Investigation of Structural Behaviour of Geopolymer

Investigation of Structural Behaviour of Geopolymer

Prestressed Concrete Beam

By

Kamal Neupane

B. E. (Civil), M. Phil.

A thesis submitted in fulfilment of the

requirements for the degree of

Doctor of Philosophy

The University of Sydney

School of Civil Engineering

Faculty of Engineering

2020

ii

CERTIFICATE OF ORIGINAL AUTHORSHIP I, hereby declare that the work in this thesis has not been previously submitted for a

degree nor has it been submitted as part of requirements for a degree except as fully

acknowledged within the text.

I also certify that the thesis has been written by me. Any help that I have received in

my research work and the preparation of the thesis itself has been acknowledged. In

addition, I certify that all information sources and literature used are indicated in this

thesis.

-----------------------------

Kamal Neupane

October 2020

iii

ACKNOWLEDGMENTS First of all, I would like to express my sincere gratitude to my principal supervisor Dr.

Ali Hadigheh and auxiliary supervisor Associate Professor Daniel Dias-da-Costa for

their guidance and valuable suggestions in this research study. I would like to thank the

School of Civil Engineering, the University of Sydney for the scholarship and other

supports provided in this research study.

I would also like to thank Cement Australia Pty Ltd, Darra, Qld. for the supply of raw

materials and Boral Materials Technical Services, Baulkham Hills, NSW for the

laboratory services provided in this study. This research would not be possible without

their valuable supports and cooperation.

I am grateful to my family, especially my parents and my wife for their continuous

encouragement and support during the hard time of my life. Last but not the least, I

would like to thank all of them who have lent their helping hand in this venture, directly

or indirectly.

Kamal Neupane

October 2020

iv

ABSTRACT

Production of ordinary Portland cement (OPC) is a carbon-intensive process that

generates significant amounts of carbon dioxide (CO2) gas from the combustion of

fossil fuels and thermal decomposition of limestone. Overall, cement industries are

responsible for around 7% of global CO2 emissions which poses a considerable threat

to global climate change because of its greenhouse effects. Geopolymer is an inorganic

polymer material having similar binding properties to OPC which can be produced from

aluminosilicate compounds, such as fly ash when activated by alkaline solution. The

recent advent of geopolymer technology shows great potential to reduce carbon

footprints by utilising industrial by-products, such as fly ash and ground granulated

blast furnace slag (GGBS), and convert into effective binding material.

The setting and hardening process of geopolymer binder is different from hydration of

OPC, called “geopolymerisation” which is the condensation process of aluminate and

silicate monomers to form a polymer chain. Generally, fly ash-based geopolymer

concrete attains relatively lower early-age strength at ambient temperature due to the

slow rate of reaction. However, geopolymer concrete based on GGBS or a combination

of fly ash and GGBS can set and harden in ambient temperature with comparable early

age strength to OPC concrete of same grade. In the recent past, several studies were

carried out to investigate mechanical, serviceability, durability and microstructural

properties of geopolymer concrete using different aluminosilicate materials. However,

limited research has been carried out on applications of geopolymer binder in structural

concrete, such as reinforced concrete beam, column and prestressed concrete beam.

Prestressed concrete is a construction technique in which flexural tensile stress

generated in the concrete member due to imposed load is counteracted by applying an

initial prestressing compressive force. The use of prestressed concrete structures has

been increasing in modern construction practices because they can withstand

significantly higher flexural load with minimal deflection and cracks than conventional

reinforced concrete (RC) members of similar cross-section. Generally, tensile strength

of concrete is ignored in the design of conventional RC structures. However, tensile or

flexural strengths of concrete are significant in the design of prestressed concrete

v

structures where tensile strength of concrete limits the maximum permissible

prestressing load according to ACI 318. Application of higher prestressing load can

increase the load-carrying capacity of prestressed concrete structures and minimize

their deflection under service load. Previous results showed that geopolymer concrete

possesses higher indirect-tensile and flexural strength than OPC concrete for the same

compressive strength. In addition, time-dependent losses of prestressing stress are the

major serviceability problems of prestressed concrete structure which reduce the load-

carrying capacity of structures and increase the deflection under service loads. The

time-dependent losses of prestressing stress are directly proportional to the amount of

shrinkage and creep strains of concrete. Having smaller drying shrinkage and creep

strains, geopolymer concrete can result in better serviceability than OPC concrete in

prestressed concrete structures. Thus, this study investigates the application of

geopolymer concrete in the prestressed concrete beam which may be a worthwhile

utilization of geopolymer concrete in concrete structures.

Despite having higher mechanical strengths and durability properties than conventional

OPC concrete, geopolymer concrete has not been widely used in structural grade

concrete, so far. The safety hazards in mixing and handling of concrete due to the use

of liquid sodium hydroxide in geopolymer binder is one of the barriers to the adaptation

of geopolymer in concrete industry. In this study, the mechanical and serviceability

properties of grade 50 MPa geopolymer concrete from sodium hydroxide-free one-part

geopolymer binder are investigated under ambient temperature curing and compared

against same grade OPC concrete. Development of strengths at an early age under

accelerated curing is investigated to study the suitability of geopolymer concrete in

precast prestressed concrete structures. Finite element models of prestressed concrete

beams of three different lengths and sizes are analysed to investigate their load-

deflection behaviours under imposed load for short-term and long-term durations using

the Abaqus program. The effects of tensile strength of concrete in load-deflection

behaviours of prestressed concrete beams are studied by comparing the results between

identical geopolymer and OPC prestressed concrete beams.

This study finds that geopolymer concrete has around 27% higher indirect-tensile and

flexural strengths than OPC concrete of same strength grade which contributes to

vi

geopolymer prestressed concrete beams to withstand around 20% higher first-crack

load than OPC concrete beams of same span. In addition, geopolymer prestressed

concrete beams show a relatively smaller loss in prestressing stress which results in a

smaller loss in flexural capacity of beams over the service life of the structure.

vii

LIST OF PUBLICATIONS Journal Paper

Neupane, K., Hadigheh, S.A., “Sodium Hydroxide-free Geopolymer Binder for

Prestressed Concrete Applications”, Under review by Journal of Construction and

Building Materials (2020).

Conference Paper

Neupane, K., Hadigheh, A. and Dias-da-Costa, D., “Numerical Study on the Structural

Behaviour of a Geopolymer Prestressed Concrete Beam”, Biennial Conference of the

Concrete Institute of Australia (Concrete 2019), Sydney, Australia, 8-12 September

2019.

viii

LIST OF ABBREVIATIONS ACI American Concrete Institute

Al aluminium metal

Al2O3 aluminium oxide (alumina)

aq aqueous solution

AS Australian Standard

ASTM American Society for Testing and Materials

C3A tricalcium aluminate

CaO calcium oxide (quick lime)

(CaO)3(Al2O3)(CaSO4)3·32H2O hydrated calcium aluminium sulphate or

ettringite

Ca(OH)2 calcium hydroxide (hydrated lime)

C-A-S-H calcium aluminate silicate hydrate gel

CDP concrete damaged plasticity

CIA Concrete Institute of Australia

CO2 carbon dioxide

C-S-H calcium silicate hydrate

DEF delay ettringite formation

EN European Standard (Europäische Norm)

Fe2O3 iron oxide (ferric oxide)

GGBS ground granulated blast furnace slag

GP general purpose Portland cement

HCL hydrochloric acid

H2CO3 carbonic acid

H2O water molecule or water

HWR high range water-reducing admixture or superplasticiser

H2SO4 sulphuric acid

K potassium metal

KOH potassium hydroxide (caustic potash)

LOI loss on ignition

M molarity of solution

ix

MgSO4 magnesium sulphate

N normality of solution

N-A neutral axis of concrete section at flexural

NZS New Zealand Standard

Na sodium metal

NaAlO2 sodium aluminate (Na2Al2O4 or Na2O·Al2O3)

NaOH sodium hydroxide (caustic soda)

Na2O sodium oxide

Na2O∙SiO2 or Na2SiO3 sodium silicate or sodium metasilicate or waterglass

Na2SO4 sodium sulphate

OPC ordinary Portland cement or Portland cement

PPR partial prestressing ratio

Pty Ltd proprietary limited

RC reinforced concrete

SCC self–compacting concrete or self-consolidating concrete

SCMs supplementary cementitious materials

Si silicon metal

SiO2 silicon dioxide or silica

SO3 sulphur trioxide

WR water-reducing admixture or normal water reducer

w/b water to binder ratio

w/c water to cement ratio

x

LIST OF NOTATIONS

Symbols Definition

�� = gross area of the beam cross-section

�� = area of the prestressing tendon

�� = area of total conventional longitudinal reinforcement

�� = area longitudinal compressive reinforcement

�� = area of conventional longitudinal tensile reinforcement

� = width or breadth of rectangular concrete section

� = effective depth of concrete section

� = overall depth of concrete section

db = diameter of embedded bar

�� = damage variable at compression

�� = depth of prestressing tendon from topmost concrete fibre

�� = depth of neutral axis from top fibre

��.� = depth of neutral axis from top fibre at ultimate load

�� = damage variable at tension

� = maximum eccentricity of prestressing tendon

�� or � = modulus of elasticity of concrete

E� = initial (undamaged) modulus of elasticity of concrete

�� = modulus of elasticity prestressing steel

�� = modulus of elasticity conventional steel

� = factor depend on curing time-ratio of concrete specimen

�� = stress on concrete at any level of strain

�� = characteristic compressive strength of concrete at 28 days

��" = maximum compressive stress of concrete in flexure

�� = mean concrete compressive strength at 28 days

�� = concrete compressive strength at prestress transfer

�� = characteristic breaking strength of prestressing steel

�� = yield strength of prestresssing steel

�� = mean flexural strength of concrete

�� = concrete flexural strength at prestress transfer

xi

�� = characteristic flexural tensile strength of concrete

�� = yield strength conventional reinforcing steel

�′�� = characteristic indirect tensile strength of concrete

�� = mean indirect tensile strength of concrete

�� = concrete tensile stress at any level of strain

�′� = characteristic tensile strength of concrete

�� = fracture energy required to open a unit area of crack

�� = second moment of area of fully cracked beam cross section

�� = effective second moment of area of beam cross section

�� = gross second moment of area of beam cross-section

��, ��, �� , �� = modification factors depending on thickness and age of concrete

� = stiffness of cohesive surface

�� = a coefficient, depends on the duration of prestressing force

�� = is a coefficient, depends on the prestressing ratio

Ld = development length of reinforcement bar

�� = cracking moment of the beam cross section

�� = ultimate moment capacity of the beam cross section

� = normal distribution factor

�� = effective prestressing load

�� = initial (applied) prestressing load

�� = ultimate load capacity of flexural members

� = prestress loss due to relaxation of tendon as following

�� = basic relaxation of tendon based on 1000 hours of duration at 20 °C

S = surface area of concrete member

s = standard deviation of concrete cylinder strength

� = elastic strain energy

�� = fracture energy required per number of crack

� = volume of concrete member

� or �� = vertical distance of bottommost fibre from neutral axis

��.�� = vertical distance of bottommost fibre from neutral axis at cracking

(first-crack) load

xii

��.� = vertical distance of bottommost fibre from neutral axis at ultimate

load

z = section modulus of beam cross section

� = a factor, depends on curing time-ratio of concrete specimen

β = tensile stress-strain parameter of concrete

� = compressive stress block factor of concrete

ΔP = prestress loss due to axial shortening of concrete member

�� = time from the end of initial curing of concrete specimen

Δσ�.�� = prestress loss due to creep strain

��.�� = prestress loss due to shrinkage strain

� = tensile displacement (cracking) on concrete

�� = critical separation of steel concrete bond

�� = maximum slippage distance of steel concrete bond

�� = maximum tensile displacement when flexural stress reaches zero

ɛ = strain in concrete at any stage of loading

�� = compressive strain at concrete

ε�� = creep strain of concrete member at any time

��

= equivalent plastic strain of concrete at compression

�� = drying shrinkage strain of concrete

��.� = basic drying shrinkage strain of concrete

��.�∗ = final basic drying shrinkage strain of concrete

�� = critical strain (strain at maximum stress) of concrete at compression

�� = tensile strain of concrete at maximum stress

ɛ�� = strain in the compressive reinforcement bar

�� = drying shrinkage of concrete specimen at any time

�� = ultimate shrinkage strain of concrete

�� = tensile strain at concrete

�� = cracking strain parameter of concrete damaged plasticity

��

= equivalent plastic strain of concrete at tension

ε� = ultimate strain of concrete at failure

� = prestressing ratio

μ = viscosity parameter

xiii

ʋ = Poisson’s ratio of concrete

ρ = mass density of concrete

�� = ratio of tensile reinforcement to concrete cross section

�� = sustained stress by concrete at level of centroid of prestressing

tendon

�� = constant stress sustained by concrete member

�� = bending stress due to the imposed load

σ� = initial (applied) prestressing stress

�� = resultant stress in the prestress concrete section

��.�� = bending stress due to the self-weight of concrete member

σ�� = maximum tensile stress (strength) of concrete

� = bond strength of reinforced steel

�� = creep coefficient of concrete or creep factor

��.� = basic creep coefficient of concrete

� = factor depends on curing time-ratio and size of concrete member

xiv

TABLE OF CONTENTS CERTIFICATE OF ORIGINAL AUTHORSHIP ......................................................... ii

ACKNOWLEDGMENTS ............................................................................................ iii

ABSTRACT .................................................................................................................. iv

LIST OF PUBLICATIONS ......................................................................................... vii

LIST OF ABBREVIATIONS ..................................................................................... viii

LIST OF NOTATIONS ................................................................................................. x

LIST OF TABLES .................................................................................................... xviii

LIST OF FIGURES .................................................................................................... xix

1. Introduction ............................................................................................................ 1

1.1 General ....................................................................................................................... 1

1.1. Research objectives .................................................................................................... 2

1.2. Scope of this study ..................................................................................................... 3

1.3. Research methodology ............................................................................................... 4

1.4. Research significance ................................................................................................. 5

1.5. Organisation of Thesis ............................................................................................... 6

2. Literature Review ................................................................................................... 9

2.1 Introduction about geopolymer binder ....................................................................... 9

2.2 Geopolymerisation process ...................................................................................... 10

a) Dissolution ................................................................................................................... 11

b) Gelation (reorganization) ............................................................................................. 11

c) Transformation (hardening) ......................................................................................... 11

2.3 Ingredients of geopolymer ....................................................................................... 12

2.3.1 Fly ash .......................................................................................................................... 12

2.3.2 Ground granulated blast furnace slag (GGBS) ............................................................. 14

2.3.3 Metakaolin ................................................................................................................... 16

2.3.4 Alkali activators ........................................................................................................... 16

2.4 Investigations of engineering properties of geopolymer concrete ........................... 16

2.4.1 Fresh concrete properties-workability .......................................................................... 17

2.4.2 Mechanical properties .................................................................................................. 18

a) Compressive strength development ......................................................................... 18

b) Tensile and flexural strength .................................................................................... 20

2.4.3 Stress-strain behaviour and modulus of elasticity ........................................................ 23

2.4.4 Poisson’s ratio .............................................................................................................. 26

2.4.5 Serviceability properties ............................................................................................... 27

a) Shrinkage ................................................................................................................. 27

b) Creep ........................................................................................................................ 30

2.4.6 Durability properties .................................................................................................... 33

2.5 Application of geopolymer binder in structural concrete ........................................ 35

2.6 Limitations of two-part geopolymer binder ............................................................. 36

2.7 Prestressed concrete ................................................................................................. 37

xv

2.7.1 General ......................................................................................................................... 37

2.7.2 Principles of prestressed concrete ................................................................................ 39

2.7.3 Types of prestressed concrete structures ...................................................................... 40

2.7.4 Prestressing tendon’s profile ........................................................................................ 41

2.7.5 Losses of prestress ....................................................................................................... 42

a) Short-term losses or immediate losses ..................................................................... 42

b) Long-term or time-dependent losses ........................................................................ 43

i. Drying shrinkage loss .................................................................... 43

ii. Creep loss ....................................................................................... 44

iii. Loss due to relaxation of tendon .................................................... 45

2.8 Structural suitability of geopolymer concrete in precast prestressed concrete ........ 47

2.9 Stress-strain behaviours of concrete and steel ......................................................... 48

2.9.1 Behaviour of concrete under load ................................................................................ 48

2.9.2 Plasticity and non-linearity of concrete ........................................................................ 51

2.9.3 Damage models of Concrete ........................................................................................ 52

2.9.4 Mathematical models of concrete under uniaxial loading ............................................ 53

a) Hognestad (1951) model .......................................................................................... 53

b) EN 1992.1.1 (2004) model for non-linear analysis ................................................. 54

c) Carreira and Chu (1986) model for uniaxial tension ............................................... 55

d) Stress-strain model for geopolymer concrete ........................................................... 56

2.9.5 Concrete damaged plasticity model ............................................................................. 58

2.5.10.1 Post failure stress-strain behaviour .......................................................................... 61

2.5.10.2 Failure mode under biaxial loading ......................................................................... 62

2.5.11 Stress-strain model for reinforcing steel ...................................................................... 64

2.10 Finite element analysis ............................................................................................. 66

2.10.1 General ......................................................................................................................... 66

2.10.2 Types of analysis in Abaqus......................................................................................... 68

2.10.3 Elements types used in finite element analysis ............................................................ 68

a) Solid continuum elements ........................................................................................ 69

b) Truss elements ......................................................................................................... 69

c) Beam elements ......................................................................................................... 70

2.11 Conclusions .............................................................................................................. 70

3. Experimental Program .......................................................................................... 72

3.1 Preamble .................................................................................................................. 72

3.2 Concrete strength grade ........................................................................................... 73

3.3 Materials .................................................................................................................. 73

3.3.1 Binders ......................................................................................................................... 73

3.3.2 Aggregates ................................................................................................................... 76

3.4 Trial mix designs and concrete mixing procedure ................................................... 78

3.5 Final mix designs and casting of concrete specimens .............................................. 82

3.6 Curing of concrete specimens .................................................................................. 84

3.6.1 Curing at ambient (standard laboratory) temperature .................................................. 85

3.6.2 Accelerated curing ....................................................................................................... 86

3.7 Investigation of engineering properties of concrete ................................................. 88

3.8 Conclusions .............................................................................................................. 89

4. Experimental Results and Discussions ................................................................. 91

xvi

4.1 Preamble .................................................................................................................. 91

4.2 Fresh concrete properties ......................................................................................... 91

4.3 Mechanical properties .............................................................................................. 93

4.3.1 Comprehensive strength development ......................................................................... 93

4.3.2 Indirect-tensile strength ................................................................................................ 96

4.3.3 Flexural strength .......................................................................................................... 99

