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Structural Analysis of Strengthened
RC Slabs
A thesis submitted to The University of Manchester for the degree of Doctor of
Philosophy in the Faculty of Science and Engineering
2018
Mohammadtaher Davvari
SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
2
Table of contents
Table of contents ........................................................................................... 2
List of figures ................................................................................................ 6
List of tables ................................................................................................ 11
Abstract ....................................................................................................... 13
Declaration .................................................................................................. 14
Copyright statement .................................................................................... 15
Acknowledgment ........................................................................................ 16
Notation ....................................................................................................... 17
1. Introduction ............................................................................................. 20
1.1. General ................................................................................................................ 20
1.2. Research objectives ............................................................................................ 22
1.3. Methodology ....................................................................................................... 23
1.4. Research significances ........................................................................................ 24
1.5. Thesis outline ...................................................................................................... 24
2. Literature review ..................................................................................... 27
2.1. Strengthening RC structures ............................................................................... 27
2.2. Fibre reinforced polymer .................................................................................... 29
2.3. Two-way RC slab behaviour .............................................................................. 33
2.4. Strengthening of two-way RC slabs ................................................................... 40
2.4.1. Flexural strengthening................................................................................. 40
2.4.2. Punching strengthening of RC slabs ........................................................... 44
2.4.2.1. Punching failure mechanism ............................................................................ 44
2.4.2.2. Effective parameters for punching strength ..................................................... 48
2.4.2.3. Punching strengthening methods ..................................................................... 52
2.5. Slabs strengthened with FRP .............................................................................. 58
2.5.1. The behaviour and failure mode of FRP strengthened slabs ...................... 58
3
2.5.1.1. FRP strengthened RC slabs with full of composite action ............................... 58
2.5.1.2. FRP strengthened RC slabs with a partial loss of composite action ................ 60
2.5.2. Bond behaviour between concrete and FRP ............................................... 62
2.5.3. Design codes estimation in composite action ............................................. 67
2.5.3.1 Evaluation of the slabs punching strength ........................................................ 67
2.5.3.2. Evaluation of the slabs flexural capacity ......................................................... 70
2.5.4. Prestressed FRP as an external reinforcement ............................................ 72
2.6. Summary ............................................................................................................. 73
3. Strengthening RC slabs with non-prestressed and prestressed FRP ...... 73
3.1. Introduction ......................................................................................................... 74
3.2. Experimental studies ........................................................................................... 75
3.2.1. Abdullah’s experimental investigation ....................................................... 75
3.2.2. Kim et al.’s experimental investigation ...................................................... 79
3.3. Numerical Modelling .......................................................................................... 83
3.3.1. Introduction ................................................................................................. 83
3.3.2. Concrete Modelling..................................................................................... 84
3.3.2.1. Compressive and tensile behaviour of concrete ............................................... 84
3.3.2.2. Concrete damage modelling ............................................................................. 87
3.3.3. Steel modelling ........................................................................................... 95
3.3.4. FRP modelling ............................................................................................ 96
3.3.5. Load applications and constraints ............................................................... 99
3.3.6. Finite element type and mesh.................................................................... 100
3.3.7. Mesh convergence..................................................................................... 104
3.3.8. Validation of finite element models .......................................................... 105
3.4. Analysis and discussion of results .................................................................... 108
3.5. The optimum FRP prestress ratio to strengthen RC slabs ................................ 123
3.6. Summary ........................................................................................................... 130
4. FRP and Shear Strengthening of RC Slabs .......................................... 132
4.1. Introduction ....................................................................................................... 132
4.2. Experimental test .............................................................................................. 133
4.2.1. Rationale behind choosing the dimension of the tested slabs ................... 134
4
4.2.2. Strengthened and non-strengthened sample layouts ................................. 136
4.2.3. Materials.................................................................................................... 139
4.2.3.1. Concrete ......................................................................................................... 139
4.2.3.2. Steel reinforcement ........................................................................................ 140
4.2.3.3. FRP composites.............................................................................................. 141
4.2.4. Experimental preparation .......................................................................... 141
4.2.4.1. Mould ............................................................................................................. 141
4.2.4.2. Support frame ................................................................................................. 142
4.2.4.3. Reinforcement ................................................................................................ 143
4.2.4.4. Casting, curing, and slab preparation ............................................................. 143
4.2.4.5. Surface preparation and bonding process ...................................................... 144
4.2.5. Measurement instrumentation ................................................................... 146
4.2.6. Test preparation and procedure ................................................................. 149
4.3. Results and discussion ...................................................................................... 150
4.3.1. Experimental and FE model results .......................................................... 150
4.3.2. Slabs with an initial low tensile reinforcement ratio (category L) ............ 152
4.3.2.1. Control specimen with a low tensile reinforcement ratio (L0) ...................... 152
4.3.2.2. Shear strengthened slab with a low tensile reinforcement ratio (LS) ............ 155
4.3.2.3. FRP strengthened slab with an initial low tensile reinforcement ratio (LF) .. 158
4.3.2.4. FRP and shear strengthened slab with low tensile reinforcement ratio (LFS)163
4.3.3. Slabs with an initial high tensile reinforcement ratio (category H) .......... 171
4.3.3.1. Control specimen with a high tensile reinforcement ratio (H0) ..................... 171
4.3.3.2. Shear strengthened slab with a high tensile reinforcement ratio (HS) ........... 174
4.3.3.3. FRP strengthened slab with an initial high tensile reinforcement ratio (HF) . 178
4.3.3.4. FRP and shear strengthened slab with high tensile reinforcement ratio (HFS) ... 184
4.3.4. Assessment of models to predict the capacity of the slabs ....................... 188
4.4. Summary ........................................................................................................... 190
5. Parametric study.................................................................................... 191
5.1. Introduction ....................................................................................................... 191
5.2. Parametric investigation ................................................................................... 192
5.2.1. The tensile reinforcement ratio ................................................................. 192
5.2.2. The compressive reinforcement ................................................................ 196
5.2.3. The pattern of FRP sheets to strengthen RC slabs .................................... 200
5
5.2.4. The number of FRP sheets ........................................................................ 201
5.2.5. The thickness of FRP sheets to strengthen RC slabs ................................ 203
5.3. Summary ........................................................................................................... 205
6. Conclusion and future work .................................................................. 205
References ................................................................................................. 211
6
List of figures
Chapter 2
Figure 2-1. Strengthening RC structures with steel members ............................................................... 27
Figure 2-2. Strengthening RC elements with FRP on the Country Hills Boulevard Bridge ................. 29
Figure 2-3. Fibre reinforced polymer matrix. ....................................................................................... 29
Figure 2-4. Unidirectional FRP, woven FRP and FRP laminate. ......................................................... 30
Figure 2-5. Strengthening RC structure using an FRP plate ................................................................. 31
Figure 2-6. Strengthening RC columns with FRP sheets. ..................................................................... 32
Figure 2-7. Stress-strain curve for FRPs and mild steel. ....................................................................... 32
Figure 2-8. One-way and two-way RC slabs. ....................................................................................... 33
Figure 2-9. Load–deflection curves of typical ductile and brittle materials ......................................... 35
Figure 2-10. Effective parameters in RC sections of flexural members. .............................................. 36
Figure 2-11. Two-way RC slab failure mode based on the steel reinforcement ratio ........................... 37
Figure 2-12. Typical load-deflection curves of flat slabs with ductile and brittle failures. .................. 37
Figure 2-13. Load-rotation curves of RC slabs with varying tensile reinforcement ratios ................... 38
Figure 2-14. Load-deflection curves of RC slabs with varying tensile reinforcement ratio ................. 39
Figure 2-15. Experimental layout of the slabs in Ebead et al. .............................................................. 41
Figure 2-16. FRP strengthening patterns in Elsayed et al. .................................................................... 43
Figure 2-17. Load-deflection curves of the specimens in Limam et al.. ............................................... 43
Figure 2-18. Slab failure in Limam et al. .............................................................................................. 44
Figure 2-19. Direct (one-way) shear and punching shear failure positions .......................................... 45
Figure 2-20. Loaded areas in one-way shear and punching failure ...................................................... 46
Figure 2-21. Slab deformation during punching test ............................................................................ 46
Figure 2-22.Radial and tangential concrete strains at different distances from the column side. ......... 47
Figure 2-23. Crack angle in a concrete flat slab ................................................................................... 48
Figure 2-24. Effective dimensions to calculate the capacity of slabs in Rankin and Long model. ....... 49
Figure 2-25. Relation between the punching strength and flexural capacity of slabs ........................... 50
Figure 2-26. Examples of shear reinforcement in RC slabs. ................................................................. 51
Figure 2-27. Details and strengthening patterns of RC slabs in Genikomsou and Polak. .................... 53
Figure 2-28. Load-deflection curves of slabs from Genikomsou and Polak ......................................... 54
Figure 2-29. Strengthening patterns from Sissakis and Sheikh ............................................................ 54
Figure 2-30. Load–deformation curves of slabs from Sissakis and Sheikh .......................................... 55
Figure 2-31. Critical shear section of slabs with and without shear reinforcement .............................. 55
Figure 2-32. Details and strengthening pattern of RC slabs from Chen and Li. ................................... 56
Figure 2-33. Load-deformation curves of the slabs from Chen and Li ................................................. 57
Figure 2-34. Details and dimensions of the specimen in Harajli and Soudki ....................................... 58
Figure 2-35. Failure modes of FRP strengthened slabs with full composite action .............................. 60
Figure 2-36. De-bonding failure modes ................................................................................................ 60
Figure 2-37. Different kinds of FRP de-bonding initiated in the concrete. .......................................... 61
Figure 2-38. CDC de-bonding .............................................................................................................. 62
Figure 2-39. De-bonding due to the unevenness of concrete. ............................................................... 62
Figure 2-40. Single and double shear tests to investigate the bond strength ........................................ 63
Figure 2-41. Shear-slip relation in differently strengthened concretes ................................................. 64
Figure 2-42. Bond-slip models in Lu et al. investigation ...................................................................... 64
7
Figure 2-43. Experimental and theoretical results of bond strength and effective length..................... 66
Figure 2-44.Control perimeters around the loaded areas according to Eurocode 2. ............................. 68
Figure 2-45. Strain and stress distribution over the slab thickness ....................................................... 69
Figure 2-46. Control perimeters around the loaded areas according to ACI 318. ................................ 70
Chapter 3
Figure 3-1. Abdullah’s test layout......................................................................................................... 76
Figure 3-2. Applying prestressed FRP plates to the RC structures surface. ......................................... 77
Figure 3-3. Abdullah’s test setup. ......................................................................................................... 78
Figure 3-4. Load-deflection curves of the RC slabs in Abdullah’s study. ............................................ 79
Figure 3-5. Kim et al.’s test layout........................................................................................................ 80
Figure 3-6. Anchorage system at the FRP`s end plate. ......................................................................... 81
Figure 3-7. Load-deflection curves of the RC slabs in Kim et al. study. .............................................. 82
Figure 3-8. Uniaxial compression stress-strain curve for concrete. ...................................................... 85
Figure 3-9. Tensile behaviour of concrete ............................................................................................ 86
Figure 3-10. Modified tensile behaviour of concrete on Abaqus. ......................................................... 86
Figure 3-11. Potential surfaces for the yield and plastic. ...................................................................... 89
Figure 3-12. The relations among the principal stresses at failure........................................................ 91
Figure 3-13. The failure surfaces in the deviatoric plane for different values of 𝐾𝑐 ............................ 92
Figure 3-14. Concrete damage parameters in compression. ................................................................. 93
Figure 3-15. Concrete damage parameters in tension. .......................................................................... 93
Figure 3-16. Parameters of flow potential ............................................................................................ 94
Figure 3-17. Stress–strain curve of steel ............................................................................................... 95
Figure 3-18. Tri-linear stress–strain curve for steel material. ............................................................... 95
Figure 3-19. Unidirectional, transversely isotropic lamina ................................................................... 97
Figure 3-20. Local and global coordinate axes. .................................................................................... 98
Figure 3-21. Boundary condition and loading situation in the FEM modelling of slab R0. ................. 99
Figure 3-22. The elements in the Abaqus library ................................................................................ 100
Figure 3-23. The different shapes of the continuum element ............................................................. 100
Figure 3-24. Finite element model partitioning. ................................................................................. 101
Figure 3-25. First- and second-order 3D elements.............................................................................. 101
Figure 3-26. Reduced and fully integrated methods ........................................................................... 102
Figure 3-27. The natural deformation of an element under a pure bending moment. ........................ 103
Figure 3-28. The deformation of a fully integrated linear element under a pure bending moment. ... 103
Figure 3-29. The deformation of a linear element to reduced integration under a bending moment. . 103
Figure 3-30. Mesh sensitivity analysis of samples R-F0 and RC-F0. ................................................. 105
Figure 3-31. Load–deflection curves of the models in Abdullah’s study. .......................................... 107
Figure 3-32. Load–deflection curves of the models in Kim et al.’s study. ......................................... 108
Figure 3-33. Concrete cracks in R0. ................................................................................................... 109
Figure 3-34. Tensile crack propagation (Tension damage) in R0. ...................................................... 109
Figure 3-35. Concrete cracks in RC0. ................................................................................................. 110
Figure 3-36. Stress distribution and sectional analysis of flexural punching failure mode. ............... 111
Figure 3-37. Concrete cracks in R-F0. ................................................................................................ 112
Figure 3-38. Concrete cracks in RC-F0. ............................................................................................. 112
Figure 3-39. Slab section at the position of the prestressed end plate. ............................................... 115
Figure 3-40. The stress zones across the section of slabs at the prestressed FRP end plate. .............. 116
8
Figure 3-41.Distributions of normal stresses in the concrete section near the end plate. ................... 116
Figure 3-42. Flexural-shear cracks cause de-bonding near the end plate in R-F30. ........................... 117
Figure 3-43. Concrete cracks on the tension surface of R-F15. .......................................................... 117
Figure 3-44.Concrete cracks in R-F30. ............................................................................................... 118
Figure 3-45.Slab section at the position of prestressed end plate in RC-F15. .................................... 120
Figure 3-46. The stress distribution in RC slab strengthened with prestressed FRP. ......................... 122
Figure 3-47. The slabs failure mode by varying the FRP prestress ratio. ........................................... 124
Figure 3-48. The optimum FRP prestress ratio for different sets of effective parameters. ................. 126
Figure 3-49. Graph provided to find the optimum FRP prestress ratio to strengthen RC slabs.......... 129
Chapter 4
Figure 4-1. Continuous and simply supported slabs. .......................................................................... 134
Figure 4-2. Bending moments of slabs in different conditions. .......................................................... 135
Figure 4-3. Continuous slabs. ............................................................................................................. 135
Figure 4-4. Category L slab layout. .................................................................................................... 136
Figure 4-5. Category H slab layout. .................................................................................................... 137
Figure 4-6. FRP sheets on the tension surface of the FRP strengthened specimens. .......................... 137
Figure 4-7. Actual and required FRP lengths. .................................................................................... 138
Figure 4-8. Positions of vertical (shear) reinforcement in the shear strengthened samples. ............... 139
Figure 4-9. Slab mould prepared for concrete casting. ....................................................................... 142
Figure 4-10. Support frame. ................................................................................................................ 142
Figure 4-11. Casting concrete in the mould and samples. .................................................................. 143
Figure 4-12. Applying vertical (shear) reinforcement. ....................................................................... 144
Figure 4-13. Slab preparation to apply FRP sheets. ............................................................................ 145
Figure 4-14. FRP sheets applied on the tension surface of the slab. ................................................... 146
Figure 4-15. Strain gauge positions relative to the tensile reinforcement of the slabs. ...................... 146
Figure 4-16. Concrete strain gauge positions around the column zone. ............................................. 147
Figure 4-17. FRP strain gauge positions. ............................................................................................ 148
Figure 4-18. Testing procedure. .......................................................................................................... 149
Figure 4-19. Load–deflection curves of the RC slabs. ........................................................................ 151
Figure 4-20. Load–deflection curves of the experimental and FE models for L0. ............................. 152
Figure 4-21. Cracks in the experimental and FE models for L0. ........................................................ 153
Figure 4-22. Load–strain curves of the internal tensile reinforcement. .............................................. 153
Figure 4-23. Load–strain curve of the concrete in the column vicinity. ............................................. 154
Figure 4-24. Sectional analysis of an RC slab with low tensile reinforcement ratio .......................... 154
Figure 4-25. Load–deflection curves of the experimental and FE models for LS. ............................. 155
Figure 4-26. Cracks in the experimental and FE models for LS. ........................................................ 156
Figure 4-27. Load–strain curves of the internal tensile reinforcement. .............................................. 156
Figure 4-28. Load–strain curve of the concrete in the column vicinity. ............................................. 157
Figure 4-29. Load–deflection curves of the experimental and FE models for LF. ............................. 158
Figure 4-30. Punching failure in the column vicinity of LF. .............................................................. 158
Figure 4-31. Load–strain curve of the concrete in the column vicinity. ............................................. 159
Figure 4-32. Load–strain curves of the internal tensile reinforcement. .............................................. 159
Figure 4-33. Load–strain curves of the CFRP composites. ................................................................ 160
Figure 4-34. Stress and strain distributions in the FRP strengthened slab section. ............................. 161
Figure 4-35. Sectional analysis of RC slabs with high tensile reinforcement ratio ............................ 162
9
Figure 4-36. Concrete cracks in the tension surface of LF. ................................................................ 163
Figure 4-37. Load–deflection curves of the experimental and FE models for LFS. ........................... 164
Figure 4-38. Punching failure initiating from the shear strengthened zone. ....................................... 164
Figure 4-39. Load–strain curve of the concrete in the column vicinity. ............................................. 164
Figure 4-40. Load–strain curves of the internal tensile reinforcement. .............................................. 165
Figure 4-41. Load–strain curves of the CFRP sheets. ......................................................................... 165
Figure 4-42. Punching failure in LF and LFS. .................................................................................... 167
Figure 4-43. Strut and tie model for punching failure of RC slabs ..................................................... 167
Figure 4-44. Effect of applied forces on the critical compressive strut of an RC flat slab. ................ 168
Figure 4-45. Vertical (shear) reinforcement mechanism to increase the slab punching strength. ...... 168
Figure 4-46. Critical compressive strut in an RC slab considering shear strengthening..................... 169
Figure 4-47. Concrete cracks in the tension surface of LFS. .............................................................. 170
Figure 4-48. Load–deflection curves of the experimental and FE models for H0. ............................. 171
Figure 4-49. Punching failure in the column vicinity of H0. .............................................................. 171
Figure 4-50. Load–strain curve of the concrete in the column vicinity. ............................................. 172
Figure 4-51. Load–strain curves of the internal tensile reinforcement. .............................................. 172
Figure 4-52. Concrete cracks in the tension surface of H0. ................................................................ 173
Figure 4-53.Load–deflection curves of the experimental and FE models for HS. .............................. 174
Figure 4-54. Flexural punching failure in HS. .................................................................................... 174
Figure 4-55. Load–strain curves of the steel reinforcement. .............................................................. 175
Figure 4-56. Load–strain curve of the concrete in the column vicinity. ............................................. 175
Figure 4-57. Punching failure in H0 and HS. ..................................................................................... 176
Figure 4-58. Concrete cracks in the tension surface of HS. ................................................................ 177
Figure 4-59. Load–deflection curves of the experimental and FE models for HF. ............................. 178
Figure 4-60. Punching failure in HF. .................................................................................................. 179
Figure 4-61. Load–strain curve of the concrete in the column vicinity. ............................................. 179
Figure 4-62. Load–strain curves of the steel reinforcement. .............................................................. 180
Figure 4-63. Load–strain curves of the CFRP composites. ................................................................ 180
Figure 4-64. RC slabs strut and tie models before and after FRP strengthening. ............................... 182
Figure 4-65. Critical compressive struts in un-strengthened and FRP strengthened slabs. ................ 183
Figure 4-66. Concrete cracks on the tension face of HF. .................................................................... 184
Figure 4-67. Load–deflection curves of the experimental and FE models for HFS. .......................... 185
Figure 4-68. Concrete cracks on the tension face of HFS................................................................... 185
Figure 4-69. Load–strain curve of the concrete strain in the column vicinity. ................................... 186
Figure 4-70. Load–strain curves of the steel reinforcement. .............................................................. 186
Figure 4-71. Load–strain curves of the CFRP composites. ................................................................ 187
Chapter 5
Figure 5-1. Slab with 0.3% tensile reinforcement ratio (S-0.3). ......................................................... 192
Figure 5-2. Slab with 0.5% tensile reinforcement ratio (S-0.5). ......................................................... 192
Figure 5-3. Slab with 0.85% tensile reinforcement ratio (S-0.85). ..................................................... 193
Figure 5-4. Slab with 1.1% tensile reinforcement ratio (S-1.1). ......................................................... 193
Figure 5-5. Slab with 1.6% tensile reinforcement ratio (S-1.6). ......................................................... 193
Figure 5-6. Load–tensile reinforcement ratio curve. ........................................................................... 194
Figure 5-7. Deflection–tensile reinforcement ratio curve. .................................................................. 195
Figure 5-8. Load–deflection curves of RC slabs with different tensile reinforcement ratio. .............. 195
10
Figure 5-9. The arrangement of reinforcements in SC-0.5. ................................................................ 197
Figure 5-10. The arrangement of reinforcements in SC-1.1. .............................................................. 197
Figure 5-11. Load–deflection curves of RC slabs with and without compressive reinforcements. .... 198
Figure 5-12. Orthogonal and skewed pattern of FRP sheets to strengthen RC slabs. ......................... 200
Figure 5-13. Load–deflection curves of strengthened RC slabs by varying strengthening patterns. .. 201
Figure 5-14. FRP strengthening patterns with different FRP layers. .................................................. 202
Figure 5-15. Load–deflection curves of strengthened RC slabs by varying FRP layers. .................... 203
Figure 5-16. Load–deflection curves of strengthened RC slabs by varying FRP thickness. .............. 204
11
List of tables
Chapter 2
Table 2-1. Characteristics of unidirectional FRP composites. .............................................................. 30
Table 3-2. Characteristics of different kinds of FRP composites ......................................................... 30
Table 2-3. Tensile reinforcement requirements for the RC flexural structures..................................... 36
Table 2-4. Effect of FRP strengthening on the flat RC slabs in Ebead et al. model ............................. 42
Table 2-5. Specimen characteristics in Elsayed et al. ........................................................................... 43
Table 2-6. Test results from Genikomsou and Polak. ........................................................................... 53
Table 2-7. Test results from Chen and Li ............................................................................................. 57
Chapter 3
Table 3-1. Properties of concrete in different samples. ........................................................................ 75
Table 3-2. Properties of the steel bars. .................................................................................................. 76
Table 3-3. Properties of FRP. ............................................................................................................... 77
Table 3-4. Ultimate load capacity of the slabs in Abdullah’s investigation. ........................................ 79
Table 3-5. Properties of the concrete. ................................................................................................... 80
Table 3-6. Properties of the steel bars. .................................................................................................. 81
Table 3-7. Properties of CFRP. ............................................................................................................. 81
Table 3-8. The ultimate load capacity of the slabs in Kim et al. investigation ..................................... 82
Table 3-9. Parameters of the CDP model ............................................................................................. 94
Table 3-10. Comparison between numerical and experimental results. ............................................. 106
Table 3-11. A comparison between R-F30 and R2-F30 in terms of load capacity. ............................ 119
Table 3-12. The effect of varying slab depth with ultimate load capacity in earlier de-bonding. ...... 119
Table 3-13. Comparing the FRP strengthened slabs based on their effective parameters. ................. 121
Table 3-14. Different variable sets of concrete tensile strength and slab depth. ................................. 127
Table 3-15. The relation between the effective parameters to find the optimum FRP prestress ratio.128
Chapter 4
Table 4-1. Slabs labelled according to the strengthening method. ..................................................... 133
Table 4-2. Estimation of the required FRP lengths based on Chen and Teng’s suggestion. .............. 138
Table 4-3. Concrete mix design. ......................................................................................................... 140
Table 4-4. Concrete properties of different slabs. ............................................................................... 140
Table 4-5. Mechanical properties of the steel bar. .............................................................................. 140
Table 4-6. CFRP composite properties ............................................................................................... 141
Table 4-7. Experimental and FE model results. .................................................................................. 150
Table 4-8. Comparison between the control and shear strengthened specimens. ............................... 157
Table 4-9. Comparison between L0 and LF. ...................................................................................... 161
Table 4-10. Comparison between L0 and LFS. .................................................................................. 166
Table 4-11. Comparison between LF and LFS. .................................................................................. 166
Table 4-12. Comparison between H0 and HS. .................................................................................... 176
Table 4-13. Comparison between H0 and HF. .................................................................................... 181
12
Table 4-14. Comparison between H0 and HFS. ................................................................................. 187
Table 4-15. Comparison between HF and HFS. ................................................................................. 188
Table 4-16. Experimental results and model estimations to predict the punching capacity of slabs. . 188
Chapter 5
Table 5-1. Concrete properties. ........................................................................................................... 191
Table 5-2. Steel reinforcements properties. ........................................................................................ 191
Table 5-3. Model results by varying their tensile reinforcement ratios. ............................................. 194
Table 5-4. The effect of different strengthening methods on RC slabs in different conditions. ......... 196
Table 5-5. Models description. ........................................................................................................... 197
Table 5-8. The effect of compressive reinforcement on the behaviour of RC slabs. .......................... 198
Table 5-9. The effect of strengthening methods on RC slabs with compressive reinforcement. ........ 199
Table 5-10. Models description. ......................................................................................................... 200
Table 5-11. The effect of different strengthening patterns on the behaviour of RC slabs. ................. 200
Table 5-12. Models description. ......................................................................................................... 202
Table 5-13. The effect of varying FRP layers on the behaviour of strengthened RC slabs. ............... 203
Table 5-14. Models description. ......................................................................................................... 203
Table 5-15. The effect of varying FRP thickness on the behaviour of strengthened RC slabs. .......... 204
13
Abstract
In this thesis, the experimental programmes and numerical investigations are described that
have been conducted to partially cover the knowledge gap in the field of strengthening two-
way reinforced concrete (RC) flat slabs. The conducted studies demonstrate that the most
common method to strengthen two-way RC slabs is by applying fibre reinforced polymers
(FRP) on the tension surface of the slabs. Applying prestressed FRP to strengthen two-way flat
slabs combines the advantages of both FRP strengthening and prestressing to enhance the
efficiency of the strengthening methods. Hence, two previous studies on strengthening two-
way flat slabs with non-prestressed and prestressed FRP are analysed to clarify the effect of
different strengthening methods on the behaviour of slabs. Both studies demonstrate the
benefits of applying non-prestressed FRP to enhance the structures’ capacities. However, for
the case of strengthening RC slabs with prestressed FRP, the results seem to be controversial
and more studies are necessary to arrive at a conclusion on whether it is feasible to strengthen
RC slabs with prestressed FRP. Further analysis indicates that there is an optimum percentage
of prestressing for the FRPs applied to RC slabs. Increasing the prestressing ratio of FRP to the
optimal percentage increases the ultimate load capacity of the RC slabs. However, increasing
the prestressing ratio of FRPs beyond the optimum value can cause de-bonding and loss of
composite action, which prevents the RC slab from reaching its expected ultimate load
capacity. The optimum prestressing ratio of FRP depends on the prestress load as well as the
concrete tensile strength and slab depth. Eventually, a formula is proposed to estimate the
optimum FRP-prestress ratio considering the effective parameters in both concrete and FRP.
Moreover, this thesis elaborates on an investigation that was conducted to make a comparison
between the effects of different strengthening methods such as FRP strengthening, applying
vertical (shear) reinforcement, and their combination, on the behaviour of flat slabs with
different conditions (tensile reinforcement ratios). To conduct the investigation, eight slab
specimens were cast, which were classified into two categories: low and high tensile
reinforcement ratios. The strengthening methods included applying FRP sheets to the tension
surface of the RC slabs externally, applying vertical (shear) reinforcement, and a combination
of both methods. The experimental and validated numerical results demonstrate that the most
efficient strengthening strategy is a combination of strengthening methods in both categories.
Strengthening with FRP sheets improves the slabs load capacity in both categories. However,
applying vertical (shear) reinforcement does not significantly affect the behaviour of RC slabs
with a low tensile reinforcement ratio. From the resulting analyses, it was concluded that the
strut and tie model of the FRP strengthened structure changes compared with the control
specimen. This enables researchers and designers to justify how FRP strengthening enhances
the punching strength of the slab, an aspect that has not been explained in previous studies. The
results also show that applying vertical (shear) reinforcement in the critical punching area
strengthens the critical compressive strut of the RC slab. This shifts the critical punching area
from the column vicinity to the outside of the shear reinforced zone and enhances the RC slabs
load capacity. A comprehensive parametric study using calibrated finite element models has
also been conducted to analyse the effect of varying different parameters such as tensile
reinforcement ratio and compressive reinforcement as well as the pattern, number and thickness
of FRP strips (applied to strengthen RC slabs) on the behaviour of flat slabs. The results
demonstrated that enhancing the tensile reinforcement ratios (including both steel
reinforcements and FRP strips) can enhance the ultimate load capacity of the strengthened
slabs, but reduces the ductility of the structure. Based on the results, flat slabs with compressive
reinforcements could reach more load capacity and deflection (which resulted in having more
ductility) as compared with the samples that do not include compressive reinforcements.
14
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.
15
Copyright statement
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copyright in it (the “Copyright”) and he has given The University of Manchester the right to
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Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in
The University’s policy on presentation of Theses.
16
Acknowledgment
First, I am grateful to The Almighty God for establishing me the ability to complete my study.
I would like to thank my respected supervisor, Dr Jack Wu, whose expertise, understanding,
generous guidance and support made it possible to carry through my thesis. I am also grateful
to my respected co-supervisor, Dr Zhenmin Zou, for his care and support. In addition, I wish
to express my sincere thanks to the staff in the laboratory for providing me with all the
necessary facilities.
Words cannot express my heartfelt thanks to my merciful mother and faithful father for their
endless support. Finally, my deepest appreciation goes to my lovely wife, Maryam, who helped
me the most with her kind support and patience.
17
Notation
Latin letters
A Fictitious punching capacity coefficient
As Area of tensile reinforcements
Av Cross-sectional of the legs of shear reinforcements
a Depth of neutral axis
b0 Perimeter of the critical section
𝑏𝑐 Width of concrete slab in bond-slip test
𝑏𝑝 Width of FRP in bond-slip test
bw RC section width
𝐶΄ Coefficient between 0 and 1 to relate punching and flexural capacity
c Column length in RC flat slabs
D RC section depth
d RC section effective depth
dc Concrete compressive damage
dt Concrete tensile damage
E Modulus of elasticity
E0 Concrete modulus of elasticity
E1 Modulus of elasticity in x-direction
E2 Modulus of elasticity in z-direction
E3 Modulus of elasticity in y-direction
Ef FRP modulus of elasticity
Efib Fibers modolus of elasticity
Er Resin modulus of elasticity
Es Steel modulus of elasticity
𝑓𝑐 ΄ Concrete compressive strength
𝑓𝑡΄ Concrete tensile strength
𝑓𝑦 Steel yield strength
G Shear modulus
Gij Shear modulus associated with directions i, j
𝐺𝑓 Fracture energy
18
𝐼1 First effective stress invariant
𝐼2 Second deviatoric stress invariant
𝐼3 Third stress invariant
K Punching strength factor
L Slab length, The FRP length
Le Effective length of FRP
𝑀0 Radial moment capacity of the outer strip in flat slabs
𝑀𝑐 Radial moment capacity in the column strip of flat slabs
𝑀𝑟 Radial moment capacity
𝑁𝐸𝑑 Longitudinal force in the prestressed structure
Pud Design bond strength of FRP-concrete
𝑝 Effective hydrostatic pressure
S Slab span
S0 Corresponding slip with the ultimate bond-shear stress in bond-slip model
s Radial spacing between the stirrups
tf Thickness of FRP
u1 Critical perimeter around the column area in flat slabs
V Applied load on the column stub in flat slabs
𝑉0 Fictitious punching shear capacity
Vflex Flexural capacity
Vg Ultimate load capacity at entire yielding of tensile reinforcements
Vn Nominal punching shear capacity
𝑉𝑅 Punching shear capacity
Vu Ultimate load capacity
vfib Volume fraction of fibres
νmin Minimum punching resistance
ν𝑝 Punching resistance
vr Volume fraction of resins
𝑤𝑓 FRP width in strengthened RC flat slabs
Greek Letters
α Fracture energy coefficient
α, β, γ Yield function coefficients
19
β1 Concrete compressive coefficient
βL FRP length ratio
βw, βp FRP width ratios
ε Strain
εc Concrete strain
ɛ𝑐 𝑖𝑛 Concrete compressive crushing strain
𝜀𝑐0 Concrete strain at the maximum concrete compressive strength
εcu Concrete ultimate strain
𝜀𝑓 FRP strain
ɛ𝑝𝑙 Plastic strain
ɛ𝑐 𝑝𝑙
Equivalent plastic strain in compression (hardening variable)
ɛ𝑡𝑝𝑙
Equivalent plastic strain in tension (hardening variable)
εs Steel strain
εst Steel hardening strain
εsy Steel yield strain
εsu Steel ultimate strain
𝜀𝑡𝑐𝑘 Concrete tensile cracking strain
ν Poisson’s ratio
ξ Effective depth coefficient, the eccentricity
η FRP strengthening efficiency factor
λ Positive coefficient in the plastic potential function
ρ Tensile reinforcement ratio
ρb Balanced tensile reinforcement ratio
ρ΄ Compressive reinforcement ratio
σ Normal stress
𝜎𝑐 Effective compressive stress
𝜎𝑡 Effective tensile stress
𝜎𝑐𝑝 Normal stresses of the critical section due to prestressing
τ Bond shear stress
ψ Slab rotation
ϕ Ultimate load capacity over the flexural capacity of the structure
Ф Diameter of the corresponding bar
20
1. Introduction
1.1. General
Reinforced concrete (RC) slabs are commonly employed in constructing roofs, floors, and
bridge decks in long-span structures. Slabs can be classified as one-way or two-way slabs
depending on their dimensions and boundary conditions. Concrete slabs can be supported by
concrete or steel beams, masonry or concrete walls, or columns [1]. Issues such as excessive
loading or deterioration due to corrosion attack, seismic action, fire damage and freezing and
thawing can lead to damage or failure of RC slabs. Therefore, RC slabs must be strengthened,
retrofitted, or rehabilitated for applications in these environments. Before the 1980s, bonding
steel plates were the most popular technique to strengthen a concrete slab. However, the
lightweight, high strength, and corrosion-resistant nature of fibre reinforced polymers (FRPs)
has pushed civil engineers to substitute steel plates with FRP for strengthening since the early
1990s [2-4].
