Mehdi Mohamamdpour Lima - Griffith University

Experimental and Numerical Study of RC Walls with OpeningStrengthened by CFRP

Author

Mohamamdpour Lima, Mehdi

Published

2016

Thesis Type

Thesis (PhD Doctorate)

School

Griffith School of Engineering

DOI

https://doi.org/10.25904/1912/3105

Copyright Statement

The author owns the copyright in this thesis, unless stated otherwise.

Downloaded from

http://hdl.handle.net/10072/367903

Griffith Research Online

https://research-repository.griffith.edu.au

Experimental and Numerical Study of RC Walls with

Opening Strengthened by CFRP

Mehdi Mohamamdpour Lima

B.Sc, M.Sc

Griffith University

School of Engineering

Science, Environment, Engineering and Technology

Submitted: April 2016

Submitted in fulfilment of the requirements of the degree of Doctor of Philosophy

This thesis was prepared under the supervision of:

Principal Supervisor: Dr. Jeung-Hwan Doh

Associate Supervisors: Dr. Sanaul Chowdhury and Associate Prof. Muhammad Hadi

i

ABSTRACT

Concrete structures regularly require strengthening due to various reasons. These structures

include bridges, buildings and infrastructure, across numerous sectors and industries. Based on

the load-carrying capacity of structures and proposed future applications, a vast array of

strengthening methods may be utilised. Due to rapid advancements in construction materials,

technology has led to the achievement of being able to secure safer, more economical and

functional buildings. Of the innovative materials, Fibre Reinforced Polymer (FRP) appears to

be an encouraging solution for the retrofitting and strengthening of Reinforced Concrete (RC)

structures because of its unique properties. These properties include: high strength-to-weight

ratio; high fatigue endurance; environmental degradation and corrosion resistance. FRP is also

durable and very flexible for application to the various shapes of structural members. Further,

it is easy to install, with a negligible increase in structural size and weight. The application of

FRP is dependent upon the type of structural member plus its behaviour. It can be used to

enhance the load capacities (axial, flexural, or shear), ductility, rigidity, the remaining fatigue

life as well as the durability against harsh environments.

RC walls are commonly used as load bearing structural elements. In order to save time and

construction costs, various methods have been developed for RC wall construction including

Tilt-Up panels. Fast-track delivery makes it possible to prefabricate the RC walls at a factory

under controlled conditions ensuring high quality products which lead to a lower operational

cost. Wall panels often experience eccentric loads due to a range of loading conditions

including: a corbel element applied to the wall; imperfections in construction; an uneven

loading condition on top of the wall or temporary loading during operation and/or maintenance.

Many researchers have investigated the behaviour of RC walls with various material properties,

geometries and boundary conditions. However, limited research has been carried out on the

ii

Carbon Fibre Reinforced Polymer (CFRP) strengthening method for RC walls under eccentric

axial loads.

The CFRP sheet orientation in a strengthened beam, column and slab is perpendicular to the

loading direction. In these situations, fibres in the CFRP will contribute to the carrying of the

load by stretching through its principal direction. Therefore, the usage of CFRP in these

elements enhances the ultimate strength of the member. It should be noted that, in the RC wall

panels, the loading direction and CFRP’s fibre orientation are parallel. As RC walls experience

a shortening in the fibre’s direction, a lower contribution of CFRP in ultimate failure load is

expected. Previous research has considered the behaviour of RC walls under one-way

action considering only two of the various CFRP layouts. More research was required to

explore the effects of support conditions and opening configurations, as well as alternate

CFRP layouts. In addition, design charts or formulae considering various parameters are

an essential for engineering applications. As a result of scarce prior published experimental

and theoretical studies on the strengthening of RC walls using CFRP, eighteen concrete walls

with openings strengthened with various CFRP layouts, were prepared and tested at

Griffith University to determine the behaviour of wall panels. The variables considered

included: CFRP layouts and support conditions (one-way action and two-way action with

three or four sides restrained). The experimental outcomes include: crack patterns, load-

deflection profiles and strain measurements of critical points that were obtained and discussed

in detail. The efficiency of various CFRP layouts was also investigated in order to determine

the optimum CFRP layout considering the alternate support conditions investigated.

Then, the behaviour of CFRP strengthened RC walls was simulated using ABAQUS software.

The main purpose of this finite element analysis was to compare the behaviour of RC walls

iii

obtained from simulation with the experimental results. After establishing that the numerical

software was a good model for the experimental outcomes, a parametric study was then carried

out for the full scaled wall panels with various support conditions, opening configurations and

CFRP layouts. Based on outcomes obtained from extensive experiments and parametric studies,

design charts were proposed for CFRP strengthened RC walls with opening, considering

various support conditions, opening configurations and CFRP layouts. A step by step design

method for CFRP strengthened RC walls was introduced which illustrated the design procedure

proposed. In order to ascertain the accuracy and reliability of the proposed method, the ultimate

load of the CFRP strengthened RC walls were evaluated against existing experimental

outcomes and available formulae from previously published research, as well as the current

experimental outcomes. The results demonstrated the accuracy and reliability of the developed

design charts for reasonably predicting the ultimate load of CFRP strengthened RC walls.

Finally, examples were presented to engineers to illustrate the application of the proposed

design charts in real projects under various support conditions, opening configurations and

CFRP layouts.

iv

DECLARATION OF ORIGINALITY

This work has not been previously submitted for a degree or diploma in any university. To the

best of my knowledge and belief, the thesis contains no material previously published or written

by another person except where due reference is made in the thesis itself.

_________________________________

Mehdi Mohammadpour Lima

v

LIST OF PUBLICATIONS

The following papers were produced to disseminate the concepts and results of the work

undertaken by the author during the course of this PhD research study.

Journal publications:

Mehdi M Lima, Jeung-Hwan Doh, Muhammad N.S. Hadi and Dane Miller (2015),” The

effects of CFRP orientation on the strengthening of reinforced concrete structures, The

Structural design of tall and Special Buildings, DOI:10.1002/tal.1282

Mehdi M Lima, Jeung-Hwan Doh, Muhammad Hadi (2016) “Behaviour of externally bonded

CFRP strengthened reinforced concrete walls with opening: an experimental study” prepared

to be submitted in “Structural Concrete” journal.

Conference publications:

Lima, M Mehdi., Doh, J-H. and Miller, D. (2014) “Numerical Study of Axially Loaded

Concrete Walls with Openings Strengthened by FRP”, The 23rd Australasian Conference on

the Mechanics of Structures and Materials (ACMSM23), Byron Bay, Australia, 9-12 December

2014.

The following papers were produced by the author during the course of this PhD candidature

not directly related to this PhD research.

Journal publications:

Lima, M Mehdi, Miller, D., Doh, J.-H. (2013) "Structural health monitoring of concrete

bridges in Guilan province based on a visual inspection method" Structural Durability & Health

Monitoring (SDHM), 9(4):269-285

Conference publications:

Miller, D., Doh, J-H., Lima, M Mehdi. and van Oers, N. (2014) “ Embodied Energy

Assessment of the Structural System in Concrete Buildings: A Case study of 7 South East

Queensland Structures” The 23rd Australasian Conference on the Mechanics of Structures and

Materials (ACMSM23) Byron Bay, Australia, 9-12 December 2014

vi

TABLE OF CONTENTS

ABSTRACT .................................................................................................................. I

DECLARATION OF ORIGINALITY ................................................................... IV

LIST OF PUBLICATIONS ....................................................................................... V

LIST OF FIGURES .................................................................................................... IX

LIST OF TABLES ................................................................................................. XIV

NOTATION ............................................................................................................ XVI

ACKNOWLEDGMENTS .................................................................................... XXII

1 INTRODUCTION...................................................................................... 24 Preamble ..................................................................................................... 24

Research background and motivation ..................................................... 25 Research objective ..................................................................................... 27 Research method overview ........................................................................ 27 Thesis layout ............................................................................................... 27

2 LITERATURE REVIEW ......................................................................... 32

Introduction ................................................................................................ 32 Wall design – Code provisions .................................................................. 34

2.2.1 Simplified wall design using AS3600 (2009) .............................................. 34

2.2.2 Simplified wall design using ACI 318 (2014) ............................................. 36

Previous study on walls with and without openings ............................... 37 2.3.1 Solid walls .................................................................................................... 37 2.3.2 Some previous research on RC walls with opening..................................... 39

Strengthening of concrete structures ....................................................... 42 Application of CFRP in concrete elements .............................................. 44

Experimental study by previous researchers .......................................... 52 2.6.1 Beam ............................................................................................................ 53

2.6.2 Column ......................................................................................................... 54 2.6.3 Slab .............................................................................................................. 55 2.6.4 RC wall ........................................................................................................ 57

Numerical simulation (Material properties and constitutive models) .. 59 2.7.1 Modelling of steel reinforcing bars .............................................................. 60 2.7.2 Concrete ....................................................................................................... 60 2.7.3 Concrete in tension ...................................................................................... 62

Concrete Damage Plasticity (CDP) model ............................................... 63 2.8.1 Damage ........................................................................................................ 64 2.8.2 Yield criterion .............................................................................................. 66 2.8.3 Flow rule ...................................................................................................... 67 2.8.4 Viscous parameter ........................................................................................ 68

FRP properties ........................................................................................... 69 FEM analysis .............................................................................................. 71

2.10.1 Mesh sensitivity ........................................................................................... 71 2.10.2 Riks Method ................................................................................................. 72

Results and discussion ............................................................................... 76 2.11.1 Crack pattern ................................................................................................ 76

vii

2.11.2 Ultimate strength .......................................................................................... 81

Summary ..................................................................................................... 87

3 EXPERIMENTAL PROGRAM ............................................................... 89

Introduction ................................................................................................ 89 Test panels .................................................................................................. 89 Material properties .................................................................................... 90

3.3.1 Concrete ....................................................................................................... 90 3.3.2 Steel.............................................................................................................. 90 3.3.3 CFRP ............................................................................................................ 91

3.3.4 Epoxy ........................................................................................................... 92

Panel designation ....................................................................................... 92 Mould preparing and casting .................................................................... 97

CFRP amount and size ............................................................................ 100 Curing, testing of concrete properties .................................................... 101

3.7.1 Compression testing of the concrete .......................................................... 102 3.7.2 Tensile test of concrete .............................................................................. 103

Application of EB-CFRP confinement ................................................... 104 Test regime ............................................................................................... 107

Data collection .......................................................................................... 111

Pilot test..................................................................................................... 113

4 EVALUATION OF TEST RESULTS ................................................... 116 Introduction .............................................................................................. 116 Concrete compressive and tensile strengths of RC walls ..................... 116

Experimental results and discussion ...................................................... 117 4.3.1 Crack pattern for walls with OW ............................................................... 117

4.3.2 Crack pattern for walls with TW3S ........................................................... 121 4.3.3 Crack Pattern for walls with TW4S ........................................................... 125

4.3.4 Deflection measurement ............................................................................ 127 4.3.5 Strain gauge data measurements ................................................................ 134 4.3.6 Ultimate strength ........................................................................................ 137

Summary ................................................................................................... 141

5 COMPARATIVE AND PARAMETRIC STUDY ................................ 144 Introduction .............................................................................................. 144

The concrete and CFRP interface .......................................................... 145 FEM analysis ............................................................................................ 147

Comparative Study .................................................................................. 148 5.4.1 One-way action wall’s crack patterns and deflected profile ...................... 149

5.4.2 Crack patterns and deflections of walls with TW3S .................................. 156 5.4.3 Crack patterns and deflections of walls with TW4S .................................. 163 5.4.4 Ultimate strength ........................................................................................ 168

Parametric study ...................................................................................... 174 5.5.1 Parametric study for OW ........................................................................... 178

5.5.2 The behaviour of the CFRP strengthened walls under OW action

considering horizontal opening location variations ................................................... 184 5.5.3 Parametric study for TW3S ....................................................................... 185 5.5.4 The behaviour of the CFRP strengthened walls with TW3S considering

horizontal opening location variations ....................................................................... 191

5.5.5 Parametric study for TW4S ....................................................................... 195

viii

5.5.6 The behaviour of the CFRP strengthened walls with TW4S considering

horizontal opening location variations ....................................................................... 200

Relations between ultimate load of RC walls under various support

condition.................................................................................................................... 204 Comparison of various CFRP layouts under different support

conditions: ................................................................................................................. 205 Efficiency investigation of CFRP layouts considering various support

conditions .................................................................................................................. 210 5.8.1 Efficiency study of RC walls in OW ......................................................... 210 5.8.2 Efficiency study of RC walls with TW3S.................................................. 211

5.8.3 Efficiency study of RC walls with TW4S.................................................. 212

Summary and conclusion ........................................................................ 213

6 DESIGN CHARTS FOR CFRP STRENGTHENED RC WALLS ..... 215 Introduction .............................................................................................. 215 Design charts ............................................................................................ 216

Proposed Method using design charts.................................................... 220 Assumptions involved in the development of proposed design charts 223 Verification of proposed design charts .................................................. 224 Examples for illustration and application of the proposed design charts

228 6.6.1 Example 1: CFRP strengthened RC wall with OW ................................... 228 6.6.2 Example 2: RC wall with TW4S: .............................................................. 232 6.6.3 Example 3: RC walls with TW3S .............................................................. 235

Summary and conclusion ........................................................................ 237

7 CONCLUSION ........................................................................................ 239 Conclusions ............................................................................................... 239 Recommendations and Scope for Future Research .............................. 242

8 REFERENCES ......................................................................................... 244

APPENDIX A: PANEL DESIGNATION AND CFRP LAYOUTS FOR OW,

TW3S AND TW4S IN PARAMETRIC ................................................................. 251

APPENDIX B: MOULD PREPARATION, CONCRETE CASTING, CURING

AND TESTING ........................................................................................................ 269

APPENDIX C: CFRP-CONCRETE INTERFACE AFTER FAILURE LOAD.

.................................................................................................................................... 273

APPENDIX D: CFRP WIDTH AND EPOXY CALCUATION FOR

EXPERIMENTS ...................................................................................................... 275

APPENDIX E: LOAD VERSUS STRAIN OF RC WALLS ................................ 278

APPENDIX F: SAMPLE OF SIMULASTION FORM ABAQUS (TW4S-WF)

.................................................................................................................................... 282

ix

LIST OF FIGURES

Figure 1-1: Research method flow-chart ..................................................................... 31

Figure 2-1: Walls with and without side’s supports (Doh and Fragomeni, 2006) ....... 35

Figure 2-2: Geometric parameters for wall with openings (Saheb and Desayi, 1990) 40

Figure 2-3: Transverse loading and CFRP orientation. ............................................... 51

Figure 2-4: Longitudinal loading and CFRP orientation. ............................................ 52

Figure 2-5: CFRP strengthened RC beam (Siddiqui, 2010) (dimensions in mm) ....... 54

Figure 2-6: CFRP strengthened RC column (Hadi and Widiarsa, 2012) (dimensions in

mm) ...................................................................................................................... 55

Figure 2-7: Slab specimen (Smith and Kim, 2009) (dimensions in mm) .................... 56

Figure 2-8: FRP application (Smith and Kim, 2009) (dimensions in mm) ................. 57

Figure 2-9: Details of specimen reinforcement and CFRP layout (Mohammed et al.,

2013) (dimensions in mm) ................................................................................... 59

Figure 2-10: Schematic stress strain behaviour of steel............................................... 60

Figure 2-11: Schematic stress-strain behaviour of concrete in tension ....................... 63

Figure 2-12: Yield surfaces of the concrete damaged plasticity model in ABAQUS

(Hibbitt et al., 2011) ............................................................................................. 67

Figure 2-13: Mesh sensitivity study for RC slab ......................................................... 72

Figure 2-14: Typical unstable static response (Hibbitt et al., 2011) ............................ 73

Figure 2-15: Modified Riks method (Hibbitt et al., 2011) ........................................... 76

Figure 2-16: Crack pattern for SB ............................................................................... 78

Figure 2-17: Crack pattern for NC ............................................................................... 78

Figure 2-18: Crack pattern for SS in the bottom side .................................................. 79

Figure 2-19: Crack pattern of RC walls (Mohammed et al., 2013) ............................. 80

Figure 2-20: FEM maximum PE of RC walls ............................................................. 80

Figure 2-21: FEM maximum PE of RC walls ............................................................. 80

Figure 2-22: Load versus deflection curve for experiments and FEM ........................ 83

Figure 3-1: Panel designation and CFRP layout for walls with OW (dimensions in mm)

............................................................................................................................. 93

Figure 3-2: Panel designation and CFRP layout for walls with TW3S (dimensions in

mm) ...................................................................................................................... 95

x


mm) ...................................................................................................................... 96

Figure 3-4: Typical formwork layout .......................................................................... 97

Figure 3-5: Actual formwork and steel reinforcement set-up ...................................... 98

Figure 3-6: Concrete curing and stocking .................................................................. 102

Figure 3-7: Concrete material testing machine ........................................................... 103

Figure 3-8: Indirect tensile test set-up ....................................................................... 104

Figure 3-9: EB-CFRP application .............................................................................. 105

Figure 3-10: Strain gauge application ........................................................................ 106

Figure 3-11: Typical strain gauges locations ............................................................. 106

Figure 3-12: Location of strain gauge on top of CFRP for CF layout ....................... 107

Figure 3-13: Strain gauge on CFRP for WF layout ................................................... 107

Figure 3-14: Test rig and hydraulic jacks (Doh, 2002) ............................................. 108

Figure 3-15: Typical test rig set-up for TW4S wall panel ......................................... 109

Figure 3-16: Uniform distribution of loading from hydraulic jacks (Doh, 2002) ..... 110

Figure 3-17: Top and bottom restraints ..................................................................... 111

Figure 3-18: Side restraints ........................................................................................ 111

Figure 3-19: Typical dial gauge locations on wall panels in compression side

(dimensions in mm) ........................................................................................... 113

Figure 4-1: Crack pattern for OW-NF ....................................................................... 119

Figure 4-2: Crack pattern for OW-DF ....................................................................... 119

Figure 4-3: Crack pattern for OW-AF ....................................................................... 120

Figure 4-4: Crack pattern for OW-CF ....................................................................... 120

Figure 4-5: Crack pattern for OW-WF ...................................................................... 120

Figure 4-6: Crack pattern for OW-PF ........................................................................ 121

Figure 4-7: Crack pattern for TW3S-NF ................................................................... 122

Figure 4-8: Crack pattern for TW3S-DF ................................................................... 123

Figure 4-9: Crack pattern for TW3S-AF ................................................................... 123

Figure 4-10: Crack pattern for TW3S-CF .................................................................. 123

Figure 4-11: Crack pattern for TW3S-WF................................................................. 124

Figure 4-12: Crack pattern for TW3S-MF ................................................................. 124

xi

Figure 4-13: Crack pattern for TW3S-FWF .............................................................. 124

Figure 4-14: Crack pattern for TW4S-NF ................................................................. 125

Figure 4-15: Crack pattern for TW4S-DF ................................................................. 126

Figure 4-16: Crack pattern for TW4S-AF ................................................................. 126

Figure 4-17: Crack pattern for TW4S-CF .................................................................. 126

Figure 4-18: Crack pattern for TW4S-WF................................................................. 127

Figure 4-19: Load versus lateral deflection curves for walls with OW ..................... 130

Figure 4-20: Load versus lateral deflection curves for walls with TW3S ................. 132

Figure 4-21: Load versus lateral deflection curves for walls withTW4S .................. 133

Figure 4-22: Load versus strain curves for OW-CF .................................................. 135

Figure 4-23: Load versus strain curves for TW3S-CF ............................................... 135

Figure 4-24: Load versus strain curves for TW4S-CF ............................................... 136

Figure 4-25: Load versus strain curves for walls with CF layout .............................. 137

Figure 4-26: Load versus strain curves for walls with WF layout ............................. 137

Figure 4-27: Axial strength ratio versus CFRP layouts ............................................. 141

Figure 5-1: Schematic shape of bilinear traction–separation constitutive law .......... 145

Figure 5-2: Mesh sensitivity study for RC walls (general seed) ................................ 148

Figure 5-3: Crack pattern comparison for OW-NF.................................................... 150

Figure 5-4: Crack pattern comparison for OW-DF.................................................... 150

Figure 5-5: Crack pattern comparison for OW-AF.................................................... 151

Figure 5-6: Crack pattern comparison for OW-CF .................................................... 151

Figure 5-7: Crack pattern comparison for OW-WF ................................................... 151

Figure 5-8: Crack pattern comparison for OW-PF .................................................... 152

Figure 5-9: Load versus lateral deflection curves for OW-NF .................................. 153

Figure 5-10: Load versus lateral deflection curves for OW-DF ................................ 154

Figure 5-11: Load versus lateral deflection curves for OW-AF ................................ 154

Figure 5-12: Load versus lateral deflection curves for OW-CF ................................ 155

Figure 5-13: Load versus lateral deflection curves for OW-WF .............................. 155

Figure 5-14: Load versus lateral deflection curves for OW-PF ................................. 156

Figure 5-15: Crack pattern comparison forTW3S-NF ............................................... 157

Figure 5-16: Crack pattern comparison for TW3S-DF .............................................. 157

xii

Figure 5-17: Crack pattern comparison for TW3S-AF .............................................. 158

Figure 5-18: Crack pattern comparison for TW3S-CF .............................................. 158

Figure 5-19: Crack pattern comparison for TW3S-WF ............................................. 158

Figure 5-20: Crack pattern comparison for TW3S-MF ............................................. 159

Figure 5-21: Load versus lateral deflection curves for TW3S-NF ............................ 160

Figure 5-22: Load versus lateral deflection curves for TW3S-DF ............................ 161

Figure 5-23: Load versus lateral deflection curves for TW3S-AF ............................ 161

Figure 5-24: Load versus lateral deflection curves for TW3S-CF ............................ 162

Figure 5-25: Load versus lateral deflection curves for TW3S-WF ........................... 162

Figure 5-26: Load versus lateral deflection curves for TW3S-MF............................ 163

Figure 5-27: Crack pattern comparison for TW4S-NF .............................................. 164

Figure 5-28: Crack pattern comparison for TW4S-DW ............................................ 164

Figure 5-29: Crack pattern comparison for TW4S-AF .............................................. 165

Figure 5-30: Crack pattern comparison for TW4S-CF .............................................. 165

Figure 5-31: Crack pattern comparison for TW4S-WF ............................................. 165

Figure 5-32: Load versus lateral deflection curves for TW4S-NF ............................ 166

Figure 5-33: Load versus lateral deflection curves for TW4S-DF ............................ 167

Figure 5-34: Load versus lateral deflection curves for TW4S-AF ............................ 167

Figure 5-35: Load versus lateral deflection curves for TW4S-CF ............................ 168

Figure 5-36: Load versus lateral deflection curves for TW4S-WF ........................... 168

Figure 5-37: Comparison of axial strength ratio versus CFRP layouts ..................... 172

Figure 5-38: Schematic view of RC walls for the parametric study .......................... 176

Figure 5-39: Ultimate load ratio for walls with OW-DF ........................................... 181

Figure 5-40: Ultimate load ratio for walls with OW-WF .......................................... 181

Figure 5-41: Ultimate load ratio for walls with OW-AF ........................................... 183

Figure 5-42: Ultimate load ratio for walls with OW-CF .......................................... 183

Figure 5-43: Ultimate load ratio for walls with OW-CF (horizontal direction) ........ 185

Figure 5-44: Ultimate load ratio for walls with TW3S-DF ....................................... 189

Figure 5-45: Ultimate load ratio for walls with TW3S-WF ...................................... 189

Figure 5-46: Ultimate load ratio for walls with TW3S-AF ....................................... 190

Figure 5-47: Ultimate load ratio for walls with TW3S-CF ........................................ 190

xiii

Figure 5-48: Ultimate load ratio for walls with TW3S-DF (horizontal direction) .... 193

Figure 5-49: Ultimate load ratio for walls with TW3S-WF (horizontal direction) ... 193

Figure 5-50: Ultimate load ratio for walls with TW3S-AF (horizontal direction) .... 194

Figure 5-51: Ultimate load ratio for walls with TW3S-CF (horizontal direction) .... 194

Figure 5-52: Ultimate load ratio for walls with TW4S-DF ....................................... 198

Figure 5-53: Ultimate load ratio for walls with TW4S-WF ...................................... 198

Figure 5-54: Ultimate load ratio for walls with TW4S-AF ....................................... 199

Figure 5-55: Ultimate load ratio for walls with TW4S-CF ........................................ 199

Figure 5-56: Ultimate load ratio for walls withTW4S-DF (horizontal direction) ..... 202

Figure 5-57: Ultimate load ratio for walls withTW4S-WF (horizontal direction) .... 202

Figure 5-58: Ultimate load ratio for walls with TW4S-AF(horizontal direction) ..... 203

Figure 5-59: Ultimate load ratio for walls withTW4S-CF (horizontal direction) ..... 203

Figure 5-60: Ultimate load ratio for walls with various opening sizes and DF layout

........................................................................................................................... 206

Figure 5-61: Ultimate load ratio for walls with various opening sizes and WF layout

........................................................................................................................... 207

Figure 5-62: Ultimate load ratio for walls with various opening sizes and AF layout

........................................................................................................................... 207

Figure 5-63: Ultimate load ratio walls with various opening sizes and CF layout .... 208

Figure 6-1: Ultimate load ratio versus opening ratio in OW action walls ................. 218

Figure 6-2: Ultimate load ratio versus opening ratio of panels with TW3S .............. 218

Figure 6-3: Ultimate load ratio versus opening locations in TW3S action walls ...... 219

Figure 6-4: Ultimate load ratio versus opening ratio for walls with TW4S .............. 219

Figure 6-5: Ultimate load ratio versus opening locations in TW4S action walls ...... 220

Figure 6-6: Flowchart for CFRP strengthened RC wall design procedure ................ 223

Figure 6-7: Schematic view of walls with OW .......................................................... 228

Figure 6-8: Schematic view of walls with TW4S ...................................................... 232

Figure 6-9: Schematic view of walls with TW3S ...................................................... 235

xiv

LIST OF TABLES

Table 2-1: Summary of the application of CFRP in beams ......................................... 46

Table 2-2: Summary of the application of CFRP in columns ...................................... 47

Table 2-3: Summary of the application of CFRP in slabs .......................................... 48

Table 2-4: FRP material properties .............................................................................. 70

Table 2-5: Mesh generation for convergence study ..................................................... 72

Table 2-6: Comparison of experimental and FEM results for beam, column and slab82

Table 2-7: Comparison of experimental and FEM results for RC walls ..................... 86

Table 2-8: Comparison of experimental and FEM results for walls with and without

CFRP .................................................................................................................... 86

Table 3-1: Properties of CFRP: SikaWrap – 230C (SIKA Australia Pty. Ltd) ........... 92

Table 3-2. Location, width and length of the applied CFRP sheets .......................... 101

Table 3-3: Summary of pilot tests .............................................................................. 115

Table 4-1: Cylinders strengths for RC walls and average panel thickness ................ 117

Table 4-2: Ultimate load of RC wall panels .............................................................. 140

Table 5-1 Mesh configurations used during the convergence study of the RC walls 148

Table 5-2: Ultimate strength comparison between FEM and experiments................ 173

Table 5-3: Opening configuration and CFRP usage for the parametric study

(HW=Lw=3000mm, tw=100mm) ......................................................................... 177

Table 5-4: Ultimate load comparison for CFRP strengthened RC walls with OW ... 180

Table 5-5: The effects of opening location on CFRP strengthened walls with OW .. 184

Table 5-6: Ultimate load comparison for CFRP strengthened RC walls in TW3S ... 188

Table 5-7: The effects of opening location (horizontal direction) on CFRP strengthened

RC walls (TW3S) ............................................................................................... 192

Table 5-8: Ultimate load comparison for CFRP strengthened walls with TW4S...... 197

Table 5-9: The effects of opening location on ultimate load of CFRP strengthened walls

........................................................................................................................... 201

Table 5-10: Ultimate load (NNF) of walls in OW, TW3S and TW4S ........................ 205

Table 5-11: The axial strength ratio comparison between walls with TW3S and OW

........................................................................................................................... 209

xv


........................................................................................................................... 209

Table 5-13: Efficiency study of CFRP strengthened RC walls with OW.................. 211

Table 5-14: Efficiency study of CFRP strengthened walls with TW3S .................... 212

Table 5-15: Efficiency study of CFRP strengthened walls with TW4S .................... 213

Table 6-1: Comparison of ultimate load using proposed design method .................. 227

Table 6-2: CFRP layouts and dimensions .................................................................. 230

Table 6-3: Predicted ultimate load of CFRP strengthened RC walls with OW

(AO/A=0.317) ..................................................................................................... 232

Table 6-4: Predicted ultimate load of CFRP strengthened RC walls with TW4S

(AO/A=0.317 and 243.0 ) .............................................................................. 235


(AO/A=0.317 and 243.0 ) .............................................................................. 237

xvi

NOTATION

@ = the distance of spacing with reinforcements

a = the depth of the equivalent rectangular stress block

A = the total area of concrete wall

fA = 2s

2

w

w

f

2s A)xt

xut(

E

E

, the CFRP cross sectional

area

Ag = Lwtw, the gross area of wall panel section

As2 = the area of additional steel reinforcement

Asv = ρvLwtw, the area of vertical steel in wall section

Ao = Lotw, the cross sectional area of opening

Aox = Loxtw, the cross sectional area of opening in x

direction

Aoy = Hoytw, the cross sectional area of opening in y

direction

Ax = Lwtw, the cross sectional area of wall in x direction

Ay = Hwtw, the cross sectional area of wall in y direction

bf = the width of CFRP layout

bc = the width of concrete wall

d = the scalar stiffness degradation variable

da = maximum aggregate size

db

= diameter of rebar

D = the cylinder diameter (mm)

vd = the viscoplastic damage increment

eloD = the initial (undamaged) elastic stiffness matrix of

the material

elD = the degraded elastic stiffness matrix

e = the load eccentricity (mm)

ea = (Hwe)2/ (2500tw) , additional eccentricity due to

deflections in the wall.

xvii

E11 = the modulus of elasticity of CFRP in the principal

direction

E22 and E33 = the modulus of elasticity in the other two non-

principal directions

Ec = the initial modulus of elasticity of concrete

Ef

= the modulus of elasticity of CFRP in principal

direction

sE = elastic modulus of steel

xE , yE and zE = the modulus od elasticity for CFRP layer in X, Y

and Z direction

ctmf = the tensile strength of the concrete

c'f = the yield strength of concrete in MPa

i'f = the axial stress of concrete on the descending

branch

tf = the concrete tensile strength under uniaxial tension

t'f = the stress of concrete at the peak point.

oF = the initial load

NF = the loading pattern

totalF = load magnitude

refF = reference load vector

syf = steel yield stress

yf = the yield strength of steel in MPa

G = flow potential

G13, G23 and G12 = the shear modulus in various direction

cG = the shear modulus of concrete

Gcr = energy needed for opening the crack,

Gf = fracture energy

iG = shear modulus of resin

xviii

nG , sG and tG = the work done by the traction and its conjugate

separation in the normal, the first and second

shear direction

csG = critical fracture energy during deformation purely

along the first shear directions

ctG = critical fracture energy during deformation along

the second shear directions

xyG = the shear modulus of CFRP in XY plane

oH = the dimension of the opening height in mm

HSC = High Strength Concrete

Hw = the height of the wall in mm

Hwe wkH Effective height

k = the effective height factor

cK = the strength ratio of concrete under equal biaxial

compression to triaxial compression

Ko = stiffness

NMoK

= the tangent stiffness

L = the cylinder length (mm)

Lb,max =

c'fctm

f

ft

fE

c ,effective anchorage length

Lc = the vertical distance between supports

LCFRP = the length of CFRP layout

Lo = the dimension of the opening length in mm

Lperiod = a user-specified total arc-length scale factor

Lw = the length of the wall in mm

NAF = the ultimate load of CFRP strengthened RC walls

using AF layout

NCF = the ultimate load of CFRP strengthened RC walls

using CF layout

xix

NDF = the ultimate load of CFRP strengthened RC walls

using DF layout

NNF = the ultimate load of CFRP strengthened RC walls

using NF layout

Nu = the ultimate design axial strength of wall per unit

length (in N/mm)

NWF = the ultimate load of CFRP strengthened RC walls

using WF layout

OW = one-way buckling with two sides supported

P = the maximum applied force

p = hydrostatic pressure stress

q = Mises equivalent effective stress

S = the effective stress deviator

ct = the concrete thickness

tf = CFRP thickness

it = the resin thickness

tw = the wall thickness

TW3S = two-way buckling with three sides supported;

TW4S = two-way buckling with four sides supported

u = concrete cover of reinforcement (mm)

u~ = the maximum absolute value of all displacement

variables

Nu and N

0 = the displacements

N

0

~ = the normalised tangential displacement vector at

the initial iterative step

Wf = Af/tf, width of the required CFRP

= eccentricity parameter

=the effective height factor for wall design

f = opening displacement at fracture,

o = the concrete strain corresponding to the peak stress

xx

1 = compressive strains in the loading direction

pl

1 = plastic strains in the loading direction

= a parameter, referred to as the eccentricity, that

defines the rate at which the function approaches

the asymptote

= the capacity reduction factor

= the size of rebars

η = the distance between the centres of gravity of an

RC wall section in plane with and without

openings

o = distance of the centres of gravity of the opening

from the left edge of the wall

ox = the distance from the left edge to opening centre

oyη = the distance from the top edge to opening centre

= distance of the centres of gravity of a wall without

an opening from the left edge of the wall

= the load proportionality factor

= coefficient for calculation of xysχ

0 = the initial load magnitude parameter

μ = viscous parameter

ρ = the concrete density

ρv = minimum requirement for vertical steel

ρh = minimum requirement for horizontal steel

= the axial stress of concrete on the descending

branch

1 = the compressive stress of concrete in the loading

direction

u = concrete compressive strength

= effective stress

n = the cohesive tensile

xxi

max̂ = the maximum principal effective stress

cobo / = the ratio of initial equibiaxial compressive yield

stress to initial uniaxial compressive yield stress.

)~(pl

cc = the effective compressive cohesion stress

max = traction stress

s = shear stresses of the interface in first shear

direction

t = shear stresses of the interface in second shear

directions

12 ; 13 ; 23 = the Poisson’s ratio of CFRP layout in various

directions

c = the Poisson’s ratio of concrete

s = the Poisson’s ratio of steel

LA

Ao , opening parameters corresponding to

opening size and location in x direction

xysχ = opening parameters corresponding to opening size

and location in both x and y direction

= the dilation angle measured in the p–q plane at

high confining pressure

inL = initial arc length increment

in = initial load proportionality factor

xxii

ACKNOWLEDGMENTS

First and foremost I would like to thank my principal supervisor, Dr Jeung-Hwan Doh,

for his guidance, instruction and knowledge. Dr Doh has been always supportive,

enthusiastic, energetic and encouraging for me and for the completion of this research.

I would not have completed this PhD without him, and for this I will remain forever

grateful.

I would like to acknowledge and thank the remainder of my supervisory team – Dr

Sanaul Chowdhury and Professor Muhammad Hadi - who have all been generous with

their guidance, support encouragement and contribution to this research.

I would also like to acknowledge and thank Mr Nicholas Coad who, through his

association with Sika Pty. Ltd, has provided the CFRP and epoxy for experimental tests

and the required information and instruction for application of CFRP in the project. I

will be forever grateful for these contributions.

I wish to express my gratitude to the laboratory manager and technicians, Mr Ian

Underhill, Mr Geoff Turner, Mr David Bellchambers, Mr Grant Pickering, and Mr

Chuen Lo for their invaluable assistance and cooperation in conducting the

experimental work.

Importantly, this research was built on work completed over many years - in

collaboration with the industry partner and supervisory team, through numerous former

students, colleagues and collaborators. I would like to personally thank all of these

contributors, of whom there are too many to name. However, a few of these contributors

xxiii

require singling out to communicate my appreciation for their inputs and efforts: Mr

Nhat-Minh Ho, Mr Bochen Zhang, Mr Mofan Zhou, and Mr Jack Zhou have all

provided extensive efforts and inputs to assist the author in completing this research. I

thank them for their efforts.

I would also like to acknowledge the RHD students with whom I have developed

friendships and spent too many hours discussing research project and progress.

Specifically to Dr Dane Miller; it would have been more difficult for me to complete

this without your support and camaraderie. I also appreciate Nima Talebian and other

colleagues and friends who helped me during the experiments. Thanks mates!

I would like to acknowledge and thank my mum and dad. Although, dad passed away

a few years ago, but he was with me during the whole PhD period and supporting me

spiritually. I do not have the words to articulate my appreciation of everything you did

for me. Also to my brothers and sisters and my friends. You have all provided assistance

through ways you might not know. To each and every one of you—thank you.

Finally and most importantly, to my best friend and greatest support - my wife. You

always supported and encouraged me during the whole period. There is no chance I

would ever have completed this without you. The sacrifices you have made are always

in my mind and I appreciate your consistent support and motivation. Thank you for

your ability to always put a smile on my face and for always keeping everything in

perspective. I look forward to the years ahead and to being able to make it all up to you.

Thank you Azita.

Chapter 1: Introduction

24

1 INTRODUCTION

Preamble

Strengthening and repair of structural members using Carbon Fibre Reinforced Polymer

(CFRP) has gained a great deal of attention. Some beneficial properties of composite

materials, including: high elastic modulus, high strength and light weight have made

them a suitable alternative to steel plates for strengthening applications. There are

numerous different types of structures that vary in quality and functional purpose. There

also exists the reality that these structures are ageing and deteriorating over time. Based

on the condition of the structures during their service life, maintenance decisions need

to be made which ensure the satisfaction of relevant building codes and standards.

Ageing is not the sole purpose for structural retrofitting, as any errors occurring during

the design or construction phase would require strengthening prior to the application of

new or increased demands due to a building use change. Sectors experiencing

increasing demand include: residential and commercial building, transportation and

infrastructure. In each of these cases it should be ascertained whether it is economically

viable to strengthen the existing structure, or replace it. The appropriate consideration

of project specifics including time and budget constraints in comparison to

strengthening alternatives will ensure improved efficiencies in overall outcomes. The

assessment of the most suitable method for strengthening is another issue which should

be carefully considered, as choosing an inappropriate process could worsen projects

outcomes. When repairing a structure is determined as an appropriate action, the

intention should be focused on increasing the load–bearing capacity of the structure.

During the rehabilitation of existing structures, one problem is related to the required

access to the areas requiring retrofitting. This problem usually arises when the

traditional methods are adopted, such as shotcrete or alternative reinforced overlays


25

placed on the outside of the structure. In this situation, adopting new materials with

beneficial properties, such as CFRP, not only improve the economic and scheduled

outcomes, but also improve the installation process. The installation of FRP products

requires less space while still delivering composite actions between the adherents.

The usage of CFRP is mostly reported in concrete structures or concrete members. A

significant amount of research has been conducted using CFRP in the strengthening of

concrete beams, columns, and shear walls, but limited research has been conducted on

the strengthening of Reinforced Concrete (RC) walls using CFRP.

RC walls are commonly used as load bearing structural elements. In order to save time

and construction costs, various methods have been developed for RC wall construction

including Tilt-Up panels. Fast-track delivery makes it possible to prefabricate the RC

walls at a factory under controlled conditions ensuring high quality products which lead

to a lower operational cost. The presence of an opening in RC wall under eccentric axial

loads results in local cracking in the vicinity of the opening as well as a reduction in

load carrying capacity. Therefore, this necessitates an improvement of the ultimate load

bearing capacity by strengthening RC walls with CFRP.

Research background and motivation

In the study of axially loaded walls, the definition of one-way and two-way action needs

to be established. A wall panel hinged at the top and bottom carrying in-plane vertical

loads developing a curvature along the loading direction is known as one-way action

(OW). A wall panel supported on all four sides exhibiting biaxial curvature under load

is known as two-way action with four sides restrained (TW4S). A wall panel supported


26

on three sides develops a curvature diagonally from three restrained corners to the

openings and then horizontally along the loading direction from the opening to the

unrestrained edge (TW3S).