4.3.4 Influence of aggregate-concrete bond on tensile strength of concrete ....................... 101

4.4 Deformation properties .......................................................................................... 102

4.5 Serviceability properties ........................................................................................ 105

4.5.1 Drying shrinkage ........................................................................................................ 105

4.5.2 Creep strain ................................................................................................................ 107

4.6 Development of strength at accelerated curing ...................................................... 111

4.7 Conclusions ............................................................................................................ 113

5. Finite Element Modelling ................................................................................... 114

5.1 Preamble ................................................................................................................ 114

5.2 Model development ............................................................................................... 114

5.2.1 Material properties and constitutive models .............................................................. 114

5.2.2 Modelling of elements................................................................................................ 118

5.2.3 Modelling of steel-concrete interaction ...................................................................... 118

a) Damage initiation ................................................................................................... 120

b) Damage evolution .................................................................................................. 120

5.2.4 Bond strength of reinforcing steel and concrete ......................................................... 121

5.2.5 Modelling of bond between prestressing steel tendon and concrete .......................... 124

5.3 Finite element analysis of reinforced concrete (RC) beams .................................. 129

5.3.1 Validation of CDP in RC beam .................................................................................. 129

5.3.2 Modelling of test RC beams ....................................................................................... 132

5.3.3 Parametric study using finite element modelling ....................................................... 133

5.3.4 Results and analysis of RC beams .............................................................................. 136

5.3.5 Effect of tensile strength in flexural capacity of reinforced concrete beam ............... 138

a) First-crack load ...................................................................................................... 138

b) Ultimate load capacity ........................................................................................... 138

c) Tension stiffening .................................................................................................. 142

d) Analogous of fibre reinforced concrete beam ........................................................ 143

5.4 Finite element modelling of prestresses concrete beams ....................................... 144

5.4.1 Validation of steel-concrete interaction in prestressed concrete beam ....................... 144

5.4.2 Modelling of test beams ............................................................................................. 148

5.4.3 Application of initial prestressing stress .................................................................... 150

5.4.4 Application of load ..................................................................................................... 151

5.5 Conclusions ............................................................................................................ 152

6. Results of Finite Element Analysis .................................................................... 154

6.1 Preamble ................................................................................................................ 154

6.2 Short-term performance ......................................................................................... 154

6.2.1 First crack load ........................................................................................................... 160

6.2.2 Ultimate load .............................................................................................................. 162

6.2.3 Effects of self-weight ................................................................................................. 163

6.3 Long term performance .......................................................................................... 163

xvii

6.4 Serviceability after 10 years ................................................................................... 169

6.5 Research outcomes ................................................................................................. 172

6.6 Conclusions ............................................................................................................ 173

7. Environmental Sustainability of Geopolymer Concrete ..................................... 175

7.1 Preamble ................................................................................................................ 175

7.2 Carbon footprint of Portland cement ..................................................................... 175

7.3 Carbon footprint of concrete production ................................................................ 176

7.4 Carbon footprint and embodied energy of concrete ingredients ............................ 178

7.5 Carbonation and CO2 uptake by OPC concrete ..................................................... 181

7.6 Evaluation of environmental sustainability of geopolymer concrete ..................... 182

7.7 Conclusions ............................................................................................................ 189

8. Conclusions and Recommendations for Future Study ....................................... 190

8.1 Conclusions of this study ....................................................................................... 190

8.2 Recommendation for further study ........................................................................ 195

References .................................................................................................................. 196

A. Appendices ......................................................................................................... 209

xviii

LIST OF TABLES

Table 2.1: Chemical compositions of Class F fly ash (Hardjito and Rangan, 2005) . 13

Table 2.2: Typical chemical composition of GGBS (Deb et al., 2014) ....................... 15

Table 2.3: Proposed models for indirect-tensile and flexural strengths ...................... 21

Table 2.4: Relationship between modulus of elasticity and compressive strength...... 25

Table 3.1: Chemical compositions of Class F fly ash, GGBS and OPC ..................... 76

Table 3.2: Physical properties of concrete aggregates ................................................. 78

Table 3.3: Trial mix designs of geopolymer and OPC concrete .................................. 80

Table 3.4: Mix compositions of Grade 50 MPa concrete ............................................ 83

Table 3.5: Investigated concrete properties and relevant standards ............................ 89

Table 4.1: Strengths development at accelerated curing ........................................... 112

Table 5.1: Mechanical properties of concrete and steel ............................................. 117

Table 5.2: Adopted parameters of concrete damaged plasticity ................................ 118

Table 5.3: Calculated bond strength .......................................................................... 123

Table 5.4: Parameters of pull-out test modelling ....................................................... 125

Table 5.5: Calculated values of critical separation .................................................... 128

Table 5.6: Details of simulated reinforced concrete beams ....................................... 131

Table 5.7: Design details of the test RC beams ........................................................ 133

Table 5.8: Details of simulated partially prestressed concrete beams ....................... 146

Table 5.9: Geometries, reinforcement details and applied prestress of test beams ... 151

Table 7.1: Carbon footprint of concrete ingredients and production process ............ 179

Table 7.2: Concrete from different studies considered for evaluation....................... 183

Table A.1: Sieve analysis of aggregates used for concrete production ..................... 209

Table A.2: Compressive strength developments of 50 MPa concrete ....................... 218

Table A.3: Indirect-tensile strength developments 50 MPa concrete ........................ 218

Table A.4: Flexural strength developments 50 MPa concrete ................................... 219

Table A.5: Shrinkage measurement of geopolymer and OPC concrete 50 MPa ....... 220

Table A.6: Creep measurement of geopolymer concrete of 50 MPa ......................... 221

Table A.7: Creep measurement of OPC concrete of 50 MPa .................................... 222

Table A.8: Compressive stress-strain model of geopolymer concrete of 50 MPa ..... 223

Table A.9: Compressive stress-strain model of OPC concrete of 50 MPa ................ 223

Table A.10: Tensile stress-strain model of geopolymer concrete of 50 MPa ............ 224

Table A.11: Tensile stress-strain model of OPC concrete of 50 MPa ....................... 225

Table A.12: Loss of prestress in geopolymer 10 m long concrete beam ................... 229

Table A.13: Loss of prestress in OPC 10 m long concrete beam .............................. 230

Table A.14: Loss of prestress in geopolymer 15 m long concrete beam ................... 231

Table A.15: Loss of prestress in OPC 15 m long concrete beam .............................. 232

Table A.16: Long-term drying shrinkage of 50 MPa concrete .................................. 233

Table A.17: Long-term creep coefficient of 50 MPa concrete .................................. 233

Table A.18: Calculated carbon emission of different concrete (kg CO2-e/kg) .......... 234

Table A.19: Calculated embodied energy of different concrete ................................ 235

xix

LIST OF FIGURES

Figure 1.1: Flow charts of research methodology ......................................................... 5

Figure 2.1: Structures of geopolymer matrix ................................................................. 9

Figure 2.2: SEM image of fly ash (Flyash-Australia, 2010)........................................ 13

Figure 2.3: SEM image of fly ash-based geopolymer (Criado et al., 2010) ................ 14

Figure 2.4: SEM image of GGBS particles (Park et al., 2017) .................................... 15

Figure 2.5: Compressive strength development of geopolymer concretes .................. 19

Figure 2.6: Indirect-tensile strength of geopolymer concrete ...................................... 22

Figure 2.7: Flexural strength of geopolymer concrete ................................................. 22

Figure 2.8: Stress-stain relationships of geopolymer concrete .................................... 24

Figure 2.9: Modulus of elasticity of geopolymer concrete .......................................... 26

Figure 2.10: Dying shrinkage growth in geopolymer concrete (Deb et al., 2015) ...... 30

Figure 2.11: Creep strain of geopolymer and OPC concrete of previous studies ........ 33

Figure 2.12: Working principles of reinforced and prestressed concrete (FHA, 2013)

...................................................................................................................................... 37

Figure 2.13: Wooden barrels with metal bands ........................................................... 38

Figure 2.14: Walnut Lane Memorial Bridge in Philadelphia (Zollman et al., 1992) .. 39

Figure 2.15: Stress profile in a prestressed concrete section ....................................... 40

Figure 2.16: Cable profiles on prestressed concrete .................................................... 42

Figure 2.17: Uniaxial stress-strain behaviour of concrete at compression (Neville,

1995) ............................................................................................................................ 49

Figure 2.18: Uniaxial tensile stress-strain curve (Guo and Zhang, 1987) ................... 50

Figure 2.19: Process of cracks developing in concrete (Kotsovos and Newman, 1977)

...................................................................................................................................... 51

Figure 2.20: Uniaxial stress-strain curve of concrete (Chen, 2007) ............................ 52

Figure 2.21: Tension stiffening model of concrete (Al-Manaseer and Phillips, 1987) 53

Figure 2.22: Stress-strain model proposed by Hognestad (1951) ................................ 54

Figure 2.23: Stress-strain model of concrete recommended by EN-1992.1.1 (2004) 55

Figure 2.24: Tensile stress-strain model for concrete (Carreira and Chu, 1986) ......... 56

Figure 2.25: Stress-strain behaviour of geopolymer concrete under uniaxial tension

(Farhan et al., 2019) ..................................................................................................... 58

Figure 2.26: Unloading response of concrete (a) elastic damage model (b) elastic-

plastic model (c) elastic-plastic damage model (Jason et al., 2006) ........................... 59

Figure 2.27: Concrete damaged plasticity model (a) compression and (b) tension

(Abaqus-Inc., 2014) ..................................................................................................... 60

Figure 2.28: Cracking strain of concrete under tension (Abaqus-Inc., 2014) .............. 62

Figure 2.29: Yield surface in plane biaxial loading (Abaqus-Inc., 2014) .................... 63

Figure 2.30: Yield surface for a deviatoric plane (Abaqus-Inc., 2014) ....................... 64

Figure 2.31: Stress-stress curve of reinforcing steel under tension (Felicetti et al.,

2009) ............................................................................................................................ 65

Figure 2.32: Idealised stress-strain curves of steel (a) Elastic and perfectly plastic (b)

Trilinear approximation (c) Complete curve (Park and Paulay, 1975) ........................ 66

xx

Figure 2.33: Flowchart of finite element analysis process .......................................... 67

Figure 2.34: Solid 8-node brick elements (a) C3D8 and (b) C3D8R .......................... 69

Figure 2.35: A typical truss element ............................................................................ 70

Figure 2.36: A typical 3D beam element ..................................................................... 70

Figure 3.1: Binding materials (a) fly ash, (b) GGBS, (c) sodium carbonate dense

(d) sodium silicate, (e) geopolymer binder and (d) Portland cement 75

Figure 3.2: Concrete aggregates (a) 20 mm coarse, (b) 10 mm coarse, (c) medium

sand and (d) fine sand .................................................................................................. 77

Figure 3.3: Particle distribution curves of concrete aggregates ................................... 78

Figure 3.4: Mixing of concrete (a) loading of materials (b) mixed geopolymer

concrete ........................................................................................................................ 81

Figure 3.5: Compressive strength of geopolymer concrete trial mixes ....................... 82

Figure 3.6: Compressive strength of OPC concrete trial mixes................................... 82

Figure 3.7: Casting of concrete specimens (a) cylinders, (b) shrinkage prisms and (c)

flexural beams .............................................................................................................. 84

Figure 3.8: Sealed cured geopolymer concrete specimens (a) cylinders, (b) shrinkage

prisms and (c) flexural beam........................................................................................ 86

Figure 3.9: Sealing of concrete cylinder for accelerated curing .................................. 87

Figure 3.10: Temperature profile for accelerated curing of concrete specimens ........ 88

Figure 4.1: Measurement of fresh concrete properties (a) slump (b) air content ........ 92

Figure 4.2: Arrangement of compressive strength test ................................................ 94

Figure 4.3: Compressive strength development of 50MPa concrete ........................... 95

Figure 4.4: Crushed concrete cylinders of grade 50 MPa (a) geopolymer (b) OPC .... 96

Figure 4.5: Test set of indirect-tensile strength measurement ..................................... 97

Figure 4.6: Indirect tensile strength of Grade 50 MPa concrete .................................. 98

Figure 4.7: Comparison of indirect-tensile strengths of concrete ................................ 99

Figure 4.8: Arrangement for modulus of rupture test of concrete ............................. 100

Figure 4.9: Flexural strength of Grade 50MPa concrete............................................ 101

Figure 4.10: Fracture surfaces (a) geopolymer concrete and (b) OPC concrete ........ 102

Figure 4.11: Test set-up of modulus of elasticity of concrete .................................... 103

Figure 4.12: Modulus of elasticity of geopolymer concrete ...................................... 104

Figure 4.13: Drying shrinkage reading of concrete specimen ................................... 105

Figure 4.14: Drying shrinkage of Grade 50 MPa concrete ........................................ 106

Figure 4.15: Arrangement of creep testing with loaded creep rigs ............................ 108

Figure 4.16: Creep coefficients of 50MPa concrete .................................................. 109

Figure 4.17: Measured specific creep of 50MPa concrete ......................................... 110

Figure 5.1: Stress-strain models of concrete a) compressive and b) tensile behaviours

.................................................................................................................................... 115

Figure 5.2: Damage parameters of constitutive models of concrete at a) compression

and b) tension ............................................................................................................. 116

Figure 5.3: Idealised stress-strain diagram of normal and prestressing steel ............ 117

Figure 5.4: Traction-separation of a cohesive bond................................................... 119

Figure 5.5: A finite element modelling of pull-out test ............................................. 126

xxi

Figure 5.6: Bond stress-slippage curves for different stiffness coefficients .............. 127

Figure 5.7: Stress level on steel bar and concrete during pulling-out ........................ 128

Figure 5.8: Profile of stress along the reinforcement bar ........................................... 129

Figure 5.9: Load-deflection responses of RC concrete beam .................................... 130

Figure 5.10: Load-deflection response of simulated RC beams ................................ 132

Figure 5.11: Modelled beams with different mesh sizes (a) fine, (b) medium (c) coarse

.................................................................................................................................... 135

Figure 5.12: Load-deflection response of 2.8 m long beam with different mesh sizes

.................................................................................................................................... 136

Figure 5.13: Load-deflection responses of modelled RC beams ............................... 137

Figure 5.14: Flexural damage in 2.8 m long geopolymer RC beam .......................... 137

Figure 5.15: A typical stress profiles on concrete (a) concrete section, (b) cracking

load, (c) yield load and (d) ultimate load ................................................................... 139

Figure 5.16: Prestressed beam sections (a) original (b) adopted in FE model

(dimensions are in mm) ............................................................................................. 145

Figure 5.17: Load-deflection responses of modelled prestressed concrete beam ...... 146

Figure 5.18: Load-deflection responses of prestressed beams (a) B.40-P-25-NE, and

(b) B.80-P-25-NE ....................................................................................................... 147

Figure 5.19: Elevation of 5000 mm modelled prestressed concrete beam (dimensions

are in mm) .................................................................................................................. 149

Figure 5.20: Cross-sections of modelled prestressed beams (a) 5 m (b) 10 m (c) 15 m

(dimensions are in mm) ............................................................................................. 149

Figure 5.21: Reinforcement arrangement in 5 m prestressed concrete beam ............ 149

Figure 5.22: Reinforcement arrangement in 10 m prestressed concrete beam .......... 149

Figure 5.23: Modelled 5 m prestressed concrete beam with 25 mm mesh size......... 150

Figure 5.24: Modelled rectangular prestressing tendon with mesh elements ............ 150

Figure 6.1: Load- deflection curves of prestressed concrete beams .......................... 155

Figure 6.2: Flexural stress in geopolymer prestressed 5 m beam at prestress-transfer

.................................................................................................................................... 156

Figure 6.3: Stress on prestressing steel tendon at prestress transfer (no-load condition)

.................................................................................................................................... 157

Figure 6.4: Flexural stress in 5 m prestressed beam at first-crack load ..................... 157

Figure 6.5: Flexural stress in 5 m prestressed beam at failure ................................... 157

Figure 6.6: Flexural stress in prestressing tendon of 5 m beam at failure ................. 158

Figure 6.7: Damage initiation after first-crack load on 5 m long prestressed beam .. 158

Figure 6.8: Progress of damage at yielding load on 5 m long prestressed beam ....... 159

Figure 6.9: Progress of damage at yielding load on 10 m long prestressed beam ..... 159

Figure 6.10: Damages on concrete at failure point on 5 m long prestressed beam ... 159

Figure 6.11: Tensile stress in normal reinforcements at ultimate failure .................. 160

Figure 6.12: Stress profiles of prestressed concrete beams at (a) prestress transfer and

(b) first-crack load...................................................................................................... 161

Figure 6.13: Losses of prestress in concrete beams (a) geopolymer 10 m, (b) OPC 10

m, (c) geopolymer 15 m and (d) OPC 15 m .............................................................. 165

xxii

Figure 6.14: Residual prestress in steel tendon (a) 10 m beams (b) 15 m beams ...... 166

Figure 6.15: Long-term load-deflection responses (a) 10 m beams, and (b) 15 m

beams ......................................................................................................................... 168

Figure 6.16: Long-term serviceably (a) drying shrinkage (b) creep coefficient ........ 170

Figure 6.17: Residual prestress in 15 m long prestressed beam ................................ 171

Figure 6.18: Reduction in load capacity of 15 m long prestressed concrete beams .. 172

Figure 7.1: Life cycle stages of concrete production ................................................. 177

Figure 7.2: Embodied carbon in a precast reinforced concrete member (Circular-

Ecology, 2020) ........................................................................................................... 178

Figure 7.3: Carbon footprint of geopolymer and Portland cement used in this study

.................................................................................................................................... 180

Figure 7.4: Contributions of ingredients to carbon footprints of geopolymer binder 181

Figure 7.5: Carbon footprints of manufacturing of unit volume of concrete............. 185

Figure 7.6: Energy consumptions of manufacturing of unit volume of concrete ...... 186

Figure 7.7: Carbon footprint of ambient cured geopolymer concrete ....................... 188

Figure A.1: Compositions of fly ash .......................................................................... 210

Figure A.2: Compositions of GGBS .......................................................................... 211

Figure A.3: Compositions of sodium silicate ............................................................ 212

Figure A.4: Geopolymer concrete being mixed ......................................................... 213

Figure A.5: Concrete cylinders being cast and vibrated ............................................ 214

Figure A.6: Measurement of concrete wert density ................................................... 215

Figure A.7: Immersed curing of OPC concrete specimens ........................................ 216

Figure A.8: Storage of shrinkage prisms in the control room.................................... 217

Figure A.9: Indirect-tensile testing frame .................................................................. 218

Figure A.10: Reinforcements schedule of modelled pull-out block (not in scale) .... 226

Figure A.11: Reinforcements schedule of modelled 5 m long RC beam (not in scale)

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

Figure A.12: Prestressed 10 m long beam with mesh elements ................................ 226

Figure A.13: Flexural stress on 5 m long prestressed beam at zero vertical deflection

.................................................................................................................................... 227


.................................................................................................................................... 227

Figure A.15: Flexural stress on 10 m long prestressed beam at first-crack load ....... 227

Figure A.16: Tensile damage initiation in prestressed 10 m beam ............................ 228

Figure A.17: Tensile stress at geopolymer 10 m prestressed beam at ultimate failure

.................................................................................................................................... 228

Chapter 1: Introduction

1

CHAPTER 1

1. Introduction

1.1 General

Concrete is one of the most widely used materials in civil constructions which needs

cement as a binder. Production of ordinary Portland cement (OPC) generates significant

amounts of carbon dioxide (CO2) gas. Globally, cement industries are responsible for

around 7% of CO2 emissions (Meyer, 2009, Turner and Collins, 2013). The production

of Portland cement poses a considerable threat to global climate change because of the

significant amount of greenhouse gas emissions.

