Structural Analysis of Strengthened RC Slabs

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

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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

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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 4-29. 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 4-33. 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

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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 4-41. 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 4-52. 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 4-57. 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 4-64. 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



Chapter 5

Figure 5-1. Slab with 0.3% tensile reinforcement ratio (S-0.3). ......................................................... 192


Figure 5-3. Slab with 0.85% tensile reinforcement ratio (S-0.85). ..................................................... 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 5-13. The effect of varying FRP layers on the behaviour of strengthened RC slabs. ............... 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

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

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectualproperty. pdf), in any

relevant Thesis restriction declarations deposited in the University Library, The University

Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations) and in

The University’s policy on presentation of Theses.

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.

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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

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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

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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

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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

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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

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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

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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.

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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

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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


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


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

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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.

143

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

144

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.

145

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.

146

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

148

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.

149

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.

152

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.

153

Figure 4-21. Cracks in the experimental and FE models for L0.

Figure 4-22. Load–strain curves of the internal tensile reinforcement.

154

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.

155

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.

156

Figure 4-26. Cracks in the experimental and FE models for LS.


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.


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.

159

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 4-32 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

160

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.

161

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.


load capacity


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

162

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.


165


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.


load capacity


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.


load capacity

Deflection Increase in

deflection

Failure mode

LF 104

19%

8.1

25%

Punching failure

LFS 123.6 10.1 Punching failure

167

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

168

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.



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.


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

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.



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



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.


load capacity


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.



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.


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.


load capacity


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.


load capacity


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).


193




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.


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%)


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


Slab Applied strengthening method Tensile steel reinforcement ratio


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.


Slab Applied strengthening method Tensile steel reinforcement ratio


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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