RC Walls often experience eccentric loads due to a range of loading conditions

including: corbel elements applied to the wall; imperfections in construction; an uneven

loading condition on the top of the wall or temporary loading during operation and/or

maintenance. The following current national codes devoted separate chapters to the

design of RC walls without CFRP such as AS3600 (2009) and ACI 318 (2014). Many

researchers have investigated the behaviour of RC walls with various material

properties, geometries and boundary conditions (Saheb and Desayi, 1989, 1990 ; Doh

and Fragomeni, 2005, 2006; Fragomeni et al., 2012). While the national codes devoted

separate chapters to FRP applications (JSCE, 2000; FIB14, 2001; ISIS, 2001; ACI440,

2002; TR55, 2012), the behaviour of FRP strengthened RC wall panels was not

included in these codes. In addition, limited research has been carried out on the CFRP

strengthening method of RC walls under eccentric axial loads. Mohammed et al. (2013)

conducted experiments on eight one-way RC walls with two different CFRP layouts

applied to the wall surface. Mohammed et al. (2013) observed that the CFRP

applications on RC walls could increase the ultimate strength of the wall from between

10% and 80%, depending on the opening size and CFRP arrangement. In addition,

design equations were also proposed for strengthened RC walls with two types of CFRP

layouts. Recently, Popescu (2015) conducted an experimental investigation on FRP

strengthened RC walls with openings under four sides restrained (TW4S). However,

neither design chart nor formula was proposed to predict the ultimate load.


27

Research objective

The objective of this research is to investigate the ultimate load of CFRP strengthened

RC walls with various opening configurations, CFRP layouts, and support conditions

under eccentric (tw/6) axial loads.

The main aims of this research are to:

- Conduct an experimental study on CFRP strengthened RC walls with openings

using various CFRP layouts and support conditions;

- Conduct numerical investigations of the experimental counterparts in order to

establish a reliable FEM and perform a parametric study of full-scaled RC walls

considering various parameters; and

- Propose and validate design charts for CFRP strengthened RC walls using

various CFRP layouts, opening configurations, and support conditions.

Research method overview

The research method included four distinct research phases: 1) knowledge acquisition;

2) experiment preparation and testing; 3) FEM analysis and 4) verification of outcomes

and development of proposed design charts. This research method was detailed for

reference in Figure 1-1.

Thesis layout

The thesis is partitioned into distinct chapters to enable a logical presentation of the

proposed research approach and outcomes. Excluding this introductory chapter, the

remainder of the thesis is presented as follows:


28

Chapter 2 explores the current state of knowledge through a review of existing design

guidelines and proposed formulae to calculate the ultimate strength of RC walls with

and without openings. Furthermore, a review of existing CFRP strengthening methods

was conducted considering various RC members including: columns, beams, slabs and

RC walls and their contribution to the ultimate load of the respective members. The

load capacity of the typical test results compared to the predicted results from the

ABAQUS software package are presented for RC beams, slabs, columns and walls.

Based on the FEM simulation and the existing experiments, a distinct difference

between the ultimate strength in strengthened RC walls was observed. The noteworthy

finding was that the CFRP sheet orientation in a strengthened beam, column and slab

was perpendicular to the loading direction. In these situations fibres in CFRP will

contribute to the carrying of the load by stretching through its principal direction

resulting in a higher ultimate strength. However, in RC walls, the loading direction and

CFRP’s fibre orientation are parallel resulting in the walls experiencing a shortening in

the fibre’s direction. Therefore, a lower contribution of CFRP in ultimate load was

expected. The shortcomings of previous methods of CFRP strengthened RC walls are

noted and discussed. It was also found that there has been limited research on CFRP

strengthened RC walls considering various support conditions, CFRP layouts and

opening configurations. Consequently, the areas given significance in this thesis are

support conditions, CFRP layouts and opening configurations. This section is shown as

phase 1 in research methodology (Figure 1-1).

In Chapter 3, a detailed description of the test planning, concrete casting, CFRP

application, test set-up and procedure is presented. In total, eighteen RC walls were

constructed and tested examining seven various CFRP layouts with three different


29

support conditions.

The experimental outcomes are discussed and compared in Chapter 4 considering

various CFRP layouts and support conditions. Load-deflection graphs, crack patterns,

ultimate strength of RC walls as well as bonding between concrete and CFRP were

presented and discussed.

The main objectives of the experimental program were to:

a) obtain comparisons between the ultimate load of RC walls considering various CFRP

layouts and support conditions; and

b) observe the effect of CFRP layouts in crack patterns of axially loaded RC walls in

various support conditions.

To obtain the information and data required, the RC walls were subjected to a uniformly

distributed in-plane axial load with an eccentricity of tw/6. This approach allowed for

comparisons with published research results and the proposed design method developed

in this research. Since, only the axial load capacities of concrete wall panels were

studied, no horizontal in-plane or lateral forces were applied. The experimental

outcomes were used to establish a reliable FEM for numerical investigation. Chapters

3 and 4 are included in phase 2 of research method as shown in Figure 1-1.

Chapter 5 includes numerical analysis using ABAQUS software, which was conducted

to validate the experimental outcomes. Furthermore, full-scale parametric studies were

carried out to investigate the effects of opening configurations, CFRP layouts, and

support conditions on the ultimate load of strengthened RC walls. The outcomes of the


30

parametric study were evaluated and discussed in detail (Phase 3 of research method

presented in Figure 1-1).

Phase 4 of research includes Chapter 6 and 7. Chapter 6 provides the proposed design

method for CFRP strengthened RC wall panels, using various CFRP layouts, opening

configurations, and support conditions. A step by step design procedure is introduced

and in order to ascertain the accuracy and reliability of the proposed design method, the

ultimate load of CFRP strengthened RC walls were evaluated against existing

experiments and available formulae.

Detailed research conclusions and recommendations for future studies were included to

summarise the project in Chapter 7.


31

Literature review

Define experimental

test variables

Various support

conditions

Various CFRP

layouts

Experimental tests

Comparative study

Verification with existing

methods and test results

Preliminary design

charts

Numerical study: define input

parameters of software

Full scale investigation

considering various parameters

Opening locations

Support conditions

Yes

CFRP layouts

No

Opening sizes

RC Wall with opening

strengthened by CFRP

Design charts/formulae

Phase 1

Phase 2

Phase 4

Phase 3

Figure 1-1: Research method flow-chart

Chapter 2: Literature review

32

2 LITERATURE REVIEW

Introduction

The complexity of structures has undergone an evolution with the development of

human society. Structures that have been used by humans throughout history are

subjected to the laws of nature, such as deterioration and natural disasters including

earthquakes and floods. Usually, structures are designed for a minimum life span and

have a precise functionality. However, besides the natural effects on structures, there

are several other causes which diminish the performance of buildings, such as change

in functionality, structural intervention, errors in design, construction faults and

accidental or unexpected events. In some cases there are combinations of actions that

happen at the same time, without responsible action, catastrophic consequences are

inevitable. Beside the bearing capacity, which is the utmost importance for the safety

of residents; durability, functionality and aesthetics are important factors that should

be considered. A high degree of complexity and long-term performance is achieved

by using new methods and modern construction. A large number of older structures,

however, are not performing according to expectations. Therefore, in order to prevent

possible collapse or having malfunctioned members, the appropriate measures should

be considered for decision-making. Usually, an economical study considering all

aspects, such as the price of raw materials and implementation time, helps to decide

the most efficient method for strengthening or retrofitting. In some cases, even

removing the member or part is economical, while in other cases using strengthening

or retrofitting are more economical. During the past decades, numbers of

strengthening methods have been used which aim to increase the gross section, the

posttensioning technique, or total removal of a member, changing the structural

system (Täljsten et al., 2003).


33

Among different systems in structures and components, using RC walls in

construction is becoming increasingly popular. The fast installation, time-saving and

the possibility of prefabrication, make RC walls potentially one of the most desirable

construction systems. RC walls are vertical structural elements designed to withstand

gravitational and lateral loadings.

RC walls can be loaded perpendicularly to the median plane or along the median

plane. Based on the loading system, different types of failures may result. The in plane

loading may induce diagonal compressive failure, diagonal tensile failure, or concrete

crushing due to bending, while the perpendicular loading produces an out of plane

bending failure. In the case of gravitational load, the most common failure is

compressive failure if the load is not eccentric. In some cases, more than one mode

of failure can occur in RC walls when it is under several simultaneously loadings.

The current national codes and standards devote separate chapters to the design of

RC walls without CFRP. The following sections discuss the salient features of two

major international codes, namely the Australian Concrete Standard (AS3600, 2009),

and American Concrete Institute Code (ACI318, 2014). In addition, previous

proposed formulae to determine the ultimate load of RC walls with and without

openings are presented. Then, a brief overview of experimental programs undertaken

by previous researchers on strengthened RC beams, columns, slabs and walls was

conducted. The load capacity of the typical test results was then compared to

predicted results from the Finite Element Method (FEM) using ABAQUS software

where a distinct difference between the ultimate loads in strengthened RC walls was

realised.


34

Wall design – Code provisions

2.2.1 Simplified wall design using AS3600 (2009)

Section 11 of AS3600 (2009) specifies a simplified equation to calculate the axial

load capacity of walls. The equation applies to walls with various support conditions

as shown in Figure 2-1. For the simplified design method proposed by AS3600

(2009), the ultimate design axial strength (Nu) per unit length (in N/mm) of a braced

wall in compression is given by the following formula:

Eq. 2-1

'f6.0)e2e2.1t(N cawu

where wt is the wall thickness (mm), ϕ (=0.6) is the capacity reduction factor, e is the

load eccentricity (mm) which has a minimum of 0.05tw, fc′ (MPa) is characteristic

compressive concrete strength and ea is equal to. (Hwe)2/(2500tw)

The effective height as specified in Clause 11.4 shall be taken as Hwe=kHw in which

the factor, k, for a wall under one-way action is 1 and 0.75 for no restraint or full

lateral restraint at both ends, respectively. This value for RC walls under two-way

buckling with three sides restrained is k=1/(1+(Hw/3Lw))2, and four sides restrained

by floors and intersecting walls is k=1/(1+(Hw/Lw)2) where Hw ≤ Lw and k=Lw/(2Hw)

where Hw > Lw in which, Hw is the floor-to-floor unsupported height, and Lw is the

horizontal length.

Load bearing walls restrained on top and bottom only, with free vertical edges, behave

in one-way action (OW, Figure 2-1(a)). Axially loaded walls can also behave in two-

way action when restrained on four sides (TW4S, Figure 2-1 (c)). In practice, concrete

walls made of High Strength Concrete (HSC) and having three sides supported


35

(TW3S, Figure 2-1(b)) or four sides supported have become common, particularly in

core walls of tall buildings.

The AS3600 (2009) guidelines for simplified wall design allow for these various

support conditions. AS3600 (2009) only allows the effects of openings in walls with

all four all sides restrained and it can be neglected if: the total area of openings is less

than 1/10 of the area of the wall, and the height of any opening is less than 1/3 of the

height of the wall. If these conditions are satisfied, the simplified design equation can

be used, ignoring any opening(s) (AS 3600, 2009). A typical crack pattern and

curvature scenario for a wall with a single opening behaving in one-way action and

two-way action is depicted in Figure 2-1. Side supports create the double curvature

scenario in both parallel and perpendicular directions. The appearance of CFRP near

opening regions could have an effect on the load capacity and cracking regime which

was the focus of this research.

Curvature

Crack

Curvature

Crack

Side restraint

Curvature

Crack

Side restraint

Side restraint

(a) OW (b) TW3S (c) TW4S

Figure 2-1: Walls with and without side’s supports (Doh and Fragomeni, 2006)

The simplified method in AS3600 (2009) has some limitations including:


36

(a) The ratio of effective height to thickness (slenderness ratio= Hw/tw) is limited to

30;

(b) The concrete compressive strength ( 'fc ) is restricted to the range of 20~100MPa;

(c) A minimum eccentricity of 0.05tw is to be applied;

(d) The reduction of load-carrying capacity due to openings is not considered; and

(e) The walls are primarily subjected to in-plane vertical forces.

2.2.2 Simplified wall design using ACI 318 (2014)

The ACI318 (2014) provide guidelines for the design of RC walls. Chapter 14 of the

ACI318 (2014) specifies a simplified equation for designing the walls with OW for

imposed load within the middle third of the overall thickness.

Eq. 2-2

2

w

cgcu

32t

k.L1A.'f.0.55.N

where ϕ=0.75, fc′ is specified compressive strength of concrete, Ag is the gross

sectional of the wall panel, Lc is the vertical distance between supports and tw is the

overall thickness of wall member. The effective length factor k is 0.8, 1, and 2 for

walls restrained against rotation in one side, unrestrained against rotation in both ends

and without bracing against lateral translation.

The limitations of ACI318 (2014) are as follows:


37

a) Limited to planar, solid rectangular sections, and generally applies to vertical load

capacity members(axial load is primary load);

b) The resultant load must fall within the middle third of the wall thickness at all

sections along the length of the undeformed wall (eccentricity not greater than

tw/6);

c) Applicable to walls simply supported at top and bottom only;

d) Walls more than 250 mm thick, except for basement walls, shall have

reinforcement in each direction placed in two layers parallel to the faces of the

wall, and shall not be spaced apart more than 3tw nor 450 mm; and

e) Equation (2.2) applies to walls where Hw/tw < 25 or Lw/tw < 25, whichever is less

for load bearing and the minimum thickness is 100mm.

Previous study on walls with and without openings

Many researchers have investigated the behaviour of reinforced concrete walls either

in one-way or in two-way action. In this section, some of these researchs on RC walls

with and without opening are peresented and discussed.

2.3.1 Solid walls

Saheb and Desayi (1989)

Saheb and Desayi (1989) have studied the structural behaviour and failure load of RC

walls without openings. The detailed information about the experiments and formula


38

can be found in the original research publication. The proposed formula for ultimate

load in solid walls with one-way action is as follows (Saheb and Desayi, 1989):

2

wL

wH ;

w

w

2

w

wsvcgu

10L

H1.2

32t

H1)Ac

'fy(f'fA 0.55N

Eq. 2-3

2wLwH

;

2

w

wsvgu

32t

H1)Ac

'fy(fc'fA 0.55N Eq. 2-4

where ϕ is the capacity reduction factor; Ag is the gross cross-sectional area of RC

walls in plane in mm2; fy and fc′ are the yield strength of steel and concrete in MPa

respectively. Asv is the area of vertical steel in the RC wall in mm2; Hw is the height

of the wall in mm; tw is the thickness of the wall in mm; and Lw is the length of the

wall in mm.

Doh and Fragomeni (2005)

Doh and Fragomeni (2005) proposed a formula for ultimate failure load of solid walls

(Nu) which is as follows:

)2e1.2e(t2.0fN aw0.7

c'

u Eq. 2-5

where tw is the wall thickness (mm); e is the load eccentricity (mm), which is required

to have a minimum of at least 0.05tw; fc′ (MPa) is compressive concrete strength; and

ea= (Hwe)2/(2500.tw). The strength reduction factor ϕ is 0.6. Hwe is the effective height

Hwe=βHw where β can be calculated as below:

- For walls with simply supported top and bottom only:


39

1β for Hw/tw < 27 Eq. 2-6 (a)

0.88

w

w

t

H

18β

for Hw/tw ≥ 25 Eq. 2-6 (b)

- For walls with four all sides restrained:

2

w

w

L

H1

1αβ

for Hw < Lw Eq. 2-7 (a)

w

w

H 2

Lαβ for Hw > Lw

Eq 2-7 (b)

where α is an eccentricity parameter and is equal to

wt

e1

1

for Hw/tw < 27

Eq. 2-8 (a)

88.0

w

w

w t

H

18

t

e1

1

for Hw/tw ≥ 27 Eq. 2-8 (b)

The walls were required to have minimum reinforcement ratios of 0.0015 vertically,

ρv, and 0.0025 horizontally, ρh.

2.3.2 Some previous research on RC walls with opening

Saheb and Desayei (1990)

Saheb and Desayei (1990) proposed a formula for determining the ultimate load of

RC panels with openings (NNF) in one-way action which is as follows:

u21NF )N.k(kN Eq. 2-9

where k1=1.25 and k2=1.22 for walls in one-way action; χ=Ao/A+η/Lw; η=(Lw/2)- η ;

η =(L2w tw/2-Lotwηo) /(Lwtw-Lotw) and Nu is ultimate failure load of solid walls; Lo and


40

Ho are the dimensions of the opening in mm; Ao=Lotw; Ag=Lwtw; η is the distance

between the centres of gravity of an RC wall section in plane with and without

openings in mm; o and are distances of the centres of gravity of the opening and

of a wall without an opening from the left edge of the wall, respectively in mm (see

Figure 2-2).

Figure 2-2: Geometric parameters for wall with openings (Saheb and Desayi,

1990)

Doh and Fragomeni (2006)

For RC walls with openings, the proposed formula by Doh and Fragomeni (2006) to

determine the ultimate loads of panels with opening (NNF) is as follows:

u21NF )N.k(kN Eq. 2-10


41

where Nu is obtained force for the corresponding solid wall (Eq. 2-5); χ is similar to

that proposed by Saheb and Desayei (1990). The values of k1 and k2 are 1.175 and

1.188 for one-way action and 1.004 and 0.933 for two-way action, respectively.

Lee (2009)

For RC walls considering various opening configurations, Lee (2009) proposed the

following formula to determine the ultimate failure load (NNF):

uXYS21NF )N.k(kN Eq. 2-11

where

λ1

H

η

A

Aλ

L

2S

xη

A

A

χw

y

y

oyx

x

ox

xys

; woww

oyow

2w

tHtH

ηwtH2

tH

2

wH

yη

,

wtoww

oxwow

2w

LtL

ηtL2

tL

2

wL

xη

; woyoy tHA ; wwy tHA ; woxox tHA ;

wwx tLA

where Ho is the opening height (mm); Hw is the wall height (mm); Lo is the opening

length (mm); Lw is the wall length (mm).; ηox is the distance from the left edge to

opening centre (mm) and ηoy is distance from the top edge to opening centre (mm).

The values of k1, k2 and λ are 1.386, 2.014 and 0.17 for RC walls under one-way

action and 1.023, 0.837 and 0.39 for RC walls under two-way action, respectively.

The proposed formula by Saheb and Desayi (1989 and 1990) is only applicable to

concrete walls with slenderness ratio Hw/tw < 12 and normal strength concrete only.

Beyond such slenderness ratio or high strength concrete panels, the formulas may

lead to inaccurate predictions. The proposed formula by Doh and Fragomeni (2005,


42

2006) is applicable for a higher range of slenderness ratio (up to 40) and applicable

for both normal and high strength concrete. The proposed formula by Lee (2009)

considers a wide range of concrete strengths and slenderness ratios as well as the

positions of an opening in both horizontal and vertical direction. The proposed

formula by Doh and Fragomeni (2005, 2006) is preferred in this research as it resulted

in more consistent outcomes with FEM. The detailed information about the

experiments and formula can be found in the original research publication.

Strengthening of concrete structures

Concrete structures regularly require strengthening due to various reasons. These

structures include bridges, buildings and infrastructure, across numerous sectors and

industries. Based on the load-carrying capacity of structures and proposed future

application, a vast array of strengthening methods may be utilised. While the

traditional method for the strengthening or retrofitting of concrete structures is steel

plates and jackets, there are some disadvantages, including an increase in the self-

weight of the structure, with additional drawbacks being that it is also labour-

intensive and susceptible to fatigue and corrosion. Due to rapid advancements in

construction materials, technology has led to the achievement of being able to secure

safer, more economical and functional buildings (Bakis et al., 2002b). Of the

innovative materials, FRP appears to be an encouraging solution for the retrofitting

and strengthening of RC structures because of its unique properties. These properties

include: high strength-to-weight ratio; high fatigue endurance; low environmental

degradation and corrosion resistance (Hollaway and Head, 2001; Teng et al., 2002;

Tumialan et al., 2002; Teng et al., 2003; Zhang et al., 2004; Zhang and Hsu, 2005;

Zhao and Zhang, 2007).


43

In contrast to the traditional method of retrofitting structures, the handling and

transportation of FRP is much more user-friendly. FRP is also durable and very

flexible for application to the various shapes of structural members. Further, it is easy

to install, with a negligible increase in structural size and weight (Alsayed et al., 2000;

Clarke, 2003; Obaidat et al., 2010; Meneghetti et al., 2014). The application of FRP

is dependent upon the type of structural member plus its behaviour. It can be used to

enhance the load capacities (axial, flexural, or shear), ductility, rigidity, the remaining

fatigue life as well as the durability against harsh environments. Experimental

research has already been conducted on FRP application for the strengthening of

concrete structures (Spadea et al., 1998; Pantelides et al., 1999; Neale, 2000; Rahimi

and Hutchinson, 2001; Nanni, 2003; Thanoon et al., 2005; Kim et al., 2012; Napoli

et al., 2013); while the national codes and standards also devoted separate chapters

to FRP applications ( JSCE 2000; FIB14 2001; ISIS 2001; ACI440 2002; TR55

2012). However, the behaviour of FRP strengthened RC wall panels was not

encompassed in these codes.

The effectiveness of the confinement between FRP and concrete is reportedly reduced

by applying loads at an eccentricity, particularly lateral FRP confined structural

elements such as columns and walls. The experimental and analytical work of beams,

columns, slabs and walls has contributed to a greater understanding of the behaviour

of FRP confinement with various concrete elements which were included in the scope

of this research.

The following sections present a brief overview of experimental programs undertaken

by previous researchers on strengthened RC beams, columns, slabs and walls. The


44

load capacity of the typical test results is then compared to predicted results from the

ABAQUS package. Non-linear geometry and material properties are employed to

analyse the behaviour of RC elements.

Application of CFRP in concrete elements

Many researchers have investigated the flexural and shear behaviour of FRP

strengthened/retrofitted RC beams, with some review papers also being published (

Bakis et al., 2002a; Smith and Teng, 2002; Pendhari et al., 2008; Chin et al., 2014).

Usually, the FRP sheet/laminate is used on the tension side of the beam and

perpendicular to cracks; the strength and stiffness increases significantly when

compared to situations where fibres are placed oblique to the cracks (Norris et al.,

1997; Grace et al., 1999; Hong et al., 2010; Altin et al., 2011; Rahai and Saberi, 2011;

Kim et al., 2015; Lu et al., 2015; Tanarslan et al., 2015; Zgür Yurdakul and Avşar,

2015). The effect of FRP on the ultimate capacity of RC beams has been reported in

several research outcomes. Some of these results, including the relevant strengthening

scheme and the observed enhancement of the ultimate strengths, are presented in

Table 2-1.

FRP confinement has been used for the strengthening of both normal and high-

strength concrete columns. To investigate the behaviour of FRP-confined concrete

columns, experimental tests and theoretical methods have been applied. The effect of

FRP in the ultimate capacity of RC columns was reported in the previous studies.

Some of these results, including the strengthening scheme, load type and

enhancement of the ultimate strength, are presented in Table 2-2. The effect of FRP

in the ultimate capacity of RC slabs has been investigated. Some of these results,


45

including the strengthening scheme and enhancement of the ultimate strength, are

presented in Table 2-3. Based on the results presented, the CFRP significantly

enhanced the ultimate strength of the slabs by up to 184% in some cases.


46

Table 2-1: Summary of the application of CFRP in beams

Author

Numbers and size

of element [#No.

clear span ×b×D

(mm)] Lo

ad t

yp

e/

spac

ing

(m

m)

Av

erag

e co

ncr

ete

stre

ng

th (

MP

a) Strengthening scheme

Max

imu

m l

oad

incr

emen

tal

(u

p t

o %

)

TS

B1

UW

2

CW

3

C4

S5

A9

06

AN

90

7

Grace et al.

(1999)

#6.

2743×152×292 SP8

4

8 73

Khalifa and

Nanni (2000)

#5. 2340 ×(T-

beam) ×(150×405

web) ×(380×100

flange)

TP9/20

0

3

5 148

Almusallam and

Al-Salloum

(2001)

#2. 2050 × 150

×200

TP

/200

3

8 190

Khalifa and

Nanni (2002)

#8. 4576 ×150 ×

305

TP/31

0

2

3 120

Alagusundaramo

orthy et al. (2003)

#12. 4576 ×230

×342

TP/91

6

3

1 50

Zhang et al.

(2004)

#12. 762 ×101

×203

SP&

TP/25

4

4

2 122

Zhang and Hsu

(2005)

#11.

1675×152×229

SP &

TP/30

4

4

5 80

Cao et al. (2005) #18.

1700×150×223

TP/40

0, 600

2

6 80

Hosny et al.

(2006)

#1. 3000 ×(T-

beam)

×4570×(160×300

web) ×(460×60

flange)

Cyclic

TP/75

0

2

5 17

Kotynia et al.

(2008)

#10. 4200 ×150

×300

TP/14

00

3

6 68

Jumaat and Alam

(2008)

#1. 2000 × 125

×250

TP/70

0

3

0 54

Ibrahim and

Mahmood

(2009)

#1. 2440 ×150 ×

250

#2. 1830 ×230 ×

380

SP&

TP/17

00

3

0 80

Siddiqui (2010) #6.

2000×200×300

TP/50

0

3

5 37

Ceroni (2010) #18.

2000×100×180

TP/24

0, 440

3

4 72

Obaidat et al.

(2010)

#4. 1560× 150 ×

300

TP/52

0

2

9 33

Sen and

Jagannatha

Reddy (2013)

#2.

1300×140×200

TP/43

3

2

2 125

El-Saikaly and

Chaallal (2015)

#6. 4164 ×(T-

beam: (152×406

web)×(508×102

flange)

TL/20

56

3

5 122

1TSB:Two sides bonding, 2UW:U-Wrap; 3CW:Complete Wrap; 4 C:Continuous; 5 S:Strip; 6A90: Angle

to longitudinal Axis=90; 7AN90: Angle to longitudinal Axis≠90, 8SP : Single point loading at centre; 9TP: Two points loading.


47

Table 2-2: Summary of the application of CFRP in columns

Author

Numbers and size of

column [#No.

column height ×b×D

(mm) or R (radius

(mm)]

Lo

ad t

yp

e/ L

oad

ecce

ntr

icit

y

(mm

)

Av

erag

e co

ncr

ete

stre

ng

th (

MP

a) Strengthening

scheme

Max

imu

m l

oad

incr

emen

tal

(up

to

%)

FW

1

PW

2

HW

3

VS

4

Parvin and

Wang (2001) #6. 305×108×108

CO5 &

EC6/7.6,15.2 21 100

Li and Hadi

(2003)

#3. 1400×R75 &

hunched R117.5 EC/42.5 100 7

Matthys et al.

(2006) #6. 2000×R200 CO 36 70

Hadi (2006) #6. 1400×R75 &

hunched R117.5 EC/42.5 32 23

Hadi (2006) #3. 925×R102.5 CO&EC/25,50 57 -

Hadi (2007) #4. 905×R102.6 EC/50 66 124

Maaddawy

(2009)

#8. 1200×125×125

&

hunched(250×250)

EC/37.5,54,71,

107.5 29 37

Sadeghian et

al. (2010)

#5. 2700×200×300

&

hunched(200×600)

EC/200,300 40 130

Bisby and

Ranger

(2010)

#12. 304×R76 CO &

EC/5,10,20,30,40 33 76

Toutanji et al.

(2010)

#2. 2000×355×355

&

#1. 2000×500×250

CO 37 12

Abdelrahman

and El-Hacha

(2012)

#4. 1200×R150 CO 40 38

Hadi and

Widiarsa

(2012)

#12. 800×200× 200 CO& EC/25,50 80 18

Wu and Jiang

(2013) #24. 300×R75

CO& EC/ 10, 20,

30,40,50 26.6 300

Gajdosova

and Bilcik

(2013)

#2.4100×150× 200 EC/40mm 32 2

Song et al.

(2013)

#4. 1500×250×250

& hunched

(400,450,500×250)

CO &

EC/20,60,100,150 30 30

Pham et al.

(2013) #9. 800×150×150 CO & EC/25, 50 73 286

1FW; Full wrap; 2PW:Partial wrap; 3HW:Helical wrap; 4VS:Vertical; 5CO: Concentric, 6EC:Eccentric.


48

Table 2-3: Summary of the application of CFRP in slabs

Author

Numbers and size of slab

[#No. clear span ×b×D

(mm)]

Lo

ad t

yp

e/L

oad

spac

ing

(m

m)

Av

erag

e co

ncr

ete

stre

ng

th (

MP

a) Strengthening

scheme

Max

imu

m l

oad

incr

emen

tal

(u

p t

o %

)

S1

A9

02

AN

90

3

Limam et al.

(2003) #1. 2600×2600×100 SP4 30 150

Mosallam and

Mosalam (2003) #4. 2640×2640×76 UP5 33 184

Tan and Zhao

(2004) #6. 2300×2400×150 TL6/1100 39 81

Enochsson et al.

(2007) #6. 2600×2600×100 UP 57 125

El Maaddawy

and Soudki

(2008)

#1. 1500×500×100 TL/500 28 38

Smith and Kim

(2009)

#2. 3200×2500×160 &

#1. 3200×800×160 TL/1800 45 62

Elgabbas et al.

(2010) #2. 3200×1200×120 TL/984 32 70

Seliem et al.

(2011) #2. 3353×NM7×115 TL/1524 18 30

Anil et al. (2013) #6. 2800×1000×150 TL/1000 20 60 1S:Strip; 2A90: Angle to longtudinal Axis=90; 3AN90: Angle to longtudinal Axis≠90; 4SP:Single point

loading at centre; 5UP: Uniform pressure; 6TL: Two lines loading; 7NM: not mentioned.

Numerous research studies have used FRP sheet for strengthening/retrofitting of RC

shear walls under various loading condition (Bakis et al., 2002; Paterson and Mitchell,

2003; Panneton et al., 2006; Ghorbanirenani et al., 2011; El-Sokkary et al., 2012).

However, limited research can be found on the behaviour of FRP strengthened load

bearing RC walls which is the main focus in this research.

Wall panels often experience eccentric loads due to a range of loading conditions

including: corbel elements applied to the wall; imperfections in construction; an

uneven loading condition on top of the wall or temporary loading during operation

and/or maintenance. Many researchers have investigated the behaviour of RC walls

with various material properties, geometries and boundary conditions ( Saheb and


49

Desayi (1989 and 1990); Doh and Fragomeni (2005 and 2006); Fragomeni et al.,

2012). However, limited research has been carried out on the CFRP strengthening

method for RC walls under eccentric axial loads. Mohammed et al. (2013) proposed

design equations (Eq. 2-12) based on experimental tests of eight RC walls, with two

different CFRP layouts including DF (450 to the corner of opening) and AF (all

around the opening). Various opening sizes (5, 10, 20, 30 percentage) were

considered at the centre of the RC wall. For all the wall series; aspect ratios (Hw/Lw),

slenderness ratios (Hw/tw) and thinness ratios (Lw/tw) were 2, 20 and 10, respectively.

The test outcomes indicated that the Externally Bonded (EB) CFRP applications on

RC walls supported on top and bottom only (one-way action) would increase the

ultimate strength of the walls between 10% and 80%, depending on the opening size

and CFRP arrangement.

NFAF )N 2.1186(2.0765N Eq. 2-12 (a)

NFDF )N 2.6099(2.4708N Eq. 2-12 (b)

where NNF is the ultimate load of the RC wall without CFRP; χ is determined as

presented in Section 2.3.2.1; NAF and NDF are representing the ultimate load of CFRP

strengthened RC walls with AF and and DF layouts.

The limitations of the Mohammed et al. (2013) study were that the proposed design

formulae were not applicable for various support conditions (two-way action) and

CFRP layouts. In addition, the effect of CFRP’s width was not included as the width

of the CFRP in their experiments was constant for various sizes of opening and

removed reinforcement. Furthermore, they reported that applied CFRP layout with

450 to the opening corners resulted in a higher contribution to ultimate strength in

comparison to cases where CFRP was applied all around the opening. Therefore,


50

additional studies were required to obtain a better understanding of the behaviour of

the RC walls strengthened with various CFRP layouts. It was essential to find the

CFRP’s contribution to the ultimate strength of the RC walls under various support

conditions considering alternate layouts.

Recently, Popescu (2015) conducted an experimental investigation on FRP

strengthened RC walls with openings under four sides restrained (TW4S). However,

no design chart or formula was proposed based on their experimental outcomes. The

FRP was fully wrapped around the opening with a mechanical anchorage also used.

Some specimens were loaded up to 75% of the reference wall’s axial capacity to

create some cracking in the wall. FRP-confinement and mechanical anchorages

increased the axial capacity of walls with small and large openings (which had 25%

and 50% reductions in cross-sectional area, respectively) by 34-50% and 13-27%.

This enhancement in ultimate failure load was up to 85-94.8% and 56.5- 63.4% of the

corresponding solid wall. Similarly, concrete crushing accompanied by de-bonding

of the FRP sheet occurred at failure.

The CFRP sheet orientation in a strengthened beam, column and slab is perpendicular

to the loading direction (see Figure 2-3 and Figure 2-4(a)). In these situations, fibres

in the CFRP will contribute to the carrying of the load by stretching through its

principal direction. Therefore, the usage of CFRP in these elements enhances the

ultimate strength of the member.


51

(a) Beam

(b) Slab

Figure 2-3: Transverse loading and CFRP orientation.

It should be noted that, in the RC wall panels, the loading direction and CFRP’s

fibre orientation are parallel. As RC walls experience a shortening in the fibre’s

direction, a lower contribution of CFRP in ultimate failure load is expected (Figure

2-4 (b)). As comparatively little research was conducted on the CFRP strengthening

of RC walls, it was necessary to evaluate the behaviour of the wall through the

numerical FEM as it is a cost- and time-effective method.


52

(a) Column (b) RC wall

Figure 2-4: Longitudinal loading and CFRP orientation.

Using the current experimental test samples (Hadi and Widiarsa, 2012; Mohammed

et al., 2013; Smith and Kim, 2009; Siddiqui, 2010), comparison tests were carried out

for the performance of the FEM. This validation study was utilised to model the

behaviour of the beam, column, slab and RC walls strengthened by CFRP.

Experimental study by previous researchers

Experimental data was obtained from previous experiments on strengthened beams

(Siddiqui, 2010), columns (Hadi and Widiarsa, 2012), slabs (Smith and Kim, 2009)

and RC walls (Mohammed et al., 2013). Detailed information on these experiments

and results can be found in the respective original research publications. The


53

following section is a brief description of each experiment, as well as the material

properties and the enhancement of ultimate strengths observed. The FRP material

properties were presented in Section 2.9. In this study all experiments were designated

with N and S at the beginning for Non-strengthened and Strengthened specimens

respectively. Therefore, the nomenclature of beams, NB and SB were referring to the

Non-strengthened and Strengthened beams. The same procedure was used for slabs

(NS, SS), columns (NC, SC) and walls (NW, SW) for Non-strengthened and

Strengthened samples, respectively. Also, in RC walls, two different CFRP layouts

were considered as SW-A and SW-D for alongside and diagonal CFRP application

respectively. The wall number was also shown with a number.

2.6.1 Beam

Six RC beams with two different reinforcement arrangements and three FRP patterns

were loaded with a four-point bending configuration with a clear span (distance

between supports) of 2000 mm, with a distance between loads of 500 mm. From these

experiments two beams (with and without CFRP) were chosen for numerical

simulation. The beams were 300 mm high, 200 mm wide and 2000 mm long. The

longitudinal steel reinforcement consisted of three 14 mm diameter bars ( 14) for

tension and one 6 mm diameter bar ( 6) for compression. Shear reinforcement was

sufficiently provided with 10 mm @100 mm rebars (as seen in Figure 2-5).

The control beams were loaded up to failure while in the other case, the CFRP was

applied as the flexural strengthening scheme, at the bottom of the beam, as well as

two u-shape anchors at the end of the beam near the restraint. The concrete


54

compressive strength was 35 MPa for both cases and the yield stress of the included

reinforcement was 420 MPa.

Application of CFRP increased the ultimate failure load from 197.2 kN to 255.2 kN

for NB and SB samples, respectively. This was about 29.5% gain in the ultimate

strength of the beam (Siddiqui 2010).

2.6.2 Column

Sixteen (16) identical RC columns were tested, with 12 of them under compression

loading and four under flexural loading. Three different FRP confinements were

investigated. From these experiments two columns (with and without CFRP) under

eccentric compression loading (eccentricity=25 mm) were chosen for numerical

simulation. The columns had a square cross-section with a side dimension of 200 mm

and a height of 800 mm. The concrete cover was 20 mm on each side of the specimen,

as well as on the top and bottom. All corners of the square cross-section were rounded

(radius of 34 mm) in order to prevent premature failure and to provide sufficient effect

of confinement of the columns. The longitudinal reinforcement consisted of four 12

mm diameter bars ( 12), and the transverse reinforcement was 8 mm diameter ( 8)

LC

30

0

26

86

143

100@10

200750500750

PP

Figure 2-5: CFRP strengthened RC beam (Siddiqui, 2010) (dimensions in

mm)


55

spaced at 100 mm while the distance was 50 mm at both ends as seen in Figure 2-6(a).

The control column was loaded up to failure and, in the strengthened case; the CFRP

was applied as one layer of CFRP with the horizontal orientation (see Figure 2-6 (b)).

A special loading plate and mechanism were designed and used in this study (see

Figure 2-6(c)). The concrete compressive strength was 79.5 MPa for both cases, and

yield stress of the included longitudinal reinforcement and stirrups were 564 MPa and

516 MPa respectively.

200

200

800

R8@100mm

200

50

100

P

124

LC

12

80

0

(a) Details of specimen reinforcement (b) FRP wrapping (c) Loading plate

Figure 2-6: CFRP strengthened RC column (Hadi and Widiarsa, 2012)

(dimensions in mm)

Application of the CFRP increased the ultimate failure load from 1950 kN to 2076

kN for NC and SC samples respectively. This was about a 6% enhancement in the

ultimate strength of the column (Hadi and Widiarsa, 2012).

2.6.3 Slab

Six simply supported one-way spanning RC slabs were tested, four of which had an

opening at the centre. All slabs were prismatic and rectangular in the cross-section


56

and nominally 3400 mm long and of 160 mm deep, with a clear span of 3200 mm.

From this experiment, two slabs (with and without CFRP) were chosen. The width of

the slab was 800 mm and the concrete cover was 20 mm on each side of the specimen.

Steel bars with 12 mm diameter were used as longitudinal and transverse

reinforcement, while the distance between bars was 200 mm and 400 mm in each

direction respectively (Figure 2-7). The control slab was loaded up to failure and, in

the strengthened case, the CFRP was applied as the flexural strengthening scheme, at

the bottom in two layers (Figure 2-8). The concrete compressive strength was 47 MPa

and 49 MPa for the control and strengthened slab, respectively. The yield stress of

the reinforcement was 564 MPa.

3000 200

16

0

100 1800100700 700

P

200

P

(a) Elevation view of slab

P

Lin

e lo

ad

400

3400

Lin

e lo

ad

Lin

e lo

ad

800

200

400

LC

LC

(b) Details of specimen reinforcement

Figure 2-7: Slab specimen (Smith and Kim, 2009) (dimensions in mm)


57

200 3000 200

5017

520

020

020

0

LC

LC

Figure 2-8: FRP application (Smith and Kim, 2009) (dimensions in mm)

The application of CFRP increased the ultimate failure load from 49.3 kN to 80.8 kN

for NS and SS samples respectively. This was an approximate 64% enhancement in

the ultimate strength of the slabs being tested (Smith and Kim, 2009).