Since, last few decades, industrial by-products, such as fly ash, ground granulated blast

furnace slag (GGBS) and silica fume have been being added to OPC concrete as

supplementary cementitious materials (SCMs) in order to reduce the carbon footprints

and improve the mechanical and durability properties of concrete (Johari et al., 2011,

Reddy and Kavyateja, 2020, Elahi et al., 2010). When mixed with OPC, these materials

react with the product of hydration of cement to develop the binding property called

pozzolanic reaction which occurs at a slower rate than hydration of OPC (Zeng et al.,

2012). Generally, the addition of SCMs can result in a significant decrease in the early-

age strength of concrete (Berry and Malhotra, 1980, Johari et al., 2011). Therefore,

SCMs can be used only as a partial replacement of OPC. Hence, there is a great interest

in developing alternative binding materials that can reduce the embodied energy of end

products (concrete) whilst maintaining the required engineering properties.

Geopolymer is a new binding material that can be produced from aluminosilicate

compounds, such as fly ash when activated by alkaline solution. The recent advent of

geopolymer technology shows considerable promise to save the environment by

utilising industrial by-products, such as fly ash and GGBS to converts into binding

materials. Previous studies suggested that geopolymer concrete possesses significantly

higher tensile and flexural strengths than OPC concrete of same grade (Hardjito and

Rangan, 2005, Sofi et al., 2007, Raijiwala and Patil, 2011). These properties of


2

geopolymer concrete are significant in the design of prestressed concrete structures

where tensile strength of concrete is an important factor.

The use of prestressed concrete structures has largely increased in modern construction

practice due to their economical and structural benefits. According to ACI-318 (2011),

the maximum level of allowable prestress in concrete structure is limited, such that

tensile stress in extreme (topmost) fibre stress should not exceed 0.25√�� (equals to

0.4��), where �� and �� are compressive and flexural strength of concrete at prestress

transfer. As geopolymer concrete possesses higher tensile or flexural strength than OPC

concrete of same grade, geopolymer prestressed concrete members can allow higher

prestressing load than OPC concrete of same grade according to ACI-318 (2011). The

load-carrying capacity of the prestressed concrete beam can be improved by applying

a higher prestressing load. Previous study suggested that drying shrinkage and creep

strains of geopolymer concrete are significantly lower than OPC concrete of same grade

(Wallah, 2009, Deb et al., 2015, Gunasekera et al., 2019). In a prestressed concrete

beam, time-dependent losses of prestress in steel tendon are mainly caused by drying

shrinkage and creep strains of concrete which can result in higher increase in deflection

and reduction of its load-carrying capacity (Asamoto et al., 2014, Warner et al., 1998).

Therefore, smaller drying shrinkage and creep strains of geopolymer concrete can result

in smaller deflection and minimal loss in load-carrying capacity (hence better

serviceability) of geopolymer prestressed concrete members.

This study investigates the engineering properties of structural grade concrete from one-

part geopolymer binder and compares with OPC concrete of same grade. In addition,

load-deflection behaviours of prestressed geopolymer and OPC concrete beams for

short-term and long-term are investigated using finite element analysis.

1.1. Research objectives

The aim of this research study is to investigate the engineering properties of structural

grade concrete from one-part geopolymer binder and load-deflection behaviours of

geopolymer prestressed concrete beam. The broader objectives of this study are as

follows:


3

a) To use sodium hydroxide free one-part geopolymer binder to produce structural

grade concrete (50 MPa) and investigate its engineering properties and compare the

results against OPC (control) concrete of same strength grade.

b) To develop a finite element models of reinforced concrete (RC) beams to

investigate the effects of flexural strengths of concrete on structural behaviour of

reinforced concrete beam under imposed load (load-deflection behaviour).

c) To develop a finite element model of prestressed concrete beam and evaluate the

applicability of cohesive surface behaviour to model the interaction between

prestressing steel and concrete.

d) To evaluate the effects of flexural strength of concrete in design of prestressed

concrete beam as well as its effect on load-deflection behaviours.

e) To evaluate the long-term serviceability of prestressed concrete beam from

geopolymer concrete and compare with OPC concrete beams of same span and

cross-section.

1.2. Scope of this study

This research is focused on investigating the load-deflection behaviour of prestressed

concrete beam from geopolymer and OPC concrete of same grade using finite element

analysis. The scopes of this study are listed as follows.

a) Mix design and production of geopolymer and OPC (control) concrete of grade 50

MPa.

b) Investigate mechanical properties of geopolymer and OPC concretes of same grade

at ambient temperature curing (23 °C) at different ages; compressive strength

development (1 to 365 days), indirect tensile strength (at 7, 14 and 28 days), flexural

strength (at 14 and 28 days) and modulus of elasticity (at 28 days) according to

relevant Australian Standards.

c) Determination drying shrinkage and creep strains of geopolymer and OPC concrete

at ambient temperature curing (23 °C) up to one year.


4

d) Finite element modelling and analysis of RC beam using concrete damaged

plasticity model in Abaqus program.

e) Evaluate the difference in load-deflection behaviour of prestressed concrete beam

from geopolymer and OPC concrete of same grade using finite element analysis for

short-term and long-term.

1.3. Research methodology

The following methodology will be adopted to achieve the above-mentioned objectives.

a) Literature review of OPC concrete and its engineering properties, such as

workability, compressive strength, flexural strength and modulus of elasticity as

well as serviceability properties, such as shrinkage and creep strains.

b) Literature review on research and development of geopolymer binders and

engineering properties of geopolymer concrete.

c) Literature review about structural design and analysis of normal reinforced concrete

and prestresses concrete structures.

d) Trial mix designs and production of grade 50 MPa concrete from one-part

geopolymer binder and OPC.

e) Investigation of workability, mechanical and serviceability properties of

geopolymer and OPC concrete of same strength grade at ambient temperature

curing (23 °C).

f) Determine early age strengths (compressive and indirect tensile strength)

development of geopolymer concrete at accelerated curing (70 °C) to investigate its

suitability in precast concrete applications.

g) Finite element analysis of RC and prestressed concrete beams using Abaqus

program and evaluate the difference in load-deflection behaviour of prestressed

concrete beam from geopolymer and OPC concrete for short-term and long-term.

The research methodology adopted in this study is summarised in a flow chart in Figure

1.1.


5

Figure 1.1: Flow charts of research methodology

1.4. Research significance

Use of geopolymer binders in structural concrete around the globe is still in a trial phase

because of the unavailability of wide range of data. The majority of previous studies

on geopolymer concrete focused on different ingredients materials, such as fly as,

GGBS, metakaolin and their engineering properties (Diaz-Loya et al., 2011, Hardjito

and Rangan, 2005, Nath and Sarker, 2012, Ryu et al., 2013). Published research on

structural applications of geopolymer concrete is still limited.

Objectives: Find out effects of tensile or flexural strength of concrete into flexural behaviours of prestressed beam using geopolymer concrete.

Experiments: Investigation of engineering properties of geopolymer and OPC concrete of

Grade 50 MPa.

Finite element modelling and analysis: Use the experimental results as input parameters of concrete damage plasticity model and finite element model analysis of simply supported prestressed concrete

beams.

Results and discussions: Evaluate the results of finite element analysis and the difference in load-deflection

behaviours of prestressed concrete beams from geopolymer and OPC concrete for short-term and long-

term.


6

Several previous studies reported that geopolymer concrete has higher mechanical

strengths, smaller shrinkage and creep and strains and better durability properties

(higher resistance to sulphate and acid attack) than conventional OPC concrete of same

strength grade. However, geopolymer concrete has not been widely accepted by

concrete industry especially in structural grade concrete, so far. One of the barriers to

the adaptation of geopolymer concrete is the safety hazards posed by sodium hydroxide

liquid used in geopolymer binder. This study uses a new type of geopolymer binder

which is free from sodium hydroxide and physically alike to conventional Portland

cement (powder form) to produce geopolymer concrete for structural applications. In

this study, mechanical and serviceability properties of grade 50 MPa geopolymer and

OPC (control) concrete are investigated under ambient curing conditions. In addition,

early-age strength development of geopolymer concrete at accelerated curing is

investigated in order to study its suitability in precast concrete structures.

The use of precast prestressed concrete structures has been largely increasing in modern

constructions due to their economical and structural benefits. To date, several books

and research papers have been published about the design and construction of OPC

concrete based precast prestressed concrete structures (Gilbert et al., 2016, Nilson,

1978). However, investigation on the applicability of geopolymer in precast prestressed

concrete structures is still very limited. As geopolymer concrete possesses higher

tensile and flexural strengths than OPC concrete, the design criteria and structural

behaviours, such as maximum applied prestress should be different for geopolymer

prestressed concrete structures. This thesis reviews the structural behaviours and

suitability of geopolymer concrete in prestressed concrete structures using finite

element analysis and the results are compared with identical beams from OPC concrete.

1.5. Organisation of Thesis

This dissertation discusses about structural (load-deflection) behaviours of geopolymer

prestressed concrete beam using finite element analysis and compares the results with

OPC prestressed concrete beams of same span and strength grade. It is divided into

different sections as followings:


7

Chapter 2 provides a literature review on the topic. This chapter discusses about

ingredients of geopolymer and geopolymerisation process. A summary of previous

studies on different geopolymer binders and their findings of workability, mechanical

strengths, serviceability and durability properties of geopolymer concretes are

presented in this chapter. In addition, a brief review about the design and analysis of

prestressed concrete structures and critical parameters are discussed in this chapter.

The details of the experimental programme are presented in Chapter 3. This chapter

includes mix designs and production of geopolymer and OPC concrete and casting of

specimens. Besides, methodologies used for curing of geopolymer concrete specimens

and measurement of engineering properties of concrete are also discussed in this

chapter.

Chapter 4 discusses the experimental results of fresh and hardened concrete properties,

such as workability and mechanical strengths as well as long-term drying shrinkage and

creep strains of geopolymer and OPC concrete of same strength grade.

Chapter 5 describes the finite element modelling and analysis of conventional

reinforced and prestressed concrete beams using Abaqus program (Abaqus-Inc., 2014).

This chapter includes the applicability of the concrete damaged plasticity (CDP) model

to predict the load-deflection responses of concrete structures and interactions of steel

reinforcements (normal and prestressing) with surrounding concrete.

The results of finite element analysis are discussed in Chapter 6. This chapter compares

and evaluates the load-deflection behaviours of prestressed concrete beams from

geopolymer and OPC concrete of same grade for short-term and long-term durations.

The effects of shrinkage and creep strains of concrete into long-term serviceability of

prestressed concrete beams are also discussed in this chapter.

Chapter 7 evaluates the environmental sustainability of geopolymer and OPC concrete

produced in this study. The carbon footprint and embodied energy of geopolymer

concrete produced in previous studies are also compared in this chapter.


8

Chapter 8 includes the conclusions of this research work and recommendations for

further study. In order to introduce geopolymer concrete in precast prestressed concrete

industry, areas of further study are suggested in this chapter.

Chapter 2: Literature review

9

CHAPTER 2

2. Literature Review

2.1 Introduction about geopolymer binder

Geopolymer is an inorganic polymer material formed by the activation of

aluminosilicate compounds (source materials) by alkaline solution (activator), which

was firstly reported by Davidovits (Davidovits, 1999). The geopolymer matrix consists

of a three-dimensional structure in which aluminium and silicon atoms create a

tetrahedral chain of SiO4 and AlO4 by sharing oxygen atoms alternatively (Davidovits,

1991). The alkali aluminosilicate compound consisting of Si-O-Al bonds possesses

binding properties similar to calcium silicon hydrate (C-S-H) paste of OPC concrete.

The geopolymer structure is called ‘poly (sialate)’ which consists of SiO4 and AlO4 in

the tetrahedral link. A general formula of poly (sialate) can be written as follows

(Davidovits 1991):

��[(��)�. ��]�. �� (2.1)

where, � is an alkali metal, such as potassium and sodium; �� and �� are the

metal oxides, silica and alumina; � is a degree of poly-condensation; � and � are

integers.

Figure 2.1: Structures of geopolymer matrix

According to the molar ratio of silicon to aluminium (Si:Al) geopolymer matrix is

classified into three different types as shown in Figure 2.1. The physical and


10

mechanical properties, such as mechanical strengths depend upon the molecular

structure of a geopolymer. For example, the compressive strength of geopolymer mortar

or concrete increases with the increase in silica content (SiO2/Al2O3) because of higher

strength of Si-O-Si bond than Si-O-Al bond (Duxson et al., 2005).

Generally, molecular structures and characteristics of the end products of geopolymer

binder are largely affected by its ingredients (source materials and alkali activators)

because they affect the whole geopolymer process (Duxson et al., 2006). Fly ash GGBS

are the two major source materials used in geopolymer binders. GGBS mainly contains

CaO, SiO2 and Al2O3, whereas fly ash mainly contains SiO2 and Al2O3. Therefore,

aluminosilicate materials referred to both, fly ash and GGBS in some studies (Oh et

al., 2010). When activated by alkaline liquid, GGBS partially produces calcium-

silicate-hydrate (C-S-H) gel or calcium-silicate-aluminate-hydrate (C-A-S-H) gel along

with geopolymer gel (Ismail et al., 2014, Oh et al., 2010). The GGBS based alkali

activated binder has been referred as alkali activated slag in previous studies (Collins

and Sanjayan, 1999, Bakharev et al., 2003). However, alkali activated slag binder are

also considered as a geopolymer in some studies (Cheng and Chiu, 2003) because both

fly ash and GGBS can be similarly activated with same alkaline liquid and the end

products are cementless binders in both cases. A combination of fly ash and GGBS has

been used as source materials to produce geopolymer binders in several previous

studies (Nath and Sarker, 2012, Parthiban et al., 2013, Kumar et al., 2009, Wagners,

2010). In this thesis, both fly ash and GGBS based binders are referred as geopolymer

binders.

2.2 Geopolymerisation process

The setting and hardening of geopolymer binder is called geopolymerisation process

which is a reaction between an aluminosilicate compound and an alkali liquid (pH level

around 14). The geopolymerisation process is the condensation of aluminate and

silicate monomers to form a polymer chain (Davidovits, 1991). The geopolymerisation

process can be categorised into three steps; dissolution, gelation (reorientation) and

transformation (hardening).


11

a) Dissolution

In this process, the Si+ and Al+ metal ions are liberated from aluminosilicate compounds

and dissolved into an alkaline solution. The rate of dissolution is dependent upon

several factors, such as types of source materials, temperature and concentration of

alkali solution. Dissolution of aluminosilicate compounds, such as, metakaolin, fly ash

and GGBS in NaOH and KOH solution increases with an increase in temperature and

concentration of alkali medium (Mikuni et al., 2007, Panagiotopoulou et al., 2007)

which eventually accelerate the geopolymerisation process.

b) Gelation (reorganization)

In this stage, aluminate monomers [Al(OH)4]¯ and silicate monomers [SiO(OH)3]¯ or

[SiO2(OH)2]2¯ start a condensation process to form a continuous three-dimensional

polymer structure. The condensation between [Al(OH)4]¯ and [SiO(OH)3]¯ results a

stable and larger product than from [Al(OH)4]¯ and [SiO2(OH)2]2¯. Therefore, the

formation of a geopolymer network depends on the proportion of [SiO2(OH)2]2¯ and

SiO(OH)3]¯ in the geopolymer system. Several factors, such as the level of alkalinity

and types of aluminosilicate compounds can control this ratio (Weng and Sagoe-

Crentsil, 2007).

c) Transformation (hardening)

In this stage, geopolymer gel starts to solidify. Depending upon the condensation

process of aluminate and silicate monomers, the structure of the final product may be

poly (sialate), Poly (sialate-siloxo) and Poly (sialate-disiloxo). Reaction of poly

(sialate); when the molar ratio (Si:Al) =1 can be written as follows:

(��1��)� + 3�� /�� (��)� − �� − � − �� − (��)� (2.2)

�(��)� − �� − � − �� − (��)� ��/�� (��, �) − (�� − � − �� − � −)� + 3�� (2.3)

� �


12

Euation 2.2 and 2.3 show that geopolymerisation takes place in presence of water, but

it releases water during the formation of end products which is different from than

hydration of OPC. This property may affect the curing methodology of geopolymer

concrete specimens.

2.3 Ingredients of geopolymer

Geopolymer binder has two major ingredients; aluminosilicate source materials and

alkali activator. Early investigations on geopolymer binders were carried out using

aluminosilicate minerals of geological origins, such as metakaolin. Nowadays, there is

more focus on the utilization of industrial by-products such as fly ash and GGBS

because of their environmental benefits (Heath et al., 2013). Calcined materials, such

as fly ash, slag and metakaolin exhibited a higher rate geopolymerisation reaction than

using non-calcined materials, for example kaolin and clay (Barbosa et al., 2000, Zhu et

al., 2009).

2.3.1 Fly ash

Fly ash is a by-product of coal-fired power plants which is one of the largest available

aluminosilicate compounds around the world. In Australia only, around 11.19 million

metric tonnes of fly ash were produced for the calendar year of 2018. Out of this, only

1.7 million metric tonnes of fly ash (around 19 % of total production) were used as

supplementary cementitious materials in concrete production (ADAA, 2019). Figure

2.2 shows a scanning electron microscopic image of fly ash where most of the particles

are round.


