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
3.7.3.2 Post-fatigue tests ............................................................................... 81
3.7.4 Interfacial shear stress distributions ..................................................... 84
3.7.4.1 Monotonic tests ................................................................................ 84
4
3.7.4.2 Post-fatigue tests ............................................................................... 85
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
5.3.2 Finite element model .......................................................................... 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
5.5.2 Finite element model .......................................................................... 171
5.5.3 Discussion of computational results and comparison with experiments
............................................................................................................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
Figure 3- 11: Fatigue load-slip responses (the number above each curve indicates
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- 8: Typical traction-separation response. ................................................... 101
Figure 4- 9: Typical traction-separation response. ................................................... 102
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
Figure 4- 18: Representative comparisons between numerical and experimental load-
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
Figure 5- 25: Finite element mesh of the quarter the CFRP-strengthened RC slabs
type (C) with a close-up view of the me .................................................................. 171
Figure 5- 26: Comparison of predicted and experimental load-mid-span deflection
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
12
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
Figure 6- 23: Contour plot of the damage initiation criterion at the CFRP/concrete
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
Figure 6- 25: Comparison of numerical and experimental load- deflection curves for
RC two-way slab under cyclic loading. ................................................................... 216
Figure 6- 26: Comparison of numerical and experimental load-strain curves in steel
and concrete for RC two-way slab under cyclic loading. ........................................ 217
Figure 6- 27: Comparison of numerical and experimental strain profiles for RC two-
way slab under cyclic loading. ................................................................................. 218
Figure 6- 28: Contour plot of the damage initiation criterion at the CFRP/concrete
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
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This page must form part of any such copies made.
iii. The ownership of certain Copyright, patents, designs, trademarks and other
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Intellectual Property and/or Reproductions.
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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
CFRP/Concrete Interface in Single Shear
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
Figure 3- 9: Fatigue load-slip responses (the number above each curve indicates
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
Figure 3- 11: Fatigue load-slip responses (the number above each curve indicates
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
3.7.3.1 Monotonic tests
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.
3.7.3.2 Post-fatigue tests
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.
3.7.4.1 Monotonic tests
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)
3.7.4.2 Post-fatigue tests
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
CFRP/Concrete Interface in Single Shear
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
Figure 4- 8: Typical traction-separation response.
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
Unloading/ Reloading path
Exponential damage response
K0
Km
102
Figure 4- 9: Typical traction-separation response.
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
Unloading/ Reloading path
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)
Figure 4- 17: Representative comparisons between numerical and experimental load-
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
)
Distance in longitudinal direction (mm)
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)
Debonding strain at ultimate load
118
(b) Post-fatigue test (P-F4)
Figure 4- 18: Representative comparisons between numerical and experimental load-
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)
Distance in longitudinal direction (mm)
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)
Debonding strain at ultimate load
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
)
Distance in longitudinal direction (mm)
(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
(Surface 1) Y-symmetry plane & B.C
U2=UR1=UR3=0
Support B.C U3=UR3=UR1=0
Support B.C U3=UR3=UR1=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).
5.3.2 Finite element model
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.
Figure 5- 14: Finite element mesh of the quarter the CFRP-strengthened RC slabs
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.
5.3.4 Discussion of computational results and comparison with experiments
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
Figure 5- 19: Comparison of predicted and experimental load-mid-span deflection
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)
S-T2L1-Exp. S-T2L1-Num.
0
200
400
600
800
1000
0 20 40 60 80
Lo
ad
(K
N)
Deflection (mm)
S-T2L2-Exp. S-T2L2-Num.
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
4 S-T2L0 399.9 NA Steel yielding 375.96 NA Steel yielding
5 S-T2L1 522.9 1.004 Fibre rupture 515.1 0.96 FRP peeling
6 S-T2L2 684.9 0.4 FRP peeling 683.2 0.25 FRP peeling
7 S-T3L0 180.5 NA Steel yielding 171.1 NA Steel yielding
8 S-T3L1 262.3 1.27 Fibre rupture 254.4 0.96 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
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.
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
5.5.2 Finite element model
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.
Figure 5- 25: Finite element mesh of the quarter the CFRP-strengthened RC slabs
type (C) with a close-up view of the me
Truss element (Steel)
3-D Solid element (concrete)
Cohesive surface interaction
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
5.5.3 Discussion of computational results and comparison with experiments
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)
C-T2L1 Exp. C-T2L1 Num.
0
200
400
600
800
1000
0 20 40 60 80
Lo
ad
(K
N)
Deflection (mm)
C-T2L2 Exp. C-T2L2 Num.