The most common method used to increase the maximum load capacity of RC slabs is the
application of FRP plates and sheets on their tension surfaces [5, 6]. Ebead and Marzouk [5]
modified the Rankin and Long model [7] to estimate the load capacity of two-way RC slabs
strengthened by FRPs on tension surfaces, based on the assumption of a perfect bond between
FRPs and concrete with a flexural failure mode. Hence, their estimation may not be
conservative in the case of punching failure, which is one of the most likely failure modes in
FRP strengthened RC slabs.
Researchers such as Sharaf et al. [8] and Chen and Li [9] conducted experimental investigations
and demonstrated that increase of the flexural capacity of RC slabs causes enhancement of their
punching resistance. These results confirm Moe’s statement [10] that there is a direct relation
between the flexural capacity and punching strength and that increasing one of them improves
the other when FRPs are used on tension surfaces. It is noteworthy that the samples failure
mode may change from flexural failure to punching failure after the application of FRP plates
on the slab’s tension surfaces [8].
21
In all the above-mentioned investigations, the emphasis was more on quantitative results rather
than explanatory analyses. Moreover, there seems to be much less research about FRP
strengthened RC slabs than FRP strengthened RC columns and beams. This has resulted in a
lack of design guidelines in most design codes, such as ACI Committee 440 [11], Eurocode 2
[12], etc. As there are different patterns that can be used when strengthening RC slabs with
FRPs, a comprehensive mechanism description considering both experimental and numerical
results is needed to analyse the structural behaviour and understand the failure process. This
would help engineers and designers to choose the most efficient strengthening pattern, which
is essential for fulfilling the specific strengthening purpose.
Another aspect that should be pointed is that the previous investigations have not substantially
considered the combination of different techniques for strengthening two-way RC slabs.
Hence, strengthening RC slabs with prestressed FRPs is another consideration in this study that
combines the advantages of both FRP strengthening and prestressing. Experimental and
numerical investigations show that the number of studies that deals with the case of two-way
RC slabs strengthened with prestressed FRP is smaller than that of studies dealing with non-
prestressed FRP. Quantrill and Hollaway [13] and Garden and Hollaway [14] postulated that
applying prestressed FRP resulted in a considerable improvement in the load capacity of
unidirectional RC structures such as beams and one-way slabs.
Abdullah [15] carried out an experimental study to investigate the behaviour of two-way RC
flat slabs strengthened with prestressed and non-prestressed FRP plates. The load capacity of
the sample strengthened with non-prestressed FRP increased significantly compared with the
control specimen. However, the RC slab strengthened with prestressed FRP did not show a
considerable increase of its maximum load capacity. The reason for such a phenomenon and
results are not yet explained clearly from the point of view of traditional structural analysis.
Kim et al. [16] investigated this aspect experimentally by considering the behaviour of flat
slabs strengthened with prestressed and non-prestressed FRP plates. Their study demonstrated
that strengthening RC slabs with non-prestressed FRP could increase the ultimate load capacity
of the samples; however, the results seemed to be in contradiction with the investigation by
Abdullah [15] with respect to strengthening with prestressed FRP. Kim et al. [16] stated that
prestressed FRP plates increase the efficiency of FRP strengthening by attaining a greater load
capacity in comparison with the sample strengthened with non-prestressed FRP. Nonetheless,
investigation by Abdullah [15] showed that the ultimate load capacities of the slabs
22
strengthened with prestressed FRP are even lower than that of the slab retrofitted with non-
prestressed FRP. In this study, the mechanism was analysed to explain the behaviour of the
samples and clarify the primary reason for contradictory results achieved in the case of
strengthening with prestressed FRPs. The analysis of experimental and numerical models
demonstrated the feasibility and efficiency of applying prestressed FRP to strengthen RC slabs.
The result analysis resulted in a formula capable of providing the FRP-prestress ratio for
strengthening RC slabs with different characteristics.
As said, previous studies [15, 16] demonstrated that FRP strengthening may lead to a punching
failure of flat slabs. Another consideration that has not been analysed substantially is the
application of FRP strengthening in combination with other retrofitting techniques (which may
strengthen the RC slabs in punching) that would widen the strengthening proposals and patterns
for different retrofitting requests. Therefore, in this study, an experimental investigation has
been conducted along with a numerical simulation to analyse the strengthened and un-
strengthened behaviour of slabs and explain mechanisms to cover the knowledge gap in the
field of strengthening RC slabs. The combination of FRP strengthening and application of
vertical (shear) reinforcements (to strengthen the critical punching area) aids decision making
on efficient strengthening patterns for RC slabs with different characteristics. To this end, eight
RC slabs were cast, which are classified into two groups (four samples in each group) of RC
slabs with low and high tensile reinforcement ratios.
In each group, there was a control specimen, a specimen strengthened with FRP, a specimen
strengthened with vertical (shear) reinforcement (by applying steel bars in the column’s
vicinity), and a specimen strengthened with both FRP and shear reinforcement. The achieved
results and slab mechanism analysis provide valuable information reflecting the effect of
strengthening methods on slab characteristics such as load capacity, ductility, and failure
modes. This may help in finding the most efficient strengthening methods and patterns that
satisfy strengthening requirements.
1.2. Research objectives
The aim of this study is to demonstrate the stress-transfer mechanism of RC flat slabs with
different tensile reinforcement ratios before and after strengthening with FRPs, vertical (shear)
23
steel bars in the vicinity of columns, and a combination of these two methods, as well as RC
slabs strengthened with prestressed FRPs. To achieve the aim of this study, the following were
performed:
• Analysing the effect of different strengthening methods and their combinations on the
behaviour of retrofitted RC flat slabs;
• Carrying out stress analyses of RC flat slabs strengthened with prestressed and non-
prestressed FRP;
• Clarifying mechanisms of the strengthening methods to analyse their efficiency in flat
slabs with different tensile reinforcement ratios;
• Proving the existence of an optimal FRP-prestress ratio for strengthening RC flat slabs
and formulating the ratio estimation with some variable effective parameters in the
validated models by applying a numerical regression method.
1.3. Methodology
Two main methods are employed in this study to analyse the behaviour of RC flats slabs:
experimental investigations and numerical simulations. With respect to experimental
investigation, RC slabs with different conditions and strengthening patterns were cast. Then,
the slabs were subject to a uniform pressure load on the column area until failure occured.
Strain gauges were placed at different parts of the samples such as the concrete in the column
vicinity, the tensile reinforcement in critical positions, and the FRP sheets in area of maximum
expected stress to improve monitoring of the specimens’ behaviour.
The other method, numerical simulation, is more cost-effective than others, and is suitable for
complex analyses of problems such as fracture mechanics and material damage. Abaqus, a tool
suitable for obtaining numerical simulation results, based on the finite element method, is used
for the analysis. As a tool capable of modelling and simulating the failure of a structure, Abaqus
was chosen in this study to simulate the experimental specimens numerically. The numerical
models were validated using experimental results to justify the accuracy of finite element
modelling. The methodologies for achieving the objectives of the study (mentioned in the
previous section) have been aligned as follows:
24
• To analyse the behaviour of slabs, both experimental and numerical analyses are carried
out for RC strengthened and un-strengthened slabs in different conditions. It is
noteworthy that the experimental results (analysed in this study) have been achieved in
previous studies as well as in the experimental investigation conducted in this study.
The numerical models are also calibrated and validated considering the experiment
results and applied to analyse and clarify the behaviour of RC slabs before and after
strengthening.
• To clarify the mechanism of different strengthening methods, the results obtained from
the experimental specimen and strain gauges (applied in different parts of the RC flat
slabs) as well as the stress-strain analysis from the validated numerical models are
considered.
• The stress analyses of the numerical models (validated on the experimental results) are
carried out to assess the behaviour of RC flat slabs strengthened with prestressed FRP
and to clarify whether applying prestressed FRP to strengthen RC flat slabs is feasible
and efficient.
• The effective parameters in the validated numerical models are varied to demonstrate
the existence of an optimum FRP-prestress ratio. Then, a regression method was
applied to relate different effective parameters and to propose a formula to estimate the
optimum FRP-prestress ratio for strengthening RC flat slabs.
1.4. Research significance
The aim of the current research is to clarify the behaviour of strengthened RC flat slabs as
existing reports on their structural behaviour are sometimes conflicting and their quality
debatable. This limits the possibilities in terms of design and wider application of structural
rehabilitation and retrofitting of RC flat slabs. The work carried out in this study and its
achievements include the following:
• Comparing different strengthening methods for RC slabs with low and high tensile
reinforcement ratios;
25
• Applying a combination of FRP strengthening and shear strengthening numerically and
experimentally;
• Explaining the mechanism of different strengthening methods and failure models;
• Identifying an optimum strengthening ratio based on the existing slab structural
behaviour and targeted objective of rehabilitation; and
• Providing a design estimation for the optimum FRP prestress-ratio to strengthen flat
slabs efficiently.
As a comprehensive investigation, the main significance of this study is that, in terms of
developing the strengthening design, this research provides an appropriate and reliable
strengthening solution which may satisfy the targeted objectives of the slab strengthening under
different reinforcement ratios. This work aims to unify and explain the existing inconsistent
experimental test results, from a mechanical point of view. This research has not only compared
the pros and cons of different strengthening methods but also showed a strengthening design
procedure using an optimal reinforcement ratio. Therefore, it is of great importance for
strengthening, maintenance, and upgrading of RC slabs.
1.5. Thesis outline
In Chapter 2, the history behind attempts to strengthen RC structures using different
rehabilitation methods and materials has been discussed to show the progression in FRPs as a
common strengthening technique. This chapter presents general FRP characteristics and
properties and explains the behaviour of RC slabs. The focus of this chapter is on introducing
various strengthening methods. The RC flat slabs possibly need to be strengthened in flexure
(in the case of low reinforcement ratios) or retrofitted in punching (in the case of high tensile
reinforcement ratios). The literature review for this kind of structure shows that FRP
strengthening seems to be the most common method used for RC slabs (considering slabs with
low and high tensile reinforcement ratios). Issues such as the FRP-to-concrete bond behaviour,
FRP effective length for carrying tensile stresses, assessment of certain codes and existing
design recommendations for FRP strengthening are discussed in detail.
Chapter 3 describes the mechanism of two-way RC slab strengthening with prestressed and
non-prestressed FRPs. Since there is a lack of knowledge, especially with respect to
26
strengthening two-way RC slabs with pre-stressed FRP, both numerical simulation and
experimental studies are analysed for two typical and contradictory test results. This chapter
deals with numerical modelling and introduces Abaqus, the software used to simulate the
strengthened and un-strengthened RC slabs and validate the numerical models. The proper
choice of elements, element interactions, and modelling of different parts of composite
structures such as concrete, steel, and FRP are described. The resultant discussion considers
both experimental and validated numerical models to provide a better understanding of the
behaviour of RC slabs strengthened with prestressed and non-prestressed FRPs. The results
indicate there is an optimum FRP-prestress ratio for strengthening RC slabs and enhancing the
slab’s load capacity. The effective parameters used to determine the optimum prestressing ratio
of the FRP for strengthening RC slabs are analysed.
In Chapter 4, the experimental and numerical investigation conducted to perform a
comprehensive survey of methods used for strengthening two-way RC slabs is discussed. The
investigated slabs include RC slabs with both low and high tensile reinforcement ratios, which
need to be strengthened in flexure or punching by applying FRP sheets, vertical (shear) steel
bars, or a combination of these two methods. The result analysis suggests a relatively effective
strengthening method or pattern design capable of satisfying structural requirements.
In Chapter 5, a comprehensive parametric study using the calibrated finite element models is
described. The effective parameters discussed in this chapter include the initial tensile
reinforcement ratio and the compressive reinforcement as well as the pattern, thickness, and
number of FRP sheets applied to strengthen RC flat slabs.
Chapter 6 presents the overall conclusions, the obtained results, and proposals for potential
future experimental and numerical studies extending the work presented in this thesis.
27
2. Literature review
2.1. Strengthening RC structures
Existing RC structures may need to be strengthened or retrofitted to overcome damages that
occur due to actions such as earthquakes, corrosion attacks, fires, and so on. Moreover, the
structure's ability to sustain the excessive design loading must be increased in some cases. The
most common method of strengthening RC structures in the past was by applying steel plates
to increase the load capacity and ductility of RC elements. Bonding steel plates externally was
put into practice in France and South Africa to strengthen RC structures in the 1960s.
Afterwards, this technique was widely used, especially in European countries and North
America, in the 1970s [17].
Figure 2-1. Strengthening RC structures with steel members [18].
Dunker et al. in 1990 [19] investigated the effect of bonding steel plates to enhance the strength
of bridges in Europe, South Africa and Japan. Chai et al. [20] and Priestly et al. [21]
investigated ways to increase the workability of the old bridge's columns strengthened by
externally bonded steel plates. The RC structures and steel plates are drilled before the plates
28
are fixed and bolted together to make a proper connection that is capable of transferring stresses
from the concrete to the steel plates. Figure 2-1 shows how an RC structure has been
strengthened by steel plates using a simple and effective technique. However, problems such
as corrosion attack and overloading can make even structures strengthened by steel plates
vulnerable.
Steel plates were substituted by FRPs to address these issues owing to the small weight and
corrosion resistance of FRPs; this was first introduced in Switzerland in the early 1990s [22].
The application of FRP to strengthen RC structures was first experimentally demonstrated by
Meier et al. [23] who conducted experiments regarding strengthening RC beams with carbon
FRP (CFRP) plates. The high strength and corrosion resistance of FRP persuaded civil
engineers to substitute steel plates for FRP for strengthening RC structures.
The corrosion resistance of FRP increased the durability of the strengthened RC structures, a
major consideration for corrosion control. Besides, the total weight of the FRP strengthened
RC structures was lower than that of RC rehabilitated with steel plates owing to the high
strength to weight ratio of FRP compared with steel materials. Darby [24] stated that the
specific strength of an FRP plate is approximately two to ten times greater than that of a steel
plate, while its weight is 80% lower than that of the steel material. This may partly justify the
application of FRP in the case of strengthening RC structures.
The Webster Parkade Strengthening Project was one of the first instances of large scale
industrial FRP strengthening of RC structures conducted by the Canadian research network
[17]. In this project, carbon and glass FRPs were applied to strengthen and reinforce columns
that had lost their initial load carrying capacity owing to the corrosion of their steel bars. FRPs
utilised in the rehabilitation of concrete beams that had not been designed in accordance with
modified standards and codes increased the shear and flexural capacity of the beams by up to
20% and 15%, respectively.
The success of the Webster Parkade Strengthening Project led to it being awarded the
Innovation Award from the Quebec Ministry of Municipal Affairs. The Country Hills
Boulevard Bridge (in Alberta), the Oyster Channel Bridge (in New South Wales) and the
Melbourne Southern Link are some of the other successful FRP strengthening and
rehabilitation projects that have shown excellent performance and demonstrated the efficiency
and proper execution of FRP strengthened structures [17, 25].
29
Figure 2-2. Strengthening RC elements with FRP on the Country Hills Boulevard Bridge [17].
2.2. Fibre reinforced polymer
Clearly, the first step in characterizing the behaviour of FRP strengthened RC structures is to
characterize FRP. FRPs are composed of fibres and resins in the form of a resin matrix
reinforced with fibres, thus making a composite material (Figure 2-3). The fibres in the matrix
improve its mechanical characteristics such as strength. The resin transfers the external loads
to the fibres and protects them from possible external damage.
Figure 2-3. Fibre reinforced polymer matrix.
Different types of resins can be used, such as epoxy and polyester resins. Fibres are classified
into different groups such as carbon fibres, glass fibres, and aramid fibres. Accordingly, the
FRPs are divided into three main groups: carbon fibre reinforced polymers (CFRP), glass fibre
30
reinforced polymer (GRP) and aramid fibre reinforced polymers (AFRP). Table 2-1 presents
typical characteristics of several unidirectional FRP composites [26].
Table 2-1. Characteristics of unidirectional FRP composites [26].
Unidirectional
FRP composites
Volume
fraction
Density
(Kg/m3)
Longitudinal modulus
of elasticity (GPa)
Tensile strength
(MPa)
GRP / Polyester resin 50–80 1600–2000 20–55 400–1800
CFRP / Epoxy 65–75 1600–1900 120–250 1200–2250
AFRP / Epoxy 60–70 1050–1250 40–125 1000–1800
Figure 2-4. Unidirectional FRP, woven FRP and FRP laminate.
The strength of an FRP composite is related to the direction of the fibres. FRP laminates, which
have fibres in different directions, can provide the required strength in different directions. A
plain woven FRP (bidirectional FRP) has the same mechanical characteristics in two
perpendicular directions of the FRP plane. Figure 2-4 shows schematically a unidirectional
31
FRP, a woven FRP and an FRP laminate. Meier and Winistorfer [27] analysed the
characteristics of the FRP categories to find the most suitable choice for different strengthening
purposes mentioned in Table 2-2.
Table 2-2. Characteristics of different kinds of FRP composites [27].
Characteristic FRP Composites
GRP CFRP AFRP
Tensile strength Very good Very good Very good
Compressive strength Good Very good Not suitable
Young modulus Suitable Very good Good
Fatigue Suitable Excellent Good
Density Suitable Good Excellent
Alkali resistance Not suitable Very good Good
Cost Very good Suitable Suitable
Figure 2-5. Strengthening RC structure using an FRP plate [28].
Two of the most common methods used to strengthen RC structures with FRP are wet layup
(hand layup) and bonding FRP plates. FRP plates are typically composed of 70% fibres and
30% resins and are applied onto the structure surface directly as seen in Figure 2-5. In the wet
layup method, the FRP fabrics, which comprise 100% fibres held together with a fine stitch,
and the resins are applied at the FRP installation site (Figure 2-6). Hence, the characteristics
and volumes of both fibres and resins and environmental conditions at the application site must
be considered when evaluating the FRP properties [28].
32
Figure 2-6. Strengthening RC columns with FRP sheets [28].
Figure 2-7. Stress-strain curve for FRPs and mild steel [29].
Despite the variation in fibre materials, all FRPs exhibit similar stress-strain behaviour and
retain their elasticity up to their fracture point [29]. In addition, FRPs are less ductile than steel;
this may decrease the ductility of the whole FRP strengthened structure. Figure 2-7 shows a
comparison between CFRP, GRP, and steel in terms of their stress–strain behaviour. Doran
33
and Cather [30] state that in micromechanics, the characteristics of a composite material (FRP
lamina), such as the modulus of elasticity, can be described by considering the interaction
between its different parts. The modulus of elasticity of the composite material is given by
Equation 2-1.
Ef = Efib . vfib + Er . vr 2-1
In the above equation, Ef is the FRP modulus of elasticity in the direction of the fibres, Efib and
Er represent the modulus of elasticity of the fibres and resin, respectively, and vfib and vr denote
the volume fraction of the fibres and resin, respectively (vfib + vr= 1).
2.3. Two-way RC slab behaviour
Figure 2-8. One-way and two-way RC slabs.
Slabs are elements whose thickness is much smaller than their length and width. The main
purpose of RC slabs is the creation of surfaces in RC structures that can transfer the load to
supports such as RC or steel beams and columns, RC or masonry walls, and foundations [1].
RC slabs may be supported only on two edges as shown in Figure 2-8a, in which case the
applied loads are transferred in only one direction. When RC slabs are supported on four edges
as shown in Figure 2-8b, the structures behave as a two-way slab, carrying the applied load in
two directions. When the ratio of the length to width in a two-way slab is greater than two, the
34
applied loads are carried in the direction of the smaller span, i.e. the slab behaves as a one-way
structure despite being supported on four edges.
The objective of this study is to analyse the behaviour of strengthened two-way RC slabs whose
behaviours have not been analysed as thoroughly as those of strengthened one-way structures.
The first step in finding the most efficient strengthening technique is understanding the
behaviour of structures and failure modes. The investigations conducted with respect to two-
way RC slabs illustrate that the tensile reinforcement ratio of the slabs can determine their
behaviour and failure modes [31, 32]. The tensile reinforcement ratio is defined as the ratio of
the area of steel bars in tension in a RC cross section over the whole effective section area. It
is known that the compressive strength of concrete is much larger than its tensile strength and
the main purpose of reinforcing a concrete structure with steel reinforcement is for the
reinforcement to carry tensile forces and improve the structure’s ductility (since concrete is
brittle).
The high tensile strength of steel may ensure a balance between tensile and compressive
strength in a steel reinforced concrete structure and compensates for concrete’s weakness in
tension. Moreover, steel bars can increase the RC structure’s ductility, which plays a significant
role in seismic and blast loading designs of structures. A structure with sufficient ductility
efficiently absorbs and dissipates dynamic energy. Therefore, such a structure may resist
earthquake and blast better than structures with higher stiffness (lower ductility of a structure
implies a lower energy absorption ability) [33].
A design with ductile failure provides sufficient warning before the complete collapse of a
structure. This gives the occupants sufficient time to take appropriate action and reduce the
possibility of loss of life. In contrast, a brittle failure happens suddenly, and there is no
noticeable deformation before failure which raises significant safety issues. The above-
mentioned reasons justify the requirement for ductile behaviour [34]. According to Vasani and
Mehta [35], ductility refers to the ability of a material to undergo large plastic deformation
before collapse. A structure’s ductility in the Vasani and Mehta [35] definition refers to the
ratio of maximum deflection, rotation, or strain to the corresponding yield strength. Ebead and
Marzouk [5] proposed that a structure’s ductility should be based on energy absorption and
evaluated by the area under the load-deflection curve. The load-deflection curves in Figure 2-
9 provide a comparison between ductile and brittle materials.
35
Figure 2-9. Load-deflection curves of typical ductile and brittle materials [35].
As mentioned, reinforcing a concrete structure with steel reinforcement increases its ductility.
However, when the tensile strength of the RC structure is greater than its compressive strength,
the structure may fail owing to compression rather than tension; this is called brittle failure.
The investigations conducted with respect to this aspect [31, 36] demonstrate that there is a
critical balance for the tensile reinforcement ratio of a RC slab that determines the behaviour
of structures and their failure modes. Standard concrete design codes recommend a balanced
tensile reinforcement ratio (ρb) for RC flexural members to provide sufficient ductility and
strength of the structure. A reinforced concrete section with a balanced tensile reinforcement
ratio is called a balanced RC section. A reinforced concrete section is balanced with respect to
the tensile reinforcement ratio when tensile reinforcements reach their yield strength, and the
concrete in compression attains its ultimate compressive strength under the same flexural load
[1, 12].
A reinforced concrete structure with а high tensile reinforcement ratio (greater than the
balanced tensile reinforcement ratio) may experience brittle concrete compressive crushing
before the tensile steel reinforcement yields, which is not a desirable failure mode. It is
noteworthy that a minimum requirement of the tensile reinforcement ratio is defined in many
standard design codes to avoid brittle failure after the first crack opening (after the concrete
tensile strength is exceeded). Table 2-3 list some requirements for the reinforcement ratio in
ACI and Eurocode 2 for RC flexural members in general [12, 37] which helps to estimate the
required tensile reinforcement ratios of slabs to satisfy the design requirements and predict the
failure modes.
36
Table 2-3. Tensile reinforcement requirements for the RC flexural structures.
Codes ACI 318 Eurocode 2
Minimum tensile steel reinforcement ratio for flexure
𝐴𝑠
𝑏𝑤 ×𝑑 ≥
1.4
𝑓𝑦
0.26𝑓𝑐΄
𝑓𝑦
Balance tensile steel reinforcement ratio for flexure
𝐴𝑠
𝑏𝑤 × 𝑑=
510 β1 𝑓𝑐΄
𝑓𝑦 (600 + 𝑓𝑦)
0.04bD
The parameters used in Table 2-3 are as follows: As represents the area of tensile steel
reinforcement, 𝑏𝑤 is the RC section width, d and D are the effective and total depth of the RC
section, respectively, 𝑓𝑐΄ and 𝑓𝑦 are the concrete cylinder compressive strength and steel
reinforcement yield strength in MPa, and β1 is a concrete coefficient for compression which is
a function of 𝑓𝑐΄ (ACI 318 section 10.2.7.3.). Figure 2-10 visualizes the parameters considered
for calculating the tensile reinforcement ratio (𝐴𝑠
𝑏𝑤 ∙ 𝑑) and the stress distribution in a balanced
RC section based on the ACI recommendation.
Figure 2-10. Effective parameters in RC sections of flexural members.
37
According to Park and Gamble [31], the RC slab failure mode is determined by the tensile
reinforcement ratio. Figure 2-11 was obtained from their study using the results of an
experimental test conducted on RC slabs. It is noteworthy that the concrete compressive cube
strengths in their samples varied between 27.5 and 38.4 MPa. The dotted line in Figure 2-11
shows a linear approximation considering different test results. According to Park and Gamble
[31], the RC slab failure mode is a flexural failure for steel reinforcement ratios smaller than
1%. The failure mode changes from flexural to punching failure when the slab steel ratio
increases. Figure 2-12 shows the typical load-deflection curves of RC flat slabs with flexural
and punching failure.
Figure 2-11. Two-way RC slab failure mode based on the steel reinforcement ratio [31].
Figure 2-12. Typical load-deflection curves of flat slabs with ductile flexural and brittle punching failure [31].
38
Figure 2-13 shows the load-rotation curves of RC slabs for varying tensile reinforcement ratios
[32]. Slab rotation is considered based on the findings of Muttoni and Schwartz [38];
specifically, the fact that the width of critical cracks in slabs is correlated to the slab rotation
(ψ) multiplied by the effective slab depth (d). Regarding the slab load-rotation curves (Figure
2-13), Muttoni [32] categorised RC slab failure modes based on their tensile reinforcement
ratio. The ACI estimation of the punching strength is shown in Figure 2-13, represented by the
dotted line.
Figure 2-13. Load-rotation curves of RC slabs with varying tensile reinforcement ratios [32].
Depending on the mentioned load-rotation curves, the RC slabs are classified into three main
categories considering their tensile reinforcement ratio (ρ) [32]. For low tensile reinforcement
ratios (ρ ≤ 0.5%), the failure is a ductile flexural failure that occurs because of the wide
development of flexural cracks as a consequence of the entire tensile reinforcement yielding.
For intermediate tensile reinforcement ratios (0.5% ≤ ρ ≤ 1%), the RC slab failure occurs before
yielding of the entire tensile reinforcement due to punching. However, the tensile
reinforcements yield partially in the column’s vicinity, which implies that this kind of failure
can be assumed as a combination of flexural and punching failure [32].
39
For high tensile reinforcement ratios (ρ > 1%), the expected failure is a pure punching that
happens before yielding of any tensile reinforcement. It must be noted that the loading capacity
of slabs increases with increasing tensile reinforcement ratio for both flexural and punching
failures. Experimental investigations by Marzouk and Hussein [36] that determined the failure
mode of RC slabs by varying the tensile reinforcement ratio also confirmed the mentioned
results. When both tensile and compressive reinforcements exist in an RC slab section, the
balanced reinforcement ratio is estimated by subtracting the compressive reinforcement ratio
from the tensile reinforcement ratio. In addition, slab deformation considerably decreased
under high tensile reinforcement ratio [32].
Figure 2-14. Load–deflection curves of RC slabs with varying tensile reinforcement ratio [39].
Criswell [39] investigated eight two-way RC slabs to analyse their behaviour by varying the
tensile reinforcement ratio; the resultant slab load–deflection curves are shown in Figure 2-14.
The black points show the estimated flexural capacity of each slab based on the yielding of the
entire tensile reinforcement. The white points indicate the failure in case of reaching the
ultimate strength of the tensile reinforcement.
Slabs 1 to 3, which have high tensile reinforcement ratios, do not reach their expected flexural
capacity because of punching failure. Slab number 4 reached its estimated flexural load
capacity but failed at its yield load; this represents a two-way RC slab with a balanced tensile
reinforcement ratio. The maximum load capacity of slabs 5 to 8, which have low tensile
40
reinforcement ratios, is more than their yield load. These results show how the RC slab failure
mode is influenced by the tensile reinforcement ratio; increasing the tensile reinforcement ratio
enhances the RC slab load capacity but reduces the slab’s ductility. In addition, RC slabs with
a high tensile reinforcement ratio cannot reach their expected flexural capacity owing to brittle
punching failure (Figure 2-14) [39].
Investigations [31, 32, 36, 38, 39] demonstrate the significance of the tensile reinforcement
ratio in determining the behaviour of slabs and their failure mode. The mentioned studies
classify two-way RC slabs as slabs which fail in flexure or punching based on their tensile
reinforcement ratio. Therefore, RC slabs are usually strengthened to increase their flexural
capacity or punching resistance. For known RC slab characteristics, the appropriate
strengthening pattern and design must be clarified to decide on an efficient strengthening
scheme that satisfies the requirements of either flexural capacity or punching resistance.
Investigations conducted so far for strengthening RC structures were mainly concerned with
the behaviour of RC beams and columns, as compared with the behaviour of strengthened two-
way RC slabs. This has resulted in a lack of knowledge and guidance regarding the
strengthening of two-way RC structures. Since the main purpose of this study is to consider the
behaviour of strengthened two-way RC slabs, the following parts and sections of this chapter
concentrate on the review of the most important experimental investigations in the
strengthening of two-way RC slabs to arrive at a better understanding of the behaviour of
strengthened RC slabs and their flexural and punching failure modes.
2.4. Strengthening of two-way RC slabs
2.4.1. Flexural strengthening
Flexural strengthening of RC slabs was first considered for the case when steel plates are
applied on the structures’ soffit [29]. This kind of strengthening is mainly considered in the
case of RC slabs with low or intermediate steel reinforcement ratios. The main motivation
behind this technique is to increase the flexural capacity of the structure by enhancing the
tensile resistance of the RC elements. Ebead and Marzouk [40] demonstrated the efficiency of
applying steel plates to increase the load capacity of two-way RC slabs. However, the most
41
commonly used method to increase the flexural capacity of the RC members is by applying
FRP sheets or plates (instead of steel plates) because of the high tensile strength and lightweight
nature of FRP compared with steel materials.
Ebead et al. [41] conducted an experimental study to increase the flexural strength of RC slabs
by applying CFRP and GRP strips. Ebead et al. [41] chose low and moderate tensile
reinforcement ratios in their study to consider retrofitting of RC slabs that experience flexural
failures before strengthening. Altogether, six slabs were cast, among which REF-0.35%
(control specimen with a 0.35% tensile reinforcement ratio) and REF-0.5% (control specimen
with a 0.5% tensile reinforcement ratio) were non-strengthened concrete slabs, CFRP-0.35%,
GRP-0.35%, CFRP-0.5%, and GRP-0.5% were concrete slabs with initial 0.35% and 0.5%
tensile reinforcement ratios; these were then strengthened with CFRP strips and GRP
laminates, respectively.