13

Figure 2.2: SEM image of fly ash (Flyash-Australia, 2010)

Based on origin and calcium content, coal fly ash has been classified into two classes;

Class F (low calcium) and Class C (high calcium). ASTM-C618 (2019) recommends

that both fly ashes should contain a minimum 50% of aluminosilicate and iron

compounds (Silicon dioxide + aluminium oxide + iron oxide) by mass to be used in

concrete. Class F fly ash can only contain a maximum 18% of calcium oxide, whereas

Class C can have more. Typical chemical compositions of Class F fly ash obtained from

a power station in Western Australia is presented in Table 2.1 which shows more than

75% of the mass is occupied by aluminosilicate compounds. Figure 2.3 shows the

microstructures of fly ash-based geopolymer at early age where round-shaped fly ash

particles are dissolved in alkali activator.

Table 2.1: Chemical compositions of Class F fly ash (Hardjito and Rangan, 2005)

Compositions SiO2 Al2O3 Fe2O3 CaO Na2O K2O TiO2 MgO P2O5 SO3 LOI

%by mass 53.4 26.49 10.8 1.34 0.37 0.80 1.47 0.77 1.43 1.70 1.39

*LOI= loss on ignition


14

Figure 2.3: SEM image of fly ash-based geopolymer (Criado et al., 2010)

Fly ash-based geopolymer concrete requires longer setting time because of slow

reaction rate at ambient temperature, therefore most of the previous researches adopted

heat curing at an early age (Hardjito and Rangan, 2005, Diaz-Loya et al., 2011,

Fernandez-Jimenez et al., 2006b, Gunasekera et al., 2019).

2.3.2 Ground granulated blast furnace slag (GGBS)

GGBS is the first material used in alkali-activated binders as an alternative to Portland

cement by Purdon (1940) and Glukhovsky (1957) before the advent of geopolymer.

GGBS is also a widely available industrial by-product of a blast furnace which is

formed during iron manufacturing process. Around 0.50 million metric tonnes of

GGBS is annually produced in Australia and New Zealand (ASA, 2017). A scanning

electron microscope image in Figure 2.4 shows that its particles are mostly irregular

shapes.


15

Figure 2.4: SEM image of GGBS particles (Park et al., 2017)

GGBS is a non-metallic material that primarily contains calcium oxide, silica and

alumina. Typical chemical compositions of GGBS is shown in Table 2.2

Table 2.2: Typical chemical composition of GGBS (Deb et al., 2014)

Compounds SiO2 Al2O3 CaO MgO Fe2O3 Na2O K2O SO3 P2O5 TiO2 LOI

% by weight 29.96 12.25 45.45 3.94 0.52 0.31 0.38 3.62 0.04 0.46 2.39

GGBS based geopolymer concrete possesses dual characteristics in early days;

geopolymerisation of aluminosilicate compounds to form geopolymer gel and

hydration of calcium and aluminosilicate compounds to form calcium-silicate-hydrate

(C-S-H) gel or calcium-silicate-aluminate-hydrate (C-A-S-H) gel (Ismail et al., 2014,

Oh et al., 2010). The C-S-H and C-A-S-H gels are responsible for the early age strength

of geopolymer concrete (Yip et al., 2005). Previous experiments showed that GGBS

based geopolymer concrete can set and harden in ambient temperature with comparable

early age strength to OPC concrete (Collins and Sanjayan, 1999, Douglas et al., 1992).

In some studies, GGBS has been used as a partial replacement of fly ash to enable fly

ash-based geopolymer concrete set and harden at ambient temperature and improve its

mechanical strengths at early as well as later ages (Nath and Sarker, 2012, Parthiban et

al., 2013, Kumar et al., 2009).


16

2.3.3 Metakaolin

Generally, metakaolin is prepared by calcination of natural kaolin clay at a temperature

between 500 to 800 °C. Metakaolin possesses a high percentage of aluminosilicate

compounds and shows higher reactivity in alkaline solution (Panagiotopoulou et al.,

2007). Since metakaolin needs lots of energy to be calcined, it has not been considered

as sustainable source material for geopolymer binder.

Some research has been carried out around the world to utilise some other types of

aluminosilicate compounds, such as mine tailing (Zhang et al., 2011) and rice husk ask

(Nazari et al., 2011). However, due to various reasons, such as availability of material,

consistency in chemical compositions and performance of end products, these materials

are not preferred as source materials for geopolymer.

2.3.4 Alkali activators

Sodium hydroxide (NaOH), Potassium hydroxide (KOH) and Sodium silicate

(Na2SiO3) are the most used alkali activators in previous studies due to their worldwide

availability and suitability. The choice of activators depends upon its availability, cost

and chemical strength. Alkali activators can be used in solid (powder) or liquid state.

Based on the physical form of alkali activators, geopolymer binders can be classified

into two categories; liquid-activated (two-part) and powder-activated (one-part)

geopolymer. Two-part geopolymer binder consists of ingredients in two different

forms; source materials in powder form and activator in a liquid state (Duxson and

Provis, 2008). Whereas, one-part geopolymer contains both, source materials and

activator in powder form which makes it physically similar to OPC.

2.4 Investigations of engineering properties of geopolymer concrete

Previous investigations on engineering properties of geopolymer concrete relevant to

this study can be divided into four different categories; fresh concrete properties,

mechanical properties, serviceability properties and durability properties.


17

2.4.1 Fresh concrete properties-workability

Workability is the property of fresh concrete which provides the easiness to place and

consolidate the concrete. There are several factors to affect the workability of concrete,

such as water content, binder property, addition of chemical admixtures and aggregate

size and proportions. Water content is one of the major factors to control the workability

of concrete (Neville, 1995). Surface texture and maximum size of coarse aggregates

also influence the workability of concrete. Generally larger sized aggregates with

smooth texture provides higher workability of concrete in same water content than with

small-sized aggregates. Generally, workability of fresh concrete is measured by slump

measurement due to its convenience to use in field as well as in laboratory (Stanley,

2011).

Fly ash or GGBS based geopolymer concrete exhibited better workability than OPC

concrete for similar water content in previous studies. Collins and Sanjayan (1999)

reported that initial slump measurements of powder-activated geopolymer and OPC

concrete were 120 mm and 75 mm, respectively for the same water/binder ratio (0.5).

In addition, geopolymer concrete showed good workability retention up to 2 hours

(decreased by 20 mm only) because of a slower rate of reaction. The higher proportion

of fly ash is one of the reasons to decrease the water demand in geopolymer concrete

because of its round-shaped and glassy textures (Siddique, 2008). In addition, fly ash

can be dispersed easily in the alkaline environment without addition of chemical

admixtures (Chindaprasirt et al., 2007). Whereas, Fang et al. (2018) suggested that an

increase of GGBS in source materials can result in a decrease in the workability of

geopolymer concrete.

The effects of chemical admixtures into workability of geopolymer concrete have not

been clearly suggested in the literature. Some studies on geopolymer concrete were

carried out using chemical admixtures (superplasticiser), however, the impacts of

addition of chemical admixtures in workability and strength development of

geopolymer concrete has not been investigated in these studies (Ahmed et al., 2011,

Diaz-Loya et al., 2011, Farhan et al., 2019, Fang et al., 2018). Hardjito and Rangan

(2005) reported that the addition of naphthalene-based superplasticiser up to 4%


18

improved the workability of fly ash-based geopolymer concrete (40 mm to 90 mm

slump) with small adverse effect in compressive strength. Albitar et al. (2014) reported

an increase in slump value of fly ash-based geopolymer concrete with addition of

superplasticizer. However, there was a significant decrease in early age as well as 28-

day compressive strength. A study by Nematollahi and Sanjayan (2014) suggested that

the effects of superplasticisers on workability and strength of fly ash based geopolymer

concrete depend on the type of the superplasticiser and alkali activator used. Their study

found that naphthalene-based superplasticiser was effective in geopolymer binder

activated by sodium hydroxide without any adverse effects, whereas polycarboxyle-

based superplasticisers were effective in geopolymer binder activated by sodium

hydroxide and sodium silicate with a significant decrease in compressive strength.

Another study by Bakharev et al. (2000) also reported an improvement in workability

of GGBS based geopolymer concrete using lignosulphonates-based chemical

admixture, however, it prolonged the setting time and decreased the concrete strength.

However, most of the studies in geopolymer binders were carried out without the

addition of chemical admixture achieving good workability of concrete in low

water/binder ratio (Fernandez-Jimenez et al., 2006b, Ryu et al., 2013, Sofi et al., 2007,

Collins and Sanjayan, 1999, Castel et al., 2016, Gunasekera et al., 2019).

2.4.2 Mechanical properties

Mechanical properties of concrete are the strength related properties; such as

compressive strength, indirect-tensile strength, flexural strength and modulus of

elasticity.

a) Compressive strength development

Compressive strength is one of the major mechanical properties of concrete to

determine the quality (strength grade) of concrete. Previous studies showed that curing

temperature plays a crucial role in the development of compressive strength of concrete

at an early age. Therefore, the compressive strength development in geopolymer

concrete is studied in two different curing conditions.


19

Compressive strength developments of geopolymer concrete under ambient curing

conditions in some studies are presented in Figure 2.5. Generally, fly ash-based

geopolymer concrete attains relatively lower early age strength than OPC concrete of

same strength grade at normal temperature, however, it can develop higher compressive

strength after a long period as shown in Figure 2.5. Whereas, GGBS based geopolymer

concrete showed a comparable early age strength to OPC. Generally, the mechanical

strengths of geopolymer concrete increase with the increase in the amount of GGBS in

source materials (Parthiban et al., 2013, Deb et al., 2014).

Figure 2.5: Compressive strength development of geopolymer concretes

At high temperature, the geopolymerisation process is accelerated due to the increase

in solubility of aluminosilicate compounds in alkaline solution (Pacheco-Torgal et al.,

2008, Sindhunata et al., 2006). Fernández-Jiménez and Puertas (1997) reported a

significant increase in the rate of geopolymerisation reaction when the curing

temperature increased from 25 °C to 60 °C which resulted in rapid setting and hardening

of geopolymer paste. Similarly, in OPC concrete, curing at higher temperature increases

the rate of hydration of cement which results in high early age strength (Das Gupta and

Tam, 1989, Nurse, 1949). Previous investigations showed that geopolymer concrete or

mortar can develop significantly high early strength when cured at high temperature

0

10

20

30

40

50

60

70

0 7 14 21 28 35 42 49 56 63 70 77 84 91

Com

pre

ssiv

e st

ren

gth

(M

Pa)

Age (day)

OPC + 40% fly ash- Elahi et al. (2010)

OPC + 30% GGBS- Eren (2002)

Collins and Sanjayan (GGBS) (1999)

Lee and Lee (fly ash +GGBS) (2013)

Nath and Sarker (fly ash +GGBS) (2012)

Albitar et al. (fly ash) (2014)

Naidu et al. (fly ash +GGBS) 2012

Wallah and Rangan (fly ash) (2006)


20

(Fernandez-Jimenez et al., 2006b, Hardjito and Rangan, 2005, Vora and Dave, 2013).

Hardjito and Rangan (2005) reported that geopolymer concrete can develop around

30% and 75% of its final compressive strength when cured for 4 hours and 24 hours,

respectively at 60 °C.

However, longer curing time at elevated temperature may not be useful in geopolymer

concrete, Hardjito and Rangan (2005) and Altan and Erdoğan (2012) showed that heat

curing after 48 hours did not increase compressive strength. On the other hand, Van

Jaarsveld et al. (2002) suggested that prolonged heat curing of geopolymer concrete

(more than 24 hours) can result in an adverse effects on geopolymer matrix due to

evaporation of structural water and excessive shrinkage.

There are some limitations of accelerated cured concrete, such as lower concrete density

and higher porosity. Higginson (1961) suggested that heat (steam) curing of OPC

concrete at an early age develops higher porosity and non-uniform microstructures of

concrete which results in higher permeability of concrete. The 28 days (and later)

strength of heat-cured concrete was found to be relatively lower than normal-

temperature cured concrete because of having large pore size. Sindhunata et al. (2006)

suggested similar effects in geopolymer; increase in total pore volume in geopolymer

mortar with the increase in curing temperature due to the loss of moisture from the

geopolymer matrix. Rovnaník (2010) reported a gradual decrease in density of

geopolymer mortar with the increase in curing temperature from 20°C to 80°C because

of an increase in pore volume.

b) Tensile and flexural strength

Generally, the tensile strength of concrete is not directly considered in design of

reinforced concrete structures because plain concrete possesses very low tensile

strength. However, it is important in design of some structures, such as pavement slabs

and prestressed concrete structures. Due to the difficulties associated with the direct

tensile test, it is measured by two indirect methods; (a) indirect-tensile (splitting) test

and (b) flexural (modulus of rupture) test.


21

Previous studies showed that geopolymer concrete has higher indirect-tensile and

flexural strengths than OPC concrete of same compressive strength (Albitar et al., 2014,

Sofi et al., 2007, Hardjito and Rangan, 2005, Raijiwala and Patil, 2011). Raijiwala and

Patil (2011) advised that geopolymer concrete possessed around 1.4 times higher

indirect-tensile and 1.6 times flexural strength than OPC concrete of same compressive

strength. There is no design standard for geopolymer concrete, so far. Different models

have been proposed to estimate indirect- tensile strength and flexural strengths of

geopolymer concrete, some of them are presented in Table 2.3. Most of the equations

in Table 2.3 estimate higher values of indirect-tensile and flexural strengths than

recommended by concrete standards of current practices, such as AS-3600 (2018) and

ACI-318 (2011).

Table 2.3: Proposed models for indirect-tensile and flexural strengths

Binder type Source Proposed models

OPC ACI-318 (2011) �′�� = 0.56√��

� = 0.62√��

AS-3600 (2018) �′�� = 0.4√��

� = 0.6√��

Geopolymer (fly ash + GGBS)

Sofi et al. (2007) �′�� = 0.5√��

� = 0.6√��

Nath and Sarker (2017) − �� = 0.93√��

Geopolymer (fly ash) Tempest (2010) �′�� = 0.616√�� -

Diaz-Loya et al. (2011) - �� = 0.69√��

Ryu et al. (2013) �� = 0.17 (��)� �⁄ -

Albitar et al. (2014) �′�� = 0.6√��

� = 0.75√��

where, �� and �� are characteristic and mean 28 days compressive strengths of

concrete, respectively; �′�� and �� are characteristic and mean indirect-tensile

strengths of concrete, respectively and �� and �� are characteristic, and mean flexural

strengths of concrete, respectively.


22

Figure 2.6: Indirect-tensile strength of geopolymer concrete

Indirect-tensile strength results of geopolymer concrete from some previous studies are

plotted in Figure 2.6. In this figure, most of the indirect-tensile strength values of

geopolymer concrete are higher than estimated values using AS 3600 (2018) and ACI-

318 (2011) for the same strength grade of concrete. Therefore, those data points are

plotted above the lines representing equations of AS 3600 (2018) and ACI-318 (2011).

Figure 2.7: Flexural strength of geopolymer concrete

0

2

4

6

8

4 5 6 7 8 9 10

Ind

irec

t te

nsi

le s

tren

tgh

(M

Pa)

√f'c (MPa)1/2

AS 3600 (2018) ACI 318 (2011)Hardjito and Rangan (2005) Sofi et al. (2007)Tempest (2010) Raijiwala and Patil (2011)Albitar et al. (2014)

0

2

4

6

8

10

4 5 6 7 8 9 10

Fle

xu

ral

stre

ngt

h (

MP

a)

√f'c (MPa)1/2

AS 3600 (2018) ACI 318 (2011)

Douglas, Bilodeau and Malhotra (1992) Diaz-Loya, Allouche and Vaidya (2011)

Raijiwala and Patil (2011) Albitar et al. (2014)

Nath and Sarker (2017)


23

Flexural strength results from some previous studies on different types of geopolymer

concrete are plotted in Figure 2.7. Alike to indirect-tensile strength, the flexural

strength values of geopolymer concrete in previous studies are higher than estimated

values using AS 3600 (2018) and ACI-318 (2011). In addition, the relationship models

for flexural strength of geopolymer concrete purposed by Albitar et al. (2014) and Nath

and Sarker (2017) estimate significantly higher values of flexural strength of

geopolymer concrete than estimated by AS 3600 (2018) and ACI-318 (2011).

There were a lot of variations in both indirect-tensile strength and flexural strength

results of geopolymer concrete. The variations in results of geopolymer concrete were

due to the differences in their ingredients; source materials and alkali activator (Duxson

et al., 2006). In addition, the types and properties of coarse aggregates used can

significantly affect the mechanical properties of concrete. For example, concrete made

from quartzite and granite exhibited higher tensile and flexural strength compared to

concrete using limestone and sandstone aggregates (Beshr et al., 2003, Wu et al., 2001).

2.4.3 Stress-strain behaviour and modulus of elasticity

Stress-strain curves of geopolymer and OPC concrete of different strength grades (40

MPa to 60 MPa) under uniaxial compression reported in previous studies are shown in

Figure 2.8 (Junaid, 2015, Noushini et al., 2016, Strukar et al., 2018, Bahraq et al., 2019,

Ali et al., 1990, Wee et al., 1996). In these studies, geopolymer concrete shows a

slightly gentler slope of the ascending branch than OPC concrete of similar strength

grade and a larger critical strain (strain at maximum stress or ��). In addition,

geopolymer concrete shows a relatively gentler descending branch than OPC concrete

in the post-peak stage which is the indication of ductile failure. As shown in Figure

2.8, the critical strain of geopolymer concrete is generally more than 0.003, which is

higher compared to OPC concrete. It is widely believed that critical strain in normal

strength grade OPC concrete lies between 0.002-0.003 under compression (Desayi et

al., 1978, Carreira and Chu, 1986, Wee et al., 1996). Therefore, higher deformation at

maximum stress and gentler slope of descending branch are the indicators of the

toughness of geopolymer concrete because it can absorb relatively higher strain energy

than OPC concrete of same strength grade before failure. Farhan et al. (2019) reported


24

a slightly brittle stress-strain behaviour of both, geopolymer and OPC concrete of 65

MPa grade. However, fly ash-based geopolymer concrete showed higher deformation

at maximum stress (��) as well as less steep descending branch than OPC concrete of

same strength grade in their study.

Figure 2.8: Stress-stain relationships of geopolymer concrete

Modulus of elasticity of concrete governs its deformation (stress-strain relation) under

load. The bending stiffness of a flexural member is directly proportional to modulus of

elasticity of concrete, hence higher modulus of elasticity of concrete decreases the

deflection of structures. Modulus of elasticity of concrete depends on several factors,

such as property of coarse aggregates, proportion of sands and amount of binder. The

amount of coarse aggregate in concrete can make a difference in modulus of elasticity

of concrete. Nikbin et al. (2014) found an increase in modulus of elasticity of concrete

with an increase in proportion of coarse aggregate. Using quality aggregates having

high modulus of elasticity, such as granite, quartzite and limestone can result in a higher

modulus of elasticity of concrete than from weaker aggregates like sandstone (Baalbaki

et al., 1991). Generally, the modulus of elasticity of concrete increases with the increase

in strength grade of concrete.

