jacks that have been calibrated using load cells, prior to the

commencement of the test.

193

Figure 6- 5: Test setup for the RC slab (a) Laboratory photograph (b) Schematic

view

Ground level

Universal Beam 610 x 305x 179

Opening slab

500kN hydraulic

jacks

Loading frame

Steel plate

Universal column 300 x 100 x 46

Universal Beam 610 305x179

Universal Beam 203 x 102 x23

194

Figure 6- 6: Load frame (all dimensions in mm)

50

50

12

Side view

750

Steel

box

Steel plate

Top view

250 250 250

250

250

250

5

0

5

0 5

750

1

2

Steel box

section Square steel plate section

195

6.7 Instrumentation

The strain in the RC slab assembly (concrete, CFRP plates and internal steel

reinforcements) was measured using both internally and externally installed strain

gauges. Four external strain gauges were bonded to the cleaned concrete surface (i.e.

compression side) after pre-coating with special adhesive, so as to achieve a smooth

surface. The installed strain gauges were then protected with layers of specialized

silicon. Each of the four strain gauges had a length of 34 mm and a base material

dimension of 6×40 mm. The strain gauges were installed around the opening in the

slab as shown in Figure 6-7. Eight external strain gauges were also bonded to the

centre line of the CFRP plate to measure strain in the longitudinal direction. Each

external strain gauge had a length of 6 mm and a base material dimension of 3.4×10

mm. Four internal strain gauges similar to the CFRP plate strain gauges were

installed on the steel reinforcement before the concrete was poured. Each strain

gauge/reinforced steel bar joint was then protected against moisture penetration

during casting, using a combination of urethane sealant, plastic black tape and

synthetic rubber adhesive. All the strain gauges used were foil-type, three-wired

temperature-compensating; with resistance of 120 Ω. Figure 6-7 shows the locations

of strain gauges on concrete, CFRP plate and steel reinforcement. Two linear

variable differential transducers (LVDTs) with additional steel extensions were

placed on the ground to connect the bottom side of the slab (tension face) at different

locations (see Figure 6-7), so as to measure vertical defection.

A data acquisition system with an interface card equipped desktop computer was

used to automatically acquire all test data (i.e. LVDT and strain gauges’ readings).

196

Figure 6- 7: Typical strain gauge and linear variable differential transducers

(LVDTs) locations (concrete, steel and CFRP plate)

6.8 Material testing

6.8.1 Concrete

The concrete was designed to give an average 28-day compressive strength of 35

MPa and the specific ratios of the concrete mix (sand, water, gravel and cement)

have been provided in Section 3.6.1. Ten cubes (with individual dimensions of

100x100x100 mm) and six cylinders (with individual dimensions of 100x200 mm)

were cast with each slab. The cubes and cylinder tests were conducted in accordance

with the specifications of BS 1881(1983) and ASTM C496 (1996)standards, so as to

determine the compressive strength and the spilt cylinder tensile strength of the

concrete respectively. All the specimens (i.e. cubes and cylinders) were treated under

the same curing condition as the two-way RC slabs (i.e. covered with nylon sheets to

X

X

8 x80 mm

: Steel strain gauge (Tension), Concrete strain gauge (Compression),

: CFRP strain gauge (Tension) , X: LVDTs

A

A

B

C D

X

A

197

maintain the moisture level for one week until three cubes were tested after 7 days

for curing control). An additional three cubes were tested at 28 days. Another set of

4 cubes and 3 cylinders were tested concurrently with the RC slab the actual day of

testing which varied from 34 to 40 days. Table 6-1 shows the average measured cube

compressive strength and the mean tensile strength from the standard spilt tensile test

on the day that both the two-way RC concrete slabs were tested. Another set of three

cylinders’ test was performed according to BS 1881-121, so as to also evaluate the

modulus of elasticity and Poisson's ratio. In order to achieve this, two strain gauges

were installed in the middle of the cylinder (i.e. one strain gauge in the longitudinal

direction and the other in the transverse direction) to measure strain during the load

application as shown in Figure 6-8. Figure 6-9 shows the stress-strain curves for the

concrete in longitudinal and lateral directions. The average concrete modulus of

elasticity was calculated to be 26435.4 MPa and average Poisson's ratio was 0.196

(which is within the normal range of 0.18 to 0.25 for normal weight concrete).

Figure 6- 8: Test for concrete compressive modulus of elasticity

198

Figure 6- 9: Stress- strain curves for concrete cylinders

Table 6- 1: Concrete material properties

6.8.2 Reinforcement steel bar

Uniaxial tensile tests of three representative samples were performed to obtain the

mechanical properties of 10 mm diameter reinforced steel bar according to the

ASTM A370-97a (1997). All samples were tested using a 100 kN-capacity

INSTRON testing machine. An extensometer was attached to the middle of the steel

bar for measuring tensile strain (Figure 6-10). The average yield strength and

modulus of elasticity were measured as 550 and 205763 MPa respectively. The

stress-strain curves for the samples are illustrated in Figure 6-11.

Slab ID

Cube compressive strength at time of test

(MPa)

Split cylinder tensile

strength at time of test

(MPa)

Average

(28 days)

Standard

deviation

Average

(Test time)

Standard

deviation

Average Standard

deviation

RC slab under

monotonic loading

(SM)

35.8 0.9 37.8 1.2 3.5 0.6

RC slab under

cyclic loading

(SC)

35.5 3 37.2 2.24 3.3 0.3

0

5

10

15

20

25

30

35

40

-3000 -2000 -1000 0 1000

Conc

rete

str

ess

(MPa

)

strain*10^6 (mm/mm)

Cylinder 1

Cylinder 2

Cylinder 3

199

Figure 6- 10: Tensile test of steel bar

Figure 6- 11: Stress-strain curves for three representative steel bars

6.8.3 CFRP composite plate

In order to obtain the mechanical properties, uniaxial tensile tests on three specimens

of T700 type CFRP plates (2 mm thickness for each late) were conducted. The

ultimate tensile strain and modulus of elasticity were measured as 18000 microstrain

0

100

200

300

400

500

600

700

0 50000 100000 150000 200000 250000

Stes

s (M

Pa)

Strain (Microstrain)

1st steel bar 2nd steel bar 3rd steel bar

200

and 115.6 GPa respectively. The specific method for preparing sample and typical

failure of CFRP plate in uniaxial tensile test has already been explained in Section

3.6.2.

6.9 Test results and discussion

In this section, the flexural behaviour of the two-way RC slabs with opening

strengthened with CFRP plate in terms of failure modes, experimental load-

deflection, load-reinforcement strain and load-concrete strain are investigated. In

particular, the main parameters examined in the testing of slabs were the effect of

load protocol (i.e. monotonic and cyclic loading) on the bond behaviour.

6.9.1 Failure modes

The failure mode of the slab subjected to the monotonic loading was a combined

mode (i.e. debonding of the CFRP plates followed by concrete crushing between the

opening corner and slab corner) as shown in Figure 6-12.

Figure 6- 12: RC two-way slab during applied load

Concrete crushing

1st

top corner crack

2nd

top corner crack

Loading frame

Steel plate

201

For the slab subjected to cyclic loading, the governing failure mode was CFRP

debonding. These two strengthening slabs have different debonding processes. For

the RC slab subjected to monotonic loading, the initiation of debonding occurs on

the CFRP plate/concrete interface at the one end of the CFRP plate and then

propagates to the opening of the slab. In the case of the RC slab subjected to cyclic

loading, the debonding commenced at the vicinity of the opening corners and the

ends of the CFRP plate simultaneously (Figure 6-13). For the slab subjected to cyclic

loading, the debonding initiation occurred during the earlier load level, which was

adjudged to be due to the breathing of intermediate flexural cracks that led to

degradations in the CFRP-adhesive interface stiffness.

Figure 6- 13: Debonding process (a) RC slab under monotonic (b) RC slab

Another factor that may influence the debonding process is the CFRP plate stiffness.

In simpler terms, a higher flexural CFRP plate stiffness leads to an increase in the

CFRP peeling effects (ACI code, 2008), where the type of bond failure can also be

observed upon test completion. It was observed that a thin layer of concrete was

attached to a significant part of the bonded CFRP plate’s surface after separation

from the concrete. The debonding at the area where the CFRP plates cross each other

near the corner of the opening was manifested by separation without any layers of

concrete attached. This may be due to the evenness in the application of the CFRP

plates in one direction and unevenness in the other direction as can be seen in Figure

6-14. Hence, concrete shearing beneath the adhesive layer is the predominant failure

mode in debonding, which indicates that the quality of bond between the CFRP plate

and the concrete was good.

Deboning onset

Debonding onset

(a) (b)

202

Figure 6- 14: Debonding near slab’s opening

During the first stage, the crack scenarios for both slabs indicate that the flexural

cracks commenced in the vicinity of the opening corners, then propagated towards

the slabs corners. The first flexural crack occurred at a load level of 45.3 kN and

39.8 kN for two-way RC slabs subjected to monotonic and cyclic loading

respectively. The flexural cracks increased in width and depth with corresponding

increase in load levels until concrete crushing occurred at the opening corner, due to

increasing cracks’ depths caused by the compression zone depth reduction.

Although, a small number of cracks were found between the opening corners and

slab corners due to the confinement provided by the CFRP plates at the bottom side

of the slabs. The typical flexural cracks pattern at failure for the two-way slab is

depicted in Figure 6-15. This crack pattern reflects the yield line pattern. The

applied load protocols (i.e. monotonic and modified FEMA) did not show substantial

changes in the overall yield line pattern.