Figure 2-15. Experimental layout of the slabs in Ebead et al. [41].
42
Figure 2-15 shows the Ebead et al. [41] model and the strengthening pattern schematically. The
FRPs were anchored at their end plate to avoid early de-bonding. Table 2-4 indicates the effect
of FRP strengthening on the load capacity of different samples. The ductility of the FRP
strengthened samples decreased in comparison with the control specimens and the failure
modes changed from ductile flexural to brittle punching.
Table 2-4. Effect of FRP strengthening on the load capacity of two-way RC slabs in Ebead et al. [41].
Load characteristics
Slab specimens
REF-0.35%
REF-0.5%
CFRP-0.35%
GRP-0.35%
CFRP-0.5%
GRP-0.5%
Load capacity (kN)
250
330
361
345
450
415
Load capacity
increase compared
with control
specimens
_
_
44%
38%
36%
26%
Elsayed et al. [42] experimentally tested the effect of applying different FRP patterns (Figure
2-16) to increase the flexural strength of the RC slabs. The researchers applied middle strips
and separated sheet strengthening patterns called S-MS and S-SS, respectively. The areas of
the RC slabs that were covered by the FRP sheets in both strengthening patterns were the same.
Table 2-5 lists the main characteristics of both the control and strengthened specimens, such as
load capacities and deflections. This enables a direct comparison of different samples.
Depending on the increase of the maximum load capacity (see Table 2-5), there is no significant
difference between applying the separated and middle FRP strips. The failure mode changed
from pure flexural failure in the control specimen to flexural punching failure for the FRP
strengthened RC slabs. The maximum increase of the load capacity for the FRP strengthened
samples was 60.5% (with the S-MS pattern) compared with the control specimen and there was
no significant difference in the crack distribution for different strengthening patterns.
43
Figure 2-16. FRP strengthening patterns in Elsayed et al. [42].
Table 2-5. Specimen characteristics in Elsayed et al. [42].
Slab Initial crack
load
(kN)
Yield load
(kN)
Ultimate load
(kN)
Deflection at ultimate load
(mm)
S0(Control) 54.5 86.6 135.6 91
S-MS 48.3 113.4 226.3 55
S-SS 55.8 109.1 217.7 53
Figure 2-17. Load-deflection curves of the specimens in Limam et al. [43].
44
Limam et al. [43] conducted an experimental study to increase the flexural strength of a two-
way RC slab with a low reinforcement ratio by applying CFRP strips. According to their
results, the load capacity increased from 48 kN in the control specimen to 120 kN in the CFRP
strengthened slab, i.e. the ultimate load capacity increased 2.5 times. Figure 2-17 shows the
load-deflection curves for the control and CFRP strengthened slabs. The load-deflection curves
demonstrate that the control RC slab’s behaviour is more ductile. Figure 2-18 shows the failure
of the control and CFRP strengthened samples.
Figure 2-18. Slab failure in Limam et al. [43].
All the above-mentioned experimental studies and investigations on RC slabs with low or
intermediate steel reinforcement ratio show that applying FRP strips to increase the flexural
strength of RC slabs increases the overall tensile reinforcement ratio. However, the behaviour
of the FRP strengthened samples is more brittle in comparison with those of the non-
strengthened. The achieved tensile reinforcement ratio (including both steel and FRP) might
be more than the critical balance tensile reinforcement ratio (as discussed before), which would
change the failure mode from ductile flexural failure to brittle punching or FRP de-bonding
failure.
2.4.2. Punching strengthening of RC slabs
2.4.2.1. Punching failure mechanism
In flexural elements such as beams and one-way slabs in which bending occurs in one direction,
the shear failure mode is limited to direct shear (one-way shear). However, when RC slabs are
45
placed and supported directly by a column and the load transfer is two-way, and then punching
failure is noted as the most likely shear failure mode [44]. It is noteworthy that punching failure
happens in the vicinity of heavy gravity loads and areas with high reaction forces [44]. Figure
2-19 shows the critical section for the direct shear, punching shear, and the associated failures
schematically. The loaded area in Figure 2-20 is assumed as the predicted area where cracks
appear in the case of shear or punching failure.
Investigations [32, 36] on two-way RC flat slabs illustrate that the expected failure modes are
flexural and punching failure and these kinds of structures are not subject to one-way shear
failure. In other words, in a two-way RC flat slab punching failure is more critical than direct
shear failure. Figure 2-20 shows the different loaded areas that may cause direct shear failure
and punching failure. Considering the dimensions of a two-way RC flat slab, the critical
perimeter that is proportional to the slab resistance against direct shear or punching failure is
most likely smaller in the case of punching failure compared with the one-way shear failure.
Hence, direct shear failure is not an expected failure mode for a two-way RC slab and can be
neglected owing to the abovementioned reasons and previous studies on this topic.
Figure 2-19. Direct (one-way) shear and punching shear failure positions [45].
46
Figure 2-20. Loaded areas in one-way shear and punching failure [45].
The nature of the flexural failure that is known as a common failure mode of RC structures
with low to moderate tensile reinforcement ratios, in which their tensile reinforcements yield
before concrete compressive crushing, has been considered in many investigations and clarified
for different kinds of RC structures. However, the punching failure mechanism is more
complicated. Moreover, it has not been considered as much as flexural failure as it is a
particular failure mode in the case of two-way RC slabs with high tensile reinforcement ratios.
Muttoni [32] analysed the punching failure mechanism by considering the amount and shape
of slab deflection. As seen from Figure 2-21, the discontinuity region is created due to the
rotation of the tension surfaces of the slabs, while flexural reinforcements around shear cracks
decrease the discontinuity. According to this, the total width of the critical punching crack
within a section is proportional to the slab rotation (ψ) multiplied by the slab effective thickness
(d) (Figure 2-21).
Figure 2-21. Slab deformation during punching test [32].
47
Muttoni [32] mentioned that concrete flat slabs at the compression surface attained their
maximum strains in the column’s vicinity, and the strain was alleviated significantly by
increasing the distance from the column. From Figure 2-22, it is observed that the radial strain
is usually lower than the tangential strain, and the radial strain in the column vicinity frequently
decreases before failure. These strain measurements provide a better understanding of the
behaviour of RC slabs and help explain their failure mechanism.
Figure 2-22. Radial and tangential concrete strains at different distances from the column side [46].
In punching shear, diagonal cracks propagate in the vicinity of the column and slab connection
and produce a pyramid or truncated cone of cracks. The first cracks appear around the column
and form an inclined circular fracture surface that propagates to the tension surface of the slab.
The angle between the fracture surface and horizontal line (θ) depends on the reinforcement
48
ratio and combination of applied loads (Figure 2-23). The angle is approximately varied from
25 to 35 degrees [12].
Figure 2-23. Crack angle in a concrete flat slab [12].
2.4.2.2. Effective parameters for punching strength
In this section, parameters that affect the punching strength of a two-way RC flat slab are
considered, which is essential for proposing an efficient strengthening.
Punching shear strength
The punching shear strength of RC structures in standard design codes and suggested formulas
is related to √𝑓𝑐΄𝑛
[12, 37, 47]. Equation 2-2 was suggested by Moe [10] to estimate the nominal
punching shear capacity of RC flat slabs. The parameters in Equation 2-2 that have not been
mentioned before are the column length, c, and the maximum load capacity when the failure
mode is a flexural failure estimated based on the Rankin and Long [7] method and calculated
using Equation 2-3, 𝑉𝑓𝑙𝑒𝑥. It is noteworthy that in case of punching failure, the maximum load
capacity would be smaller than the required load for a fully yielded slab (𝑉𝑓𝑙𝑒𝑥) as an RC slab
that fails in punching cannot reach its estimated flexural capacity, which would have happened
if the tensile reinforcement fully yielded.
Vn =1.25(1−0.075
𝑐
𝑑 ) √𝑓𝑐
΄
1+ 0.44 𝑏0𝑑√𝑓𝑐
΄
𝑉𝑓𝑙𝑒𝑥
b0d 2-2
49
𝑉𝑓𝑙𝑒𝑥 = 8 𝑀𝑟 ( 𝐿
𝑆−𝑐 - 0.172) 2-3
The geometric parameters in Equation 2-3 have been shown in Figure 2-24, which shows the
yield line crack pattern based on the Rankin and Long [7] model, where c is the column width,
L is the slab length, S denotes the slab span, and 𝑀𝑟 represents the radial moment capacity of
the structures. These equations illustrate that increasing the concrete compressive strength can
enhance the punching resistance of the slab.
Figure 2-24. Effective dimensions used to calculate the flexural capacity of slabs in Rankin and Long model [7].
Reinforcements
Flexural reinforcement
According to Yitzhaki [48], increasing the flexural reinforcement resistance will increase the
punching shear strength of a flat slab. Moe [10] obtained Equation 2-4 and Figure 2-25 from
the relation between 𝑉𝑛/𝑉0 and 𝑉𝑛/𝑉𝑓𝑙𝑒𝑥.
(𝑉𝑛/𝑉0) + 𝐶΄ (𝑉𝑛/𝑉𝑓𝑙𝑒𝑥) = 1 2-4
Here, 𝑉𝑛 denotes the nominal punching shear strength that can be evaluated using Equation 2-
2 and 𝑉𝑓𝑙𝑒𝑥 represents the maximum load capacity in case of a ductile flexural failure. 𝐶΄ is a
coefficient between 1 and 0 and V0 is the fictitious punching shear capacity of flat slabs at a
critical section which is given as follows.
𝑉0 = 𝐴 𝑏0 d√𝑓𝑐΄ 2-5
50
Figure 2-25. Relation between the punching strength and flexural capacity of slabs [10].
The parameters used to calculate 𝑉0 are as follows: 𝐴 is a coefficient based on statistical
analysis, 𝑏0 and d arethe perimeter of the critical section and the effective slab depth,
respectively, and 𝑓𝑐΄ is the concrete compressive strength. It should be noted that 𝑉𝑓𝑙𝑒𝑥 can be
treated as the RC slab load capacity when the tensile reinforcement ratio is not greater than the
balanced tensile reinforcement ratio and the slabs fail in a ductile flexural mode. In case of a
flexural failure, 𝑉𝑛 would be equal to 𝑉𝑓𝑙𝑒𝑥 and (𝑉𝑛/𝑉0) will be a constant parameter [10].
Therefore, for slabs with a flexural failure mode, i.e. preferred ductile failure mechanism, 𝑉𝑛
can be estimated independently from the flexural reinforcement ratio considering Equations 2-
4 and 2-5. However, when the tensile reinforcement ratio is greater than the requirement for a
balanced section, 𝑉𝑛 would be less than 𝑉𝑓𝑙𝑒𝑥; furthermore, it increases with increasing tensile
reinforcement ratio based on Equation 2-4 and Figure 2-25. Figure 2-25 and Equations 2-4 and
2-5 may provide a better understanding of the behaviour and failure mode of RC slabs
considering their flexural and punching capacities.
Compression reinforcement
Elstner and Hognested [49] demonstrated that the effect of compression reinforcement on
punching strength depends on the tension reinforcement ratio and 𝑉𝑛
𝑉𝑓𝑙𝑒𝑥. When the tensile
51
reinforcement ratio is low or 𝑉𝑛
𝑉𝑓𝑙𝑒𝑥≥1, the effect of compression reinforcement on punching
behaviour is not considerable. However, when 𝑉𝑛
𝑉𝑓𝑙𝑒𝑥<1, the punching strength increases with
increasing the compression reinforcement ratio.
Shear reinforcement
Figure 2-26. Examples of shear reinforcement in RC slabs [50-53].
The main reason for applying shear reinforcements is to increase the ductility and strength of
the column and slab connections. Shear reinforcements resist the propagation of inclined cracks
and can be classified into three different groups [50-53].
1) Steel sections as shear heads
2) Stirrups, bent bars, and shear bands
52
3) Shear bolts and shear studs such as those in composite structures
Figure 2-26 shows examples of shear reinforcements that are applied to enhance the punching
shear capacity of RC flat slab connections. It is noteworthy that most of the shear
reinforcements such as stirrups and shear heads are placed at the time of a structure’s
construction. There are only limited kinds of shear reinforcements that can be applied to
existing structures such as shear bolts [15, 50].
There are other parameters such as in-plane restraints, the span-depth ratio of slabs, aggregate
size, and size and shape of the loaded area that can also affect the shear behaviour of concrete
slabs. However, these parameters cannot be changed owing to some restriction such as the
slabs’ dimensions [15].
2.4.2.3. Punching strengthening methods
Methods used to strengthen two-way RC slabs with respect to punching shear can be classified
into two categories: direct punching shear strengthening by applying shear reinforcements and
indirect punching strengthening by the enhancement of the slabs’ flexural resistance [15, 54].
In flexural strengthening, issues such as corrosion attack and overloading encourage the
substitution of steel plates with FRP to overcome these mentioned technical problems [29, 54].
Direct punching shear strengthening
The main motivation behind direct punching shear strengthening is the enhancement of the
resistance of the critical punching area against the initiation and propagation of inclined
concrete cracks and against crushing which may cause punching failure. Genikomsou and
Polak [55] studied two-way RC slabs strengthened against punching by applying steel bolts in
holes through the slab thickness.
Figure 2-27 shows the RC slab dimension, reinforcement details, and strengthening patterns.
The failure mode of the control specimen was a brittle punching failure that was converted to
a relatively ductile flexural punching or ductile flexural failure in strengthened slabs.
53
Figure 2-27. Details and strengthening patterns of RC slabs in Genikomsou and Polak [55].
The results in Table 2-6 and load-deflection curves in Figure 2-28 from Genikomsou and Polak
[55] also demonstrate the efficiency of the strengthening method for enhancing the load
capacity (up to 42%) and ductility of the strengthened specimens.
Table 2-6. Test results from Genikomsou and Polak [55].
Slab
Number of rows
of shear bolts
Failure load
(kN)
Displacement at failure load
(mm)
Failure mode
S1 (Control) 0 253 11.9 Punching
S2 2 366 17.1 Flexural punching
S3 3 378 25.9 Flexural
S4 4 360 29.8 Flexural
54
Figure 2-28. Load-deflection curves of slabs from Genikomsou and Polak [55].
Sissakis and Sheikh [56] strengthened RC flat slabs in punching with CFRP. The main principle
behind their method is similar to the application of steel bolts as a shear head. First, holes are
made by drilling through the slab thickness. CFRPs are then braided through the holes in
different patterns to create shear reinforcement in the column’s vicinity as seen from Figure 2-
29. Figure 2-30 compares the load-deformation curves for the control specimen (non-
strengthened slab) and slabs with different FRP strengthening patterns. The results confirm a
significant enhancement in both ductility and shear strength of slabs owing to the application
of CFRP strips as shear heads. Moreover, the critical section perimeter increases because of
the mentioned punching strengthening; this may decrease the possibility of punching failure
compared with the un-strengthened specimen (Figure 2-31).
Figure 2-29. Strengthening patterns from Sissakis and Sheikh [56].
55
Figure 2-30. Load-deformation curves of slabs from Sissakis and Sheikh [56].
Figure 2-31. Critical shear section of slabs with and without shear reinforcement [56].
Despite the advantages of using FRP strips or shear bolts as shear reinforcement, technical
issues may occur during the strengthening process owing to drilling through the slab thickness
in the abovementioned methods. The internal steel reinforcement might get cut or damaged
when enough information about construction design is not available.
56
Indirect punching strengthening
The main principle behind this method is the bonding of FRP or steel plates on the tension face
of slabs to enhance their flexural capacity, which in return increases the punching strength of
the slabs [10]. Chen and Li [9] conducted an experimental investigation to observe the effect
of GRP sheets on the punching strength of two-way RC slabs. Figure 2-32 shows the dimension
of the slabs, reinforcement details and strengthening pattern. The results from Chen’s and Li’s
investigation [9] are summarized in Table 2-7 and the specimen load-deflection curves in
Figure 2-33 illustrate the ability of the strengthening method to increase the slab load capacity
(up to 54%). The specimens with designations "a" and "b" have identical design properties.
Figure 2-32. Details and strengthening pattern of RC slabs from Chen and Li [9].
57
Table 2-7. Test results from Chen and Li [9]
Slab
Number of GRP
layers
Failure load
(kN)
Increase of the failure
load %
Failure mode
SF0 (Control) 0 146.1 _ Punching
SF1a 1 188.4 29 Punching
SF1b 1 190.8 31 Punching
SF2a 2 223.7 53 Punching
SF2b 2 224.7 54 Punching
Figure 2-33. Load-deformation curves of the slabs from Chen and Li [9].
An experimental study by Harajli and Soudki [57] investigated the effect of externally bonding
FRP sheets on the flexural and punching strength for a variety of slabs (from low to high tensile
reinforcement ratios) as well as failure modes. In total, four specimens designated as control
specimens and another twelve RC slabs strengthened with FRP sheets were cast. Figure 2-34
shows the details and dimensions of the specimens. According to the results, the failure modes
changed from a ductile flexural failure to a brittle punching shear failure or flexural punching
failure by CFRP strengthening in RC slabs with an initially low tensile reinforcement ratio.
The results confirmed that the ultimate load carrying capacity and cracking strength of the
strengthened specimens were enhanced considerably. According to Harajli and Soudki [57],
CFRP sheets resist the propagation of tensile cracks or an increase in the flexural stresses in
58
the connection of columns and slabs. The results showed that the punching capacity increased
from 17% to 45% and the flexural strength increased from 26% to 73% due to FRP
strengthening.
Figure 2-34. Details and dimensions of the specimen in Harajli and Soudki [57].
2.5. Slabs strengthened with FRP
2.5.1. The behaviour and failure mode of FRP strengthened slabs
A review of previous studies demonstrates that the most common method used to strengthen
RC slabs against both flexural and punching failures involves the application of FRPs on the
tension surface of slabs. The behaviour of the FRP strengthened slab needs to be considered in
more detail to be aware of the potential scenarios that can happen in the different situations.
The workability of the FRP strengthened slab mainly depends on the proper composite action
of the strengthening.
59
2.5.1.1. FRP strengthened RC slabs with full of composite action
In the case of full composite action, the failure behaviour of the FRP strengthened RC slabs
can be classified into three modes [15, 47, 58].
1) Pure flexural failure that occurs because of the yielding of flexural steel reinforcement
followed by FRP rupture is expected as a failure mode in slabs with a low tensile reinforcement
ratio, including both steel and FRP reinforcement. Higher ductility and deformation at failure
is expected for FRP strengthened slabs which fail in flexure, compared with FRP strengthened
slabs with other kinds of failure. Rankin and Long [7] stated that a tensile reinforcement ratio
below the balanced reinforcement requirements causes the spread of yielding to approach the
full yield-line pattern (Figure 2-35a). It is noteworthy that a full yield-line pattern happens in
RC slabs with ductile behaviour because of the wide yielding of the tensile reinforcement.
2) Flexural punching failure that occurs due to the yielding of flexural steel reinforcement
followed by concrete compressive crushing is a common failure mode for slabs with a moderate
tensile reinforcement ratio, including both steel and FRP reinforcement. Figure 2-35b shows
the flexural cracks that develop due to the partial yielding of tensile steel reinforcement (by
reaching the yield stress of the steel material in the principal axis of steel reinforcement) in the
column’s vicinity, which may propagate owing to shear cracks. The concrete compressive
crushing is followed by a partial yielding of steel reinforcement that may cause a flexural
punching failure. The flexural punching failure is more brittle than a ductile flexural failure.
3) Punching shear failure that happens due to the combination of concrete compressive
crushing and shear cracks is the usual failure mode for slabs with a comparatively high steel
reinforcement and FRP ratio. Owing to high tensile stiffness, failure probably occurs by
concrete crushing before reinforcement yielding. Concrete crushing is triggered by
compressive fracture that occurs because of bi-axial compression as well as the vertical load
applied to the column. Shear cracks may follow concrete crushing to form the punching failure
and cause the failure of the FRP strengthened structure (see Figure 2-35c). Punching failure is
the most common brittle failure mode in FRP strengthened slabs with full composite action
compared with the other two failure modes.
60
Figure 2-35. Failure modes of FRP strengthened slabs with full composite action [7, 15].
2.5.1.2. FRP strengthened RC slabs with a partial loss of composite action
The performance of composite structures is completely related to the bond behaviour between
FRP and concrete. In fact, when there is proper bond behaviour, stresses can be transferred
from concrete to FRP sheets or plates. Hence, it is very important to consider the possibility of
FRP de-bonding when analysing the behaviour of structures as this may cause loss of
composite action. When local de-bonding propagates, the composite action is lost, and the
FRPs cannot carry the load. De-bonding is a brittle failure and occurs all suddenly. It is
noteworthy that de-bonding failure can happen in different layers of FRP strengthened RC
slabs according to the position of de-bonding; de-bonding types are listed below (see Figure 2-
36) [15, 59].
Figure 2-36. De-bonding failure modes.
61
1) De-bonding in the concrete
2) De-bonding in the epoxy adhesive
As the tensile and shear strengths of the epoxy resin are normally greater than that of concrete,
this failure is not common and occurs rarely. This mode of failure can only happen in high
strength concrete or under high temperatures.
3) De-bonding at the interface between concrete and epoxy resin or within FRPs
Normally, FRP and epoxy resins are more resistant to the development and propagation of
cracks than concrete. Consequently, the first category of de-bonding failure is much more
common compared with other de-bonding fracture modes. Hence, more attention should be
paid to this category of de-bonding failure in FRP strengthened RC slabs.
As for the initiation point of the de-bonding process, the de-bonding failure may be initiated
from:
1) Cover de-bonding, which may happen in the vicinity of a weak layer of concrete, e.g. along
the direction of tensile steel reinforcement, or end separations (see Figure 2-37)
Figure 2-37. Different kinds of FRP de-bonding initiated in the concrete [59].
2) De-bonding by critical diagonal cracks (CDC), which are initiated owing to shear cracks (or
a combination of shear and flexural cracks), that cause vertical and horizontal openings of
concrete (see Figure 2-38) that may result in FRP de-bonding
62
Figure 2-38. CDC de-bonding [15].
3) De-bonding by flexural cracks or intermediate cracks (IC) that happens owing to the
propagation of vertical cracks and results in FRP de-bonding in an area away from the endplate
as shown in Figure 2-37.
4) De-bonding due to the unevenness of the concrete surface, which could cause a diverting
force from the concrete surface after loading RC structures in flexure and which may result in
FRP de-bonding (Figure 2-39). This kind of failure can be avoided by considering proper
concrete surface preparation.
Figure 2-39. De-bonding due to the unevenness of concrete.
2.5.2. Bond behaviour between concrete and FRP
To carry out appropriate de-bonding analyses, the bond behaviour and failure mechanism
should be clarified. If there is a proper bond between, for example, concrete and FRP, then
63
FRP plates will strengthen RC structures effectively and stresses between concrete and FRP
are transferred properly. The bond behaviour between concrete and FRP was investigated by
considering cohesion strength experiments such as single shear tests (Taljsten [60]) and double
shear tests (Neubauer and Rostasy [61]) as shown in Figure 2-40.
Figure 2-40. Single and double shear tests to investigate the bond strength between concrete and FRP.
The bond behaviour between concrete and FRP may be defined by the bond-slip relation, which
is based on the variation of shear stresses (between concrete and FRP) against the relative
displacement (slip) between the materials. Figure 2-41 shows an example of the shear-slip
relation for concretes that are differently strengthened. The FRP–concrete bond is stiffer than
the bond between concrete and ribbed steel bars. However, the bond capacity of ribbed steel
bars and concrete is greater than the FRP–concrete bond capacity (the areas below the curves
in Figure 2-41 indicate the fracture energy Gf required to break the bond) [29].
64
Figure 2-41. Shear-slip relation in differently strengthened concretes [15].
Figure 2-42. Bond-slip models in Lu et al. investigation [59].
Lu et al. [59, 62] considered different bond-slip models and proposed their bond-slip model
shown in Figure 2-42. The bond shear stresses and fracture energy (𝐺𝑓) in the Lu et al. [59]
model is calculated using the following equation.
Bond shear stress {τ = 𝜏𝑚𝑎𝑥√
𝑆
𝑆0 if 𝑆 ≤ 𝑆0
τ = 𝜏𝑚𝑎𝑥 exp(−α(𝑆
𝑆0− 1)) if 𝑆 > 𝑆0
2-6
65
τmax represents the maximum shear stress and is calculated as
τmax = 1.5 βw 𝑓𝑡 2-7
𝑓𝑡 in Equation 2-7 denotes the concrete tensile strength in MPa and βw represents the FRP width
ratio given by
βw=√(2.25 −𝑏𝑝
𝑏𝑐)/(1.25 +
𝑏𝑝
𝑏𝑐). 2-8
𝑏𝑝 and 𝑏𝑐 in Equation 2-8 represent the width of FRP and concrete slab in mm (Figure 2-40),
respectively. S0 in Equation 2-6 is an effective parameter that represents the corresponding slip
with the ultimate bond shear stress in Figure 2-42 and is given by
S0 = 0.0195 βw 𝑓𝑡 2-9
α in Equation 2-6 is another parameter that is related to the energy required for cracking the
interfacial bond per unit area and is calculated as
α = 1
( 𝐺𝑓
(𝜏𝑚𝑎𝑥 𝑆0) −
2
3) 2-10
𝐺𝑓 represents the interfacial fracture energy and is estimated as
𝐺𝑓 = 0.308 𝛽𝑤2√𝑓𝑡 2-11
It is noteworthy that according to these models, the interfacial fracture energy and bond
strength are related to the concrete strength. The bond resistance can therefore be enhanced by
increasing the concrete strength. Maeda et al. [63] and Yuan et al. [64] conducted experimental
investigations and fracture mechanics analyses to identify the bond behaviour between concrete
and FRP. According to their investigations, increasing the length of FRP does not always
enhance the FRP bond strength. They concluded that there is an effective length for the bonded
FRP, and increasing the FRP length beyond this does not enhance the FRP bond capacity [63,
66
64]. Chen and Teng [65] analysed the experimental and theoretical studies in this area and
proposed a comprehensive model that estimates the bond strength and effective bond length as
follows.
Pu (Bond strength) = 0.427 βp βL√𝑓𝑐′ bp Le (N) 2-12
βL = {1 if L ≥ 𝐿𝑒
𝑆𝑖𝑛 𝜋 𝐿
2 𝐿𝑒 if L < 𝐿𝑒
2-13
βp= √(2 −𝑏𝑝
𝑏𝑐)/(1 +
𝑏𝑝
𝑏𝑐) 2-14
Le (Effective length) = √𝐸𝑓 𝑡𝑓
√𝑓𝑐′ (mm) 2-15
In the above equations, Ef and tf represent the FRP modulus of elasticity and thickness in MPa
and mm, respectively, 𝑓𝑐′ denotes the concrete cylinder compressive strength in MPa, and L is
the FRP length. The Chen and Teng [65] model provides a simple way to estimate the effective
length of FRP (based on experimental and theoretical analyses) in the design of FRP
strengthened RC structures.
Figure 2-43. Experimental and theoretical results of bond strength and effective length [65].
67
Considering the safety factor and standard deviation of test results, Chen and Teng [65] have
further suggested the following equation for design proposes.
Pud (Design bond strength) = 0.315 βp βL√𝑓𝑐′ bp Le (N) 2-16
As observed from Figure 2-43, there is no significant change in the bond strength of the FRP-
to-concrete joint when the de-bonding length is larger than the effective length of FRP; this
justifies the concept of effective length in FRP strengthened RC elements.
2.5.3. Design codes estimation in composite action
The results of the experimental or analytical investigations can be compared with estimations
from design codes to justify the accuracy of the design. However, if there is a difference
between the estimation from design codes and research results, a logical explanation of the
difference or better understanding of the applicability of relevant design codes is required. The
predicted values by Eurocode 2 and ACI 318 may estimate the punching strength of specimens.
Ebead˗Marzouk and Elstner˗Hognestad models can evaluate their flexural capacity. It is natural
that a brief introduction to these codes and models is given here for comparative analyses in
Chapters 3 and 4.
2.5.3.1 Evaluation of the slabs punching strength
Eurocode 2
The punching shear capacity (𝑉𝑅) is estimated using Equation 2-17.
𝑉𝑅= 𝜈𝑝 .𝑢1.𝑑 2-17
Here, 𝑢1 is the critical perimeter around the column area and d is the effective depth of the slab.
The control perimeters in Eurocode 2 are a function of the effective depth and can be calculated
as shown in Figure 2-44. In case of two-way RC slabs with tensile steel reinforcement in two
directions, d is considered as the average effective depth. The punching shear resistance of the
critical section in a two-way RC slab is given [12] by
68
𝑣𝑝 = 0.18 𝑘 (100 𝜌 𝑓𝑐΄)
1
3 + 0.1 𝜎𝑐𝑝 ≥ 𝜈min + 0.1 𝜎𝑐𝑝 2-18
Figure 2-44. Control perimeters around the loaded areas according to Eurocode 2 [12].
In the above formulation, 𝑓𝑐΄ is the concrete compressive strength in MPa and k is calculated as
follows.
𝑘 = 1 + √(200
𝑑) ≤ 2.0 2-19
𝜌 is the ratio of the flexural reinforcement that can be estimated by Equation 2-20 in two-way
RC flat slabs.
𝜌 = √(𝜌𝑥. 𝜌𝑧) ≤ 0.02 2-20
𝜌𝑥 and 𝜌𝑧 in Equation 2-20 represent the flexural reinforcement ratios in the x and z directions,
respectively. It is noteworthy that the x and z directions are in-plan and the y direction is out
of the plan in the slabs considered in this thesis. The flexural reinforcement ratio in each
direction is defined as the ratio of the reinforcement area over the product of the section width
(which is calculated as 3d at each column side plus the column width) and section effective
depth. The equivalent tensile reinforcement ratio in case of FRP strengthened slabs is
calculated using Equation 2-21 for RC slab sectional analysis. The effective parameters in
Equations 2-21 and 2-22 are shown in Figure 2-45. Mr in Equation 2-22 is the radial moment
capacity of the RC section in Figure 2-45.
69
𝜌 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 = 𝐶𝑐
𝑏𝑤 × 𝑑 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 × 𝑓𝑠
2-21
𝑑 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡= 𝑀𝑟
𝐶𝑐 +
𝑎
2 2-22
Other parameters that are essential for the estimation of the punching resistance in Equation 2-
18 are as follows.
νmin= 0.035 𝑘3/2√𝑓𝑐΄ 2-23
𝜎𝑐𝑝= (𝜎𝑐𝑥+𝜎𝑐𝑧)/2 2-24
𝜎𝑐𝑥 and 𝜎𝑐𝑧 are the normal stresses at the critical section in the x and z directions, respectively;
these are given by the expressions in Equation 2-25.
𝜎𝑐𝑥 = 𝑁𝐸𝑑,𝑥
𝐴𝑐𝑥 , 𝜎𝑐𝑧 =
𝑁𝐸𝑑,𝑧
𝐴𝑐𝑧 2-25
𝑁𝐸𝑑 in the above formula denotes the longitudinal forces in the prestressed case in the x and z
directions and 𝐴𝑐 is the concrete cross-sectional area.
Figure 2-45. Strain and stress distribution over the slab thickness [12, 15].
70
ACI 318
The critical perimeter around the column area is different from the Eurocode 2 estimation and
can be calculated as shown in Figure 2-46.
Figure 2-46. Control perimeters around the loaded areas according to ACI 318 [37].
The punching shear capacity (𝑉𝑅) of a two-way RC slab in ACI is given [37] by the following
equations considering whether there are shear reinforcements in RC slabs or not.
𝑉𝑅 = 0.33 √𝑓𝑐΄ × u1 × d (Slabs without shear reinforcements) 2-26
𝑉𝑅 = 0.17 √𝑓𝑐΄ × u1 × d + 𝐴𝑣 𝑓𝑦 𝑑
𝑠≥ 0.5 √𝑓𝑐΄ × u1 × d (Slabs with shear reinforcements) 2-27
The parameters in the two equations above which have not been introduced before are 𝐴𝑣which
is the cross-sectional area of the legs of shear reinforcements around the loaded area in mm2,
𝑓𝑦 is the yield stress of shear reinforcements in MPa and s is the radial spacing between the
stirrups in mm.
2.5.3.2. Evaluation of the slabs flexural capacity
Ebaed and Marzouk model
Ebead and Marzouk [5] modified the Rankin and Long [7] formula to evaluate the flexural
capacity of the square slabs by taking into consideration the effect of FRP.