2.6.4 RC wall

Eight one-way RC walls were tested with two different patterns. Panels had various

opening sizes (5, 10, 20, 30 percentage) and were located at the centre. For all the

wall series; aspect ratios (Hw/Lw), slenderness ratios (Hw/tw) and thinness ratios

(Lw/tw) were 2, 20 and 10, respectively. From these experiments two RC walls (with

and without CFRP) were chosen. The height, width and thickness of the walls were

800, 400, 40 mm, respectively. The concrete cover was 20 mm on each side of the

specimen. The 5 mm diameter steel bars were used as longitudinal and transverse

reinforcement, and the reinforcement ratio of 0.004 and 0.007 in vertical and

horizontal respectively, as seen in Figure 2-9 (a) and (d). The control wall was loaded

up to failure, while in the strengthened cases the CFRP was applied at the tension face

as one layer all around the corner and 450 to the corner (Figure 2-9 (b), (c) and (e),(f)).

The concrete compressive strength was 15.57 MPa, 18.24 MPa and 16.36 MPa for

NW1, SW1-A and SW1-D, respectively. The concrete compressive strength for


58

NW2, SW2-A and SW2-D was 15.79 MPa, 15.06 MPa and 17.04 MPa, respectively.

The yield stress of the included reinforcement was 478 MPa.

The application of CFRP around the corner of the openings increased the ultimate

failure load from 85 kN to 108 kN for NW1 and SW1-A specimens respectively. This

was an approximate 27% enhancement in the ultimate strength of the RC wall. For

SW1-D the failure load was recorded as 138.5 kN, which was an approximate 62%

gain in the strength of the RC wall (Mohammed et al., 2013). The application of CFRP

around the corner of the openings increased the ultimate failure load from 73.7 kN to

82 kN for NW2 and SW2-A specimens respectively. This was an approximate 11.2%

enhancement in the ultimate strength of RC wall. For SW2-D, the failure load was

recorded as 84.8 kN, which was an approximate 15% gain in the strength of the RC

wall (Mohammed et al., 2013).


59

80

0

40

34

023

023

0

P 185 107107

LC

LC

60

570

tw

6

185 107107

LC

LC

185 107107

LC

LC

(a) NW1 (b) SW1-A (c) SW1-D

(d) NW2 (e) SW2-A (f) SW2-D

Figure 2-9: Details of specimen reinforcement and CFRP layout

(Mohammed et al., 2013) (dimensions in mm)

Numerical simulation (Material properties and constitutive models)

The materials used in the FEM analysis included steel reinforcing bars, concrete and

FRP. In the following section the input material properties and associated constitutive

models are discussed.


60

2.7.1 Modelling of steel reinforcing bars

The stress-strain curve of the reinforcement bar was assumed to be an elastic perfect

plastic material and identical in compression and tension, as shown in Figure 2-10. In

ABAQUS, the bond-slip between concrete and steel is not considered, and the steel

reinforcement was simulated as truss elements embedded in a concrete region in

which the concrete and the reinforcement share the same node where a perfect bond

is assumed. The elastic modulus, Es, and yield stress, fy, for all experiments were

presented in Section 2.6, and these values were used in the FEM model. For those

experiments where elastic modulus was not reported a value of 210 GPa was

considered for the FEM simulation. A Poisson's ratio of 0.3sυ was used for the

steel reinforcement in all models.

Figure 2-10: Schematic stress strain behaviour of steel

2.7.2 Concrete

The uniaxial compressive strength c'f for all samples was presented in the previous

section. The concrete strain o , corresponding to the peak stress c'f , is usually around

the range of 0.002-0.003. A representative value ( 003.0o ) suggested by ACI318-


61

14 (2014) is used in the analysis. The Poisson’s ratio ( cυ ) of concrete under uniaxial

compressive strength ranges from 0.15-0.22 and, in this study, the Poisson’s ratio of

concrete was assumed to be 0.2cυ for all concrete instances. The initial modulus of

elasticity of concrete cE is highly correlated to its compressive strength and can be

calculated with reasonable accuracy from the following empirical equation AS3600

(2009):

c'fρE 1.5

c MPa where 40MPac'f

Eq. 2-13 (a)

0.12]c'f[0.024ρE 1.5

c MPa where 40MPac'f Eq. 2-13 (b)

where ρ is the concrete density.

The stress-strain relationship proposed by Saenz (1964) was used to construct the uni-

axial compressive stress-strain curve for confined concrete.

3

o

c

2

o

c

o

cE

ccc

ε

εR

ε

ε1)(2R

ε

ε2)R(R1

εEσ

Eq. 2-14

where ε

2ε

σE

R

1

1)(R

1)(RRR

,

o

cE

E

ER ,

o

oε

c'f

E and 4R σ , 4R ε were used as

suggested by Hu and Schnobrich (1989).

For unconfined concrete, the stress-strain relationship proposed by Hsu and Hsu

(1994) was used:

dε ε 0 , nβo

o 'c

cε/ε1nβ

ε/ε βfn σ

; Eq. 2-15


62

where 59.223.65

f3

c'

. The strain ( o ) represents the peak strain and d

corresponds to a stress value of c'f3.0 in the descending branch of the stress-strain

curve. For oεε 0 the value of n is equal to one. For do ε εε the value of n is

equal to one, two, three and five for MPa 62f0 c' , MPa 76f 62 c

' ,

MPa 90f76 c' ; and MPa 90'f c , respectively.

2.7.3 Concrete in tension

The tensile property of the reinforced concrete was modelled using a simple tension

stiffening model. A linear softening model (see Figure 2-11) was applied to represent

the post failure behaviour in tension where the area below the curve is the fracture

energy fG . In order to define the tension stiffening response, the stress-fracture

energy approach was used with the fracture energy. For concrete under uniaxial

tension, tf and fG may be estimated from the following equations (FIB Bulletin 14,

1990):

3

2

10

8c'f

1.4tf

Eq. 2-16

0.7

2

10

c'f

26a0.5da0.0469dfG

Eq. 2-17

where tf is the concrete tensile strength under uniaxial tension, fG is the fracture

energy required to create a stress-free crack over a unit area and ad is the maximum

aggregate size. In the present study, if no test data is provided it was assumed


63

that ad = 20 mm. Note that in Eq. 2-17, c'f and ad are in MPa and mm respectively

and fG has a unit of N/mm (Bažant and Becq-Giraudon, 2002).

Figure 2-11: Schematic stress-strain behaviour of concrete in tension

Concrete Damage Plasticity (CDP) model

The concept of either damage, plasticity, or both, can be applied to model the non-

linear behaviour of concrete under compression (Maekawa et al., 2003). Damage and

plasticity are usually defined by the reduction of elastic constants and permanent

deformation respectively. In the literature, both reduction in stiffness and

unrecoverable deformation have been reported in concrete compression tests,

indicating that the combination of the damage concept and plasticity is required to

represent the non-linear behaviour of concrete (Maekawa et al., 2003).

In this study the simulation of RC beams, columns, slabs and walls was carried out

using the concrete damage plasticity model. In order to represent the inelastic

behaviour of concrete, the CDP in ABAQUS uses concepts of isotropic damage in

combination with isotropic tensile and compressive plasticity (Hibbitt et al., 2011).


64

This method is briefly presented in this section. It assumes that the main two failure

mechanisms are tensile cracking and compressive crushing of the concrete material.

The key aspects of this model for concrete in compression are: damage variable; yield

criterion; the flow rule and viscous parameter. A summary of these factors are

presented as follows:

2.8.1 Damage

The scalar damaged elasticity equation was adopted, which takes the following form:

)(:D)(:D)d1( plelplelo Eq. 2-18

where eloD is the initial (undamaged) elastic stiffness matrix of the material, elD is

the degraded elastic stiffness matrix and d is the scalar stiffness degradation

variable, varying from zero to one. Eq. 2-18 can be simplified to Eq. 2-19 when

concrete is subjected to uniaxial monotonic compression:

)ε(εd)E(1σpl

11c1 Eq. 2-19

where 1 is the compressive stress of concrete in the loading direction; 1 and pl

1ε

are the compressive and plastic strains in the loading direction, respectively; and cE

is the initial elastic modulus of concrete. The effective stress is defined as:

d1

σσ

Eq. 2-20

The plastic flow potential function and the yield surface make use of two stress

invariants of the effective stress tensor, namely the hydrostatic pressure stress ( p )

and Mises equivalent effective stress ( q ):

)σtrace(3

1p , )S:S(

2

3q Eq. 2-21


65

where S is the effective stress deviator, defined as .IpS

It was assumed that the damage up to the concrete compressive strength ('cf ) was

zero and after that point, the concrete compression damage increased monolithically

in the softening branch (Jankowiak and Lodygowski, 2005). The compression

damage was calculated according to equation 2-22:

'cf

σ1d Eq. 2-22

where sigma (σ ) is the axial stress of concrete on the descending branch and 'cf is

the stress of concrete at the peak point. The concrete behaviour in tension was linear

elastic until cracking was initiated. ABAQUS software has three options to simulate

the behaviour of concrete in tension including: stress-strain, stress-displacement and

fracture energy. To overcome unreasonable mesh sensitivity issues, the fracture

energy approach was used instead of the tensile strain. This was calculated as a ratio

of the total external energy supply ( fG ) per unit area required to initiate cracking in

the concrete. This approach was suggested in a previous study (Sümer and Aktaş,

2014).

In order to minimise mesh sensitivity in the slab, the post failure behaviour of

concrete was specified in terms of the stress-displacement response (Enochsson et al.,

2007). These damage parameters were similar to that of previous research carried out

by Enochsson et al. (2007), where the fracture energy ( fG ) of the area under the

stress-displacement curve was estimated to be 100 N/m. It was assumed that the

damage up to the concrete tensile strength ( tf ) was zero and after that point, concrete


66

tensile damage increased monolithically in the softening branch and was calculated

based on the following formula:

tfif1d

Eq. 2-23

Where if is the axial stress of concrete on the descending branch and tf is the stress

of concrete at the peak point.

2.8.2 Yield criterion

The CDP model makes use of the yield function of Lubliner et al. (1989), with the

modifications proposed by Lee and Fenves (1998) to account for the different

evolution of strength under tension and compression, as shown in Figure 2-12. The

evolution of the yield surface is controlled by the hardening variables, pl

t~ and

plc

~

:

0)ε~(cσmaxσ̂γmaxσ̂)ε~β(p3αqα1

1)ε~,σF(

plc

plpl

Eq. 2-24

where

1)/σ2(σ

1)/σ(σα

cobo

cobo

; 0.12α0.08 Eq. 2-25

α)(1α)(1)ε~(σ

)ε~(cσβ

pltt

plc

Eq. 2-26

1c2K

)cK3(1γ

Eq. 2-27

where max̂ is the maximum principal effective stress and cobo / is the ratio of

initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress.

The most reliable in this regard are the experimental results reported by Kupfer et al.

(1969). Based on their approximation with the elliptic equation, uniform biaxial

compression strength ( bo ) is equal to 1.16248 co . The ABAQUS user’s manual


67

specifies a default value 1.16/σσ cobo , which was used in all simulations. Kc is the

strength ratio of concrete under equal biaxial compression to triaxial compression.

Typical yield surfaces in the deviatoric plane are shown in Figure 2-12 for different

values of Kc. It must satisfy the condition 0.5≤ Kc ≤1.0. The default value (2/3) was

used in all FEM simulation; )plc

~(c is the effective compressive cohesion stress and

)plt

~(t is the effective tensile cohesion stress.

biaxial

tension

uniaxial

tension

uniaxial

compression

biaxial

compression

co2 σσβp3αqα1

1

ˆ

co1 σσβp3αqα1

1

ˆ

coσp3αqα1

1

coσ)σ,(σ

boco

boσ

2̂

1̂

Kc=2/3

Kc=1

T.M.

C.M.

-S3

-S1-S2

(a) in plane stress (b) in the deviatoric plane

Figure 2-12: Yield surfaces of the concrete damaged plasticity model in

ABAQUS (Hibbitt et al., 2011)

2.8.3 Flow rule

The concrete damaged plasticity model assumes non-associated potential plastic

flow. The flow potential G used for this model is the Drucker-Prager hyperbolic

function:


68

tanψpq)tan(G 22to

Eq. 2-28

Where toσ is the uniaxial tensile stress at failure,ψ is the dilation angle measured in

the p–q plane at high confining pressure and ξ is a parameter, referred to as the

eccentricity, that defines the rate at which the function approaches the asymptote (the

flow potential tends to a straight line as the eccentricity tends to zero). The default

flow potential eccentricity is 1.0 , which implies that the material has almost the

same dilation angle over a wide range of confining pressure stress values. In all FEM

analysis, 0.1ξ was used. The dilation angle for concrete slabs, beams and columns

were 120, 370 and 80, respectively. Similar dilation angles for each case study were

used in previous FEM investigations (Enochsson et al., 2007; Obaidat et al., 2011;

Majewski et al., 2008). However, as there was not any FEM investigation and

proposed value for dilation angle of RC walls, a value of 200 was selected which was

in between of the previous proposed values for the other type of RC elements.

2.8.4 Viscous parameter

The viscoplastic regularisation can be applied using the concrete damage plasticity

for the generalising of the Devaut-Lions approach. A viscous parameter, μ, which

upgrades the plastic strain tensor and the damage parameter, is derived using

additional relaxation time. The viscoplastic strain rate is determined as:

)ε(εμ

1ε

plv

plplv

Eq. 2-29

In the same way, the viscoplastic damage increment is defined as:

)d(dμ

1d vv Eq. 2-30


69

where μ denotes the viscous stiffness degradation variable. The relation for the stress-

strain according to the viscoplastic model is such that:

)ε(ε:)Ed(1σpl

vov Eq. 2-31

In specimens with a convergence problem, a small viscosity parameter (μ=10-5) was

considered after many sensitivity analyses were performed. This value was defined

to improve the convergence rate in the concrete softening and stiffness degradation

regimes. Similar approaches was used in previous research studies where it was

reported that if the viscosity parameter set to zero, the solution would become plastic

and divergence would obtained directly after cracking (Genikomsou and Polak,

2014).

FRP properties

The FRP material was considered as a linear elastic orthotropic material. Since the

composite is unidirectional, it is obvious that the behaviour is essentially orthotropic.

FRP is primarily stressed in the fibre direction, therefore, the modulus in the fibre

direction is the more important parameter.

The elastic modulus in the fibre direction of the unidirectional FRP material used in

the FEM was provided in the previous experiments. Detailed information about the

FRP material can be found in the original published research articles. A summary of

the FRP material properties are presented in


70

Table 2-4. A perfect bond was considered between FRP and concrete in all samples

as the simulation of FRP debonding was outside the scope of this research at this

stage. The modulus of elasticity in the principal direction was considered as the value

given in the experiments. The modulus of resin was designated as the modulus of

elasticity in the other two directions (E22 and E33). In cases where the information of

resin was not given in the experiments, 1%-2% of E11 was assumed for the E22 and

E33 (Mosallam and Mosalam, 2003). Since the CFRP was subjected to uniaxial

tension in the fibre direction only, these assumed parameters would not affect the

uniaxial tensile behaviour of the CFRP. The Poisson’s ratios were designated as 0.3,

0.3, 0.45 for 12 , 13 , 23 , respectively. The shear moduli (G12, G13, G23) were

calculated based on the following formula:

xxyyx

yxxy

E2EE

EEG

Eq. 2-32

Table 2-4: FRP material properties

Specimen

CFRP

Nominal

thickness

(mm)

Modulus of

elasticity

(MPa)

Elongation

at rapture

(mm/mm)

Tensile

strength

(MPa)

Beam (Siddiqui, 2010) 1.00 77280 0.011 846

Column (Hadi and Widiarsa,

2012) 0.45 75400 0.0186 1399

Slab (Smith and Kim, 2009) 0.117 259000 0.0099 2559

Wall (Mohammed et al., 2013) 0.167 230000 0.021 4800


71

FEM analysis

In all numerical models, a full scale of the element was analysed. In the FEM, 8-node

brick elements (C3D8R) were used to model the concrete in beams, columns, slabs

and RC walls. As the FRP is relatively thin in comparison to the concrete section, it

was modelled by the 4-node shell element. The FRP shell elements were attached to

the concrete surface directly, and the interface between concrete and FRP was

assumed to be fully bonded. An appropriate contact was also considered between

loading plate and concrete element.

2.10.1 Mesh sensitivity

Mesh convergence sensitivity was performed for all specimens in order to minimise

discrepancies in the element behaviour and failure load. An attempt was carried out

to have a square element for all specimens. Herein, the mesh sensitivity study for RC

slabs was presented. Three mesh configurations were used, (Figure 2-13), including

coarse, medium and fine mesh. In order to investigate the mesh sensitivity in the RC

slab, the sizes of mesh for other parts, such as reinforcement bars were maintained.

Using a coarse mesh resulted in lower peak loads compared to the experimental

outcomes. The deflection response was much lower than that of the medium and fine

mesh. The peak loads predicted for the varied mesh densities are provided in Table

2-5. The difference between the ultimate failure loads by using fine and medium mesh

was approximately identical, while the time cost for the fine mesh was much higher.

Therefore, the medium size mesh was adopted.


72

(a) Coarse (b) Medium (c) Fine

Figure 2-13: Mesh sensitivity study for RC slab

Table 2-5: Mesh generation for convergence study

Mesh The size of the

mesh seed

Number of

elements

Maximum load for NS (kN)

Numerical

Numerical Experimental Experimental

Coarse 100 3562 41.60

49.30

0.84

Medium 50 11722 55.52 1.13

Fine 30 31620 57.30 1.16

2.10.2 Riks Method

In this study the Riks method was used for analysis of all numerical models. The Riks

method is usually used to predict the unstable, geometrically non-linear collapse of a

structure, and can include the non-linear materials. Additionally, the Riks method

often follows an eigenvalue buckling analysis to provide complete information about

a structure's collapse. As finding the failure load of the structure was the main purpose

of this study, and in order to have a consistent analysis method in all RC elements,

the Riks method was preferred.

The Riks method, originally proposed by Riks (1972 and 1979) and Wempner (1971)

tracks the non-linear structural equilibrium path. This method has been modified and

developed further by Crisfield (1981), Powell and Simons (1981) and Ramm (1981),

and has become the main method used in in the analysis of non-linear structural

stability problems. The essence of the method is that the solution is viewed as the


73

discovery of a single equilibrium path in a space defined by the nodal variables and

the loading parameter.

For unstable problems it is often necessary to obtain non-linear static equilibrium

solutions where the load-displacement response can exhibit the type of behaviour

presented in Figure 2-14. This is during periods of the response when the load and/or

displacement may decrease as the solution evolves. The modified Riks method is an

algorithm that allows effective solution of such cases. Development of the solution

requires this path to transverse as far as required. The Newton method remains as the

basic algorithm; therefore, at any time there will be a finite radius of convergence.

Further, it is essential to limit the increment size as many of the materials or loading

of interest will have path-dependent response.

Figure 2-14: Typical unstable static response (Hibbitt et al., 2011)

In the modified Riks algorithm the increment size is limited by moving a given

distance (determined by the standard, convergence rate-dependent, and automatic

incrimination algorithm for static case in ABAQUS/Standard) along the tangent line


74

to the current solution point. In the next step, it searches for equilibrium in the plane

that passes through the point thus obtained (which is orthogonal to the same tangent

line). In this study the distance was determined by the automatic increase in

convergence speed in this algorithm, and did not have to be artificially restricted in

the computational process. The computation principle is described as follows:

(a) A reference load is defined and the proportionality factor, λ , of this load to

the ultimate load corresponding to RC wall failure is calculated.

ABAQUS/Standard uses the “arc length ( L )” along the static equilibrium path

in the load–displacement space to measure the progress of the solution and

determines the relationships between load, arc length and displacement.

(b) The load always applies proportionally. The load magnitude ( totalF ) is defined

as )oFrefλ(FoFtotalF where oF is the initial load; refF is the reference

load vector; and λ is the load proportionality factor, which is considered as a

part of the solution. ABAQUS/Standard determines the current value of the

load proportionality factor at each increment.

(c) In order to obtain the non-linear equilibrium equations, Newton’s method is

used. The modified Riks procedure extrapolates only a 1% strain increment. In

the Riks step definition, the ABAQUS program provides an initial arc length

increment )inL( along the static equilibrium path. The initial load

proportionality factor )in( is computed as:


75

period

inin

L

ΔLΔλ Eq. 2-33

where periodL is a user-specified total arc-length scale factor (typically equal to 1).

This value is used during the first iteration of a Riks step. The λ value is computed

automatically for the subsequent iterations and increments.

(d) The modified Riks method addresses the unstable collapse and conducts post-

buckling analysis more effectively than the Riks method (see Figure 2-15). The

initial load proportionality factor can be determined using this method as

follows: the solution is assumed to have developed to point )λ ;u~

A oN

o( o ; the

tangent stiffness )(KNM

o has been formed and NMo

NMo FνK has been

determined. Based on a specified path length )inL( in the solution space, the

increment size (o

A to 1A in Figure 2-14) is selected. Therefore:

2in

No

No

2o ΔL;1)ν~(:;1)ν~(Δλ Eq. 2-34

Thus:

1)ν~ν~(

ΔLΔλ

No

No

ino

Eq. 2-35

where oλ is the initial load magnitude parameter in the modified Riks method; N

and M denote the degrees of freedom of the model; NF is the loading pattern as may

be defined with one or more of the loading options in ABAQUS ; Nu and Noν are

the displacements; Noν

~ is the normalised tangential displacement vector at the initial

iterative step, where N0ν

~ is No scaled by u~ ; and u~ is the maximum absolute

value of all displacement variables. The value inΔL is initially suggested by the user


76

and is adjusted using the ABAQUS/Standard load increment method in static

problems based on the convergence rate. Automatic stability was also used to avoid

a divergence solution. For considering the geometric nonlinearity, Nlgeom setting

was also activated.

Figure 2-15: Modified Riks method (Hibbitt et al., 2011)

Results and discussion

2.11.1 Crack pattern

Figure 2-16 to Figure 2-21 show a comparison between the maximum plastic strain

(PE) distributions obtained from finite element analysis as well as the crack patterns

obtained from the experiments for the control and strengthened specimens. In

ABAQUS, by visualising maximum principle plastic strain (PE), which in the

material model is defined as cracking strain, it is possible to determine the area

experiencing cracks or fractures. The cracks obtained in the experiments and

correlated maximum PE in the simulations were similar, which indicates that models

were able to capture the failure mechanism in the specimens. The PE was used in


77

previous research in order to determine the crack pattern or the areas that experienced

either cracks or fractures (Enochsson et al., 2007; Genikomsou and Polak, 2015).

Figure 2-16(a) shows the failure of RC beams reported by Siddiqui (2010) where the

failure mode was concrete crushing. The applied CFRP anchor in both sides of the

beam tackled the debonding issue in the sample. The FEM results also present the

maximum PE in the same area at the mid-span of the beam (Figure 2-16(b)) where a

larger area was damaged in tension side of the beam and greater value of maximum

PE was achieved.

Figure 2-17 shows the failure of the concrete column with eccentric axial loads where

the concrete column experienced severe damage in the compression side. An

analogous behaviour has been detected in the FEM where the maximum PE was

obtained in the areas were the concrete column suffered severe damage. The greater

value of maximum PE was obtained in the area where concrete experienced crushing

in experiment (Hadi and Widiarsa, 2012).

Figure 2-18 (a) shows the cracks in the bottom side of RC slab under the applied line

load, and several distributed cracks (parallel to the line load direction) that were

reported in the experiment (Smith and Kim, 2009). An analogous behaviour was

detected in the FEM, which was shown as discontinuous lines in Figure 2-18 (b). Both

numerical and experimental results show that cracks were distributed between two

restraints and the section out of this area did not experience any cracking (Smith and

Kim, 2009).


78

(a) Experiment (Siddiqui, 2010)

(b) FEM maximum PE

Figure 2-16: Crack pattern for SB

(a) Experiment (Hadi and Widiarsa, 2012) (b) FEM maximum PE

Figure 2-17: Crack pattern for NC


79

(a) Experiment (Smith and Kim, 2009)

(b) FEM maximum PE

Figure 2-18: Crack pattern for SS in the bottom side

Figure 2-19 to Figure 2-21 show the cracks in the RC walls for both experimental and

numerical simulation. Based on the experimental observation reported by

Mohammed et al. (2010, 2013), RC walls usually experience cracks in the upper

corner of the opening. In FEM, the maximum PE, which represents either cracking or

crushing in concrete, was obtained in the same area of the wall. A comparison of

corresponding maximum PE between the FEM results of NW and SW was presented

in Figure 2-20 and Figure 2-21 . The maximum PE of all RC walls was occurring near

the top corner of the opening which represents the correlated damaged areas in

experiments.


80

(a) NW2 (b) SW2-D (c ) SW2-A

Figure 2-19: Crack pattern of RC walls (Mohammed et al., 2013)

(a) NW1 (b) SW1-D (c ) SW1-A

Figure 2-20: FEM maximum PE of RC walls

(a) NW2 (b) SW2-D (c ) SW2-A

Figure 2-21: FEM maximum PE of RC walls


81

2.11.2 Ultimate strength

In order to show how the FRP changes the ultimate strength of RC members, a

comparison between the ultimate failure load of samples before and after

strengthening is presented in Table 2-6 and Table 2-8. These results indicate that the

application of FRP considerably enhances the ultimate strength of columns, beams

and slabs. However, there were negligible changes in the RC walls strengthened by

CFRP. In beams and slabs, the orientation of FRP was perpendicular to the loading

direction; therefore, it makes a significant contribution to FRP in a load-carrying

capacity. In fact, when the FRP was applied in the axial direction of beams, it has the

highest stiffness and strength in its fibre direction. In columns the concrete was

completely confined to FRP and, in this case, the FRP experienced a pressure

perpendicular to the FRP orientation. However, in RC strengthened walls, the loading

application is parallel to the FRP orientation and the wall experiences shortening in a

vertical direction. In this condition, FRP may not considerably contribute to

enhancing the ultimate strength.

An enhancement of about 29.5% was reported in the ultimate strength of the RC beam

in Siddiqui 2010. The simulation results show a 26% enhancement in the ultimate

failure load for SB. The CFRP application in slabs improved the ultimate strength

gain of the slab by about 64%, while an increase of about 58% was observed in the

FEM. The ultimate strength of the SC was increased by about 6.5% and 12.8% in

experiments and FEM simulation, respectively. A comparison between the

experiments and FEM for beams, columns and slabs is presented in Table 2-6 where

the mean (numerical/test) of 1.04 and standard deviation of 0.07 was achieved.


82

Table 2-6: Comparison of experimental and FEM results for beam, column

and slab

Structural Element Model

designation Ultimate load (kN)

Numerical

Experimental Numerical Experimental

Beam

(Siddiqui, 2010)

NB 197.20 193.00 0.98

SB 255.20 243.00 0.95

Column (Hadi and

Widiarsa, 2012)

NC 1950.00 2007.00 1.03

SC 2076.00 2264.00 1.09

Slab (Smith and Kim,

2009)

NS 49.30 55.52 1.13

SS 80.80 87.95 1.08

Mean 1.04

STDV 0.07

The load–deflection graphs for each typical sample of the beam, column and slab are

presented in Figure 2-22 to verify the numerical modelling with the experiment

outcomes. These results were well matched, however, the load deflection graph for

RC walls was not provided in the experiments and therefore, only the outcomes of

the FEM were presented in Figure 2-22(d).


83

(a) Beam (SB) (b) Column(SC)

(c) Slab (NS) (d) RC wall

Figure 2-22: Load versus deflection curve for experiments and FEM

The ultimate load obtained from FEM for a RC wall control sample was compared

with the experiment, and a considerable discrepancy was observed. Therefore, an

attempt was performed to compare both experimental and FEM simulation results

with existing empirical formula. Many researchers have studied the structural

behaviour and failure load of RC walls with openings (Saheb and Desayi (1989,

1990); Doh and Fragomeni (2005, 2006); Fragomeni et al., 2012). These studies have

proposed a simplified formula to calculate the ultimate failure load. Based on the

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35 40

Lo

ad (

kN

)

Mid-span deflection (mm)

Exp-SB

Num-SB

0

400

800

1200

1600

2000

2400

0 2 4 6 8

Lo

ad (

kN

)

Axial deflection (mm)

Exp-SC

Num-SC

0

10

20

30

40

50

60

70

80

0 20 40 60 80

Lo

ad (

kN

)

Mid-span deflection (mm)

Exp-NS

Num-NS

0

10

20

30

40

50

60

70

80

0 5 10

Lo

ad (

kN

)

Mid-height deflection (mm)

Num-SW1-A

Num-NW1


84

material properties and dimensions of the NW specimen: 25c'f MPa; slenderness

ratio (Hw/tw < 16); aspect ratio (Hw/Lw < 2); thinness ratio (Lw/tw < 8) and opening

aspect ratio (Ho/Lo≈1.8), using the formula suggested by Saheb and Desayi (1989 and

1990) was preferred. The detailed information about the experiments and formula can

be found in the original research publication. Their proposed formula for ultimate

load in RC walls with openings experiencing one-way action is presented in Eq. 2-9.

A detailed comparison of ultimate failure load for NW1 and NW2 are presented at

Table 2-7. The results show about a 6.33% and 3.62% difference between the

numerical and empirical formula for NW1 and NW2, respectively and also

represented that the FEM was capable of capturing the RC wall behaviour and

ultimate failure load. However, the difference between experiment outcomes and

numerical simulations is up to 44.55%. This difference between the existing empirical

formula and experiments outcomes is up to 39.31%. These findings indicate the

obtained ultimate load of RC walls in experiments were significantly higher than

those obtained from numerical simulation and existing empirical formula in control

specimens.

As shown in Table 2-8, a significant discrepancy was observed between experiments

and numerical outcomes considering both strengthened and control specimens of RC

walls with the mean (numerical/test) of 0.66 and standard deviation of 0.09. The

application of CFRP enhanced the ultimate load for SW1-A about 8.3% in the

experimental test, while an increase of 4.8% was observed in the FEM. For SW1-D,

the application of CFRP enhanced the ultimate load of the wall by about 55% in the

experimental test (Mohammed et al., 2013), while an increase of 0.2% was observed


85

in the FEM. The same procedure was conducted to find out the effect of CFRP

confinement on SW2-A and SW2-D. The results showed that CFRP only increased

the capacity of RC wall 6.7% and 3.6% for SW2-A and SW2-D respectively.

However, these values were reported as 16.4% and 6.9% in previous experimental

studies (Mohammed et al., 2013). In FEM it was evident that the CFRP has greater

contribution in ultimate strength of the wall when the opening size increases. These

results contradict the outcome of experiments where, with an increase in the opening

size, less CFRP contribution on the wall capacity was reported (Mohammed et al.,

2013).

The outcome from the FEM analysis contradicts the results obtained by (Mohammed

et al., 2013). By applying CFRP at 450 to the opening corners, the ultimate strength

of the wall was enhanced significantly, while a negligible change was observed in the

FEM. Additionally, unlike the experiment’s outcome, the FEM simulation shows that

the pattern applied to the SW-A had a better effect on the strength of the RC wall, as

the weakest part of the wall was strengthened. Further, unlike the experiment’s

results, FEM outcomes showed that by increasing the opening size a greater

contribution of CFRP was achieved.


86

Table 2-7: Comparison of experimental and FEM results for RC walls

Model

designation

Ultimate load (kN) Eq. 2-9 (%) Eq. 2-9 (%) Numerical (%)

Experimental

(Mohammed et al., 2013) Numerical Eq. 2-9

Experimental Numerical Experimental

NW-1 85.0 63.8 60.0 29.41 6.33 33.23

NW-2 73.0 49.0 50.5 39.31 3.62 44.55

Table 2-8: Comparison of experimental and FEM results for walls with and without CFRP

Model designation f'c (MPa)

Ultimate load (kN) Numerical

Experimental

(Mohammed et al., 2013) Numerical

Experimental

NW-1 15.6 85.00 63.80 0.75

SW1-A 18.3 108.00 78.45 0.73

SW1-D 16.4 138.50 67.20 0.49

NW-2 15.8 73.70 50.50 0.69

SW2-A 15.1 82.00 51.50 0.63

SW2-D 17.0 84.80 56.30 0.66

Mean 0.66

STDV 0.09


87

Based on the outcomes from experiments and numerical studies, there was evidence

that CFRP had a great influence on the ultimate strength of beams, columns and slabs.

However, in the case of the RC wall there was a significant discrepancy observed

between the FEM and experimental outcomes. This may arise from the CFRP’s fibre

orientation being parallel to the loading direction and walls experiencing a shortening

in the fibre’s direction. As a result of scarce previous experimental and theoretical

studies on the strengthening of RC walls using CFRP, this field needed urgent attention

to support a better understanding of the behaviour of the wall and CFRP’s contribution

to the ultimate strength. Further investigations were also required to determine the

behaviour of RC walls with various material properties and CFRP patterns under

different boundary conditions (two, three and four sides restrained).

Summary

Based on the FEM simulation and the existing experiments, a distinct difference

between the ultimate strength in strengthened RC walls was realised. The FEM was

capable of simulating the behaviour of the various RC members and the FRP

contribution in the ultimate strength of beams, columns, and slabs. However, for RC

walls, consistency in the results of both experimental and numerical simulations was

not achieved. The outcomes of existing experiments significantly overestimate the

ultimate load of RC walls in comparison to numerical simulation. Therefore, further

numerical, theoretical and experimental analysis was required to enable the study of the

behaviour of the strengthened RC walls. Additionally, the effect of the boundary

condition (concrete walls with three and four sides restrained) as well as the opening

size and location should be considered to be able to properly evaluate the contribution

of the FRP in search of the ultimate strength of the strengthened RC wall.


88

Unquestionably it was essential that different FRP pattern applications also be

investigated to ensure a full understanding of the optimum strengthening solutions for

practical applications. To conclude, the provision of a simplified guideline/formula for

calculating the capacity of strengthened walls was a necessary requirement for

engineering applications. Given the outcomes of this chapter, a comprehensive

experimental and numerical study was undertaken to propose reliable recommendations

for engineering applications. The study investigated a number of concrete walls with

different parameters, such as various boundary conditions and CFRP layouts and

information related to experiments and numerical simulation were presented in the

following chapters.

Chapter 3: Experimental Program

89

3 EXPERIMENTAL PROGRAM

Introduction

This chapter presents the detail of the extensive experimental program undertaken on

reinforced concrete wall panels with openings strengthened with various CFRP layouts, in

one- and two-way actions, subjected to eccentric axial loads. As highlighted in Chapter 2,

the outcomes of FEM showed a significant discrepancy between the FEM findings and the

experimental results when analysing CFRP strengthened RC panels with opening. Also,

the limitations of previous research were discussed in Chapter 2.

In view of the limited scope of previous studies, eighteen concrete wall panels, with

opening strengthened with various CFRP layouts, were prepared and tested at Griffith

University to determine the behaviour of wall panels. The variables considered included:

varying CFRP layouts; and varying support conditions (one-way action and two-way

action with three or four all sides restrained). However, wall and opening geometries were

kept constant.

In this chapter a detailed description of the test planning, casting, CFRP application,

experimental set-up and testing procedure is given. The testing conditions are identical to

those employed by Doh (2002).

Test panels

Experimental tests were undertaken on RC walls with and without CFRP, working under one-

way action (OW), two-way action with both three sides restrained (TW3S) and two-way action

with four all sides restrained (TW4S). Eighteen one-third scaled wall panels were constructed

and tested. Details of the test specimen’s dimensions are provided in Figures 3-1 to 3-3. All


90

panels produced were of square geometry with the length and height being 1200 mm and the

thickness equal to 40 mm. Each wall configuration exhibited a slenderness ratio (Hw/tw)

of 30. Seven different CFRP layouts were applied to the RC wall panels to investigate the

contribution of the CFRP to the ultimate strength of the RC wall. In the current AS3600 (2009),

the effects of openings can be neglected for TW4S if the total area of the openings is less than

10% of the area of the wall and the height of any opening is less than 1/3 of the height of the

wall. Therefore, in this research the opening ratio of the wall was chosen to be 14% which is

beyond the limit of AS3600 (2009) for walls with TW4S. In order to have consistency

throughout the experiments, the same opening ratio was considered for walls with OW and

TW3S.

Material properties

The material properties of the concrete, steel and CFRP used in the test specimens are presented

in this section.

3.3.1 Concrete

In view of the available literature, it was decided that normal strength concrete would be used

in experimental test specimens. The compressive strength of concrete for all RC panels is

presented in Chapter 4. The concrete was obtained from a local ready mix supplier using

general purpose cement, sand and 10 mm aggregates. Considering the available spacing

between the single layer reinforcement in the 40 mm thick wall panel, the use of small size

aggregates (smaller than 10 mm) was justified. In addition, when the concrete was cast and

placed in such a confined thickness, the concrete mix was more workable.

3.3.2 Steel

A single mesh layer of steel reinforcement was incorporated into the concrete wall panels.


91

As the primary purpose of this investigation was to analyse the influence of strengthening

patterns and the structural behaviour of one-way and two-way action (with three and four all

sides restrained), the reinforcement ratio was kept constant for all RC walls. Single

reinforcement mesh F41 (rebars with 4 mm diameter) was placed centrally in the cross section

of the panels. The reinforcement ratio conformed to the minimum requirements of the relevant

standards (AS3600, 2009). The space between the bars in both vertical and horizontal

directions was 100 mm. The mesh provides a cross-sectional area of 126 mm2 in both directions

of wall panel of 40 mm thickness. This provides a steel ratio of ρ=0.0015 which also conform

to the minimum requirement for vertical and horizontal steel (ρv=0.0015 and ρh=0.0025,

respectively) as specified in AS3600 (2009). The welded wire mesh F41 has nominal yield

strength of 500 MPa. Based on the previous experimental and theoretical investigation by

Fragomeni (1995), the placement of the minimum required reinforcement at the mid-depth of

wall panels has little effect on axial strength, especially when placed in a single layer only.

3.3.3 CFRP

The selected CFRP sheets (Sika-wrap 230C) used in the experimental program were provided

by Sika Pty Ltd. This type of CFRP can be used to strengthen reinforced concrete structures,

to increase flexural, shear and axial loading capacities. These may be used for some of the

following applications: increasing the loading capacity of structural elements; improving

service life and durability; structural upgrading to comply with current standards; replacing

missing or inadequate steel reinforcement; enabling changes in use/alterations and

refurbishment; correcting structural design and/or construction defects or increasing resistance

to seismic movement (SIKA Australia Pty. Ltd). Some advantages of this type of CFRP

include: flexibility and accommodation of different surface planes and geometry; low density

for minimal additional structural weight; availability in various lengths; flexibility, fits around


92

any given structural element and extremely cost effective in comparison to traditional

strengthening techniques. The material properties of Sika Wrap are listed for reference (Table

3-1)

Table 3-1: Properties of CFRP: SikaWrap – 230C (SIKA Australia Pty. Ltd)

Areal weight

(g/m2)

Thickness

(mm)

Density

(g/cm3)

Tensile Modulus

(MPa)

Tensile Strength

(MPa)

Elongation

at Failure

(%)

230±10 0.128 1.8 234000 4300 1.8

3.3.4 Epoxy

A thixotropic epoxy based impregnating resin/adhesive (Sikadur-330) was provided by Sika

Pty. Ltd for the experimental program. Sikadur-330 can be used for impregnation resin for

Sika-wrap fabric reinforcement using the dry application method. It consists of two parts: Part

A: resin and part B: hardener. The mixing ratio is A:B = 4:1 by weight. The exact mixing ratio

must be safeguarded by accurately weighting and dosing each component.

Panel designation

Based on the investigation acquired from previous research, the selection of the test panel

dimension was dependent on a number of factors. These included the capacity of the testing

machine, the actual full scale wall dimension being modelled, the available laboratory space

and the concrete strength adopted.