At the top side of the two-way slabs, subsequent tensile cracks around the slabs’

corners were observed at an angle of approximately 45o

to the internal steel

reinforcements, which is visibly shown in Figure 6-12. These negative cracks were

formed as a result of the corners' uplift restraints, which originated from the steel

plates applied at the slabs' corners. Moreover, these cracks have negligible effects on

the overall behaviour of the two-way RC slabs strengthened with CFRP plate. Top

first corner crack for the first RC slab occurred at 110 kN load level (monotonic),

while the top first corner crack for the second RC slab occurred at 114.5 kN load

level (cyclic).

CFRP plate pulls away

from concrete substrate

Inclined flexural cracks

Slab opening Debonding progresses through the cement matrix

Gap due to

unevenness surface

203

Figure 6- 15: crack pattern for RC two-way slabs at failure load (a) RC slab under

monotonic loading (b) RC slab under cyclic loading

(a)

(b)

204

6.9.2 Load- deflection behaviour

Two reinforced concrete slabs with opening strengthened with CFRP plate were

tested under monotonic and modified FEMA load protocol to examine the effect of

the load histories on their behaviours and ultimate load capacities of the reinforced

concrete slabs. Experimental investigations on the behaviour of load versus

deflection curves for these slabs are presented in this section. Figure 6-16 (a) and (b)

show the experimental load- deflection curves for the RC two-way slabs under

monotonic and cyclic loading respectively. The load was applied as a line load

around the opening, measured through the aid of a load actuator. The deflections

were recorded using LVDTs at points (A) and (D) as shown in Figure 6-7. The

LVDTs at point (D) did not work well in cyclic test so that there are only one load

deflection curve. The experimental investigation shows that the slab subjected to

monotonic loading behaved linearly up to the point of the first crack at 45.3 kN, after

which the load deflection curve began to increase nonlinearly until the point of the

ultimate load carrying capacity of 161.3 kN, then started decreasing rapidly. This

reduction in the load carrying capacity occurred as result of the complete debonding

in the CFRP plates at this stage.

The slab subjected to modified FEMA load protocol showed that the envelope of the

load deflection curve basically traced the monotonic curve, although both slabs

possessed similar strengthening schemes. However, the hysteresis load deflection

curve has a lower recorded load than the monotonic curve with ultimate load

capacity of 142.9 kN. The cyclic load deflection curves exhibited ascending and

descending branches that formed the hysteresis loops. The area enclosed by the loops

is increased significantly with increase in number of cycles, which provides an

indication of the energy dissipation during each cycle. The energy dissipation is due

to the fact that the load cycling may influence the bond between the CFRP plate and

the concrete (bond degradation under cyclic load is discussed in Section 3.7.2.2).

Also, the loading cycles have pronounced effects on the stiffness reduction of the

concrete, which is induced as a result of the formation of several flexural cracks

within the bottom side of the slab. As expected, both slabs exhibited non-ductile

behaviour which can be attributed to the addition of high stiffness CFRP plates. This

high CFRP stiffness is due to the fact that the ACI guidance code adopted elastic

205

assumptions in the CFRP plates design. Table 6-2 shows the test results for two-way

RC slabs strengthened with CFRP plate.

Table 6- 2: Test results for two-way RC slabs

Pcr(+): the load at the first bottom crack. Pcr(-):the load at the first top crack

Figure 6- 16: Load-deflection for strengthened RC slab tested load (a) RC slab under

monotonic loading (b) RC slab under cyclic loading

Specimen ID

Cracking load

(kN)

Yield load

(kN)

Max. Load

(kN)

Failure mode

Pcr (+) Pcr(-)

RC slab under

monotonic loading 45.3 110 127.16 161.4 CFRP debonding +

Concrete crushing

RC slab under

cyclic loading

39.8 96 - 142.9 CFRP debonding

0

40

80

120

160

200

0 10 20 30 40 50

Loa

d (

kN

)

Deflection (mm)

A D

0

40

80

120

160

0 10 20 30 40 50

Load

(k

N)

Deflection (mm)

A

(a)

(b)

206

6.9.3 Steel reinforcement and concrete strain measurements

Figure 6-17 (a) shows the experimental load- strain relationships that exist between

the steel reinforcement and concrete of CFRP RC slab under monotonic loading at

the four different locations of the strain gauges. These four strain gauges were

installed at approximately 30 mm around the slab’s opening (see Figure 6-7). The

figure shows that the measured load strain of the steel reinforcement have similar

trends with the load deflection curves. It was observed that yielding of the steel

occurred in the corners of the opening at a load level of 127.16 kN, while the

yielding of steel occurred at the mid-point between the two corners at a load level of

158.97 kN. The measured steel strains also showed that the maximum strain

occurred at the corners, where the steel strain reached approximately 3259.7

microstrain at the failure load. For the strain gauges at the mid-points between the

two corners, the strain at the failure load barely reached 2814.5 microstrain. In the

case of the concrete, it can be seen from Figure 6-17 (a) that the recorded strain is

relatively linear prior to the first crack. The compressive strains steadily increased

with increase in loading after crack formation. The highest compressive strain value

observed at the vicinity of the opening corners was 1859.4 microstrain. It was also

observed that the concrete compressive strain at the centre point between the two

opening corners suddenly showed significant decrease at 500 microstrain strain and

then increased again. At this stage, the observed reduction in concrete compressive

strain due to cracking occurred in the bottom side of the concrete, owing to the fact

that tensile strain at failure in standard concretes typically occurs between 100 and

1000 microstrain (ABAQUS Manual). Figure 6-17 (b) shows typical experimental

load strain behaviours in steel reinforcement and concrete as obtained from the

cyclic loading test. The characteristic envelope behaviours exhibited by the load

strain curves in cyclic regime is similar to that displayed by the monotonic regime.

The measured steel strains showed that the maximum strain (i.e. approximately 2500

microstrain at the failure load) occurred at the corners, which was still lower than the

yielding strain. For the concrete, it can be seen that the highest compressive strain

value (i.e. 1650 microstrain) was observed at the vicinity of the opening corners. The

residual strain remained after the unloading for both steel and concrete.

207

Figure 6- 17: Load-strain relationships for steel reinforcement and concrete of CFRP

RC slab under (a) monotonic loading (b) cyclic loading

0

40

80

120

160

200

-2000 -1000 0 1000 2000 3000 4000

Lo

ad

(k

N)


A B C D

Steel Concrete

(a)

(b)

208

6.9.4 Tensile strain profiles along the CFRP plate

Figure 6-18 (a) and (b) show the predicted tensile strain profile along CFRP at four

different load levels for the CFRP RC slab under monotonic and cyclic loading

respectively. From Figure 6-18 (a), it can be seen that the strain profiles fluctuate

with increased loading due to flexural cracks that occurred in the tension side of the

RC slab. However, the strain profiles show that the maximum strain (i.e. 5287

microstrain) occurs near the corners of the slab opening at a load level of 136 kN.

Figure 6-18 (b) shows the strain profiles for the CFRP RC slab subjected to modified

FEMA cyclic loading at four load levels. It is vital to state that the selection of the

load levels in Figure 6-18 (b) was governed by the previously identified deflection

values under monotonic loading. The figures (Figures 6-18 (a)-(b)) also show a

considerable reduction in the maximum strain values of the CFRP plates, due to the

effects of cyclic loading. These reductions in strain results from the fracture energy

degradation during each loading cycle. Furthermore, the strain profiles indicate that

the maximum strain (i.e. 3817.7 microstrain) at a load level of 121 kN occurred near

the corners of the slab’s opening. This therefore implies that debonding commenced

near the opening corners of the slab and propagated towards the end of the attached

CFRP plates. This observation was expected, owing to the formation of flexural

cracks in the corners of the slab opening. At the fourth load level, the strain profile

was observed to be significantly lower than that recorded at the second load level,

which is due to the loss of bonding (i.e. bonding between CFRP plate and concrete)

strength after the third load level. In general, the peak strain values at the four load

levels under cyclic loading are lower than those determined under monotonic

loading. The maximum cyclic debonding strain is also less than the maximum

monotonic debonding strain by 27.8 %, which leads to a conclusion that the strain

values are significantly affected by the types of load protocols.

209

Figure 6- 18: strain profile along CFRP plate (a) monotonic loading (b) cyclic

loading

6.10 Validation of the numerical simulation model against the

author’s experimental results

The results obtained from experimental tests conducted on the CFRP-strengthened

two-way RC slabs with opening (one under monotonic loading and the other under

modified FEMA cyclic loading), which the results have been discussed in the

preceding sections are now used for validating a numerical simulation model in the

current section. The validation of the numerical simulation model comprises of the

(a)

(b)

Distance from the slab centre toward end of support (mm)

Opening edge


Opening edge

210

load- defection curves; strains in concrete; strains in steel and CFRP plate; as well as

the failure modes. The main purpose of this section is to theoretically simulate all the

experimental scenarios previously described. The consistence of the observations

from both the experimental and numerical simulation modelling will then be

compared, so as to establish the validity of findings.


Considering the advantages offered by the symmetry of loading, boundary

conditions and geometry, only a quarter of the slab has been used in the 3D-FE

analysis shown in Figure 6-19. The restrained degrees of freedom at the boundary

conditions (where the edges are symmetric) are also shown in Figure 6-19. In order

to model the two-way RC slabs strengthened with CFRP plate, it is necessary to

simulate each part of the current specimen with actual material behaviours. The main

materials used for this study are concrete, steel, CFRP and the adhesive layer.

Details of the behaviours of these materials have been provided in Chapters 4 and 5.

Figure 6-20 however shows the typical 3D FE mesh of the two-way RC slab.