0

10

20

30

40

50

60

70

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Co

mp

ress

ive

stre

ss (

MP

a)

Strain

Junaid (2015)- Geopolymer

Junaid (2015)- Geopolymer

Noushini et al. (2016)- Geopolymer

Bahraq et al. (2019)- OPC

Strukar et al. (2018)- OPC

Wee et al. (1996)- OPC

Ali et al. (1990)- OPC


25

In some previous studies, modulus of elasticity of geopolymer concrete was found to

be lower than OPC concrete of same compressive strength (Fernandez-Jimenez et al.,

2006a, Hardjito and Rangan, 2005, Noushini et al., 2016) which were heat cured at

early age. Those results were significantly lower than the estimated modulus of

elasticity estimated by AS-3600 (2018) and ACI-318 (2011). However, some studies

of fly ash and GGBS based geopolymer concrete at ambient temperature curing found

modulus of elasticity of geopolymer concrete close to modulus of elasticity of OPC

concrete of same grade (Douglas et al., 1992, Thomas and Peethamparan, 2015,

Yildirim et al., 2011, Sofi et al., 2007). These studies reported good correlations

between modulus of elasticity of geopolymer concrete and estimated values using AS-

3600 (2018) and ACI-318 (2011). Some of the equations proposed for the modulus of

elasticity of geopolymer concrete are presented in Table 2.4. In this table, all the

proposed equations for geopolymer concrete estimate lower values of modulus of

elasticity than AS-3600 (2018) and ACI-318 (2011).

Table 2.4: Relationship between modulus of elasticity and compressive strength

Binder type Source Proposed relationships (in

MPa)

OPC ACI-318 (2011) �� = 0.043(�)�·�√��

OPC AS-3600 (2018), �� ≤ 40 MPa �� = (�)�·�0.043√��

AS-3600 (2018), �� > 40 MPa �� = (�)�·�(0.024�� + 0.12)

Geopolymer Tempest (2010) �� = 3421√��

Geopolymer (fly ash+

GGBS)

Noushini et al. (2016) �� = −11400 + 4712√��

Geopolymer (fly ash) Diaz-Loya et al. (2011) �� = 0.037(�)�·�√��

A comparison of modulus of elasticity results of geopolymer concrete from some

previous studies is plotted in Figure 2.9. Data points in this figure show that

geopolymer concrete cured at ambient temperature (Douglas et al., 1992, Thomas and

Peethamparan, 2015, Yildirim et al., 2011) are plotted close with model lines of AS-

3600 (2018) and ACI-318 (2011). Hence, the existing models of modulus of elasticity

are also applicable for geopolymer concrete cured at ambient temperature.


26

Figure 2.9: Modulus of elasticity of geopolymer concrete

Pauw (1960) suggested that density is one of the major factors to affect modulus of

elasticity of concrete which is widely accepted by concrete standards (AS-3600, 2018,

ACI-318, 2011). Heat curing at early age of geopolymer concrete evaporates water

from the geopolymer matrix and results in higher porosity and lower density of concrete

(Temuujin et al., 2009). Therefore, the curing method can also be one of the major

factors to influence in modulus of elasticity of geopolymer concrete because it affects

the concrete density.

2.4.4 Poisson’s ratio

Concrete standards recommend Poisson’s ratio of concrete as 0.2 irrespective of

concrete strength grade (AS-3600, 2018, ACI-318, 2011). Depending on the types of

aggregates, Poisson’s ratio of concrete can be in the range of 0.15 to 0.22 under

compressive loading (Neville, 1995). Carrasquilio, Nilson & Slate (1981) also

suggested average Poisson’s ratio of OPC concrete as 0.2 regardless of the compressive

strength of concrete (32.0 MPa to 77 MPa).

Hardjito and Rangan (2005) reported Poisson’s ratio of geopolymer concrete between

0.13 to 0.16 for the range of compressive strength from 44 to 89 MPa. A study of Diaz-

0

10

20

30

40

50

4 5 6 7 8 9 10

Mo

du

lus

of e

last

icit

y (

GP

a)

√fcm (MPa)1/2

AS 3600-2018ACI 318 (2011)Douglas et al. (1992)Hardjito and Rangan (2005)Fernandez-Jimenez et al. (2006)Tempest (2010)Diaz-Loya et al. (2011)Yildirim et al. (2011)Thomas and Peethamparan (2015)


27

Loya et al. (2011) found Poisson’s ratio of geopolymer concrete in the range of 0.08 to

0.22 irrespective of compressive strength. Thomas and Peethamparan (2015) reported

Poisson’s ratio of geopolymer concrete as low as 0.126 to 0.134 with no notable

relationship with compressive strengths for a range of 16 MPa to 53 MPa. Considering

these results, Poisson’s ratio of geopolymer concrete can be taken as similar to

conventional OPC concrete.

2.4.5 Serviceability properties

Serviceability properties of concrete are related to the long-term usage of concrete

structures to keep them in serviceable and usable conditions. Shrinkage and creep are

the major serviceability properties of concrete that are responsible for cracks and

deflections concrete of structure during their service life.

a) Shrinkage

Shrinkage is the contraction of concrete due to the removal or consumption of water

from its capillary pores either by hydration of cement, called autogenous shrinkage, or

by evaporation of water to atmosphere, called drying shrinkage. As the

geopolymerisation process recycles water molecules, autogenous shrinkage may not be

applicable in geopolymer concrete. Similar to OPC concrete, it is expected that the main

mechanism for drying shrinkage in geopolymer concrete is the building of negative

pressure within the capillary network of the binder paste as menisci form, this stresses

lead to contraction of the concrete (Sagoe-Crentsil et al., 2013). Drying shrinkage

causes an increase in tensile stress, which may lead to cracking and deformation of

concrete structure even without an imposed load. AS-1379 (2017) recommends that

drying shrinkage of normal grade concrete should be less than 1000 micro-strains at 56

days of age to meet the serviceability requirements of structures. AS 3600 (2018)

recommends an empirical relationship to estimate drying shrinkage strain of a concrete

member on the basis of surrounding air environment, member thickness and concrete

age as following.

�� = ��.� (2.4)


28

where, �� is a constant determined by the thickness and age of concrete member; value

of k� depends upon the climatic zone (0.5 to 0.7); ��.� is the basic drying shrinkage

strain, depends on the concrete strength grade which can be estimated as:

��.� = (0.9 − 0.005 ��). ��.�

∗ (2.5)

where, ��.�∗

is the final basic drying shrinkage strain of a concrete depends upon the

quality of aggregates used, can be taken as 800 to 1000 micro-strain.

The drying shrinkage of concrete specimen at any time ‘��’ can be estimated using the

equation suggested by ACI-209.2R (2008) as following:

�� = �(��)�

��(��)�� . �� (2.6)

where, �� is the time from the end of initial curing and ε�� is the ultimate shrinkage

strain which can be taken as 780 microstrains in the absence of specific data, � and �

are factors depend on curing time-ratio and shape and size of specimen. For the standard

7 days of moist curing conditions, values of � and � can be taken as 35 and 1,

respectively.

For a concrete member having a different size than the standard specimen and cured

under different conditions (temperature and humidity) other than standard, a

modification factor "ϒ��" should be applied to estimate its shrinkage. The modification

factor is the product of correction factors, such as curing factor "ϒ��.��", shape factor

"ϒ��.��" and relative humidity factor "ϒ��.��".

Drying shrinkage of concrete depends on several factors, such as amount of water and

binder content and types of aggregates. Generally, higher water content results in a

higher volume of capillary pores which can increase the drying shrinkage of concrete

(Neville, 1995). Drying shrinkage of concrete also increases with the increase in

water/binder ratio and binder content (Brooks, 1989, Neville, 1995). However,

Bissonnette, Pierre & Pigeon (1999) reported that the drying shrinkage of concrete is


29

more dependent on binder content (paste volume) in concrete than water/binder ratio.

Concrete standards (AS-3600, 2018, EN-1992.1.1, 2004) recommend that the ultimate

drying shrinkage of concrete decreases with concrete strength grade which is a function

of water/binder ratio. Hence, water/cement ratio can be regarded as the major factor to

affect the drying shrinkage of concrete (Brooks, 2005). Concrete made from quality

aggregates such as, granite and quartz experiences smaller drying shrinkage than from

inferior quality aggregates, such as sandstone.

Previous studies which were carried out by heat curing reported significantly lower

drying shrinkages of geopolymer concrete (Wallah, 2009, Tempest, 2010, Sagoe-

Crentsil et al., 2013). Heat curing evaporates water from micro-pores of concrete, hence

less water remains in concrete to effect in long-term shrinkage of concrete (Davidovits,

1999). However, Sennour and Carrasquillo (1989) suggested only a small reduction in

drying shrinkage of OPC concrete by heat curing at early age. Castel et al. (2016)

reported that the drying shrinkage of fly ash and GGBS based geopolymer concrete

depends on the curing temperature. In their study, geopolymer concrete cured at 80 °C

for one day suffered three times less drying shrinkage than the same concrete cured at

40 °C for one day. The drying shrinkage of heat-cured geopolymer concrete reported

by Tempest (2010) and Wallah (2009) were 120 microstrains at 112 days and 100

microstrains at 1 year, respectively.

However, higher drying shrinkage of geopolymer concrete has been reported at ambient

curing conditions in some studies. Collins and Sanjayan (1999) and Wallah and Rangan

(2006) reported drying shrinkage of ambient cured geopolymer concrete around 1600

micro-strains (112 days) and 1200 microstrain (84 days). Whereas, Deb et al. (2015)

reported a smaller drying shrinkage of ambient cured geopolymer concrete (482

microstrains at 180 days) as shown in Figure 2.10 which was lower than drying

shrinkage of OPC concrete of same grade and estimated shrinkage using AS-3600

(2018). Drying shrinkage increases rapidly at early age, then slows down because the

rate of moisture loss from concrete is higher at early age and only a small amount of

moisture remains for later age.


30

Figure 2.10: Dying shrinkage growth in geopolymer concrete (Deb et al., 2015)

The seviceability properties of geopolymer concrete can be affected by the proportions

of ingredients of geopolymer binder. Deb et al. (2015) reported that increasing the

amount of GGBS from 10% to 20% and decreasing in sodium silicate/sodium

hydroxide ratio from 2.5 to 1.5 resulted in a reduction of drying shrinkage of fly ash-

based geopolymer concrete significantly. In both of these cases, compressive strength

of concrete increased, which might be a cause to decrease the drying shrinkage of

concrete. Similar to OPC concrete, Un et al. (2015) suggested that water/binder ratio

is a major factor to affect the drying shrinkage of geopolymer concrete.

b) Creep

Creep is the long-term deformation in a hardened concrete member under sustained

load (in the same direction to loading). Creep strain generally causes axial shortening

of vertical members under compression. In flexural concrete members, creep strain

gradually increases the vertical deflection of structures with time and makes them

unserviceable. In addition, higher deflection in flexural member results in excessive

cracks in the tensile zone which can create several structural problems and lead to the

failure of structure. In OPC concrete, it is assumed that creep occurs due to the sliding

of colloidal sheet of C-S-H paste which are separated by spaces containing adsorbed

0

100

200

300

400

500

600

700

0 14 28 42 56 70 84 98 112 126 140 154 168 182

Dry

ing

sh

rin

kag

e (M

icro

stra

in)

Age (days)

AS 3600

OPC concrete

Geopolymer concrete


31

water (Neville, 1995). Castel et al. (2016) suggested that creep in concrete is a complex

mechanism, in addition to sliding of colloidal sheet, there is a removal of the interlayer

water from hydrated cement gel and deformation of aggregates and binder paste.

Similar to drying shrinkage, creep strain of concrete is inversely proportional to its

compressive strength because higher grade concrete has smaller pore volume and

higher modulus of elasticity to resist the deformation (Neville, 1995). Aggregates are

volumetrically more stable than the cement paste, therefore an increase in the amount

of aggregates in concrete mix decreases the creep strain in concrete (Park and Paulay,

1975). Creep of concrete also depends on the age of loading. Bryant and Vadhanavikkit

(1987) reported that concrete loaded at an early age suffered significantly higher creep

strain than it loaded at later age because pore volume in concrete gradually decreases

with the curing period of concrete.

A study by Sennour and Carrasquillo (1989) concluded that heat curing at early age

reduces the creep strain of conventional concrete due to accelerated hydration of cement

and loss of moisture before subjecting to creep load. However, being a new material,

effects of accelerated curing on the creep behaviour of geopolymer concrete has not

been studied in detail, so far. Concrete standards (AS-3600, 2018, ACI-209.2R, 2008),

generally define creep property of concrete by creep coefficient (��) which can be

calculated as follows:

�� = ��

�� (2.7)

Specific creep (creep strain per unit of sustain stress) can be calculated from,

Specific creep = ��

�� (2.8)

AS 3600 (2018) recommends a relationship to estimate the creep strain (ε��) of a

concrete member at any time ‘t’ based on of its creep coefficient and sustained load as

follows:

�� = ��/�� (2.9)


32

where, σ� is the constant stress sustained by concrete member.

Using AS-3600 (2018), the creep coefficient of concrete can be estimated from:

�� = ��.� (2.10)

where, ϕ��.� is the basic creep coefficient of concrete depending upon the strength

grade; k� , k�, k� and k� are modification factors depending upon the thickness of the

member, age of concrete, local climatic zone and factor for high strength concrete,

respectively.

Similar to drying shrinkage, the creep coefficient of concrete specimen (��) at any

time can be estimated using ACI-209.2R (2008) as following:

�� = �(��)�

��(��)�� . �� (2.11)

where, �� is the time from the end of initial curing and ϕ�� is the ultimate creep

coefficient which can be taken as 2.35 in the absence of specific data for local

aggregates and conditions, � and d are factors for curing time-ratio and shape and size

of specimen. For the standard 7 days moist curing conditions, values of � can be taken

as 1 and � = 26��·��×��(� �⁄ )�, where � �⁄ is the volume to surface ratio of the

specimen.

For a concrete member having different size than standard specimen and cured under

different conditions (temperature and humidity) other than standard, a modification

factor "ϒ��" should be applied to estimate its creep coefficient similar to shrinkage

calculation as discussed earlier.

Previous studies reported smaller creep strains of geopolymer concrete than OPC

concrete of same strength grade. Wallah (2010) reported a 22 microstrain/MPa specific

creep of geopolymer concrete (compressive strength 57 MPa) for one year compared

to around 60 microstrain/MPa in OPC concrete of same strength (Warner et al., 1998).

Gunasekera et al. (2019) reported around 1.9 creep coefficient of fly ash-based


33

geopolymer concrete having a compressive strength of 36 MPa for one-year compare

to a 3.0 creep coefficient in OPC concrete of same compressive strength. Their study

suggested that the difference in pore size distribution and pore volume between OPC

and geopolymer concrete may be one of the factors to make difference in their creep

strain. Sagoe-Crentsil et al. (2013) measured around 0.5 basic creep coefficient of

geopolymer concrete of grade 40 MPa for one year, which was 40–60% lower than the

creep coefficient OPC concrete of same grade.

Creep strain measured by Gunasekera et al. (2019) in Figure 2.11 shows that increase

in creep strain of geopolymer concrete after 56 days was very small compared to OPC

concrete. The lower shrinkage and creep strains in geopolymer concrete positively

impact the serviceability of prestressed concrete structures by minimising loss of

prestressing stress over the service life of structure.

Figure 2.11: Creep strain of geopolymer and OPC concrete of previous studies

2.4.6 Durability properties

Durability of geopolymer binder is one of its major significances over OPC because the

geopolymer binder does not rely on calcium compounds and is free from calcium

hydroxide Ca(OH)2 and tricalcium aluminate (C3A) (CIA, 2011, Davidovits, 1994). The

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Cre

ep c

offi

cien

t

Age (days)

OPC-Gunasekera et al. (2019)

Geopolymer-Gunasekera et al. (2019)

AS 3600

Geopolymer-Sagoe-Crentsil et al. (2013)

Geopolymer-Wallah (2010)


34

presence of Ca(OH)2 and C3A make hardened OPC paste vulnerable towards sulphate

and acid attacks which results in deterioration of concrete strength (Fernandez-Jimenez

et al., 2006a). Previous studies suggested that geopolymer concrete possesses better

resistance against sulphate and acid attack than OPC concrete (Bakharev, 2005, Wallah

and Rangan, 2006). Some studies suggested that there was small or no alkali-silica

reaction in both, fly ash and GGBS based geopolymer concrete (Talling and Brandstetr,

1989, Fernandez-Jimenez et al., 2006a, Kupwade-Patil and Allouche, 2011). A study

of fly ash and GGBS based geopolymer concrete by (Kurtoglu et al., 2018) exposing

them in 5% sulfuric acid, 5% magnesium sulphate and 3.5% seawater found that both

geopolymer concrete showed higher resistivity against acid and sulphate attack than

OPC concrete. Corrosion of steel reinforcement is another durability issue of OPC

concrete. Reddy et al. (2011) suggested that there was no loss of mass of reinforcing

steel inside geopolymer concrete compare to 60% losses of a mass of reinforcing steel

in OPC concrete for similar exposure.

Formation of hydrated calcium aluminium sulphate ((CaO)3(Al2O3)(CaSO4)3·32H2O)

or “ettringite” in the later age; delay ettringite formation (DEF) is one of the serious

durability problems in heat-cured precast OPC concrete structures (Czarnecki, 2016,

Hime, 1996). Ettringite is an expansive compound which is a product of reaction

between sulphate and calcium aluminate during hydration of Portland cement. It is not

harmful when it forms during the plastic stage of concrete. However, when

ettringite forms in a hardened cementitious system in the form of crystals, the

volumetric expansion creates internal tensile stress which results in cracking and failure

of a concrete structure. When concrete is exposed to a higher temperature (around 70

ºC) in the early age, the hydration process of Portland cement is altered. In the presence

of water and high temperature, ettringite decomposes to non-expansive calcium

monosulfoaluminate. In the later age, at normal temperature and presence of moisture,

ettringite reforms back. On the other hand, there is no presence of sulphate and C3A in

the geopolymer binder system, hence there is no possibility of DEF in the heat-cured

geopolymer concrete (Gourley and Johnson, 2005).


35

2.5 Application of geopolymer binder in structural concrete

Application of geopolymer in structural grade concrete is still in trial phase.

WAGNERS, a Queensland based cement and concrete company used its Grade 40 MPa

fly ash and GGBS based geopolymer concrete named Earth Friendly Concrete (EFC)

in the precast floor beams of the Global Change Institute building at the University of

Queensland. It was reported that EFC concrete exhibited higher mechanical strengths

than OPC concrete of same grade and complied with the requirements of AS 3600.