93

375 450 375

37

5450

375

40 Support

LC

LC

Support 375 450 375

37

5450

375

40

LC

LC

(a) OW-NF (b) OW-DF

375 450 375

37

5450

375

40LC

LC

375 450 375

375

450

375

40LC

LC

(c) OW-AF `(d) OW-CF

375 450 375

37

5450

375

40

LC

LC

375 450 375

375

45

0375

40LC

LC

(e) OW-WF (f) OW-PF

Figure 3-1: Panel designation and CFRP layout for walls with OW (dimensions in

mm)


94

375 450 375

37

5450

375

40 Side restraint

LC

LCSupport

Support

375 450 375

37

5450

375

40

LC

LC

(a) TW3S-NF (b) TW3S-DF

375 450 375

37

5450

375

40

LC

LC

375 450 375

37

5450

375

40

LC

LC

(c) TW3S-AF (d) TW3S-CF

375 450 375

37

5450

375

40

LC

LC

375 450 375

37

5450

375

40

LC

LC

(e) TW3S-WF (f) TW3S-MF


95

375 450 375

37

5450

375

40

LC

LC

(g) TW3S-FWF


mm)

The panels have been designated as follows and are detailed in Figures 3-1 to 3-3.

OW- one-way buckling with two sides supported;

TW3S- two-way buckling with three sides supported;

TW4S- two-way buckling with four sides supported;

NF- no CFRP (Control specimen);

AF using CFRP alongside the opening;

DF using CFRP diagonal to the opening;

CF using CFRP as combination of AF and DF;

WF using CFRP wrapped around the opening;

PF using CFRP parallel to the opening;

MF mixed using of CFRP diagonal and parallel to the opening and

FWF using fully wrapped CFRP around the opening.


96

375 450 375

37

54

50

37

5

Side restraint

LC

LC

Side restraintSupport

Support

375 450 375

37

5450

37

5

LC

LC


375 450 375

37

54

50

37

5

LC

LC

375 450 375

375

45

03

75

LC

LC


375 450 375

375

45

03

75

LC

LC

(e) TW4S-WF


mm)


97

Mould preparing and casting

Timber moulds were used in the casting process in order to ensure the dimensions of the test

wall panels were as accurate and reproducible as possible. The size of the mould was

1200×1200×40 mm. For the edges of the mould, a 40 mm×40 mm timber cross-section was

used and for the base a structural marine plywood sheet (20 mm thickness) was used. The

structural marine plywood provides a smooth surface for the concrete specimens during the

curing period. The 40 mm×40 mm timber beams were used for the trimming and edging of the

specimens. In order to attach timber beams to the plywood, galvanised screws at 200 mm

centres were used (Figure 3-4). To ensure that the heads of the screws did not protrude above

the 40 mm height of the edge beam, they were countersunk accordingly. In addition, sticking

tape was used to ease the process of de-moulding.

(a) Top view

(b) Side view

Figure 3-4: Typical formwork layout


98

Wall panels were cast horizontally in the timber moulds described, with steel reinforcement

secured at the centre of the cross-section using tie wires on 20 mm high chairs. In each casting,

a total of six moulds were used with typical reinforcement layout as shown in Figure 3-5.

(a) Framework and reinforcement layout (b) Placing of concrete in progress

(c) vibration of concrete in progress (d) Trowelled concrete surface

Figure 3-5: Actual formwork and steel reinforcement set-up

The mesh was cut in 1200×1200 mm squares and placed in the moulds. Then, the opening

position was marked out and this area of mesh was removed. Approximately 10 mm was

trimmed from the edge of the squares of mesh and also from around the opening to ensure

adequate concrete cover.

The mesh was placed on 20 mm high bar chairs and secured with tie wires to ensure the steel

reinforcement was cast centrally within the wall panels. To prevent floating of the mesh to the

surface when the wet concrete was vibrated, the tie wires were also used to fix the steel mesh


99

to the sides of the mould. This required small holes at the edges of mould to allow the steel

reinforcement to be appropriately tied in the correct position.

To ensure openings were formed in the places required, high density polystyrene foam was

placed in specific positions on the timber moulds. This material was preferred for the opening

as it could easily be cut to the required size of the openings needed and could also be easily

removed for testing of the wall panels. The piece of polystyrene was secured to the plywood

base so that no part protruded above the 40 mm thickness of the wall (see Figure 3-5 (a)). Wall

panels were cast in batches of six, to maximise the usage of moulds and concrete delivered.

The moulds were lightly sprayed with a Lanolin based concrete release agent before casting

of the wall panels. In order to prevent the head of the countersunk screws being covered in

wet concrete, the surfaces of the moulds were covered with a tape sheet. The completed

moulds were placed on large pieces of black plastic sheets in the indoor area of the

Engineering Laboratory. Once the moulds had been prepared and arranged, the concrete

was delivered and gradually poured into the moulds. For spreading the concrete evenly

throughout the moulds, shovels were used. After placing adequate amounts of concrete into

each mould, the concrete was levelled to the same height as the edges to ensure appropriate

thickness of the panels was achieved. A vibrating screed was used for this process which

simultaneously removed air voids from the concrete and provided a uniform thickness for each

panel. After completion of the screeding process, the wall panels were trowelled and floated so

that the finished wall panels resulted in a smooth and uniform surface.


100

CFRP amount and size

In order to find the appropriate amount of CFRP required for strengthening of the RC walls, a

simplified method proposed by Enochsson et al. (2007) was applied to CFRP strengthening in

RC wall panels. The method was to investigate the replacement of reinforcement in the vicinity

of the opening of the two-way RC slab to the minimum CFRP sheet surrounding the opening

region. This method was based on the Swedish Building Administration’s handbook on

concrete structures BBK04 (2004). Figures 3-1 to 3-3 illustrate the typical CFRP layout for

OW, TW3S and TW4S specimens. The width and anchorage length of the CFRP layout was

calculated based on the following formulae (Eqs 3-1 to 3-4):

L'f85.0

fAa

c

sy2s

Eq. 3-1

85.0

ax

Eq. 3-2

2s2

w

w

f

2sf A)

xt

xut(

E

EA

Eq. 3-3

f

ff

t

AW

Eq. 3-4

where: c'f is concrete compressive strength; Lw is concrete wall length; fsy is steel yield stress;

tw and tf are the thickness of wall and CFRP, respectively; Es and Ef are modulus of elasticity

of steel and CFRP, respectively; u is concrete cover of reinforcement in mm; As2 and Af are

the area of additional steel reinforcement and CFRP cross sectional area, respectively; a is the

depth of the equivalent rectangular stress block, and Wf is width of the required CFRP.

The width of CFRP layout was 105 mm for all test specimens, except the wall with TW3S-

FWF where a width of 450mm was used to fully wrap the opening. In order to have an

estimation of the effective anchorage length (Lbmax) of CFRP, a proposed formula (Eq. 3-5) for


101

concrete beams was used (FIB Bulletin 14, 1990). Based on the recommendation provided in

FIB Bulletin 14 (1990), an increase in anchorage length does not result in an increase in

resisting tensile stress due to the limitation of fracture energy.

c'ff

tEcL

ctm

ffbmax

Eq 3-5

where c=1.44 (constant) and fctm is the tensile strength of the concrete. In order to find the total

length of CFRP, the effective anchorage length was added to the opening size. In addition,

extra length was considered to have a cross coverage on the layer of CFRP perpendicular to

the initial one. The minimum amount of CFRP sheet required was determined and presented

(Table 3-2). For all CFRP applications, the width of layout was the same, while the width of

the FWF layout was equal to the opening length.

Table 3-2. Location, width and length of the applied CFRP sheets

CFRP

layout

Location in relation to edges of the opening /

(confinement, tension or compression side)

Width Length (mm)

(mm) Individual Total

NF - - - -

DF In corner (450) / tension 105 450 1800

AF Along (0/900) / tension 105 770 3080

WF In corner (450) and wrapped (0/900) / tension and

compression 105 450 & 440 5320

CF In corner (450) and along (0/900)/ tension 105 450 & 770 4880

PF Along(900)/ tension 105 1480 2960

MF In corner (450) and along (900)/ tension 105 1480 & 1380 4240

FWF Fully wrapped around opening / confinement 450 850 1700

Curing, testing of concrete properties

Once the wall panels had been cast they were covered with wet hessian. In order to keep the

panels moist throughout the initial hardening stage of the curing process, the hessian sheet was

soaked and kept wet (Figure 3-6). Fourteen (14) days after pouring, the panels were uncovered


102

and removed from the moulds. The timber edges of the moulds and the Styrofoam was

removed. The panels were then lifted and stacked to cure in a controlled indoor environment.

After the minimum 28 day curing period, the wall panels were considered to have achieved the

required concrete strength to apply the CFRP layout.

In order to obtain the actual properties of the concrete utilised for these specimens, at least

three standard cylinders (200 mm height and 100 mm diameter) were cast for compression and

one for the tensile splitting test for each wall panel. In this section, the procedures for these

tests are outlined. All tests were carried out in accordance with AS1012.8.1 (2000), AS1012.9

(2014) and AS1012.10 (2000).

(a) concrete curing (b) stocking RC walls

Figure 3-6: Concrete curing and stocking

3.7.1 Compression testing of the concrete

Compression testing was conducted using a concrete testing machine (Figure 3-7). This machine

was used for testing of the concrete cylinders in the engineering laboratory. The cylinders had

the standard capping using the natural rubber in accordance with AS1012.9 (2014) Section 6. The

cylinders were placed and tested in accordance with the standard AS1012.9 (2014) Section 8.


103

In order to determine the actual concrete strength of the wall panel on the day of testing, three

cylinders, which were cast simultaneously with the wall panel, were tested. The average

compressive strength of cylinders corresponding to the wall panel tested at the same age was

taken as the mean concrete strength of panel as presented in Chapter 4. Standard sized cylinders

(100 mm diameter and 200 mm height) were cast and cured by storing the specimen in lime

saturated water based on AS1012.8.1 (2000).

Figure 3-7: Concrete material testing machine

3.7.2 Tensile test of concrete

In addition to the compressive tests, indirect tensile testing of concrete cylinders was

undertaken using the Brazil test or splitting test in accordance with AS1012.10-(2000). The

tensile test results are given in Chapter 4. Unlike compressive testing, for the Brazil tests, the

concrete cylinders were placed on their side in a standard Brazil test apparatus between the two

loading plates of the testing machine as shown in Figure 3-8. Then, a continuously increasing

compressive force was applied until failure. To determine the actual tensile strength, t'f (MPa),


104

the maximum applied force, P (kN), is substituted into the following equation:

)LD/(P2000t'f , where L and D are the cylinder length and diameter (mm), respectively.

Figure 3-8: Indirect tensile test set-up

In numerical analysis of the wall panels presented in Chapter 5, a linear softening model is

used to represent the post failure behaviour in tension where the area below the curve is the

fracture energy - fG . The stress-fracture energy approach was used with the fracture energy in

order to define the tension stiffening response. For concrete under uniaxial tension,

t'f and fG were estimated from the CEB-FIP (1990).

Application of EB-CFRP confinement

Before applying the CFRP, the substrate should be appropriately prepared. Any dust, loose

particles and laitance should be removed using an industrial vacuum cleaner. Based on the

regulation provided by Sika Pty Ltd., the substrate should be free of grease and oil and have a

maximum moisture content of 4%. The surface to be bonded must be level. Steps and formwork

marks should be no greater than 0.5mm. Structural corners were rounded to a radius of at least

10mm where required. This was achieved using a grinder. The CFRP was cut to the desired

shape and size based on the CFRP layouts and pattern. In the next stage, Sikadur-330 was


105

supplied in factory proportioned units comprising the correct quantities. Then, both

components were thoroughly stirred separately using a slow running drill/stirrer with a helical

paste mixer (max. speed 600 rpm). Application of the Sika Wrap (Dry) system was conducted

as follows (Figure 3-9):

The well mixed Sikadur-330 was applied to the prepared substrate by lamb skin roller. This

sealed the substrate and promotes adhesion. Then, Sika Wrap-230C was placed onto the resin

coating in the required direction. The fabric into the resin was carefully worked with a plastic

roller until the resin was squeezed out between the rovings. In cases where the CFRP layers

had overlapped, more resin was applied within the suggested time (within 1 hour (at 20°C)).

In the last stage the concrete wall panels were separated from the rest of the laboratory in

accordance with the required curing process.

Figure 3-9: EB-CFRP application

The strain gauges were installed on critical points of the concrete and CFRP as well as in

between the two materials (interface) in order to monitor any de-bonding observed during the

experiments (Figure 3-10). Typical strain gauge locations are presented in Figures 3-11 to 3-

13.


106

(a) Strain gauge on top of CFRP Layout (b) Strain gauges between CFRP layout and

concrete

Figure 3-10: Strain gauge application

375 450 375

37

5450

37

5

40LC

LC

Strain Gauge on CFRP

Strain Gauge on Concrete (interface)

Figure 3-11: Typical strain gauges locations


107

Figure 3-12: Location of strain gauge on top of CFRP for CF layout

Figure 3-13: Strain gauge on CFRP for WF layout

Test regime

Three hydraulic jacks utilised in the test rig distributed the axial loading on the top edge of

the panels with an eccentricity as presented (Figure 3-14). Details of the test setup and support


108

conditions in one- and two-way actions with three and four sides restrained are described in

this section.

Figure 3-14: Test rig and hydraulic jacks (Doh, 2002)

Using three hydraulic jacks (800 kN), the test rig was capable of supporting axial loads of up

to 2700kN as shown in Figure 3-15. The rig was originally built by Doh (2002) and consists of

two main steel 310UC118 columns each 4000 mm high and a series of channel members

(2×380PFC) used as cross beams to support the loading test frame.

A uniformly distributed load was transmitted, using three jacks, across the top through a loading

beam (250UC72). Three pairs of load bearing stiffeners added to the loading beam were used

for even support. This setup was previously statically verified by Doh (2002). The stiffeners

were used to resist the load and to minimize the partially unloaded region between jacks. The


109

supporting beam (250UC72) on the strong floor was identical to the loading beam.

Figure 3-15: Typical test rig set-up for TW4S wall panel

In order to provide a uniformly distributed load from the concentrated loads subjected by three

hydraulic jacks, pairs of loading beams (200UC72) were assembled into the test rig located on

the top and bottom of the wall specimen. In creating the distributed load, the dispersed force

from the jacks through the beam at slope of 1:1 was considered adequate, as presented in Figure

3-16.


110

Figure 3-16: Uniform distribution of loading from hydraulic jacks (Doh, 2002)

A pair of hinged support conditions was each simulated by placing a steel rod of 39mm

diameter on a steel plate (PL-6,150) at the top and bottom as presented by the design detail

(Figure 3-17). A pair of equal angles (EA-40×40) was clamped to the steel plate by a

combination of bolts and welding. The steel rod was also welded along the steel plate with an

eccentricity of tw/6 from the centre line. The concrete wall panels were restrained by the angels

with a series of screw bolts and a couple of control plates as shown in Figure 3-17.

For two-way action with three and four all sides restrained, the edges of the wall panels had to

be effectively stiffened perpendicularly with allowed rotation along the wall panels. To achieve

this, a pair of channels (150PFC) combined with a square hollow section (SHS-40×40×5.0)

was placed on both sides of the wall panels as a side restraint. The side restraints were

connected with high tensional bolts (D16@100 CRS) along the channels through the SHS, to

take advantage of the stronger axis of the section, as shown in Figure 3-18.


111

(a) Top and bottom restraint (b) Schematic view of top restraint

Figure 3-17: Top and bottom restraints

(a) Top view of side restraint (b) Schematic view of side restraint (Doh, 2002)

Figure 3-18: Side restraints

Data collection

Four types of test results were recorded. The first type was the load increments and ultimate

tw/6


112

failure loads; the second was lateral deflection history of four dial gauges and vertical deflection

history; the third was a strain history on the CFRP and concrete, and the fourth was the crack

patterns and crack propagation.

Dial gauges were used to measure the lateral and vertical deflections of the wall panels during

testing. The positioning of dial gauges for the wall panels is indicated in Figure 3-19. Four dial

gauges were positioned midway between the edges of the panel and the edges of the opening.

Also, one dial gauge was placed to measure the vertical shortening of the RC walls. In order to

ensure that no damage would occur to the gauges from crushing particles, all dial gauges were

located on the compression side of the wall (see Figure 3-15).

The dial gauges located at the mid-height of the wall panels (Right and Left in Figure 3-19)

measure the maximum deflection of the wall panels under one-way action.

The information from the dial gauges was used to investigate the axial load versus lateral and

vertical displacement characteristics and deflection profiles as the wall approached failure.


113

Figure 3-19: Typical dial gauge locations on wall panels in compression side

(dimensions in mm)

Pilot test

A load cell was positioned between the centre hydraulic jack and the upper loading beam.

Loading increments were applied to the wall panel at approximately 4.9 kN per hydraulic jack

on a load-cell. The walls were therefore loaded in 14.7 kN increments measured by the load-

cell up to failure and the loading was force-control. At each load increment, crack patterns,

deflections and strains were recorded. Importantly the maximum deflections were obtained just

prior to the failure load. Some of the panels failed in a brittle mode and the sudden failure of

these panels made it difficult to record the maximum deflection, strain and the collapse load

precisely at failure. Thus in the load versus deflection responses, the collapse load and

corresponding deflection magnitude could not be indicated, but the ultimate load was recorded


114

and used to analyse the capacity of the wall panels.

At each load increment, crack patterns and deflections were observed to allow observations of

the failure mechanisms. Different failure mechanisms that can be encountered in RC wall

panels with openings are: crushing in compression, rupture in tension, slip in shear, bending

and buckling as well as stress concentrations around the opening.

To identify test set-up problems during the test procedure, six trial tests were undertaken. The

trial wall panels were with and without CFRP layouts under one- and two-way action with three

and four sides restrained. Table 3-3 gives a summary of the trial test results. The first trial wall

panel was a one-third scale specimen tested under one-way action. Other panels were one-third

scale specimens tested in two-way action with three and four sides restrained with different

CFRP layouts.

In these trial tests, difficulties arose in obtaining eccentric loading. This was due to the uneven

wall thicknesses along the four edges and in each corner of the panel as well as the position of

the top steel rod which was not properly located at the required eccentricity (tw/6). Careful

alignment of the wall specimen was therefore required to obtain the axial load eccentricity

(tw/6). The test setup allowed for precise adjustment to ensure this eccentricity was achieved.

Packing steel plates were required to be placed on either one side or both sides of the top and

bottom hinged edges. Also, the importance of the transducer calibration and correct wall

positioning were realised.

During the testing phase of the project, special consideration was given to the required post-

test retention of the panels within the test frame. To address this issue a custom safety frame

was built in the engineering laboratory to retain the failed panel sections, eliminating any post


115

failure danger as a result of a collapsing RC wall panel. Also the loading rate was adjusted

during the testing so that explosive failure types were minimised. It was, however, realised that

a constant loading rate was essential so that all testing was uniform.

The preliminary testing also identified a contact issue between the side and top restraints, where

restriction was observed at different stages of loading. In order to rectify this problem, the top

and bottom loading plate were altered to ensure adequate clearance was obtained. In addition,

a steel bar with greater diameter was also used to ensure that the contact restriction problem

will not be an issue even after rotation has occurred as a result of loading.

Table 3-3: Summary of pilot tests

Type of Restraint CFRP layout 'cf (MPa) Failure Load (kN)

OW NF 52.0 459.0

TW3S DF 59.0 700.0

TW4S NF 63.0 914.0

TW4S DF 61.0 982.0

TW4S DF 58.0 751.0

Chapter 4: Evaluation of test results

116

4 EVALUATION OF TEST RESULTS

Introduction

This chapter focuses on examining the structural behaviour of eighteen one-third scale RC

walls with openings under one-way and two-way action, strengthened with various CFRP

patterns, subjected to eccentric (tw/6) axial loads. Concrete material properties in both tension

and compression were determined. The experimental outcomes include: crack patterns, load-

deflection profiles and strain of critical points that have been obtained and discussed in detail.

The efficiency of various CFRP layouts was also investigated in order to determine the

optimum CFRP layout considering the alternate support conditions investigated.

Concrete compressive and tensile strengths of RC walls

The concrete tensile and compressive cylinder strength results and actual panel thicknesses for

the wall panels are presented in Table 4-1. A minimum of six standard concrete cylinders

(dimensions: 100 mm diameter and 200 mm height) were cast and tested for each wall

specimen at the same time and were subjected to the same curing conditions. The cylinders

were tested in compression and tension, at the same time as the walls, using the standard

method prescribed in AS1012.8.1 (2000), AS1012.10 (2000) and AS1012.9 (2014). Detailed

testing procedures were presented in Chapter 3, Section 3.7.1 and Section 3.7.2. The average

value of the three cylinders was taken as the compressive and tensile strength of the tested

concrete panel. These strengths were subsequently used in the theoretical analyses (Chapter 5)

for the prediction of the ultimate loads for the panels, as well as for a comparison with the test

results. The nominal thickness of wall panel was 40 mm. The actual panel thicknesses were

calculated as the average of the thicknesses measured at the four corners and at four middle

side positions in each panel. In some cases, due to difficulty in finishing surface, the thickness

of the panel was more than 40 mm which are presented in Table 4-1.


117

Table 4-1: Cylinders strengths for RC walls and average panel thickness

Wall

designation

Wall

thickness

tw (mm)

Casting

date

Testing

date

Curing

duration

'fc

(MPa) tf

(MPa)

OW-NF 40.0 23/01/2014 19/04/2014 86 54.7 4.0

OW-DF 40.0 23/01/2014 16/05/2014 113 55.1 4.1

OW-AF 40.0 23/01/2014 19/04/2014 86 54.7 4.0

OW-WF 43.5 09/05/2014 21/07/2014 73 62.6 4.6

OW-CF 46.0 09/05/2014 21/07/2014 73 62.6 4.6

OW-PF 40.0 21/03/2014 13/06/2014 84 64.9 4.8

TW3S-NF 40.0 21/03/2014 11/06/2014 82 60.0 4.3

TW3S-DF 44.0 05/09/204 12/11/2014 68 57.0 4.1

TW3S-AF 43.0 05/09/2014 12/11/2014 68 58.5 4.3

TW3S-WF 46.0 09/05/2014 22/07/2014 74 62.3 4.5

TW3S-CF 40.0 21/03/2014 28/05/2014 68 62.3 4.5

TW3S-MF 40.0 21/03/2014 13/06/2014 84 65.0 4.9

TW3S-FWF 40.0 05/09/2014 13/11/2014 69 58.4 4.2

TW4S-NF 40.0 05/09/2014 11/11/2014 67 57.6 4.1

TW4S-DF 40.0 05/09/2014 11/11/2014 67 57.6 4.1

TW4S-AF 40.0 05/09/2014 11/11/2014 67 56.2 4.1

TW4S-WF 40.0 09/05/2014 23/07/2014 75 64.7 4.8

TW4S-CF 40.0 09/05/2014 23/07/2014 75 63.2 4.5

Experimental results and discussion

The failure characteristics of the wall panels with OW, TW3S and TW4S action are presented

in this section. The behaviour of the wall panels tested up to failure was observed visually and

the failure characteristics discussed with reference to the variable support conditions and CFRP

layouts. The test results were used to study the influence of parameters such as CFRP layouts

and side restraints on the axial load capacity of wall panels with openings.

4.3.1 Crack pattern for walls with OW

One-way action was achieved by providing restraints at the top and bottoms the RC wall

without any CFRP (OW-NF), with expected horizontal cracks throughout the middle of the


118

opening (Figure 4-2). Similar bending failure for RC walls with openings under eccentric axial

loading has been reported in previous studies (Doh and Fragomeni, 2006; Fragomeni et al.,

2012). The crack patterns observed on the tension and compression face of the wall panels

tested under one-way action, after failure, are presented (Figures 4-1 to 4-6). The application

of the CFRP changed the load path and therefore changed the shape of the crack patterns due

to the resistance of the CFRP provided. In most cases, applying CFRP induced distributed

cracks when compared to the corresponding control specimens without CFRP.

Wall with OW-DF developed a few large cracks on the tension face, similar to the failure mode

observed for the OW-NF. This indicates that the CFRP layout on the DF wall under one-way

action did not provide additional load capacity, while also experiencing a brittle failure mode.

In contrast to the experimental results obtained by Mohammed et al. (2013), the results showed

only a 15% increases in the ultimate strengths between OW-DF and OW-NF. However, CFRP

application alongside the opening for OW-AF, OW-CF and OW-PF panels resulted in more

distributed cracks across the opening region on the tension side. This indicates that those CFRP

layouts near opening regions intensified the ultimate strength of RC wall. Although bending

failure was predominant in those panels, there was adequate evidence to suggest that some

compressive crushing failure also occurred as shown in OW-CF (see Figure 4-4(b)).

Walls with the OW-WF layout, observed a catastrophic collapse with some yielding of

reinforcement, as the concrete was wrapped with CFRP on both the tension and compression

sides - around the corners of opening. The failure pattern exhibited for the OW-WF panel was

still a flexural bending failure. The brittle nature and failure across the thickness of the panel

can be explained by the strong bond between compression and tension CFRPs inside the panel

which forced the compression segment of CFRPs to fracture through the tensile segment.


119

As shown in Figure 4-1 to 4-6, on the tension side of the wall panels, there was no evidence of

de-bonding between CFRP and concrete before ultimate load was achieved. For OW-DF and

OW-WF panels, there was no evidence of de-bonding even after failure. The strain values

obtained from the strain gauges where installed on top of the CFRP layout as well as at the

concrete-CFRP interface. An example of the full bonding of the CFRP-concrete interface is

provided in Figure 4-22 and discussed in Section 4.6

(a) Tension side (b) Compression side

Figure 4-1: Crack pattern for OW-NF


Figure 4-2: Crack pattern for OW-DF


120


Figure 4-3: Crack pattern for OW-AF


Figure 4-4: Crack pattern for OW-CF


Figure 4-5: Crack pattern for OW-WF


121


Figure 4-6: Crack pattern for OW-PF

4.3.2 Crack pattern for walls with TW3S

All of the tested TW3S panels exhibited crack patterns and failure modes that are consistent

with the expected behaviour of wall panels supported on three sides. Biaxial curvature is

evident as idealised in Figure 2-1. It was evident that the majority of cracking propagated

diagonally from the restrained corners to the opening and then horizontally from the opening

to the unrestrained edge. This unique cracking mode indicates typical two-way behaviour close

to the restrained ends and one-way behaviour between unsupported edges. Also highlighted in

Figure 4-7, similar crack patterns were reported in the experimental tests conducted by Doh et

al. (2010).

The application of the CFRP changed the load path and therefore changed the shape of the

crack patterns due to the resistance the CFRP provided. The crack patterns on the tension and

compression face, of the RC walls with three sides retrained, are presented (Figures 4-7 to 4-

13). Walls with CFRP perpendicular to the crack direction (TW3S-DF, -CF, -WF and -MF),

exhibited more ductile behaviour with a number of distributed cracks evident in Figures 4-8 to

4-14. In walls with TW3S-DF, by applying the CFRP perpendicular to the typical cracks


122

direction, more distributed cracks propagating through the area where CFRP was not supplied

were observed.

Wall with TW3S-AF developed three large cracks, commencing at the restrained corners of

the tension face, then a single crack horizontally towards the unrestrained edge. This indicates

a brittle failure mode, with possibly some yielding of reinforcement occurring. In contrast,

TW3S-FWF exhibited more ductile behaviour with a number of parallel cracks evident as

shown in Figure 4-13. As no CFRP layer was supplied perpendicular to the crack direction near

the restrained corners to the opening, the crack pattern was analogous to that observed on walls

without CFRP. In this case, the fibre orientation was parallel to the crack propagation in the

free edge. CFRP layers were supplied perpendicular to the crack directions in TW3S-MF,

therefore, more distributed cracks were observed. The CFRP prevented cracks from

propagating through regions where it was supplied. In all cases, the CFRP was bonded with

the substrate until the failure load was achieved.


Figure 4-7: Crack pattern for TW3S-NF


123


Figure 4-8: Crack pattern for TW3S-DF


Figure 4-9: Crack pattern for TW3S-AF


Figure 4-10: Crack pattern for TW3S-CF


124


Figure 4-11: Crack pattern for TW3S-WF


Figure 4-12: Crack pattern for TW3S-MF


Figure 4-13: Crack pattern for TW3S-FWF


125

4.3.3 Crack Pattern for walls with TW4S

The crack patterns on the tension and compression face of TW4S walls are presented (Figures

4-14 to 4-19). The two-way action walls with openings (TW4S-NF) showed typical double

curvature bending failure characterised by diagonal cracking from the corners that propagate

to the corner of the opening, similar to the ideal scenario.

The distinct differences in failure modes for panels of different strengths is again noted, for

TW4S walls with CFRP layouts (Figures 4-14 to 4-19) producing distinct brittle cracks whereas

more smeared diagonal cracks were evident in the tension side of the walls by preventing them

from propagating toward the corners of the opening.

It should also be noted that the diagonal crack patterns do deviate a little depending on wall

irregularities and loading but the anticipated crack pattern was generally achieved in most

cases. The CFRP was bonded with the substrate until the failure load was achieved. Having a

combination CFRP in both the diagonal and parallel direction to the opening of the TW4S-CF

sample, increased the rigidity of the wall around the opening.


Figure 4-14: Crack pattern for TW4S-NF


126


Figure 4-15: Crack pattern for TW4S-DF


Figure 4-16: Crack pattern for TW4S-AF


Figure 4-17: Crack pattern for TW4S-CF


127


Figure 4-18: Crack pattern for TW4S-WF

4.3.4 Deflection measurement

The loads versus lateral deflections for all panels are presented in Figures 4-19 to 4-22. The

vertical deflections were also recorded to investigate shortening of the walls. Importantly the

maximum deflections were obtained just prior to the failure load being reached. Most of the

panels tested failed in a brittle mode and the sudden failure of these panels made it difficult to

record deflection precisely at failure. Thus in these figures, the absolute maximum failure loads

and the corresponding maximum deflections are not shown.

For walls with OW and TW3S, the maximum lateral deflection was reported at the midway

between the free edge of the panel and the edges of the opening (shown as Right Gauge in

Figure 3-16). As shown in Figure 4-19, the maximum shortenings were generally smaller than

the maximum lateral deflection in most of the RC walls. It is also evident from Figures 4-19

to 4-21 that the RC wall panels under one-way action exhibited smaller vertical shortenings

compared to the TW3S and TW4S walls at the same load level.

For walls with one-way action (OW), the recorded deflection at the left side of the opening was


128

similar to that at the right side. The deflection at the top of the opening was slightly greater

than that on the bottom of the RC walls. Depending on the corresponding CFRP layout, the

maximum lateral deflection of strengthened RC wall panels was increased to various extents.

The deflection profile of OW walls showed a fairly uniform curvature along the height as

expected with the maximum deflection at mid-height. The profile of all walls tested under OW

action generally showed similar characteristics. In the early stages of loading, slight deflections

were produced and then more pronounced deflections occurred as the test panels were

progressively loaded to failure.

The distinct advantages of walls with three sides restrained (TW3S) compared to one-way walls

are also evident with less deflections being achieved for the same load level. The deflections

near unrestrained supports (Right Gauge) indicate that a greater maximum deflection occurred

for all cases in TW3S walls. The vertical shortening of TW3S panels was recorded where

greater deflections were observed compared to TW4S walls at the same load level. The

deflection profiles for the free edge of TW3S panels were similar to that of panels with OW.

Based on deflection profiles, it can be seen that the layer of CFRP assisted the wall panels to

tolerate greater deflections when compared to wall panels without CFRP. A similar

circumstance was observed for some walls with four sides restrained (TW4S).

Generally, in TW4S walls the deflections at the left and right were similar to observed

deflections at the top and bottom locations. This was obvious as the side, top and bottom-

quarter points should have moved, approximately, by the same amount due to the curvatures

taking place in both the vertical and horizontal directions. However, an irregular vertical

deflection was also observed for the TW4S-CF panel (Figure 4-21 (d)), where the CFRP layout

provided a robust lateral support around the opening and the major failure mechanism was


129

concrete crushing at the top restraint. For this case, given the restraint conditions, the CFRP

layout prevented the walls ability to deflect laterally or appropriately rotate.


130

(a) OW-NF (b) OW-DF

(c) OW-AF (d) OW-CF

(e) OW-WF (f) OW-PF

Figure 4-19: Load versus lateral deflection curves for walls with OW

0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-NF

LeftRightTopBottomVertical 0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-DF

LeftRightTopBottomVertical

0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-AF


0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-CF


0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-WF


0

200

400

600

-4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

OW-PF



131



(e) TW3S-WF (f) TW3S-MF

0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-NF

Left

Right

Top

Bottom0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-DF


0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-AF


0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-CF

Left

Right

Top

Bottom

Vertical

0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-WF


0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW4S-MF

Left

Right

Top

Bottom


132

(g) TW3S-FWF

Figure 4-20: Load versus lateral deflection curves for walls with TW3S

0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-FWF



133



(e) TW4S-WF

Figure 4-21: Load versus lateral deflection curves for walls withTW4S

0

200

400

600

800

1000

-6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-NF

Left

Right

Top

Bottom

Vertical0

200

400

600

800

1000

-6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-DF


0

200

400

600

800

1000

-6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-AF

LeftRightTopBottomVertical 0

200

400

600

800

1000

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-CF


0

200

400

600

800

1000

-6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-WF



134

4.3.5 Strain gauge data measurements

Strain measurements were also recorded to monitor the strain values at critical points such as

the corner of the wall openings, top of the CFRP and at the CFRP-concrete interface for

detecting any potential de-bonding. Strain was recorded at each load increment for all wall

panels tested. These measurements were utilised to investigate the behaviour of the CFRP-

concrete interface and monitor possible de-bonding as well as strain variations of critical parts

of the wall panels after introducing the CFRP layout. Based on the observation from strain

gauge measurements and visual inspection, in all cases the CFRP was bonded with the substrate

until the failure load was achieved. Generally, an abrupt change was noted in the obtained strain

data during the last stage of loading and failure. Figures 3-11 to 3-13 presents the location of

the strain gauges on the top of the CFRP layer and concrete (interface) for OW-CF and Figure

4-22 depicts the load versus strain graph for the strain gauges. As shown in Figure 4-22, the

measurement of strain for gauges on the top of the CFRP layout was identical to that of the

gauge located at the CFRP-concrete interface. This was further evidence that the concrete and

CFRP were intact and fully bonded until the failure load. The load versus strain was linear for

the initial loading regimes, and then followed by non-linear trends with strain increasing

rapidly as failure was approached. The linearity of the curve was approximately 30% for OW-

CF of the ultimate loads for the panels. A similar observation was noted for TW3S-CF (Figure

4-23) and TW4S-CF (Figure 4-24). For the TW3S-CF and TW4S-CF, the curves are essentially

straight lines with relatively low strain. Those specimens showed a more brittle type of failure

in that they were unable to sustain any more loading after reaching the maximum load. The

linearity was up from 70 to 80% of the ultimate loads for these panels.


135

Figure 4-22: Load versus strain curves for OW-CF

Figure 4-23: Load versus strain curves for TW3S-CF

0

200

400

600

0 200 400 600 800 1000

Lo

ad (

kN

)

Strain (µmm/mm)

OW-CF

Concrete (interface)

CFRP

0

200

400

600

800

0 200 400 600 800 1000

Lo

ad (

kN

)

Strain (µmm/mm)

TW3S-CF

Concrete interface CFRP


136

Figure 4-24: Load versus strain curves for TW4S-CF

Further investigations were carried out on the strain of the CFRP layout on wall panels with

various boundary conditions. The strain gauges were installed on top of the CFRP layer and

they recorded strain values up to the failure load. No abrupt change was noted in the obtained

strain data during testing and before the last stage of loading to failure. Figures 4-25 and 4-26

present the load versus strain curves for CF and WF layouts under OW, TW3S and TW4S.

These results indicated that the CFRP layer contributed to increasing the ultimate failure load

of the wall panels tested and that it also remained bonded to the concrete. It was also evident

that the strain values increased significantly as the applied load was approaching the failure

load.

0

200

400

600

800

1000

0 200 400 600 800 1000

Lo

ad (

kN

)

Strain (µmm/mm)

TW4S-CF

Concrete interface

CFRP


137

Figure 4-25: Load versus strain curves for walls with CF layout

Figure 4-26: Load versus strain curves for walls with WF layout


The failure loads for all the panels were recorded and are expressed as a dimensionless quantity

- the axial strength ratio (NNF(*F)/ 'fc .Lw.tw), in Table 4-2 and Figure 4-27. In this table, N*F

represents the ultimate load of CFRP strengthened RC walls with various CFRP layouts. The

subscript * was replaced D, A, C, and W for CFRP layout of DF, AF, CF and WF, respectively.

NNF was the ultimate load of walls without CFRP. These results were used to study the effects

of two primary parameters: CFRP layouts and support conditions.

0

200

400

600

800

1000

0 200 400 600 800 1000

Lo

ad (

kN

)

Strain (µmm/mm)

CF

OW

TW3S

TW4S

0

200

400

600

800

1000

0 200 400 600 800 1000

Lo

ad (

kN

)

Strain (µmm/mm)

WF

OW

TW3S

TW4S


138

In Table 4-2, the numbers in the parentheses give the percentage increase in the axial strength

ratios between the control walls (without CFRP i.e. NF) and with CFRP strengthened panels

for each support condition. The experimental failure ratios NNF(*F)(OW)/NNF(*F)(TW3S) and

NNF(*F)(OW)/NNF(*F)(TW4S) are also given in Table 4-2.

The ultimate strength of RC walls in one-way action was approximately 60% and 40% of that

in counterparts with TW3S and TW4S, respectively. The results were similar to the

experimental tests obtained by Doh et al. (2010), which was used as a reference for verification.

This outcome indicates adding side supports increases the load capacity of walls irrespective

of the type of CFRP layout.

It can also be observed from Table 4-2, that varying CFRP layouts had a significant effect on

axial strengths. The ultimate strengths of walls under one-way action (OW) with DF, AF, WF,

CF and PF layouts have led to a strength increase of 15.5%, 26.2%, 25.4%, 59.7% and 14.0%,

respectively. However, this observation contradicts the results obtained by Mohammed et al.

(2013). Their study presented DF pattern walls achieving a higher load capacity than walls with

an AF layout of CFRP. The higher contribution of CFRP in ultimate strength of OW-AF panel

is related to the CFRP application around the opening, as the weakest part of the wall was

strengthened.

Further, for the walls under two-way bending with three side supports (TW3S), the CFRP

layouts had a significant effect on ultimate strengths. Ultimate strengths increased by 28.2%,

40.8 %, 33.2%, 40.8%, 32.9% and 3.0% for DF, AF, WF, CF, MF and FWF respectively. The

axial strength ratio of the walls with AF and CF layouts tend to be the largest load capacity for

the TW3S support condition, while the FWF layout had an insignificant contribution to the


139

ultimate load of the RC wall as the fibre orientation was provided parallel to the bending

direction and crack propagation.

Further analysis was carried out to investigate the influence of the amount of CFRP compared

with the corresponding gain in ultimate strength. Therefore, the efficiency of each CFRP layout

was studied which considered the ratio of ultimate load increase (%) to the total length of CFRP

layout (LCFRP) in meters. This was included for clarification of the contribution of the CFRP

layout in the gain of the wall strength based on the amount of CFRP utilised.

The findings indicated that the WF pattern produced the least increase in ultimate strength in

respect to the amount of CFRP usage in all three categories of walls under OW, TW3S and

TW4S.

For walls under one-way action (OW), the efficiency of CFRP for the CF layout had the highest

value, where ultimate strength was enhanced up to 59.7%. AF and DF layouts yielded similar

efficiency while PF and WF layouts exhibited the lowest value.