Figure 6- 19: Finite element model for 3D analysis of quarter model of the CFRP-

strengthened two-way RC slab with opening

(Surface 1) X-symmetry plane & B.C

U1=UR2=UR3=0


U2=UR1=UR3=0


Corner B.C U1=U2=U3=0

Load

plate

CFRP plate

U: 1, 2, 3 = Translation in X, Y and Z directions

respectively UR: 1, 2, 3 =Rotation about X, Y and Z directions

respectively


211

Three main types of elements used in this FE simulation are solid, shell and truss

elements. The selection of the different was mainly governed by the variations in the

geometrical shapes of the structural components. The 3D eight-node linear brick

elements with reduced integration and hourglass control (C3D8R) were adopted for

modelling the concrete. For the CFRP plate, linear three dimensional four-node

doubly curved general purpose shell elements with reduced integration and hourglass

control were used, which accounted for the finite membrane strains with five degrees

of freedom per node (S4R5). For the embedded reinforcement bars, a linear 3D two

node truss element with three degrees of freedom at each node (T3D2) was used.

The cohesive contact was applied between the CFRP plate and concrete slab, using

the cohesive surface technique. During the application of the FE model boundary

conditions, the movement of the two-way RC slab corner was restrained in the X, Y

and Z directions, so as to adequately represent actual case. Also, vertical movement

at the perimeter of the slab was restricted, so as to represent a simply supported

boundary condition. Furthermore, the movement of each of the nodes for the

concrete slab, steel reinforcements and CFRP plates in the symmetrical face passing

through the middle of the slabs were also restrained in the X and Y directions for

surface 1 and surface 2 respectively, as illustrated in Figure 6-19. The test load was

applied as a uniform pressure on the top surface of the steel square bearing plate (2.5

mm width and 375 mm length, which is around the opening, so as to uniformly

distribute the line load across the concrete surface). The loads were applied using

the dynamic/explicit method available in the ABAQUS software. The method

basically involves employing an explicit dynamic finite element formulation in order

to integrate the dynamic quantities (accelerations, velocities, dynamic stresses and

strains) over the time increment. The time increment must be small enough in order

to assume a constant acceleration during the analysis, so as to guarantee the accuracy

of the results within each increment. The value of applied load is computed

automatically after each increment, based on element strain increments. The time

period of the full analysis is given on the data line while the initial increment time

will be adjusted automatically if the increment fails to converge.

212

Figure 6- 20: Finite element mesh of the quarter the CFRP-strengthened two-way

RC slab with opening with a close-up view of the mesh


6.10.2.1 CFRP-strengthened two-way RC slabs with opening under

monotonic loading

The comparisons of the load-deflection and load-strain were performed for only two

locations (i.e. points D and A in Figure 6-7) on the slab, owing to the fact that only a

quarter slab was analysed in the current numerical simulation. Figure 6-21 shows a

comparison between the load-deflection curves obtained from numerical simulation

predictions and experimental analysis; where a good agreement between both sets of

results is visible throughout the entire loading range. However, the curve obtained

from the numerical simulation prediction showed stiffer behaviour in comparison to

that obtained from the experimental load deflection behaviour after first crack, which

can be attributed to a significant scatter in the tensile strength of concrete in practice

(Bhatt et al., 2014). The ultimate experimental load at point (A) was 161.4 kN at a

Truss element (Steel) 3-D Solid element (concrete)


Shell element (FRP)

213

deflection of 31.3 mm, while the ultimate numerical simulation failure load was

168.5 kN at 40.6 mm. This implies that the numerical simulation failure load is 4.4%

higher than the experimental load.


RC two-way slab under monotonic loading

Similarly, Figure 6-22 shows that the experimental and numerical simulation load –

strain curves for concrete are in conformance throughout the entire loading range.

The ultimate concrete strains at point (D) were 1861.7 and 1709.6 microstrain for the

experimental and numerical investigations respectively. The numerical ultimate

concrete strain is 8.1% less than the experimental strain.

0

40

80

120

160

200

0 10 20 30 40 50

Lo

ad

(k

N)

Deflection (mm)

A (FEM) A (EXP.)

0

40

80

120

160

200

0 10 20 30 40

Load

(k

N)

Deflection (mm)

D (FEM) D (EXP.)

214

On the other hand, the numerical prediction of strains in steel reinforcements in the

tension side at the corner of the slab’s opening is reasonably close to the strains

measured during the experiment. The steel did not fully yield at failure, during both

experimental investigation and numerical simulation. The yielding of the steel at the

corner of the slab opening occurred at load levels of 127.16 kN and 143.9 kN for

experimental and numerical investigations respectively. This therefore implies that

the numerical simulation yielding load is 13.1% greater than the experimental

yielding load.

6


and concrete for RC two-way slab under monotonic loading.

0

40

80

120

160

200

-1000 -500 0 500 1000 1500 2000 2500 3000 3500

Loa

d (

kN

)


A (FEM) A (EXP.)

Steel Concrete

0

40

80

120

160

200

-2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000

Lo

ad

(k

N)


D (FEM) D (EXP.)

Steel Concrete

215

The comparison between the numerical and experimental strain profiles for the RC

two-way slab under monotonic loading shown in Figure 6-24 indicates that the

failure modes for both investigations (experimental and numerical simulation) are

similar, owing to the occurrence of debonding failure between the CFRP plate and

concrete surface in both instances. The debonding initiation occurred in the

numerical simulation analysis when the damage initiation criterion at the

CFRP/concrete interface was satisfied (i.e. the value of the damage initiation

criterion reaches unity as discussed in Section 5.2.1.1.1).), as illustrated by the

contour plot in Figure 6-23. Figure 6-24 also shows that the maximum experimental

debonding strain was 5287 microstrain at a load of 136 kN, while the maximum

numerical debonding strain was 7301 microstrain at a load of 156.9 kN (i.e. 27.5%

difference).


interface for RC two-way slab under monotonic loading.


way slab under monotonic loading.


Opening edge

216

6.10.2.2 CFRP-strengthened two-way RC slabs with opening under modified

FEMA cyclic loading

Figure 6-25 shows significant similarities between the experimental and numerical

simulation load deflection behaviours of the RC slab subjected to cyclic loads.

However, the numerical load deflection curve does not show pronounced

degradation. This is because the interfacial bond stress and fracture energy for the

cyclic case is limited for the specific chosen load protocol (i.e loading range70%-

15%). The maximum numerical simulation load was 162.3 kN at a deflection of 33

mm, while the maximum experimental load was 142.9 kN at a deflection of 27.2

mm, which corresponds to 11.9% difference (i.e. numerical simulation load is 11.9%

greater than experimental load).


RC two-way slab under cyclic loading.

Also, a comparison between the experimental and numerical simulation load-strain

curves for top corner concrete and steel reinforcement at corner is displayed in

Figure 6-26. The results presented a reasonably close agreement between both

approaches and thus highlight the fact that the concrete average strains predicted by

numerical simulation model overestimate the behaviour when compared to the

concrete strain measured experimentally. This observation is expected, since the

C3D8R element that contains a single integration point was used. Although, other

elements such as the C3D20R that contain as many as 8 integration points would

naturally provide more detailed strain variations across the entire section, however,

0

40

80

120

160

200

0 10 20 30 40 50

Lo

ad

(k

N)

Deflection (mm)

A(FEM) A (EXP.)

217

such elements require more computational time and are not available in the dynamic

explicit analysis element library. The ultimate concrete strains at point (D) were

1650 and 1668.8 microstrain for the experimental and numerical simulation

investigations respectively. Thus, the accuracy of the FE model in representing the

experimental ultimate concrete strain is approximately 98.9%. Furthermore, the

strain in steel reinforcement on the tension side at the corner of the slab for both

approaches (experimental and FE) are also in agreement, which again clarifies the

fact that the reinforcement did not yield prior to slab failure as a result of debonding

between CFRP plates and concrete.


and concrete for RC two-way slab under cyclic loading.

0

40

80

120

160

200

-2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000

Loa

d (

kN

)


D (FEM) D (EXP.)

Steel Concrete

218

Further comparisons between the experimental (obtained from slab test) and

numerical simulation strain profile curves at the CFRP plate under three different

load levels is shown in Figure 6-27. It can be seen that the experimental strain profile

under the third load level is lower than that of the second load level. On the contrary,

the numerical strain profile under the third load level is higher than that of the

second load level. This observation might be due to a stress concentration induced by

crack localisation formed in the tensile side of the tested slab, thus causing early

debonding. The accurate simulation of such phenomena in dynamic explicit analysis is

extremely difficult, especially for materials such as concrete. The governing failure

mode observed in the numerical simulation analyses is debonding failure which

occurred at the slabs’ corners and the CFRP plate ends simultaneously as represented

by the contour plot in Figure 6-28. Therefore, the numerical simulation modelling is

capable of accurately predicting the debonding process observed from experiment.


way slab under cyclic loading.


interface for RC two-way slab under cyclic loading.


Opening edge

219

6.10.2.3 Evolutions of crack pattern

The damage plasticity model in ABAQUS/ Explicit is capable of recording the

concrete crack pattern at each applied load increment. Figure 6-29 shows the

evolutions of crack patterns developing on the lower surface of the strengthened RC

slab under monotonic loading at four different load levels. The crack always appears

in a plane perpendicular to the principal plastic stress direction. Once the maximum

principal stress in the integration points of the concrete solid element exceeds the

ultimate tensile strength of the concrete, cracks represented by lines shown in Figure

6-29, ABAQUS (2011). As indicated by the figure, during earlier load levels, the

flexural crack began to occur at the opening corner and then spread horizontally to

the slab support with increase in applied load. At a load level of 117 kN, skew cracks

at approximately 45o become conspicuous at the slab corner, due to the effects of

uplifting resistance from the restrained steel plate. Finally, the tensile cracks on the

lower surface of the strengthened slab spread into wider zones and form a yield

lines’ pattern between the opening and the slab corner, which resembled the

observations recorded from the experimental tests shown in Figure 6-15. However,

the cracks in the final stage appear much smaller than the cracks in the other three

stages. This is could represent the post-crack that defined the strain-softening

behaviour for cracked concrete. The RC slab subjected to cyclic loading has the

same cracking patterns development scenario.