71
𝑉𝑓𝑙𝑒𝑥= 8𝑀𝑟 (𝑆
𝐿−𝑐 - 0.172) 2-28
Here, 𝑉𝑓𝑙𝑒𝑥 is the flexural load carrying capacity in kN. S is the side length of the square slab
in mm. L represents the side dimensions between supports of the square slab in mm and C
denotes the side length of the column in mm (see Figure 2-24). 𝑀𝑟 is the radial moment capacity
of the strengthened section in N.mm/mm and is given by
𝑀𝑟= 𝑀𝑟1+ 𝑀𝑟2 2-29
𝑀𝑟1 represents the radial moment capacity of the un-strengthened section, which is evaluated
according to ACI 318 [37] as
𝑀𝑟1= b𝑑2(ρ - ρ΄)𝑓𝑦(1 0.59 (𝜌_ 𝜌΄)
𝑓𝑐΄ 𝑓𝑦) + ρ΄𝑓𝑦𝑑(𝑑 - 𝑑΄) 2-30
𝑑 and 𝑑΄ in Equation 2-30 represent the effective depths for tensile and compressive steel
reinforcement in mm, respectively, ρ and ρ΄ denote the tensile and compressive reinforcement
ratios, and 𝑓𝑦 represents the yield stress of steel reinforcement. 𝑀𝑟2 is the contribution of FRP
sheets or plates to the loading capacity of the strengthened RC slab and is estimated as
𝑀𝑟2= 𝐸𝑓𝑡𝑓𝜀𝑓 (h ̵ 𝑎
2)
𝑤𝑓
𝜂 . 𝐿 2-31
where 𝐸𝑓 is the FRP material modulus in MPa, 𝑡𝑓 is the thickness of FRP material in mm and
𝜂 is the strengthening efficiency factor, h and 𝑤𝑓 denote the slab thickness and FRP width in
mm, and a represents the depth of the neutral axis, which is calculated as
a = (0.8𝑑εcu/(εcu+εsu)) 2-32
where 𝜀𝑓 represents the FRP strain evaluated from strain compatibility in sectional analysis
estimated by
𝜀𝑓= (ℎ
𝑑 - 1) εcu +
ℎ
𝑑 εsu 2-33
εcu and εsu in Equation 2-33 represent the ultimate strains of concrete and steel, respectively.
72
Elstner and Hognestad model
Elstner and Hognestad [49] have proposed the following equation to evaluate the ultimate
flexural capacity of RC flat slabs.
𝑉𝑓𝑙𝑒𝑥= 8 𝑀𝑐 ( 1
1− 𝑐 𝐿⁄− 3 + 2√2 +
𝑀𝑐𝑀0 ⁄ − 1
𝐿𝑐⁄ − 1
) 2-34
Herein, 𝑀𝑐 is radial moment capacity in the column strip and 𝑀0 is the radial moment resistance
of the outer strip.
2.5.4. Prestressed FRP as an external reinforcement
Imposing longitudinal forces such as compressive forces called prestress load could reinforce
the structure by partially cancelling out tensile stresses. This may result in a reduction in the
size and number of cracks and a decrease in the deflection in case of serviceability as well as
the enhancement of the loading capacity of structures [66-68].
Applying prestressed FRP plates on the tension surface of slabs may benefit them from both
prestressing and FRP strengthening. Quantrill and Hollaway [13] and Garden and Hollaway
[14] conducted investigations into the effect of prestressing FRPs in strengthening
unidirectional structures such as one-way slabs and beams. According to their results, using
prestressed FRPs improved the ultimate load owing to an increase in the bending resistance
compared with non-prestressed FRPs. Moreover, the authors reported a significant decrease in
deflections, and the number and width of cracks. Hence, use of prestressed FRP plates may
increase the efficiency of FRP strengthening. However, the technical difficulty in the
prestressing process limited investigation in this area.
Abdullah [15] and Kim et al. [16] conducted experimental studies that considered the behaviour
of two-way RC slabs strengthened with prestressed and non-prestressed FRPs. The
experiments demonstrated that strengthening RC slabs with non-prestressed FRP could
increase the ultimate load capacity of the samples; however, the results seem to be in
contradiction with prestressed FRP strengthening. Kim et al. [16] concluded that applying
prestressed FRP sheets increased the efficiency of FRP strengthening compared with samples
strengthened with non-prestressed FRP. However, Abdullah [15] demonstrated that the
73
ultimate load capacity of slabs strengthened with prestressed FRPs was lower than the load
capacity of slabs retrofitted with non-prestressed FRP plates. For slabs strengthened with
prestressed FRP, there is so far no convincing explanation for such contradictive results and
behaviour.
2.6. Summary
As mentioned before, there are very few studies on the strengthening of two-way RC slabs
compared with strengthening of other RC structures such as one-way RC structures and
columns, which has resulted in a knowledge gap. Considering the literature review, the gaps
considered in this thesis are as follows. The mentioned investigations demonstrate that the most
common retrofitting method used in both flexural and punching strengthening strategies is the
application of FRP on the tension surfaces of RC slabs. Abdullah [15] and Kim et al. [16]
conducted experimental studies to study the effects of FRP strengthening and prestressing by
applying prestressed FRP to enhance the flexural and punching capacity of RC slabs. Both
studies confirmed the efficiency of applying non-prestressed FRP to enhance the load capacity
of the slabs. However, the contradictory results in the case of strengthening with prestressed
FRP is a critical point in the literature review that should be justified considering logical
explanations about the load transfer mechanism based on experimental results and validated
numerical models, which is described in Chapter 3.
The advantages and disadvantages of all the flexural and punching strengthening methods show
that the efficiency of the strengthening technique may differ from specimen to specimen.
Hence, comparing the effect of different strengthening methods such as FRP strengthening,
applying vertical (shear) reinforcements in the column’s vicinity, and their combination may
result in finding efficient strengthening strategies that benefit from different rehabilitation
methods. The literature review shows that the combination of different strengthening methods
has not been studied substantially with regards to strengthening two-way RC slabs. Hence, in
this study, an investigation is conducted that considers different strengthening methods in
addition to FRP strengthening and their combination to retrofit two-way RC slabs in different
conditions; this covers the research gap in this area and is discussed in Chapter 4.
74
3. Strengthening RC slabs with non-prestressed and
prestressed FRP
3.1. Introduction
The strengthening of RC slabs with prestressed FRP is an innovative engineering application
that has not been substantively considered in experimental and numerical investigations. This
has led to gaps in knowledge of the area. In this chapter, two experimental cases involving RC
slabs strengthened with prestressed and non-prestressed FRP, conducted by Abdullah [15] and
Kim et al. [16], respectively, are analysed. This will provide an additional explanation of the
mechanism of the strengthening of RC slabs that can be referenced for future FRP
strengthening designs in engineering applications.
The two experimental cases were considered because their results in the case of the
strengthening of RC slabs with prestressed FRP appeared contradictory, and led to concerns
about the suitability of prestressed FRP to strengthen RC slabs. As a main objective of this
chapter is to clarify whether it is feasible to strengthen RC slabs with prestressed FRP, a
thoughtful analysis of the mechanism is provided in this chapter after considering both the
experimental and the numerical analyses.
A brief description of the experiments by Abdullah [15] and Kim et al. [16], including the
experimental settings used and the results obtained, is first provided. The numerical simulation
and validation of each case of strengthening with non-prestressed and prestressed FRP (where
there was an apparent contradiction in the results) are presented in a comprehensive analysis
of the mechanism. This may lead to novel implications for strengthening design. The last part
of this chapter proposes a formula to estimate the optimum prestress ratio for the FRP
strengthening of RC slabs based on the explanation provided and the resultant regression
analysis for the cases considered.
75
3.2. Experimental studies
3.2.1. Abdullah’s experimental investigation
Abdullah [15] conducted an experimental investigation into the behaviour of load carrying
capacity, yielding load, deflection, crack pattern and the failure mode in the strengthening of
RC slabs at our heavy structure laboratory in Manchester University a few years ago. He
considered the effect of strengthening flat RC slabs with prestressed and non-prestressed FRP
plates (bonded externally to the tension surface of the RC slabs).
A total of five slab specimens were listed where R0 was an un-strengthened concrete slab
(control specimen). R-F0 was a concrete slab strengthened by non-prestressed FRP plates and
R-F15 was a specimen strengthened by 15% (of FRP-strength) prestressed FRP plates. R-F30
and R2-F30 were samples strengthened with 30% prestressed FRP. The concrete properties for
R-F30 and R2-F30 were different (Table 3-1) in order to investigate the effect of these
properties on the behaviour of the RC slabs strengthened at the same prestressing ratio of FRP.
Concrete cylinders were tested after 28days to measure such concrete properties as tensile and
compressive strength as well as the modulus of elasticity. Figure 3-1 shows the geometrical
details of the test specimens. The column stubs and slabs were designed to be constructed at
the same time. The concrete cover was 20 mm based on the Eurocode 2 [12] recommendation
in light of the maximum size of the aggregate (which was 10mm) and the diameter =12mm
of the steel reinforcements.
Table 3-1. Properties of concrete in different samples.
Slab Modulus of elasticity
(GPa)
Compressive strength
(MPa)
Tensile strength
(MPa)
Poisson’s
ratio
R0, R-F0, R-F15, R-F30 28 33.10 3.39 0.2
R2-F30 30 38.85 4.53 0.2
In addition to the dimensions and steel reinforcement ratios of all slabs, the boundary
conditions for all specimens were also identical, which allowed for a direct comparison and a
better understanding of the effect of prestressed and non-prestressed FRP strengthening of RC
slabs. It was observed that a low reinforcement ratio was chosen to make reasonable space for
76
the application of post-strengthening FRP plates. The mechanical properties of the steel bars
and FRP were the same in all slabs, as indicated in Tables 3-2 and 3-3, respectively.
Figure 3-1. Abdullah’s [15] test layout.
Table 3-2. Properties of the steel bars.
Diameter (mm) Modulus of elasticity
(GPa)
Yield strength
(MPa)
Ultimate strength
(MPa)
Yield strain
12 200 570 655 0.0034
8 200 576 655 0.0030
77
Table 3-3. Properties of FRP.
Density
(g/cm3)
Cross section
(mm2)
Tensile strength
(MPa)
Rapture
strain
Volume
fraction
Poisson’s
ratio (𝝂𝒙𝒚)
Young’s modulus of
elasticity (GPa)
Shear modulus
(GPa)
𝐸𝑥 𝐸𝑦 𝐺𝑥𝑦 𝐺𝑦𝑧
1.7 100×1.2 2970 0.0168 70% 0.29 165 14 5.1 4.3
The FRP plates used were CFK 150/2000, manufactured by S&P, Switzerland. The
recommended adhesive material applied to paste FRP plates was the Weber Tec EP structural
adhesive. The prestressing forces in the concrete RC slabs were transferred from prestressed
plates by adhesive bonding and the anchored end plates, which were used to avoid early de-
bonding at the ends of the FRP plates.
The samples were cured and maintained for three weeks. For the strengthened samples, the
concrete substrates were ground and cleaned of dust in preparation for FRP attachments. A
putty filler or a primer with the tensile strength of 3 N/mm2 was applied to remove major
discontinuities. The minor imperfections in the substrates could be levelled using the structural
adhesive, and the plates’ bonding process was carried out within 24 hours of levelling the
surface according to the manufacturer’s recommendation. When both the concrete substrates
and the FRP plates (the FRP side attached to the concrete substrate) were covered with adhesive
material, and the plates were pushed to the concrete substrates, a roller passed back and forth
along the FRP plate to remove air bubbles and squeeze extra adhesives before tightening the
steel bolts at the anchored end plates.
Figure 3-2. Applying prestressed FRP plates to the RC structures surface.
Figure 3-2 shows the prestressing mechanism of the strengthening technique used to bond the
prestressed FRP plate to the concrete surface. Following the preparation of the concrete
substrate, the FRP plate was prestressed by a hydraulic jack to the required level. The
78
prestressed level of the FRP plate was monitored by load cells. Steel clamps were installed at
the end plates to retain the required prestress level of the FRP plates. After curing the adhesive
material, the steel clamps were released and unbolted. The excess lengths of the FRP plates
were cut after releasing the prestressed system. All slabs were tested after a 28-day curing.
Figure 3-3. Abdullah’s [15] test setup.
The load acting at the centre of the column was applied at a rate of 10kN/min by a hydraulic
ram (see Figure 3-3). The RC slabs were simply supported. A data internalisation system
connected to a computer was used to collect test data, such as load, deflection and strains. The
steel reinforcement strains were measured with the embedded strain gauges which could
determine the slab’s yield strain. External strain gauges were mounted in the vicinity of the
column and the FRP plates to monitor the behaviour of the concrete (especially in case of
punching failure) and measure the longitudinal strain on the FRP. A group of linear
potentiometers were used to determine the slab deflection profile.
Figure 3-4 shows a comparison of load–deflection curves for all five slab samples. Table 3-4
lists the ultimate load of the concrete slab specimens achieved in the experimental study and
calculated according to Eurocode 2 and the method proposed by Ebead-Marzouk [5]. The
consistency between the code prediction and the experimental values in R0 and R-F0 was
acceptable. However, there was a considerable difference between the code estimations and
the experimental results in the samples strengthened with prestressed FRP. Different failure
modes in different samples were also observed.
79
Figure 3-4. Load-deflection curves of the RC slabs in Abdullah’s [15] study.
Table 3-4. Ultimate load capacity of the slabs in Abdullah’s [15] investigation.
3.2.2. Kim et al.’s experimental investigation
Kim et al. [16] conducted an experimental investigation to consider the effects of strengthening
using prestressed and non-prestressed FRP plates (bonded externally to the tension surface of
the RC slabs) on the behaviour of the RC slab. They cast three slab specimens where RC0 was
an un-strengthened concrete slab (control specimen), RC-F0 was a concrete slab strengthened
with non-prestressed FRP sheets, and RC-F15 was a specimen strengthened with 15% (of FRP
Slab Vu, Predicted (kN) Vu (kN) Failure mode
Eurocode 2 Ebead–Marzouk Method Experimental
R0 231.4 299 284 Flexural
R-F0 359 376.1 405 Flexural punching
R-F15 364 378.2 240 De-bonding
R-F30 374 381.9 220 De-bonding
R2-F30 396 449.7 307 De-bonding
80
strength) prestressed FRP sheets. Figure 3-5 shows the geometrical details of the specimens.
Concrete properties (Table 3-5), steel reinforcement ratios (1.44%) and properties (Table 3-6),
geometrical dimensions and the boundary conditions (simply supported) for all specimens were
the same. The mechanical behaviour of FRP is listed in Table 3-7.
Figure 3-5. Kim et al.’s [16] test layout.
Table 3-5. Properties of the concrete.
Modulus of elasticity (GPa) Compressive strength (MPa) Tensile strength (MPa) Poisson’s ratio
28 33 3.16 0.2
81
Table 3-6. Properties of the steel bars.
Diameter (mm) Modulus of elasticity
(GPa)
Yield strength
(MPa)
Ultimate strength
(MPa)
Yield strain
20 195 454 560 0.0029
15 213 548 575 0.0030
Table 3-7. Properties of CFRP.
Density
(g/cm3)
Cross section
(mm2)
Tensile strength
(MPa)
Rapture
strain
Volume
fraction
Poisson’s
ratio (𝜈𝑥𝑦)
Young’s modulus of
elasticity (GPa)
Shear modulus
(GPa)
𝐸𝑥 𝐸𝑦 𝐺𝑥𝑦 𝐺𝑦𝑧
1.7 150×0.33 2970 0.0167 70% 0.28 227 21 6.5 5.1
The samples were subjected to a uniform pressure load applied to the column stub. The concrete
surface was prepared by grinding the surface imperfections before applying the FRP sheets.
The sheets were bonded to the concrete by epoxy resin and fixed at their ends by steel
anchorage plates to avoid earlier de-bonding. In case of strengthening with prestressed FRP,
the prestress was exerted by tightening the nuts to reach the required prestress level. The
prestress forces were measured and monitored by the load cells. The steel clamps kept the
sheets tight and prevented them from lifting off the slab (see Figure 3-6).
Figure 3-6. Anchorage system at the FRP`s end plate.
Figure 3-7 shows the load-deflection curves of all samples. Table 3-8 also lists the ultimate
loads of the concrete flat slab specimens achieved in the experimental study and calculated
82
according to the Eurocode 2 and Ebead-Marzouk methods. An acceptable consistency was
observed between the code prediction and the experimental data for the ultimate load capacity.
Figure 3-7. Load-deflection curves of the RC slabs in Kim et al. [16] study.
Table 3-8. The ultimate load capacity of the slabs in Kim et al. [16]
Both experimental tests proved the efficiency of applying FRP plates to enhance the load
capacity of RC slabs. However, a contradiction in case of the suitability of strengthening RC
slabs with prestressed FRPs arose because the ultimate load capacity of slabs strengthened with
prestressed FRP in Abdullah’s [15] study was even lower than that of the non-prestressed FRP
strengthened slab. However, there was an improvement in the load capacity of the slab
strengthened with prestressed FRP in Kim et al.’s [16] study compared with the slab
strengthened with non-prestressed FRP. This phenomenon and factors that caused this
difference should be clarified before further application of prestressed FRP in the post-
Slab Vu, Predicted (kN) Vu (kN) Failure mode
Eurocode 2 Ebead–Marzouk Method Experimental
RC0 419 361 372.6 Flexural punching
RC-F0 429 376 411.0 Punching
RC-F15 433 391 443 Punching
83
strengthening RC slabs. The remaining of this chapter is trying to carry out a thoughtful
numerical modelling to determine if any potential mechanism can be found to explain them.
More details of the experimental studies will be reported with the numerical results.
3.3. Numerical Modelling
3.3.1. Introduction
Many problems in engineering can be described and modelled by differential equations.
Solving these equations was complicated, time-consuming and, in some cases, impossible in
the past. However, a revolution has since occurred in this respect through the development of
and improvement in engineering software. The principles of engineering software used to
model structures have been based on numerical methods, such as the finite difference method
(FDM), the finite element method (FEM) and the finite volume method (FVM). For each
category of engineering issues, one of these numerical methods or a combination can serve as
effective practical solutions [69].
The FEM is a useful technique to analyse such issues as fracture mechanics, crack propagation,
static and dynamic loadings, complicated interactive behaviour and composite structures. Such
advantages as its ability to model structures with complicated geometric dimensions,
generating an imaginable model and the ability to deal with different kinds of loadings have
caused the FEM to be widely applied to analyse structural behaviour. The main idea underlying
FEM is to decompose the model into smaller parts (elements) that can be analysed more simply
to find a numerically approximate solution for partial differential equations that describe model
behaviour. The partial differential equations are defined (based on shape function estimations)
to describe the physical behaviour of the elements [69],which are linked by nodes where the
main parameters (such as stress and strain) are used to estimate all elemental behaviour using
the assumed shape function. Within an element, the nodal force and the corresponding nodal
displacement are governed by [69, 70]:
[Stiffness] × [Displacement] = [Force] 3-1
84
Stiffness is associated with the assumed geometry of the element, and its material behaviour
and assumed shape function. By assembling similar equilibrium equations for all elements and
considering initial and/or boundary conditions to describe the model, a final, discretely
assembled simultaneous equation can be computed.
The finite element method as a technique to analyse engineering and industrial models has been
used since the early 20th century. In 1943, Cournat applied triangular elements to analyse a
continuous system. The company Boeing simulated the parts of planes by applying triangular
shapes in 1950. Clough is one of the pioneers of digital coding in finite element analysis. A
number of modelling software products are based on finite element methods, such as Abaqus,
Ansys, Adina and Nastaran [71, 72].
The core of the Abaqus is based on a PhD thesis, and was improved by researchers and
scientists to yield the simulation software [73]. Abaqus can define concrete properties in both
linear and nonlinear structural behaviour as well as those of reinforcement, such as steel and
FRP. The large number of published papers and PhD theses on it show that Abaqus is one of
the most efficient software for finite element modelling and the analysis of structural
behaviour. The accuracy of structural modelling with Abaqus has been proved in past
experimental and analytical studies [72, 73]. The following sections of this chapter introduce
some properties of materials and the fundamentals of Abaqus. The samples in Abdullah [15]
and Kim et al.’s [16] studies are then validated numerically to determine if a mechanism can
explain the contradictory results in the samples strengthened with prestressed FRP. The
numerical validation of these case studies will serve as a basis for finite element simulations in
the following chapters.
3.3.2. Concrete Modelling
3.3.2.1. Compressive and tensile behaviour of concrete
Hognestad [74], and Kent and Park [75] suggested Equation 3-2 to model the ascending curve
of the concrete behaviour shown in Figure 3-8. According to the Eurocode 2 [12], concrete
retains its elasticity until 0.4𝑓𝑐΄, as shown in Figure 3-8. Based on the claim by Kent and Park
85
[75], the descending part of the concrete model in compression can be linear, and is not allowed
to approach any stress lower than 0.2𝑓𝑐΄. Karson and Jirsa [76], and Darwin and Pecknold [77]
have also concluded that 0.2𝑓𝑐΄ is the lowest stress that concrete could approach in the
descending parts of their models.
Figure 3-8. Uniaxial compression stress-strain curve for concrete.
𝑓𝑐 = 𝑓𝑐΄ [
2𝜀𝑐
𝜀𝑐0– (
𝜀𝑐
𝜀𝑐𝑜)2] 3-2
𝜀𝑐0 = 1.7𝑓𝑐
΄
E0 3-3
E0 = 19800(𝑓𝑐
΄
10)0.3 3-4
The parameters in Equations 3-2 to 3-4 are as follows: 𝑓𝑐΄ and 𝑓𝑐 are the ultimate concrete
cylindrical compressive strength and the concrete compressive stress, respectively, 𝜀𝑐0 is the
strain at the ultimate concrete compressive strength calculated by Equation 3-3 [74], E0 is the
concrete (with limestone as fine aggregates) modulus of elasticity, and can be estimated from
Equation 3-4, which is based on Eurocode 2 with reasonable accuracy [12]. Hognestad [74]
86
suggested 0.0038 as the strain for the concrete post failure stress at 0.85𝑓𝑐΄ in the linear
descending part of Figure 3-8. 𝜀𝑐𝑢 is the ultimate concrete strain that can be seen in Figure 3-
8.
Figure 3-9. Tensile behaviour of concrete [78, 79].
Figure 3-10. Modified tensile behaviour of concrete on Abaqus.
Gilbert and Warner [78], and Nayal and Rasheed [79] suggested the model shown in Figure 3-
9 to describe the tensile behaviour of concrete. 𝑓𝑡΄is its ultimate tensile strength and 𝜀𝑡0 the
strain at this strength in the model. Wahalathantri et al. [80] modified the model by slanting
87
from (0.8𝑓𝑡΄, 𝜀𝑡0) to (0.77𝑓𝑡
΄, 1.25𝜀𝑡0) to avoid runtime errors in the Abaqus simulation. A lower
limit on post-failure stress, assumed to be 1% of the ultimate tensile strength, was imposed to
prevent potential numerical stability problems [81]. Figure 3-10 shows that the modified model
was applied in this study to simulate the tensile behaviour of concrete.
3.3.2.2. Concrete damage modelling
The first step in creating a suitable structural model of concrete is to accurately define concrete
properties. In spite of quite a number of studies on concrete structures, damage modelling in
the descending part and the loading-unloading cycle of the concrete stress-strain curves are
among the most controversial areas of research due to the nature of concrete. Three popular
models are used to describe the damage behaviour of concrete, i.e., smeared cracks, brittle
crack and damage plasticity, which are more employable in the numerical modelling of
concrete. A brief description of each is provided below.
Smeared cracking
Smeared cracking is a suitable model to simulate concrete failure when tensile cracks are
dominant and compressive crushing can be neglected. This model has only been employed in
Abaqus/Standard (implicit method). Since concrete behaviour is brittle and nonlinear, applying
the implicit method can cause a divergence problem. Furthermore, it is difficult to describe and
analyse the interactive properties among different parts of structures by using an implicit
method [72].
Brittle cracking
This model can only be applied using the explicit method. A disadvantage of the brittle cracking
model is that it does not consider the compressive damage to the material. Therefore, this model
can be applied to simulate materials such as stones, which are not expected to be damaged in
compression.
88
Concrete damage plasticity
In this study, the concrete damage plasticity (CDP) model is considered to simulate concrete
failure due to cracking in tension and crushing in compression. The principal concepts and
background of damage theory, which led to concrete damage plasticity, are described here as
well as CDP. It is noteworthy that an initial model to explain concrete behaviour was a plastic
model that assumes concrete behaviour similar to that of steel. The main assumption of the
initial concrete plastic model is loading and reloading with the same initial stiffness that is not
completely reliable in the case of concrete cracks and fractures [82, 83].
Kachanov [84] first introduced the effective stress theory, a preliminary thesis to damage
theory, which considers damage to brittle material such as concrete. According to damage
theory, the strain in the damaged part under nominal stress is equal to that in the undamaged
part under effective stress. The tensors for nominal strain (σ) and effective strain (𝜎) are related
to each other by a scalar isotropic damage variable (ɷ) in the following equation:
σ = (1 –ɷ) 𝜎 3-5
The effective stress tensor can be written as Equation 3-6, where 𝐷0𝑒𝑙 is the initial undamaged
elasticity and ɛ𝑒 is the elastic strain tensor:
𝜎 = 𝐷0𝑒𝑙ɛ𝑒 3-6
Since the damage models do not consider plastic strain, a combination of plastic and damage
models are required to generate a more realistic model that can explain concrete behaviour
[84]. One of the main considerations in modelling concrete behaviour is considering a proper
yield function that considers both the plastic and damage behaviour of concrete and defines a
scalar relation between the variables for plastic stress and strain. The yield function can be
defined as follows (Equation 3-7), where σ and k are stress and stiffness, respectively [85]:
F = F (σ , k) 3-7
The behaviour of elasto˗plastic materials can be defined by considering the increment in the
yield function. For instance, the yield function increment defined as the derivative of the
function of the stress variables can demonstrate the material’s tendency to enter the plastic
phase (𝜕F/𝜕σ > 0) or remain in the elastic phase (𝜕F/𝜕σ ≤ 0). Figure 3-11 shows the yield
surface which determines the material’s elastic boundary and the yield function increment [86].
89
The plastic potential function in Figure 3-11 defines the surface that shows strain along the
direction of the increment.
Figure 3-11. Potential surfaces for the yield and plastic.
It is noteworthy that the yield function increment is based on a hardening rule, which is a
function of plastic strain. The increment vector of plastic strain was perpendicular to the tangent
of the plastic potential surface in the principal stresses field as shown in Figure 3-11. The plastic
flow rule defines a relation between the increment in stress and plastic strain based on the
plastic potential function, and is written as Equation 3-8:
d ɛ𝑝𝑙= λ × 𝜕𝑄 (𝜎)
𝜕𝜎 3-8
In the above, dɛ𝑝𝑙 is the increment in plastic strain, Q describes the potential plastic surfaces,
σ is the normal stress and λ is a positive coefficient [87]. The rules of plastic flow are
categorised as associated (Figure 3.11a) and non-associated flow rules (Figure 3.11b). The
plastic potential surface and yield surface are the same in the associated flow rule. This is why
the increment in the plastic strain vector and the normal vector of the yield surface were in the
same direction, as shown in Figure 3.11a [88].
The non-associated flow rule was applied to the case where the increment in the plastic strain
vector was not perpendicular to the tangent of the yield surface [88]. Hence, a potential plastic
90
surface was defined, and its normal vector and the plastic strain increment were in the same
direction, as shown in Figure 3.11b. These rules and function are needed to generate a more
realistic model to simulate plastic behaviour and damage to elasto˗plastic materials such as
concrete. Considering a suitable failure behaviour model for a concrete structure would yield
a more realistic simulation that could provide a better understanding of the concrete structures.
The failure function in the concrete damage plasticity model applies a combination of Lublinear
[85] model modified by Lee and Fenves [89] for the yield surface [90].
The Lubliner model [85], also called the Barcelona model, describes all damage characteristics
by a scalar damage variable based on fracture energy. However, this model cannot simulate
concrete damage behaviour in cyclic loadings because tensile and compressive damage cannot
be evaluated by using the same scalar damage variable. Hence, Lee and Fenves [89] modified
the Barcelona model by considering two separate parameters for tensile and compressive
damage. This allowed their model to simulate concrete under periodic loading. The yield
function is applied to the CDP model is as follows:
F = 1
(1−𝛼) {�̅� – 3α�̅�+ β (𝜎𝑚𝑎𝑥) – γ (–𝜎𝑚𝑎𝑥)} – 𝜎𝑐 3-9
in which
�̅� = – 1
3𝐼1̅ 3-10
𝐼1̅ = 𝜎11 + 𝜎22+ 𝜎33 3-11
�̅� = √3
2𝐼2̅𝐼2̅ 3-12
𝐼2̅ = 𝜎 + �̅�I 3-13
In the above, 𝑝 is the effective hydrostatic pressure that is calculated based on the first effective
stress invariant (𝐼1̅). The first effective stress invariant is equal to the summation of the stress
components along the principal diagonal directions of the Cauchy stress tensor. q is the
Von˗Mises equivalent effective stress that is calculated based on the second effective deviatoric
stress invariant (𝐼2̅), and 𝜎𝑚𝑎𝑥 and 𝜎𝑐 are the maximum principal effective stress and the
91
effective compressive stress, respectively. The parameters α, β and γ are calculated by the
following equations [90]:
α =
𝜎𝑏0
𝑓𝑐΄ − 1
2 𝜎𝑏0
𝑓𝑐΄ − 1
3-14
γ = 3 (1−𝐾𝑐)
2 𝐾𝑐−1 3-15
β = �̅�𝑐 (ɛ𝑐
𝑝𝑙)
�̅�𝑡 (ɛ𝑡𝑝𝑙
) (1 – α) – (1 + α) 3-16
To calculate α in Equation 3-14, 𝜎𝑏0
𝑓𝑐΄ , which is the ratio of the biaxial to the uniaxial compressive
failure stresses, is assumed to be 1.16 based (for concrete with a range of compressive strength
from 31 to 56 MPa) on Kupfer et al.’s investigation [91] (see Figure 3-12). Another parameter
considered to calculate γ is 𝐾𝑐, and is equal to the ratio of the second stress invariant on the
failure tension and the compression meridian. 𝐾𝑐 is assumed to be 2
3 based on the concrete
damage plasticity recommendation [90].
Figure 3-12. The relations among the principal stresses at failure [91].
92
Figure 3-13 shows failure surfaces in the deviatoric plane for different values of 𝐾𝑐, where 𝜎𝑐
and 𝜎𝑡 are the effective compressive and tensile stresses, which are functions of (hardening
variables) ɛ𝑐𝑝𝑙
(equivalent plastic strain in compression) and ɛ𝑡𝑝𝑙
(equivalent plastic strain in
tension).
Figure 3-13. The failure surfaces in the deviatoric plane for different values of 𝐾𝑐 [90].
Figures 3-14 and 3-15 show the parameters considered in the concrete damage plasticity model
in the tensile and compressive states of concrete behaviour. ɛ𝑐𝑖𝑛 is the compressive crushing
strain and 𝜀𝑡𝑐𝑘 the tensile cracking strain. The concrete compressive and tensile damage
variables (dc and dt) control the slope of reloading (for the concrete post-failure phase) in
Figures 3-14 and 3-15. The CDP model uses the damage variables to consider tensile cracks
and compressive crushes in concrete. The value of the damage variables can be calculated by
estimating the ratio of stress for the descending part of the curve to the ultimate concrete
strength [81, 92]. Due to the evaluation of the damage variables ɛ𝑐𝑝𝑙
(equivalent plastic strain in
compression) and ɛ𝑡𝑝𝑙
(equivalent plastic strain in tension) are assumed to be hardening variables
in the compression and tension evaluated by the following Equations 3-17 and 3-18 [92, 93]:
ɛ𝑐𝑝𝑙
= 𝜀𝑐𝑖𝑛– (
𝑑𝑐
1−𝑑𝑐
𝑓𝑐
𝐸0) 3-17
ɛ𝑡𝑝𝑙
= 𝜀𝑡𝑐𝑘 – (
𝑑𝑡
1−𝑑𝑡
𝑓𝑡
𝐸0) 3-18
93
Figure 3-14. Concrete damage parameters in compression.
Figure 3-15. Concrete damage parameters in tension.
In addition to the modified Barcelona model, the CDP model considers the Drucker–Prager
hyperbolic function for potential flow based on the non-associated flow rule [73]. The potential
flow function for the CDP model is as follows:
G = √( 𝜉𝜎𝑡0 tan𝜓)2 + �̅�2– �̅� tan ψ 3-19
94
In the above, Ψ is the dilation angle in the �̅�˗�̅� plane, as shown in Figure 3-16. The asymptote
of the hyperbolic potential flow function is the linear function, and tan ψ is the asymptote
inclination. 𝜉 is the eccentricity, and represents the rate at which the function approaches the
asymptote line. The hyperbolic function is linear when eccentricity is zero. The CDP model
assumes that eccentricity is 0.1 by default [73, 90].