For walls under two-way action with three side supports (TW3S), the maximum efficiency was

obtained by the DF layout in which the minimum amount of CFRP was utilised. Although, the

maximum usage of CFRP was for the WF pattern, the lowest efficiency was reached. One

noteworthy point was that DF and WF configurations eventuated in similar ultimate strength

increases; while the amount of applied CFRP for the WF pattern was triple that of the DF

pattern. The AF and CF patterns improved the capacity of RC panels identically (by 40.8%),

while the efficiency of DF pattern is clearly superior to that of AF.


140

Table 4-2: Ultimate load of RC wall panels

Wall

designation

'fc

(MPa)

tw

(mm)

NNF(*F)

(kN)

NNF(*F) (OW)

Axial strength ratio

NNF(*F) /('fc .Lw.tw)

Efficiency

[Increase of

ultimate load (%)

to LCFRP (m)]

NNF(*F) (TW3S)

or

NNF(*F) (OW)

NNF(*F) (TW4S)

OW-NF 54.7 40.0 266.00 - 0.101 -

OW-DF 55.0 40.0 309.00 - 0.117(15.5%) 8.6

OW-AF 54.7 40.0 335.70 - 0.128(26.2%) 8.5

OW-WF 62.6 43.5 415.05 - 0.127(25.4%) 4.8

OW-CF 62.6 46.0 559.00 - 0.162(59.7%) 12.2

OW-PF 64.9 40.0 359.85 - 0.1165(14.0%) 4.8

TW3S-NF 60.0 40.0 440.00 0.7 0.153 -

TW3S-DF 57.0 44.0 589.35 0.6 0.196(28.2%) 15.7

TW3S-AF 58.5 43.0 649.50 0.6 0.215(40.8%) 13.2

TW3S-WF 62.3 46.0 700.05 0.6 0.204(33.2%) 6.3

TW3S-CF 62.3 40.0 643.35 0.8 0.215(40.8%) 8.4

TW3S-MF 65.0 40.0 633.45 - 0.203(32.9%) 7.8

TW3S-FWF 58.4 40.0 441.00 - 0.157(3.0%) 1.8

TW4S-NF 57.6 40.0 647.25 0.4 0.234 -

TW4S-DF 57.6 40.0 766.05 0.4 0.277(18.4%) 10.2

TW4S-AF 56.2 40.0 753.45 0.5 0.279(19.3%) 6.2

TW4S-WF 64.7 40.0 894.30 0.4 0.288(23.0%) 4.3

TW4S-CF 63.2 40.0 887.25 0.6 0.293(24.9%) 5.1


141

Figure 4-27: Axial strength ratio versus CFRP layouts

Summary

Eighteen CFRP strengthened RC walls with opening were constructed and tested under

eccentric axial loads. Seven types of CFRP layouts were considered and the effect of these

layouts on the behaviour of RC walls in three distinct support conditions was investigated.

From the comparison and investigation between the different types of CFRP layouts and

support conditions, a number of conclusions were drawn:

a) Externally bonded CFRP can significantly increase the strength of RC walls;

b) Varied success was achieved in ultimate strength gains under different support

conditions and CFRP layouts. For RC walls with OW an enhancement of ultimate

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

NF DF AF WF CF PF MF FWF

Axai

l st

rength

rat

io (

NN

F(*

F)/

(f' c.

Lw

.tw)

Wall designation

OW

TW3S

TW4S


142

strength between 14.0-59.7% was observed, while this range for walls with TW3S

and TW4S were 3.0-40.8% and 18.4-24.9%, respectively;

c) Considering various support conditions, the ultimate strength of RC walls with OW

were 60% and 40% of that with TW3S and TW4S, respectively;

d) The application of the CFRP changed the load path resulting in altered crack patterns

due to the resistance of the CFRP provided. Especially in cases with CFRP applied

perpendicular to the typical crack directions, more distributed cracks were observed

propagating through the area where CFRP was not supplied

e) Generally, more deflection was observed in CFRP strengthened RC walls in

comparison to counterparts without CFRP;

f) De-bonding was not an issue before failure load. The strain gauges were installed to

monitor the probable de-bonding of the CFRP–concrete interface and it was evident

that the concrete and CFRP was bonded up to the failure load; and

g) The efficiency of CFRP layouts were also investigated where WF layout presented the

least efficient pattern of strengthening, whereas, CF and DF were the most effectual

layouts for walls in one-way and two-way action, respectively.

Further research is required to determine the behaviour of RC walls with various opening

sizes and locations using alternative CFRP layouts. The outcomes of this research provide


143

a platform to establish a future reliable FEM model to conduct a parametric study

considering various factors.

Chapter 5: Comparative and parametric study

144

5 COMPARATIVE AND PARAMETRIC STUDY

Introduction

CFRP strengthened RC walls were analysed using ABAQUS software. The main purpose of

this study was to compare the behaviour of RC walls obtained from simulation (ABAQUS

software) with the current experimental results (Chapter 4) and conduct a parametric study

considering various factors.

A brief overview of the input parameters for the software modelling is presented followed by

the CFRP-concrete interface modelling. The FEM analysis for the current CFRP strengthened

RC walls (Chapter 4) was conducted to verify the experimental outcomes including the ultimate

loads, deflected shapes and crack patterns. After establishing that the numerical software was

a good comparison for experimental outcomes, a parametric study was then carried out for the

full scaled wall panels with various CFRP layouts, support conditions, opening sizes and

configurations.

The geometric and material nonlinearity was considered in this investigation. Nonlinear

material properties of concrete were considered using the Concrete Damage Plasticity (CDP)

approach. The input parameters for CDP, material properties (including concrete, steel and

CFRP) as well as their associated constitutive models were discussed in Section 2.4. Therefore,

a summary of the parameters are presented herein, with only the simulation of concrete-CFRP

interface being detailed in this chapter.

The behaviour of the steel reinforcement bar was assumed to be an elastic perfect plastic

material with elastic modulus, yield stress and Poisson’s ratio of 210 GPa, 500 MPa and 0.3

respectively. The concrete behaviour in compression was simulated using Hsu and Hsu (1994)

and the fracture energy concept was used to simulate concrete behaviour in tension. The

Poission’s ratio of concrete was assumed as 0.2.


145

The CFRP layout was assumed as an orthotropic material where the modulus of elasticity was

considered as E11 = 234 GPa, E22 = E33 = 4.5 GPa in various directions of layout. The Poisson’s

ratio was designated as 0.3, 0.3, 0.45 for 12

, 13 and 23 , respectively. G12=2.77 GPa;

G13=G23=1.5 GPa was used as the shear modulus of the CFRP layer in the various directions.

The plastic damage parameters of concrete were assumed as follows: dilation angle: 120; the

flow potential eccentricity: 0.1, the ratio of initial equibiaxial compressive yield stress to initial

uniaxial compressive yield stress: 1.16, the ratio of the second stress invariant on the tensile

meridian to that on the compressive meridian: 0.667 and the viscosity parameter: 10-5.

The concrete and CFRP interface

A cohesive contact was utilised to simulate the CFRP-concrete interface. In Figure 5-1, a

schematic shape of a simple bilinear traction–separation law was presented based on the

effective traction, max and effective opening displacement, .

Figure 5-1: Schematic shape of bilinear traction–separation constitutive law


146

The initial stiffness of interface was defined based on the proposed method by Guo et al. (2005)

as follows:

c

c

i

i

o

G

t

G

t

1K

Eq. 5-1

Where it and ct were the resin and concrete thickness, respectively. iG and cG were the shear

modulus of resin and concrete, respectively. An upper limit for the maximum shear stress (

max ) was calculated based on Eq. 5-2 proposed by Lu et al. (2005).

twmax f5.1 Eq. 5-2

where

c

f

c

f

w

b

b1.25

b

b2.25

β Eq. 5-3

where f

b and c

b are the CFRP and concrete width and t

f is the concrete tensile strength.

Damage initiation was based on a quadratic traction function involving the nominal stress

ratios. The initiation of damage occurs when the submission of these values reached the one as

denoted by Hibbitt et al. (2011):

1

2

ot

t

2

os

s

2

on

n

Eq. 5-4

where n is the cohesive tensile stress and s and t are shear stresses of the interface, and n

, s , and t refer to the direction of the stress component.

The energy release concept was employed to define the interface damage evolution.

Benzaggah–Kenane fracture criterion was applied to specify the dependence of the fracture

energy on the mode mix (Hibbitt et al., 2011), shown as follows :


147

ccn

cs

cn G

G

G)GG(G

Eq. 5-5

where ts GGG , ns GGG , and were the material parameters. nG , sG and tG

refer to the work done by the traction and its conjugate separation in the normal, the first and

the second shear directions, respectively.

FEM analysis

In all numerical models, a full scale of the element was analysed. In the FEM, 8-node brick

elements (three degrees of freedom per node), were used to model the concrete, CFRP and

restraints. The reinforcement was simulated using a 2-D truss element. An appropriate contact

was also considered between the restraints and concrete elements. In this study the Riks method

was used for analysis of all numerical models. Detailed information about Riks method was

presented in Chapter 2.

Mesh convergence sensitivity was performed for all specimens in order to achieve minimum

discrepancy in the element behaviour and failure load. An attempt was carried out to have a

square element for all specimens. Herein, the mesh sensitivity study is presented considering

three configurations including coarse, medium and fine meshes (Figure 5-2). In order to

investigate the mesh sensitivity in the RC wall panels, the mesh sizes for other parts, such as

reinforcement bars and supports were maintained. Using a coarse mesh resulted in lower peak

loads and deflection compared to the experimental outcomes. The peak loads predicted for the

varied mesh densities are provided in Table 5-1. The outcomes for ultimate loads and deflection

by using fine and medium mesh were similar; however, the fine mesh generation was deployed

to accurately consider the eccentric load application. In addition, as the CFRP-concrete

interface was simulated using cohesive contact, the fine mesh was able to capture the behaviour

of the contact more precisely.


148

(a) Coarse (b) Medium (c) Fine

Figure 5-2: Mesh sensitivity study for RC walls (general seed)

Table 5-1 Mesh configurations used during the convergence study of the RC walls

Mesh

Number of

layers in

thickness

Size of

the mesh

seed

Number of

elements

Ultimate load (kN) Num

Exp

Num1 Exp2

Coarse

5 100 8068 252.58

266.00

0.95

7 100 8356 268.80 1.01

10 100 8788 271.44 1.02

Medium 5 50 10068 242.40 0.91

7 50 11156 244.80 0.92

Fine 5 30 14628 243.60 0.92

7 30 17540 249.15 0.94 1Num: Numerical, 2Exp: Experimental

Comparative Study

A comparison between FEM and experimental results was carried out and presented in this

section. It includes crack patterns, deflections and ultimate loads of RC walls under various

support conditions. As discussed in Chapter 2, in ABAQUS software, by visualising maximum

principle plastic strain (PE), which in the material model is defined as cracking strain, it is

possible to determine the area experiencing cracks or fractures. The cracks obtained in the

experiments and correlated maximum PE in the simulations was similar, which indicates that

models were able to capture the failure mechanism in the specimens. The PE was used in


149

previous research in order to determine the crack pattern or the areas experiencing either cracks

or fractures (Enochsson et al., 2007; Genikomsou and Polak, 2015).

5.4.1 One-way action wall’s crack patterns and deflected profile

The numerical outcomes for one-way action walls with openings under eccentric axial loads

have been presented in this section. Similar crack patterns obtained from ABAQUS were

observed in comparison to the experimental results. By providing restraints at the top and

bottom, the RC walls typically experience horizontal cracks throughout the middle of the

opening.

Maximum principle plastic strains (PE) in the tension side of each specimen under one-way

action are presented in Figures 5-3 to 5-8. For OW-NF, the maximum principal strain (PE) of

the wall panel occurs around the opening. As this wall was not strengthened by CFRP, a

uniform distribution of PE was observed throughout the opening height.

For the OW-DF specimen, the applied CFRP changed the crack distribution. The maximum

PE was observed in the area of the wall where the CFRP was not provided. However, as the

weakest part of the wall (mid-height) was not strengthened, the ultimate strength of the RC

wall was not considerably increased. A similar outcome was observed for the OW-WF, where

maximum PE was observed in the mid-height of the panel. In the OW-WF panel, as a U-shaped

CFRP layout was applied around the corner of the opening, a greater increase in ultimate

strength was observed compared to the DF layout. This was attributed to more wall area

experiencing bending with the CFRP applied to assist with load distribution.

However, CFRP application alongside the opening in panels with OW-AF, OW-CF and OW-

PF resulted in more distributed cracks across the opening region on the tension side. This was

demonstrated by the maximum PE where more distributed plastic strain was observed in these


150

cases in comparison to OW-WF and OW-DF walls. Based on the type of CFRP layout, various

degrees of enhancement were observed in ultimate wall strength. In the FEM simulation, no

evidence of de-bonding between concrete and CFRP for RC walls was observed which was

identical to the observation of the experiments.

(a) FEM maximum PE (b) Experimental

Figure 5-3: Crack pattern comparison for OW-NF


Figure 5-4: Crack pattern comparison for OW-DF


151


Figure 5-5: Crack pattern comparison for OW-AF


Figure 5-6: Crack pattern comparison for OW-CF


Figure 5-7: Crack pattern comparison for OW-WF


152


Figure 5-8: Crack pattern comparison for OW-PF

The loads versus deflections from FEM are presented for wall panels with OW and compared

with corresponding experimental outcomes (Figures 5-9 to 5-14). As mentioned in Chapter 4,

as a result of the sudden failure of panels during the experiments, it was difficult to record

deflection precisely at failure. Thus in these figures, the maximum deflections of experiments

are not shown. However, the maximum deflection of RC panels in FEM is presented.

Similar to the experimental outcomes, for walls with OW, the maximum lateral deflection was

reported at the midway between the free edge of the panel and the edges of the opening (shown

as Right Gauge). The vertical deflection of RC walls was generally smaller than the maximum

lateral deflection of the walls under OW. Similar outcomes were observed in the experimental

program.

For walls with one-way action (OW), the deflection at the left side of the opening was similar

to that at the right side from the FEM outcomes. The deflection at the top of the opening was

slightly greater than at the bottom of the RC walls. Similar results were observed in

experiments. Depending on the corresponding CFRP layout, the maximum lateral deflection

of strengthened RC wall panels was increased to various extents. In panels with CFRP applied


153

alongside the opening (OW-AF, -CF, -PF), more ductile behaviour was observed when the

walls experienced greater deflection compared to OW-NF specimens. However, in walls with

CFRP 450 to the opening’s corner, including: OW-DF and OW–WF, the lateral deflection was

similar to the OW-NF sample. Similar to the experimental outcomes, the deflection profile of

OW walls showed a fairly uniform curvature along the height as expected with the maximum

deflection at mid-height. The profiles obtained from FEM indicated that in the early stages of

loading, slight deflections were produced and then more pronounced deflections occur as the

test panels were loaded to failure. In general, the FEM was able to accurately predict the load-

deflection profile of CFRP strengthened walls with OW.

Figure 5-9: Load versus lateral deflection curves for OW-NF

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-NF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


154

Figure 5-10: Load versus lateral deflection curves for OW-DF

Figure 5-11: Load versus lateral deflection curves for OW-AF

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-DF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-AF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


155

Figure 5-12: Load versus lateral deflection curves for OW-CF

Figure 5-13: Load versus lateral deflection curves for OW-WF

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-CF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-WF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


156

Figure 5-14: Load versus lateral deflection curves for OW-PF

5.4.2 Crack patterns and deflections of walls with TW3S

The entire FEM outcome for TW3S panels exhibited crack patterns and failure modes that were

consistent with the expected behaviour of wall panels supported on three sides (Figures 5-15

to 5-20). Similar to the experimental outcomes, the maximum PE occurs diagonally from the

restrained corners to the opening and then horizontally from the opening to unrestrained edge.

It was evident that these walls had typical two-way behaviour close to the restrained ends and

one-way behaviour between unsupported edges.

By applying the CFRP perpendicular to the typical cracks direction in the TW3S-DF wall, the

crack path changed (as shown in Figure 5-16), where maximum PE was observed through the

area where CFRP was not supplied. A similar behaviour was observed in TW3S-WF. The PE

for TW3S-DF and TW3S–WF in the restraint free side were similar to that of NF.

The maximum PE in the wall with TW3S-AF, TW3S-CF and TW3S–MF indicated more

distributed cracks in panels, particularly in TW3S-CF where cracks were propagated through

0

100

200

300

400

500

600

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Lo

ad (

kN

)

Deflection (mm)

OW-PF

Left-Num

Right-Num

Top-Num

Bottom-Num

Series9

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


157

the majority of the walls. Similar behaviour was observed for the experimental counterparts.

The maximum PE at the top and bottom of the opening area were consistent with vertical cracks

observed in the experiments. In general, applying CFRP alongside the opening at the free edge

of the wall (for TW3S-AF, -CF, -MF) caused uniformly distributed maximum plastic strain

while more concentrated PE was observed in panels with DF and WF layouts. These outcomes

indicated that FEM was able to capture the behaviour of CFRP strengthened RC walls in TW3S

with various CFRP layouts.


Figure 5-15: Crack pattern comparison forTW3S-NF


Figure 5-16: Crack pattern comparison for TW3S-DF


158


Figure 5-17: Crack pattern comparison for TW3S-AF


Figure 5-18: Crack pattern comparison for TW3S-CF


Figure 5-19: Crack pattern comparison for TW3S-WF


159


Figure 5-20: Crack pattern comparison for TW3S-MF

The loads versus deflections from FEM are presented for walls with TW3S and compared with

the corresponding experimental outcomes (Figures 5-21 to 5-26). Similar to walls with OW,

the maximum deflections of experiments are not shown as a result of sudden failure in walls.

However, the maximum deflection of RC panels from the FEM is presented.

Similar to the experimental outcomes, for walls with TW3S, the maximum lateral deflection

was reported at the midway between the free edge of the panel and the edges of the opening

(shown as Right Gauge). The vertical deflection of RC walls was generally smaller than the

maximum lateral deflection. Similar outcomes were recorded during the experiments.

The outcomes of the numerical simulation indicated that walls with TW3S experienced less

deflection at the same load level when compared to the corresponding wall under one-way

action. The deflection at the top of the opening was slightly greater than that of the bottom in

most cases, for walls with TW3S. Similar results were observed during the experimental

program. The vertical shortening of panels with TW3S was recorded with less deflections being

achieved when compared to walls with OW at the same load level. A larger deflection was

observed at the free edge of walls with TW3S, which resembles the observed behaviour of

panels with OW. The CFRP layout affected the load-deflection behaviour of RC walls, where


160

in most cases a greater lateral deflection was observed when compared to wall panels without

CFRP. However, in panels with TW3S-CF, the CFRP layout provided a robust lateral support

around the opening and less deflection was observed in the FEM when compared to the

experimental outcomes.

Figure 5-21: Load versus lateral deflection curves for TW3S-NF

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-NF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


161

Figure 5-22: Load versus lateral deflection curves for TW3S-DF

Figure 5-23: Load versus lateral deflection curves for TW3S-AF

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-DF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-AF

Right-NumLeft-NumTop-NumBottom-NumVertical-NumLEFT-EXPRIGHT-EXPTOP-EXPBOTTOM-EXPVERTICAL-EXP


162

Figure 5-24: Load versus lateral deflection curves for TW3S-CF

Figure 5-25: Load versus lateral deflection curves for TW3S-WF

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-CF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-WF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


163

Figure 5-26: Load versus lateral deflection curves for TW3S-MF

5.4.3 Crack patterns and deflections of walls with TW4S

The crack patterns of the experiment and correlated maximum PE for the FEM on the tension

side of walls with TW4S are presented in Figures 5-27 to 5-31. Similar to the crack patterns

observed during the experiments, the maximum PE showed typical double curvature bending

failure characterised by diagonal cracking from the corners that make their way to corner of

the openings. As the walls were restrained on all sides, maximum PE was symmetrically

distributed in the wall. For walls with TW4S, the application of CFRP changed the crack

pattern to various extents depending upon the CFRP layouts. However, in all FEM cases, the

anticipated crack pattern was generally achieved.

By applying the CFRP perpendicular to the typical cracks direction for the TW4S-DF wall, the

crack path changed (as shown in Figure 5-17), where maximum PE was observed through the

area where the CFRP was not present. Similar behaviour was observed in the TW4S-WF

specimen. The vertical cracks on the top and bottom of the opening were constrained in cases

where CFRP was applied alongside the opening.

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6 8 10 12 14

Lo

ad (

kN

)

Deflection (mm)

TW3S-MF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


164

The CFRP was bonded with the substrate until the failure load was achieved. Having a

combination CFRP in both the diagonal and parallel direction to the opening of the TW4S-CF

sample, increased the rigidity of the wall around the opening.


Figure 5-27: Crack pattern comparison for TW4S-NF


Figure 5-28: Crack pattern comparison for TW4S-DW


165


Figure 5-29: Crack pattern comparison for TW4S-AF


Figure 5-30: Crack pattern comparison for TW4S-CF


Figure 5-31: Crack pattern comparison for TW4S-WF

The loads versus deflections from FEM are presented for walls with TW4S and compared with

corresponding experimental outcomes (Figures 5-32 to 5-36).


166

Similar to the experimental results, the FEM outcomes indicated that in walls with TW4S the

deflections at left and right were similar to the top and bottom deflections.

The outcomes from the numerical simulation indicated that walls with TW4S experienced less

deflection at the same load level when compared to the OW and TW3S panels. The vertical

shortening of panels with TW4S was recorded with less deflections being achieved when

compare to walls with TW3S and OW at the same load level.

The CFRP layout enhanced the capacity and deflection of RC walls and in most cases a greater

lateral deflection was observed when compared to wall panels without CFRP. Generally, the

FEM was able to capture the load-deflection behaviour of RC walls when compared to

experimental outcomes with a sound agreement observed.

Figure 5-32: Load versus lateral deflection curves for TW4S-NF

0

100

200

300

400

500

600

700

800

900

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-NF

Left-NumRight-NumTop-NumBottom-NumVertical-NumLEFT-EXPRIGHT-EXPTOP-EXPBOTTOM-EXPVERTICAL-EXP


167

Figure 5-33: Load versus lateral deflection curves for TW4S-DF

Figure 5-34: Load versus lateral deflection curves for TW4S-AF

0

100

200

300

400

500

600

700

800

900

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-DF


0

100

200

300

400

500

600

700

800

900

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-AF



168

Figure 5-35: Load versus lateral deflection curves for TW4S-CF

Figure 5-36: Load versus lateral deflection curves for TW4S-WF


The failure loads for all the panels were recorded and are expressed as a dimensionless quantity

- axial strength ratio (NNF(*F)/'fc .Lw.tw), in Table 5-2 and Figure 5-37. These results were used

to study the effects of two primary parameters: CFRP layouts and support conditions. In this

0

100

200

300

400

500

600

700

800

900

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-CF


0

100

200

300

400

500

600

700

800

900

-8 -6 -4 -2 0 2 4 6 8 10

Lo

ad (

kN

)

Deflection (mm)

TW4S-WF

Left-Num

Right-Num

Top-Num

Bottom-Num

Vertical-Num

LEFT-EXP

RIGHT-EXP

TOP-EXP

BOTTOM-EXP

VERTICAL-EXP


169

table, N*F represents the ultimate load of CFRP strengthened RC walls with various CFRP

layouts. The subscript * was replaced D, A, C, and W for CFRP layout of DF, AF, CF and WF,

respectively. NNF was the ultimate load of walls without CFRP.

In Table 5-2, the numbers in the parentheses give the percentage increase in the axial strength

ratios between the without CFRP (NF) walls and CFRP strengthened panels for each support

condition considered. The experimental failure ratios NNF (*F) (OW)/ NNF (*F) (TW4S) and NNF

(*F) (OW)/ NNF (*F) (TW4S) are also given in Table 5-2.

Similar to outcomes obtained from the experimental program, the ultimate load of RC walls

under one-way action were 60% and 40% of that counterparts with TW3S and TW4S,

respectively. The results are similar to the experimental tests conducted by Doh et al. (2010).

This outcome indicates adding side supports increases the load capacity of walls irrespective

of the CFRP layout used.

It is evident from Table 5-2, that varying the CFRP layouts has a significant effect on axial

wall strengths. The ultimate strengths of walls under one-way action (OW) with DF, AF, WF,

CF and PF layouts have led to a strength increase of 3.0%, 24.1%, 7.1%, 31.6% and 12.7%,

respectively. However, this observation contradicts the results obtained by Mohammed et al.

(2013). Their study presented the DF pattern walls achieving a higher load capacity than walls

with the AF layout of CFRP. The higher contribution of CFRP in ultimate strength for the OW-

AF panel is related to the CFRP application around the opening as the weakest part of the wall

was strengthened. Based on the results presented in Table 5-2, it was evident that the FEM was

able to accurately estimate the ultimate strength of RC walls under one-way action.

Further, for the walls under two-way bending with three side supports (TW3S), the CFRP

layouts had a significant effect on ultimate strengths. Ultimate strengths increased by 13.6%,


170

15.4 %, 15.5%, 24.4% and 5.2% for DF, AF, WF, CF and MF, respectively. Similar to the

experimental outcomes, the axial strength ratio of the walls with AF and CF layouts tend to be

the largest load capacity for TW3S. The comparison results presented in Table 5-2 indicated

that the FEM was able to accurately estimate the ultimate strength of RC walls in TW3S.

For the walls under two-way action, with four sides restrained (TW4S), the CFRP layout

contributed an average 17.7% gain in ultimate strength. The increases in ultimate strengths

were: 15.7%, 14.7%, 17.9% and 22.4% for DF, AF, WF and CF, respectively. It was also

observed that the WF and CF layouts contributed significantly to the ultimate load of the

respective panels. These outcomes were in agreement with experimental outcomes (presented

in Chapter 4). The discrepancy between the ultimate load obtained from experimental and

numerical analysis was around 3% which indicated the accuracy of FEM (Table 5-2).

Considering the outcomes from both the numerical and experimental investigation, it was

evident that the axial strength ratio of the walls with CF layout resulted in the largest load

capacity for the RC walls considered. This indicated that the CF layout of CFRP may be the

best strengthening or retrofitting method for walls under any support conditions. Considering

the experimental and FEM outcomes for all RC walls, it could be concluded that the FEM was

able to estimate the behaviour of CFRP strengthened panels with a mean accuracy of 0.92 and

a standard deviation of 0.07.

Further analysis was carried out to investigate the influence of the amount of CFRP compared

with the corresponding gain in ultimate strength. Therefore, the efficiency of each CFRP layout

was studied which considered the ratio of ultimate load increase (%) to the total length of CFRP

layout (LCFRP) in meters. This was included for clarification of the contribution of the CFRP

layout in the gain of the concrete strength based on the amount of utilised CFRP. The findings

indicated that the WF pattern produced the lowest enhancement of ultimate strength in respect


171

to the amount of CFRP usage in all three categories of walls, being: OW, TW3S and TW4S.

For walls under one-way action (OW), the efficiency of CFRP for CF layout was the highest

value where ultimate strength was greatly enhanced up to 59.7%. AF and DF layouts yielded

similar efficiency, while PF and WF exhibited the lowest value.

For walls under two-way action with three side supports (TW3S), the maximum efficiency was

obtained by DF layout in which the minimum amount of CFRP was utilised. Although, the

maximum usage of CFRP was for the WF pattern, it achieved the lowest efficiency. One

noteworthy point was that the DF and WF configurations eventuated in similar ultimate

strength gains; while the amount of applied CFRP for the WF pattern was triple that of the DF

pattern. The AF and CF both improved the capacity of the RC panels by 40.8%, while the

efficiency of the AF pattern was superior to that of CF. For walls under two-way action with

all four side restrained (TW4S), the overall enhancement of ultimate load was similar; however,

the DF layout resulted in the optimum value of efficiency.


172

Figure 5-37: Comparison of axial strength ratio versus CFRP layouts

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

NF DF AF WF CF PF MF

Axia

l st

rength

rat

io (

NN

F(*

F)/

f'c.

Lw.t

w)

Wall designation

EXP-OW

NUM-OW

EXP-TW3S

NUM-TW3S

EXP-TW4S

NUM-TW4S


173

Table 5-2: Ultimate strength comparison between FEM and experiments

Wall

Designation f'c

(MPa)

Wall

Thickness

(mm)

Ultimate Load

NNF(*F)

(kN)

NNF(*F) (OW) or

NNF(*F)(OW) Axial strength ratio

NNF(*F)/ f'c.Lw.tw Efficiency

NNF(*F)(TW3S) NNF(*F)(TW4S)

Exp1 Num2 Exp Num Exp Num Num

EXP Exp Num

OW-NF 54.7 40.0 266.00 261.07 - - 0.101 0.099 0.98 - -

OW-DF 55.0 40.0 309.00 270.36 - - 0.117(15.5%) 0.102(3.0%) 0.87 8.63 1.66

OW-AF 54.7 40.0 335.70 324.00 - - 0.128(26.2%) 0.132(24.1%) 0.97 8.51 7.83

OW-WF 62.6 43.5 415.05 348.00 - - 0.127(25.4%) 0.106(7.1%) 0.84 4.77 1.34

OW-CF 62.6 46.0 559.00 452.00 - - 0.162(59.7%) 0.131(31.6%) 0.81 12.23 6.47

OW-PF 64.9 40.0 359.85 349.20 - - 0.1165(14.0%) 0.124(12.7%) 0.97 4.74 4.30

TW3S-NF 60.0 40.0 440.00 446.53 0.7 0.6 0.153 0.155 1.01 - -

TW3S-DF 57.0 44.0 589.35 530.00 0.6 0.6 0.196(28.2%) 0.176(13.6%) 0.90 15.65 7.55

TW3S-AF 58.5 43.0 649.50 540.00 0.6 0.7 0.215(40.8%) 0.179(15.4%) 0.83 13.26 4.99

TW3S-WF 62.3 46.0 700.05 616.00 0.6 0.6 0.204(33.2%) 0.179(15.5%) 0.88 6.25 2.92

TW3S-CF 62.3 40.0 643.35 576.60 0.8 0.7 0.215(40.8%) 0.193(24.4%) 0.90 8.36 4.99

TW3S-MF 65.0 40.0 633.45 508.80 - - 0.203(32.9%) 0.163(5.2%) 0.80 7.76 1.22

TW4S-NF 57.6 40.0 647.25 643.20 0.4 0.4 0.234 0.233 0.99 - -

TW4S-DF 57.6 40.0 766.05 744.00 0.4 0.4 0.277(18.4%) 0.269(15.7%) 0.97 10.20 8.71

TW4S-AF 56.2 40.0 753.45 720.00 0.5 0.5 0.279(19.3%) 0.267(14.7%) 0.96 6.27 4.78

TW4S-WF 64.7 40.0 894.30 852.00 0.4 0.4 0.288(23.0%) 0.274(17.9%) 0.95 4.32 3.37

TW4S-CF 63.2 40.0 887.25 864.00 0.6 0.5 0.293(24.9%) 0.285(22.4%) 0.97 5.11 4.60

Mean 0.92

STDV 0.07 1Exp: Experimental; 2Num: Numerical


174

Parametric study

In order to better understand the behaviour of CFRP strengthened RC walls, a parametric study

was carried out using ABAQUS software to obtain the failure load of walls considering various

opening configurations and CFRP layouts. The accuracy, reliability and effectiveness of the

numerical modelling techniques were assured based on satisfactory results obtained from the

comparative study - where ultimate strength, load-deflection responses and crack patterns were

consistent with those of the experimental outcomes.

The ultimate strength of full scale RC walls strengthened with four various CFRP layouts were

investigated. The panel dimensions were 3000mm by 3000mm by 100mm corresponding to

the height, length and thickness, respectively. A single layer of F60 (6 mm diameter) steel mesh

with 100 mm spacing was placed in the centre of the RC walls in order to satisfy the

requirements of AS3600 (2009) for both vertical and horizontal steel ratios. The yield strength

of the steel (fy) and compressive strength of concrete were taken as 500MPa and 50MPa,

respectively. The loading was applied as a pressure along the top edge of the model to simulate

a uniformly distributed load at an eccentricity of tw/6. Appropriate boundary conditions were

applied to simulate the actual restraints used in the experiments, in both one-way and two-way

actions with three and four sides restrained.

Increasing the opening height together with the opening length had the most critical effect on

the ultimate load carrying capacity of concrete walls without CFRP in one-way and two-way

action (Lee, 2009). Therefore changing the opening height and length simultaneously resulted

in square openings for the RC walls considered.

Four various opening sizes were investigated. These included: 6%, 10%, 14% and 17% of the

wall area. The opening sizes were selected in a way to consider the strengthening of newly

constructed RC walls (opening size up to 10% as determined in AS3600) as well as


175

strengthening of existing walls with larger opening sizes.

A large opening in walls may not enable strengthening using a single layer of CFRP, therefore

alternate methods should be available. For example, assuming the width and height of a wall

was 3000 mm and the thickness was 100 mm with a minimum amount of horizontal and vertical

bars, usually a single layer of mesh. Assume that a single layer of F60 @ 100 mm (with 6 mm

diameter) in both the horizontal and vertical directions was used. Incorporating an opening of

30% means a square cut out with 1640 mm width and height. If the same procedure was used

to calculate the amount of required CFRP, the width of CFRP would amount to 718 mm. If the

AF layout was utilised for this example RC wall panel, then the height of the opening added to

the width of CFRP layouts on both the top and bottom of the opening would result in:

718+718+1640=3076 mm which is greater than the walls dimension. If the opening was located

above or below the wall centre, this discrepancy would worsen. For larger opening sizes it

may be suitable to use another technique such as CFRP wrapping around the opening or

applying two layers of CFRP as opposed to a single layer. Therefore, for the parametric study,

the maximum opening sizes were limited to 17% of the wall area. Required amounts of CFRP

were calculated based on the procedure outlined in Chapter 3.

Variations of opening location in the vertical direction were also included in this research. Four

alternate locations were considered for each opening size. The location of the opening was

determined to enable the application of a single layer of CFRP within the concrete wall

dimension. The width of required CFRP for larger openings constrained the movement of

opening location in vertical direction. For a smaller opening size (6%), the required width of

CFRP was 300 mm, the location of the opening was moved in the vertical direction around

50%. However, as the width of required CFRP was 505 mm for an opening size of 17%, the

location of the opening in vertical direction was limited to a maximum of 20%.


176

For the parametric study, the modelling techniques were the same as outlined in Sections 5.1

to 5.4. In total 288 RC walls were simulated considering various support conditions, opening

configurations and CFRP layouts with the results presented in the following sections. The

details of all wall panels were presented in Appendix A, B, and C, however, a summary of

opening sizes, locations and CFRP amount for each layout was presented in Figure 5-38 and

Table 5-4. In this table, “C” was used to denote walls where an opening was located in the

centre of the wall. “L” and “R” indicated having an opening in the left and right side of the

centre of the wall. In addition, NNF was the ultimate load for RC walls without CFRP and NAF,

NDF, NCF and NWF were the ultimate load of CFRP strengthened RC walls with AF, DF, CF

and WF layout.

H1

Ho

100

LC

LC

L1 Lo

Hw

Lw

Figure 5-38: Schematic view of RC walls for the parametric study


177

Table 5-3: Opening configuration and CFRP usage for the parametric study (HW=Lw=3000mm, tw=100mm)

Opening

designation

Opening location and dimension

(mm)

CFRP dimension (mm) Total amount of CFRP usage

(×106 mm2)

Width Length

DF AF CF WF L1 H1 Ho (=Lo) DF AF CF WF

C0 1125 1125

750 300 #4.×750 #4.×1550

#4.×750

&

#4.×1550 #12.×750 0.9 1.9 2.8 2.7

C1 1125 1325

C2 1125 1525

C3 1125 1725

C0 1025 1025

950 380 #4.×950 #4.×1910

#4.×950

&

#4.×1910

#12.×950 1.4 2.9 4.3 4.3

C1 1025 1225

C2 1025 1325

C3 1025 1425

L0 550 1025

L3 550 1425

R0 1500 1025

R3 1500 1425

C0 937.5 937.5

1125 465 #4.×1125 #4.×2255

#4.×1125

&

#4.×2255

#12.×1125 2.1 4.2 6.3 6.3 C1 937.5 1100

C2 937.5 1150

C3 937.5 1200

C0 875 875

1250 505 #4.×1250 #4.×2460

#4.×1250

&

#4.×2460

#12.×1250 2.5 5 7.5 7.6 C1 875 950

C2 875 1000

C3 875 1050


178

5.5.1 Parametric study for OW

The ultimate load capacities of CFRP strengthened RC walls under OW action were

investigated considering various opening configurations and CFRP layouts (DF, AF, CF and

WF). The outcomes of this study are presented in Table 5-4.

Considering various opening ratios (from 6% to 17%), application of CFRP with the DF layout

insignificantly contributed to the ultimate strength of walls under OW action where an

approximate 3% enhancement was observed. This might be attributed to the CFRP layout not

being provided in the area where RC walls were experiencing bending. A similar trend was

observed for the WF pattern, whose failure load increased slightly more than that of the DF

pattern. This was attributed to more wall area experiencing bending having CFRP applied to

assist with the load distribution. The amount of applied CFRP for RC walls with the WF layout

was triple that of walls with the DF pattern; however, both layouts resulted in similar rates of

enhancement in ultimate load. As shown in Table 5-4, walls under OW action were also

designed to investigate the results of a change in opening location in the vertical directions. It

was found that changing the location of the opening in the vertical direction (up to 53% in some

cases) did not affect the ultimate strength of RC walls with DF and WF layouts. It was evident

that by moving an opening in the vertical direction, the wall panels were experiencing bending

through the opening area resulting in similar ultimate strengths.

The dimensionless ratio of ultimate loads versus opening ratio (Ao/A) are presented in Figure

5-39 and Figure 5-40, where Ao and A were the cross sectional area of the opening and wall,

respectively. This outcome demonstrated that the DF and WF layouts insignificantly

contributed to increased ultimate strength of the RC walls, even when considering various

locations (indicated as C0, C1, C2 and C3), opening sizes (from 6% to 17%) and width of the

applied CFRP (from 300 mm to 505 mm).


179

In addition, changing the location of openings in the vertical direction was also investigated. It

was evident that by moving the opening location in the vertical direction, the walls under OW

action were experiencing bending through the opening area resulting in an identical ultimate

load with variations around 1% observed.


180

Table 5-4: Ultimate load comparison for CFRP strengthened RC walls with OW

Wall designation Ultimate load (kN) Failure load increase (%)

NNF1 NAF

2 NDF3 NCF

4 NWF5 NAF/NNF NDF/NNF NCF/NNF NWF/NNF

OW-750-C0 1826.40 2054.40 1870.94 2087.10 1893.00 12.48 2.44 14.27 3.65

OW-750-C1 1831.80 2061.00 1872.00 2088.00 1887.00 12.51 2.19 13.99 3.01

OW-750-C2 1858.20 2054.40 1889.40 2087.10 1902.00 10.56 1.68 12.32 2.36

OW-750-C3 1865.10 2054.68 1926.74 2073.82 1935.00 10.16 3.30 11.19 3.75

OW-950-C0 1644.00 1944.00 1683.46 1978.80 1695.00 18.25 2.40 20.36 3.10

OW-950-C1 1638.00 1968.00 1682.37 1972.50 1692.00 20.15 2.71 20.42 3.30

OW-950-C2 1642.50 1968.30 1692.00 1969.50 1701.00 19.84 3.01 19.91 3.56

OW-950-C3 1653.37 1957.94 1698.00 1991.70 1707.00 18.42 2.70 20.46 3.24

OW-1125-C0 1484.70 1889.10 1518.00 1926.30 1530.00 27.24 2.24 29.74 3.05

OW-1125-C1 1476.73 1887.00 1509.00 1923.00 1536.00 27.78 2.19 30.22 4.01

OW-1125-C2 1474.95 1884.92 1508.32 1921.20 1542.00 27.80 2.26 30.26 4.55

OW-1125-C3 1479.45 1869.00 1512.00 1929.30 1539.00 26.33 2.20 30.41 4.03

OW-1250-C0 1371.47 1886.21 1398.00 1894.50 1425.60 37.53 1.93 38.14 3.95

OW-1250-C1 1364.70 1834.20 1398.00 1877.70 1422.00 34.40 2.44 37.59 4.20

OW-1250-C2 1356.74 1827.00 1389.24 1878.90 1419.00 34.66 2.40 38.49 4.59

OW-1250-C3 1356.85 1818.30 1390.81 1875.00 1410.00 34.01 2.50 38.19 3.92

1NNF: ultimate load of RC wall without CFRP; 2NAF: ultimate load of CFRP strengthened RC walls with AF layout; 3NDF: ultimate load of CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP strengthened RC walls with CF layout; 5NWF: ultimate load of CFRP strengthened RC walls with WF layout.