220

Figure 6- 29: Evolution of crack pattern of CFRP-strengthened two-way RC slabs

with opening under monotonic (a) 50.7 kN (b) 80.1 kN (c) 117 kN (d) 168.5 kN

6.11 Summary

The principal outcomes of the present experimental and numerical investigations are

outlined below:

The required area of CFRP plates used for strengthening two-way RC slabs

with opening, was calculated based on ACI 318 1995 code suggestions

Debonding failure was the dominant mode of failure for the two CFRP RC

slabs. However, the onset of debonding for the slab subjected to monotonic

(a) (b)

(c) (d)

221

loading occurred on the CFRP plate/concrete interface at one end of the

CFRP and then propagated towards the opening of the slab. On the other

hand, the initiation of debonding in the RC slab subjected to cyclic loading

was at the vicinity of the opening’s corners and the CFRP plate ends

simultaneously.

The applied load protocols (i.e. monotonic and modified FEMA) did not

exhibit any remarkable changes in the overall yield line pattern.

The CFRP RC slab subjected to modified FEMA load protocol showed a

lower recorded load and debonding strain, as compared to that subjected to

monotonic loading. The ultimate load and maximum debonding strain were

142.9 kN and 3817.7 microstrain respectively (as obtained from test

conducted under cyclic loading). The test conducted under monotonic

loading produced an ultimate load of 161.4 kN and a maximum debonding

strain of 5287 microstrain. This indicates that the ultimate loads and

maximum debonding strains under cyclic loading are respectively 11.4% and

27.8% lower than the values recorded under monotonic loading.

The ABAQUS/Explicit FE code was adopted for modelling the strengthened

RC two-way slabs under monotonic and cyclic loadings, so as to overcome

the problems of convergence that often result from a large degree of

nonlinearity. For instance, the bond between the CFRP plate and the concrete

must be handled by contact interaction using surface cohesive based model.

In comparison with the experimental behaviour, numerical results obtained

from the ABAQUS/Explicit FE code for load deflection, load- strain in steel

and concrete, strain profile in CFRP plate and failure modes were very

similar.

The numerical simulation load deflection curves show a stiffer behaviour

when compared to the experimental results, which is probably due to a

significant scatter in the tensile strength of concrete in practice. Also, the

behaviour of quasi brittle materials such as concrete is highly dependent on

the crack localisation formed in the tensile side.

222

Chapter Seven

A Parametric Study of the Bond Behaviour of

CFRP-Strengthened Two-Way RC Slabs with

Openings under Monotonic and Cyclic Loading

7.1 Introduction

This Chapter mainly focuses on providing a thorough understanding of the effects of

various parameters on the bonding behaviour of two-way RC slabs with a central

opening strengthened with CFRP plate. The parameters considered include concrete

compressive strength, CFRP bonded plate width and opening size. According to the

values identified by the test data presented in Section 6.3 of chapter Six (such as

CFRP plate bond length equals1500 mm, CFRP bonded plate width equals 50 mm,

CFRP bonded plate thickness equals 2 mm, concrete compressive strength equals 38

MPa and opening size 550x550 mm) were selected as reference parameters for the

subsequent studies. These slabs were designed to fail in debonding failure modes due

to high CFRP plate stiffness and stress concentrations generated at the corners of

opening. To simulate different concrete strengths, the values of concrete compressive

strengths selected are 33 and 45 MPa. Also, the simulation of different bond width

ratios of the CFRP bonded plate to the concrete substrate was achieved by

respectively selecting 75, 100 and 125 mm CFRP bonded plate width. Finally,

different opening sizes were simulated using opening dimensions of 350x350 mm

and 750x750 mm respectively. Table 7-1 lists the ranges of the parameters. Finally,

the numerical simulation results were compared with the existing design codes for

externally bonded FRP systems.

223

Table 7- 1 : Main parameters investigated in numerical simulation

7.2 Effect of concrete compressive strength

For the numerical simulation, two concrete compressive strengths fc (33 and 45 MPa)

were considered. Figure 7-1 shows the comparison between monotonic and cyclic strain

profile along the CFRP plate at three different load levels for RC two-way slab with

compressive strengths 33 and 45 MPa. From this Figure 7-1, it can be observed that the

strain profiles have identical trends in monotonic and cyclic loadings, where the

maximum strain values were recorded at the opening’s corner. This implies that the

debonding onset commenced around the opening and then propagated towards the CFRP

plate ends. Also, the debonding strain increases with increased compressive strain in both

load regimes. For concrete compressive strength fc equal to 33 MPa, the maximum

monotonic debonding strain was 2278 microstrain at a load of 174.7 kN, compared to

1911 microstrain at a load of 135 kN obtained from cyclic loading. The maximum

debonding strain for the RC slab subjected to cyclic loading is less than the maximum

debonding strain for RC slab subjected to monotonic loading by as much as 16.1 %.

Similarly, for the concrete compressive strength fc equals 45 MPa, the maximum

monotonic debonding strain was 3963 microstrain at a load of 247.6 kN, compared with

3863 microstrain at a load of 227 kN obtained from cyclic loading. Hence, the maximum

debonding strain for the RC slab subjected to cyclic loading is less than maximum

debonding strain for RC slab subjected to monotonic loading by 2.5 %.

Parameter Concrete

compressive

strength (MPa)

CFRP bonded

plate width bf

(mm)

Opening size

(mm)

33 50 550 x 550

45

bf

38 75 550 x 550

100

125

Opening size 38 50 350 x 350

750 x 750

224

Figure 7- 1: Comparison of strain profile at monotonic and cyclic loading. (a) fc = 33

MPa, (b) fc = 45 MPa

7.3 Effect of the CFRP bonded plate width

Three CFRP plate widths (75, 100 and 125 mm) were investigated in this section.

Figure 7-2 shows a comparison between monotonic and cyclic loading of predicted

tensile strain profiles along CFRP at three different load levels. It is obvious from

Figure 7-2 that increasing the CFRP plate width effectively increases the CFRP

debonding strain for both load regimes. This is perhaps due to the fact that

(a)

(b)


Opening edge

Opening edge


225

strengthening with higher CFRP plate width helps in controlling the propagation of

the shear cracks and in turn enhances confinement of the strengthening RC slabs. On

the other hand, the cyclic loading had a considerable influence on the reduction of

debonding strain for the specific CFRP plate width as expected. For RC slab

strengthened with CFRP plate width of 75 mm, the maximum monotonic debonding

strain was 2750 microstrain at a load of 182 kN, compared to 2558 microstrain at a

load of 160 kN obtained from cyclic loading. Therefore, the maximum debonding

strain for RC slab subjected to cyclic loading is less than the maximum debonding

strain for RC slab subjected to monotonic loading by 6.9 %. For the RC slab

strengthened with CFRP plate width of 100 mm, the maximum monotonic

debonding strain was 2058 microstrain at a load of 190 kN, compared to 1851

microstrain at a load of 128.6 kN obtained from cyclic loading. The maximum

debonding strain for the RC slab subjected to cyclic loading is less than the

maximum debonding strain for the RC slab subjected to monotonic loading by 10 %.

Finally, for the RC slab strengthened with CFRP plate width of 125 mm, the

maximum monotonic debonding strain was 1955 microstrain at a load of 195.2 kN,

compared to 1732 microstrain at a load of 147 kN obtained from cyclic loading.

Therefore, the maximum cyclic debonding strain is less than the maximum

monotonic debonding strain by 11.4 %.

(a)

Opening edge


226

Figure 7- 2: Comparison of strain profile at monotonic and cyclic loading. (a) CFRP

plate width 75 mm, (b) CFRP plate width 100 mm, (c) CFRP plate width 125 mm

7.4 Effect of opening size

A square opening positioned at the centre of the strengthened RC two-way slab, with

two different sizes (350 x 350 mm and 750 x 750 mm) were studied in this section.

Figure 7-3 shows the comparison between monotonic and cyclic loading of predicted

tensile strain profiles along CFRP at three different load levels. It can be observed

that both monotonic and cyclic CFRP plate strains decrease with increased slab

opening. This is could be due to an earlier formation of cracks during an opening

size of 750x750 mm. For the RC slab with an opening size of 350 x 350 mm, the

(c)

(b)

Opening edge


Opening edge


227

maximum monotonic debonding strain was 2612 microstrain at a load of 181.9 kN,

compared to 2870 microstrain at a load of 173 kN that was obtained from cyclic

loading. Therefore, the maximum debonding strain for the RC slab subjected to

cyclic loading is higher than the maximum debonding strain for an RC slab subjected

to monotonic loading by 9.8%. On the contrary, the RC slab with an opening size of

750 x 750 mm provided a maximum monotonic debonding strain of 2351

microstrain at a load of 130 kN, compared to 2222 microstrain at a load of 120.9 kN

obtained from cyclic loading. Hence, the maximum cyclic debonding strain is less

than the maximum monotonic debonding strain by 5.5%.

Figure 7- 3: Comparison of strain profile at monotonic and cyclic loading. (a)

Opening size 750x750 mm, (b) Opening size 350x350 mm

(a)

(b)

Opening edge


Opening edge


228

7.5 Comparison of code provisions with numerical simulation

results

In this section, the debonding strain results obtained from numerical simulations on

two-way RC slabs with openings strengthened with CFRP plate and subjected to two

different load regimes (i.e. monotonic and modified FEMA 461cyclic load protocol)

were compared with existing design codes for externally bonded FRP. The aim of

this comparison is to examine the applicability of existing codes’ design equations

for predicting the debonding strain of flexural RC members strengthened with FRP

and subjected to monotonic or cyclic loading. Table 7-2 provides a summary of the

different codes used for evaluating debonding tensile strains in CFRP plate and a

comparison between these codes and the debonding strain results obtained from the

current numerical simulation.