Figure 3-16. Parameters of flow potential [15, 73].
The above-mentioned hardening variables (equivalent plastic strains) control the evolution of
the concrete yield or failure surface. Other parameters required to define the CDP model were
assumed based on past studies on concrete damage modelling and the recommendations of the
Abaqus package [73, 92, 93] (see Table 3-9).
Table 3-9. Parameters of the CDP model [73, 93].
Parameters Value
Dilation angle 36
Eccentricity 0.1
The ratio of the biaxial to the uniaxial compressive strength (𝑓𝑏0
𝑓𝑐0⁄ ) 1.16
The ratio of distances between the hydrostatic axis, and the tension and
the compression meridian in the deviatoric cross section (𝐾𝑐), respectively
0.667
Viscosity parameter 0
95
3.3.3. Steel modelling
Figure 3-17. Stress–strain curve of steel [94].
Figure 3-17 shows a typical stress–strain curve for structural steel, such as steel bars and
profiles. The proportional limit determines the point until which steel follows Hooke’s law,
which means that the stress is equal to the strain multiplied by the modulus of elasticity (Es).
The yield point represents the point at which there is a noticeable elongation without applying
more load.
Figure 3-18. Tri-linear stress–strain curve for steel material [95].
96
The ideal simplified tri˗linear graph (shown in Figure 3-18) has been proposed by Liang [95],
and can be applied to model the behaviour of steel. σs and εs are the stress and strain of the
material, respectively. The slope of the first straight line indicates the modulus of elasticity for
steel (Es), 𝑓𝑦 is its yield strength and εsy the yield strain. εst is the strain on the steel during
hardening, and 𝑓𝑠𝑢 and εsu are its ultimate strength and strain, respectively. εst and εsu were set
to 10εsy and 0.2, respectively [95].
3.3.4. FRP modelling
A combination of fibres and a matrix, which consisted of fibre reinforced polymers, was
assumed as homogeneous material. The characteristics of the materials in general can be
described according to Hooke’s law as follows [96, 97]:
𝜎𝑖𝑗= 𝐶𝑖𝑗𝑘𝑙𝜀𝑘𝑙 3-20
where:
[𝜎]= [
𝜎11 𝜎12 𝜎13𝜎21
𝜎31
𝜎22
𝜎32
𝜎23
𝜎33
] , [𝜀]= [
𝜀11 𝜀12 𝜀13𝜀21
𝜀31
𝜀22
𝜀23
𝜀23
𝜀33
] , C ijkl = C jikl and C ijkl = C jilk
In matrix and vector representation, Equation 3-20 can be written as follows:
σi = Cij εj 3-21
In the above, i , j = 1,2,...,6, and Cij = Cji (matrix stiffness expression) can be seen in the
following matrices:
[𝐶] =
[
𝐶11 𝐶12 𝐶13
𝐶22 𝐶23
𝐶33
𝐶14 𝐶15 𝐶16
𝐶24 𝐶25 𝐶26
𝐶34 𝐶35 𝐶36
𝑆𝑦𝑚𝑚𝑒𝑡𝑟𝑦
𝐶44 𝐶45 𝐶46
𝐶55 𝐶56
𝐶66]
3-22
Hence, there were up to 21 independent coefficients to define the properties of the material in
general. Orthotropic materials have nine independent coefficients in the stiffness matrix
97
(Equation 3-22) to describe their characteristics. The FRPs used in this study were considered
unidirectional, transversely isotropic lamina categorised as a special orthotropic material [98],
as shown schematically in Figure 3-19. Their material (stiffness) coefficients can be written as
following matrix (Equation 3-23) [99]:
[C] =
[ 𝐶11 𝐶12 𝐶12
𝐶12 𝐶22 𝐶23
𝐶12 𝐶23 𝐶22
0 0 0 0 0 0 0 0 0
0 0 00 0 00 0 0
𝐶44 0 0 0 𝐶44 0 0 0 𝐶66]
, C66 = 1
2 (𝐶11 − 𝐶12) 3-23
Figure 3-19. Unidirectional, transversely isotropic lamina [100].
Kaw [100] claimed that the material properties of a transversely isotropic material can be
expressed using engineering constants as
E2 = E3 , ν12 = ν23 , G12 = G13 , G23 = 𝐸2
2(1+ν23) 3-24
and the stiffness matrix for FRP is defined as follows:
98
Figure 3-20. Local and global coordinate axes.
To model FRP, which is not an isotropic material; the local coordinate axes must be defined
unless the main axes are assumed to be the FRP’s local coordinates. The local coordinate axes
are assigned to the FRP’s, the main directions of which are not parallel to x-axis of the global
coordinate. There is no need to define and assign local coordinate axes to the FRPs, as their
main axis is the x-axis, and their local coordinate axes and the main axes coincide. Figure 3-20
shows local coordinate axes assigned to the FRPs as well as the global axes.
99
3.3.5. Load applications and constraints
The load used for all specimens in this study was a uniformly distributed pressure load applied
to the column stub (Figure 3-21). The residual stresses of the prestressed FRPs had to be
initially considered to simulate the behaviour of RC slabs strengthened with prestressed FRP
plates. On the basis of experimental observation (which was also the basis of the numerical
modelling), there was no fracture or failure in the adhesive material, or between the adhesive
and the FRP or concrete. Hence, a tie bond between the FRP and concrete was assumed in the
numerical models. When there is a possibility of bond failure (due to adhesive fracture),
cohesion contact needs to be defined to simulate the behaviour of the adhesive material. All
steel reinforcements and stirrups were embedded in the concrete slab.
Figure 3-21. Boundary condition and loading situation in the FEM modelling of slab R0.
The FRP sheets of some models in this study were prestressed. Their residual or initial stresses
were defined in the load module by applying predefined stress. Two methods are available in
Abaqus to consider initial stresses in FRP sheets or plates, direct specification and the output
data base file. In the direct specification method (applied in this study), the stress values in the
different local axes of the material are evaluated by considering the properties and dimensions
of the material as well as the load applied to prestress the FRPs. In the output database file, the
FRPs are analysed by Abaqus separately (before analysing the entire model) and the results are
imported from the database file to consider the residual stresses.
100
3.3.6. Finite element type and mesh
Abaqus contains a library of elements where each describes different characteristics. There are
different families of elements in the Abaqus library, such as continuum, shell and truss, as
shown in Figure 3-22. The different shapes of the continuum element are shown in Figure 3-
23. It is recommended that hexahedral elements (Figure 3-23) be used for continuum elements
for more realistic results with shorter processing times [101]. The wedge, pyramid and
tetrahedral elements (Figure 3-23) can be used when it is not possible to use hexahedral
elements due to the complicated geometry of the models [101].
Figure 3-22. The elements in the Abaqus library [101].
Figure 3-23. The different shapes of the continuum element [101].
In this study, the partitioning of the finite element models by datum plane (as shown in Figure
3-24), to use hexahedral elements, is necessary to analyse the structure. It is noteworthy the
order of interpolation was defined by considering the number of nodes of the elements. Figure
3-25 shows the three-dimensional (3D) elements of different orders. The elements that only
have nodes in the corners (Figure 3-25a); called linear or first-order elements, use a linear
interpolation in each direction. The elements with intermediate nodes, called quadratic or
second-order elements, (Figure 3-25b and c) apply second-order interpolation to analyse
element behaviour. It is noteworthy that a hexahedral linear element was chosen in this study
101
to simulate the 3D parts of the samples, as hexahedral quadratic elements are not available in
the Abaqus/Explicit package [101].
Figure 3-24. Finite element model partitioning.
Figure 3-25. First- and second-order 3D elements [101].
The explicit procedure was preferred primarily because of the difficulty in convergence when
applying implicit methods (in Abaqus/Standard) to simulate samples exhibiting nonlinear
behaviour and complexity in the nature of contact, which occurs because of the large number
of iterations required to satisfy the equilibrium conditions of the equations. However,
Abaqus/Explicit does not iterate to determine the solution and satisfy the stability of the
structure in any increment by considering the stable state given its previous increment, which
enhances the software’s capability to reach a convergent solution. Hence, the Abaqus/Explicit
102
package is more efficient for modelling samples with nonlinear and complicated contact
behaviours [101]. Shorter time required and smaller space needed for the explicit procedure,
compared with the implicit method, is another advantage of applying the Abaqus/Explicit
package to simulate the behaviour of nonlinear samples.
Abaqus applies numerical integration methods to evaluate the structural response of the
elements. It uses the Gaussian quadratic method to calculate the response of the material at
each integration point for most elements. The method of integration for the elements can be
classified as fully integrated or reduced integration. For the element subjected to reduced
integration, there is one integration node fewer in each direction compared with fully integrated
elements [101]. Figure 3-26 shows the 2D fully integrated elements and those subjected to
reduced integration for both linear and quadratic elements along with the positions of the
integration nodes.
Figure 3-26. Reduced and fully integrated methods [101].
Applying elements using different methods of integration may affect the simulation results. For
example, applying linear elements with the full integration method in the simulation can cause
the shear locking issue, which increases the bending stiffness of the elements [101, 102]. The
element under a pure bending moment should naturally be deformed as shown in Figure 3-27
[103]. Since the angles between the dotted lines have not been altered (Figure 3-27), the shear
stress at the integration points is zero. However, the linear fully integrated element was
deformed, as shown in Figure 3-28, and could not simulate the real behaviour of elements
because of the changing angles between the dotted lines. This phenomenon results in shear
103
stress at the integration points that is not appropriate for an element under pure bending moment
[102].
Figure 3-27. The natural deformation of an element under a pure bending moment.
Figure 3-28. The deformation of a fully integrated linear element under a pure bending moment.
The above-mentioned problem can be avoided by using elements subjected to the reduced
integration method. Figure 3-29 shows a linear element subjected to reduced integration under
pure bending. As shown in Figure 3-29, the angle between the dotted lines (at the intersection
of the dotted lines, which is the point of element integration) was not changed after bending,
which might have simulated the natural deformation scenario that should obtain for an element
based on the concepts of structural analysis [103]. Most elements with reduced integration have
the letter “R” at the end of their name, such as C3D8R.
Figure 3-29. The deformation of a linear element subjected to reduced integration under a bending moment.
104
The elements subjected to reduced integration may be too flexible due to a numerical problem
called hour-glassing. As shown in Figure 3-29, the length of the dotted lines as well as the
angles between them do not change, which might have resulted in zero stress components at
the integration point. The Abaqus software considers synthetic stiffness for elements subjected
to reduced integration to overcome this issue. This strategy can be useful when applying
relatively fine mesh. Another benefit of applying fine mesh is to reduce the possibility of
element distortion. Hence, it is proposed that fine, reduced integrated linear elements, such as
C3D8R, be used to simulate continuum elements in the case of models with high distortion to
avoid both shear locking and hour-glassing issues.
The types of elements chosen to simulate the different materials of the samples in this study
were as follows: The C3D8R (solid continuum 3D eight-node element with reduced
integration) elements were employed to analyse the linear or nonlinear behaviour of concrete
by considering the parameters of plasticity, interactive characteristics and large deformations.
The S4R (Shell four-node element with reduced integration) elements were applied to model
the FRP plate structures, where variations in their stress in their third dimension (thickness)
were negligible. It is noteworthy that the direction of the shell element must be defined by
assigning a local coordinate system, as shown in Figure 3-14. Since the main duty of steel
reinforcements is to transfer the axial forces, the T3D2 (Truss 3D two-node element) is the
element used to model steel bars.
3.3.7. Mesh convergence
The results of the numerical models depend on mesh size. Increasing the number of elements
may enhance the accuracy of modelling and the possibility of reaching convergent results.
However, the reduction in element size increases computation time and the space required to
achieve convergent results. Thus, the mesh refinement process should be iterated to determine
the proper mesh size to provide a convergent result such that variation by reducing mesh size
is negligible. In this study, mesh sensitivity analysis was conducted on each sample to find the
most compatible element size that could satisfy the requirement for consistency between the
results of the experiments and the finite element analysis and save computation time.
105
Figure 3-30. Mesh sensitivity analysis of samples R-F0 and RC-F0.
Figure 3-30 shows an example of a comparison between the load˗deflection curves of the
experimental and the finite element models for samples R-F0 and RC-F0 by varying element
size, which highlights the convergence of the results obtained in the finite element models. As
it can be seen from Figure 3-30, the approximate mesh sizes have been chosen are 20 mm, 15
mm and 10 mm. The results demonstrate that the difference between the results gained from
numerical samples with 15 mm and 10 mm as mesh size are negligible. By considering Figure
3-30 and applying mesh sensitivity analysis to all other samples studied by Abdullah [15] and
Kim et al. [16], 15 mm was chosen as the proper mesh size to simulate all slabs mentioned in
this chapter.
3.3.8. Validation of finite element models
A comparison between the numerical models and the experimental results can help verify finite
element modelling. Table 3-10 shows a comparison between numerical results obtained by the
finite element modelling by the author in this study and experimental results obtained by both
Abdullah [15] and Kim et al.’s [16]. The numerical results for the differences between the
106
numerical and the experimental results (for all measured parameters, such as load and
deflection) showed reasonable accuracy. There were no cracks within the adhesive material
and at the interface of the adhesive material and the FRP or concrete during the experimental
tests (before the ultimate load capacities of the slabs were reached) due to the high strength of
the adhesive material and the use of a proper bonding technique. The steel reinforcements were
simulated by the truss elements, and yielded when the principle stress exceeded the yield
strength of steel.
Table 3-10. Comparison between numerical and experimental results.
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
EXP FEM EXP FEM EXP FEM
R0 171.6 185 284 247 27.3 28.1 Flexural
R-F0 273.4 265 405 357 21.4 23.9 Flexural punching
R-F15 240 275 240 275 15.2 17.2 De-bonding
R-F30 220 252 220 252 16.3 15.6 De-bonding
R2-F30 307 330 307 332 14.8 15.9 De-bonding
RC0 316 290 376 368 24.0 24.7 Punching
RC-F0 362 340 411 420 21.7 22.5 Punching
RC-F15 307 365 443 455 22.4 20.5 Punching
None of the samples failed due to FRP rupture, which shows that the FRP plates did not reach
their maximum tensile strength. To consider the evolution of concrete failure, the finite element
models used two internal variables, compressive damage (DAMAGEC) to observe
compressive crushes and tensile damage (DAMAGET) to record tensile cracks. According to
an assessment of compressive and tensile damage, plastic strains could be observed
(considering the CDP model) to compare crack propagation in the numerical and the
experimental samples. Figures 3-31 and 3-32 show the load-deflection curves of the
experimental results and the finite element models.
The curves show a reasonable consistency between the numerical and the experimental results.
The RC slabs strengthened with FRP plates exhibited a slightly larger initial stiffness than the
control specimen. The experimental and validated numerical results are analysed in the
107
following section to clarify the strengthening mechanism of strengthened and un-strengthened
flat slabs.
Figure 3-31. Load˗deflection curves of the experimental results and the finite element models in Abdullah’s study.
108
Figure 3-32. Load˗deflection curves of the experimental results and the finite element models in Kim et al.’s study.
3.4. Analysis and discussion of results
In the case of a fully composite action, failure modes can be classified as pure flexural, flexural
punching and pure punching failures. Flexural failure occurs due to steel reinforcement
yielding (that causes tensile cracks), which can be followed by FRP fracture; flexural punching
failure occurs due to partial steel yielding followed by concrete compressive crushing. Higher
ductility of the samples has been observed in pure flexural and flexural punching failures than
in brittle punching failures, which occur in cases with comparatively high tensile
reinforcements.
According to experimental and numerical results, the failure mode of the control specimen (R0)
is a flexural failure that occurs due to the wide development of yield lines (that occurs after
109
steel reinforcement yielding) on the tension surface. Figure 3-33 shows the development of the
yield lines with wide flexural cracks in R0, which results in ductile flexural failure. Figure 3-
34 shows the propagation of concrete tensile cracks in the RC0 slab section.
Figure 3-33. Concrete cracks in R0.
Figure 3-34. Tensile crack propagation (Tension damage) in R0.
The behaviour of RC0 (the control specimen in Kim et al.’s study) was different from R0 (the
control specimen in Abdullah’s study) due to the higher tensile reinforcements in the former.
The failure mode of the RC0 specimen was a punching failure caused by concrete compressive
110
crushing in the column vicinity due to a high tensile reinforcement ratio. Figure 3-35 shows
the RC0 cracks in the experimental and the finite element models.
Figure 3-35. Concrete cracks in RC0.
Compared with the un-strengthened sample (R0), a considerable improvement in the load
capacity of R-F0 was observed due to the enhancement of the tensile resistance of the critical
section in the column vicinity by FRP strengthening. The numerical and experimental results
showed that the failure mode of the sample was flexural punching failure, which occurs due to
partial tensile steel reinforcement yielding, and is followed by concrete compressive crushing.
Figure 3-36 shows the failure process, where a combination of tensile crack propagation and
compressive crushing prevails.
By installing FRP plates on the tensile surface of the concrete slab, the effective tension area
and the tensile resistance of the strengthened section increased compared with those of the
control specimen. When the overall tensile reinforced ratio (due to contributions from both
steel reinforcement and the FRP plates) exceeded a critical value (balanced reinforced),
compressive plastic strains could have developed in the compression zone before the
propagation of tensile cracks. This resulted in a descending of the neutral axis to a lower level
(compared with R0) to balance the compressive and tensile forces, and the reinforced concrete
might have failed in compression rather than tension. This process can increase the maximum
load capacity in the FRP strengthened area and decrease the ductility of the failure mode.
Failure progression outside the FRP strengthened area was different from that considered the
FRP-rehabilitated zone. Outside the FRP-reinforced zone, flexural cracks were initiated by
111
partial steel reinforcement yielding and propagated by shear stresses. Due to the formation and
propagation of the tensile cracks, the neutral axis ascended to a higher level than the neutral
axis before cracking.
Figure 3-36. Stress distribution and sectional analysis of flexural punching failure mode.
However, in the FRP strengthened area, the applied plates could have substituted the yielded
steel reinforcements to bear the excess tensile stresses, and there was no need to increase the
neutral axis to a higher level to allow more concrete to sustain the extra tensile stresses. After
the partial yielding of the steel reinforcements (outside the FRP strengthened zone), parts of
112
the concrete that had not cracked participated in carrying the tensile loads instead of the yielded
reinforcements, which was the primary reason for the ascent of the neutral axis. The low
concrete resistance in tension and shear stresses caused the tensile cracks to propagate (see
Figure 3-36) and join the compression crushing area in the column vicinity to form long cracks
that caused flexural punching failure. The flexural punching failure in R-F0 was due to partial
FRP strengthening on the tension surface of the slab in the column vicinity. The strengthened
sample showed more brittle failure than the control specimen, which can be seen in their
load˗deflection curves in Figure 3-32. Figure 3-37 shows concrete cracks in the finite element
and the experimental models of R-F0.
Figure 3-37. Concrete cracks in R-F0.
Figure 3-38. Concrete cracks in RC-F0.
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With regard to RC-F0 in Kim et al.’s study, it suffered punching failure due to its high tensile
reinforcement ratio, including both steel reinforcements and the FRP sheets. Figure 3-38 shows
the concrete cracks and crushes on the tension surface of the RC-F0 slab. It is noteworthy that
FRP strengthening in both studies enhanced the load capacity of the control specimens, but
there was a controversy in the case of slabs strengthened with prestressed FRP. The main issue
here was why strengthening RC slabs with prestressed FRP in Kim et al.’s [16] study efficiently
improved sample load capacity, but applying prestressed FRP in Abdullah’s [15] study caused
FRP de-bonding, and the samples had been unable to attain their expected ultimate load
capacity.
To analyse RC slabs strengthened with prestressed FRP, the effect of applying prestressed FRP
to strength the specimens is briefly explained here. Prestressing the FRP plates increases the
effective sectional area with residual tensile stress and leads to higher bending resistance in the
section due to transverse loading compared with non-prestressed FRP in principle. The slabs
strengthened with prestressed FRP could have greater load capacity in theory than those
strengthened with non-prestressed FRP. The experimental and numerical results for the RC
slab strengthened with prestressed FRP in Kim et al.’s work (RC-F15) showed an improvement
in the load capacity of the slabs in comparison with both control specimens (RC0) and RC-F0.
This result supports, to some extent, the claim pertaining to RC structures strengthened with
prestressed FRP.
However, the behaviour of samples strengthened with prestressed FRP plates in Abdullah’s
work were different from the scenario described in the case of RC-F15: the ultimate failure
load of the slabs with prestressed FRP plates had even lower loading capacity than slabs with
non-prestressed FRP plates (see both the experimental and the numerical results in Table 3-
10).
To explain the behaviour and failure mode of the RC samples strengthened with prestressed
FRP, it should be pointed out that the success of the composite structures is entirely related to
full composite action. When an FRP strengthened concrete sample is used as a unified
structure, the forces must be properly transferred from concrete to the FRP plates, or vice versa.
A common reason for the loss of a composite action in FRP strengthened RC slabs is FRP de-
bonding. Most de-bondings occur locally. When local de-bonding propagates, the composite
action can be lost and the FRP plates cannot carry any more load. Therefore, to correctly
114
simulate the behaviour of an FRP strengthened structure, it is vital to consider the de-bonding
failure mechanism.
As mentioned in the literature review (Section 2.5.1.2) de-bonding failure can happen in
different layers of FRP strengthened RC slabs. Bearing this in mind and rechecking the failure
category in this study it was observed that there was no de-bonding in the adhesive layer and
at the interfaces of the adhesive and the FRP or concrete, whereas de-bonding did occur in the
concrete layer. Both R-F15 and R-F30 (their concrete properties were the same as that of the
control specimen) failed due to de-bonding in the concrete, and there was no significant
increase in the load capacities of the samples. Hence, the numerical and sectional analyses
considered here are intended to clarify the main mechanism of such de-bonding, which is
necessary for us to understand the behaviour of RC samples strengthened with prestressed FRP.
Further observation concerning the experimental tests has confirmed that concrete fracture
causes FRP de-bonding near the end plate. The finite element simulation of the strengthened
samples with prestressed FRP revealed that the concrete fracture was in turn caused by a
combination of tensile stresses in the domain of the above steel reinforcement, and below the
neutral axis (which could not have been avoided with the anchorage system used) and the shear
stress around the neutral axis.
Near the FRP endplate, stress transfer from the prestressed FRP developed a local compression
zone near the concrete surface, and a local tension zone above the steel reinforcements and
below the primary neutral axis of the concrete section. The primary neutral axis was the neutral
axis of the entire section, and the local neutral axis was the neutral axis created locally in the
concrete section around the FRP-prestressed plate by applying prestressed FRP (see Figures 3-
39 and 3-40).
The numerical simulation (Figure 3-39) shows how the stress distribution and redistribution
led to this failure mode. It is noteworthy that the position of the neutral axis can be traced by
considering the sign change of the stresses from positive in tension to negative in compression,
and vice versa. Figure 3-40 (based on Figure 3-39) schematically shows how applying
prestressed FRP can change the position of the primary neutral axis.
According to Figures 3-39 and 3-40, the primary neutral axis of the slab section was lifted to
the area above the FRP end plates. The tensile stress superposition of the global and the local
tension zones as well as the local compression zone (due to applying the prestressed FRP and
115
the prestressed FRP՚s elongation when external load is applied), which occupied an area in the
initial global tension zone, were the main reasons for lifting the primary neutral axis to balance
the tensile and compressive stresses near the end plate. Since the shear stresses reached their
maximum magnitude near the neutral axis, they had both the primary and the local neutral axes
that created two areas eligible for the development of shear cracks near the top and bottom of
the slab, which could increase the possibility of concrete fracture.
Figure 3-39. Slab section at the position of the prestressed end plate.
116
Figure 3-40. The stress zones and neutral axes across the section of slabs at the prestressed FRP end plate.
Figure 3-41. Distributions of normal stresses in the concrete section near the end plate.
Figure 3-41 clarifies the distribution of normal stresses by considering the effect of prestressed
FRP installation and the application of external load on the column stub. Figure 3-41 considers
a combination of stress analysis that includes the effect of applying the prestressed FRP plate
and the external load on the column stub near the FRP end plate. According to Figure 3-41, the
superposition of tensile stresses in the local tension zone caused by the applied prestressed FRP
and its elongation (owing to external load) as well as those created by applying external load
to the column stub enhanced the overall tensile stress level in the region above the steel
reinforcements and below the primary neutral axis.
117
The above mentioned process might first have led to concrete flexural cracks in the
superposition zone of two tensions (global and local) when the overall tensile stresses exceeded
the tensile strength of concrete. The flexural cracks joined the shear cracks near the neutral
axes. The shear cracks were initiated due to shear stresses (which reached their maximum
around the neutral axis) and could propagate, especially when there was no shear
reinforcement. The flexural-shear cracks in the concrete were initiated by flexural cracks, and
developed due to the shear stresses. The crack propagation caused concrete fracture, which in
turn led to the de-bonding of the FRP plates.
Figure 3-42. Flexural-shear cracks cause de-bonding near the end plate in R-F30.
Figure 3-43. Concrete cracks on the tension surface of R-F15.
118
The flexural-shear concrete cracks, which caused the de-bonding of the FRP plates, are shown
in Figure 3-42. Figures 3-43 and 3-44 show concrete fracture near the FRP end plate in R-F15
and R-F30 that caused de-bonding.
Figure 3-44. Concrete cracks in R-F30.
Increasing the prestressing ratio of FRP can increase the tensile stresses of the local zone, which
enhances the tensile stress level after stress superposition and can increase the possibility of
earlier de-bonding. R-F15 and R-F30 had the same concrete properties as the control specimen
and the non-prestressed FRP strengthened sample (R0 and R-F0), and FRP de-bonding was the
main cause of the slabs not being able to reach their expected ultimate load capacity at full
composite action. Increasing the FRP-prestressing ratio from 15% in R-F15 to 30% in R-F30
had an adverse effect on load capacity, which explains why the loading capacity of R-F30 was
even smaller than that of R-F15 (see Table 3-10).
The comparison between the R-F30 and R2-F30 samples shows that there can be a direct
relation between concrete tensile strength and the ultimate load capacity of an RC slab
strengthened with prestressed FRP under the failure mechanism of FRP de-bonding (see Table
3-11), since the only difference between these two specimens was in their concrete properties.
They were both strengthened with 30% prestressed FRP plates, and their failure modes were
all FRP de-bonding. However, as the concrete tensile strength increased from 3.39 MPa in R-
F30 to 4.53 MPa in R2-F30, the experimental and numerical results for R2-F30 showed 39%
and 32% enhancement in load capacity, respectively, in comparison with those for R-F30.
119
Table 3-11. A comparison between R-F30 and R2-F30 in terms of load capacity.
Slab Concrete
tensile
strength
Concrete tensile
strength
increase
Ultimate load
capacity
(EXP)
Ultimate load
capacity
increase (EXP)
Ultimate load
capacity
(FEM)
Ultimate load
capacity increase
(FEM)
R-F30
R2-F30
3.39
4.53
34%
220
307
39%
252
332
32%
The consistency between the increment in the percentage of the concrete tensile strength and
that in the ultimate load capacity can show that the ultimate load capacity of the RC slab
strengthened with prestressed FRP correlated well with the concrete tensile strength in the case
of earlier de-bonding failure. Another parameter that seemed effective for the ultimate load
capacity of slabs strengthened with prestressed FRP, and had failed in earlier de-bonding due
to concrete fracture, is slab depth considered in the numerical models. Table 3-12 shows the
effect of slab depth on the load capacity of R-F30 by keeping all other parameters constant and
varying slab depth in light of the validated numerical results.
Table 3-12. The effect of varying slab depth with ultimate load capacity in case of earlier de-bonding.
Slab Concrete tensile
strength
Slab depth
(mm)
Slab depth
increase
Ultimate load
capacity (FEM)
Ultimate load capacity
increase (FEM)
R-F30
R-F30 (200)
3.39
150
200
33%
252
322
28%
The consistency between the enhancement in the percentage of the slab depth and that in
ultimate load capacity shows that slab depth is positively correlated with the ultimate load
capacity of the RC slab strengthened with prestressed FRP in the case of earlier de-bonding. It
is noteworthy that the steel reinforcement ratio did not considerably affect the results of the
slabs strengthened with prestressed FRP and had failed in earlier de-bonding (due to concrete
fracture), considering the numerical models and explanations of the mechanism. This might
have obtained because the steel reinforcements (which could have been locally affected by the
prestressed FRP) were located near the local neutral axes (see Figures 3-41), which is not an
efficient position to bear the applied forces.
120
As mentioned above, the RC slab strengthened with prestressed FRP in Kim et al.’s study (RC-
F15) showed an improvement in its load capacity over the control specimen (RC0) and the slab
strengthened with non-prestressed FRP (RC-F0). However, no RC slab strengthened with
prestressed FRP in Abdullah’s study reached its expected ultimate load capacity due to FRP
de-bonding. Noting that the analysis of the mechanism of RC slabs strengthened with
prestressed FRP should be applicable to both Abdullah and Kim et al.’s studies, it is not clear
why a controversy persists, in spite of acceptable explanations (considering the experimental
and numerical models) for both contradictory results.
As mentioned above, the main reason for not obtaining the expected ultimate load capacity in
the samples strengthened with prestressed FRP in Abdullah’s study was FRP de-bonding due
to concrete fracture near the FRP end plate, where the stress state was the superposition of
tensile stresses due to the application of external load on the column and stress transfer from
prestressed FRP, as shown in Figure 3-39. The finite element model (see Figure 3-45) shows
that the same scenario that obtained for slabs strengthened with prestressed FRP in Abdullah’s
study (Figures 3-39 and 3-40) occurred for slab RC-F15, which was strengthened with
prestressed FRP in Kim et al.’s study. However, the analysis of numerical stress and the
experimental results shows that there was no FRP de-bonding in RC-F15, despite the use of
slabs strengthened with prestressed FRP in Abdullah’s study. The reasons for this phenomenon
need to be explained by considering the effective parameters involved to clarify the feasibility
of applying prestressed FRP to strengthen RC slabs.
Figure 3-45.Slab section at the position of prestressed end plate in RC-F15.
The effective parameters, including the characteristics of the RC slab such as concrete strength
and slab depth as well as the properties of the prestressed FRP used to explain the reasons for
121
the phenomenon mentioned above, were considered. Table 3-13 makes a comparison among
the effective parameters in different samples.
Table 3-13. Comparing the samples strengthened with prestressed FRP based on their effective parameters.
Experimental
study
Sample Concrete tensile
strength (MPa)
Slab depth
(mm)
FRP cross-
section (mm2)
FRP
prestressed
ratio
𝐹𝑓𝑟𝑝
(kN)
𝐹𝑓𝑟𝑝
𝑤𝑓
(kN/m)
Failure
mode
Abdullah
R-F15 3.39 150 100×1.2 15% 62 620 De-bonding
R-F30 3.39 150 100×1.2 30% 103 1030 De-bonding
R2-F30 4.53 150 100×1.2 30% 103 1030 De-bonding
Kim et al. RC-F15 3.22 150 150×0.33 30% 30 200 Punching
As evident from Table 3-13, the slab depth (D) (one of the effective parameters to enhance slab
resistance against earlier de-bonding) was the same for all specimens. Moreover, the concrete
tensile strength was almost the same in RC-F15 as in some samples (R-F15 and R-F30) failed
by FRP de-bonding. Hence, the difference in concrete tensile strength and/or slab depth seemed
not to be the main reason for the contradictory results in Abdullah and Kim et al.’s studies.
From Table 3-13, it can be observed that 𝐹𝑓𝑟𝑝
𝑤𝑓 (which was the applied load on the prestress
FRPs per unit FRP width) explains the varying behaviour, whereas the controversy seems to
lie in the results. Suppose 𝑥𝑓 is the percentage of the prestressing of FRPs, 𝑢𝑓 is the ultimate
strength of the FRP in tension, 𝑡𝑓 is the thickness of the FRP and 𝑤𝑓the width, 𝐹𝑓𝑟𝑝
𝑤𝑓 and 𝑓𝑓𝑟𝑝
(FRP-prestress level) are calculated as follows (Equations 3-26 and 3-27):
𝐹𝑓𝑟𝑝
𝑤𝑓 = 𝑥𝑓× 𝑢𝑓× 𝑡𝑓 3-26
𝑓𝑓𝑟𝑝 = 𝑥𝑓× 𝑢𝑓 3-27
As seen in Table 3-13, 𝐹𝑓𝑟𝑝
𝑤𝑓 in the slabs strengthened with prestressed FRP in Abdullah’s study
was at least three times greater than that for RC-F15. The greater magnitude of (𝐹𝑓𝑟𝑝
𝑤𝑓) in
Abdullah’s samples caused an enhancement in the superposition of tensile stresses (as
mentioned in Figure 3-41) compared with Kim et al.’s slab (RC-F15). As the superposition of
tensile stresses in Abdullah’s samples exceeded the concrete tensile strength (see Figure 3-
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46a), concrete fracture near the FRP end plate occurred, which resulted in FRP de-bonding,
and the samples could not attain their expected ultimate load capacity. The smaller magnitude
of (𝐹𝑓𝑟𝑝
𝑤𝑓) in Kim et al.’s sample caused the superposition of tensile stress not to exceed the
concrete tensile strength (see Figure 3-46b).