181

Figure 5-39: Ultimate load ratio for walls with OW-DF

Figure 5-40: Ultimate load ratio for walls with OW-WF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

ND

F/N

NF

AO/A

OW-DF

DF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NW

F/N

NF

AO/A

OW-WFWF/NF


182

Application of the AF layout in walls under OW action significantly contributed to the ultimate

load. The ultimate strength of CFRP strengthened RC walls with the AF layout were enhanced

by 12% and 34% for walls with opening sizes of 6% and 17%, respectively. It was evident that

by increasing the size of the opening and consequently applying additional CFRP, the ultimate

strength of the RC walls were linearly enhanced. A similar trend was also observed for the CF

patterns. Even though, the amount of applied CFRP in the CF pattern was 50% more than that

of the AF layout, only a 3% enhancement in ultimate strength of the walls was observed in

comparison to walls with the AF layout

The dimensionless ultimate loads ratio versus opening ratio (Ao/A) is presented in Figure 5-41

and Figure 5-42 for walls with the AF and CF layouts, respectively. In both of these layouts,

CFRP was applied all around the opening where the walls were experiencing bending. As such,

these types of layouts significantly increased the ultimate loads of the RC wall panels.

However, changing the location of the opening in the vertical direction (up to 53%) resulted in

identical ultimate strength outcomes which were also observed in the OW-WF and OW-DF

results.


183

Figure 5-41: Ultimate load ratio for walls with OW-AF

Figure 5-42: Ultimate load ratio for walls with OW-CF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NA

F/N

NF

AO/A

OW-AFAF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NC

F/N

NF

AO/A

OW-CFCF/NF


184

5.5.2 The behaviour of the CFRP strengthened walls under OW action considering

horizontal opening location variations

The effects of having an opening to the left or right side of the walls’ centre were also

investigated and the results are presented in Table 5-5. Parameter, , is the same as defined in

Chapter 2. Based on a case study conducted on the CF layout, it was observed that having an

opening on the left or right side of the centre of the wall negligibly affected (less than 1%)

ultimate loads of the RC wall panels (Figure 5-43). A similar behaviour was expected from

walls with other CFRP layouts; therefore, those results were not presented in this section. It

was evident that the opening size significantly affected ultimate strength; however the location

of the opening had an insignificant effect on ultimate load for walls under OW action.

Table 5-5: The effects of opening location on CFRP strengthened walls with OW

Wall designation χ Ultimate load (kN) NCF

NNF1 NCF

2 NNF

OW-950-C0-L 0.243

1645.8 1969.2 1.20

OW-950-C3-L 1654.2 1968.9 1.19

OW-950-C0 0.317

1644 1978.8 1.20

OW-950-C3 1653.36 1991.7 1.20

OW-950-C0-R 0.39

1645.99 1965.3 1.19

OW-950-C3-R 1654.2 1993.16 1.20

1NNF: ultimate load of RC wall without CFRP; 2NCF: ultimate load of CFRP strengthened RC walls with CF layout.


185

Figure 5-43: Ultimate load ratio for walls with OW-CF (horizontal direction)

5.5.3 Parametric study for TW3S

The ultimate strength of CFRP strengthened panels with TW3S were investigated considering

various opening configurations and CFRP layouts (DF, AF, CF and WF). The outcomes of this

study are presented in Table 5-6

Considering various opening ratios (6% to 17%), application of CFRP with the DF layout

increased the ultimate strength of walls to various extents. This enhancement was 2% and 16%

for an opening size of 6% and 17% respectively (Figure 5-44). This rate of CFRP contribution

in ultimate strength of walls was attributed to the CFRP pattern being provided perpendicular

to the crack direction in the area where RC walls experience bending for this loading scenario

(around the corners of the opening). A similar trend was observed for the WF pattern (Figure

5-45). Failure loads of TW3S-WF were slightly more (around 2%) than that in walls with the

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40

NC

F/N

NF

OW-CFCF/NF


186

DF pattern for most cases. However, the amount of applied CFRP for walls with the WF layout

was triple that of walls with the DF pattern.

As shown in Table 5-6, walls with TW3S were also designed to investigate the resultsof a

change in opening location in the vertical direction. It was found that changing the location of

an opening in the vertical direction affected the ultimate strength of RC walls with the DF and

WF layouts up to 5%. More variation was observed in walls with small opening sizes, as the

opening was moved in by up to 53%. Generally, moving the opening location in the vertical

direction resulted in lower ultimate strengths when compared to that of the walls with openings

at the centre. It was evident that the effects of changing the location of openings in the vertical

direction in walls under TW3S were more than that in walls under OW action.

Application of the AF layout in walls with TW3S contributed considerably to the wall capacity.

The ultimate strength of CFRP strengthened walls with the AF layout was enhanced by 5% and

25% for walls with opening sizes of 6% and 17%, respectively. It was evident that by increasing

the size of the opening and consequently applying additional CFRP, the ultimate strength of

the RC walls was enhanced (up to 25%). A similar trend was observed for the CF patterns.

Even though, the amount of applied CFRP in the CF pattern was 50% more than that of the AF

layout, an approximate 4% enhancement in ultimate strength of walls was observed when

compared to the AF layout.

The non-dimensional ultimate load ratio versus opening ratio (Ao/A) is presented in Figure

5-46 and Figure 5-47, for walls with the AF and CF layouts respectively. In walls with TW3S,

the AF and CF layouts were applied around the opening and strengthened the free edge of the

RC walls, which resulted in higher ultimate loads when compared to the DF and WF layouts.

However, changing the location of the opening in the vertical direction resulted in up to a 5%

variation in ultimate strength. The lower range of this capacity was obtained when the opening


187

was close to the top restraint. In most cases, the maximum contribution of the CFRP layer was

observed when the opening was located near the top restraint. This finding indicated that CFRP

layer was able to change the load path and distribute the imposed load to the area away from

the restraint.


188

Table 5-6: Ultimate load comparison for CFRP strengthened RC walls in TW3S

1NNF: ultimate load of RC wall without CFRP; 2NAF: ultimate load of CFRP strengthened RC walls with AF layout; 3NDF: ultimate load of CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP

strengthened RC walls with CF layout; 5NWF: ultimate load of CFRP strengthened RC walls with WF layout.


NNF1 NAF

2 NDF3 NCF


TW3S-750-C0 3046.20 3165.90 3051.593 3168.75 3107.50 3.93 0.18 4.02 2.01

TW3S-750-C1 3054.43 3131.04 3128.318 3153.68 3101.25 2.51 2.42 3.25 1.53

TW3S-750-C2 3052.96 3112.78 3082.043 3174.33 3096.75 1.96 0.95 3.98 1.43

TW3S-750-C3 2966.21 3126.93 3054.593 3179.06 3061.80 5.42 2.98 7.18 3.22

TW3S-950-C0 2838.68 2986.88 2889.735 2937.86 2892.00 5.22 1.80 3.49 1.88

TW3S-950-C1 2755.95 2918.75 2844.173 2906.25 2843.75 5.91 3.20 5.45 3.19

TW3S-950-C2 2740.63 2900.39 2810.52 2890.63 2813.25 5.83 2.55 5.47 2.65

TW3S-950-C3 2690.63 2834.46 2821.17 2875.00 2801.56 5.35 4.85 6.85 4.12

TW3S-1125-C0 2382.00 2755.06 2666.34 2843.75 2691.98 15.66 11.94 19.38 13.01

TW3S-1125-C1 2375.00 2714.06 2588.64 2787.50 2656.25 14.28 9.00 17.37 11.84

TW3S-1125-C2 2365.63 2666.25 2573.048 2756.25 2625.00 12.71 8.77 16.51 10.96

TW3S-1125-C3 2339.06 2660.82 2582.783 2739.06 2606.25 13.76 10.42 17.10 11.42

TW3S-1250-C0 2125.00 2575.00 2452.635 2639.06 2496.75 21.18 15.42 24.19 17.49

TW3S-1250-C1 2025.00 2550.00 2387.5 2596.25 2422.50 25.93 17.90 28.21 19.63

TW3S-1250-C2 2010.00 2475.00 2340.758 2500.00 2375.00 23.13 16.46 24.38 18.16

TW3S-1250-C3 1987.50 2438.75 2343.75 2468.75 2380.50 22.70 17.92 24.21 19.77


189

Figure 5-44: Ultimate load ratio for walls with TW3S-DF

Figure 5-45: Ultimate load ratio for walls with TW3S-WF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

ND

F/N

NF

AO/A

TW3S-DFDF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NW

F/N

NF

AO/A

TW3S-WFWF/NF


190

Figure 5-46: Ultimate load ratio for walls with TW3S-AF

Figure 5-47: Ultimate load ratio for walls with TW3S-CF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NA

F/N

NF

AO/A

TW3S-AF

AF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NC

F/N

NF

AO/A

TW3S-CF

CF/NF


191

5.5.4 The behaviour of the CFRP strengthened walls with TW3S considering horizontal

opening location variations

The effects of opening locations in the horizontal direction for walls with TW3S were

investigated and the results are presented in Table 5-7. The outcomes demonstrated that

moving the location of the opening in the horizontal direction affected the ultimate load of

the investigated RC walls (Figures 5-48 to 5-51). It was evident that having an opening to

the left or right side of the wall’s centre could affect the ultimate strength of the RC wall

panels to various extents (up to 11%). CFRP layout significantly contributed to the ultimate

load of panels with an opening near the free edge. However, having an opening near the

restraint resulted in an insignificant contribution of CFRP layouts. Generally, applying the

CF and AF layouts, provided the greatest increase in ultimate strength (up to 11%), while

lower contributions were obtained for walls with the DF layout (up to 7%) and WF pattern

(up to 9%). The most contribution of the CFRP was observed in cases with an opening at

the free edge of the wall and close to the top restraint (TW3S-950-C3-R). This finding

indicated that the CFRP layer was able to change the load path and distribute the imposed

load to the area away from restraint.


192

Table 5-7: The effects of opening location (horizontal direction) on CFRP strengthened RC walls (TW3S)




NNF1 NDF

2 NAF3 NCF

4 NWF5 NDF/NNF NAF/NNF NCF/NNF NWF/NNF

TW3S-950-C0-L

0.243

2937.00 2940.00 2962.50 3000.00 2955.00 1.00 1.01 1.02 1.01

TW3S-950-C3-L 2822.25 2841.00 2967.75 3037.50 2895.75 1.01 1.05 1.08 1.03

TW3S-950-C0

0.317

2838.68 2889.74 2986.88 2937.86 2892.00 1.02 1.05 1.03 1.02

TW3S-950-C3 2690.63 2821.17 2834.46 2875.00 2801.56 1.05 1.05 1.07 1.04

TW3S-950-C0-R

0.39

2812.50 2902.50 3009.00 3075.00 2955.00 1.03 1.07 1.09 1.05

TW3S-950-C3-R 2625.75 2797.50 2910.00 2988.75 2872.50 1.07 1.11 1.14 1.09


193

Figure 5-48: Ultimate load ratio for walls with TW3S-DF (horizontal direction)

Figure 5-49: Ultimate load ratio for walls with TW3S-WF (horizontal direction)

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40

ND

F/N

NF

TW3S-DFDF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40

NW

F/N

NF

TW3S-WFWF/NF


194

Figure 5-50: Ultimate load ratio for walls with TW3S-AF (horizontal direction)

Figure 5-51: Ultimate load ratio for walls with TW3S-CF (horizontal direction)

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40

NA

F/N

NF

TW3S-AFAF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40

NC

F/N

NF

TW3S-CFCF/NF


195

5.5.5 Parametric study for TW4S

The ultimate strength of the CFRP strengthened panels with TW4S were investigated

considering various opening configurations and CFRP layouts (DF, AF, CF and WF). The

outcomes of this study were presented in Table 5-8.

Considering various opening sizes, application of the CFRP with the DF layout increased the

ultimate strength of walls to various extents. This enhancement was 5% and 21% for an

opening size of 6% and 17% respectively (Figure 5-52). This rate of CFRP contribution to

increased ultimate strength of walls was attributed to the CFRP pattern being provided

perpendicular to the crack direction in the area where the RC walls experience bending for this

loading scenario (around the corners of the opening). A similar trend was observed for the WF

pattern (Figure 5-53). Failure loads of walls with the TW4S-WF were slightly more (up to 4%)

than that in walls with the DF pattern. However, the amount of applied CFRP for walls with

WF layout was triple that of the walls with the DF pattern.

As shown in Table 5-8, walls with TW4S were also designed to investigate the results of a

change in opening location in the vertical direction. It was found that changing the location of

the opening in the vertical direction affected the ultimate strength of RC walls for the DF and

WF layouts up to 5%. More variation was observed in walls with small opening sizes as the

opening was moved up to 53%. Generally, moving the opening location in the vertical

direction resulted in lower ultimate strengths when compared to walls with openings at the

centre. It was evident that the effects of changing the location of the opening in the vertical

direction for walls under TW4S were more than that in walls under OW action. In most cases,

the maximum contribution of CFRP was observed when the opening was located near the top

restraint. These findings indicated that the CFRP layer was able to change the load path and

distribute the imposed load to the area away from the restraint.


196

The non-dimensional ultimate loads ratio versus opening ratio (Ao/A) is presented in Figure

5-54 and Figure 5-55, for walls with the AF and CF layouts respectively.

Application of the AF layout in walls with TW4S contributed to the wall capacity by various

extents. The ultimate strength of CFRP strengthened RC walls with the AF layout were

enhanced by 8% to 24% for walls with opening sizes of 6% and 17%, respectively. It was

evident that by increasing the size of the opening and consequently applying additional CFRP,

the ultimate strength of the RC walls were linearly enhanced. A similar trend was observed for

the CF patterns. Even though, the amount of applied CFRP in the CF pattern was 50% more

than that of the AF layout, ultimate strength was enhanced only around 3% more than that in

walls with the AF layout. Changing the location of the opening in the vertical direction resulted

in up to 5% more CFRP contribution to increased ultimate strength. The higher improvements

were observed in cases with openings close to the top restraint.


197

Table 5-8: Ultimate load comparison for CFRP strengthened walls with TW4S



Wall designation

Ultimate load (kN) Failure load increase (%)

NNF1 NAF

2 NDF3 NCF


TW4S-750-C0

TW4S-750-C1

TW4S-750-C2

TW4S-750-C3

4012.50 4312.50 4087.50 4350.00 4076.25 7.48 1.87 8.41 1.59

3993.75 4305.00 4220.25 4320.00 4126.06 7.79 5.67 8.17 3.31

3945.00 4215.00 4215.00 4245.00 4201.00 6.84 6.84 7.60 6.49

3930.00 4150.00 4089.00 4200.00 4120.00 5.60 4.05 6.87 4.83

TW4S-950-C0

TW4S-950-C1

TW4S-950-C2

TW4S-950-C3

3937.50 4267.50 4125.08 4343.25 4141.56 8.38 4.76 10.30 5.18

3862.50 4312.50 4200.75 4366.58 4215.00 11.65 8.76 13.05 9.13

3787.50 4207.50 4126.50 4207.50 4158.00 11.09 8.95 11.09 9.78

3760.00 4275.00 4025.00 4252.50 4125.00 13.70 7.05 13.10 9.71

TW4S-1125-C0

TW4S-1125-C1

TW4S-1125-C2

TW4S-1125-C3

3705.00 4350.00 4125.00 4417.50 4254.00 17.41 11.34 19.23 14.82

3680.00 4298.25 4095.00 4354.00 4121.00 16.80 11.28 18.32 11.98

3568.00 4293.75 3954.00 4314.75 4085.00 20.34 10.82 20.93 14.49

3498.00 4156.00 3854.00 4289.00 4025.00 18.81 10.18 22.61 15.07

TW4S-1250-C0

TW4S-1250-C1

TW4S-1250-C2

TW4S-1250-C3

3378.00 4125.90 3987.00 4187.00 4052.00 22.14 18.03 23.95 19.95

3226.50 3901.05 3845.00 3982.50 3912.00 20.91 19.17 23.43 21.25

3187.50 3910.00 3845.00 3971.00 3884.00 22.67 20.63 24.58 21.85

3152.00 3920.00 3825.00 3942.00 3845.00 24.37 21.35 25.06 21.99


198

Figure 5-52: Ultimate load ratio for walls with TW4S-DF

Figure 5-53: Ultimate load ratio for walls with TW4S-WF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

ND

F/N

NF

AO/A

TW4S-DFDF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NW

F/N

NF

AO/A

TW4S-WFWF/NF


199

Figure 5-54: Ultimate load ratio for walls with TW4S-AF

Figure 5-55: Ultimate load ratio for walls with TW4S-CF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NA

F/N

NF

AO/A

TW4S-AFAF/NF

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

NC

F/N

NF

AO/A

TW4S-CFCF/NF


200

5.5.6 The behaviour of the CFRP strengthened walls with TW4S considering horizontal

opening location variations

The effects of opening location in the horizontal direction for walls under TW4S action were

investigated and the outcomes are presented in Table 5-9. As walls with TW4S have a

symmetrical behaviour, the effect of openings in the left side of the wall’s centre were

considered. The results indicated that moving the location of the opening in the horizontal

direction insignificantly affected the ultimate load of the investigated RC walls (Figure 5-56 to

5-59). Generally, in walls with TW4S, CFRP layouts enhanced the ultimate load of panels with

almost identical ratios. Commonly, by applying the CF and AF layout, the contribution of

CFRP to ultimate strength enhancement was up to 14%. Lower ratios of increased ultimate

load capacity were observed for walls with the DF layout (up to 8%) and WF pattern (up to

10%). The greatest contribution of the CFRP was observed in cases with an opening near the

edge of the wall and close to the top restraint indicating that the CFRP layout could change the

load path and transfer loads from the restraint.


201

Table 5-9: The effects of opening location on ultimate load of CFRP strengthened walls

Wall designation

Ultimate load (kN) Failure load increase (%)

NNF1 NDF

2 NAF3 NCF

4 NWF5 NDF/NNF NAF/NNF NCF/NNF NWF/NNF

TW4S-950-C0-L

0.243

3765.00 3975.00 4072.50 4110.00 4012.50 1.06 1.08 1.09 1.07

TW4S-950-C3-L 3750.00 4050.00 4192.50 4267.50 4087.50 1.08 1.12 1.14 1.09

TW4S-950-C0

0.317

3937.50 4125.08 4267.50 4343.25 4141.56 1.05 1.08 1.10 1.05

TW4S-950-C3 3760.00 4025.00 4275.00 4252.50 4125.00 1.07 1.14 1.13 1.10

1NNF: ultimate load of RC wall without CFRP; 2NAF: ultimate load of CFRP strengthened RC walls with AF layout; 3NDF: ultimate load of CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP strengthened RC walls with CF layout; 5NWF: ultimate load of CFRP strengthened RC walls with WF layout.


202

Figure 5-56: Ultimate load ratio for walls withTW4S-DF (horizontal direction)

Figure 5-57: Ultimate load ratio for walls withTW4S-WF (horizontal direction)

0.8

1.0

1.2

1.4

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34

ND

F/N

NF

TW4S-DFDF/NF

0.8

1.0

1.2

1.4

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34

NW

F/N

NF

TW4S-WFWF/NF


203

Figure 5-58: Ultimate load ratio for walls with TW4S-AF(horizontal direction)

Figure 5-59: Ultimate load ratio for walls withTW4S-CF (horizontal direction)

0.8

1.0

1.2

1.4

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34

NA

F/N

NF

TW4S-AFAF/NF

0.8

1.0

1.2

1.4

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34

NC

F/N

NF

TW4S-CFCF/NF


204

Relations between ultimate load of RC walls under various support condition

The obtained ultimate loads of RC walls without a CFRP strengthening scheme from Section

5-5 are presented in Table 5-10. As discussed in Chapter 2, the ultimate load of RC walls with

openings under one-way action and two-way action with four sides restrained can be calculated

using existing proposed formulae. However, there has not been a formula for calculation of

ultimate load in walls with TW3S.

In this section, an attempt was conducted to calculate the ultimate load of walls with TW3S

from that of walls with OW and TW4S. It was found that the ultimate load of RC walls with

openings under TW3S action can be reasonably estimated as follows:

2

)(N+)(N=)(N

TW4SNFOWNFTW3S

*NF Eq. 5-6

This proposed procedure provided a sound estimate of the failure load for all panels with the

mean ((NNF) TW3S / (NNF)*TW3S) of 0.98 with standard deviation of 0.07. Further investigation was

conducted to determine the relationship between ultimate loads of walls under one-way and

two-way action. The ultimate load of RC walls with TW4S was 2.1 to 2.5 more than that of

walls under OW action. The ratio of ultimate load in RC walls with TW3S to that of OW walls

varied between 1.5 and 1.8.


205

Table 5-10: Ultimate load (NNF) of walls in OW, TW3S and TW4S

Opening

size (mm2)

opening

location

Ultimate load (kN)

(NNF)TW3S

(NNF)OW (NNF)TW3S (NNF)TW4S (NNF)*TW3S (NNF)*

TW3S

750×750

C0 1826.40 3046.20 4012.50 2919.45 1.04

C1 1831.80 3054.43 3993.75 2912.78 1.05

C2 1858.20 3052.96 3945.00 2901.60 1.05

C3 1865.10 2966.21 3930.00 2897.55 1.02

950×950

C0 1644.00 2838.68 3937.50 2790.75 1.02

C1 1638.00 2755.95 3862.50 2750.25 1.00

C2 1642.50 2740.63 3787.50 2715.00 1.01

C3 1653.37 2690.63 3760.00 2706.69 0.99

C0-L 1645.80 2937.00 3765.00 2705.40 1.09

C3-L 1654.20 2822.25 3750.00 2702.10 1.04

1125×1125

C0 1484.70 2382.00 3705.00 2594.85 0.92

C1 1476.73 2375.00 3680.00 2578.37 0.92

C2 1474.95 2365.63 3568.00 2521.48 0.94

C3 1479.45 2339.06 3498.00 2488.73 0.94

1250×1250

C0 1371.47 2125.00 3378.00 2374.74 0.89

C1 1364.70 2025.00 3226.50 2295.60 0.88

C2 1356.74 2010.00 3187.50 2272.12 0.88

C3 1356.85 1987.50 3152.00 2254.43 0.88

Mean 0.98

STDV 0.07

Comparison of various CFRP layouts under different support conditions:

A comparison study was conducted for AF, DF, WF and CF layouts based on various support

conditions and the outcomes are presented in Figures 5-60 to 5-63.

Based on outcomes shown in Figure 5-60 and Figure 5-61, the contribution of the DF and WF

layouts in ultimate strength gains of the walls under OW action was insignificant. However the

DF and WF layouts considerably enhanced the ultimate load of walls under TW3S and TW4S.

This contribution for TW4S was slightly higher than TW3S.


206

Figure 5-62 indicates that the AF layout significantly enhanced the ultimate load of RC walls

under OW action. However, less contribution of CFRP layouts were observed in walls with

TW3S and TW4S. The CFRP influence for walls with TW4S was slightly greater than that in

walls with TW3S, while for an opening ratio around 17%, both support conditions resulted in

identical contributions to the wall’s capacity.

As demonstrated in Figure 5-63, the CF layout significantly contributed to ultimate load

increases for RC walls under OW action. However, this contribution for walls with TW3S and

TW4S was less than that under OW action (approximately 50%). The CFRP influence in

ultimate loads of walls with TW4S was slightly greater than TW3S, however, similar to the AF

layout, in larger openings (around 17%) the CF layout resulted in similar ratios of enhancement

in ultimate load for walls with TW3S and TW4S.

Figure 5-60: Ultimate load ratio for walls with various opening sizes and DF layout

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

DF OW-DF

TW3S-DF

TW4S-DF


207

Figure 5-61: Ultimate load ratio for walls with various opening sizes and WF layout

Figure 5-62: Ultimate load ratio for walls with various opening sizes and AF layout

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

WF

OW-WF

TW3S-WF

TW4S-WF

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

AF

OW-AF

TW3S-AF

TW4S-AF


208

Figure 5-63: Ultimate load ratio walls with various opening sizes and CF layout

In Table 5-11 and Table 5-12, the failure ratios NNF (*F)(OW)/NNF(*F)(TW3S) and NNF(*F)(OW)/

NNF(*F)(TW4S) are given. The ultimate strength of RC walls in one-way action was

approximately 60% and 40% of that in counterparts with TW3S and TW4S, respectively. The

results are similar to the experimental tests performed by Doh et al. (2010). This outcome

indicates that adding side supports increases the load capacity of walls irrespective of the type

of CFRP layout. Similar outcomes were observed in the experiments conducted during this

research (Chapter 4).

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

CF

OW-CF

TW3S-CF

TW4S-CF


209


Opening

size (mm2)

Opening

location

NNF(*F)(OW)/NNF(*F)(TW3S)

NF AF DF CF WF

750×750

C0 0.60 0.65 0.61 0.66 0.61

C1 0.60 0.66 0.60 0.66 0.61

C2 0.61 0.66 0.61 0.66 0.61

C3 0.63 0.66 0.63 0.65 0.63

950×950

C0 0.58 0.65 0.58 0.67 0.59

C1 0.59 0.67 0.59 0.68 0.59

C2 0.60 0.68 0.60 0.68 0.60

C3 0.61 0.69 0.60 0.69 0.61

1125×1125

C0 0.62 0.69 0.57 0.68 0.57

C1 0.62 0.70 0.58 0.69 0.58

C2 0.62 0.71 0.59 0.70 0.59

C3 0.63 0.70 0.59 0.70 0.59

1250×1250

C0 0.65 0.73 0.57 0.72 0.57

C1 0.67 0.72 0.59 0.72 0.59

C2 0.67 0.74 0.59 0.75 0.60

C3 0.68 0.75 0.59 0.76 0.59


Opening

size (mm2)

Opening

location NNF(*F)(OW)/ NNF(*F)(TW4S)

NF AF DF CF WF

750×750

C0 0.46 0.48 0.46 0.48 0.46

C1 0.46 0.48 0.44 0.48 0.46

C2 0.47 0.49 0.45 0.49 0.45

C3 0.47 0.50 0.47 0.49 0.47

950×950

C0 0.42 0.46 0.41 0.46 0.41

C1 0.42 0.46 0.40 0.45 0.40

C2 0.43 0.47 0.41 0.47 0.41

C3 0.44 0.46 0.42 0.47 0.41

1125×1125

C0 0.40 0.43 0.37 0.44 0.36

C1 0.40 0.44 0.37 0.44 0.37

C2 0.41 0.44 0.38 0.45 0.38

C3 0.42 0.45 0.39 0.45 0.38

1250×1250

C0 0.41 0.46 0.35 0.45 0.35

C1 0.42 0.47 0.36 0.47 0.36

C2 0.43 0.47 0.36 0.47 0.37

C3 0.43 0.46 0.36 0.48 0.37


210

Efficiency investigation of CFRP layouts considering various support conditions

An efficiency study was conducted for various CFRP strengthened RC walls based on the type

of support conditions considered. The amount of CFRP usage is presented in Table 5-3 and the

ultimate load enhancement for walls under OW, TW3S and TW4S were adopted from Section

5.5.

The efficiency was the ratio of the increase in ultimate load (%) to the total amount of CFRP

layout in meters squared (m2). As the length of CFRP was different in various opening sizes,

the area of CFRP layout was preferred rather than its length. This study was included for

clarification of the contribution of the CFRP layout in the gain of the concrete wall strength

based on the amount of CFRP used.

5.8.1 Efficiency study of RC walls in OW

The efficiency of various CFRP layouts for RC walls under OW action was investigated in this

section and is presented in Table 5-13. For walls under OW action, the efficiency of CFRP for

the AF layout was the highest, where ultimate strength was greatly enhanced (up to 34%). The

CF layout was the second most efficient layout for strengthening of walls under OW action.

However, the ratio of ultimate strength gain to the amount of CFRP usage in DF and WF

layouts exhibited the lowest efficiency.


211

Table 5-13: Efficiency study of CFRP strengthened RC walls with OW

Wall

designation

Failure load increase (%) Efficiency [Increase of ultimate load

(%) to ACFRP (m2)]

NAF1/NNF

2 NDF3/NNF NCF

4/NNF NWF/NNF5 AF DF CF WF

OW-750-C0 12.48 2.44 14.27 3.65 6.71 2.71 5.17 1.35

OW-750-C1 12.51 2.19 13.99 3.01 6.73 2.43 5.07 1.11

OW-750-C2 10.56 1.68 12.32 2.36 5.68 1.87 4.46 0.87

OW-750-C3 10.16 3.3 11.19 3.75 5.46 3.67 4.05 1.39

OW-950-C0 18.25 2.4 20.36 3.1 6.29 1.66 4.68 0.72

OW-950-C1 20.15 2.71 20.42 3.3 6.94 1.88 4.70 0.76

OW-950-C2 19.84 3.01 19.91 3.56 6.83 2.08 4.58 0.82

OW-950-C3 18.42 2.7 20.46 3.24 6.35 1.87 4.71 0.75

OW-1125-C0 27.24 2.24 29.74 3.05 6.49 1.07 4.73 0.49

OW-1125-C1 27.78 2.19 30.22 4.01 6.62 1.05 4.81 0.64

OW-1125-C2 27.8 2.26 30.26 4.55 6.63 1.08 4.81 0.72

OW-1125-C3 26.33 2.2 30.41 4.03 6.28 1.05 4.84 0.64

OW-1250-C0 37.53 1.93 38.14 3.95 7.55 0.76 5.09 0.52

OW-1250-C1 34.4 2.44 37.59 4.2 6.92 0.97 5.02 0.55

OW-1250-C2 34.66 2.4 38.49 4.59 6.98 0.95 5.14 0.61

OW-1250-C3 34.01 2.5 38.19 3.92 6.84 0.99 5.10 0.52

Mean 6.58 1.63 4.81 0.78

1NAF: ultimate load of CFRP strengthened RC walls with AF layout; 2NNF: ultimate load of RC wall without CFRP; 3NDF: ultimate load of

CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP strengthened RC walls with CF layout; 5NWF: ultimate load of CFRP strengthened RC walls with WF layout.

5.8.2 Efficiency study of RC walls with TW3S

For walls under TW3S, the maximum efficiency was obtained by the DF layout in which the

minimum amount of CFRP was utilised. The efficiency study for the CFRP strengthened RC

walls with TW3S is presented (Table 5-14). The maximum usage of CFRP was for the WF

pattern, which also returned the lowest efficiency. A similar trend was observed during the

experiments. One noteworthy point was the DF and WF configurations resulted in similar

ultimate strength enhancements. The AF and CF improved the capacity of RC panels

identically (around 24%), while the efficiency of the AF layout was superior to that of the CF


212

pattern. The DF layout enhanced the ultimate load up to 16% for an opening size around 17%

and this layout resulted in the optimum efficiency.

Table 5-14: Efficiency study of CFRP strengthened walls with TW3S

Wall

designation

Failure load increase (%) Efficiency [Increase of ultimate load

(%) to ACFRP (m2)]

NAF1/NNF

2 NDF3/NNF NCF

4/NNF NWF5/NNF AF DF CF WF

OW-750-C0 3.93 0.18 4.02 2.01 2.11 0.20 1.46 0.74

OW-750-C1 2.51 2.42 3.25 1.53 1.35 2.69 1.18 0.57

OW-750-C2 1.96 0.95 3.98 1.43 1.05 1.06 1.44 0.53

OW-750-C3 5.42 2.98 7.18 3.22 2.91 3.31 2.60 1.19

OW-950-C0 5.22 1.8 3.49 1.88 1.80 1.25 0.80 0.43

OW-950-C1 5.91 3.2 5.45 3.19 2.04 2.22 1.25 0.74

OW-950-C2 5.83 2.55 5.47 2.65 2.01 1.77 1.26 0.61

OW-950-C3 5.35 4.85 6.85 4.12 1.84 3.36 1.58 0.95

OW-1125-C0 15.66 11.94 19.38 13.01 3.73 5.70 3.08 2.07

OW-1125-C1 14.28 9 17.37 11.84 3.40 4.30 2.76 1.89

OW-1125-C2 12.71 8.77 16.51 10.96 3.03 4.19 2.63 1.75

OW-1125-C3 13.76 10.42 17.1 11.42 3.28 4.98 2.72 1.82

OW-1250-C0 21.18 15.42 24.19 17.49 4.26 6.11 3.23 2.31

OW-1250-C1 25.93 17.9 28.21 19.63 5.22 7.09 3.76 2.59

OW-1250-C2 23.13 16.46 24.38 18.16 4.65 6.52 3.25 2.40

OW-1250-C3 22.7 17.92 24.21 19.77 4.57 7.10 3.23 2.61

Mean 2.95 3.86 2.26 1.45

1NAF: ultimate load of CFRP strengthened RC walls with AF layout; 2NNF: ultimate load of RC wall without CFRP; 3NDF: ultimate load of

CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP strengthened RC walls with CF layout; 5NWF: ultimate load of

CFRP strengthened RC walls with WF layout.

5.8.3 Efficiency study of RC walls with TW4S

For walls under TW4S, the overall enhancement in ultimate load was similar in all cases;

however, the DF layout resulted in the optimum efficiency. A similar trend was observed

during the experiments. The outcome of this investigation was presented in Table 5-15. In this

type of boundary condition, all layouts presented similar effectiveness, while the DF and AF

resulted in a higher efficiency in compare to CF and WF layouts.


213

Table 5-15: Efficiency study of CFRP strengthened walls with TW4S

Wall

designation

Failure load increase (%) Efficiency [Increase of ultimate

load (%) to ACFRP (m2)]

NAF1/NNF

2 NDF3/NNF NCF

4/NNF NWF5/NNF AF DF CF WF

TW4S-750-C0 7.48 1.87 8.41 1.59 4.02 2.08 3.05 0.59

TW4S-750-C1 7.79 5.67 8.17 3.31 4.19 6.30 2.96 1.23

TW4S-750-C2 6.84 6.84 7.6 6.49 3.68 7.60 2.75 2.40

TW4S-750-C3 5.6 4.05 6.87 4.83 3.01 4.50 2.49 1.79

TW4S-950-C0 8.38 4.76 10.3 5.18 2.89 3.30 2.37 1.20

TW4S-950-C1 11.65 8.76 13.05 9.13 4.01 6.07 3.00 2.11

TW4S-950-C2 11.09 8.95 11.09 9.78 3.82 6.20 2.55 2.26

TW4S-950-C3 13.7 7.05 13.1 9.71 4.72 4.88 3.01 2.24

TW4S-1125-C0 17.41 11.34 19.23 14.82 4.15 5.42 3.06 2.36

TW4S-1125-C1 16.8 11.28 18.32 11.98 4.01 5.39 2.91 1.91

TW4S-1125-C2 20.34 10.82 20.93 14.49 4.85 5.17 3.33 2.31

TW4S-1125-C3 18.81 10.18 22.61 15.07 4.48 4.86 3.60 2.40

TW4S-1250-C0 22.14 18.03 23.95 19.95 4.46 7.14 3.20 2.63

TW4S-1250-C1 20.91 19.17 23.43 21.25 4.21 7.59 3.13 2.81

TW4S-1250-C2 22.67 20.63 24.58 21.85 4.56 8.17 3.28 2.88

TW4S-1250-C3 24.37 21.35 25.06 21.99 4.90 8.46 3.34 2.90

Mean 4.12 5.82 3.00 2.13

1NAF: ultimate load of CFRP strengthened RC walls with AF layout; 2NNF: ultimate load of RC wall without CFRP; 3NDF: ultimate load of CFRP strengthened RC walls with DF layout; 4NCF: ultimate load of CFRP strengthened RC walls with CF layout; 5NWF: ultimate load of

CFRP strengthened RC walls with WF layout.

Summary and conclusion

Numerical investigations were conducted on CFRP strengthened walls with openings. A brief

overview of the input parameters for the software was presented followed by the CFRP-

concrete interface behaviour. The behaviour of reinforced concrete walls obtained from

simulation was compared with previous experimental outcomes (Chapter 4), with consistent

results observed for crack patterns, load-deflection profiles and ultimate strengths of the RC

walls. Having established that the numerical software is a good comparison for experimental

outcomes, a parametric study was then carried out for the full scaled wall panels with various

CFRP layouts, support conditions, opening sizes and configurations.


214

The FEM outcomes showed the load carrying capacity of RC walls with openings strengthened

by CFRP were improved. The contribution of each alternate CFRP layout was investigated and

presented. This study found the CFRP application provided varied success in achieving

ultimate strength gains under different support conditions, opening configurations and CFRP

layouts. Based on the examined efficiency, the WF layout presented the least efficient pattern

for RC wall strengthening. The AF and DF patterns were the most effective CFRP layouts for

walls under OW and TW action, respectively.

In the next chapter, design charts are proposed based on three different support conditions. The

charts are evaluated against existing results and available formulae from previously published

research. In addition, the instructions for the application of these graphs are presented in detail,

through providing worked practical examples.

Chapter 6: design charts for CFRP strengthened RC walls

215

6 DESIGN CHARTS FOR CFRP STRENGTHENED RC WALLS

Introduction

The analysis of CFRP strengthened RC walls is more complex than the analysis of walls

without CFRP layouts. The application of CFRP changes the load path and crack

patterns generally resulting in higher ultimate strengths being achieved. Although

researchers have derived equations for the ultimate load of CFRP strengthened walls,

these equations are only applicable for walls under OW action and consider only limited

CFRP layouts. The shortcomings of these previous equations have already been

discussed in Chapter 2.

The main aim of this research is to provide design charts/formulae to design CFRP

strengthened RC walls considering various boundary conditions, opening

configurations and CFRP layouts. Based on the parametric study discussed in Chapter

5, design charts are proposed for CFRP strengthened walls under OW, TW3S and

TW4S. Design charts present a dimensionless quantity for N*F/NNF versus Ao/A, in

which: NNF is the ultimate load of the RC wall without CFRP and N*F represents the

ultimate load of CFRP strengthened RC walls with various CFRP layouts. The subscript

* was replaced D, A, C, and W for CFRP layout of DF, AF, CF and WF, respectively.

Ao and A are the cross sectional area of the opening (Ao=Lotw) and that of the wall

(A=Lwtw), respectively. In the design charts, the equation for each CFRP strengthening

scheme was also provided where a general trend was observed as follows:

bχ)or /A (A a/NN oNFF* Eq. 6-1

Where: a is the slop of the line and b is the N*F/NNF intercept. These equations can be

used in cases where geometric properties (opening locations or sizes) are beyond that


216

of those investigated during the parametric study (Chapter 5). The instructions for the

application of these charts are presented in details for illustration purposes.

Furthermore, the reliability and accuracy of the proposed charts are verified using other

researchers’ experiments and the current experimental test results (from Chapter 4).

Finally, a typical case study is presented to illustrate the extended scope of the proposed

design rules.