WAGNERS also utilised its Grade 40 MPa EFC to construct 435 mm thick

unreinforced concrete runway pavement in Brisbane West Wellcamp Airport,

Queensland (Glasby et al., 2015). Higher flexural strength of geopolymer concrete may

be a major advantage in such pavement applications (5.8 MPa at 28 days). Recently,

VicRoads, Victoria has endorsed application of geopolymer concrete in general use of

road constriction, such as road pavements and drainage pipes (Andrews-Phaedonos,

2014).

Studies on the behaviour of geopolymer reinforced concrete column by Sarker (2008b)

suggested that geopolymer concrete column can be analysed and designed according to

the concrete standards, such as AS 3600 with very close experimental results to

predicted values. Similarly, Sumajouw et al. (2007) found that the load capacity of

geopolymer concrete columns complied with the design provisions of AS 3600 and

ACI 318.

Jeyasehar et al. (2013) carried out an experimental study to evaluate the performance

of fly ash-based geopolymer concrete in reinforced concrete beams, railway sleepers

and prestressed concrete beams. In their experiment, reinforced geopolymer concrete

beams of 3000 mm exhibited higher first-crack and ultimate load capacities (around

12%) than identical OPC concrete beams. Similarly, precast railway sleepers from

geopolymer concrete showed higher, first-crack and ultimate load capacities than from

OPC concrete. In addition, few geopolymer concrete beams were cast, accelerated

cured and post-tensioned in a similar way to conventional OPC concrete beams. Load

testing showed that geopolymer prestressed concrete beams can bear a similar ultimate

load to OPC concrete beam (35 kN).


36

Yost et al. (2012) investigated the flexural performance of fly ash-based geopolymer

reinforced concrete beams with different reinforcement configurations. Their study

suggested that load-deflection behaviours of both geopolymer and OPC concrete beams

were similar and their load capacity can be closely estimated using conventional

equations. The ratios of measured/calculated flexural load capacity were slightly higher

in geopolymer concrete beams compared to OPC concrete beams.

2.6 Limitations of two-part geopolymer binder

To date, sodium silicate and sodium hydroxide based two-part geopolymer binder has

been mostly used in research experiments and field applications (Hardjito and Rangan,

2005, Diaz-Loya et al., 2011, Puertas et al., 2000, Deb et al., 2015, Jeyasehar et al.,

2013). However, two-part geopolymer binder has some limitations to be used in

concrete because of the hazardous nature of alkali liquids. Sodium and potassium

hydroxide solutions can cause severe burns to the human body and eye damage (ERCO-

Worldwide, 2012). In addition, concentrated sodium hydroxide solution can be

corrosive to several metals such as tin, aluminium, zinc, copper and lead and can

dissolve glass (OxyChem, 2013, Helmenstine, 2013). Therefore, mixing and handling

of these liquids can cause physical injuries. Some studies have been carried out recently

to replace sodium hydroxide with sodium carbonate in alkali activator to make

geopolymer binder, however, the activators were used in a liquid state (similar to two-

part geopolymer) in those experiments (Abdalqader and Al-Tabbaa, 2015, Ishwarya et

al., 2019).

The concentration of sodium hydroxide can bring significant differences in workability

and mechanical properties of geopolymer concrete which can be easily altered by the

addition of free water in mixing process. So, a higher skilled manpower is needed for

mixing and handling of this two-part geopolymer binder. These limitations of

geopolymer binder hinder its adoption in concrete industry despite having better

mechanical, serviceability and durability properties than conventional OPC concrete.

In order to use geopolymer binder in concrete industry, it is necessary to develop a

sodium hydroxide-free, one-part geopolymer binder which can be mixed and handled

in a conventional way.


37

2.7 Prestressed concrete

2.7.1 General

By nature, concrete is strong in compression but very weak in tension. In conventional

reinforced concrete (RC) structures, steel bars are placed to bear the flexural tensile

load generated by imposed load. In general utilizations, middle span of RC structures

(flexural members) experience a sagging bending moment under service load

(downwards) which generates a tensile stress in the bottom section of the structure. The

bottom section of RC structures suffers cracking and deflection due to flexure.

Therefore, RC sections are not feasible for long flexural members, such as long beam

and bridge girders.

Prestressed concrete is a construction technique in which the flexural tensile stress

generated in the concrete member due to imposed load is counteracted by an initial

prestressing compressive force. Generally, the initial prestressing stress is achieved by

stretching high-strength steel strands ducted below the centroid axis of concrete section.

Using this technology, same flexural member can carry a significantly higher imposed

load than conventional reinforced concrete section. Hence, a slim prestressed concrete

section can replace a large RC section and reduce self-weigh and material costs. Figure

2.12 shows the difference between reinforced and prestressed concrete methods.

Figure 2.12: Working principles of reinforced and prestressed concrete (FHA, 2013)


38

The concept of prestressing was discovered from the technique of making a wooden

barrel, where metal bands were wound around wooden staves (Figure 2.13). The metal

bands were tightened under tensile stress such that they compress wooden staves and

enable them to bear interior liquid pressure.

Figure 2.13: Wooden barrels with metal bands

It took a long time for prestressing concept to be applied in practice. In 1872, P. H.

Jackson, an engineer from California, patented a prestressing system that used a tie rod

to construct beams and arches from individual blocks. His effort was followed in 1888

by C.W. Doehring who obtained a patent in Germany for prestressing slabs with metal

wires (Aalami, 2007). By nature, concrete suffers from shrinkage and creep strains

which result in gradual loss of prestressing stress over time due to axial shorting of a

member. In order to hold higher stress by prestressing strands for a long time (despite

some losses), a high-strength steel (yield strength above 1000 MPa) should be used in

prestressing strands. However, due to the unavailability of high-strength steel, efforts

to make prestressed concrete structures were not successful at that time. In 1928,

Eugene Freyssinet used a new high-strength steel strand and higher strength concrete

to overcome the prestress losses and successfully construct prestressed members in

France and he acquired the patent for prestressed concrete (Xercavins et al., 2010). The

first use of prestressed concrete in U.S.A. was on the Walnut Lane Memorial Bridge in

Philadelphia in 1951 (Figure 2.14). The bridge had precast post-tensioned girders

designed by Gustave Magnel (Zollman et al., 1992). By early 1950 construction of


39

lifted slabs was widely introduced in the U.S.A. using prestressed concrete technology

to limit cracks and reduce deflections in thin flat slabs in buildings (Aalami, 2007).

Figure 2.14: Walnut Lane Memorial Bridge in Philadelphia (Zollman et al., 1992)

The use of prestressed concrete structures is increasing in modern construction practice

because of their economical and structural benefits. The major advantages of using

prestressed concrete are to control the deflection and cracks of flexural members under

service loads (Warner et al., 1998). Generally, using prestressed concrete technology

can reduce around 25% of concrete material and 65% of steel in structures (Ganz,

2008).

2.7.2 Principles of prestressed concrete

In prestressed concrete, concrete member is subjected to an initial compressive force

which generates compressive stress and a small deformation opposite to the direction

of imposed load. At prestress transfer (no-load condition), the resultant stress

(σ��) in bottommost concrete fibre can be expressed as,

�� =��.�.�

��+

��

��− ��.�� (2.12)

For a crack-free section, the resultant stress in bottommost fibre under service load

condition can be expressed as,


40

�� =��.�.�

��+

��

��− ��.�� − �� ≤ ��

� (2.13)

where, �� is effective prestressing load, ��.�� is the bending stress due to the self-

weight; �� is the gross area of the beam cross-section; �� is the second moment of area

of the beam cross-section; � is the maximum eccentricity of prestressing tendon from

the centroid of the beam section; � is the distance of extreme tensile fibre from neutral

axis; �� is the bending stress due to the imposed load.

Prestressed concrete structures are designed to minimise the tensile stress below the

neutral axis of section in order to maintain a crack-free section. The profile of resultant

stress in Figure 2.15 shows that there is a minimal tensile stress in a prestressed

concrete section under service (imposed) load condition.

Figure 2.15: Stress profile in a prestressed concrete section

2.7.3 Types of prestressed concrete structures

According to the method of construction prestressed concrete structures can be

categorised into two types; pre-tensioned and post-tensioned. In pretensioned concrete

member, prestressing tendons are initially tensioned between the end abutments, and

concrete member is cast around the stretched tendons. When the concrete is sufficiently

strong, the stretched tendons are cut from the abutments and anchored to the ends of

concrete member. Pretensioned concrete members are generally precast at the factory

because they need a very strong formwork to hold the stress of stretched tendon for a

long time.


41

In post-tensioning method, a concrete member is cast with a hollow duct. The

prestressing tendons (not stressed) can be inserted into the duct before casting concrete

or later. When the concrete reaches sufficient strength, the tendons are tensioned to the

desired stress level using jacks. Then, tendons are anchored firmly in either end using

end anchorage plates. In bonded tendons, the duct is grouted to prevent the tendons

from corrosion and to develop a bond between prestressing tendons and surrounding

concrete. The gap is left open in unbounded tendons with application of some corrosion

preventing measures. Depending upon the nature of work, a post-tensioned concrete

member can be both, precast or cast-in-situ. Generally, larger structures, such as floor

slabs and long beams are cast-in-situ.

2.7.4 Prestressing tendon’s profile

Selection of tendon’s profiles, such as straight, harped and parabolic depends on the

nature of work and designer’s choice, however it can affect the performance of

prestressed concrete members. While the straight profile is the easiest one, harped and

parabolic profiles provide higher upward deflection in flexural member due to the

difference in eccentricity along the longitudinal axis. Theoretically, parabolic tendon is

the most effective profile because it has a constant curvature which uniformly exerts

distributed equivalent load on the concrete member along the length (Warner et al.,

1998). However, a finite element analysis by Dixit and Khurd (2017) suggested that

harped (trapezoidal) profile gives maximum upward deflection than other profiles for

the same eccentricity and prestressing force. Figure 2.16 shows different cable profiles

generally used in prestressed concrete.


42

Figure 2.16: Cable profiles on prestressed concrete

2.7.5 Losses of prestress

From the beginning of the prestressing process, prestressing force in the steel tendon

decreases continuously thought out the service life of the structure due to several

factors. These losses decrease the load-carrying capacity of prestressed concrete

structures which are divided into two categories: short-term and long-term losses.

a) Short-term losses or immediate losses

Short-term or immediate losses occur during or immediately after the prestress transfer

process, such as elastic loss, friction loss and anchorage slip. As these losses are

predictable, a higher calculated prestressing load can be applied to the prestressing

tendons to achieve a desired effective prestress.

During the prestress transfer process, concrete member undergoes elastic compression

and the prestressing tendon loses some stress, which is called loss due to axial

shortening or elastic loss. This loss depends upon the concrete strength (modulus of

elasticity) at the time of prestress transfer and can be estimated as follows:

�� = ��

��+

��

��

��

��. �� (2.14)


43

where, �� is initial prestressing load, �� and �� are the moduli of elasticity of

prestressing steel and concrete, respectively and �� is the area of the prestressing

tendons.

Friction loss generally occurs in the post-tensioned concrete member during the process

of stretching the prestressing tendons. This loss depends upon the layout of tendon

profile i.e. cumulative angle change in tendon direction and degree of bending. Straight

tendon profile offers the minimum friction loss because there is no bending in tendon

layout.

During prestress transfer, a small slip occurs between prestressing tendon and end

anchorage plates in most of post-tensioning systems. The amount of slip depends on

the type of anchorage and strands and number of strands. Information on magnitude of

slip losses can be obtained from the manufacturer’s datasheets. Nowadays, due to the

advent of technology and quality of equipment, prestress loss due to slip is considerably

small, however, it can be significant for short-span prestressed members.

b) Long-term or time-dependent losses

The prestressing stress in steel tendon gradually declines over the service life of

concrete member because of deformations of concrete and steels due to time-dependent

effects; drying shrinkage and creep in concrete and relaxation of steel tendon.

i. Drying shrinkage loss

Drying shrinkage of concrete causes axial shortening of prestressed concrete members

which results in gradual loss of stress in steel tendon over the service life of the

structure. Theoretically, prestress loss in tendon due to free shrinkage ��.�� is

calculated as:

��.��= �� (2.15)

Structural concrete members are generally cast with conventional steel reinforcements.

The bonded steel reinforcements provide a restrain against the contraction of concrete


44

due to shrinkage. AS 3600 (2018) suggests prestress loss in tendon due to shrinkage

(��.��) as following:

��.�� = ��.��

�� /�� (2.16)

where, �� is drying shrinkage strain and �� is the area of total conventional

longitudinal reinforcement.

ii. Creep loss

In prestressed concrete member, creep strain causes axial shortening of concrete due to

constant compressive stress generated by prestressing load which results in gradual loss

of stress in steel tendon over the service life of the structure. Theoretically, prestress

loss due to creep strain (��.��) can be estimated as follows:

��.�� = �� = ��. ��. ��/�� (2.17)

where, �� is the sustained stress in the concrete at the level of the centroid of the

prestressing tendons.

The presence of conventional steel reinforcement in prestressed concrete members

causes gradual stress redistribution in the concrete section, with transfer of compressive

stress from the concrete to the steel bars. As a result, effective compressive stress in

concrete reduces which also decreases the creep strain of concrete. In this case,

Equation (2.17) overestimates the actual loss of prestress due to concrete creep. The

creep analysis becomes mathematically more complex in such a case which requires a

rigorous computation and therefore not appropriate for normal design calculations. An

approximate calculation of creep of concrete member having conventional

reinforcement can be achieved using pseudo-elastic analysis based on the effective

modulus of elasticity concept (Warner et al., 1998), however, this method is not within

the scope of this study.


45

Some studies were done in the past, about the effects of conventional reinforcement in

prestress losses. Batchelor et al. (1998) suggested that losses in prestressing stress due

to shrinkage and creep in concrete decrease with a decrease in partial prestressing ratio.

Partial prestressing ratio (��) can be calculated from,

�� =��.��

��.��.�� (2.18)

where, �� and �� are the cross-sectional areas of the prestressing tendon and

conventional tensile reinforcement, respectively, and �� and �� are their

corresponding yield strengths. Thus, for a prestressed concrete member without

conventional reinforcements, partial prestressing ratio is 1.

Naaman and Hamza (1993) further reported that time-dependent losses in the

prestressing tendon, generally decrease with a decrease in the partial prestressing ratio,

up to a 30% decrease was observed when partial prestressing ratio decreased from 1 to

0.2. In absence of more rigorous analysis, AS 3600 (2018) recommends around 20%

reduction in the theoretical loss of prestress in prestressed concrete member with

conventional reinforcements due to creep strain as following,

��.�� = 0.8 ��. ��. ��/�� (2.19)

where, �� is the sustained load in the concrete at the level of the centroid of the tendons

(MPa) calculated using the initial prestressing force prior to any time-depended losses

and the sustained portions of all the service loads.

iii. Loss due to relaxation of tendon

A stretched steel tendon gradually loses a part of its stress due to the tensile creep of

steel called stress relaxation. The amount of relaxation largely depends upon the

prestressing ratio (�) which can be expressed as:

� = ��/�� (2.20)


46

where, σ� is the initial prestressing stress and �� is the characteristic minimum

breaking strength of prestressing tendon.

The stress relaxation of tendon is very small when λ is less than 0.5 but its value

increases rapidly as λ approaches 1.0 (Trevino and Ghali, 1985). Considering this

effect, ACI-318 (2011) recommends that maximum tension applied in prestressing

tendon while jacking should not be greater than 0.8�� and in case of post-tensioned

tendons, stress in tendon immediately after prestress transfer should not be greater than

0.7��. AS 3600 (2018) recommends the prestress loss due to relaxation of tendon as

following:

� = �� (2.21)

where, �� is a coefficient, depends on the duration of prestressing force which can be

calculated as:

�� = ��5.4(�)�/�� (2.22)

�� is a coefficient, depends on the prestressing ratio (λ). AS-3600 (2018) recommends

value of k� ranging from 0 to 2 based on value of λ.

�� is a function of average annual temperature and R� is the basic relaxation of tendon

based on 1000 hours of duration at 20°C which can be taken as 1% for low relaxation

wire, 2% for low relaxation strand and 3% for alloy steel bars.

The time-dependent losses in prestressing tendon depend on the stress history of

concrete. As stress in prestressed concrete varies with time, the subsequent losses

depend on the stress level in prestressing tendon at that particular time. In addition, the

time-dependent losses of prestress interact with each other, this interaction should be

considered when effects of all losses are determined. For example, shrinkage and creep

strains in concrete decrease the prestressing stress in the steel tendon, which contribute

to reduce the relaxation loss. Thus, the individual equations for time-dependent losses

provided in concrete standards of current practice do not estimate the realistic value,

however, they are the simple and the closest solutions for those losses. Concrete


47

member loaded (prestress transfer) at later age suffers less time-dependent loss of

prestress than loaded at early age because growth in shrinkage and creep strains of

concrete are higher at early age. Batchelor et al. (1998) reported a measurable

difference in time-dependent losses of prestress in steel tendon when loaded at 7 days

and 28 days.

2.8 Structural suitability of geopolymer concrete in precast prestressed

concrete

The high early age strength development of geopolymer concrete at accelerated curing

shows its potential application in the precast concrete sector where early age strength

and shorter curing periods are desirable for early stripping of formwork. Generally, in

a precast production plant, a 15-16 hours of curing cycle of maximum temperature of

70 °C is needed for a precast OPC concrete member to attain a sufficient strength to be

released from the formworks (Humes, 1998). For a geopolymer concrete, the curing

cycle can be reduced to 8-10 hours to attain the same level of strength for a precast

concrete member.

The structural behaviour of prestressed concrete member, such as first-crack load and

deflection are governed by the initial prestressing stress. According to ACI-318 (2011),

maximum level of allowable prestress (before time-dependent losses) in the concrete is

limited such that extreme fibre stress in tension should not exceed 0.25√�� (equals to

0.4��), where �� and �� are compressive and flexural strength of concrete at prestress

transfer. At prestress transfer, the equation of topmost concrete fibre is as following:

��.�.�

��−

��

��− ��.�� = 0.4�′� (2.23)

Equation (2.23) suggests that the maximum allowable prestress is dependent on flexural

strength of concrete. As geopolymer concrete holds around 25% higher flexural

strength than OPC concrete of same grade, a higher prestressing force can be applied

in this concrete member. Prestressed concrete structures are generally designed to

achieve crack-free sections and smaller deflection under service load. Crack initiates in

the bottommost fibre of concrete structures when the bending stress exceeds the flexural


48

strength of concrete. Imposed load of that point is called first-crack load and moment

called cracking moment. Cracking moment of the prestressed concrete section (��)

can be calculated as follows:

��.�.�

��+

��

��− ��.�� + ��

� = ��. �/�� (2.24)

Equation (2.24) shows that cracking moment of prestressed concrete structure is

directly controlled by prestressing stress and flexural strength of concrete. So, a higher

flexural strength of geopolymer concrete can result in a higher first-crack load of the

prestressed concrete structure. In addition, accelerated cured geopolymer concrete

attains significantly higher early age strength which enables it to bear higher stress at

prestress transfer.