Figure 3-46. The stress distribution in RC slab strengthened with prestressed FRP.
This is why the slab strengthened with prestressed FRP in Kim et al. did not experience
concrete fracture (which can result in FRP de-bonding), and could reach its expected ultimate
load capacity. Taking everything into consideration, the efficiency of strengthening the RC
slab with prestressed FRPs depends on whether the superposition of tensile stresses in Figure
3-46 reaches the concrete tensile strength. If the above-mentioned superposition reached the
concrete tensile strength (Figure 3-46a), the strengthened sample might have experienced FRP
de-bonding due to concrete fracture and, consequently, the slab would not have reached its
expected load capacity.
However, if the superposition of the tensile stresses does not reach the concrete tensile strength
(Figure 3-46b), no concrete fracture occurs (to cause FRP de-bonding). Moreover, an
123
improvement obtains in the slab’s maximum load capacity (compared with non-strengthened
samples as well as those strengthened with non-prestressed FRPs), which is expected in classic
structural theories. Hence, a higher (𝐹𝑓𝑟𝑝
𝑤𝑓) may increase the possibility of FRP debonding due
to concrete fracture in samples strengthened with prestressed FRP.
Furthermore, the overall analysis of the results shows that the effective parameters used to
determine the behaviour of RC slabs strengthened with prestressed FRP can be classified into
two categories. The first consists of effective parameters that may increase slab strength to
resist earlier de-bonding (due to concrete fracture) which are concrete tensile strength (see
Table 3-11) and slab depth (see Table 3-12). The second category consists of parameters that
can enhance the possibility of earlier de-bonding (such as 𝑥𝑓, 𝑢𝑓 and 𝑡𝑓) represented by 𝐹𝑓𝑟𝑝
𝑤𝑓
(see Table 3-13 and Equation 3-26). Classifying and analysing these parameters may yield
comprehensive results to propose a formula that proposes an FRP-prestress ratio to strengthen
the RC slab, which enhances the slab’s ultimate load capacity without causing earlier de-
bonding.
3.5. The optimum FRP-prestress ratio to strengthen RC slabs
The explanation provided above states that the enhancement in FRP-prestress ratio 𝑥𝑓 (which
was positively correlated with 𝐹𝑓𝑟𝑝
𝑤𝑓 considering Equation 3-26) in RC-F15 (that did not fail in
FRP de-bonding due to concrete fracture) might have caused FRP de-bonding. Furthermore, a
reduction in the FRP-prestress ratio (𝑥𝑓) in samples strengthened with prestressed FRP in
Abdullah’s study (which failed in FRP de-bonding as a result of concrete fracture) might have
changed the samples’ failure mode and led to an improvement in their ultimate load capacity.
To justify this claim, the following graphs (see Figure 3-47) are provided by varying the FRP-
prestress ratio in samples R-F15 and RC-F15 and measuring their load capacities. All other
parameters and dimensions of the slabs were kept constant to observe the effect of the FRP-
prestress ratio on the load capacity of the strengthened slabs. The graphical data was collected
124
from finite element models, and their accuracy was confirmed in light of the experimental
results of this study.
Figure 3-47 shows that varying the FRP-prestress ratio can change the behaviour of FRP
strengthened slabs, such as load capacity and failure modes. As shown in Figure 3-47, the load
capacity of the samples increased in the ascending parts of the curves by the enhancement of
the FRP-prestress ratio. The failure mode of the samples in the ascending parts of the curves
represents punching failure. The curves continue ascending to reach the point where the
strengthened sample determines the maximum load capacity. This point can be called the
optimum FRP-prestress ratio for the FRP strengthened slab. When the curves exceeded their
optimum FRP-prestress ratio, they began descending. In the descending parts of the curves, the
enhancement of FRP-prestress ratio decreases the slab’s load capacity, and the samples’ failure
mode changes from punching failure in the ascending part to FRP de-bonding due to concrete
fracture near the FRP end plate.
Figure 3-47. The slabs failure mode by varying the FRP-prestress ratio.
Hence, the FRP-prestress ratio can determine the efficiency of applying prestressed FRPs to
strengthen RC structure. In other words, there is an optimum prestress ratio for the FRPs. The
enhancement of the FRP-prestress ratio up to the optimum point improves load capacity.
125
However, a further increase of the FRP-prestress ratio (beyond the optimum point) may cause
FRP de-bonding, and the strengthened RC structure cannot reach its expected load capacity
(see Figure 3-47). Therefore, an estimation of the optimum FRP-prestress ratio is valuable
which will be beneficial to the efficient application of prestressed FRP and can provide useful
design recommendations and selections. To this end, a formula is proposed to evaluate such an
optimum FRP-prestress ratio by considering the results of finite element modelling.
As shown in Figure 3-47, the failure modes of both curves in their ascending parts represent
punching failure; and when the curves reached their descending parts, their failure modes
changed from punching to de-bonding. Increasing the FRP-prestress ratio increases the load
capacity of the strengthened samples if it does not cause FRP de-bonding. To confine the
loading capacity to the ascending part of the curves, the optimum point should be positioned at
the transition point from punching to de-bonding failures. In other words, the optimum FRP-
prestress ratio is the point at which there is a balance among the parameters causing and
resisting FRP de-bonding to reach the highest load capacity with full composite action.
Therefore, the first step to estimate the optimum FRP-prestress ratio involves considering
parameters that may affect FRP de-bonding in samples strengthened with prestressed FRP. The
explanations and mechanism identified so far show that the effective parameters can be
classified as follows:
• Parameters the increase in the values of which can improve the resistance of the slab to
earlier de-bonding—the concrete tensile strength and slab depth (considering Tables 3-
11 and 3-12).
• Parameters the increase in the values of which can cause earlier de-bonding, FRP
thickness (𝑡𝑓), the ultimate strength of FRP (𝑢𝑓) and the FRP prestress ratio (𝑥𝑓), which
are represented by their product (𝐹𝑓𝑟𝑝
𝑤𝑓) (considering Equation 3-26 and Table 3-13).
If the FRP-prestress ratio is equal to the optimum FRP-prestress ratio, a balance is obtained
among all the above-mentioned parameters causing and resisting FRP de-bonding. As a main
objective of this section is to evaluate the optimum FRP-prestress ratio, all effective parameters
were numerically varied one by one to find an optimum FRP-prestress ratio for the maximum
loading capacity by balancing all parameters causing and resisting FRP de-bonding under
126
specified parameter combinations. Figure 3-48 shows the effective parameters and their values
in samples R-F15 and RC-F15.
Figure 3-48. The optimum FRP-prestress ratio for different sets of effective parameters.
127
As can be seen from Figure 3-48, there were 12 sets of variables for each group. Each branch
in Figure 3-48 provides a set of effective parameters with an exclusive optimum FRP-prestress
ratio. The optimum FRP prestress ratio for each set of variables was found by considering
different FRP-prestress ratios and monitoring the one with the highest improvement in the
slab’s load capacity, which provides balance in parameter design. The FRP tensile strengths
were kept constant (2970 MPa and 3800 MPa in R-F15 and RC-F15, respectively) during
variable analysis. It is noteworthy that the concrete tensile strength and slab depth were varied
such that their individual and product effects on slab behaviour could be examined.
Table 3-14. Different variable sets with the same multiplication of concrete tensile strength and slab depth.
Sample
group
Concrete tensile
strength (𝑓𝑡΄)
(MPa)
Slab depth
(D)
(mm)
𝑓𝑡΄ × D
(MPa.mm)
FRP thickness
(𝑡𝑓)
(mm)
FRP tensile
strength (𝑢𝑓)
(MPa)
𝑡𝑓× 𝑢𝑓
(MPa.mm)
Optimum FRP
prestress ratio
(𝑥𝑜𝑓)
R-F15
4 150 600 0.6 2970 1782 17%
5 120 600 0.6 2970 1782 18%
4 150 600 1.2 2970 3564 9%
5 120 600 1.2 2970 3564 8.5%
RC-F15
4 150 600 0.33 3800 1254 21%
5 120 600 0.33 3800 1254 24%
4 150 600 0.9 3800 3420 8%
5 120 600 0.9 3800 3420 9.5%
As stated above, concrete tensile strength (𝑓𝑡΄) and the slab depth (D) are both parameters whose
values could be increased to improve slab resistance against earlier de-bonding. Table 3-14
shows different sets of data in Figures 3-48 with varying slab depths and concrete tensile
strengths but the same product of slab depth and concrete tensile strength (while keeping FRP
properties constant). These samples are highlighted in the same colour in Table 3-14. The
results in Table 3-14 show that there was no considerable difference in the optimum FRP-
prestress ratio for the samples with the same products of concrete tensile strength and slab
depth (when the FRP properties were identical as well). Therefore, the product of concrete
tensile strength (𝑓𝑡΄) and slab depth (D), (𝑓𝑡
΄ × D), can be considered the main parameter
representing factors resisting FRP de-bonding (instead of considering slab depth and concrete
tensile strength separately) while conducting optimal analysis of the FRP-prestress ratio.
128
Table 3-15. The relations between the effective parameters to find the optimum prestress ratio of FRP.
Samples
group
𝑓𝑡΄
(MPa)
D
(mm)
𝑓𝑡΄ × D
(MPa.mm)
𝑤𝑓
(mm)
𝑡𝑓
(mm)
𝑢𝑓 (MPa) 𝑥𝑜𝑓
(%)
(𝑥𝑜𝑓 × 𝑡𝑓×𝑢𝑓) = 𝐹𝑜𝑓𝑟𝑝
𝑤𝑓
(MPa.mm)
R-F15
3.39 150 508.5 100 0.6 2970 13.5 240.57
3.39 200 678 100 0.6 2970 19 338.58
3.39 150 508.5 100 1.2 2970 7.5 267.3
3.39 200 678 100 1.2 2970 8.5 302.94
4 100 400 100 0.6 2970 12 213.84
4 150 600 100 0.6 2970 17 302.94
4 100 400 100 1.2 2970 6.5 231.66
4 150 600 100 1.2 2970 9 320.76
5 120 600 100 0.6 2970 18 320.76
5 200 1000 100 0.6 2970 27.5 490.05
5 120 600 100 1.2 2970 8.5 302.94
5 200 1000 100 1.2 2970 13.5 481.14
RC-F15
3.22 150 483 150 0.33 3800 19 238.26
3.22 200 644 150 0.33 3800 26.5 332.31
3.22 150 483 150 0.9 3800 6 205.2
3.22 200 644 150 0.9 3800 9 307.8
4 100 400 150 0.33 3800 14.5 181.83
4 150 600 150 0.33 3800 21 263.34
4 100 400 150 0.9 3800 5.5 188.1
4 150 600 150 0.9 3800 8 273.6
5 120 600 150 0.33 3800 24 300.96
5 200 1000 150 0.33 3800 39 489.06
5 120 600 150 0.9 3800 9.5 324.9
5 200 1000 150 0.9 3800 14.5 495.9
Considering all of the above, the product of slab depth (D) and concrete tensile strength (𝑓𝑡΄)
(𝑓𝑡΄ × D) was the major factor resisting FRP de-bonding. As mentioned above,
𝐹𝑓𝑟𝑝
𝑤𝑓 also
represents factors that may cause FRP de-bonding equal to the product of FRP tensile strength
(𝑢𝑓), FRP thickness (𝑡𝑓) and the FRP-prestress ratio (𝑥𝑓). If the FRP-prestress ratio (𝑥𝑓) is equal
to the optimum ratio (𝑥𝑜𝑓) in the multiplication, the applied load to prestress FRPs per unit
FRP width (𝐹𝑓𝑟𝑝
𝑤𝑓) could be assumed to be the optimum applied load to prestress FRPs per unit
129
FRP width (𝐹𝑜𝑓𝑟𝑝
𝑤𝑓). Furthermore, a balance between the parameters may cause FRP de-bonding
represented by (𝐹𝑜𝑓𝑟𝑝
𝑤𝑓), and the parameters may resist FRP de-bonding represented by (𝑓𝑡
΄ × D).
To determine if there is a formula or proper coefficient to correlate (𝐹𝑜𝑓𝑟𝑝
𝑤𝑓) and (𝑓𝑡
΄ × D), all
parameters in Figure 3-48 and their products have been mentioned in Table 3-15.
Figure 3-49. Graph provided by data regression to find the optimum FRP-prestress ratio to strengthen RC slabs.
Figure 3-49 shows the scatter values of 𝑓𝑡΄ × D and
𝐹𝑜𝑓𝑟𝑝
𝑤𝑓 from the data listed in Table 3-15 as
well as the trend line estimated based on the regression method in order to provide a
mathematical relation between 𝑓𝑡΄ × D and
𝐹𝑜𝑓𝑟𝑝
𝑤𝑓. This can show how the parameters causing
and resisting earlier FRP de-bonding could correlate with one another in a balanced situation.
The linear regression on Excel generated Equation 3-28 according to the best-fitting trend line
to correlate 𝐹𝑜𝑓𝑟𝑝
𝑤𝑓 and 𝑓𝑡
΄ × D. The results were collected from 24 finite element models by
varying the effective parameters (seen in Table 3-15). They showed a proper fit with the
regression line (Figure 3-49).
130
𝐹𝑜𝑓𝑟𝑝
𝑤𝑓= 𝑥𝑜𝑓 × 𝑡𝑓×𝑢𝑓 = 0.49 (𝑓𝑡
΄× D) 3-28
Equation 3-28 can be rewritten as follows (Equation 3-29) to find the optimum FRP prestress
ratio to strengthen RC slabs:
𝑥𝑜𝑓 = 0.49 (𝑓𝑡
΄× D)
𝑡𝑓×𝑢𝑓 3-29
3.6. Summary
The experimental and numerical models in this chapter show that the efficiency of
strengthening the RC slab with prestressed FRPs depends on whether there has been full
composite action or earlier FRP de-bonding. Earlier FRP de-bonding (in case of a proper
anchorage system) is mainly caused by inner concrete fracture near the end plates for slabs
strengthened with prestressed FRP, owing to the synergic action of the increment in tensile
stresses in the region above the steel reinforcement and below the neutral axis, and shear
stresses near the neutral axes.
Thus, applying prestressed FRP to strengthen RC slabs is more efficient than strengthening
with non-prestressed FRP in the case of full composite action. The results also indicate that
there can be an optimal prestress ratio of FRP for the given RC slab that can enhance its load
capacity without causing earlier de-bonding, which can be predicted approximately by the
formula proposed. The enhancement of the FRP-prestress ratio up to the optimum point
improves load capacity. However, a further increase in the FRP-prestress ratio (beyond the
optimum point) may cause FRP de-bonding, and the strengthened RC structure hence cannot
reach its desired load capacity.
One of the main requirements of strengthening RC structures with prestressed FRP strips is to
apply a proper anchorage system to prevent early failure at the FRP end plate. The
investigations here show that FRP plates should be prestressed in the range of 50% of ultimate
strength to render this strengthening method an economical choice, in light the costs of
anchorage systems and prestressing the strips [13, 14]. Moreover, the mechanism for the
131
optimum FRP-prestress ratio (mentioned in this chapter) formulates and limits the range of
FRP-prestress ratio to avoid early FRP de-bonding.
Hence, applying prestressed FRPs to strengthen RC flat slabs may not be considered as an
efficient and comprehensive technique to rehabilitate structures. That is why the flat slabs
tested in the next chapter were strengthened only using non-prestressed FRP, which can
provide more feasible results for future studies on strengthening RC flat slabs.
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4. FRP and Shear Strengthening of RC Slabs
4.1. Introduction
Based on a literature review, the strengthening of two-way reinforced concrete (RC) slabs,
which is the main consideration in this study, may be categorised as flexural or punching. RC
structures with low tensile reinforcement ratio are commonly strengthened to enhance their
flexural capacity, and RC structures with high tensile reinforcement ratios are retrofitted to
increase their punching strength. So far, studies have demonstrated that applying fibre
reinforced plastic (FRP) is the most suitable technique to realise both flexural and punching
strengthening for rehabilitation purposes.
However, the literature review indicated that studies on strengthening RC slabs with FRP have
been more quantitative in nature with a lack of explanation for the failure mechanism. In fact,
the mechanism of how FRP strengthens RC slabs, especially in the case of punching
strengthening, has not been considered substantially. In addition, there have been very few
studies on the strengthening of two-way RC slabs compared with the retrofitting of other RC
structures such as beams and columns. This has resulted in insufficient knowledge and few
suggestions in relevant design codes for the strengthening of two-way RC slabs compared with
other kinds of RC structures.
Other strengthening methods are available for enhancing the punching strength of two-way RC
slabs, such as applying vertical reinforcement (i.e. shear reinforcement) in the column vicinity
to avoid enhancing the punching shear resistance of the slab. Combining this shear
reinforcement method with FRP strengthening may provide a more efficient strengthening
pattern to satisfy strengthening requirements. The effectiveness of different strengthening
methods and their combinations for RC slabs with different properties (e.g., low or high
reinforcement) is an engineering issue that needs to be considered. This can help find the most
suitable strengthening pattern, which may not have been properly considered in previous
studies.
This chapter presents comprehensive experimental work with the corresponding numerical
investigation to examine the effect of different rehabilitation methods on the strengthening
133
behaviour of two-way RC slabs. It is intended to cover the knowledge gap discussed above.
This chapter includes information such as geometric parameters of the strengthened and non-
strengthened slab samples, strengthening patterns, material properties, and test layout in the
experimental investigation. Note that the finite element (FE) models presented in this chapter
were simulated based on the numerical modelling explained and validated in Section 3.3. The
results from the experimental work and FE models provide the basis of the mechanism analysis
for different specimens. The purpose is to realise a better understanding of the behaviour of RC
slabs strengthened with different retrofitting methods and their combinations, which may lead
to the development of guidelines on determining the most efficient strengthening strategy for
rehabilitating RC slabs under different conditions.
4.2. Experimental test
An experimental programme was conducted to consider the strengthening effect on the load
carrying capacity, structural ductility, deflection, crack patterns, and failure modes of RC flat
slabs. Altogether, eight two-way RC slab specimens were prepared and classified into two
categories: low and high tensile reinforcement ratios.
Table 4-1. Slabs labelled according to the strengthening method.
Two-way RC slab category Slab Applied strengthening method
L
(Low tensile reinforcement ratio)
L0 (Control specimen) ________
LF FRP sheets
LS Vertical (shear) reinforcement
LFS FRP sheets and shear reinforcement
H
(High tensile reinforcement ratio)
H0 (Control specimen) ________
HF FRP sheets
HS Vertical (shear) reinforcement
HFS FRP sheets and shear reinforcement
For each category, there was a control specimen that was not strengthened. One of the slabs in
each group was strengthened by pasting FRP sheets onto its tension surface. Another specimen
in each group was strengthened by applying shear reinforcement in the column vicinity. The
134
remaining specimens were strengthened with both FRP sheets and shear reinforcement. Table
4-1 presents the sample labels and applied strengthening methods.
Using two-way RC slabs with different tensile reinforcement ratios helped us find the
efficiency of different FRP retrofitting techniques for different RC slabs. Note that the
contribution of the FRP sheets was not considered for the tensile reinforcement ratio to classify
the slabs. The experimental results for the two-way RC slabs and explanation of the mechanism
will help civil engineers design the appropriate strengthening pattern to satisfy the retrofitting
requirements efficiently.
4.2.1. Rationale behind choosing the dimensions of the tested slabs
Figure 4-1 shows continuous and simple slabs supported by columns in RC structures.
Figure 4-1. Continuous and simply supported slabs [1, 31].
Using continuous slabs rather than simply supported ones has several advantages that may push
a designer to apply them. The net bending moments in continuous slabs (due to the moment
redistribution) are less than those of simply supported ones (see Figure 4-2); this reduces the
required bending strength and make it a cost-effective option to design and construct compared
135
to simply supported slabs. The maximum deflection in continuous slabs is less than that of
simple slabs, which may be owing to the shorter effective spans of the former compared with
the latter (see Figure 4-1). These reasons allow larger spans to be designed by increasing the
distance between columns that support continuous slabs compared to those for simply
supported slabs. This may cause continuous slabs to be preferred over simply supported ones
[1, 31].
Figure 4-2. Bending moments of slabs under different conditions [1, 31].
The flat slabs studied in this thesis include the critical parts of the continuous slabs (see Figure
4-3) because both the maximum bending moment (which may cause flexural failure) and
probable punching failure happen in the vicinity of columns. Figure 4-3 shows inflection points
in continuous slabs at which the bending moment is zero.
Figure 4-3. Continuous slabs [1, 31].
136
Thus, the part between two inflection points (which includes the critical part) can be modelled
as a separate slab with a column area at its centre and simply supported around its corners to
model the inflection points at which the bending moments are zero. Hence, the lengths of flat
slabs considered in this study were approximately 0.42 of the slab span for a continuous frame
(considering Figures 4-2 and 4-3). The thickness of the slabs was chosen based on the
recommendations of ACI and Eurocode as well as initial numerical modelling to ensure that
all of the slabs satisfied the required punching capacity. Moreover, there were some limitations
to choose the dimensions of the tested slabs instead of having full scale samples. Note that the
flat slabs experimentally tested by Harajli and Soudki [57] had almost the same dimensions as
the flat slabs tested and described in this chapter.
4.2.2. Strengthened and non-strengthened sample layouts
Figure 4-4 shows the slab layouts, including the reinforcement and geometric details of the
samples. All of the slabs in the experimental programme were 650 × 650 mm2 square
specimens with a thickness of 60 mm; these dimensions were chosen to simulate common RC
slab behaviour in reality based on previous relevant investigations [9, 56, 57] and the argument
in the previous subsection. The specimens in the first category with initial low tensile
reinforcement ratio (L) were reinforced with five ribbed bars having a diameter of 6 mm that
were distributed at intervals of 150 mm (Figure 4-4). The slabs in the second category with a
high tensile reinforcement ratio (H) were reinforced with seven ribbed bars having a diameter
of 8 mm that were positioned at intervals of 100mm (Figure 4-5).
Figure 4-4. Category L slab layout.
137
Figure 4-5. Category H slab layout.
The initial tensile reinforcement ratios of categories L and H were 0.5 and 1.1, respectively,
based on the designs shown in Figures 4-4 and 4-5. To model the behaviour of a column at a
column and slab connection, a steel cube (100 mm3) was positioned at the centre of the slab.
The region under the column area was reinforced with four 8mm diameter ribbed bars. The
concrete cover below the flexural steel bars was 10 mm thick in accordance with Eurocode 2
[12].
Figure 4-6. FRP sheets on the tension surface of the FRP strengthened specimens.
138
The FRP sheets were bonded to the tension surfaces of the samples. Figures 4-6 and 4-7 show
the FRP positions of the category L and H slabs. The required FRP length to transfer the stresses
properly was estimated on the basis of Chen and Teng’s [64] suggestion for the effective FRP
length in strengthened beams (see Section 2.5.2) and other considerations such as the critical
punching space (assumed to be two times the effective depth (2d) away from the column side
based on Eurocode 2 [12]) and column length (Figure 4-7).
Figure 4-7. Actual and required FRP lengths.
Table 4-2 presents the estimated required FRP lengths for both categories. The main difference
in the required FRP length for the different categories was due to the difference in the effective
slab depth (d) caused by the diameter of the tensile reinforcement. The final FRP length in all
FRP strengthened samples was 550 mm.
Table 4-2. Estimation of the required FRP lengths based on Chen and Tang’s [64] suggestion.
Category Column length
(mm)
Effective slab depth (d)
(mm)
Le (Effective length)
(mm)
Required FRP length
(mm)
L 100 44 110 386
H 100 42 110 378
Figure 4-8 shows the positions of vertical (shear) bars in samples strengthened with shear
reinforcement. The shear reinforcement was 8 mm diameter ribbed bars (16 bars in total) that
covered the critical punching area around the column. The space between shear reinforcement
increased with distance from the column side. The above pattern was chosen because the
139
amount of stress, which can cause concrete fracture, increases with decreasing distance to the
column centre.
Figure 4-8. Positions of vertical (shear) reinforcement in the shear strengthened samples.
4.2.3. Materials
The slabs consisted of materials such as concrete, steel rebar, and FRP. Understanding the
mechanical properties of these constituents is essential to explain the behaviour of the slab
samples and the FE simulation of the specimens.
4.2.3.1. Concrete
The concrete mixture was designed to reach a 28-day cube compressive strength of 50 MPa.
The maximum aggregate size was 10mm, and the water–cement ratio was 0.48 with a cement
content of 433 kg/m3. Table 4-3 presents the concrete mix design used in the current study.
140
Table 4-3. Concrete mix design.
Cement (kg) Water (kg) Coarse aggregate (kg) Fine aggregate (kg)
433 208 1000 655
Three 100 mm3 cubes and three 100 mm2 × 200 mm cylinder control samples were used in the
28-day concrete strength tests. The control cubes were tested in accordance with BS1881-P116
[104] to evaluate the concrete compressive strength. The cylinder samples were used to find
the concrete tensile strength based on ASTM C496-96 [105]. The concrete modulus of
elasticity was calculated based on Eurocode 2 [12], as given in Equation 3-4. Bangash [106]
stated that the concrete strain for visible compressive crushing is 0.0035. Table 4-4 presents
the compressive and tensile strengths for different concrete slabs.
Table 4-4. Concrete properties of different slabs.
Slab
Cube compressive strength
(MPa)
Cylinder tensile strength
(MPa)
L0 51.41 4.26
LS 54.76 4.73
LF 53.40 4.24
LFS 54.29 4.61
H0 52.82 4.48
HS 56.17 5.02
HF 55.45 4.87
HFS 51.03 4.19
4.2.3.2. Steel reinforcement
Table 4-5. Mechanical properties of the steel bar.
Steel rebar
diameter
(mm)
Modulus of
elasticity
(GPa)
Yield
strength
(MPa)
Yield
strain
Ultimate
strength
(MPa)
Ultimate
strain
6 200 560 0.0030 632 0.0139
8 200 551 0.0031 620 0.0131
141
The steel reinforcement used for either tensile or shear reinforcement was 6 and 8mm diameter
ribbed bars with the mechanical properties given in Table 4-5, as determined in accordance
with ASTM A370-97a [107].
4.2.3.3. FRP composites
The FRP sheet to strengthen the RC slabs was a unidirectional carbon fibre fabric supplied by
Easycomposites [108], UK. The carbon FRP (CFRP) sheet was bonded to the concrete surface
with Weber Tech EP, which is a two-component epoxy adhesive [28]. The adhesive material
was composed of 2/3 epoxy resin mixture with 1/3 hardener and was supplied by Weber
Building Solutions [28], UK. Together the CFRP sheet and adhesive material composed a
CFRP composite in accordance with Concrete Society Technical Report No.55 [109]. The
mechanical properties of the CFRP composite applied in this study were tested at the Heavy
Structure Laboratory of the University of Manchester and are given in Table 4-6 [110].
Table 4-6. CFRP composite properties [110].
Thickness
(mm)
Modulus of elasticity
(GPa)
Tensile strength
(MPa)
Shear modulus
(GPa)
Rupture
strain
Ex Ey Tx Ty Gxy Gyz
0.0095
0.8
96.3
6.7
911
40
2.8
2.5
x = direction parallel to the fibre direction; y and z = orthogonal directions perpendicular to the
fibre direction
4.2.4. Experimental preparation
4.2.4.1. Mould
The mould was made of plywood parts and covered with mould release oil before the concrete
casting.
142
Figure 4-9. Slab mould prepared for concrete casting.
4.2.4.2. Support frame
The support frame was made of steel profiles. Four steel bars were welded on top of the steel
frame to provide realistic roller supports during the experiment. The frame height provided
enough space to accommodate the potentiometer measuring the slab deflection under an
external load (Figure 4-10).
Figure 4-10. Support frame.
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4.2.4.3. Reinforcement
Different kinds of reinforcement were used in this experimental study, such as steel
reinforcement and FRP sheets. The tensile steel reinforcement was welded together at the
corners and fixed at the ends by plastic clamps to make sure their positions would not change
during the casting process. The spacers below the bottom of the tensile reinforcement were
placed to fix the flexural reinforcement at the right positions (Figure 4-9). The vertical (shear)
and column reinforcements were placed and FRP sheets were bonded after the concrete was
cast. This is explained in the upcoming sections.
4.2.4.4. Casting, curing, and slab preparation
Figure 4-11. Casting concrete in the mould and samples.
The same batch of concrete mixture was used to cast one of the slabs, three control 100 mm2 ×
200 mm cylinders, and three 100 mm3 cubes. The mould was placed on the shaking table, and
the concrete was cast in three steps. The shaking table was turned on after one third was cast
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to make sure the concrete has settled properly until the mould was filled with concrete to reach
the overall slab thickness. The top concrete was levelled with a ruler to ensure a smooth surface.
The same process was used to cast the control samples. Figure 4-11 shows a levelled cast slab
and its control specimens on the shaking table. Half an hour after casting, the column
reinforcement and vertical (shear) reinforcement were inserted into the concrete in their
specified positions. The cast slab surface was marked before the vertical reinforcement was
placed to specify the exact positions of each piece of vertical (shear) reinforcement. Figure 4-
12 shows one of the cast slabs after the vertical reinforcement was placed.
Figure 4-12. Applying vertical (shear) reinforcement.
The cast slab and control specimens were covered with nylon cloth 1 h later. After 24 h, the
slab and corresponding cylinder and cube samples were de-moulded, labelled, and left in water
for 14 days to help with cement hydration. The slabs and control samples were then removed
from the water and left for another 14 days to reach their expected strength for the mechanical
test.
4.2.4.5. Surface preparation and bonding process
In order to make a proper FRP–concrete bond, preparing the concrete surface before the FRP
is applied is essential. The slabs proposed to be strengthened with FRPs were cured in water
for 14 days, as described in the previous section, and dried at laboratory temperature for 2 days.
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According to the technical documents of the Weber Company [28], the minimum concrete
tensile strength required for a proper bond between FRP and the concrete substrate is 1.5
N/mm2. If the minimum required tensile strength is not achieved, the substrate needs to be
improved by the application of primer or removal of the poor substrate and replacement with
high-strength concrete [28]. These actions did not need to be considered in this study because
all of the samples satisfied the minimum concrete tensile strength.
The slab substrates that were to be strengthened with FRP were first marked to determine the
specified positions of the FRP sheets. Figure 4-13 shows the mesh lines that were drawn to
show the FRP positions. The marked parts for FRP were ground to remove the mortar layer or
substrate imperfections to provide a suitable flat substrate for a proper FRP–concrete bond.
The grinding dust was removed, and the slab substrate was cleaned of any dirt that may impair
adhesion when the FRP sheets were applied, as shown in Figure 4-13.
Figure 4-13. Slab preparation to apply FRP sheets.
The next step was applying the adhesive material to both the FRP sheets and prepared concrete
substrate. Note that a layer of the adhesive material could be applied 1 h before the main layer
was applied on both the FRP and concrete substrate to make sure all of the fine holes and minor
imperfections were levelled, according to the suggestion of the adhesive supplier [28]. Then,
the FRP was placed at the specified positions, as shown in Figure 4-14. A roller was passed
backwards and forwards over the FRP sheets to squeeze the resin from the sides and eliminate
air bubbles that could have weakened the FRP–concrete bond in order to achieve the same level
of adhesion throughout the FRP sheets. Finally, the excess adhesive material was removed
from the slabs.
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Figure 4-14. FRP sheets applied on the tension surface of the slab.
4.2.5. Measurement instrumentation
Figure 4-15. Strain gauge positions relative to the tensile reinforcement of the slabs.
External and internal measurements were applied to each slab. The steel bars were ground at
specified parts to apply the strain gauges. The ground parts were cleaned with methanol,
147
conditioner-A (i.e. water-based acidic surface cleaner), and neutraliser in successive order.
Then, three linear three-wire strain gauges with a resistance of 120 Ω and length of 6mm were
bonded to the steel bars to monitor and measure the longitudinal tensile bar strain. The
protection and coating of the strain gauges on the steel bars needed to be carefully applied
because of the severe moisture environment during the time of casting. Hence, protective
materials such as M-Coat A (i.e. air-drying polyurethane coating) and silicon varnish were
applied after the strain gauges and wires were soldered to enhance the strain gauges’ resistance
against humidity absorption and dirt [111]. Figure 4-15 shows the strain gauge positions
relative to the steel reinforcement in the category L and H slabs.