It was observed that the existing ACI design code as well as fib-1 over predict the

debonding strain in the CFRP plate of flexural member subjected to monotonic or

cyclic loading. For the ACI code, the maximum, minimum and average ratios are

3.75, 0.88 and 2.58, respectively, while the range of prediction ratio is 2.86 (with a

standard deviation of 0.78). For the fib-1 code, the maximum, minimum and average

ratio calculated are 2.37, 0.65 and 1.86 respectively, with a standard deviation of

0.51. On the other hand, both the fib-2 and the CNR- DT202 codes show

conservative predictions for the debonding strain in the CFRP plate. For the fib-2

code, the maximum, minimum and average ratios are 0.95, 0.23 and 0.66,

respectively, with a standard deviation of 0.19. In case of CNR- DT202 code, the

maximum, minimum and average ratios are 0.23, 0.95 and 0.66, respectively; with a

standard deviation of 0.19. However, TR55 and JSCE codes provided results that

were relatively similar to the numerical simulation results with respect to the average

ratio. The average allowable-to- numerical simulation debonding strain ratio

calculated by TR55 and JSCE codes are 1.03 and 1.06 with standard deviations of

0.28 and 0.30, respectively. For the proposal model, the average analytical-to-

numerical simulation debonding strain ratio is 0.60 with a standard deviation of 0.16.

229

Based on above observation, the proposed model gives more conservative results and

has the lowest level of variation than the other existing design codes. This variation

in prediction debonding strain is a reflection of the considerable uncertainty in the

debonding mechanism, mainly the differences between CFRP plates debonding in

two-way slabs and single shear tests; difference in applied load protocol Also, the

proposed model may not be wholly applicable for CFRP stiffness higher than 115

kN/mm as explained in Section 4.8.

7.6 Summary

The maximum cyclic debonding strain is less than the maximum monotonic

debonding strain by 16.1% and 2.5% for concrete compressive strengths of

33 and 45 MPa respectively.


debonding strain by 6.9%, 10% and 11.4% for the RC slabs strengthened

with CFRP plate widths of 75, 100, 125 mm respectively.


debonding strain by 5.5% for the RC slab with an opening of 750 x 750 mm.

On the other hand, the maximum cyclic debonding strain is higher than the

maximum monotonic debonding strain by 9.8% for the RC slab with an

opening of 350 x 350 mm

The highest strain in the CFRP plates was observed near the opening corners.

This observation suggests that debonding is initiated in the opening corner

regions and then propagates towards the end of CFRP plates

Finally, for the series of parameters investigated, while the average tensile

strain value is over predicted for both ACI and fib-1codes, it is under

predicted for the fib-2, CNR- DT202 codes and proposal model. However,

the average tensile strain value is acceptable for TR55 and JSCE codes. On

the other hand, the proposed model shows a lower level of discrepancy than

the international design codes. This may be attributed to the regression

230

analysis for the proposed model based on the post-fatigue debonding strain

data.

The proposed model shows the lowest average ratio with the numerical results

because of differences in the debonding mechanism as well as the load protocol

in two-way slabs and single shear tests.

The simulation analysis showed meaningful insight into the influences of

different design parameters on the bond behaviour. The key observation is that

the strains in the CFRP plates were reduced at the overlapped regions. Therefore,

the bond behaviour might be enhanced by providing transverse plates at the end

of the CFRP plates (Committee440, 2008) and near corners of the opening.

231

Table 7- 2: Numerical simulation results and evaluated debonding tensile strain in CFRP plates (Code)

Load

regime

CFRP

width

(mm)

Opening

size

(MPa)

FE

(Microstrain)

(Microstrain)

ACI fib-1 fib-2 TR55 DT

202

JSCE Proposal

model

ACI

fib-1

fib-2

TR55

DT

202

JSCE

Proposal

model

Monotonic 50 550x550 38 7301 6487 4719.9 1651.4 2622.1 1676.2 2967.7 1535.5 0.88 0.64 0.22 0.36 0.23 0.41 0.21

Monotonic 75 550x550 38 2750 6487 4660.1 1651.4 2588.9 1665.6 2930.2 1514.6 2.35 1.69 0.60 0.94 0.61 1.06 0.55

Monotonic 100 550x550 38 2058 6487 4601.5 1651.4 2556.4 1655.1 2893.3 1494.2 3.15 2.23 0.80 1.24 0.80 1.40 0.72

Monotonic 125 550x550 38 1955 6487 4544 1651.4 2524.4 1644.7 2857.1 1474.1 3.31 2.32 0.84 1.29 0.84 1.46 0.75

Monotonic 50 350x350 38 2612 6487 4737.2 1651.4 2631.7 1679.3 2978.6 1541.6 2.48 1.81 0.63 1 0.64 1.14 0.59

Monotonic 50 750x750 38 2351 6487 4695.9 1651.4 2608.8 1672 2952.6 1527.1 2.75 1.99 0.70 1.10 0.71 1.25 0.65

Monotonic 50 550x550 33 2278 6487 4524.5 1560.8 2513.6 1584.3 2905.7 1352.5 2.84 1.98 0.68 1.10 0.69 1.27 0.59

Monotonic 50 550x550 45 3963 6487 5147 1798.9 2859.4 1826 3099.1 1787.9 1.63 1.29 0.45 0.72 0.46 0.78 0.45

Cyclic 50 550x550 38 3369 6487 4719.9 1651.4 2622.1 1676.2 2483 1535.5 1.92 1.40 0.49 0.77 0.49 0.74 0.45

Cyclic 75 550x550 38 2558 6487 4660.1 1651.4 2588.9 1665.6 2451.6 1514.6 2.53 1.82 0.64 1.01 0.65 0.96 0.59

Cyclic 100 550x550 38 1851 6487 4601.5 1651.4 2556.4 1655.1 2420.7 1494.2 3.50 2.48 0.89 1.38 0.89 1.31 0.80

Cyclic 125 550x550 38 1732 6487 4544 1651.4 2524.4 1644.7 2390.4 1474.1 3.74 2.62 0.95 1.46 0.95 1.38 0.85

Cyclic 50 350x350 38 2870 6487 4737.2 1651.4 2631.7 1679.3 2492.1 1541.6 2.26 1.65 0.57 0.92 0.59 0.86 0.53

Cyclic 50 750x750 38 2222 6487 4695.9 1651.4 2608.8 1672 2470.3 1527.1 2.92 2.11 0.74 1.17 0.75 1.11 0.68

Cyclic 50 550x550 33 1911 6487 4524.5 1560.8 2513.6 1584.3 2431 1352.5 3.39 2.36 0.81 1.32 0.83 1.27 0.71

Cyclic 50 550x550 45 3863 6487 5147.0 1798.9 2859.4 1826 2592.9 1787.9 1.67 1.33 0.46 0.74 0.47 0.67 0.46

Average

2.59 1.86 0.65 1.03 0.66 1.06 0.60

STD

0.78 0.51 0.19 0.28 0.19 0.30 0.16

232

Chapter Eight

Conclusions and Recommendations for Future

Research

8.1 Introduction

The main objective of this thesis was to investigate the behaviour of reinforced

concrete strengthened with CFRP under cyclic loading using both numerical

modelling and experimental methods; primarily the interfacial bond behaviour

between the concrete and CFRP plate under static and fatigue loading was focussed

upon. Following this the specific application to slabs, including those with openings

was explored. Through this investigation it is possible to assess the existing design

equations which are used to address the bond failure in static and cyclic conditions.

Based on the aforementioned, the following sections provide the detailed

conclusions obtained from experimental and numerical evidences as well as

recommendations for future research studies.

8.2 Conclusions of this research

From the results and observations presented in this Ph.D. thesis, the following

conclusions can be highlighted from each phase of the investigation.

8.2.1 Experimental investigation of CFRP/concrete interface in single shear

under monotonic and cyclic loading

Based on the results obtained from an experimental investigation into the static and

fatigue behaviour of the interfacial bond between CFRP composite plate and the

concrete substrate, the following conclusions are presented:

233

Concrete shearing is the predominant failure mode for the fatigue tests

among the three different failure types (CFRP rupture, concrete shearing and

concrete-adhesive interface failure) observed in both monotonic and post-

fatigue tests.

The fatigue life of the single shear pull-out specimens was influenced by the

load amplitude range.

Experimental results indicated a reduction in both the ultimate load capacity

as well as the debonding strain of the bonding system. This is due to steady

fracture energy release with repeated fatigue cycles prior to monotonic

loading. Therefore, the design guidelines for externally bonded plates should

consider these reductions in practice.

The reduction in debonding strain ranged from 35% for the 1 mm M46J

CFRP plate (M1) to 5.6% for the 0.2 mm T700 CFRP plate (M5). At the

same time, the reduction in ultimate load carrying capacity ranged from

27.5% for the1 mm M46J CFRP plate to 13.3% for the 0.2 mm T700 CFRP

plate.

The post- fatigue bond stress-slip relationship (i.e. the ultimate bond strength

and fracture energy) is more sensitive to plate stiffness compared to the

concrete compressive strength. These reductions are due to cyclic loading

history, whereby each single shear pull-out test was subjected to load cycles

until 0.4 mm slip between the CFRP and concrete substrate was reached.

8.2.2 Numerical investigation of post-fatigue behaviour of CFRP/concrete

interface in single shear

This study has presented a new analytical model to calculate the ultimate

strengths and debonding strains for externally bonded CFRP plates to concrete

under post-fatigue loading behaviour. This new analytical model is based on

extensive numerical simulations, examining the influences of different design

parameters including the concrete strength, the CFRP plate stiffness, the CFRP

width to concrete width ratio and the CFRP bonded length. The numerical

simulation results were also used to assess accuracy of the various currently used

design methods. Based on the results, the following conclusions may be drawn:

234

The finite element model presented is able to accurately capture the test

failure modes, load-slip relationships as well as strain profiles under

monotonic and post-fatigue loading.