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)
FE analysis (FEMA461 load protocol)
FE analysis (experment load protocol)
0
50
100
150
200
250
300
0 10 20 30 40 50 60
Load
(KN
)
Deflection (mm)
FE analysis (FEMA461 load protocol)
FE analysis (experment load protocol)
(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
)
Distance along the CFRP sheet (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)
Distance from the line load to the end of CFRP sheet (mm)
154 KN 256 KN 279.2 KN
154 KN -Static 256 KN -Static 279.3 KN -Static
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)
Distance along the CFRP sheet (mm)
110 KN -Static 160 KN -Static 237.6 KN -Static
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)
Distance from the line load to the end of CFRP sheet (mm)
110 KN -Static 160 KN -Static 237.6 KN -Static
110 KN 160 KN 230.3 KN
-2000
-1000
0
1000
2000
3000
0 500 1000 1500 2000 2500 3000 3500Mic
ro
stra
in
Distance along the CFRP sheet (mm)
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
Distance from the line load to the end of CFRP sheet (mm)
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)
Strain (Microstrain)
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
Distance from the slab centre toward end of support (mm)
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.
6.10.1 Finite element model
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
(Surface 2) Y-symmetry plane & B.C
U2=UR1=UR3=0
Support B.C U3=UR3=UR2=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
Support B.C U3=UR3=UR2=0
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 Discussion of computational results and comparison with experiments
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)
Cohesive surface interaction
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.
Figure 6- 21: Comparison of numerical and experimental load- deflection curves for
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
Figure 6- 22: Comparison of numerical and experimental load-strain curves in steel
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
)
Strain (Microstrain)
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)
Strain (Microstrain)
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).
Figure 6- 23: Contour plot of the damage initiation criterion at the CFRP/concrete
interface for RC two-way slab under monotonic loading.
Figure 6- 24: Comparison of numerical and experimental strain profiles for RC two-
way slab under monotonic loading.
Distance from the slab centre toward end of support (mm)
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).
Figure 6- 25: Comparison of numerical and experimental load- deflection curves for
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.
Figure 6- 26: Comparison of numerical and experimental load-strain curves in steel
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
)
Strain (Microstrain)
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.
Figure 6- 27: Comparison of numerical and experimental strain profiles for RC two-
way slab under cyclic loading.
Figure 6- 28: Contour plot of the damage initiation criterion at the CFRP/concrete
interface for RC two-way slab under cyclic loading.
Distance from the slab centre toward end of support (mm)
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)
Distance from the slab centre toward end of support (mm)
Opening edge
Opening edge
Distance from the slab centre toward end of support (mm)
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
Distance from the slab centre toward end of support (mm)
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
Distance from the slab centre toward end of support (mm)
Opening edge
Distance from the slab centre toward end of support (mm)
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
Distance from the slab centre toward end of support (mm)
Opening edge
Distance from the slab centre toward end of support (mm)
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.
The maximum cyclic debonding strain is less than the maximum monotonic
debonding strain by 6.9%, 10% and 11.4% for the RC slabs strengthened
with CFRP plate widths of 75, 100, 125 mm respectively.
The maximum cyclic debonding strain is less than the maximum monotonic
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
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245
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)
Distance in longitudinal direction (mm)
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)
Distance in longitudinal direction (mm)
8.5 KN (EXP) 8.5 KN (FEM) 21.6 KN (EXP) 21.6 KN (FEM)
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)
1.54 KN (EXP) 1.6 KN (FEM) 9.15 KN (EXP) 9.15 KN (FEM)
10.7 KN (EXP) 10.4 KN (FEM) 13.1 KN (EXP) 12.1 KN (FEM)
M6
0
2000
4000
6000
8000
10000
12000
0 50 100 150 200 250 300
De
bo
nd
ing
str
ain
(M
icro
n)
Distance in longitudinal direction (mm)
6.KN (EXP) 6 KN (FEM) 12 KN (EXP) 10.9 KN (FEM)
11.98 KN (EXP) 11.1 KN (FEM) 11.91 KN (EXP) 11.2 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 (EXP) post-fatigue (EXP)
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)
pre-fatigue (EXP) post-fatigue (EXP)
pre-fatigue (FEM) post-fatigue (FEM)
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)
pre-fatigue (EXP) post-fatigue (EXP)
pre-fatigue (FEM) post-fatigue (FEM)
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)
Distance in longitudinal direction (mm)
3.78 KN (EXP) 4 KN (FEM) 11 KN (EXP) 11 KN (FEM)
18.4 KN (EXP) 18.2 KN (FEM) 25.1 KN (EXP) 24.1 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)
Distance in longitudinal direction (mm)
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
)
Distance in longitudinal direction (mm)
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)
3.7 KN (EXP) 3.8 KN (FEM) 5.8 KN (EXP) 5.8 KN (FEM)
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)
S-T1L2-Num. S-T1L2-Exp.
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)
S-T3L2-Num. S-T3L2-Exp.
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)
S-T3L1-Num. S-T3L1-Exp.
0
50
100
150
200
0 30 60 90 120 150
Lo
ad
(k
N)
Deflection (mm)
S-T3L0-Num. S-T3L0-Exp.
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)
C-T1L2 Num. C-T1L2 Exp.
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)
C-T1L0 Num. C-T1L0 Exp.
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