Figure 4-16. Concrete strain gauge positions around the column zone.
The next group of strain gauges was mounted tangentially along the column perimeter to
externally gauge the concrete compressive strains in the column vicinity, as shown in Figure
4-16. The concrete surface was ground in the specified parts to mount the strain gauges until a
uniform exposure of the aggregate was achieved. The ground dust was removed, and the
surface was cleaned with methanol and neutraliser (i.e. water-based alkaline surface cleaner).
A thin layer of M-bond adhesive was applied to ensure proper gauge installation in the case of
any unevenness.
Three-wire linear strain gauges with a resistance of 120 Ω and length of 30 mm were then
bonded with strain gauge adhesive to the specified concrete surfaces. The strain gauge length
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was chosen based on the maximum size of concrete aggregate and has been suggested to be at
least 25 mm [112]. The strain gauges were finally coated with M-Coat A for environmental
protection. The strain gauges were soldered to the bondable terminals, which were soldered to
the wires connected to the data monitor and recorder during the experiment.
Four more 6 mm linear strain gauges were installed on each FRP sheet to monitor the FRP
behaviour. Each strain gauge, which had three wires with a resistance of 120 Ω, were bonded
and coated in the same manner as those for concrete strain measurement in order to measure
the longitudinal strains of the FRP. One strain gauge was assigned to each FRP sheet. Figure
4-17 shows the strain gauge positions on the FRP sheets.
Figure 4-17. FRP strain gauge positions.
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4.2.6. Test preparation and procedure
Figure 4-18. Testing procedure.
The support frame and linear potentiometer were placed and fixed on the testing machine
before the slabs were set. The slabs were carefully positioned on the support frame to ensure
their symmetry. The column area of the slabs was flattened with dental plaster paste before the
steel cube was placed to ensure a uniform distribution of the applied load. The strain gauges
and a potentiometer were connected to a data internalisation computer and initialised by the
data acquisition system. The linear potentiometer was used to gauge the maximum deflection
of the slabs. Test data such as the load, maximum deflection, and strain of the slab were
measured with the data acquisition system connected to a personal computer to record and
monitor the data.
All of the slabs were finally tested under a pressure load acting on the steel cube placed in the
column area (i.e. centre of the slab, as shown in Figure 4-18). The loading mechanism was
displacement control, and the loading machine crosshead speed was 2.4 mm/min. This was
applied by a 2000 kN capacity hydraulic ram against the support frame. The applied load was
increased until failure, which could be due to yielding of the reinforcement, concrete crushing,
150
or FRP de-bonding. After the experiment was completed, the slab was removed from the test
machine and flipped over for closer observation of the failure mechanism and mode.
4.3. Results and discussion
4.3.1. Experimental and FE model results
Table 4-7 presents the experimental and FE model results for the yield and ultimate loads,
deflections, and failure mode of the slabs. The consistency between the experimental and
numerical results illustrates the accuracy of the FE simulation, which may be helpful for
analysis of the slab behaviour. The approximate mesh size in the FE models was 8 mm based
on the mesh sensitivity analysis.
Table 4-7. Experimental and FE model results.
Specimen
category
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
EXP FEM EXP FEM EXP FEM
L
L0 26 28.2 43.4 46.5 18.2 19.3 Flexural
LS 27.1 28.5 45.6 47 16.8 18.9 Flexural
LF 95.7 94.6 104 101.8 8.1 8.2 Punching
LFS 123.6 119.3 123.6 119.3 10.1 10.5 Punching
H
H0 82.9 87.2 82.9 87.2 10.4 10.2 Punching
HS 83.7 88.9 94.1 99.5 12.5 13.3 Flexural punching
HF 117.9 122.6 117.9 122.6 6.2 6.7 Punching
HFS 138 134.8 138 134.8 7.3 7.6 De-bonding
The experimental data were used for a comprehensive analysis of the RC slab behaviour. The
load was assumed to be a suitable link to connect different kinds of collected data. Previous
experimental studies have used curves linking the load variation and changes to other collected
data (e.g. the material strain and sample deflection) as a conventional way to explain the
behaviour of a structure. Figure 4-19 shows the load–deflection curves for all of the samples
tested in this experimental study. Different retrofitting methods such as FRP sheets, shear
reinforcement, and a combination of both methods were considered to determine the efficiency
of different strengthening patterns for RC structures with various properties.
151
Figure 4-19. Load–deflection curves of the RC slabs.
As shown in Figure 4-19, the slab load capacity was increased significantly with CFRP sheets,
especially for the L category samples. However, the specimen deflections were reduced with
CFRP strengthening. In addition, the figure indicates that applying shear reinforcement to
enhance the load capacity may be more effective for RC slab with a high tensile reinforcement
ratio rather than a low one. Using shear reinforcement may also enhance the slab ductility.
More details of the comparison analysis are presented in the following sections.
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4.3.2. Slabs with an initial low tensile reinforcement ratio (category L)
4.3.2.1. Control specimen with a low tensile reinforcement ratio (L0)
L0 was the control specimen with low tensile reinforcement ratio (0.5%) and no strengthening.
The control specimen was used as a reference to determine the effect of different strengthening
methods on the slab behaviour. Figure 4-20 indicates suitable consistency between the load–
deflection curves of the experimental and FE models of L0.
Figure 4-20. Load–deflection curves of the experimental and FE models for L0.
The load–deflection curves in Figure 4-20 demonstrate ductile failure because the curves nearly
plateau around the maximum load zone with a gentle decrease after the peak loading, which
caused considerable slab deflection. Greater slab deflection may increase the ductility and
energy absorption ability, which is defined as the area below the load–deflection curves [5].
The curve indicates characteristics that represent a typical ductile flexural failure, which is
expected for a slab with low tensile reinforcement ratio. Flexural failure occurs because of a
wide range of tensile reinforcement yielding and the development of tensile cracks on the
concrete tension surface. Figure 4-21 shows the concrete cracks in the experimental and FE
models of L0. Figure 4-22 shows the load–strain curves of the tensile steel reinforcement at
different distances of 60 mm (S1), 150 mm (S2) and 250 mm (S3) from the slab centre. A
vertical line in the figure indicates the yield strain of steel. The steel reinforcement in the
column vicinity (S1) reached the yield strain at a lower load than the steel reinforcement far
from the slab centre.
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Figure 4-21. Cracks in the experimental and FE models for L0.
Figure 4-22. Load–strain curves of the internal tensile reinforcement.
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Figure 4-23. Load–strain curve of the concrete in the column vicinity.
Figure 4-23 shows the load–strain curve for the concrete in the column vicinity (the strain
gauge positions have been mentioned in section 4.2.5 Figure 4-16). The concrete strain was
negative because the concrete was in compression. The maximum concrete strain shown in
Figure 4-23 was less than the concrete strain for visible compressive crushing. Hence, no
concrete compressive crush was expected. This was confirmed by experimental observation.
Figure 4-24. Sectional analysis of an RC slab (with low tensile reinforcement ratio) in flexural failure mode.
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Figure 4-24 explains the flexural failure process, which is an expected failure mode in the case
of slabs with a low tensile reinforcement ratio. The tensile cracks that formed in the concrete
tension face from tensile reinforcement yielding caused the neutral axis to rise compared with
its position before the tensile reinforcement yielding. The main reason behind the ascent of the
neutral axis is that the concrete, which had not cracked yet, bore the tensile stress in addition
of the yielded reinforcement in order to balance the compressive and tensile forces in the RC
slab section. As the loading increased, the tensile strain (and hence tensile stress) in the concrete
tension zone increased too. Because concrete has low tensile resistance, the tensile cracks
propagated continuously, which resulted in slab failure.
4.3.2.2. Shear strengthened slab with a low tensile reinforcement ratio (LS)
Figure 4-25. Load–deflection curves of the experimental and FE models for LS.
LS was the slab with a low tensile reinforcement ratio that had been strengthened with vertical
(shear) reinforcement, as noted previously in this chapter. Figure 4-25 shows the consistency
between the experimental and FE models of LS based on their load–deflection curves.
According to the load–deflection curves, the failure mode was expected to be ductile flexural
failure like for the control specimen. This was confirmed by the experimental and numerical
results. Figure 4-26 shows the concrete cracks in both the experimental and FE models of LS.
The slab failure mode was flexural failure, which occurred due to the wide development of
yield lines as a result of extensive steel reinforcement yielding.
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Figure 4-26. Cracks in the experimental and FE models for LS.
Figure 4-27. Load–strain curves of the internal tensile reinforcement.
157
Figure 4-27 shows the load–strain curve of the tensile steel reinforcement at different distances
from the slab centre. The steel strain exceeded the steel yield strain and indicated the
development of tensile reinforcement yielding. This was the main cause of ductile flexural
failure. The experimental load–strain curve of the concrete (Figure 4-28) in the column vicinity
showed that the concrete was not crushed in compression because the concrete strain did not
exceed the concrete compressive crushing strain.
Figure 4-28. Load–strain curve of the concrete in the column vicinity.
Table 4-8 compares the current slab (LS) with the control specimen (L0) and demonstrates the
effect of shear reinforcement on an RC slab with a low tensile reinforcement ratio. There was
no considerable improvement in the load capacity of LS compared with L0. Hence, applying
shear reinforcement is not a productive method to improve the slab flexural capacity. This
result was expected because the main reason for applying vertical (shear) reinforcement is to
enhance the slab’s punching strength. The results demonstrate that the failure mode of LS was
still flexural failure, the same as the control specimen (L0).
Table 4-8. Comparison between the control and shear strengthened specimens.
Slab Load capacity Increase in
load capacity
Deflection Decrease in
deflection
Failure mode
L0 43.4
5%
18.2
7%
Flexural
LS 45.6 16.8 Flexural
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4.3.2.3. FRP strengthened slab with an initial low tensile reinforcement ratio (LF)
LF is the slab with low initial tensile reinforcement ratio that was strengthened by applying
CFRP sheets on its tension surface. Figure 4-29 shows that there was acceptable consistency
between the experimental and FE results. The load–deflection curves represent a brittle failure
mode because there was a sudden drop in the experimental curve after the maximum load
capacity was reached.
Figure 4-29. Load–deflection curves of the experimental and FE models for LF.
Figure 4-30. Punching failure in the column vicinity of LF.
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The failure mode of this slab was brittle punching failure. This was confirmed by experimental
observations (see Figure 4-30) and the load–strain curve of the concrete in the vicinity of the
column (see Figure 4-31), which demonstrated that the concrete strain exceeded the
compressive crushing strain.
Figure 4-31. Load–strain curve of the concrete in the column vicinity.
Figure 4-32. Load–strain curves of the internal tensile reinforcement.
Figure 4-32 shows the load–strain curves for the steel reinforcement at different distances from
the slab centre. The strain gauges showed that the steel reinforcement in the vicinity of the
column yielded. However, partial yielding of the tensile reinforcement did not change the slab
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behaviour significantly because the CFRP sheets bore tensile stresses and compensated for the
yielded parts of the steel bars.
Figure 4-33 shows the load–strain curves of the CFRP sheets. The strain gauge positions on
the CFRP sheets and other details are given in Section 4.2. Each strain gauge represented the
strain of one of the CFRP composites. This helped us monitor and calibrate the testing
behaviour of all CFRP sheets during the experiment. Based on the load–strain curves, the
ultimate strain achieved by CFRP for LF was 0.0042–0.0048, which is less than the CFRP
rupture strain of about 0.0095. This means the CFRP sheets for LF did not rupture. Because
FRP materials follow linear behaviour and their strain range is almost half of the CFRP rupture
strain, the maximum CFRP stress for this slab would be about 47% of their ultimate strength.
Figure 4-33. Load–strain curves of the CFRP composites.
Figure 4-34 shows the stress and strain distributions in this slab section; the FRP strengthened
slabs failed in punching. Based on the strain compatibility shown in the slab section, the CFRP
sheets achieved greater strain than the steel reinforcement under the same load. This was
confirmed by the steel and CFRP load–strain curves shown in Figures 4-32 and 4-33. Figure
4-34 also indicates that the concrete ultimate stress and strain in the compression zone may not
necessarily occur at the same position in the slab section. According to this figure, the
maximum concrete compressive strain occurs at the outer concrete fibre. However, the
maximum concrete stress occurs inside the slab between the concrete outer side and neutral
axis.
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Figure 4-34. Stress and strain distributions in the FRP strengthened slab section.
Table 4-9 compares the current slab (LF) with the control specimen (L0) to demonstrate the
effect of applying CFRP sheets to strengthening RC slabs with a low tensile reinforcement
ratio. LF showed a significant improvement of 140% in the load capacity compared with L0.
However, the slab deflection and ductility decreased, which could be due to the enhanced slab
stiffness from the FRP strengthening. Note that the slab failure mode changed from ductile
flexural failure for L0 to brittle punching failure for LF. This means that the overall tensile
reinforcement ratio, which includes both the CFRP and initial tensile reinforcement, exceeded
the critical balance tensile reinforcement ratio.
Table 4-9. Comparison between L0 and LF.
Slab Load capacity Increase in
load capacity
Deflection Decrease in
deflection
Failure mode
L0 43.4
140%
18.2
55%
Flexural failure
LF 104 8.1 Punching failure
The main reason for the increased load capacity of LF compared to L0 is due to the enhanced
tensile resistance of the slab. Enhancing the slab’s tensile resistance by applying tensile
reinforcement such as FRP to carry more tensile stress can improve the load capacity of slabs
with a low tensile reinforcement ratio. Figure 4-35 compares L0 and LF. The tensile
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reinforcement of LF, which included both steel reinforcement and CFRP sheets, provided more
tensile resistance and effective tension area compared with L0. Hence, the neutral axis
descended to a lower level in LF compared with L0 in order to provide more concrete area that
could resist the compressive stress.
Figure 4-35. Sectional analysis of RC slabs (with high tensile reinforcement ratio).
As the neutral axis lowered, the tensile forces (i.e. tensile stresses in the tension zone multiplied
by the effective tension area) and compressive forces (i.e. compressive stresses in the
compression zone multiplied by the compression area) of the slab section became balanced. In
fact, the neutral axis was positioned to neutralise the tensile and compressive forces. The failure
mode of LF mainly depended on its tensile reinforcement ratio considering both the initial steel
reinforcement ratio and CFRP sheets.
When the overall reinforced ratio, including both steel reinforcement and FRP sheets, exceeded
a critical balance value, compressive plastic strains developed in the compression area before
the propagation of tensile cracks. This caused compressive crushing of the concrete before the
tensile reinforcement yielded. This is why the failure mode changed from ductile flexural
failure for L0 to brittle punching failure for (LF): the overall reinforced ratio was greater than
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the balance value. Figure 4-36 shows the concrete cracks on the slab tension surface from the
experimental and numerical models.
Figure 4-36. Concrete cracks in the tension surface of LF.
4.3.2.4. FRP and shear strengthened slab with an initial low tensile reinforcement
ratio (LFS)
LFS is the slab with a low initial tensile reinforcement ratio that was strengthened by applying
CFRP sheets on its tension surface and vertical (shear) steel bars covering the critical punching
area of the slab. Figure 4-37 shows the consistency between the experimental and FE results.
The experimental load–deflection curves show a sudden fall after the ultimate load capacity
was approached, which indicates a brittle failure mode for LFS. The experimental observations
in Figure 4-38 indicated that LFS failed by brittle punching failure that was initiated from
outside the shear strengthened zone. Hence, the concrete strain in the column vicinity of LFS
(see Figure 4-39) was not as critical as the concrete strain in the column vicinity of LF (see
Figure 4-31).
164
Figure 4-37. Load–deflection curves of the experimental and FE models for LFS.
Figure 4-38. Punching failure initiating from the shear strengthened zone.
Figure 4-39. Load–strain curve of the concrete in the column vicinity.
165
Figure 4-40. Load–strain curves of the internal tensile reinforcement.
Figure 4-40 shows the load–strain curves of the steel reinforcement at different distances from
the slab centre. The strain gauge data indicate that the steel reinforcement did not yield. Figure
4-41 shows the load–strain curves of the CFRP composites. Each strain gauge represents the
strain of one of the CFRP sheets, which helped with monitoring the behaviour of all the CFRP
sheets during the experiment. Based on the CFRP load–strain curves, the ultimate strain
achieved by the CFRP for LFS was 0.0062–0.0068, which is less than the CFRP rupture strain
of about 0.0095. Hence, the CFRP sheets for LFS did not rupture.
Figure 4-41. Load–strain curves of the CFRP sheets.
166
Because the FRP materials followed linear behaviour and their strains were about 68% of the
CFRP rupture strain, the CFRP stress was about 68% of their ultimate strength. Based on this
strain and the deformation compatibility shown in Figure 4-34, the CFRP sheets achieved
greater strain than the steel reinforcement under the same load. This was confirmed by the
CFRP and steel load–strain curves shown in Figures 4-40 and 4-41.
Table 4-10 compares the characteristics of this slab (LFS) and the control specimen (L0), such
as their ultimate loads and deflections, to demonstrate the effect of combining FRP and shear
strengthening methods to retrofit RC slabs with a low tensile reinforcement ratio. LFS showed
a considerable improvement in the load capacity compared with L0. However, the slab
deflection and ductility were reduced. In addition, the slab failure mode changed from flexural
failure for L0 to punching failure for LFS.
Table 4-10. Comparison between L0 and LFS.
Slab Load capacity Increase in
load capacity
Deflection Decrease in
deflection
Failure mode
L0 43.4
185%
18.2
44%
Flexural failure
LFS 123.6 10.1 Punching failure
Table 4-11 compares the results of LFS (strengthened with shear reinforcement and CFRP) and
LF (strengthened with CFRP) to consider the effect of applying shear reinforcement to the slabs
already strengthened with FRP. Note that both slabs failed in punching. However, the critical
punching area shifted from the column vicinity for LF to outside the shear reinforced area for
LFS, as shown in Figure 4-42. The test data confirmed that both the ultimate load capacity and
deflection of LFS were enhanced compared to LF, which enhanced the slab’s energy
absorption. This needs to be explained by considering the vertical (shear) reinforcement
mechanism to strengthen RC slabs that fail by punching.
Table 4-11. Comparison between LF and LFS.
Slab Load capacity Increase in
load capacity
Deflection Increase in
deflection
Failure mode
LF 104
19%
8.1
25%
Punching failure
LFS 123.6 10.1 Punching failure
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Figure 4-42. Punching failure in LF and LFS.
Figure 4-43. Strut and tie model for punching failure of RC slabs [32].
Strut and tie modelling (STM) which has been confirmed by Eurocode 2 to be accurate for
modelling the behaviour of RC structures [12], was applied here to explain how the vertical
(shear) reinforcement can effectively enhance the slab punching resistance. STM is based on a
truss analogy to simplify the behaviour of the structure, where tie and strut members are used
to model the tensile and compressive elements. Ritter was the first to apply the truss mechanism
to explain the behaviour of an RC flexural member [113]. Muttoni [32] applied STM to an RC
flat slab with a relatively high tensile reinforcement ratio but without shear reinforcement, as
shown Figure 4-43. The most critical element in RC slabs that fail by punching is the
compressive strut element. Concrete crushing of the assumed compressive strut element causes
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punching failure. Figure 4-44 presents an ideal strut and tie model of the punching region to
show how forces affect the compressive strut according to Hong and Ha’s [114] assumption.
Figure 4-44. Effect of applied forces on the critical compressive strut of an RC flat slab.
Figure 4-45. Vertical (shear) reinforcement mechanism to increase the slab punching strength.
Vertical (shear) reinforcement enhances the capacity of the compressive strut to carry more of
the applied forces. Figure 4-45 shows the compressive strut and applied vertical (shear)
169
reinforcement. Because the compressive strut in the column vicinity is the most critical element
(before vertical reinforcement is applied) for RC slabs that fail by punching, enhancing its
strength can increase the load capacity of the whole structure. As shown in Figure 4-45, the
tensile force carried by the shear (vertical) reinforcement (FS) has two components. The
component in the direction of the compressive strut (FS∙sin 𝜃) resists the enhanced compressive
forces in the critical strut, which increases the required applied load to crush it. The other
component perpendicular to the compressive strut (FS∙cos 𝜃) resists the propagation of inclined
cracks in combination with shear.
Thus, applying vertical (shear) reinforcement in the column vicinity of an RC slab not only
resist the crack propagation from shear combination but also strengthens the critical
compressive strut by partially neutralising the compression forces of this strut. Hence, the
vertical (shear) reinforcement enhances the punching strength by increasing the critical
compressive strut capacity to carry compressive forces along with shear strengthening.
Enhancing the capacity of the compressive strut in the column vicinity to carry compressive
forces needs to be balanced by an increase in the tensile stresses in the tensile reinforcements.
The greater tensile forces required in the slab tension face are provided by greater slab
deflection compared to slabs that have not been strengthened by vertical (shear) reinforcement.
This explains the increased deflection of LFS compared to LF.
Figure 4-46. Critical compressive strut in an RC slab considering shear strengthening.
170
Note that strengthening the compressive strut in the column vicinity may shift the most critical
element of the structure in STM outside the shear strengthened zone (see Figure 4-46). When
the compressive strut in the column vicinity is strengthened, an un-strengthened compressive
strut outside the shear reinforced region may reach its ultimate capacity first. This situation
results in punching failure being initiated outside the shear reinforced zone and explains the
experimental observations shown in Figure 4-42 of the punching failure shifting from the
column vicinity for LF to outside the shear reinforced region for LFS. Figure 4-47 shows the
concrete cracks on the slab tension surface according to the experimental and numerical
models.
Figure 4-47. Concrete cracks in the tension surface of LFS.
171
4.3.3. Slabs with an initial high tensile reinforcement ratio (category H)
4.3.3.1. Control specimen with a high tensile reinforcement ratio (H0)
Figure 4-48. Load–deflection curves of the experimental and FE models for H0.
Figure 4-49. Punching failure in the column vicinity of H0.
H0 was the control specimen with a high tensile reinforcement ratio (1.1%) that had not been
strengthened. It was used as a reference to observe the influence of different strengthening
172
techniques on the slab characteristics. Figure 4-48 shows that the load–deflection curves of the
experimental and numerical models had acceptable consistency. The experimental load–
deflection curve demonstrated a brittle punching failure as there was a sudden drop after the
ultimate load capacity of the slab was reached. Note that brittle punching failure was expected
for H0 because of its high tensile reinforcement ratio and was confirmed by the experimental
observations, as shown in Figure 4-49. The load–strain curve of the concrete in the column
vicinity (see Figure 4-50) demonstrated concrete compressive crushing because the concrete
strain exceeded the crushing strain.
Figure 4-50. Load–strain curve of the concrete in the column vicinity.
Figure 4-51. Load–strain curves of the internal tensile reinforcement.
173
Figure 4-51 shows the load–strain curves of the steel bars, which demonstrated no yielding of
the tensile reinforcement in H0. This is common in RC slabs with a high tensile reinforcement
ratio that fail in punching. The punching failure mechanism of H0 is the same as that explained
for LF. Figure 4-52 shows the concrete cracks on the slab’s tension surface according to the
experimental and numerical models.
Figure 4-52. Concrete cracks in the tension surface of H0.
174
4.3.3.2. Shear strengthened slab with a high tensile reinforcement ratio (HS)
Figure 4-53. Load–deflection curves of the experimental and FE models for HS.
Figure 4-54. Flexural punching failure in HS.
HS was the slab with a high tensile reinforcement ratio that was strengthened with vertical
(shear) bars. Figure 4-53 shows the experimental and numerical load–deflection curves for HS.
The experimental load–deflection curves showed that the failure mode was not completely
ductile or brittle. Hence, the expected failure mode can be assumed to be a mixture of flexural
175
and punching failure called flexural punching. This was confirmed by experimental
observations (see Figure 4-54) and the data obtained from the steel and concrete strain gauges
(see Figures 4-55 and 4-56).
Figure 4-55. Load–strain curves of the steel reinforcement.
Figure 4-56. Load–strain curve of the concrete in the column vicinity.
Flexural punching failure of slab punching followed by partial yielding of the tensile
reinforcement was confirmed by the load–strain curves of the steel reinforcement shown in
Figure 4-55. The concrete load–strain curve (Figure 4-56) showed that the concrete strain in
the column vicinity did not exceed the concrete visible crushing strain. In addition, the concrete
strain achieved in the column vicinity of HS was not as critical as the concrete strain in the
176
column vicinity of H0 (Figure 4-50), which demonstrates the effect of vertical (shear)
reinforcement.
Table 4-12 compares the properties of the current slab (HS) and control specimen (H0), such
as their maximum deflection and ultimate load, to demonstrate the influence of vertical (shear)
reinforcement in the critical punching area on the slab characteristics. Both the load capacity
and deflection of HS were enhanced with vertical reinforcement, which may have enhanced
the energy absorption. Furthermore, the failure mode changed from brittle punching failure to
moderately ductile flexural punching failure, which indicates the enhanced ductility of HS. In
addition, the concrete compressive crushing that caused punching shifted from the column
vicinity for H0 to outside the shear reinforced region for HS, as shown in Figure 4-57.
Table 4-12. Comparison between H0 and HS.
Slab Load capacity Increase in load
capacity
Deflection Increase in
deflection
Failure mode
H0 82.9
13%
10.4
20%
Punching failure
HS 94.1 12.5 Flexural punching failure
Figure 4-57. Punching failure in H0 and HS.
Note that the partial yielding of the steel reinforcement in the column vicinity was mainly due
to the vertical (shear) reinforcement because the tensile reinforcement in H0 did not yield. By
applying vertical bars in the column vicinity, the critical compressive strut (for which failure
177
may cause punching failure of the slab) was strengthened in compression and shear, which
increased the capacity of HS to carry more applied forces. As the externally applied forces
increased, the section of HS carried more tensile stresses compared with H0 to balance the
compressive and tensile forces. This explains why the tensile reinforcement yielded partially
in HS, but there was no yielding in H0. Because the tensile reinforcement ratios were the same
for H0 and HS, the shear strengthened slab (HS) needed to deflect more to provide the required
excessive tensile stresses.
Figure 4-58. Concrete cracks in the tension surface of HS.
178
Note that vertical reinforcement did not considerably affect the stiffness of HS compared with
H0, based on the slopes of the load–deflection curves in Figure 4-19. These slopes represent
the stiffness of a structure based on Ebead and Marzouk’s [5] assumption. However, FRP
strengthening increases the slab stiffness while enhancing the load capacity, which may reduce
a specimen’s deflection, ductility, and energy absorption. This clarifies why shear
strengthening can enhance both the slab load capacity and ductility despite FRP strengthening,
which enhances the load capacity of the slab but may reduce the ductility. Figure 4-58 shows
concrete cracks in the tension surface of HS according to both the experimental and numerical
models.
4.3.3.3. FRP strengthened slab with an initial high tensile reinforcement ratio (HF)
Figure 4-59. Load–deflection curves of the experimental and FE models for HF.
HF was the slab with a high initial tensile reinforcement ratio that was strengthened by
mounting CFRP sheets on its tension surface. Figure 4-59 shows the load–deflection curves of
the experimental and FE models for HF. The sudden drop in the experimental load–deflection
curve after the ultimate load capacity was reached indicates the brittle failure mode of punching
failure (see Figure 4-60). The concrete load–strain curve (see Figure 4-61) shows that the
compressive crushing strain was exceeded, which was expected because of punching in the
column vicinity.
179
Figure 4-60. Punching failure in HF.
Figure 4-61. Load–strain curve of the concrete in the column vicinity.
Figure 4-62 shows the load–strain curves of the steel reinforcement at different distances from
the slab centre. The strain gauges show that the steel reinforcement did not yield. Figure 4-63
shows the load–strain curves of the CFRP sheets; each curve represents the strain of one of the
sheets. The ultimate CFRP strain achieved for HF was 0.0029–0.0032, which is less than the
CFRP rupture strain of about 0.0095. This means that the sheets did not rupture. The CFRP
sheet stress was about 32% of the ultimate FRP strength considering the linear behaviour of
FRP composites.
180
Figure 4-62. Load–strain curves of the steel reinforcement.
Figure 4-63. Load–strain curves of the CFRP composites.
Table 4-13 compares the current slab (HF) and control specimen (H0) to indicate the effect of
applying CFRP sheets to strengthen RC slabs with a high tensile reinforcement ratio. HF
showed a 42% improvement in the load capacity compared with H0. However, the slab
deflection and ductility were reduced, which may have been due to the increased slab stiffness
181
with FRP strengthening. Both HF and H0 had high tensile reinforcement ratios, and their failure
mode was brittle punching failure due to concrete compressive crushing in the column vicinity.
Table 4-13. Comparison between H0 and HF.
Slab Load capacity Increase in
load capacity
Deflection Decrease in
deflection
Failure mode
H0 82.9
42%
10.4
39%
Punching failure
HF 117.9 6.2 Punching failure
The analysis results indicate that FRP strengthening increases the load capacity of RC slab with
both low and high tensile reinforcement ratios. CFRP increases the load capacity of RC slabs
with low tensile reinforcement by increasing the tensile reinforcement, as explained in Section
4.3.2.3. The present section clarifies how FRP strengthening enhances the punching resistance
of RC slabs with high tensile reinforcement ratio, which already fail by punching. This has not
been considered in previous studies.
As noted earlier, RC slabs with a high tensile reinforcement ratio (>1%) fail by punching failure
[32] due to concrete compressive crushing. Hence, the enhanced tensile reinforcement from
applying CFRP sheets on the slab tension face for slabs with a low tensile reinforcement ratio
cannot explain the increased load capacity enhancement for slabs with an initial high tensile
reinforcement ratio. Previous studies [9, 57] have confirmed the increased punching strength
by applying FRP on the slab tension face. However, no mechanism has been determined for
how the strengthening process may enhance the punching strength of the slab. In this study,
STM was used to explain the behaviour of a slab with an initial high tensile reinforcement ratio
that had been strengthened by applying FRP sheets or plates to the tension face.
Figure 4-64 shows STM examples for RC slabs before and after FRP strengthening to show
how applying FRP on the slab tension surface can rearrange the struts and ties for proper
modelling of the RC slab behaviour. STM explains the stiffer behaviour of FRP strengthened
slabs compared with un-strengthened samples by the new arrangement of elements. Note that
the slope of the load–deflection curves indicates stiffer behaviour in the FRP strengthened
samples compared with the control specimens in Figure 4-19.
182
Figure 4-64. RC slabs strut and tie models before and after FRP strengthening.
Figure 4-65 shows the critical compressive strut in the column vicinity before and after FRP
strengthening and the forces from Figure 4-64. This can clarify the effect of applying CFRP
sheets to strengthen an RC slab by comparing the critical strut situations of the FRP
strengthened and un-strengthened samples. As shown in Figure 4-65, the angle between the
critical compressive strut and horizontal line increased with FRP strengthening compared to
the control specimen (β > θ).
The applied forces in Figure 4-65 shows that the inclined (critical) and horizontal compressive
struts can carry the compressive forces (C). However, the vertical forces (P) are only carried
by the inclined compressive strut. If the slab fails to carry the compressive forces (C), the most
critical element would be the horizontal compressive element, whose main duty is carrying the
compressive forces (C), similar to the tensile steel reinforcement that forms the tensile tie and
mainly carries the tensile forces (T). Note that the failure of the tensile tie to carry tensile forces
may cause ductile flexural failure, which is common in RC slabs with a low tensile
reinforcement ratio.
183
Figure 4-65. Critical compressive struts in un-strengthened and FRP strengthened slabs.
However, the critical element for which failure causes punching failure of the slab is the
inclined compressive element in the column vicinity. As noted earlier, the compressive forces
(C) can be carried by the horizontal strut, whereas the inclined strut is the only element in the
slab strut and tie model that can carry the vertical forces (P). In other words, the compressive
forces in the inclined strut are adjusted to equilibrate between the vertical forces (P) and vertical
component of the compressive forces. The failure of the inclined strut to carry the vertical
forces may cause a strut fracture that can result in punching.
Figure 4-65 shows that the forces in the critical strut are equal to the multiplication of the strut
force (S) and the sine of the angle between the strut and horizontal line, which represents the
vertical component of the compressive strut forces. Hence, the same amount of strut force (S)
in the FRP strengthened sample can support a larger vertical force than that in the un-
strengthened sample (S × sin β > S × sin θ) because sin β is greater than sin θ. In other words,
more vertical forces can be carried by the compressive strut of the FRP strengthened sample
than that of the un-strengthened sample. This explains how FRP strengthening can enhance the
slab resistance to punching due to the failure of the critical strut to carry vertical forces. Figure
4-66 shows the slab cracks on the tension surface of the experimental and FE models. The
CFRP sheets de-bonded after punching failure.