Equations (2.16) and (2.19) show that loss of prestress in steel tendons is directly

propositional to the shrinkage and creep strains of concrete. Having relatively lower

shrinkage and creep strains, geopolymer prestressed concrete member will experience

less time-dependent prestress loss and remain more serviceable than OPC concrete

member.

2.9 Stress-strain behaviours of concrete and steel

One of the objectives of this study is finite element modelling and analysis of

prestressed geopolymer concrete beam to predict their load-deflection behaviours.

Before preparing a finite element model, the stress-strain behaviour of its materials

(concrete and steel) should be studied carefully.

2.9.1 Behaviour of concrete under load

The stress-strain behaviour of concrete is a complex mechanism because it varies with

the stress level. Under uniaxial compressive stress, initially concrete undergoes elastic

deformation, followed by an elastic-inelastic state and fully plastic behaviour at

maximum stress. After reaching the maximum stress, stress level in concrete decreases

rapidly due to developing cracks which leads to failure. The ability of concrete holding


49

some stress beyond the maximum stress i.e. post-peak or post-crack strength, is

represented by a descending branch of the stress-strain curve. Generally, the slopes of

both, ascending and descending branches of stress-strain curves became steeper with

the increase in strength grade of concrete as shown in Figure 2.17. The brittleness of

concrete increases with an increase in concrete strength grade due to a decrease in

length of descending branch. Besides, Figure 2.17 shows that the critical strain of

concrete (strain at maximum stress, �� or ��) also increases with an increase in strength

grade of concrete. Typically, the critical strain of a 100 MPa concrete lies in the range

of 0.003 to 0.004, whereas 20 MPa concrete may have around 0.002 of critical strain

(Neville, 1995).

Figure 2.17: Uniaxial stress-strain behaviour of concrete at compression (Neville,

1995)

Being an anisotropic material, concrete possesses very small tensile strength compared

to its compressive strength. A typical stress-strain curve of concrete under tension is


50

shown in Figure 2.18. Generally, the elastic limit of concrete under tension is

considered about 60-80% of the tensile strength. Further increase of load creates micro-

cracks in the aggregate-paste matrix interface which damages the concrete and degrades

its elasticity. It becomes fully plastic at maximum stress level i.e. its tensile strength,

then the stress level drops very quickly and reaches the failure point. Failure of concrete

at tension is more brittle than at compression because its tensile deformation is very

small.

Figure 2.18: Uniaxial tensile stress-strain curve (Guo and Zhang, 1987)

Failure of concrete is governed by the degradation of the aggregate-binder interfacial

bond which is responsible for concrete strength. The process of crack development in

concrete is shown in Figure 2.19. Concrete may initially contain some micro-cracks in

the aggregate-paste interface as a result of volumetric change in concrete. When a

external load (higher than elastic limit) is applied, further micro-cracks initiate in the

aggregate-paste interface as shown in Figure 2.19 (b). Under the increment of external

load, more cracks are generated in the aggregate-paste matrix interface and propagate

over the concrete cross-section and become larger (Figure 2.19 c). Some aggregate-

paste matrix bonds start to fail individually in this stage. Further increase of load results

in propagation and merging of the cracks in the concrete cross-section and cracking of


51

the binder paste matrix as well. This propagation of cracks creates a fracture plane in

concrete section and leads to the failure of the section as shown in Figure 2.19 (d).

Figure 2.19: Process of cracks developing in concrete (Kotsovos and Newman, 1977)

2.9.2 Plasticity and non-linearity of concrete

The nonlinear behaviour of concrete may be attributed to the damage and cracking

mechanism of the aggregate-binder interfacial bond. A generalised stress-strain curve

of concrete proposed by Chen (2007) is presented in Figure 2.20. Under compression,

concrete initially exhibits almost linear elastic behaviour up to the elastic limit, point

A. Generally, stress up to 40% of maximum stress of concrete can be considered as

linear elastic (Neville, 1995). Upon increment of load, concrete is gradually weakened

by the initiation and propagation of internal micro-cracks. As a result, concrete starts to

lose its elastic property due to the non-reversible damage that happened to the

aggregate-binder interfacial bond. Concrete becomes fully plastic at maximum stress

(point C), and holds the maximum stress for a very small period (CD), which can be

shorter than in Figure 2.20. Then, concrete stress degrades rapidly due to developing

cracks in aggregate-binder interfacial bonds which leads to failure.


52

Figure 2.20: Uniaxial stress-strain curve of concrete (Chen, 2007)

2.9.3 Damage models of Concrete

Damage in concrete is mainly caused by the initiation, propagation and merging of

micro-cracks inside concrete under imposed load. The initiation and growth of micro-

cracks result in a decrease of strengths and stiffness of concrete material. Continuum

damage model was firstly introduced by Kachanov (1958), then it has been widely

adopted to model the progressive failure and stress-softening response of concrete

under imposed load (Leckie, 1978, Mazars and Pijaudier-Cabot, 1989). In addition,

different constitutive theories have been proposed in the past to model the stress-strain

behaviour of concrete under compressive and tensile load, such as the fracture energy

model by Kotsovos (1980) and plasticity damage model by Lubliner et al. (1989).

Concrete can resist some tensile stress after reaching maximum stress which is

represented by a descending branch in the stress-stain curve (Figure 2.18). This

descending branch reflects the tension stiffening effects of the concrete between the

cracks. Tension stiffening is a method of retaining some amount of stress that is not

released when cracks occur. In reinforced concrete member, the tension stiffening is a


53

mechanism by which concrete provides a bond with steel reinforcement and keep

carrying tensile stress even after starting of crack under imposed load (Gilbert, 2007).

A tension stiffening model purposed by Al-Manaseer and Phillips (1987) is presented

in Figure 2.21.

Figure 2.21: Tension stiffening model of concrete (Al-Manaseer and Phillips, 1987)

2.9.4 Mathematical models of concrete under uniaxial loading

Mathematical relationships and equations have been proposed to model the stress-stress

behaviour of concrete under uniaxial loading, some of them are as following:

a) Hognestad (1951) model

Hognestad (1951) suggested a mathematical model for the uniaxial compression of

concrete based on several experimental results. This model assumes the ascending

branch of the stress-strain curve of concrete as a second-order parabola and the

descending branch as an oblique straight line as shown in Figure 2.22. This model

assumes the maximum compressive stress in flexure as 85% of concrete strength (i.e.

��" = 0.85f�

�) which is equal to the maximum stress in the compressive stress block

adopted in concrete standards of current practice (ACI-318, 2011, AS-3600, 2018).


54

Figure 2.22: Stress-strain model proposed by Hognestad (1951)

Using this model, compressive stress on concrete at any point can be calculated as

following:

�� = ��" �2 �

�

�� − �

�

��

�

� when ɛ ≤ �� (2.25)

�� = ��" �1 − 0.15 �

��

�� when ɛ < �� (2.26)

where, �� is stress in concrete corresponding to strain ɛ; ε� is the strain at the maximum

compressive stress whose average value is taken as 0.002; and ε� is the ultimate strain

at failure, whose value is taken as 0.0038.

b) EN 1992.1.1 (2004) model for non-linear analysis

EN-1992.1.1 (2004) has proposed a parabolic curve to model the stress-strain behaviour

of concrete for non-linear analysis of concrete structures as shown in Figure 2.23. This

model assumes secant modulus of elasticity (or chord modulus) within 40% of

maximum stress (0.4��) of concrete which also complies with the experimental

methods.


55

Figure 2.23: Stress-strain model of concrete recommended by EN-1992.1.1 (2004)

In this model, stress-strain relationship of concrete under short-term uniaxial

compression is expressed using following equation:

��

��=

��

��(��) (2.27)

where, n =��/�� and �� is the strain at peak stress and

� = 1.05��/�� (2.28)

c) Carreira and Chu (1986) model for uniaxial tension

The tensile stress-strain behaviour of concrete can be modelled using the equation

proposed by Carreira and Chu (1986) as follows:

��

��=

�(� ��⁄ )

��(� ��⁄ )� (2.29)


56

where, �� is the concrete tensile stress corresponding to strain ε; �′� is the tensile

strength of concrete; �� is the strain at the maximum tensile stress; β is a stress-strain

parameter such that, 1.56 ≤ β ≤ 2.1.

The stress-strain relationship model of concrete under uniaxial tension proposed by

Carreira and Chu (1986) is shown in Figure 2.24. In this model, the ascending branch

is almost linear (elastic) up to 80% of maximum stress (�′�) and the post-peak

descending branch is a parabolic curve. The value of �� is taken around 0.00018 for

normal-weight concrete. This model gives a very similar curve to the experimental

stress-stress response of concrete under tensile load as shown in Figure 2.18.

Figure 2.24: Tensile stress-strain model for concrete (Carreira and Chu, 1986)

d) Stress-strain model for geopolymer concrete

Due to the difference in the chemistry of binding materials, geopolymer concrete

exhibits higher tensile strength than OPC concrete of same grade. However, both

concrete can undergo similar damage mechanisms and progressive failure behaviour

under compressive load with small difference in stress-strain behaviours. As shown

earlier in Figure 2.8 geopolymer concrete generally shows slightly higher deformation

at maximum stress than OPC concrete of same strength grade as well as less brittle

behaviour.


57

Currently, there is no separate mathematical equations to model the stress-strain

behaviour of geopolymer concrete. Sarker (2008a) suggested that stress-strain

behaviour of OPC based concrete proposed by Thorenfeldt (1987) can be applicable for

geopolymer concrete with some modifications as following:

��

�� =

�

��·

�

��

��

�� (2.30)

where, �� is the concrete strain at maximum compressive stress i.e. ��; � is the curve

fitting factor; � is a factor depends on ��

�� ratio, it equals 1 when

��

�� is less than 1.

In case of geopolymer concrete, the value of � (in SI units) is as following:

� = 0.8 +��

�

�� (2.31)

This modified equation showed a reasonable correlation with the stress-strain curve of

fly ash-based geopolymer concrete tested by Hardjito et al. (2004), for the ascending

branch only. However, this equation does not show a good correlation with the stress-

strain curve of geopolymer concrete suggested in other studies (Junaid, 2015, Noushini

et al., 2016).

The stress-strain behaviour of geopolymer concrete under tension has not been studied

in detail yet. Farhan et al. (2019) reported that indirect-tensile and flexural strengths of

geopolymer concrete were around 15% and 10% higher than OPC concrete of same

grade, respectively and similar direct tensile strengths. Despite the small difference in

strength, geopolymer concrete showed a higher deformation at maximum stress (critical

strain or ��) as shown in Figure 2.25. For all cases, fly ash-based geopolymer concrete,

exhibited higher tensile strength (direct, indirect and flexural) and higher critical strain

than OPC concrete and GGBS based geopolymer concrete. As discussed earlier, GGBS

based geopolymer concrete also contains C-H-S gel in the binder paste which creates a

weaker bond between aggregate and binder paste compared to geopolymer gel. As a

result, GGBS based geopolymer concrete can resist slightly less tensile strength and

deformation than fly ash-based geopolymer concrete of same strength grade. This


58

experiment, however, could not capture the post-peak behaviour (descending branch of

stress-strain curve) of both; OPC and geopolymer concrete.

Figure 2.25: Stress-strain behaviour of geopolymer concrete under uniaxial tension

(Farhan et al., 2019)

2.9.5 Concrete damaged plasticity model

Constitutive behaviour of concrete is difficult to predict using elastic damage models

or elastic-plastic laws. The elastic damage model cannot capture the irreversible strains

properly because in this model, zero stress at unloading corresponds to a zero strain as

shown in Figure 2.26 which inadequately estimates the damage value (Sümer and

Aktaş, 2015). Whereas, in the elastic-plastic model, the strain is overestimated because

the unloading curve descends in the same slope of initial elastic modulus (Figure 2.26

b). Concrete damaged plasticity (CDP) model combines these two approaches as

elastic-plastic damage model to capture realistic constitutive behaviour by considering

the effect of damage in unloading curve (Figure 2.26 c).

0

1

2

3

4

0.00000 0.00005 0.00010 0.00015 0.00020 0.00025

Ten

sile

str

ess

(MP

a)

Tensile strain

OPC 65 MPa

GGBS Geopolymer 65 MPa

Fly ash Geopolymer 65 MPa

OPC 35 MPa

Fly ash Geopolymer 35 MPa


59

Figure 2.26: Unloading response of concrete (a) elastic damage model (b) elastic-

plastic model (c) elastic-plastic damage model (Jason et al., 2006)

Concrete damaged plasticity model has been adopted in finite element program, such

as Abaqus to analyse the in-elastic behaviour of concrete under different types of

loading. This model assumes two main failure mechanisms of concrete; tensile cracking

and compressive crushing. It provides a general capability for finite element modelling

of concrete and other quasi-brittle materials in all types of structures (beams, trusses,

shells, and solids). In this model, evolution of the failure of the yield surface is

controlled by two hardening variables, ɛplc and ɛ

plt , linked to failure mechanisms under

compressive and tensile stress, respectively as shown in Figure 2.27. Under uniaxial

tension, the stress-strain response follows a linear elastic relationship until the

maximum stress, ��. Beyond the maximum stress, the formation of cracks is

represented by a softening stress-strain response. Under uniaxial compression, the

response is linear until yield strength, ��. In the plastic regime, the response is

characterised by strain-hardening followed by strain-softening beyond the maximum

stress, ��.


60

(a)

(b)

Figure 2.27: Concrete damaged plasticity model (a) compression and (b) tension

(Abaqus-Inc., 2014)

In CDP model, damage variable (�� or �� ), starts from zero (undamaged state) to one

(total loss of strength). The damage variable or damage index can be calculated as

flowing:


61

�� = 1 − ��/�� (2.32)

If E0 is the initial (undamaged) elastic stiffness or modulus of elasticity of the material,

the stress-strain relations under uniaxial tension and compression loading are,

respectively:

�� = (1 − ��). �� − ɛ��

� (2.33)

�� = (1 − ��). �� − ɛ��

� (2.34)

where, �� and �� are the tensile and compressive strains, respectively at any point; ��

and ��

are the equivalent plastic strains for tension and compression, respectively and

�� is the undamaged elastic modulus of concrete.

The CDP model assumes that the modulus of elasticity of concrete decreases with the

decrease in its strength due to damage. For example, the reduced modulus of elasticity

of concrete under compression can be estimated at any stage as follows:

� = (1 − ��). �� (2.35)

2.5.10.1 Post failure stress-strain behaviour

The post-failure behaviour is modelled as tension stiffening to define the strain-

softening behaviour for cracked concrete. This behaviour also allows the effects of the

interaction of reinforcement with concrete to be simulated in a simple manner. Tension

stiffening is specified by means of a post-failure stress-strain relation or by applying a

fracture energy cracking criterion (Abaqus-Inc., 2014). Figure 2.28 shows the concept

of cracking strain in concrete (��) adopted by Abaqus program.


62

Figure 2.28: Cracking strain of concrete under tension (Abaqus-Inc., 2014)

In Abaqus-Inc. (2014), the post-failure behaviour of a reinforced concrete structure is

defined as a function of cracking strain. The cracking strain (��) is defined as the total

strain minus the elastic strain that corresponds to the undamaged material as following:

�� = �� − ��

�� (2.36)

where, �� is the total strain and �� is the undamaged material strain at that point

2.5.10.2 Failure mode under biaxial loading

Under biaxial loading, the strength of concrete at failure may be different compared to

uniaxial loadings due to effect of stress subjected in orthogonal direction. The yield

surface diagram of concrete under biaxial stress adopted by Abaqus is similar to the

failure diagram originally suggested by Kupfer et al. (1969) which is shown in Figure

2.29. Kupfer et al. (1969) suggested that strength of concrete in biaxial compression

may be as much as 27 % higher than the uniaxial strength. For equal biaxial

compressive stresses, the strength increase is approximately 16 %. The strength under

biaxial tension is approximately equal to the uniaxial tensile strength. However, the


63

combined effect of tensile and compression stress reduces both the tensile and the

compressive stresses of concrete at failure. In Abaqus, the ratio of initial biaxial

compressive stress to initial uniaxial compressive stress, σb0/σc0, is taken as the default

value of 1.16.

Figure 2.29: Yield surface in plane biaxial loading (Abaqus-Inc., 2014)

The deviatoric stress under compression and tension can be affected by the values of

shape factor parameter (��). �� can be defined as the ratio of �(��)/�(��), where �(��)

and �(��) are the von Mises equivalent stresses on the tensile meridian (TM) and on

the compressive meridian (CM), which are shown in Figure 2.30. The default value of

�� adopted in Abaqus is 2/3.


64

Figure 2.30: Yield surface for a deviatoric plane (Abaqus-Inc., 2014)

2.5.11 Stress-strain model for reinforcing steel

Reinforcing steel is an isotropic material, such that its stress-strain behaviours are

similar in both, compression and tension. A stress-strain curve of reinforcing steel bar

experimented by Felicetti et al. (2009) at 20 °C temperature is shown in Figure 2.31.

Similar to other metals, steel has two distinct stress values; yield strength and ultimate

strength. Generally, yield strength is taken as strength of steel for design purpose of

steel and reinforced concrete structures because the elongation and increment of stress

in steel after this point is difficult to predict.


65

Figure 2.31: Stress-stress curve of reinforcing steel under tension (Felicetti et al.,

2009)

Some idealised stress-strain curves of reinforcing steel are shown in Figure 2.32.

Among these, elastic strain followed by a perfectly plastic response of steel (Figure

2.32 a) is the most commonly used stress-strain behaviour of steel in design of

structures because this assumption is simple and easy for analytical calculations as well.

Strength of steel beyond yield strength can be considered as an additional factor of

safety of structure. In all cases, steel is assumed to be elastic until the yield strength.

The trilinear (Figure 2.32 b) and complete curve (Figure 2.32 c) models consider the

strain-hardening behaviour of steel after yielding. These models are based on realistic

stress-strain behaviour of steel, however, the amount of plastic strain before strain

hardening (��) is difficult to predict.