Design charts

In sections 5.6.1 and 5.6.2, the parametric studies obtained from the CFRP strengthened

walls under OW action were discussed and presented in Figures 5-40 to 5-44. A

summary of these outcomes are provided in Figure 6-1. As discussed in Section 5.5,

the ultimate loads of panels under OW action are not affected by the location of the

opening at mid-height, only when shifted horizontally. Therefore, the proposed design

chart for OW action does not consider the position of the openings. The behaviour of

walls under OW action was also investigated by moving the opening location in the

vertical direction where insignificant variation was observed in ultimate strength of

panels. For these cases, the average ultimate load ratio versus opening ratios of panels

are presented in Figure 6-1.

The results for CFRP strengthened walls with TW3S are provided in Figure 6-2 and 6-

3. These charts are prepared based on the outcomes discussed in Sections 5.6.3 and

5.6.4. As the structural behaviour of walls with TW3S is not symmetrical, the positions

of an opening (), moving horizontally is also considered and presented in a separate

chart (Figure 6.3). Note that the effects of moving the location of the opening in the


217

vertical direction was also investigated in walls with TW3S and average values of the

ultimate load ratio are plotted against the opening ratio in Figure 6-2.

In walls without CFRP (NNF), the axial strength ratio of TW3S with the opening located

near the side restraint tends to be greater than the opening near the free edge. However,

the presence of any CFRP layout indicates increased ultimate strengths when the

opening was located near the free edge resulting in a greater strength ratio (N*F/NNF).

The results for CFRP strengthened walls under TW4S are provided in Figures 6-4 and

6-5. These charts are prepared based on the outcomes discussed in sections 5.6.5 and

5.6.6. As a result of the symmetrical behaviour of wall in this type of support condition,

only the effects of the opening on the left side of the centre of wall was considered and

presented. Based on the obtained results, various CFRP layouts had identical increases

in ultimate strength of the walls with openings at the centre or left side. However, larger

increases were observed in walls with greater opening sizes, as the amount of applied

CFRP was higher when compared to the smaller opening ratio. The effect of moving

the location of the opening in the vertical direction was also investigated. Generally, a

greater contribution was observed in cases with the opening close to the top restraint,

which indicates the CFRP layout was able to change the load path and distribute the

loads to the areas far from the restraint. A similar behaviour was observed for walls

under TW3S.


218

Figure 6-1: Ultimate load ratio versus opening ratio in OW action walls

Figure 6-2: Ultimate load ratio versus opening ratio of panels with TW3S

NDF/NNF=-0.01 (Ao/A) + 1.03

NWF/NNF = 0.17(Ao/A)+ 1.00

NCF/NNF = 1.52(Ao/A) + 0.74

NAF/NNF=1.39(Ao/A) + 0.76

0.8

1.0

1.2

1.4

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

DF/NF

WF/NF

CF/NF

AF/NF

NDF/NNF = 0.92(AO/A) + 0.77

NWF/NNF= 1.02 (AO/A) + 0.74

NCF/NNF = 1.29(AO/A) + 0.69

NAF/NNF = 1.18x + 0.72

0.8

1.0

1.2

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

DF/NF

WF/NF

CF/NF

AF/NF


219

Figure 6-3: Ultimate load ratio versus opening locations in TW3S action walls

Figure 6-4: Ultimate load ratio versus opening ratio for walls with TW4S

NDF/NNF = 0.31χ + 0.93

NWF/NNF = 0.34χ + 0.93

NAF/NNF = 0.41χ + 0.93

NCF/NNF= 0.44χ + 0.93

0.8

1.0

1.2

0.20 0.25 0.30 0.35 0.40

N*F/N

NF

DF/NFWF/NFAF/NFCF/NF

NDF/NNF = 0.85(AO/A) + 0.82

NWF/NNF= 1.00 (AO/A) + 0.78

NCF/NNF= 1.03(AO/A) + 0.81

NAF/NNF= 0.96(AO/A) + 0.82

0.8

1.0

1.2

0.20 0.25 0.30 0.35 0.40 0.45

N*F/N

NF

AO/A

DF/NF

WF/NF

CF/NF

AF/NF


220

Figure 6-5: Ultimate load ratio versus opening locations in TW4S action walls

Proposed Method using design charts

The proposed design charts from previous sections are based on the principle of

numerical prediction for the practical application of CFRP strengthened walls under

various support conditions. In this section, a step-by-step design method for CFRP

strengthened walls is introduced as an illustrative design procedure. A comparative

study is then carried out to verify the accuracy and effectiveness of the proposed

method. The design process is carried out as follows:

Step 1: Define the type of support condition

The type of support condition should be defined. If there is a core box, it should be

divided into wall elements and then each segment can be strengthened separately.

NDF/NNF = -0.12χ + 1.10

NAF/NNF = 0.14χ + 1.07

NCF/NNF = 0.03χ + 1.12

NWF/NNF = -0.05χ + 1.09

0.8

1.0

1.2

0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34

N*F/N

NF

DF/NF

AF/NF

CF/NF

WF/NF


221

Step 2: In this step a few parameters should be determined. This step can be further

subdivided into the following:

Step 2-1: Identify geometric properties

The geometric properties of the RC walls including: dimension of the wall (Hw, Lw, tw),

opening size (Ho, Lo) and location should be determined.

Step 2-2: Identify material properties

It is vital to have the material properties of the RC walls and CFRP. The properties of

material used for the RC walls are: concrete strength (f'c); concrete density,

reinforcement yield stress (fy), the reinforcement ratios vertically (ρv) and horizontally

(ρh ). The properties of the CFRP layer, such as: thickness, density, tensile modulus and

tensile strength should be identified.

Step 2-3: Determine CFRP layout

The type of CFRP layout (DF, WF, AF and CF) should be determined and the

dimension of the CFRP layer should be calculated based on Eqs. 3-1 to 3-5.

Step 3: Define Ao/A and χ

Calculate the ratio of the cross sectional area of the opening (Ao=Lotw) to the cross

sectional area of the wall (A=Lwtw). The χ is obtained from Eq. 2-13 which is shown in

Chapter 2. Based on the size of the opening and its location, as well as the support

condition, an appropriate chart should be chosen from Figures 6-1 to 6-5.

Step4: Calculate the ultimate load of RC walls with opening


222

The ultimate load of RC walls with opening can be obtained from existing formula

(Eqs. 2-9 to 2-11) proposed by previous researchers, which were presented in Chapter

2. Although there have been several proposed formulas for RC walls (with opening and

without CFRP) under OW and TW4S, there has not been a formula to determine the

ultimate load of RC walls (with opening and without CFRP) under TW3S. However,

as shown in Chapter 5, Section 5.6, the ultimate strength of walls with TW3S can be

reasonably estimated from the proposed formula for OW and TW4S action (Eq. 5-4).

Step 5: Calculate the ultimate load of CFRP strengthened RC walls:

Based on the ratio of Ao/A or χ as well as the desired CFRP layout, the ratio of ultimate

load of CFRP strengthened walls (N*F) to that of without CFRP (NNF) can be easily

achieved using the proposed design charts (Figures 6-1 to 6-5). Having the ratio

(N*F/NNF) from the chart and also the ultimate load for the wall without CFRP

(calculated in step 4), the ultimate load of the CFRP strengthened RC walls (N*F) can

be determined. The flowchart of CFRP strengthened RC wall design is summarised in

Figure 6-6.


223

Figure 6-6: Flowchart for CFRP strengthened RC wall design procedure

Assumptions involved in the development of proposed design charts

Assumptions involved in the development of the charts/formula are as follows:

a) The panel contains at least the minimum amount of steel in the vertical

direction (i.e. ρ = 0.003).

b) The widths of CFRP layouts were calculated from Eqs. 3-1 to 3.4 which are

based on the Swedish Building Administration’s handbook on concrete

structures (BBK, 2004).

c) The axial load was applied at an eccentricity of tw/6.


224

d) The opening ratio was limited to between 6% and 17% and the opening was

located away from the edges of the RC walls.

e) This design method is proposed considering single opening in walls, therefore,

for RC walls with multiple openings more investigation is required prior to

using design charts.

Verification of proposed design charts

Comparisons of failure load for walls under OW and TW action was conducted using

the proposed design method and previously recommended equations (Eq. 2-12), against

the test results (by previous researchers and current) (Table 6-1). The mean of the ratio

(predicted/test) and its coefficient of variation were calculated and are also presented

(Table 6-1).

In this table, WO1b-WO4b and WO1C-WO4C were the RC walls strengthened by AF

and DF layouts considering various opening sizes, respectively (Mohammed et al.,

2013). The proposed formulae by Doh and Fragomeni (2005, 2006) were used to

predict the ultimate strength of the RC panels both with (Nu) and without openings

(NNF). From the comparison and investigation between the existing formula and

proposed design method, a number of conclusions are drawn:

a) The proposed design method is able to estimate the ultimate load of CFRP

strengthened RC walls considering various support conditions, CFRP layouts and

opening configurations.


225

b) The proposed charts give a safe estimate of failure load for all panels and the mean

(predicted/test) of 0.81 and standard deviation of 0.15. Even though Eq. 2-12 has

a marginally higher mean (0.82), the standard deviation is slightly higher as well

(0.19). Considering the current experimental outcomes (Chapter 4) in both OW and

TW action walls, the proposed design method gives the mean (predicted/test) of

0.89 with standard deviation of 0.06. This suggests that the proposed design charts

safely predict the ultimate load and are also more reliable due to the lower standard

deviation.

c) The existing equation (Eq. 2-12) is only applicable for RC walls under OW action.

However, the current proposed design method not only predicts the ultimate loads

of RC walls under OW action, but can also accurately (with 10% discrepancy)

predict the ultimate load of walls under TW action.

d) The proposed design method can reasonably predict the ultimate load of RC walls

strengthened with various CFRP layouts including DF, AF, CF and WF. However,

Eq. 2-12 is only applicable for two types of CFRP layouts, being the DF and AF

layouts.

e) The application of Eq. 2-12 to determine the ultimate load of RC walls resulted in

an unsafe prediction for walls strengthened with the DF layout as some ratios

(predicted/test) are greater than 1. This suggests that Eq. 2-12 sometimes over-

estimates the failure load, where a 17% higher ultimate load was achieved when

compared to the experimental counterpart for walls with OW-DF. In contrast, the


226

proposed design method is acceptable as all the experimental test results fall well

above the predicted design load.

f) For OW action, walls with the AF layout and an opening ratio of 14%, the proposed

design method and Eq. 2-12 resulted in an identical outcome.

g) The proposed design method is able to predict the ultimate load of CFRP

strengthened RC walls for a wide range of concrete strengths ( c'f =15 MPa to 65

MPa); slenderness ratios (Hw/tw=20 to 30) and aspect ratios (Hw/Lw=1 to 2). It

could also reasonably predict the ultimate load of walls with larger opening sizes

(up to 30%). This suggests that the proposed design method is not only applicable

for a newly constructed wall, in which the opening ratio is limited to 10% (AS

3600) and a good concrete quality is expected, but also it can be applied to the

rehabilitation and retrofitting of panels in existing buildings.


227

Table 6-1: Comparison of ultimate load using proposed design method

Wall

designation χ or Ao/A c

'f

(MPa)

tw

(mm)

Ultimate failure load (kN) Eq. 2-12

Exp

Proposed

Exp Exp1 Eq. 2-122 Proposed3

Moham

med

et

al.

(2013 )

WO1b 0.238 15.0 40.0 149.90 143.43 99.38 0.96 0.66

WO2b 0.338 17.1 40.0 139.10 118.01 106.50 0.85 0.77

WO3b 0.463 18.2 40.0 108.00 80.43 102.82 0.74 0.95

WO4b 0.575 15.1 40.0 82.00 43.29 78.56 0.53 0.96

WO1C 0.238 14.7 40.0 175.40 166.76 92.38 0.95 0.53

WO2C 0.338 15.6 40.0 157.20 129.57 83.46 0.82 0.53

WO3C 0.463 16.4 40.0 138.50 85.89 69.50 0.62 0.50

WO4C 0.575 17.0 40.0 84.80 53.35 56.15 0.63 0.66

Cu

rren

t

OW-DF 0.375 55.1 40.0 309.00 360.19 253.41 1.17 0.82

OW-AF 0.375 54.7 40.0 335.70 315.96 315.61 0.94 0.94

OW-WF 0.375 62.6 43.5 559.00 - 486.93 N/A 0.87

OW-CF 0.375 62.6 46.0 415.05 - 329.41 N/A 0.79

TW3S-DF 0.375 57.0 44.0 589.35 - 552.65 N/A 0.94

TW3S-AF 0.375 58.5 43.0 649.50 - 570.26 N/A 0.88

TW3S-WF 0.375 62.3 46.0 700.05 - 649.90 N/A 0.93

TW3S-CF 0.375 62.3 40.0 643.35 - 549.84 N/A 0.85

TW4S-DF 0.375 57.6 40.0 766.05 - 717.48 N/A 0.94

TW4S-AF 0.375 56.2 40.0 753.45 - 733.37 N/A 0.97

TW4S-WF 0.375 63.2 40.0 894.30 - 717.10 N/A 0.80

TW4S-CF 0.375 64.7 40.0 887.25 - 819.72 N/A 0.92

Mean 0.82 0.81

STDV 0.19 0.15

Exp: experimental; 2Eq. 2-12: proposed equation by Mohamamd et al. (2013); 3Proposed: current proposed design method

Chapter 6: design chart for strengthened RC walls

228

Examples for illustration and application of the proposed design charts

The purpose of these examples was to illustrate and apply the current proposed design

chart in a real project.

6.6.1 Example 1: CFRP strengthened RC wall with OW

It was assumed that the wall size and properties of the RC wall panel were as follows:

Hw=3000 mm, Lw=3000 mm, tw=100 mm, MPa50'cf , fy=450 MPa, e=tw/6 and the

opening size was Ho=950 mm, Lo=950 mm (10 % opening)

Figure 6-7: Schematic view of walls with OW

The step-by-step procedure for strengthening of RC walls was as follows:


229

Step 1: Define the type of support condition: this wall was experiencing one-way action

(OW)

Step 2: In this step a few parameters should be determined. This step can be subdivided

into the following steps:

Step 2-1: Identify the geometric properties

The height (Hw) and length (Lw) of wall are equal to 3000mm with a thickness (tw) of

100mm. The height (Ho) and length (Lo) of the opening are equal to 950 mm.

Step 2-2: Identify material properties

The concrete compressive strength (f'c) is 50 MPa and yield strength of reinforcement

(fy) is 450 MPa. The reinforcement ratios are identical in both the vertical (ρv) and

horizontal (ρh ) direction and equal to 0.0029 which conform to the AS3600

requirement. The CFRP material properties in this example are the same as the material

properties presented in Table 3-1.

Step 2-3: Determine CFRP layout

Using the proposed equation in Chapter 3 (Eqs. 3-1 to 3-5), the width and length of

each CFRP layout was calculated and presented in Table 6-2. These values are the same

as the CFRP dimension presented in Table 5-3 for an opening size of 10%.


230

Table 6-2: CFRP layouts and dimensions

CFRP dimension (mm) Total amount of CFRP

usage (×106 mm2)

Width Length

DF AF CF WF DF AF CF WF

380 #4.×950 #4.×1910

#4.×950

&

#4. ×1910

#12.×950 1.44 2.90 4.35 4.33


0.3171003000

100950

A

Ao

mm 1975ηo

mm 1279.881009501003000

197595010030001002

1

tLtL

ηotLwt2

1

η

2

woww

oLw2w

mm 220.121279.882

3000η

2

Lη

0.393000

220.12

1003000

100950

L

η

A

Aχ

o

For RC walls under OW action, shifting the opening horizontally resulted in an identical

outcome as having an opening at the wall’s centre. Therefore, for RC walls under OW

action, the ratio of Ao/A must be considered instead of χ in Figure 6-1

Step 4: Calculate the ultimate load of the RC walls with openings

Firstly, the ultimate load of the corresponding solid wall should be calculated. In this

section the proposed formula by Doh and Fragomeni (2005) was used.

mm 16.667100/6/6te w


231

For 27/tH ww ; 0.90241

t

H

18β

0.88

w

w

mm 2707.243000 0.90241βHweH

mm 29.3166100)/(2500(2707.24)2500tHae 2w

2we

29.3166)216.6671.2(100(50)2)2e1.2e(t)f2.0(N 0.7aw

0.7cu

=660.765 kN/m

kN 1982.33660.765Nu

In the next step, the proposed formula by Doh and Fragomeni (2006) was used to

determine the ultimate load of RC walls with openings under OW action.

kN 1410.71982.30.39)1.188(1.175uχ)Nk(kN .21NF

Step 5: Calculate the ultimate load of CFRP strengthened RC walls

In this stage, the type of CFRP layout should be defined first. Then, based on the value

of Ao/A, the ratio of N*F/NNF can be found from the vertical axis of Figure 6-1, or by

using the provided equations in the design chart. The ultimate load of RC walls without

CFRP was calculated in step 4, which was equal to NNF, therefore the ultimate load of

the CFRP strengthened RC walls can be calculated as follows, for various CFRP layouts

(Table 6-3).


232

Table 6-3: Predicted ultimate load of CFRP strengthened RC walls with OW

(AO/A=0.317)

1NNF: ultimate load of RC walls without CFRP; 2N*F: ultimate load of CFRP strengthened RC walls with

various CFRP layouts

6.6.2 Example 2: RC wall with TW4S:

It was assumed that the size and properties of the RC wall were as follows:



LC

LC

Ho

Lo

LwSupport

Hw

(b) Front view (a) Side view

Side restraintSupport

Side restraint

tw

tw/6

P270@10

Figure 6-8: Schematic view of walls with TW4S

Type of CFRP

layout

Proposed ratio from chart

N*F/NNF

NNF1

(kN)

N*F2

(kN)

NF - 1410.70 -

DF -0.01×0.317+1.03=1.03 - 1453.02

AF 1.39×0.317+0.76=1.20 - 1692.84

CF 1.52×0.317+0.74=1.22 - 1721.05

WF 0.17×0.317+1.03=1.08 - 1523.55


233

The step-by-step procedure to calculate the ultimate load of CFRP strengthened RC

walls is as follows:

Step 1: Define the type of support condition: this wall was experiencing two-way action

with four sides restrained (TW4S).

Step 2: In this step a few parameters should be determined. This step is identical to that

in walls under OW action which discussed in Example 1.


0.3171003000

100950

A

Ao

mm 1025ηo

mm 220.121720.122

3000η

2

Lη

w

0.2433000

220.12

1003000

100950

L

η

A

Aχ

w

o

Step 4: Calculate the ultimate load of the RC walls with opening

Firstly, the ultimate load of the corresponding solid wall should be calculated. In this

section the proposed formula by Doh and Fragomeni (2005) for walls under two-way

action was used.

mm 16.67100/6/6te w

for 27/tH ww :

mm 1720.121009501003000

102595010030001002

1

tLtL

ηLtLt2

1

η

2

woww

o0w2ww


234

1.0829

100

3000

18

100

16.671

1

t

H

18

t

e1

1α

0.880.88

w

w

w

for ww LH : 0.54145

3000

30001

11.0829

L

H1

1αβ

22

w

w

mm 1624.3530000.54145βHweH

mm 10.554100)/(2500(1624.35)2500tHae 2w

2we

10.554)2 16.671.2 (100(50)2)2e1.2e(t'2.0fN0.7

aw

0.7

cu

kN/m 1821.23

kN 5463.731821.23Nu

For panels with openings, the proposed formula by Doh and Fragomeni (2006) for

ultimate loads of panels with opening is: u)N.k-(kN 21NF where uN was the

obtained force from step 2 for the corresponding solid wall. The values of 1k and 2k

are 1.004 and 0.933 for walls under TW4S.

kN 4245.305463.70.243)0.933(1.004).N.k(kN u21NF


In this stage, the type of CFRP layout should be defined. Then, based on 243.0 the

value for N*F/NNF can be found from the vertical axis of Figure 6-5, or by using the

provided equations in the design chart. The ultimate load of the RC walls without CFRP

was calculated in step 4 which is equal to NNF. Therefore the ultimate load of the CFRP

strengthened RC walls was computed and presented in Table 6-4.


235


(AO/A=0.317 and 243.0 )



6.6.3 Example 3: RC walls with TW3S

It was assumed that the size and properties of RC walls were as follows:



LC

LC

Ho

Lo

Lw

Support

Support

Hw

(b) Front view (a) Side view

Side restraint

tw

tw/6

P270@10

Figure 6-9: Schematic view of walls with TW3S

Type of

CFRP

layout

Proposed ratio from chart

N*F/NNF

NNF1

(kN)

N*F2

(kN)

Required

amount of

CFRP (m2)

NF - 4245.30 - -

DF -0.12×0.243+1.10=1.07 - 4542.471 1.44

AF 0.14×0.243+1.07=1.10 - 4669.83 2.90

CF 0.03×0.243+1.12=1.13 - 4797.189 4.35

WF -0.05×0.243+1.09=1.08 - 4584.924 4.33


236

Step 1: Define the type of support condition: this wall was experiencing two-way action

with three sides restrained (TW3S).

Step 2: In this step a few parameters should be determined. These parameters are

identical to that in walls under one-way action which discussed in Example 1, therefore,

those parameters are not listed here. .


0.3171003000

100950

A

Ao

mm 1025ηo

mm 220.121720.122

3000η

2

Lη

w

0.2433000

220.12

1003000

100950

L

η

A

Aχ

w

o

Step 4: Calculate the ultimate load of RC walls with opening

Unlike OW and TW4S, there is no proposed formula in the published literature for

calculating the ultimate load of RC walls with openings under two-way action with

three sides restrained. However, as discussed in Section 5.6, the ultimate load of RC

walls (without CFRP) under TW3S can be determined using Eq. 5-4.

mm 1720.121009501003000

102595010030001002

1

tLtL

ηLtLt2

1

η

2

woww

oow2ww


237

The ultimate loads of RC walls under OW and TW action with four sides restrained

were calculated in Sections 6.5.1 and 6.5.2. Then, the ultimate load of RC walls under

TW3S can be obtained as follow:

kN 2828.002

1410.704245.30

2

)(N)(N)(N TW4SNFOWNFTW3SNF


In this stage, the type of CFRP layout should be defined first. Then, based on 243.0

the value for N*F/NNF can be found from the vertical axis of Figure 6-3 or by using the

provided equations in the design chart. The ultimate load of RC walls without CFRP

was calculated in step 4 which is equal to NNF. Therefore the ultimate load of the CFRP

strengthened RC walls was computed and presented in Table 6-5.


(AO/A=0.317 and 243.0 )



Summary and conclusion

Design charts are proposed for CFRP strengthened RC walls with openings,

considering various support conditions (OW, TW3S and TW4S). A step by step design

method for CFRP strengthened RC walls is introduced which illustrated the design

Type of CFRP

layout

Proposed ratio from

chart N*F/NNF

NNF1

(kN)

N*F2

(kN)

Required amount of

CFRP (m2)

NF - 2828.00 - -

DF 0.31×0.243+0.93=1.01 - 2856.28 1.44

AF 0.41×0.243+0.93=1.03 - 2912.84 2.90

CF 0.44×0.243+0.93=1.04 - 2941.12 4.35

WF 0.34×0.243+0.93=1.01 - 2856.28 4.33


238

procedure proposed. In order to ascertain the accuracy and reliability of the proposed

method, the ultimate load of the CFRP strengthened RC walls were evaluated against

existing experimental outcomes and available formulae from previously published

research, as well as the current experimental outcomes (Chapter 4). The results

demonstrated the accuracy and reliability of the developed design charts for reasonably

predicting the ultimate load of CFRP strengthened RC walls. Finally, three examples

were presented to illustrate for engineers the application of the proposed design charts

with sample problems under various support conditions, opening sizes and CFRP

layouts.

Chapter 7: Conclusions

239

7 CONCLUSION

Conclusions

This research has focused on the development of design charts and a new design method

for eccentric axially loaded CFRP strengthened RC wall panels. Many researchers have

investigated the behaviour of RC walls with various material properties, geometries and

boundary conditions. However, little research was previously carried out on the CFRP

strengthening method for RC walls under eccentric axial loads.

The main aims of this research were to:

- Conduct an experimental study on CFRP strengthened RC walls with openings

using various CFRP layouts and support conditions;

- Conduct numerical investigations of the experimental counterparts in order to

establish a reliable FEM and perform a parametric study of full-scale RC walls

considering various parameters; and

- Propose and validate design charts for CFRP strengthened RC walls using

various CFRP layouts, opening configurations, and support conditions.

After an extensive literature review, it was concluded that there was only one design

equation for CFRP strengthened RC walls under one–way action considering only two

CFRP layouts (DF and AF).

Therefore, the following research gaps were identified:

1- The lack of an existing design chart/methods for CFRP strengthened RC walls

under one-way action with various CFRP layouts and opening configurations;


240

2- The lack of an existing design chart/methods for CFRP strengthened RC walls

under two-way action with three sides restrained with various CFRP layouts

and opening configurations;

3- The lack of existing design chart/methods for CFRP strengthened RC walls

under two-way action with four sides restrained in with various CFRP layouts

and opening configurations.

The experimental study was undertaken on eighteen RC walls with openings under one-

way and two-way action with three and four sides restrained. The walls were loaded

with an eccentricity of tw/6, and these one-third specimens exhibited a slenderness ratio

of 30. Seven different CFRP patterns were applied and results showed the load carrying

capacity of RC walls with openings strengthened by CFRP were improved. This study

found the CFRP application provided varied success in achieving ultimate strength

gains under different support conditions and CFRP layouts. Crack distribution patterns

were observed to change after applying the CFRP layers to the RC walls. Strain gauges

were installed to monitor possible debonding of the CFRP–concrete interface and it was

evident that the concrete and CFRP remained bonded up to the failure loads that were

achieved. Based on the efficiency investigation, the WF layout achieved the lowest

efficiency observed for RC wall strengthening. The CF and DF patterns were the most

efficient CFRP layouts for walls under one-way and two-way action, respectively.

As it was not practical to conduct more experiments as a result of resource restraints,

FEM was used as a cost-effective tool for the further investigations on CFRP

strengthened RC walls considering various parameters. Nonlinear FEM using

ABAQUS software was conducted as an accurate analytical method for the comparison


241

and validation of the experimental test results. The behaviour of reinforced concrete

walls obtained from simulation was compared with experiments and consistent

outcomes were observed in crack patterns, load-deflection profiles and ultimate

strength of walls. Having established that the numerical software is a good comparison

with experimental outcomes, a parametric study was then carried out for the full scaled

wall panels with various CFRP layouts, support conditions, opening sizes and

configurations. The outcomes showed the CFRP application provided varied

enhancement in ultimate strength of RC walls under different support conditions,

opening configurations and CFRP layouts. Efficiency investigation of CFRP layouts

was also conducted and presented.

Based on the parametric study discussed in Chapter 5, dimensionless design charts were

proposed for CFRP strengthened walls with one-way and two-way action. A step by

step design method for CFRP strengthened RC walls was introduced which illustrated

the design procedure proposed. In order to ascertain the accuracy and reliability of the

proposed method, the ultimate loads of CFRP strengthened RC walls were evaluated

against existing experiments and available formulae from previously published

research as well as the current experimental outcomes (presented in Chapter 4). The

results demonstrated the accuracy and reliability of the developed design charts to

reasonably predict the ultimate load of CFRP strengthened RC walls. Finally, three

examples were presented for engineers to illustrate the application of the proposed

design charts in sample problems under various support conditions, opening sizes and

CFRP layouts.

The main aims of this research were achieved by:


242

- Conducting an experimental study on CFRP strengthened RC walls with

openings using various CFRP layouts and support conditions;

- Conducting numerical investigations of CFRP strengthened RC walls

considering various opening sizes, locations and CFRP layouts under one-way

and two-way actions; and

- Providing design charts for CFRP strengthened RC wall panels for the three

types of support conditions investigated.

Recommendations and Scope for Future Research

The following areas of research concerning CFRP strengthened RC wall panels remain

relatively unexplored and could form the basis of future research:

1. More laboratory testing should be carried out on RC walls under one-way action

and two-way action with three and four sides restrained considering various

eccentricities and aspect ratios (particularly H/L < 1);

2. Detailed investigations of the strength and behaviour of CFRP strengthened

wall panels with openings (doors and windows) would lead to more practical

design information;

3. Proving a new method or formula for calculation of the amount of CFRP and

the effects of CFRP width on ultimate failure load of RC walls;

4. Applying other types of FRPs such as GFRP or CFRP laminate on RC walls to

compare their performance with CFRP sheet;

5. Applying other layout patterns such as fully wrapping CFRP around any

openings or other alternatives based on further consideration of the loading

scenario experienced.


243

6. Contribution of CFRP layouts in ultimate strength of walls considering a

combination of vertical and lateral forces;

7. Further investigation, modification and evaluation on the ultimate strength of

RC walls with TW3S based on that of RC walls with OW and TW4S needs to

be undertaken for any meaningful application of other formula;

8. Contribution of CFRP layouts in cases where the opening is located at the edge

of RC wall; and

9. Investigate the behaviour of CFRP strengthened RC walls under cyclic loading.

References

244

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Appendix A

251

APPENDIX A: PANEL DESIGNATION AND CFRP LAYOUTS FOR OW,

TW3S AND TW4S IN PARAMETRIC

Appendix A

252

1125 750 1125

11

25

750

11

25

100

LC

LCSupport

Support

750

925

100

13

25

1125 750 1125

LC

Figure A 1: NF-750-C0 Figure A 2: NF-750-C1

75

07

25

100

15

25

1125 750 1125

LC

LC

75

0525

100

1725

1125 750 1125

LC

LC


1025 950 1025

1025

950

10

25

100

LC

LC

1225

950

825

100

1025 950 1025

LC

LC


Appendix A

253

1325

950

72

5

100

1025 950 1025

LC

LC

14

25

95

0

625

100

1025 950 1025

LC

LC


937.5 1125 937.5

LC

LC

93

7.5

1125

93

7.5

100

937.5 1125 937.5

LC

LC

11

00

1125

775

100


937.5 1125 937.5

LC

LC

11

50

11

25

72

5

100

937.5 1125 937.5

LC

LC

12

00

11

25

67

5

100


Appendix A

254

875 1250 875

LC

LC

87

51

25

0875

100

875 1250 875

LC

LC

950

12

50

80

0

100


875 1250 875

LC

LC

1000

12

50

75

0

100

875 1250 875

LC

LC

10

50

12

50

70

0

100


LC

LC

1125 750 1125

11

25

75

01

12

5

100

LC

LC

1125 750 1125

750

925

100

13

25

Figure A 17: DF-750-C0 Figure A 18: DF-750-C1

Appendix A

255

LC

LC

1125 750 1125

750

72

5

100

15

25

LC

LC

1125 750 1125

75

0525

100

1725


LC

LC

1025 950 1025

10

25

95

0

10

25

100

LC

LC

1025 950 1025

1225

95

0825

100


LC

LC

1025 950 1025

1325

95

0

72

5

100

LC

LC

1025 950 1025

1425

95

0

625

100


Appendix A

256

937

.51

12

59

37.5

100

LC

LC

937.5 1125 937.5

1100

11

25

77

5

100 LC

937.5 1125 937.5


11

50

11

25

72

5

100

LC

LC

937.5 1125 937.5

12

00

11

25

675

100

LC

LC

937.5 1125 937.5


87

51

25

0875

100

LC

LC

875 1250 875

950

12

50

80

0

100

LC

LC

875 1250 875


Appendix A

257

1000

12

50

75

0

100

C

LC

875 1250 875

10

50

12

50

700

100

LC

LC

875 1250 875


LC

LC

1125 750 1125

1125

750

11

25

100

LC

LC

1125 750 1125

750

92

5

100

13

25

Figure A 33: AF-750-C0 Figure A 34: AF-750-C1

LC

LC

1125 750 1125

750

72

5

100

1525

LC

LC

1125 750 1125

75

0525

100

1725


Appendix A

258

LC

LC

1025 950 1025

10

25

95

0

1025

100

LC

LC

1025 950 1025

1225

95

0825

100


LC

LC

1025 950 1025

1325

95

0

72

5

100

LC

LC

1025 950 1025

14

25

95

0

625

100


LC

LC

937.5 1125 937.5

937

.51125

93

7.5

100

C

LC

937.5 1125 937.5

11

00

1125

775

100


Appendix A

259

LC

LC

937.5 1125 937.5

11

50

11

25

72

5

100

LC

LC

937.5 1125 937.5

12

00

1125

675

100


LC

LC

875 1250 875

87

51

25

0875

100

LC

LC

875 1250 875

95

01250

80

0

100


LC

LC

875 1250 875

1000

12

50

75

0

100

LC

LC

875 1250 875

10

50

12

50

70

0

100


Appendix A

260

LC

LC

1125 750 1125

1125

750

11

25

100

LC

LC

1125 750 1125

750

92

5

100

13

25

Figure A 49: CF-750-C0 Figure A 50: CF-750-C1

LC

LC

1125 750 1125

750

72

5

100

1525

LC

LC

1125 750 1125

750

52

5

100

17

25


LC

LC

1025 950 1025

10

25

950

1025

100

LC

LC

1025 950 1025

1225

95

0825

100


Appendix A

261

LC

LC

1025 950 1025

1325

95

0

72

5

100

LC

LC

1025 950 1025

14

25

950

625

100


LC

LC

937.5 1125 937.5

93

7.5

11

25

937

.5

100

LC

LC

937.5 1125 937.5

11

00

1125

775

100


LC

LC

937.5 1125 937.5

11

50

1125

72

5

100

LC

LC

937.5 1125 937.5

1200

1125

67

5

100


Appendix A

262

LC

LC

875 1250 875

875

12

50

87

5

100

LC

LC

875 1250 875

950

1250

800

100


LC

LC

875 1250 875

10

00

1250

750

100

LC

LC

875 1250 875

1050

1250

700

100


LC

LC

1125 750 1125

1125

75

01

12

5

100

LC

LC

1125 750 1125

750

925

100

13

25

Figure A 65: WF-750-C0 Figure A 66: WF-750-C1

Appendix A

263

LC

LC

1125 750 1125

750

72

5

100

15

25

LC

LC

1125 750 1125

750

52

5

100

1725


LC

LC

1025 950 1025

1025

950

10

25

100

LC

LC

1025 950 1025

1225

95

0825

100


LC

LC

1025 950 1025

13

25

950

72

5

100

LC

LC

1025 950 1025

14

25

95

0

625

100


Appendix A

264

LC

LC

937.5 1125 937.5

93

7.5

1125

93

7.5

100

LC

LC

937.5 1125 937.5

11

00

1125

775

100


LC

LC

937.5 1125 937.5

11

50

11

25

72

5

100

LC

LC

937.5 1125 937.5

12

00

1125

675

100


LC

LC

875 1250 875

87

51

25

08

75

100

LC

LC

875 1250 875

950

12

50

80

0

100


Appendix A

265

LC

LC

875 1250 875

1000

1250

75

0

100

LC

LC

875 1250 875

10

50

1250

700

100


LC

LC

550 950 1500

1025

950

10

25

100

LC

LC

1500 950 550

1025

950

10

25

100

Figure A 81: NF-950-L0 Figure A 82: NF-950-R0

LC

LC

14

25

950

625

100

550 950 1500

LC

LC

1425

95

0

625

100

1500 950 550

Figure A 83: NF-950-L3 Figure A 84: NF-950-R3

Appendix A

266

LC

LC

550 950 1500

1025

950

10

25

100

LC

LC

1500 950 550

1025

950

10

25

100

Figure A 85: DF-950-L0 Figure A 86: DF-950-R0

LC

LC

14

25

950

625

100

550 950 1500

LC

LC

1425

95

0

625

100

1500 950 550

Figure A 87: DF-950-L3 Figure A 88: DF-950-R3

LC

LC

550 950 1500

1025

950

10

25

100

LC

LC

1500 950 550

1025

950

10

25

100

Figure A 89: AF-950-L0 Figure A 90: AF-950-R0

Appendix A

267

LC

LC

14

25

950

625

100

550 950 1500

LC

LC

1425

95

0

625

100

1500 950 550

Figure A 91: AF-950-L3 Figure A 92: AF-950-R3

LC

LC

550 950 1500

1025

950

10

25

100

LC

LC

1500 950 550

1025

950

10

25

100

Figure A 93: CF-950-L0 Figure A 94: CF-950-R0

LC

LC

14

25

950

625

100

550 950 1500

LC

LC

1425

95

0

625

100

1500 950 550

Figure A 95: CF-950-L3 Figure A 96: CF-950-R3

Appendix A

268

LC

LC

550 950 1500

1025

950

10

25

100

LC

LC

1500 950 550

1025

950

10

25

100

Figure A 97: WF-950-L0 Figure A 98: WF-950-R0

LC

LC

14

25

950

625

100

550 950 1500

LC

LC

1425

95

0

625

100

1500 950 550

Figure A 99: WF-950-L3 Figure A 100: WF-950-R3

Appendix B

269

APPENDIX B: MOULD PREPARATION, CONCRETE CASTING,

CURING AND TESTING

Figure B 1: Mould preparation Figure B 2: Cutting rebars for desired

length

Figure B 3: Applying lanoline Figure B 4: Cutting rebars of opening

area

Figure B 5: A completed mould Figure B 6: A group of mould prepared

for concrete casting

Appendix B

270

Figure B 7: Slump test in progress Figure B 8: Slump test: measuring

Figure B 9:Placing of concrete in progress

Figure B 10: Vibration of concrete in

progress

Figure B 11: Concrete cylinder

prepared for compressive and tensile

test

Figure B 12: Trowelled concrete surface Figure B 13: Curing of concrete panels

and cylinders

Appendix B

271

Figure B 14: Surface preparation for strain

gauge installation

Figure B 15: Applied strain gauge on

the corner of the opening

Figure B 16: Surface prearing for CFRP application

Figure B 17: CFRP application in progress

(TW3S-MF)

Figure B 18: Completion of CFRP

application (OW-PF)

Appendix B

272

Figure B 19: Epoxy curing under a laboratory environment and controlled

tempreature

Figure B 20: Prepared panel for testing

(OW)

Figure B 21: Prepared panel for testing

(TW4S)

Appendix C

273

APPENDIX C: CFRP-CONCRETE INTERFACE AFTER FAILURE

LOAD.

Figure C 1: Concrete-CFRP interface for OW-CF

Figure C 2: Concrete-CFRP interface for TW3S-DF

Figure C 3: Concrete-CFRP interface for TW3S-WF

Appendix C

274



Appendix D

275

APPENDIX D: CFRP WIDTH AND EPOXY CALCUATION FOR

EXPERIMENTS

The width of CFRP was calculated based on the Swedish Building Administration’s handbook

on concrete structures BBK04 (2004). The material properties considered for this calculation

were includes: MPa 50c'f ; Lw = 1200 mm; fsy = 500 MPa; tw = 40 mm and tf = 0.128; Es=

210 GPa and Ef = 234 GPa .The width of the CFRP layout was calculated as follows:

222bs2 mm 62.835π(4/2)5π/2)(dA

0.621200500.85

50062.83

L0.85f'

fAa

wc

sys2

0.720.85

0.6115

0.85

ax

22

5

5

s22

w

wt

f

s2f mm 13.5762.83)

0.7240

0.722040(

102.34

102.10A)

xt

xu(

E

EA

mm 1050.128

13.57

t

AW

f

ff

The required epoxy for experiments were calculated based on the products manual provided

by Sika Pty Ltd where it was suggested that each meter square of CFRP requires 0.7 - 1.2 kg

of epoxy. Sikadur-330 was supplied in factory proportioned units comprising the correct

quantities of Part A and Part B (A:B=4:1 by weight).