For CFRP plates with low stiffnesses, the failure mode of single shear

specimens changed from concrete shearing to CFRP plate rupture with

increasing concrete compressive strength.

When increasing the bonded length, the bond ultimate load and ultimate

debonding strain increases until an effective bond length (Le) is reached,

beyond which an extension of the bonded length cannot increase the ultimate

load and debonding strain any further.

The strain distributions in the CFRP showed that the stress transfer zone of a

constant length is shifted with increase bond width ratio. This phenomenon

should be considered in the anchorage designs of an externally bonded plate.

For CFRP plates with high stiffness (>115kN/mm), the fracture energy

dissipation through the concrete underneath the CFRP plate is quite high

during the cyclic loading stage prior to monotonic loading. This caused such

CFRP plates to have more complex behaviour than CFRP plates with lower

stiffness.

A comparison between the simulation results and calculation results using the

currently available design methods has shown that both the ACI and fib-1

methods highly overestimated the debonding strain limit, but this limit was

underestimated by the fib-2 and the CNR- DT202 methods. The calculation

results for the debonding strain limit are generally acceptable when using the

TR55 and JSCE methods. However, if the CFRP plate stiffness is high,

predictions of these two codes are non-conservative.

The numerical simulation results have revealed strong dependency of both

the debonding strain limit and the effective bond length on concrete

compressive strength , width ratio and CFRP plate

stiffness . This study has proposed new regression equations between

the debonding strain limit, the effective bond length with these three

variables. For the series of specimens investigated, the new regression

equations predict the simulation results with an average analysis result/

235

simulation result ratio of 100.8% and standard deviation of 29.6% for the

debonding strain; the respective values for the effective bond length are 99.9

% and 4.7% respectively. The accuracy in predicting the debonding strain

increases to 95.4 % (average) and 12.2 % (standard deviation) for CFRP

plates with stiffness not exceeding 115 kN/mm.

8.2.3 Numerical investigation of CFRP-strengthened one- way RC slabs

under cyclic loading

This work has described two series of one-way RC slabs with externally attached

CFRP sheets on their tension sides. One series of tests had a simply supported span

subjected to two-point loading, while the other series of tests had an overhang at one

extremity subjected to two-point loading. A surface cohesive based model was used

to describe the interaction between the CFRP and the concrete slab. The strain

profile of CFRP, slip at interface in monotonic and cyclic loading and reduction in

the ultimate load due to cyclic loading were observed. The following major

conclusions are drawn from the numerical results:

For both one-way RC slabs types (S) and (C), the mid-span deflection of the

unstrengthened slab exhibits a higher deflection than the slabs strengthened

with 800 mm and 1500 mm width of CFRP respectively.

The predicted interfacial slip values for the slabs tested under the modified

FEMA461 load protocol are higher than those of the specimens tested under

the monotonic load protocol. It has also been shown that the difference

between the interfacial slip profiles of two different load protocols are

increased significantly with increased load levels. This is due to the fact that

there is a gradual loss of stiffness for concrete, steel and interface bond

resulting from cyclic loading.

The predicted tensile strains in the longitudinal direction of CFRP sheet

(corresponding to the specimens subjected to modified FEMA461 load

protocol) become much smaller than the specimens subjected to monotonic

loading, as the load level rise.

The monotonic and fatigue responses lead to different failure mode

predictions; this is due to the fact that fracture energy degradation and

236

interface bond strength reduction resulting from cyclic loading change the

mode of failure from CFRP rupture to separation of the CFRP sheet.

8.2.4 Experimental investigation of CFRP-strengthened two-way RC slabs

with openings under monotonic and cyclic loading

The behaviour of full scale CFRP-strengthened two-way RC slabs, simply supported

on four sides with a central opening and characterised by different loading hysteresis

(i.e. static (monotonic) and modified FEMA cyclic load protocol) was investigated

experimentally. These investigations were performed through observing the

deflection, ultimate load capacity, crack patterns, strains and failure mode. The

following conclusions are presented.

Debonding failure was the dominant mode of failure for the two CFRP RC

slabs. However, different debonding scenarios are noticed. For the slab

subjected to monotonic loading the debonding started at the end of the CFRP

plate and then propagated towards the opening of the slab. In contrast, the

initiation of debonding in the RC slab subjected to cyclic loading was at the

vicinity of the opening’s corners and the CFRP plate ends simultaneously.

In both specimens, the crack pattern for flexural failure was similar. The

flexural cracks appear in the bottom face and they initiate from opening

corners and move to the end supports of the slabs. The crack width and

number continues to increase till the CFRP plates fail (debonding of CFRP).

The CFRP RC slab subjected to modified FEMA load protocol showed a

lower recorded load and debonding strain, as compared to that subjected to

monotonic loading. The ultimate loads and maximum debonding strains

under cyclic loading are respectively 11.4% and 27.8% lower than the values

recorded under monotonic loading.

237

8.2.5 Numerical investigation of CFRP-strengthened two- way RC slabs under

cyclic loading

The slabs in the test series were then analysed using the validated FE model

previously discussed. The following conclusions can be drawn:

The comparison between the test results and numerical predictions obtained

from the ABAQUS/Explicit FE code showed good agreement in terms of

load deflection, load- strain in steel and concrete, strain profile in CFRP plate

and failure modes.

The numerical simulation program was used to investigate the following

parameters, concrete compressive strength, CFRP plate width and opening

size that could all influence the flexural behaviour of the RC two-way slabs

strengthened with CFRP plates were subjected to monotonic and cyclic

loading.

For the slabs tested, while the tensile strain is over-predicted by both the ACI

and fib-1codes, it is under-predicted for the fib-2 and CNR- DT202 codes.

However, the tensile strains are acceptable for TR55 and JSCE codes

respectively.

238

8.3 Recommendations for future research works

Based on the findings of this work, the following areas are suggested for future

investigation:

1. Numerical analysis of single shear tests can be extended to investigate the

bond behaviour under long-term cyclic effect.

2. Further experimental tests should be undertaken to investigate the fatigue

bond behaviour of near surface mounted CFRP strengthened concrete

substrate.

3. As the present experimental single shear study was conducted under low

fatigue, it is recommended to study experimentally the bond behaviour in

single shear under high fatigue.

4. More experimental tests can be conducted to investigate the influence of

lightweight concrete on the failure behaviour of the single shear fatigue

test. This investigation can also be extended by inclusion of steel fibres in

the light weight concrete.

5. As the current study was conducted using Carbon FRP plate, it is

recommended to undertake experiments on single shear and RC two-way

slabs with opening reinforced with other types of FRP such as Glass FRP

reinforcement.

6. Further research is required to understand the bond behaviour in

strengthened structural members subjected to cyclic thermal stresses.

7. Further to the present study, it is recommended to investigate the bond

behaviour of other structural members subjected to cyclic loading such as

concrete retaining walls or concrete columns strengthened with CFRP

plate.

8. Behaviour of CFRP strengthened two-way RC slabs with and without

openings under dynamic impact or blast loading conditions.

9. Further research is required to test the applicability of the current adopted

analytical model to other loading ranges and concrete strengths.

239

References ABAQUS 2011. Theory Manual, User Manual and Example Manual. Version

6.10, Providence, RI. ABDULLAH, A. M. 2011. Analysis of repaired/strengthened RC structures

using composite materials: punching shear. ACI440.2R-08. Year. Guide for the design and construction of externally

bonded FRP systems for strengthening concrete structures. In, 2008. Farmington Hills, Mich American Concrete Institute.

ACI 1995. 318. Building Code Requirements for Reinforced Concrete (ACI 318-95) ACI, Detroit, USA.

AIDOO, J., HARRIES, K. A. & PETROU, M. F. 2004. Fatigue behavior of carbon fiber reinforced polymer-strengthened reinforced concrete bridge girders. Journal of composites for construction, 8, 501-509.

AL-ROUSAN, R. & ISSA, M. 2011. Fatigue performance of reinforced concrete beams strengthened with CFRP sheets. Construction and Building Materials, 25, 3520-3529.

AL-SARAJ, W. K. A. 2007. Fatigue Behavior of Reinforced Concrete Beams Strengthened With GFRP Sheets. Journal of Engineering and Development, 11.

ALI-AHMAD, M., SUBRAMANIAM, K. & GHOSN, M. 2006. Experimental investigation and fracture analysis of debonding between concrete and FRP sheets. Journal of engineering mechanics, 132, 914-923.

ARDUINI, M., NANNI, A. & ROMAGNOLO, M. 2004. Performance of one-way reinforced concrete slabs with externally bonded fiber-reinforced polymer strengthening. ACI structural journal, 101.

ASTM 1996. Standard test method for splitting tensile strength of cylindrical concrete specimens ASTM International, C496/C496M-11 West conshohocken, PA, USA.

ASTM 1997. Standard test methods and definitions for mechanical testing of steel products. ASTM International, (A370-97a) West Conshohocken, PA, USA.

AZARI, S., PAPINI, M. & SPELT, J. 2011. Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints–Part I: Experiments. Engineering Fracture Mechanics, 78, 153-162.

BHATT, P., MACGINLEY, T. J. & CHOO, B. S. 2014. Reinforced Concrete Design to Eurocodes: Design Theory and Examples, CRC Press.

BIZINDAVYI, L. & NEALE, K. 1999. Transfer lengths and bond strengths for composites bonded to concrete. Journal of composites for construction, 3, 153-160.