184
Figure 4-66. Concrete cracks on the tension face of HF.
4.3.3.4. FRP and shear strengthened slab with an initial high tensile reinforcement
ratio (HFS)
HFS was the slab with a high initial tensile reinforcement ratio that was strengthened by
applying CFRP sheets on its tension surface and vertical (shear) bars to cover the critical
punching area. Figure 4-67 compares the load–deflection curves of the experimental and FE
models to demonstrate the consistency of the results. The sudden drop after the slab reached
the ultimate load capacity in the experimental load–deflection curve was due to FRP de-
bonding. Figure 4-68 shows the FRP de-bonding in the experimental and numerical models of
HFS.
185
Figure 4-67. Load–deflection curves of the experimental and FE models for HFS.
Figure 4-68. Concrete cracks on the tension face of HFS.
186
The load–strain curve of the concrete (Figure 4-69) indicates no concrete compressive crushing
in the column vicinity, which was expected because there was no punching failure in the
experimental observation. In addition, the concrete strain achieved for this slab was less than
that for HF (Figure 4-61), which may indicate the effect of applying vertical (shear)
reinforcement in the column vicinity.
Figure 4-69. Load–strain curve of the concrete strain in the column vicinity.
Figure 4-70. Load–strain curves of the steel reinforcement.
Figure 4-70 shows the load–strain curves of the steel reinforcement at different distances from
the slab centre. The strain gauges show that the steel reinforcement did not yield. According to
187
the load–strain curves of the CFRP (Figure 4-71), the ultimate strain of different sheets ranged
from 0.0036 to 0.004, which is less than the CFRP rupture strain of 0.0095. Hence, the CFRP
sheets in this slab were not supposed to rupture, which was confirmed by the experimental
observations. Based on the linear behaviour of CFRP composites, the CFRP sheets reached
about 40% of their ultimate strength.
Figure 4-71. Load–strain curves of the CFRP composites.
Table 4-14 compares the characteristics of the current slab (HFS) and control specimen (H0)
to demonstrate the effect of applying FRP sheets and shear steel bars to strengthening an RC
slab with a high tensile reinforcement ratio. The load capacity of HFS was significantly
improved compared with H0. However, the slab deflection decreased. In addition, the failure
mode changed from punching failure to FRP de-bonding.
Table 4-14. Comparison between H0 and HFS.
Slab Load capacity Increase in
load capacity
Deflection Decrease in
deflection
Failure mode
H0 82.9
66%
10.4
31%
Punching failure
HFS 138 7.3 FRP de-bonding
Table 4-15 compares the results of HFS and HF to demonstrate the effect of applying vertical
(shear) reinforcement to strengthening a slab already strengthened with FRP. The test data
show that the load capacity and maximum deflection of HFS were increased compared to HF,
188
which increased the ductility and energy absorption. In addition, the slab failure mode changed
from punching failure to FRP de-bonding.
Table 4-15. Comparison between HF and HFS.
Slab Load capacity Increase in
load capacity
Deflection Increase in
deflection
Failure mode
HF 117.9
15%
6.2
18%
Punching failure
HFS 134.8 7.3 FRP de-bonding
The main reason for the FRP de-bonding of HFS was the high shear inter-laminar stress, which
has also been observed in previous studies [115, 116]. Based on the data for slabs with both
high and low initial steel reinforcement ratios, the inter-laminar stresses between the composite
and concrete layers increase with the initial tensile reinforcement ratio. Hence, FRP de-bonding
is more likely for RC slabs with a high initial tensile steel reinforcement ratio than those with
a low ratio.
4.3.4. Assessment of models to predict the capacity of the slabs
This section presents an assessment of different models for predicting the capacity of flat slabs
tested considering the experimental results. The punching strengths of the slabs were evaluated
based on the suggestions of Eurocode 2 and ACI 318 (see Section 2.5.3.1), and the slabs՚
flexural capacities were estimated according to the Ebead–Marzouk and Elstner–Hognestad
models (see Section 2.5.3.2) that were considered in the literature review. Table 4-16 presents
the experimental results and model predictions for different slabs to distinguish the most
suitable and accurate model and equation for predicting the capacity of RC slabs with different
tensile reinforcement ratios.
The results demonstrated that the model predictions for the flexural capacities of the slabs may
provide a reasonable estimation for RC slabs with a low tensile reinforcement ratio that fail by
ductile flexural failure. However, these models may not be accurate for estimating the ultimate
load capacity of RC slabs with high tensile reinforcement ratios (including both tensile steel
reinforcement and FRP sheets) because these slabs cannot reach their expected ultimate
flexural capacity and fail by brittle punching failure. The ultimate load capacity of slabs with
189
a high tensile reinforcement ratio may be estimated by considering the codes’ predictions to
evaluate the slabs՚ punching capacity.
Table 4-16. Experimental results and model estimations to predict the punching capacity of the slabs.
Specimen Ultimate load
(kN)
Punching strength
(kN)
Flexural capacity
(kN)
Failure mode
EXP ACI Eurocode 2 Ebead–Marzouk Elstner–Hognestad
L0 43.4 61.4 44.7 42.5 48 Flexural
LS 45.6 83.2 65.4 42.5 48 Flexural
LF 104 61.4 80.3 117.3 130.7 Punching
LFS 123.6 83.2 102 117.3 130.7 Punching
H0 82.9 59.8 73.7 91.2 99.6 Punching
HS 94.1 81.5 90.6 91.2 99.6 Flexural punching
HF 117.9 59.8 101.2 133 152.3 Punching
HFS 138 81.5 134 133 152.3 De-bonding
According to the results, there is an acceptable consistency between the ultimate loads of the
experimental models that fail by ductile flexural failure and the models’ estimations for the
slabs՚ flexural capacity. The results indicated that the Ebead–Marzouk model provides a more
reliable evaluation than the Elstner–Hognestad model, which overestimated the slabs՚ flexural
capacity.
The results showed that the Eurocode 2 estimation for evaluating the slabs՚ punching strength
may be more reliable than the ACI evaluation. This may be because Eurocode 2 considers the
effect of tensile reinforcements to estimate the punching capacity of slabs, while ACI does not.
It should be noted that the parameters considered by ACI to predict the punching capacity of
flat slabs are concrete compressive strength, slabs՚ effective depth and column dimensions as
well as shear reinforcements՚ properties and patterns. So, these results in ACI estimating the
same punching strength for RC slabs with different tensile reinforcement ratios, which
contradicts the fact that increasing the tensile reinforcement ratio, may enhance the slabs՚
punching strength. Note that both codes underestimated the slabs՚ punching strength.
Based on this assessment of the code and models’ estimations according to the experimental
results, the following recommendations and advice are presented. First, the failure modes of
the slabs should be considered to determine which code or model estimation is relevant for
evaluating the slabs՚ ultimate load capacity. The ultimate load capacities of the slabs with a
190
low tensile reinforcement ratio (which fail in flexure) should be estimated with the Ebead–
Marzouk model because these slabs can reach their flexural capacities. In the case of slabs with
a high tensile reinforcement ratio (which fail in punching), the slabs՚ ultimate load capacities
should be evaluated based on Eurocode 2 (which calculates the punching strength of the slabs)
because these slabs cannot reach their expected flexural capacities due to punching failure.
4.4. Summary
As discussed in this chapter, eight RC flat slabs were tested and classified into two categories:
low and high tensile reinforcement ratios. Each category had four slabs, including a control
specimen, slab strengthened with FRP, specimen with shear reinforcements, and slab
strengthened with both FRP and shear reinforcements.
The results demonstrated that increasing the tensile reinforcement ratios can enhance the
ultimate load capacity for slabs with both low and high initial tensile reinforcement ratios. The
main reason to increase the load capacity of RC slabs with low tensile reinforcement ratio (by
applying FRP sheets) is to enhance their tensile strength, which allows the structure to carry
more tensile stress. However, FRP strengthening of RC slabs with an initial high tensile
reinforcement ratio changes the structure’s failure mechanism, and the slabs՚ ultimate load
capacity is enhanced by the increased punching strength of the slab. Increasing the slabs՚ tensile
reinforcement ratio can decrease the ductility of the slabs and cause brittle failure (such as
punching), which is not a desirable failure mode.
In spite of FRP strengthening, applying shear reinforcements are only effective for specimens
with high tensile reinforcement ratio (including both steel reinforcement and FRP strips).
Increasing the shear reinforcement ratios may enhance the ductility of flat slabs with a high
tensile reinforcement ratio. The results also indicate that slabs strengthened with both FRP
sheets and shear reinforcement could reach a higher load capacity than slabs strengthened with
only one of the mentioned strengthening methods. The possibility of FRP de-bonding failure
is more likely in RC slabs with high initial tensile reinforcement ratios.
191
5. Parametric study
5.1. Introduction
A comprehensive parametric study using calibrated finite element models has been conducted
in this chapter to investigate and analyse the effect of different parameters on the behaviour of
flat slabs. This may provide guidance to suggest the most efficient strengthening strategy to
satisfy the required objectives of strengthening flat slabs considering their properties and
conditions. The effective parameters considered in this chapter are as follows:
• The tensile reinforcement ratios of flat slabs
• The compressive reinforcements of flat slabs
• The pattern, thickness and number of FRP sheets applied to strengthen flat slabs
The models have been validated and calibrated based on the experimental and numerical
models in Chapter 4. All of the slabs in the parametric study were 650 × 650 mm2 square
specimens with a thickness of 60 mm and simply supported; which are the same as the
experimental samples in Chapter 4. The properties of concrete and steel reinforcements in
different samples are mentioned in the following tables. The properties of FRP sheets are the
same as mentioned in Chapter 4 (Table 4-6). The uniform pressure load is applied on the
column stub of flat slabs till failure happens. The deflections of the samples have been
measured in the centre of the slabs.
Table 5-1. Concrete properties.
Modulus of elasticity
(GPa)
Cube compressive
strength (MPa)
Cylinder tensile
strength (MPa)
Poisson’s ratio
33 53.45 4.16 0.2
Table 5-2. Steel reinforcements properties.
Steel rebar diameter
(mm)
Modulus of
elasticity (GPa)
Yield strength
(MPa)
Yield
strain
Ultimate
strength
(MPa)
Ultimate
strain
6 200 560 0.0030 632 0.0139
8, 10 200 551 0.0031 620 0.0131
192
5.2. Parametric investigation
5.2.1. The tensile reinforcement ratio
Five flat slabs are modelled numerically in this section to investigate the effect of tensile
reinforcement ratios on the behaviour of RC samples. The tensile reinforcement ratios of the
slabs were 0.3%, 0.5%, 0.85%, 1.1% and 1.6%. The work aimed to consider the effect of
varying the tensile reinforcement ratios on the behaviour of flat slabs. Figures 5-1 to 5-5 show
the arrangements of the tensile reinforcements for RC slabs with the different tensile
reinforcement ratios 0.3%, 0.5%, 0.85%, 1.1% and 1.6%, which are named as S-0.3, S-0.5, S-
0.85, S-1.1 and S-1.6, respectively.
Figure 5-1. Slab with 0.3% tensile reinforcement ratio (S-0.3).
Figure 5-2. Slab with 0.5% tensile reinforcement ratio (S-0.5).
193
Figure 5-3. Slab with 0.85% tensile reinforcement ratio (S-0.85).
Figure 5-4. Slab with 1.1% tensile reinforcement ratio (S-1.1).
Figure 5-5. Slab with 1.6% tensile reinforcement ratio (S-1.6).
194
Table 5-3. Model results by varying their tensile reinforcement ratios.
Specimen Tensile
reinforcement ratio
Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
S-0.3 0.3% 20.7 35.5 21.4 Flexural
S-0.5 0.5% 28.2 46.5 19.3 Flexural
S-0.85 0.85% 61.8 72.4 13.8 Flexural-punching
S-1.1 1.1% 87.2 87.2 10.2 Punching
S-1.6 1.6% 98.1 98.1 7.9 Punching
Table 5-3 shows the tensile reinforcement ratio, yield load, load bearing capacity, ultimate
deflection and the failure mode of the slabs. As it can be seen from Table 5-3 and Figures 5-6
and 5-7, the load capacity of the slabs has been increased by the enhancement of the tensile
reinforcement ratios; however, the deflection of the slabs has been reduced due to the raising
of the tensile reinforcement ratios. It is noteworthy that the tensile reinforcements widely
yielded in slabs with low tensile reinforcement ratios (S-0.3, S-0.5), which resulted in ductile
flexural failure.
Figure 5-6. Ultimate load capacity–tensile reinforcement ratio curve.
The failure mode of S-0.85 with moderate tensile reinforcement ratio is a flexural-punching
that happens due to the partial yielding of tensile reinforcements which is followed by concrete
compressive crushing in the column vicinity. The results clarify that there is no tensile
reinforcement yielding in slabs with high tensile reinforcement ratios (S-1.1 and S-1.6) and
their failure mode is brittle punching failure which happens due to concrete compressive
195
crushing before the yielding of tensile reinforcements. Therefore, the yield load and ultimate
load in slabs with high tensile reinforcement ratios (S-1.1 and S-1.6) are the same.
Figure 5-7. Deflection–tensile reinforcement ratio curve.
The mentioned results confirm Park and Gamble’s [31] statement that the failure mode is
changed from ductile flexural failure to brittle punching failure when the tensile reinforcement
ratio exceeds 1%.
Figure 5-8. Load–deflection curves of RC slabs with different tensile reinforcement ratio.
196
Figure 5-8 shows the load–deflection curves of the slabs by varying their tensile reinforcement
ratios. According to the load–deflection curves, the ductility of the slabs has been decreased by
the enhancement of the tensile reinforcement ratios. The ductility of the slabs can be estimated
based on their energy absorption, which is evaluated by the area under the load–deflection
curves [5].
Table 5-4 shows how effective different strengthening strategies would be for the slabs
considered in this section, based on numerical modelling and the slabs՚ behaviours. It is
noteworthy that the pattern of FRP and shear strengthening mentioned here is the same as the
strengthening pattern applied in Chapter 4 (see Figures 4-6 and 4-8). Table 5-4 shows that the
efficiency of applying FRP sheets (to strengthen RC slabs) decreases by increasing the slabs՚
tensile reinforcement ratios.
Table 5-4. The effect of different strengthening methods on RC slabs with different tensile reinforcement ratios.
Specimen
Strengthening methods
FRP strengthening Shear strengthening FRP and shear strengthening
S-0.3 Very good Not suitable Very good
S-0.5 Very good Not suitable Very good
S-0.85 Good Suitable Very good
S-1.1 Good Good Very good
S-1.6 Suitable Good Good
5.2.2. The compressive reinforcement
In this section, a comparison is made between samples with and without compressive
reinforcements. Altogether, four slabs are considered in this section; they are categorised into
two groups as slabs with low (0.5%) and high (1.1%) tensile reinforcement ratios. The slabs
without compressive reinforcements (S-0.5 and S-1.1), which are the control slabs have been
considered in the previous section. Table 5-5 shows the tensile reinforcement ratios of the slabs
considered in this section and whether they have compressive reinforcements or not.
197
Table 5-5. Models description.
Tensile reinforcement ratio Specimen Compressive reinforcement
Low tensile reinforcement ratio
(0.5)
S-0.5 Without compressive reinforcement
SC-0.5 With compressive reinforcements
High tensile reinforcement ratio
(1.1)
S-1.1 Without compressive reinforcement
SC-1.1 With compressive reinforcements
Two more slabs (SC-0.5 and SC-1.1) are simulated numerically to investigate the effect of the
compressive reinforcements on the behaviour of flat slabs. SC-0.5 and SC-1.1 (see Figures 5-
9 and 5-10) have the same dimension and tensile reinforcement ratios as S-0.5 and S-1.1 (see
Figures 5-2 and 5-4), respectively, but with compressive reinforcements. This provides an
opportunity to see the effect of having compressive reinforcements in RC slabs.
Figure 5-9. The arrangement of reinforcements in SC-0.5.
Figure 5-10. The arrangement of reinforcements in SC-1.1.
198
Table 5-6 shows the yield load, load-bearing capacity, ultimate deflection and the failure modes
of the slabs considered in this section. The load deflection-curves of the slabs can be seen in
Figure 5-11. The results demonstrate that the effect of having compressive reinforcements in
RC slabs with low tensile reinforcement ratio is not considerable. This was expected, as the
main reason for failure in slabs with low tensile reinforcement ratio is yielding of tensile
reinforcements before concrete compressive crushing, which causes a ductile flexural failure.
Thus, compressive reinforcements applied to increase the capacity of structures in compression
may not be effective in RC slabs that fail in flexure.
Table 5-6. The effect of compressive reinforcements on the behaviour of RC slabs.
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
S-0.5 28.2 46.5 19.3 Flexural
SC-0.5 30.4 48.9 20.1 Flexural
S-1.1 87.2 87.2 10.2 Punching
SC-1.1 95.5 109.7 13.6 Flexural-punching
Figure 5-11. Load–deflection curves of RC slabs with and without compressive reinforcements.
199
However, the compressive reinforcements in RC slabs with high tensile reinforcement ratio
may change the slabs՚ behaviour by increasing both the slabs՚ load capacity and ductility.
Applying compressive reinforcements enhances the compressive strength of RC slabs, which
increases their punching capacity that may happen due to concrete compressive crushing. The
enhancement of the slabs՚ punching capacity could delay the punching failure, which provides
an opportunity for the tensile reinforcements in RC slabs to reach more tensile stresses.
This may cause wide yielding of the tensile reinforcement and provide more ductile behaviour
and failure. It is noteworthy that the failure mode has been changed from brittle punching
failure in S-1.1 (without compressive reinforcement) to a more ductile flexural-punching
failure in SC-1.1 (with compressive reinforcement), which confirms the aforementioned
statement.
Table 5-7 shows how efficient different strengthening strategies would be for the different slabs
considered in this section, based on the findings in Chapter 4 and the slabs՚ behaviours. It is
noteworthy that the pattern of FRP and shear strengthening mentioned here is the same as the
strengthening pattern applied in Chapter 4 (see Figures 4-6 and 4-8).
Table 5-7. The effect of different strengthening methods on RC slabs with and without compressive reinforcements.
Specimen
Strengthening methods
FRP strengthening Shear strengthening FRP and shear strengthening
S-0.5 Very good Not suitable Very Good
SC-0.5 Very good Not suitable Very Good
S-1.1 Good Good Very Good
SC-1.1 Good Suitable Very Good
5.2.3. The pattern of FRP sheets to strengthen RC slabs
In this section, different FRP strengthening patterns are considered to see the effect of the
pattern of FRP sheets on the behaviour of strengthened RC slabs. Figure 5-12 shows the
different FRP strengthening pattern applied in this section. The FRP sheets applied to
strengthen the RC slabs in Figure 5-12a are orthogonal. However, the FRPs applied in Figure
5-12b have been skewed.
200
Figure 5-12. Orthogonal and skewed pattern of FRP sheets to strengthen RC slabs.
Table 5-8. Models description.
Tensile reinforcement ratio Slab Applied strengthening method
Low tensile reinforcement ratio
(0.5%)
S-0.5 (Control specimen) ________
SFO-0.5 Orthogonal FRP sheets
SFS-0.5 Skewed FRP sheets
High tensile reinforcement ratio
(1.1%)
S-1.1 (Control specimen) ________
SFO-1.1 Orthogonal FRP sheets
SFS-1.1 Skewed FRP sheets
As can be seen from Table 5-8, altogether six slabs are considered in this section; they are
categorised into two groups: low (0.5%) and high (1.1%) tensile reinforcement ratios. There
are two un-strengthened slabs (S-0.5 and S-1.1), which are the control slabs that have been
considered in the previous sections. There are two more slabs in each category which have
been strengthened with FRP sheets in different patterns to find the most efficient FRP
strengthening arrangements. Table 5-9 shows the yield load, load-bearing capacity, ultimate
deflection and the failure modes of the slabs. The load deflection-curves of the slabs in this
section can be seen in Figure 5-13. The results demonstrate that there is no considerable
difference between the behaviours of the strengthened slabs with orthogonal and skewed FRP
strengthening patterns.
201
Table 5-9. The effect of different strengthening patterns on the behaviour of RC slabs.
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
S-0.5 28.2 46.5 19.3 Flexural
SFO-0.5 101.8 101.8 8.2 Punching
SFS-0.5 104 104 8.1 Punching
S-1.1 87.2 87.2 10.2 Punching
SFO-1.1 117.9 117.9 6.2 Punching
SFS-1.1 121.3 121.3 5.9 Punching
Figure 5-13. Load–deflection curves of strengthened RC slabs with different strengthening patterns.
5.2.4. The number of FRP sheets
Another parameter that is considered in this section is the effect of different numbers of FRP
sheets in strengthening RC slabs by modelling slabs including the control specimen (S-0.5) and
three more slabs by varying the number of FRP sheets (see Table 5-10). Figure 5-14 shows the
FRP strengthening pattern with different FRP layers applied to investigate the effect of the
number of FRP strips in strengthening RC slabs.
202
Table 5-10. Models description.
Slab Applied strengthening method Tensile steel reinforcement ratio
S-0.5 (Control specimen) ________
0.5% SF1 FRP strengthening (1 strip in each direction)
SF2 FRP strengthening (2 strips in each direction)
SF3 FRP strengthening (3 strips in each direction)
Figure 5-14. FRP strengthening by varying FRP layers.
Table 5-11 shows the yield load, load bearing capacity, ultimate deflection and the failure
modes of the slabs. The load–deflection curves of the slabs considered in this section can be
seen in Figure 5-15. The results demonstrate that increasing the number of FRPs may enhance
the ultimate load capacity of the structure, but decrease the ductility of the samples as well as
their failure modes.
203
Table 5-11. The effect of varying FRP layers on the behaviour of strengthened RC slabs.
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
S-0.5 28.2 46.5 19.3 Flexural
SF1 68 76.1 12.5 Flexural-punching
SF2 101.8 101.8 8.2 Punching
SF3 113.4 113.4 7.7 Punching
Figure 5-15. Load–deflection curves of strengthened RC slabs by varying FRP layers.
5.2.5. The thickness of FRP sheets to strengthen RC slabs
In this section, the effect of the thickness of FRP sheets in strengthening RC slabs is
investigated by varying the FRP thickness and considering its effect on the slabs՚ load
capacities and deflections. As can be seen from Table 5-12, altogether four slabs are considered
in this section.
Table 5-12. Models description.
Slab Applied strengthening method Tensile steel reinforcement ratio
S-0.5 (Control specimen) ________
0.5% SF-0.8 1 layer- FRP strengthening (FRP thickness:0.8)
SF-1.6 2 layers- FRP strengthening (FRP thickness:1.6)
SF-2.4 3 layers -FRP strengthening (FRP thickness:2.4)
204
There is an un-strengthened slab (S-0.5), which is the control slab, and three more slabs, which
have been strengthened with one to three layers of FRP sheets, respectively. The arrangement
of the tensile reinforcement in all the slabs in this section is the same as S-0.5 (control
specimen) that can be seen in Figure 5-2. Figure 5-14b shows the arrangements of the FRP
sheets applied to strengthen the RC slabs. Table 5-13 shows the yield load, load-bearing
capacity, ultimate deflection and the failure modes of the slabs. The load deflection-curves of
the slabs can be seen in Figure 5-16.
Table 5-13. The effect of varying FRP thickness on the behaviour of strengthened RC slabs.
Specimen Yield load
(kN)
Ultimate load
(kN)
Ultimate deflection
(mm)
Failure mode
S-0.5 28.2 46.5 19.3 Flexural
SF-0.8 101.8 101.8 8.2 Punching
SF-1.6 122.1 122.1 6.5 Punching
SF-2.4 120.3 120.3 5.8 FRP de-bonding
Figure 5-16. Load–deflection curves of strengthened RC slabs by varying FRP thickness.
The results demonstrate that increasing the FRP thickness from 0.8 mm in SF-0.8 to 1.6 mm
in SF-1.6 enhanced the ultimate load capacity of the structure; however, increasing the FRP
thickness to 2.4 mm in SF-2.4 has not enhanced the ultimate load capacity of the slabs. The
main reason why the slab’s load capacity in SF-2.4 was not enhanced could be because of high
205
inter-laminar shear stresses which have caused FRP de-bonding. Thus, the enhancement of
FRP thickness may increase the ultimate load capacity of the strengthened slabs if it does not
cause FRP de-bonding.
5.3. Summary
A comprehensive parametric study using calibrated finite element models has been conducted
in this chapter to analyse the effect of varying different parameters such as tensile
reinforcement ratio and compressive reinforcement as well as the pattern, number and thickness
of FRP strips (applied to strengthen RC slabs) on the behaviour of flat slabs.
The results demonstrated that enhancing the tensile reinforcement ratios may enhance the
ultimate load capacity of the strengthened slabs, but reduces the ductility of the structure.
Considering the effect of having compressive reinforcement, it is clear that flat slabs with
compressive reinforcements could reach more load capacity and deflection (which resulted in
having more ductility) as compared with the samples that do not include compressive
reinforcements.
According to the results, there is no significant difference in RC slabs strengthened with
orthogonal and skewed FRP sheets. However, the results show that the thickness and number
of FRPs applied to strengthen flat slabs need to be considered carefully to satisfy the
strengthened slabs՚ requirements. Based on the results, increasing the number of FRPs may
enhance the ultimate load capacity of the structure, but decrease the ductility of the samples as
well as their failure modes. It is noteworthy that increasing the thickness of the FRP strip may
also enhance the slab’s load capacity if it does not cause FRP de-bonding (as a result of high
inter-laminar shear stresses explained in section 4.3.3.4.).
206
6. Conclusions and future work
The main conclusions of this study are as follows:
• RC slabs with a low tensile reinforcement ratio have a ductile flexural failure mode
owing to the development of wide tensile cracks on the face with slab tension owing to
the yielding of tensile reinforcement. The typical load–deflection curves of RC slabs
with a low tensile reinforcement ratio followed a smooth line around the ultimate load
capacity of the slab as a result of the wide yielding of the steel reinforcement. This may
increase slab deflection, ductility and energy absorption compared with slabs with a
high tensile reinforcement ratio, which exhibit a brittle failure mode.
• Applying vertical (shear) reinforcement in the vicinity of the column of RC slabs with
a low tensile reinforcement ratio does not considerably change slab behaviour, and
cannot be assumed to be an efficient strengthening technique.
• Applying FRPs to the tension surface of RC slabs with a low tensile reinforcement ratio
is an efficient method for increasing load capacity. However, slab deflection and
ductility may be reduced. The higher load capacity in FRP-strengthened RC slabs with
a low tensile reinforcement ratio can be attributed to the increased overall tensile
reinforcement in the slab. FRP strengthening may be more efficient for retrofitting RC
slabs with a low tensile reinforcement ratio than a high ratio.
• The most common failure mode of two-way RC slabs with a high tensile reinforcement
ratio is brittle punching failure.
• Slab stiffness is not considerably affected by applying vertical (shear) steel bars to the
critical punching area. However, applying CFRP sheets to the tension surface enhances
slab stiffness according to the load–deflection curves.
• Applying vertical (shear) reinforcement in the critical punching area of two-way flat
slabs (with a high tensile reinforcement ratio) can increase load capacity and energy
absorption by strengthening the critical compressive strut in the vicinity of the column,
and can prevent the propagation of shear cracks. Applying FRPs to the tension surface
207
of RC slabs with a high tensile reinforcement ratio can enhance load capacity by
changing the slab mechanism to enable the critical compressive strut to carry greater
applied force.
• The possibility of FRP de-bonding owing to high shear inter-laminar stresses increases
for slabs with a high initial tensile reinforcement ratio.
• Applying a combination of FRP and shear strengthening methods to two-way RC slabs
may be the most efficient strengthening technique by both enhancing load capacity and
controlling brittle behaviour to some extent.
• The efficiency of strengthening RC slabs with prestressed FRPs depends on whether
there is full composite action or earlier FRP de-bonding. Applying prestressed FRP to
strengthen RC slabs is more efficient than strengthening with non-prestressed FRP in
the case of full composite action. However, the RC slab strengthened with prestressed
FRP cannot reach its expected load capacity in the case of earlier FRP de-bonding.
• Earlier FRP de-bonding (in the case of proper anchorage system) is mainly caused by
inner concrete fracture near the end plates for slabs strengthened with prestressed FRP
owing to the synergic action of the increment in tensile stresses in the region above the
steel reinforcement and below the neutral axis, and shear stresses near the neutral axes.
Near the end plates, stress transfer of prestressed FRPs creates a local compression zone
close to the concrete surface and a local tension zone above the steel reinforcements.
The superposition of the tensile stresses of the local tension zone and the tensile stresses
produced by applying external load on the column increases overall tensile stress level
in the relevant area. This process leads to concrete fracture, which propagates due to
shear stresses and, hence, causes the de-bonding of FRPs.
• By considering the results from both tests and the finite element analyses, it appears
that there can be an optimal prestress ratio of FRP for the given RC slab that can
increase its load capacity without causing earlier de-bonding that can be found by the
formula proposed.
208
• The mechanism revealed in this study may provide better understanding of the
strengthening strategy for different purposes in RC slabs rehabilitation.
• RC flat slabs with compressive reinforcements could reach more load capacity and
deflection (which resulted in having more ductility) as compared with the samples that
do not include compressive reinforcements.
• Increasing the number of FRPs may enhance the ultimate load capacity of the structure,
but decrease the ductility of the samples as well as their failure modes.
• Increasing the thickness of the FRP strips may enhance the slab’s load capacity if it
does not cause FRP de-bonding.
Some proposals for further experimental and numerical studies following this one are briefly
considered.
• One aspect that follows thesis studies concerns the strengthening of RC structures with
prestressed FRP plates. A formula was proposed in this study to estimate the optimum
FRP prestress ratio that may improve the load capacity of RC slabs without causing
FRP de-bonding. An experimental investigation can be conducted in this aspect by
varying the effective parameters in Equation 3-29 that can justify the accuracy of the
formula or modify it. Moreover, the accuracy of the formula to estimate the optimum
FRP prestress ratio for one-way RC structures, such as RC beams, can also be tested to
prove whether it is possible to use it comprehensively for one-way as well as two-way
RC structures.
• As explained in the analysis of the mechanism of RC slabs strengthened with
prestressed FRP, the main reason of FRP de-bonding is to initiate tensile cracks in the
region above the tensile steel reinforcement that propagate due to shear cracks that
result in FRP de-bonding. Hence, applying tensile reinforcements in the tensile crack
initiation zone (by drilling through the concrete to place steel bars or mounting tensile
reinforcement in the relevant area before casting the concrete) can reduce the possibility
of earlier FRP de-bonding. This process can enhance the optimum prestress ratio of
FRPs to strengthen RC slabs. Furthermore, other novel techniques can be considered to
209
reduce the possibility of prestressed FRP de-bonding, which is an undesirable failure
mode.
• As explained in the analysis of the results of slabs strengthened with vertical (shear)
reinforcements, the forces in the shear bars consist of two components that are parallel
and perpendicular to the direction of the critical compressive strut of the slabs that fail
in punching. The parallel component can reduce the compressive forces in the critical
compressive strut to increase its capacity, which can result in the enhancement of the
slabs’ load capacity. The perpendicular component can also resist the initiation and
propagation of shear cracks. Hence, the angle between the steel bars is called shear
reinforcements, and the critical compressive strut in the assumed strut and the tie model
of the slab can affect the efficiency of this strengthening method to enhance the slabs’
load capacity.
• To investigate the effect of varying the angle, the combinations of vertical and inclined
reinforcements (with different angles) can be applied to observe the effects of different
shear reinforcement arrangements on the behaviour of slabs by comparing the results
for shear strengthened slabs with the control specimens. More slabs with different
tensile reinforcement ratios can also be constructed to widen the range of samples
examined. An analysis of the results considering experimental and validated numerical
models in this respect may lead to the most efficient arrangement (considering the space
and angle of shear reinforcements) to position the steel bars, called shear reinforcement
in RC slabs with different tensile reinforcement ratios that fails in punching. Further
analysis in this respect can lead to a formula to estimate the optimal angle of steel bars
(positioned in the critical punching area) along the vertical or horizontal line to improve
the load capacity of the slabs by considering different tensile reinforcement ratios.
• The experimental investigation and the literature review in this study show that among
the most common methods to enhance the punching strength of column slabs involves
applying FRPs on their tension surface. The experimental layouts in the investigations
in the area so far have shown that FRPs have been commonly applied to the critical
punching area to enhance the punching strength of the slabs. Further investigation in
this respect can involve considering different strengthening patterns to clarify whether
210
the position of the FRPs can change the effect of FRP strengthening on the behaviour
of the RC flat slabs.
211
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