The amount of required epoxy for AF layout was calculated as follows:

The total area of applied CFRP in this layout

AAF= 4×105×770= 323400.00 mm2=323.40×10-3 m2

Appendix D

276

It was assumed that 1 m2 of CFRP requires 1 kg of epoxy, then the total amount of epoxy was

calculated as 323.40×10-3×1 kg= 323.4 g

According to the correct quantities of Part A and Part B (A:B=4:1 by weight), the amount of

part A and B were calculated as follows:

Part A : g00.260g72.25814

423.403

Part B: 65gg 64.6814

1323.40

The amount of required epoxy for CF layout was calculated as follows:


ACF= 4×105×770+4×105×450= 512400 mm2=512.40×10-3 m2





Part A: g 410g 409.9214

4512.40

Part B: g 103g 102.4814

1512.40

The amount of required epoxy for DF layout was calculated as follows:


ACF= 4×105×450= 189000 mm2=189.00×10-3 m2





Appendix D

277

Part A: g 521g 20.51114

400.891

Part B: g 83g 80.7314

100.891

Appendix E

278

APPENDIX E: LOAD VERSUS STRAIN OF RC WALLS

Load versus strain graphs of some of CFRP strengthened RC walls are presented in this part.

In the following graphs the yellow and red colours indicate the strain gauge instalment on

CFRP layout and concrete, respectively. The following abbreviation was applied to identify

the location of strain gauges:

CCV: strain gauge installed on concrete wall and corner of opening in vertical direction;

CCH: strain gauge installed on concrete wall and corner of opening in horizontal direction;

CCD: strain gauge installed on concrete wall and corner of opening in diagonal direction;

CS: strain gauge installed on concrete wall and side of opening;

FD: strain gauge installed on CFRP layout diagonal to the opening;

FV: strain gauge installed on CFRP layout in vertical direction

Appendix E

279

375 450 375

37

54

50

37

5

40

LC

LCSupport

Figure E 1: The placement of strain gauges on OW-DF

Figure E 2: Load versus strain curves for OW-DF

0

100

200

300

400

0 100 200 300 400 500 600

Lo

ad (

kN

)

Strain (µmm/mm)

OW-DF

CS FD

Appendix E

280

375 450 375

375

45

0375

40LC

LC

Figure E 3: The placement of strain gauges on OW-PF

Figure E 4: Load versus strain curves for OW-PF

0

100

200

300

400

0 100 200 300 400 500 600 700

Lo

ad

(k

N)

Strain(µmm/mm)

OW-PF

CCH

CCV

CCD

CS

FV

Appendix E

281

375 450 375

37

54

50

37

5

40Side restraint

SupportLC

LC

Figure E 5: The placement of strain gauges on TW3S-MF

Figure E 6: Load versus strain curves for TW3S-MF

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800 900 1000 1100

Lo

ad

(k

N)

Strain (µmm/mm)

TW3S

CS

FV

Appendix F

282

APPENDIX F: SAMPLE OF SIMULASTION FORM ABAQUS (TW4S-

WF)

*Heading

** Job name: TW4S-WF Model name: TW4S-WF

** Generated by: Abaqus/CAE 6.14-2

*Preprint, echo=NO, model=NO, history=NO, contact=NO

**

** PARTS

**

*Part, name=CFRP-DF-SOLID

*Node

1, -350., 105., 0.

2, -332.692322, 105., 0.

3, -315.384613, 105., 0.

4, -298.076935, 105., 0.

5, -280.769226, 105., 0.

6, -263.461548, 105., 0.

7, -246.153839, 105., 0.

8, -228.846161, 105., 0.

*Elset, elset=Set-5, instance=TOP-RESTRAINT-1-rad-2, generate

121, 240, 1

*Nset, nset=Set-6, instance=RESTRAINT-SIDE-1

4, 10, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65,

66

67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,

82

83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,

98

99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,

114

115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129,

130

131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145,

146

147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161

*Elset, elset=Set-6, instance=RESTRAINT-SIDE-1

4, 5, 12, 13, 20, 21, 28, 29, 36, 37, 44, 45, 52, 53, 60,

61

68, 69, 76, 77, 84, 85, 92, 93, 100, 101, 108, 109, 116, 117, 124,

125

Appendix F

283

132, 133, 140, 141, 148, 149, 156, 157, 164, 165, 172, 173, 180, 181, 188,

189

196, 197, 204, 205, 212, 213, 220, 221, 228, 229, 236, 237, 244, 245, 252,

253

260, 261, 268, 269, 276, 277, 284, 285, 292, 293, 300, 301, 308, 309, 316,

317

324, 325, 332, 333, 340, 341, 348, 349, 356, 357, 364, 365, 372, 373, 380,

381

388, 389, 396, 397, 404, 405, 412, 413, 420, 421, 428, 429, 436, 437, 444,

445

452, 453, 460, 461, 468, 469, 476, 477, 484, 485, 492, 493, 500, 501, 508,

509

516, 517, 524, 525, 532, 533, 540, 541, 548, 549, 556, 557, 564, 565, 572,

573

580, 581, 588, 589, 596, 597, 604, 605, 612, 613, 620, 621, 628, 629, 636,

637

644, 645, 652, 653, 660, 661, 668, 669, 676, 677, 684, 685, 692, 693, 700,

701

708, 709, 716, 717, 724, 725, 732, 733, 740, 741, 748, 749, 756, 757, 764,

765

772, 773, 780, 781, 788, 789, 796, 797, 804, 805, 812, 813, 820, 821, 828,

829

836, 837, 844, 845, 852, 853, 860, 861, 868, 869, 876, 877

*Nset, nset=Set-7, instance=TOP-RESTRAINT-1

1, 2, 9, 10, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,

44

45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,

60

61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75,

76

77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91,

92

93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107,

108

109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,

124

125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,

140

141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 509, 510, 511, 512,

513

514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528,

529

Appendix F

284

530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544,

545

546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560,

561

562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576,

577

578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592,

593

594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608,

609

610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624,

625

626, 627

*Elset, elset=Set-7, instance=TOP-RESTRAINT-1, generate

121, 240, 1


4, 10, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65,

66

67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,

82

83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,

98

99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,

114

115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129,

130

131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145,

146

147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161


4, 10, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65,

66

67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,

82

83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,

98

99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,

114

115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129,

130

131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145,

146

Appendix F

285

147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161


4, 5, 12, 13, 20, 21, 28, 29, 36, 37, 44, 45, 52, 53, 60,

61

68, 69, 76, 77, 84, 85, 92, 93, 100, 101, 108, 109, 116, 117, 124,

125

132, 133, 140, 141, 148, 149, 156, 157, 164, 165, 172, 173, 180, 181, 188,

189

196, 197, 204, 205, 212, 213, 220, 221, 228, 229, 236, 237, 244, 245, 252,

253

260, 261, 268, 269, 276, 277, 284, 285, 292, 293, 300, 301, 308, 309, 316,

317

324, 325, 332, 333, 340, 341, 348, 349, 356, 357, 364, 365, 372, 373, 380,

381

388, 389, 396, 397, 404, 405, 412, 413, 420, 421, 428, 429, 436, 437, 444,

445

452, 453, 460, 461, 468, 469, 476, 477, 484, 485, 492, 493, 500, 501, 508,

509

516, 517, 524, 525, 532, 533, 540, 541, 548, 549, 556, 557, 564, 565, 572,

573

580, 581, 588, 589, 596, 597, 604, 605, 612, 613, 620, 621, 628, 629, 636,

637

644, 645, 652, 653, 660, 661, 668, 669, 676, 677, 684, 685, 692, 693, 700,

701

708, 709, 716, 717, 724, 725, 732, 733, 740, 741, 748, 749, 756, 757, 764,

765

772, 773, 780, 781, 788, 789, 796, 797, 804, 805, 812, 813, 820, 821, 828,

829

836, 837, 844, 845, 852, 853, 860, 861, 868, 869, 876, 877


4, 5, 12, 13, 20, 21, 28, 29, 36, 37, 44, 45, 52, 53, 60,

61

68, 69, 76, 77, 84, 85, 92, 93, 100, 101, 108, 109, 116, 117, 124,

125

132, 133, 140, 141, 148, 149, 156, 157, 164, 165, 172, 173, 180, 181, 188,

189

196, 197, 204, 205, 212, 213, 220, 221, 228, 229, 236, 237, 244, 245, 252,

253

260, 261, 268, 269, 276, 277, 284, 285, 292, 293, 300, 301, 308, 309, 316,

317

324, 325, 332, 333, 340, 341, 348, 349, 356, 357, 364, 365, 372, 373, 380,

381

Appendix F

286

388, 389, 396, 397, 404, 405, 412, 413, 420, 421, 428, 429, 436, 437, 444,

445

452, 453, 460, 461, 468, 469, 476, 477, 484, 485, 492, 493, 500, 501, 508,

509

516, 517, 524, 525, 532, 533, 540, 541, 548, 549, 556, 557, 564, 565, 572,

573

580, 581, 588, 589, 596, 597, 604, 605, 612, 613, 620, 621, 628, 629, 636,

637

644, 645, 652, 653, 660, 661, 668, 669, 676, 677, 684, 685, 692, 693, 700,

701

708, 709, 716, 717, 724, 725, 732, 733, 740, 741, 748, 749, 756, 757, 764,

765

772, 773, 780, 781, 788, 789, 796, 797, 804, 805, 812, 813, 820, 821, 828,

829

836, 837, 844, 845, 852, 853, 860, 861, 868, 869, 876, 877

*Elset, elset=_CFRP-INSIDE_S1, internal, instance=CFRP-DF-SOLID-1, generate

1, 182, 1

*Elset, elset=_CFRP-INSIDE_S1, internal, instance=CFRP-DF-SOLID-1-rad-2,

generate

1, 182, 1


generate

1, 182, 1


generate

1, 182, 1

*Elset, elset=_CFRP-INSIDE_S5, internal, instance=WF-FINAL-1, generate

155, 245, 1

*Elset, elset=_CFRP-INSIDE_S5, internal, instance=WF-FINAL-1-lin-1-2,

generate

155, 245, 1

*Elset, elset=_CFRP-INSIDE_S5, internal, instance=WF-FINAL-1-lin-1-2-rad-2,

generate

155, 245, 1

*Elset, elset=_CFRP-INSIDE_S5, internal, instance=WF-FINAL-1-rad-3, generate

155, 245, 1


generate

155, 245, 1


155, 245, 1

Appendix F

287


generate

155, 245, 1


155, 245, 1


64, 154, 1


generate

64, 154, 1


generate

64, 154, 1


64, 154, 1


generate

64, 154, 1


64, 154, 1


generate

64, 154, 1


64, 154, 1


1, 49, 1


generate

1, 49, 1


generate

1, 49, 1


1, 49, 1


generate

1, 49, 1


1, 49, 1


generate

Appendix F

288

1, 49, 1


1, 49, 1

*Surface, type=ELEMENT, name=CFRP-INSIDE

_CFRP-INSIDE_S1, S1

_CFRP-INSIDE_S5, S5

_CFRP-INSIDE_S2, S2

_CFRP-INSIDE_S3, S3

*Elset, elset=_Surf-1_S2, internal, instance=TOP-RESTRAINT-1, generate

121, 240, 1

*Surface, type=ELEMENT, name=Surf-1

_Surf-1_S2, S2

*Elset, elset=_WF-CONCRETE-INTERFACE_S1, internal, instance=CFRP-DF-SOLID-

1, generate

1, 182, 1


1-rad-2, generate

1, 182, 1


1-rad-4, generate

1, 182, 1


1-rad-3, generate

1, 182, 1

*Elset, elset=_WF-CONCRETE-INTERFACE_S5, internal, instance=WF-FINAL-1,

generate

155, 245, 1

*Elset, elset=_WF-CONCRETE-INTERFACE_S5, internal, instance=WF-FINAL-1-lin-

1-2, generate

155, 245, 1


1-2-rad-2, generate

155, 245, 1

*Elset, elset=_WF-CONCRETE-INTERFACE_S5, internal, instance=WF-FINAL-1-rad-

3, generate

155, 245, 1


1-2-rad-4, generate

155, 245, 1


2, generate

155, 245, 1

Appendix F

289


1-2-rad-3, generate

155, 245, 1


4, generate

155, 245, 1


generate

64, 154, 1


1-2, generate

64, 154, 1


1-2-rad-2, generate

64, 154, 1


3, generate

64, 154, 1


1-2-rad-4, generate

64, 154, 1


2, generate

64, 154, 1


1-2-rad-3, generate

64, 154, 1


4, generate

64, 154, 1


generate

1, 49, 1


1-2, generate

1, 49, 1


1-2-rad-2, generate

1, 49, 1


3, generate

1, 49, 1

Appendix F

290


1-2-rad-4, generate

1, 49, 1


2, generate

1, 49, 1


1-2-rad-3, generate

1, 49, 1


4, generate

1, 49, 1

*Surface, type=ELEMENT, name=WF-CONCRETE-INTERFACE

_WF-CONCRETE-INTERFACE_S1, S1




*Elset, elset=_m_Surf-2_S5, internal, instance="concrete wall-1"

649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660,

1984, 1985, 1986, 1987

1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 3319, 3320, 3321, 3322,

3323, 3324, 3325, 3326

3327, 3328, 3329, 3330, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661,

4662, 4663, 4664, 4665

5989, 5990, 5991, 5992, 5993, 5994, 5995, 5996, 5997, 5998, 5999, 6000,

7324, 7325, 7326, 7327

7328, 7329, 7330, 7331, 7332, 7333, 7334, 7335, 8659, 8660, 8661, 8662,

8663, 8664, 8665, 8666

8667, 8668, 8669, 8670


985, 998, 1011, 1024, 1037, 1050, 1063, 1076, 1089, 1102, 1115, 1128,

1141, 1154, 1167, 1180

1193, 1206, 1219, 1232, 1245, 1258, 1271, 1284, 1297, 1310, 1323, 2320,

2333, 2346, 2359, 2372

2385, 2398, 2411, 2424, 2437, 2450, 2463, 2476, 2489, 2502, 2515, 2528,

2541, 2554, 2567, 2580

2593, 2606, 2619, 2632, 2645, 2658, 3655, 3668, 3681, 3694, 3707, 3720,

3733, 3746, 3759, 3772

3785, 3798, 3811, 3824, 3837, 3850, 3863, 3876, 3889, 3902, 3915, 3928,

3941, 3954, 3967, 3980

3993, 4990, 5003, 5016, 5029, 5042, 5055, 5068, 5081, 5094, 5107, 5120,

5133, 5146, 5159, 5172

Appendix F

291

5185, 5198, 5211, 5224, 5237, 5250, 5263, 5276, 5289, 5302, 5315, 5328,

6325, 6338, 6351, 6364

6377, 6390, 6403, 6416, 6429, 6442, 6455, 6468, 6481, 6494, 6507, 6520,

6533, 6546, 6559, 6572

6585, 6598, 6611, 6624, 6637, 6650, 6663, 7660, 7673, 7686, 7699, 7712,

7725, 7738, 7751, 7764

7777, 7790, 7803, 7816, 7829, 7842, 7855, 7868, 7881, 7894, 7907, 7920,

7933, 7946, 7959, 7972

7985, 7998, 8995, 9008, 9021, 9034, 9047, 9060, 9073, 9086, 9099, 9112,

9125, 9138, 9151, 9164

9177, 9190, 9203, 9216, 9229, 9242, 9255, 9268, 9281, 9294, 9307, 9320,

9333

*Elset, elset=_m_Surf-2_S1, internal, instance="concrete wall-1", generate

1, 1335, 1


8011, 9345, 1

*Surface, type=ELEMENT, name=m_Surf-2

_m_Surf-2_S5, S5

_m_Surf-2_S6, S6

_m_Surf-2_S2, S2

_m_Surf-2_S1, S1

*Elset, elset=_m_Surf-4_S6, internal, instance=TOP-RESTRAINT-1-rad-2,

generate

1201, 1560, 1

*Elset, elset=_m_Surf-4_S1, internal, instance=TOP-RESTRAINT-1-rad-2,

generate

721, 1080, 1


_m_Surf-4_S6, S6

_m_Surf-4_S1, S1


12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144,

156, 168, 180, 192

204, 216, 228, 240, 1347, 1359, 1371, 1383, 1395, 1407, 1419, 1431,

1443, 1455, 1467, 1479

1491, 1503, 1515, 1527, 1539, 1551, 1563, 1575, 2682, 2694, 2706, 2718,

2730, 2742, 2754, 2766

2778, 2790, 2802, 2814, 2826, 2838, 2850, 2862, 2874, 2886, 2898, 2910,

4017, 4029, 4041, 4053

4065, 4077, 4089, 4101, 4113, 4125, 4137, 4149, 4161, 4173, 4185, 4197,

4209, 4221, 4233, 4245

Appendix F

292

5352, 5364, 5376, 5388, 5400, 5412, 5424, 5436, 5448, 5460, 5472, 5484,

5496, 5508, 5520, 5532

5544, 5556, 5568, 5580, 6687, 6699, 6711, 6723, 6735, 6747, 6759, 6771,

6783, 6795, 6807, 6819

6831, 6843, 6855, 6867, 6879, 6891, 6903, 6915, 8022, 8034, 8046, 8058,

8070, 8082, 8094, 8106

8118, 8130, 8142, 8154, 8166, 8178, 8190, 8202, 8214, 8226, 8238, 8250


565, 577, 589, 601, 613, 625, 637, 1900, 1912, 1924, 1936, 1948,

1960, 1972, 3235, 3247

3259, 3271, 3283, 3295, 3307, 4570, 4582, 4594, 4606, 4618, 4630, 4642,

5905, 5917, 5929, 5941

5953, 5965, 5977, 7240, 7252, 7264, 7276, 7288, 7300, 7312, 8575, 8587,

8599, 8611, 8623, 8635

8647,


1323, 1324, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 1332, 1333, 1334,

1335, 2658, 2659, 2660

2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 2670, 3993, 3994,

3995, 3996, 3997, 3998

3999, 4000, 4001, 4002, 4003, 4004, 4005, 5328, 5329, 5330, 5331, 5332,

5333, 5334, 5335, 5336

5337, 5338, 5339, 5340, 6663, 6664, 6665, 6666, 6667, 6668, 6669, 6670,

6671, 6672, 6673, 6674

6675, 7998, 7999, 8000, 8001, 8002, 8003, 8004, 8005, 8006, 8007, 8008,

8009, 8010, 9333, 9334

9335, 9336, 9337, 9338, 9339, 9340, 9341, 9342, 9343, 9344, 9345


1, 1335, 1


8011, 9345, 1


_m_Surf-6_S4, S4

_m_Surf-6_S6, S6

_m_Surf-6_S2, S2

_m_Surf-6_S3, S3

_m_Surf-6_S1, S1


1, 1335, 1


_m_Surf-13_S1, S1


Appendix F

293

145, 157, 169, 181, 193, 205, 217, 229, 805, 817, 829, 841,

853, 865, 877, 889

901, 913, 925, 937, 949, 961, 973, 1480, 1492, 1504, 1516, 1528,

1540, 1552, 1564, 2140

2152, 2164, 2176, 2188, 2200, 2212, 2224, 2236, 2248, 2260, 2272, 2284,

2296, 2308, 2815, 2827

2839, 2851, 2863, 2875, 2887, 2899, 3475, 3487, 3499, 3511, 3523, 3535,

3547, 3559, 3571, 3583

3595, 3607, 3619, 3631, 3643, 4150, 4162, 4174, 4186, 4198, 4210, 4222,

4234, 4810, 4822, 4834

4846, 4858, 4870, 4882, 4894, 4906, 4918, 4930, 4942, 4954, 4966, 4978,

5485, 5497, 5509, 5521

5533, 5545, 5557, 5569, 6145, 6157, 6169, 6181, 6193, 6205, 6217, 6229,

6241, 6253, 6265, 6277

6289, 6301, 6313, 6820, 6832, 6844, 6856, 6868, 6880, 6892, 6904, 7480,

7492, 7504, 7516, 7528

7540, 7552, 7564, 7576, 7588, 7600, 7612, 7624, 7636, 7648, 8155, 8167,

8179, 8191, 8203, 8215

8227, 8239, 8815, 8827, 8839, 8851, 8863, 8875, 8887, 8899, 8911, 8923,

8935, 8947, 8959, 8971

8983,


252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384,

396, 408, 420, 576

588, 600, 612, 624, 636, 648, 997, 1010, 1023, 1036, 1049, 1062,

1075, 1088, 1101, 1114

1127, 1140, 1153, 1166, 1179, 1587, 1599, 1611, 1623, 1635, 1647, 1659,

1671, 1683, 1695, 1707

1719, 1731, 1743, 1755, 1911, 1923, 1935, 1947, 1959, 1971, 1983, 2332,

2345, 2358, 2371, 2384

2397, 2410, 2423, 2436, 2449, 2462, 2475, 2488, 2501, 2514, 2922, 2934,

2946, 2958, 2970, 2982

2994, 3006, 3018, 3030, 3042, 3054, 3066, 3078, 3090, 3246, 3258, 3270,

3282, 3294, 3306, 3318

3667, 3680, 3693, 3706, 3719, 3732, 3745, 3758, 3771, 3784, 3797, 3810,

3823, 3836, 3849, 4257

4269, 4281, 4293, 4305, 4317, 4329, 4341, 4353, 4365, 4377, 4389, 4401,

4413, 4425, 4581, 4593

4605, 4617, 4629, 4641, 4653, 5002, 5015, 5028, 5041, 5054, 5067, 5080,

5093, 5106, 5119, 5132

5145, 5158, 5171, 5184, 5592, 5604, 5616, 5628, 5640, 5652, 5664, 5676,

5688, 5700, 5712, 5724

Appendix F

294

5736, 5748, 5760, 5916, 5928, 5940, 5952, 5964, 5976, 5988, 6337, 6350,

6363, 6376, 6389, 6402

6415, 6428, 6441, 6454, 6467, 6480, 6493, 6506, 6519, 6927, 6939, 6951,

6963, 6975, 6987, 6999

7011, 7023, 7035, 7047, 7059, 7071, 7083, 7095, 7251, 7263, 7275, 7287,

7299, 7311, 7323, 7672

7685, 7698, 7711, 7724, 7737, 7750, 7763, 7776, 7789, 7802, 7815, 7828,

7841, 7854, 8262, 8274

8286, 8298, 8310, 8322, 8334, 8346, 8358, 8370, 8382, 8394, 8406, 8418,

8430, 8586, 8598, 8610

8622, 8634, 8646, 8658, 9007, 9020, 9033, 9046, 9059, 9072, 9085, 9098,

9111, 9124, 9137, 9150

9163, 9176, 9189


1, 1335, 1


8011, 9345, 1


_m_Surf-20_S6, S6

_m_Surf-20_S4, S4

_m_Surf-20_S2, S2

_m_Surf-20_S1, S1

*Elset, elset=_s_Surf-2_S6, internal, instance=TOP-RESTRAINT-1, generate

1201, 1560, 1


721, 1080, 1

*Surface, type=ELEMENT, name=s_Surf-2

_s_Surf-2_S6, S6

_s_Surf-2_S1, S1

*Elset, elset=_s_Surf-4_S5, internal, instance="concrete wall-1"

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

1336, 1337, 1338, 1339

1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 2671, 2672, 2673, 2674,

2675, 2676, 2677, 2678

2679, 2680, 2681, 2682, 4006, 4007, 4008, 4009, 4010, 4011, 4012, 4013,

4014, 4015, 4016, 4017

5341, 5342, 5343, 5344, 5345, 5346, 5347, 5348, 5349, 5350, 5351, 5352,

6676, 6677, 6678, 6679

6680, 6681, 6682, 6683, 6684, 6685, 6686, 6687, 8011, 8012, 8013, 8014,

8015, 8016, 8017, 8018

8019, 8020, 8021, 8022


Appendix F

295

241, 253, 265, 277, 289, 301, 313, 325, 337, 349, 361, 373,

385, 397, 409, 421

433, 445, 457, 469, 481, 493, 505, 517, 529, 541, 553, 1576,

1588, 1600, 1612, 1624

1636, 1648, 1660, 1672, 1684, 1696, 1708, 1720, 1732, 1744, 1756, 1768,

1780, 1792, 1804, 1816

1828, 1840, 1852, 1864, 1876, 1888, 2911, 2923, 2935, 2947, 2959, 2971,

2983, 2995, 3007, 3019

3031, 3043, 3055, 3067, 3079, 3091, 3103, 3115, 3127, 3139, 3151, 3163,

3175, 3187, 3199, 3211

3223, 4246, 4258, 4270, 4282, 4294, 4306, 4318, 4330, 4342, 4354, 4366,

4378, 4390, 4402, 4414

4426, 4438, 4450, 4462, 4474, 4486, 4498, 4510, 4522, 4534, 4546, 4558,

5581, 5593, 5605, 5617

5629, 5641, 5653, 5665, 5677, 5689, 5701, 5713, 5725, 5737, 5749, 5761,

5773, 5785, 5797, 5809

5821, 5833, 5845, 5857, 5869, 5881, 5893, 6916, 6928, 6940, 6952, 6964,

6976, 6988, 7000, 7012

7024, 7036, 7048, 7060, 7072, 7084, 7096, 7108, 7120, 7132, 7144, 7156,

7168, 7180, 7192, 7204

7216, 7228, 8251, 8263, 8275, 8287, 8299, 8311, 8323, 8335, 8347, 8359,

8371, 8383, 8395, 8407

8419, 8431, 8443, 8455, 8467, 8479, 8491, 8503, 8515, 8527, 8539, 8551,

8563

*Elset, elset=_s_Surf-4_S1, internal, instance="concrete wall-1", generate

1, 1335, 1


8011, 9345, 1


_s_Surf-4_S5, S5

_s_Surf-4_S6, S6

_s_Surf-4_S2, S2

_s_Surf-4_S1, S1

*Elset, elset=_s_Surf-6_S6, internal, instance=RESTRAINT-SIDE-1, generate

1431, 1760, 1


1, 880, 1


991, 1320, 1


_s_Surf-6_S6, S6

_s_Surf-6_S4, S4

Appendix F

296

_s_Surf-6_S1, S1


553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564,

1888, 1889, 1890, 1891

1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 3223, 3224, 3225, 3226,

3227, 3228, 3229, 3230

3231, 3232, 3233, 3234, 4558, 4559, 4560, 4561, 4562, 4563, 4564, 4565,

4566, 4567, 4568, 4569

5893, 5894, 5895, 5896, 5897, 5898, 5899, 5900, 5901, 5902, 5903, 5904,

7228, 7229, 7230, 7231

7232, 7233, 7234, 7235, 7236, 7237, 7238, 7239, 8563, 8564, 8565, 8566,

8567, 8568, 8569, 8570

8571, 8572, 8573, 8574


660, 672, 684, 696, 708, 720, 732, 744, 756, 768, 780, 792,

804, 816, 828, 840

852, 864, 876, 888, 900, 912, 924, 936, 948, 960, 972, 984,

1995, 2007, 2019, 2031

2043, 2055, 2067, 2079, 2091, 2103, 2115, 2127, 2139, 2151, 2163, 2175,

2187, 2199, 2211, 2223

2235, 2247, 2259, 2271, 2283, 2295, 2307, 2319, 3330, 3342, 3354, 3366,

3378, 3390, 3402, 3414

3426, 3438, 3450, 3462, 3474, 3486, 3498, 3510, 3522, 3534, 3546, 3558,

3570, 3582, 3594, 3606

3618, 3630, 3642, 3654, 4665, 4677, 4689, 4701, 4713, 4725, 4737, 4749,

4761, 4773, 4785, 4797

4809, 4821, 4833, 4845, 4857, 4869, 4881, 4893, 4905, 4917, 4929, 4941,

4953, 4965, 4977, 4989

6000, 6012, 6024, 6036, 6048, 6060, 6072, 6084, 6096, 6108, 6120, 6132,

6144, 6156, 6168, 6180

6192, 6204, 6216, 6228, 6240, 6252, 6264, 6276, 6288, 6300, 6312, 6324,

7335, 7347, 7359, 7371

7383, 7395, 7407, 7419, 7431, 7443, 7455, 7467, 7479, 7491, 7503, 7515,

7527, 7539, 7551, 7563

7575, 7587, 7599, 7611, 7623, 7635, 7647, 7659, 8670, 8682, 8694, 8706,

8718, 8730, 8742, 8754

8766, 8778, 8790, 8802, 8814, 8826, 8838, 8850, 8862, 8874, 8886, 8898,

8910, 8922, 8934, 8946

8958, 8970, 8982, 8994


1, 1335, 1


Appendix F

297

8011, 9345, 1


_s_Surf-8_S3, S3

_s_Surf-8_S4, S4

_s_Surf-8_S2, S2

_s_Surf-8_S1, S1


1431, 1760, 1


1, 880, 1


991, 1320, 1


_s_Surf-10_S6, S6

_s_Surf-10_S4, S4

_s_Surf-10_S1, S1

*Elset, elset=_s_Surf-11_S1, internal, instance=TOP-RESTRAINT-1-rad-2

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

13, 14, 15, 16

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,

29, 30, 31, 32

33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,

45, 46, 47, 48

49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,

61, 62, 63, 64

65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,

77, 78, 79, 80

81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,

93, 94, 95, 96

97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,

109, 110, 111, 112

113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,

125, 126, 127, 128

129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,

141, 142, 143, 144

145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156,

157, 158, 159, 160

161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172,

173, 174, 175, 176

177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188,

189, 190, 191, 192

Appendix F

298

193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204,

205, 206, 207, 208

209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,

221, 222, 223, 224

225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236,

237, 238, 239, 240

241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252,

253, 254, 255, 256

257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268,

269, 270, 271, 272

273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284,

285, 286, 287, 288

289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300,

301, 302, 303, 304

305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316,

317, 318, 319, 320

321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332,

333, 334, 335, 336

337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348,

349, 350, 351, 352

353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364,

365, 366, 367, 368

369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380,

381, 382, 383, 384

385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396,

397, 398, 399, 400

401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412,

413, 414, 415, 416

417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428,

429, 430, 431, 432

433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444,

445, 446, 447, 448

449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460,

461, 462, 463, 464

465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476,

477, 478, 479, 480

481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492,

493, 494, 495, 496

497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508,

509, 510, 511, 512

513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524,

525, 526, 527, 528

Appendix F

299

529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540,

541, 542, 543, 544

545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,

557, 558, 559, 560

561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572,

573, 574, 575, 576

577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588,

589, 590, 591, 592

593, 594, 595, 596, 597, 598, 599, 600, 721, 722, 723, 724,

725, 726, 727, 728

729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740,

741, 742, 743, 744

745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756,

757, 758, 759, 760

761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772,

773, 774, 775, 776

777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788,

789, 790, 791, 792

793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804,

805, 806, 807, 808

809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820,

821, 822, 823, 824

825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836,

837, 838, 839, 840

841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852,

853, 854, 855, 856

857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868,

869, 870, 871, 872

873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884,

885, 886, 887, 888

889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900,

901, 902, 903, 904

905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916,

917, 918, 919, 920

921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932,

933, 934, 935, 936

937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948,

949, 950, 951, 952

953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964,

965, 966, 967, 968

969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980,

981, 982, 983, 984

Appendix F

300

985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996,

997, 998, 999, 1000

1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012,

1013, 1014, 1015, 1016

1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028,

1029, 1030, 1031, 1032

1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044,

1045, 1046, 1047, 1048

1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060,

1061, 1062, 1063, 1064

1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076,

1077, 1078, 1079, 1080

*Elset, elset=_s_Surf-11_S6, internal, instance=TOP-RESTRAINT-1-rad-2,

generate

1201, 1560, 1


_s_Surf-11_S1, S1

_s_Surf-11_S6, S6

*Elset, elset=_s_Surf-12_S1, internal, instance=TOP-RESTRAINT-1

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

13, 14, 15, 16

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,

29, 30, 31, 32

33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,

45, 46, 47, 48

49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,

61, 62, 63, 64

65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,

77, 78, 79, 80

81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,

93, 94, 95, 96

97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,

109, 110, 111, 112

113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,

125, 126, 127, 128

129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,

141, 142, 143, 144

145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156,

157, 158, 159, 160

161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172,

173, 174, 175, 176

Appendix F

301

177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188,

189, 190, 191, 192

193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204,

205, 206, 207, 208

209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,

221, 222, 223, 224

225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236,

237, 238, 239, 240

241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252,

253, 254, 255, 256

257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268,

269, 270, 271, 272

273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284,

285, 286, 287, 288

289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300,

301, 302, 303, 304

305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316,

317, 318, 319, 320

321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332,

333, 334, 335, 336

337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348,

349, 350, 351, 352

353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364,

365, 366, 367, 368

369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380,

381, 382, 383, 384

385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396,

397, 398, 399, 400

401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412,

413, 414, 415, 416

417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428,

429, 430, 431, 432

433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444,

445, 446, 447, 448

449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460,

461, 462, 463, 464

465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476,

477, 478, 479, 480

481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492,

493, 494, 495, 496

497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508,

509, 510, 511, 512

Appendix F

302

513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524,

525, 526, 527, 528

529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540,

541, 542, 543, 544

545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556,

557, 558, 559, 560

561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572,

573, 574, 575, 576

577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588,

589, 590, 591, 592

593, 594, 595, 596, 597, 598, 599, 600, 721, 722, 723, 724,

725, 726, 727, 728

729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740,

741, 742, 743, 744

745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756,

757, 758, 759, 760

761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772,

773, 774, 775, 776

777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788,

789, 790, 791, 792

793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804,

805, 806, 807, 808

809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820,

821, 822, 823, 824

825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836,

837, 838, 839, 840

841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852,

853, 854, 855, 856

857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868,

869, 870, 871, 872

873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884,

885, 886, 887, 888

889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900,

901, 902, 903, 904

905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916,

917, 918, 919, 920

921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932,

933, 934, 935, 936

937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948,

949, 950, 951, 952

953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964,

965, 966, 967, 968

Appendix F

303

969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980,

981, 982, 983, 984

985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996,

997, 998, 999, 1000

1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012,

1013, 1014, 1015, 1016

1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028,

1029, 1030, 1031, 1032

1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044,

1045, 1046, 1047, 1048

1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060,

1061, 1062, 1063, 1064

1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076,

1077, 1078, 1079, 1080


1201, 1560, 1


_s_Surf-12_S1, S1

_s_Surf-12_S6, S6

*Elset, elset=_s_Surf-15_S1, internal, instance=CFRP-DF-SOLID-1, generate

1, 182, 1

*Elset, elset=_s_Surf-15_S1, internal, instance=CFRP-DF-SOLID-1-rad-2,

generate

1, 182, 1


generate

1, 182, 1


generate

1, 182, 1


_s_Surf-15_S1, S1

*Elset, elset=_s_Surf-17_S1, internal, instance=CFRP-DF-SOLID-1, generate

1, 182, 1


generate

1, 182, 1


generate

1, 182, 1


generate

Appendix F

304

1, 182, 1


_s_Surf-17_S1, S1

** Constraint: REB TO CONC

*Embedded Element, host elset="concrete wall-1"."CONCRETE WALL"

REBARS-1.REBARS

*End Assembly

**

** MATERIALS

**

*Material, name=CFRP

*Density

0.0003,

*Elastic, type=ENGINEERING CONSTANTS

234000.,4500.,4500., 0.3, 0.3, 0.45,2779.,2779.

1550.,

*Material, name=CONCRETE-MATERIAL

*Density

0.0026,

*Elastic

30678., 0.2

*Concrete Damaged Plasticity

12., 0.1, 1.16, 0.67, 0.00001

*Concrete Compression Hardening

12.267, 0.

18.3797, 0.0002

24.4429, 0.0004

30.4065, 0.0006

36.2001, 0.0008

41.7336, 0.001

46.9014, 0.0012

51.5888, 0.0014

55.6818, 0.0016

60.7621, 0.001921

64.6772, 0.0025

62.9724, 0.003

61.2813, 0.0032

59.1806, 0.0034

53.22, 0.0038716

48.619, 0.0042074

*Concrete Tension Stiffening, type=GFI

4.4, 94.9

Appendix F

305

*Concrete Compression Damage

0., 0.

0., 0.0002

0., 0.0004

0., 0.0006

0., 0.0008

0., 0.001

0., 0.0012

0., 0.0014

0., 0.0016

0., 0.001921

0., 0.0025

0.0263591, 0.003

0.0525054, 0.0032

0.0849857, 0.0034

0.177145, 0.0038716

0.248283, 0.0042074

*Material, name=STEEL-REBARS

*Density

7.85e-06,

*Elastic

210000., 0.3

*Plastic

450.,0.

*Material, name=STREEL-RESTRAINT

*Density

7.85e-06,

*Elastic

210000., 0.3

**

** INTERACTION PROPERTIES

**

*Surface Interaction, name=COHESIVE

1.,

*Cohesive Behavior

1750.,650.,650.

*Damage Initiation, criterion=MAXS

2.5, 1.5, 1.5

*Damage Evolution, type=ENERGY, softening=EXPONENTIAL, mixed mode

behavior=BK, power=1.45

0.09, 0.9, 0.9

*Surface Interaction, name=FRICTIONLESS

Appendix F

306

1.,

*Friction

0.,

*Surface Interaction, name=INTEARCTION

1.,

*Friction, rough

*Surface Behavior, pressure-overclosure=HARD

*Surface Interaction, name=TANGENTIAL

1.,

*Surface Behavior, pressure-overclosure=HARD

**

** INTERACTIONS

**

** Interaction: BOTTOM-RESTRAINT

*Contact Pair, interaction=INTEARCTION, type=SURFACE TO SURFACE, adjust=0.0,

tied

s_Surf-11, s_Surf-4

** Interaction: COHESIVE CONTACT

*Contact Pair, interaction=COHESIVE, small sliding, type=SURFACE TO SURFACE,

adjust=0.0, tied

WF-CONCRETE-INTERFACE, m_Surf-20

** Interaction: SIDE-LEFT

*Contact Pair, interaction=FRICTIONLESS, small sliding, type=SURFACE TO

SURFACE, adjust=0.0, tied

s_Surf-10, s_Surf-8

** Interaction: SIDE-RIGHT

*Contact Pair, interaction=FRICTIONLESS, small sliding, type=SURFACE TO

SURFACE, adjust=0.0,

s_Surf-6, m_Surf-6

** Interaction: TOP-RESTRAINT

*Contact Pair, interaction=INTEARCTION, type=SURFACE TO SURFACE, adjust=0.0,

tied

s_Surf-12, m_Surf-2

** ----------------------------------------------------------------

**

** STEP: RIKS

**

*Step, name=RIKS, nlgeom=YES, inc=1000000

*Static, riks

0.05, 20., 1e-25, , ,

**

** BOUNDARY CONDITIONS

Appendix F

307

**

** Name: BC-BOT Type: Displacement/Rotation

*Boundary

Set-5, 1, 1

Set-5, 2, 2

Set-5, 3, 3

** Name: BC-TOP Type: Displacement/Rotation

*Boundary

Set-7, 1, 1

Set-7, 3, 3

** Name: SIDE-RESTRAINT Type: Displacement/Rotation

*Boundary

Set-8, 1, 1

Set-8, 3, 3

Set-8, 4, 4

Set-8, 6, 6

**

** LOADS

**

** Name: LOAD Type: Pressure

*Dsload

Surf-1, P, 5.

**

** OUTPUT REQUESTS

**

*Restart, write, frequency=0

**

** FIELD OUTPUT: F-Output-1

**

*Output, field

*Node Output

CF, RF, RM, U, UR, UT

*Element Output, directions=YES

DAMAGEC, DAMAGET, LE, MISES, PE, PEEQ, PEEQT, PEMAG, S

*Contact Output

CDISP, CSTATUS, CSTRESS, CSTRESSETOS

**

** HISTORY OUTPUT: DEFLECTION-MID-WAY

**

*Output, history

*Node Output, nset=DEFLECTION

U3,

Appendix F

308

**

** HISTORY OUTPUT: REACTIN FORCE

**

*Node Output, nset=REACTION-FORCE

RF2,

*End Step

Mehdi Mohamamdpour Lima - Griffith University

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