BIZINDAVYI, L., NEALE, K. & ERKI, M. 2003. Experimental investigation of bonded fiber reinforced polymer-concrete joints under cyclic loading. Journal of composites for construction, 7, 127-134.

BSI 1983. Testing concrete: Method for determination of compressive strength of concrete. British Standard Institution, London, UK., BS 1881- 116

BSI 2004. Eurocode 2: Design of Concrete Structures, London, UK., British Standards Institution.

240

CAMANHO, P. P. & DÁVILA, C. G. 2002. Mixed-mode decohesion finite elements for the simulation of delamination in composite materials. NASA-Technical paper, 211737, 33.

CAMATA, G., SPACONE, E., AL-MAHAIDI, R. & SAOUMA, V. 2004. Analysis of test specimens for cohesive near-bond failure of fiber-reinforced polymer-plated concrete. Journal of composites for construction, 8, 528-538.

CARLONI, C. & SUBRAMANIAM, K. V. 2010. Direct determination of cohesive stress transfer during debonding of FRP from concrete. Composite Structures, 93, 184-192.

CARLONI, C., SUBRAMANIAM, K. V., SAVOIA, M. & MAZZOTTI, C. 2012. Experimental determination of FRP–concrete cohesive interface properties under fatigue loading. Composite Structures, 94, 1288-1296.

CAROLIN, A. 2003. Carbon fibre reinforced polymers for strengthening of structural elements. Division of Structural Engineering, Department of Civil and Mining Engineering, Lulea University of Technology, Sweden, 194.

CARSTENSEN, J. V. 2011. Material Modelling of Reinforced Concrete at Elevated Temperature Master Master, Technical University of Denmark.

CHAJES, M. J., FINCH JR, W. W., JANUSZKA, T. F. & THOMSON JR, T. A. 1996. Bond and force transfer of composite-material plates bonded to concrete. ACI structural journal, 93.

CHAUDHARI, S. & CHAKRABARTI, M. 2012. Modeling of concrete for nonlinear analysis Using Finite Element Code ABAQUS. International Journal of Computer Applications, 44, 14-18.

CHEN, J. & TENG, J. 2001. Anchorage strength models for FRP and steel plates bonded to concrete. Journal of Structural Engineering, 127, 784-791.

CNR-DT200 2004. Guide for the design and construction of externally bonded FRP systems for strengthening of existing structures. Rome,

Italy: National Research Council, Advisory Committee on Technical

Regulations for Constructions, 200 CNR-DT202 2005. Guide for the design and construction of externally

bonded FRP systems for strengthening of existing structures. Rome,

Italy: National Research Council, Advisory Committee on Technical

Regulations for Constructions, 202. CONCRETE..SOCIETY 2012. Design guidance for strengthening concrete

structures using fibre composite materials, Surrey, UK, Technical Report 55.

DAI, J., UEDA, T. & SATO, Y. 2005. Development of the nonlinear bond stress–slip model of fiber reinforced plastics sheet–concrete interfaces with a simple method. Journal of composites for construction, 9, 52-62.

DAUD, R. A., CUNNINGHAM, L. S. & WANG, Y. C. 2015. Static and fatigue behaviour of the bond interface between concrete and externally bonded CFRP in single shear. Engineering Structures, 97, 54-67.

DE LORENZIS, L., MILLER, B. & NANNI, A. 2001. Bond of fiber-reinforced polymer laminates to concrete. ACI Materials Journal, 98.

241

EBEAD, U. & MARZOUK, H. 2004. Fiber-reinforced polymer strengthening of two-way slabs. ACI structural journal, 101.

ELSAYED, W. E., EBEAD, U. A. & NEALE, K. W. 2009. Mechanically fastened FRP-strengthened two-way concrete slabs with and without cutouts. Journal of composites for construction, 13, 198-207.

ENOCHSSON, O. 2005. CFRP strengthening of concrete slabs, with and without openings. Experiment, analysis, design and field application, Licentiate thesis, Luleå University of Technology.

ESFAHANI, M. R., KIANOUSH, M. & TAJARI, A. 2007. Flexural behaviour of reinforced concrete beams strengthened by CFRP sheets. Engineering Structures, 29, 2428-2444.

F.E.M.A. 2007. Interim Testing Protocols for Determining the Seismic Performance Characteristics of Structural and Nonstructural Components. Federal Emergency Management Agency Washington, DC. USA.

FAELLA, C., MARTINELLI, E. & NIGRO, E. Year. Direct versus Indirect identification of FRP-to-concrete interface relationships. In: Asia-Pacific Conference on FRP in Structures. Hong Kong (China), 12-14 December 2007, 2007.

FERREIRA, J., REIS, P., COSTA, J. & RICHARDSON, M. 2002. Fatigue behaviour of composite adhesive lap joints. Composites Science and Technology, 62, 1373-1379.

FIB 2001. Externally bonded FRP reinforcement for RC structures, Bulletin 14 Lausanne, Switzerland: Fe´de´ration Internationale du Be´ton 14, 138. GUO, Z., CAO, S., SUN, W. & LIN, X. Year. Experimental study on bond

stress-slip behaviour between FRP sheets and concrete. In: FRP in construction, proceedings of the international symposium on bond behaviour of FRP in structures, 2005. 77-84.

GUSSENHOVEN, R. & BRENA, S. 2005. Fatigue behavior of reinforced concrete beams strengthened with different FRP laminate configurations. ACI Special Publication, 230.

HARRIES, K. A. & AIDOO, J. 2006. Debonding-and fatigue-related strain limits for externally bonded FRP. Journal of composites for construction, 10, 87-90.

HILLERBORG, A., MODÉER, M. & PETERSSON, P.-E. 1976. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and concrete research, 6, 773-781.

HÖRMANN, M., MENRATH, H. & RAMM, E. 2002. Numerical investigation of fiber reinforced polymers poststrengthened concrete slabs. Journal of engineering mechanics, 128, 552-561.

HOSSEINI, A. & MOSTOFINEJAD, D. 2014. Effective bond length of FRP-to-concrete adhesively-bonded joints: Experimental evaluation of existing models. International Journal of Adhesion and Adhesives, 48, 150-158.

JSCE 2001. Recommendations for upgrading of concrete structures with use of continuous fiber sheets, Research Committee on Upgrading of Concrete Structures with use of Continuous Fiber Sheets, Japan Society of Civil Engineers.

242

KAMEL, A. S., ELWI, A. & CHENG, R. 2004. Experimental investigation on FRP sheets bonded to concrete. Emirates Journal for Engineering Research, 9, 71-76.

KHOMWAN, N., FOSTER, S. J. & SMITH, S. T. 2010. FE modeling of FRP-repaired planar concrete elements subjected to monotonic and cyclic loading. Journal of composites for construction, 14, 720-729.

KIM, Y. J. & HEFFERNAN, P. J. 2008. Fatigue behavior of externally strengthened concrete beams with fiber-reinforced polymers: State of the art. Journal of composites for construction, 12, 246-256.

KIM, Y. J., LONGWORTH, J. M., WIGHT, R. G. & GREEN, M. F. 2008. Flexure of two-way slabs strengthened with prestressed or nonprestressed CFRP sheets. Journal of composites for construction, 12, 366-374.

KOTYNIA, R., WALENDZIAK, R., STOECKLIN, I. & MEIER, U. 2010. RC slabs strengthened with prestressed and gradually anchored CFRP strips under monotonic and cyclic loading. Journal of composites for construction, 15, 168-180.

LEE, J. & FENVES, G. L. 1998. Plastic-damage model for cyclic loading of concrete structures. Journal of engineering mechanics, 124, 892-900.

LIMAM, O., FORET, G. & EHRLACHER, A. 2003. RC two-way slabs strengthened with CFRP strips: experimental study and a limit analysis approach. Composite Structures, 60, 467-471.

LOO, K. Y. M., FOSTER, S. J. & SMITH, S. T. 2012. FE modeling of CFRP-repaired RC beams subjected to fatigue loading. Journal of composites for construction, 16, 572-580.

LU, X., TENG, J., YE, L. & JIANG, J. 2005a. Bond–slip models for FRP sheets/plates bonded to concrete. Engineering Structures, 27, 920-937.

LU, X., TENG, J., YE, L. & JIANG, J. 2007. Intermediate crack debonding in FRP-strengthened RC beams: FE analysis and strength model. Journal of composites for construction, 11, 161-174.

LU, X., YE, L., TENG, J. & JIANG, J. 2005b. Meso-scale finite element model for FRP sheets/plates bonded to concrete. Engineering Structures, 27, 564-575.

LUBLINER, J., OLIVER, J., OLLER, S. & ONATE, E. 1989. A plastic-damage model for concrete. International Journal of solids and structures, 25, 299-326.

LUNDQVIST, J. 2007. Numerical analysis of concrete elements strengthened with carbon fiber reinforced polymers. Luleå University of Technology.

MAZZOTTI, C. & SAVOIA, M. 2009. FRP-concrete bond behaviour under cyclic debonding force. Advances in Structural Engineering, 12, 771-780.

MAZZOTTI, C., SAVOIA, M. & FERRACUTI, B. 2003. NON LINEAR INTERFACE LAW FOR MODELLING OF FRP-CONCRETE DELAMINATION.

MOFIDI, A., THIVIERGE, S., CHAALLAL, O. & SHAO, Y. 2013. Behavior of reinforced concrete beams strengthened in shear using L-shaped CFRP plates: Experimental investigation. Journal of composites for construction, 18.

243

MOSALLAM, A. S. & MOSALAM, K. M. 2003. Strengthening of two-way concrete slabs with FRP composite laminates. Construction and Building Materials, 17, 43-54.

NIGRO, E., DI LUDOVICO, M. & BILOTTA, A. 2010. Experimental investigation of FRP-concrete debonding under cyclic actions. Journal of Materials in Civil Engineering, 23, 360-371.

NIU, H. & WU, Z. 2005. Numerical Analysis of Debonding Mechanisms in FRP‐Strengthened RC Beams. Computer‐Aided Civil and Infrastructure Engineering, 20, 354-368.

PANDEY, P., SHANKARAGOUDA, H. & SINGH, A. K. 1999. Nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives. Computers & structures, 70, 387-413.

PAPAKONSTANTINOU, C. G., PETROU, M. F. & HARRIES, K. A. 2001. Fatigue behavior of RC beams strengthened with GFRP sheets. Journal of composites for construction, 5, 246-253.

PARNAS, R., SHAW, M. T. & LIU, Q. 2007. Basalt fiber reinforced polymer composites.

PELLEGRINO, C., TINAZZI, D. & MODENA, C. 2008. Experimental study on bond behavior between concrete and FRP reinforcement. Journal of composites for construction, 12, 180-189.

PERERA, R., RECUERO, A., DE DIEGO, A. & LÓPEZ, C. 2004. Adherence analysis of fiber-reinforced polymer strengthened RC beams. Computers & structures, 82, 1865-1873.

PINTO, P. & FILIPPOU, F. 1996. CEB: RC Elements Under Cyclic Loading. Thomas Telford.

QUATTLEBAUM, J. B., HARRIES, K. A. & PETROU, M. F. 2005. Comparison of three flexural retrofit systems under monotonic and fatigue loads. Journal of Bridge Engineering, 10, 731-740.

REDDY, J. N. 2004. Mechanics of laminated composite plates and shells: theory and analysis, CRC press.

REVERIE LTD., U. 2014. <http://www.reverie.ltd.uk/>; [Online]. [Accessed]. ROSENBOOM, O. & RIZKALLA, S. 2005. Fatigue behavior of prestressed

concrete bridge girders strengthened with various CFRP systems. ACI Special Publication, 230.

RUSINOWSKI, P. 2005. Two-way concrete slabs with openings: experiments, finite element analyses and design.

SAID, H. & WU, Z. 2008. Evaluating and proposing models of predicting IC debonding failure. Journal of composites for construction, 12, 284-299.

SEIM, W., HÖRMAN, M., KARBHARI, V., AND SEIBLE, F. 2001. External FRP Poststrengthening of Scaled Concrete Slabs. Journal of composites for construction, 5, 67-75.

SHAHAWY, M. & BEITELMAN, T. E. 1999. Static and fatigue performance of RC beams strengthened with CFRP laminates. Journal of Structural Engineering, 125, 613-621.

SUBRAMANIAM, K., CARLONI, C. & NOBILE, L. 2011. An understanding of the width effect in FRP–concrete debonding. Strain, 47, 127-137.

SUBRAMANIAM, K. V., CARLONI, C. & NOBILE, L. 2007. Width effect in the interface fracture during shear debonding of FRP sheets from concrete. Engineering Fracture Mechanics, 74, 578-594.

http://www.reverie.ltd.uk/%3e;

244

TOUTANJI, H., ZHAO, L. & ZHANG, Y. 2006. Flexural behavior of reinforced concrete beams externally strengthened with CFRP sheets bonded with an inorganic matrix. Engineering Structures, 28, 557-566.

TURON, A., COSTA, J., CAMANHO, P. & DÁVILA, C. 2007. Simulation of delamination in composites under high-cycle fatigue. Composites Part A: applied science and manufacturing, 38, 2270-2282.

TURON TRAVESA, A. 2006. Simulation of delamination in composites under quasi-static and fatigue loading using cohesive zone models, Universitat de Girona.

TYAU, J. S. 2009. Finite Element Modelling of Reinforced Concrete Using 3-

Dimensional Solid Elements with Discrete Rebar. Master, Brigham Young

University. WANG, T. & HSU, T. T. 2001. Nonlinear finite element analysis of concrete

structures using new constitutive models. Computers & structures, 79, 2781-2791.

WEBER BUILDING SOLUTION, U. 2014. <http://www.netweber.co.uk/home.html>.

WONG, R. S. & VECCHIO, F. J. 2003. Towards modeling of reinforced concrete members with externally bonded fiber-reinforced polymer composites. ACI structural journal, 100.

YAO, J., TENG, J. & CHEN, J. 2005. Experimental study on FRP-to-concrete bonded joints. Composites Part B: Engineering, 36, 99-113.

YUAN, H., TENG, J., SERACINO, R., WU, Z. & YAO, J. 2004. Full-range behavior of FRP-to-concrete bonded joints. Engineering Structures, 26, 553-565.

YUN, Y., WU, Y.-F. & TANG, W. C. 2008. Performance of FRP bonding systems under fatigue loading. Engineering Structures, 30, 3129-3140.

ZHOU, Y.-W., WU, Y.-F. & YUN, Y. 2010. Analytical modeling of the bond–slip relationship at FRP-concrete interfaces for adhesively-bonded joints. Composites Part B: Engineering, 41, 423-433.

http://www.netweber.co.uk/home.html%3e

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Appendix A

Numerical results of single shear (Monotonic series)

0

5

10

15

20

25

30

35

40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Lo

ad

(K

N)

Slip (mm)

1mm (M46J) EXP 1 mm (M46J) FEM

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8

Loa

d (

KN

)

Slip (mm)

1mm (T700) EXP 1 mm (T700) FEM

246

Figure A-1: Total load versus slip

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Loa

d (

KN

)

Slip (mm)

0.2 mm (T700) EXP 0.2 mm (T700) FEM

0

3

6

9

12

15

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Lo

ad

(K

N)

Slip (mm)

0.15mm (M46J) EXP 0.15mm (M46J) FEM

247

M1

0

1000

2000

3000

4000

5000

0 50 100 150 200 250 300

De

bo

nd

ing

stra

in (

Mic

ro

n)


1.5 KN (EXP) 1.5 KN (FEM) 12.83 KN (EXP) 12.5 KN (FEM)

22.82 KN (EXP) 22.5 KN (FEM) 24.02 KN (EXP) 24 KN (FEM)

0

1000

2000

3000

4000

5000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)



28.2 KN (EXP) 28 KN (FEM) 34 KN (EXP) 35.5 KN (FEM)

M2

248

Figure A-2: strain profile along the bonded CFRP plate

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)

Distance in longitudinal direcion (mm)



M6

0

2000

4000

6000

8000

10000

12000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)


6.KN (EXP) 6 KN (FEM) 12 KN (EXP) 10.9 KN (FEM)


M5

249

Numerical results of single shear (Post-fatigue series)

0

3

6

9

12

15

18

21

24

27

0 0.2 0.4 0.6 0.8

Load

(KN

)

Slip (mm)


pre-fatigue (FEM) post-fatigue (FEM)

P-F1

0

3

6

9

12

15

18

21

0 0.2 0.4 0.6 0.8 1 1.2

Loa

d (

KN

)

Slip(mm)



P-F2

250

Figure A-3: Total load versus slip

P-F5

0

3

6

9

12

0 0.4 0.8 1.2 1.6 2 2.4

Load

(KN)

Slip (mm)



0

3

6

9

12

0 0.5 1 1.5 2 2.5

Load

(kN

)

Slip (mm)

pre-fatigue (EXP) post-fatigue (EXP)pre-fatigue (FEM) post-fatigue (FEM)

P-F6

251

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)


3.78 KN (EXP) 4 KN (FEM) 11 KN (EXP) 11 KN (FEM)


P-F1

0

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)


3.7KN (EXP) 3.8 KN (FEM) 9.2 KN (EXP) 9.2 KN (FEM)

15.8 KN (EXP) 15.4 KN (FEM) 19.2 KN (EXP) 19 KN (FEM)

P-F2

252

Figure A-4: Strain profile along the bonded CFRP plate

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300

De

bo

nd

ing

stra

in (

Mic

ron

)


4.9 KN (EXP) 4.3 KN (FEM) 9.2 KN (EXP)

8.9 KN (FEM) 9.8 KN (EXP) 9.8 KN (FEM)

P-F5

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300

De

bo

nd

ing

str

ain

(M

icro

n)

Distanice in longitudinal direction (mm)


8.5 KN (EXP) 7.7 KN (FEM) 10.9 KN(EXP) 10.2 KN (FEM)

P-F6

253

Appendix B

Numerical results of one-way slabs series (S-T1)

0

100

200

300

0 20 40 60 80

Lo

ad

(k

N)

Deflection (mm)

S-T1L1-Num. S-T1L1-Exp.

0

100

200

300

400

0 20 40 60 80 100

Lo

ad

(k

N)

Deflection (mm)


254

Figure B-1: Total load versus deflection for slab (S-T1)

Numerical results of one-way slabs series (S-T3)

0

60

120

180

0 20 40 60 80 100 120

Lo

ad

(k

N)

Deflection (mm)

S-T1L0-Num. S-T1L0-EXP.

0

100

200

300

400

0 20 40 60 80 100

Lo

ad

(k

N)

Deflection (mm)


255

Figure B-2: Total load versus deflection for slab (S-T3)

0

100

200

300

0 20 40 60 80 100

Lo

ad

(k

N)

Deflection (mm)


0

50

100

150

200

0 30 60 90 120 150

Lo

ad

(k

N)

Deflection (mm)


256

Numerical results of one-way slabs series (C-T1)

0

50

100

150

200

250

300

0 20 40 60 80 100

Lo

ad

(k

N)

Deflection (mm)

C-T1L1 Num. C-T1L1 Exp.

0

100

200

300

400

0 20 40 60 80 100

Lo

ad

(k

N)

Deflection (mm)


257

Figure B-3: Total load versus deflection for slab (C-T1)

0

60

120

180

0 30 60 90 120

Lo

ad

(k

N)

Deflection (mm)


Behaviour of Reinforced Concrete Slabs Strengthened ...

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