0

100

200

300

400

500

600

700

800

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Ten

sile

str

ess

(MP

a)

Strain


66

Figure 2.32: Idealised stress-strain curves of steel (a) Elastic and perfectly plastic (b)

Trilinear approximation (c) Complete curve (Park and Paulay, 1975)

2.10 Finite element analysis

2.10.1 General

Finite element analysis is a numerical method to achieve an approximate solution by

dividing (meshing) a large region into small sub-regions called finite elements. An

individual mathematical equation predicts the behaviour of each element. Then, all the

individual behaviours are integrated to predict the behaviour of the whole object. Thus,


67

finite element analysis program is a computerised method to predict the response of an

object or structure under the effect of loads/forces, vibration and other physical effects.

Figure 2.33: Flowchart of finite element analysis process

A typical flowchart of the finite element analysis process is shown in Figure 2.33.

Finite element analysis is generally carried out in three steps; pre-processing, analysis

and post-processing. Pre-processing is the process of preparing of finite element model

of a structure and defining the properties of materials and other relevant parameters.

Analysis is the process of solving the numerical equations by the software. Several

parameters can influence the analysis and its outcome, such as type of loads (static or

Pre-processing

Analysis and solving


68

dynamics), number and size of mesh and boundary conditions. Post-processing is the

final step where the results obtained from the finite element analysis are extracted and

evaluated.

2.10.2 Types of analysis in Abaqus

Abaqus is a finite element software used in academic and industrial sectors. Abaqus

can provide multi-discipline solutions across a number of areas, such as aerospace,

automotive and structural engineering. Depending on the nature of jobs, Abaqus offers

two different modes of analysis; Abaqus/Standard (implicit) analysis and

Abaqus/Explicit analysis.

Abaqus/Standard is based on the basic principle of finite element analysis, i.e. matrix

operations between stiffness matrix and load matrix. This stiffness-based solution

technique used in Abaqus/Standard is unconditionally stable. This analysis is primarily

used for static problems that do not exhibit severe discontinuities (Abaqus-Inc., 2005).

Abaqus/Standard is more efficient for solving smooth linear and nonlinear static

problems.

Abaqus/Explicit does not use stiffness and mass matrices, however, the position, speed

and acceleration of each node in space in the next time step is calculated from the

previous states and the interacting nodes (nodes in contact). It can be applied to those

portions of the analysis where short duration dynamics, nonlinear quasi-static, transient

response dominates the solution (Abaqus-Inc., 2005).

2.10.3 Elements types used in finite element analysis

In the finite element modelling of solid objects, such as beam, slab and layered objects,

different types of elements are used. In Abaqus, a wide range of element library

provides flexibility in modelling different geometries and structures. The selection of

element depends on the nature of modelled objects, expected output variables and

applicability of the element type for a particular case.


69

a) Solid continuum elements

The solid (or continuum) elements can be used for linear analysis and complex

nonlinear analyses involving contact, plasticity, and large deformations. They are

available for stress, heat transfer, acoustic, electromagnetic and coupled thermal-

electrical analyses. Solid elements have their standard shapes and number of nodes.

Solid elements possess bending, shear and torsional stiffness and can show stress and

deformations in all directions.

(a) (b)

Figure 2.34: Solid 8-node brick elements (a) C3D8 and (b) C3D8R

Generally, hexahedral (bricks) elements, such as C3D8 are mostly used in 3D solid

modelling because they provide a solution of equivalent accuracy at a less

computational time (Abaqus-Inc., 2014). The C3D8 element is a general-purpose 8

nodes linear brick element, fully integrated (8 integration points) and C3D8R element

is a linear brick element, with reduced integration (1 integration point). C3D8R takes

significantly less time for integration. Geometric sketches of solid 8-node brick

elements (C3D8 and C3D8R) are shown in Figure 2.34 with integration points.

b) Truss elements

Truss elements are used in modelling of two or three-dimensional slender and linear

structures, such that load exerts only along the longitudinal axis. These elements can

carry tensile or compressive loads only, and are useful for modelling of pin-jointed


70

frames and truss and tension cables. T3D2 is the commonly used truss element. A

typical 2-node truss element is shown in Figure 2.35.

Figure 2.35: A typical truss element

c) Beam elements

A beam element is a unidimensional linear element that has stiffness associated with

deformation of its longitudinal axis, such as axial stretch, curvature change (bending).

Beam elements are geometrically simple, have few degrees of freedom and shear

flexibility. Reinforcement bars are generally modelled using beam elements. B31 (shear

flexible with linear interpolation) and B32 (shear flexible with quadratic interpolation)

are commonly used beam elements. A typical 3D linear beam element is shown in

Figure 2.36.

Figure 2.36: A typical 3D beam element

2.11 Conclusions

This chapter reviews the ingredients and engineering properties of geopolymer binder

concrete. Previous studies suggested that geopolymer concrete has higher indirect-

tensile and flexural strengths (15%-40%) than OPC concrete of same strength grade as


71

well as relatively smaller long-term shrinkage and creep strains. Despite the difference

in their tensile strengths, both geopolymer and OPC concrete can follow similar

progressive failure and stress-softening (after maximum stress) behaviour under

compressive load with small differences in magnitude of strain. Geopolymer concrete

generally shows slightly higher deformation at maximum stress and higher ultimate

deformation under both, compressive and tensile loads.

In addition, a brief discussion about the design and analysis of prestressed concrete

structures and critical parameters are presented in this chapter. Unlike to conventional

RC structures, tensile or flexural strengths of concrete are significant in the design of

prestressed concrete structures where tensile strength of concrete limits the maximum

permissible prestressing load according to ACI-318 (2011). In addition, time-dependent

losses of prestressing stress caused by shrinkage and creep strains of concrete are the

major serviceability issues of prestressed concrete structure which reduce the load-

carrying capacity of structures and increase the deflection under service loads.

Despite having higher mechanical strengths and durability properties than conventional

OPC concrete, geopolymer concrete has not been widely used in structural grade

concrete, so far. The safety hazards in mixing and handling of geopolymer concrete due

to the use of liquid sodium hydroxide is one of the barriers to the adaptation of

geopolymer binder in concrete industry. Therefore, a research and development work

is necessary to develop sodium hydroxide-free geopolymer binder to be used in

structural grade concrete and investigate its effects on load-deflection behaviours of the

structure. The following points outline the need of further research.

Replacement of sodium hydroxide in geopolymer binder to minimize the safety

hazards in mixing and handling process.

Use of geopolymer concrete in structural grade concrete.

Investigate the effect of higher tensile strength of geopolymer concrete in flexural

behavior of reinforced and prestressed concrete structures.

Investigate the effect of shrinkage and creep strains of geopolymer concrete in the

long-term serviceability of prestressed concrete structures.

Chapter 3: Experimental program

72

CHAPTER 3

3. Experimental Program

3.1 Preamble

Engineering properties of concrete, such as tensile strength, modulus of elasticity and

drying shrinkage and creep strains are generally the function of compressive strength

or strength grade of concrete. In case of OPC concrete, standard equations are available

in concrete standards to estimate other engineering properties, such as flexural strength

and modulus of elasticity using 28 days compressive strength. Being a new binding

material, such standard equations are not available for geopolymer concrete, so far.

Geopolymer binders can be made from a combination of different source materials,

such as fly ash, GGBS and metakaolin and alkali activators, such as sodium silicate,

sodium hydroxide and potassium hydroxide. Types of source materials and activators

can largely affect the engineering properties of geopolymer concrete due to their

influence on the geopolymerisation process and structure of geopolymer matrix

(Duxson et al., 2006).

The safety hazards in mixing and handling of geopolymer concrete due to the use of

liquid sodium hydroxide is one of the barriers to the adaptation of geopolymer binder

in concrete industry. This study aims to use sodium hydroxide-free one-part

geopolymer binder to produce structural grade geopolymer concrete for prestressed

concrete application. Hence, an experiential programme is necessary to investigate the

engineering properties of geopolymer such as workability, compressive and tensile

strengths, modulus of elasticity and shrinkage and creep strains. These engineering

properties of geopolymer concrete can be used as input parameters of finite element

modelling of prestressed concrete beams which is one of the major objectives of this

study. OPC (control) concrete of same strength grade and workability level was also

produced in this study using same types of aggregates, such that their engineering

properties can be compared.

In order to study the application of geopolymer concrete in general construction

practice i.e. cast-in-situ concrete, all the engineering properties were measured under


73

ambient temperature (standard laboratory temperature) curing. However, the

compressive strength and indirect-tensile strength of geopolymer concrete were also

measured under accelerated curing to study its applicability in precast concrete sector.

Serviceability properties of concrete, such as shrinkage and creep strains were

investigated to study their effects on long-term serviceability of prestressed concrete

structure.

3.2 Concrete strength grade

Prestressed concrete structures need higher grade and quality concrete because they are

subjected to higher stress due to prestressing load. In addition, concrete stress in a

prestressed concrete member not only changes by magnitude but also changes its

direction (compression to tensile and vice versa) with the increase of imposed loads.

Generally, concrete of 40 to 65 MPa grades is commercially used for prestressed

concrete (Gilbert et al., 2016). Grade 50 MPa geopolymer and OPC concrete were mix

designed and produced in this study to investigate their engineering properties.

According to AS-1379 (2017), the 28 days concrete target mean compressive strength

(��) can be obtained by:

�� = �� + �. � (3.1)

where, f�� is the characteristic compressive strength of concrete at 28 days; � is a normal

distribution factor equal to 1.65 for less than 5% defective test samples; and s is the

standard deviation of concrete cylinder strength.

In the case of unknown production data of similar concrete, AS-3600 (2018)

recommends a mean concrete cylinder strength for each standard grade of concrete, for

a characteristic strength of 50 MPa, 28 days target mean strength is 59 MPa.

3.3 Materials

3.3.1 Binders

Most of the previous studies in geopolymer concrete were carried out using a two-part

geopolymer with liquid sodium hydroxide and sodium silicate as activator (Hardjito


74

and Rangan, 2005, Deb et al., 2015, Diaz-Loya et al., 2011, Raijiwala and Patil, 2011).

The limitations of sodium hydroxide based two-part geopolymer binder are discussed

earlier in Chapter 2. One of the objectives of this research study was to replace sodium

hydroxide with a less hazardous alkali material and use of one-part geopolymer binder

in structural grade concrete, such that it can be used in concrete in a similar way to

conventional OPC.

One of the possible replacement of sodium hydroxide is sodium carbonate (Na2CO3 or

soda ash), which is available in powder form and classified as non-dangerous goods

according to the Australian Dangerous Goods Code (Redox, 2015). Sodium carbonate

is an indirect means of alkalinity in the geopolymer system with minimal hazards.

When sodium carbonate dissolves in water, it breaks down into the water and carbonic

acid as shown in the following reaction.

Na2CO3 (aq) + 2 H(OH) → H2CO3 (aq) + 2 NaOH (aq) (3.2)

Carbonic acid (H2CO3) is a weak acid, which decomposes into CO2 gas and H2O. The

main product, sodium hydroxide drives pH level up and takes part in further reactions

to form geopolymer matrix. The GGBS available in the geopolymer binder contains

Ca2+ ions. Any free CO2 generated from the breakdown of Na2CO3 in the geopolymer

matrix quickly reacts with Ca2+ ion and precipitates into nano calcium carbonate as

stable product. This reaction takes place continuously with time and does not pose any

safety hazard during the mixing or handling of green concrete.

The one-part geopolymer binder used in this study consisted of a combination of fly

ash and GGBS in source materials, such that it could set and harden at ambient

temperature. All the source materials and activators (in powder form) were blended in

a fixed proportion to make the one-part geopolymer binder. The proportions of

activators were determined by trial mix designs (taking their molecular mass as

reference), such that minimum amount of activators could give optimum results

(optimum setting time and compressive strength of concrete at ambient temperature).

Proportions of the ingredients in this binder were; 50% of fly ash, 32 % of GGBS, 9%

of sodium silicate and 9% of sodium carbonate by mass.


75

_ (a) (b)

_ (c) (d)

_ (e) (f)

Figure 3.1: Binding materials (a) fly ash, (b) GGBS, (c) sodium carbonate dense

(d) sodium silicate, (e) geopolymer binder and (d) Portland cement


76

Photo images of general-purpose Portland cement and one-part geopolymer binder and

its ingredients; fly ash, GGBS, sodium silicate and sodium carbonate are presented in

Figure 3.1. This figure shows that one-part geopolymer binder seemed physically very

similar to conventional OPC.

The fly ash and GGBS used in this study were sourced from Gladstone Power Station,

Gladstone, Queensland and Bulwer Island Grinding Mill, Pinkenba, Queensland,

respectively. The fineness (percentage of mass passing from 45-micron sieve) of fly

ash and GGBS tested according to AS-3583.1 (2016) were 92% and 93%, respectively.

Other relevant data of fly ash and GGBS are presented in Appendices. Sodium silicate

powder (SiO2 / Na2O =2) was supplied from PQ Australia Pty Ltd, Victoria which

contains around 82% of sodium silicate and 18% of chemically bound water. Sodium

carbonate (soda ash dense) powder was supplied by Rodex, Pty Ltd, Minto, NSW which

contains around 99% of sodium carbonate.

A general-purpose ordinary Portland cement blended with 20% fly ash was used to

produce control concrete of the same grade. The chemical composition of low calcium

fly ash, GGBS and OPC used in this experiment are presented in Table 3.1.

Table 3.1: Chemical compositions of Class F fly ash, GGBS and OPC

Compositions (% by mass)

SiO2 Al2O3 Fe2O3 CaO Na2O K2O TiO2 MgO P2O5 SO3 Mn2O3 LOI*

Fly ash 61.6 21.3 7.2 4.4 0.37 1.36 1.0 1.4 0.9 0.2 0.1 1.0

GGBS 34.6 14.6 1.03 41.8 0.22 0.33 0.8 6.8 0.1 0.5 0.3 -1.1

OPC 19.1 4.9 2.8 63.5 0.01 0.5 0.3 1.3 0.1 3.1 0.2 4.5

*LOI = loss on ignition

3.3.2 Aggregates

In order to produce a quality concrete with low porosity, a combination of well-graded

crushed coarse aggregates of 20 mm and 10 mm maximum sizes and medium sands and

fine sands were used in the concrete mix. Coarse aggregates were granite rocks and

sourced from Peppertree Quarry, Marulan NSW. Both grains of sand were sourced from

Dunmore NSW which were classified as quartzite sands. Photo images of individual


77

aggregates are shown in Figure 3.2. Images show that all aggregates were clean, free

from dirt and clay particles. The coarse aggregates were well-shaped and without any

visual cracks.

_

(a) (b)

_

(c) (d)

Figure 3.2: Concrete aggregates (a) 20 mm coarse, (b) 10 mm coarse, (c) medium

sand and (d) fine sand

The grading curves of individual aggregates are shown in Figure 3.3. Data points in

this figure shows that all aggregates were well graded and represented by “S” curves in

the particle distribution graphs.


78

Figure 3.3: Particle distribution curves of concrete aggregates

The physical properties of aggregates used in concrete mix are shown in Table 3.2.

Data points show that the concrete aggregates complied with AS-2758.1 (2014) in terms

of water absorptions (maximum 2%), surface saturated dry specific gravity for normal-

weight aggregates (2.1 to 3.2) and Los Angeles value for grade A aggregates (maximum

loss 35% by weight).

Table 3.2: Physical properties of concrete aggregates

Properties 20 mm aggregate

10 mm aggregate

Medium sand Fine sand

Water absorption 0.5 0.5 0.9 0.5

Specific gravity (SSD) 2.77 2.76 2.67 2.59

Los Angles value (% loss) 15 15 - -

3.4 Trial mix designs and concrete mixing procedure

In order to compare the engineering properties of geopolymer and OPC concrete, the

mix design of both concrete was carried out on the basis of comparable 28 days

compressive strength (target mean strength 59 MPa) and workability level (100 ± 20

mm slump); not based on an equal amount of binder. Equal amount of binder or

0

20

40

60

80

100

0.01 0.1 1 10 100

Per

cen

tag

e o

f p

ass

ing

Sieve size (mm)

Fine sand

Medium sand

10 mm aggregate

20 mm aggregate


79

water/binder ratio can result in different compressive strengths of geopolymer and OPC

concrete due to the difference in their binding strength.

As geopolymer is a new binding material, the mix design of concrete from this binder

may be different than conventional OPC concrete in terms of water/binder ratio and

amount of binder needed. Some trial mix design works were carried in order to find out

the optimum concrete mix that can attain the desired workability (100 ±20 mm slump)

and 28 days mean compressive strength (59 ± 2.5 MPa). The mix design guidelines of

OPC concrete (Teychenné et al., 1997) were also followed in geopolymer concrete with

some adjustment in amount binder and water. Both geopolymer and OPC concrete were

mixed in a rotating pan mixer of 70 litres capacity in a conventional way. The following

steps were carried out in the concrete mixing process.

At first, all weighted aggregates were loaded into the mixing pan and the initial

amount of water (around 50% of calculated) was added into the aggregates.

Aggregates were mixed around for 1 minute.

Mixing was stopped and binder was added into the aggregates and mixing was

continued for 3 minutes. Around 40% of calculated water and water reducing

admixtures (for OPC concrete) were added during the mixing. More water was

added if concrete looked too dry.

Mixing was stopped around for 2 minutes and then continued for another 2

minutes (this process was to overcome the false setting in case of OPC concrete).

Mixing was stopped around for 2 minutes and an initial slump test of concrete

was done. According to the slump result, additional water was added if

necessary.

The used concrete was returned to the pan, and mixing was continued for another

2 minutes.

Mixing was stopped for around 2 minutes and a second slump test was done to

confirm the desired workability level of concrete (100 ± 20 mm slump).

The used concrete was returned to the pan and mixing was continued for another

1 minute. Then concrete was ready for the casting of specimens.

Numbers of trial geopolymer and OPC concrete mixes were produced and tested for

compressive strengths at different ages as shown in Table 3.3. Production of trial


80

concrete mixes found that one-part geopolymer binder can be mixed and handled in the

similar way to conventional OPC with low safety hazards. The desired workability level

of concrete could be achieved by addition of free water as in OPC concrete. Another

objective of this trial mix design was to investigate the effects of adding high range

water reducing admixture (superplasticizer) in workability and compressive strength of

geopolymer concrete. As discussed earlier in Chapter 2, commercially available

chemical admixtures may not be useful in case of geopolymer concrete, so a new type

of superplasticizer developed for high alkalinity by BASF Australia; GP 100 (HWR)

was used in geopolymer concrete within the recommended doses.

As shown in Table 3.3, the binder contents and water/binder ratios in the trial mixes of

geopolymer concrete were varied gradually. In each stage, a pair of trial mixes with or

without chemical admixtures were tested to investigate the effect of superplasticiser. In

case of OPC concrete, 3 numbers of trials were done to confirm the mix design for

Grade 50 MPa. In order to control the water demand for the desired workability, Sika

Plastiment 10 (WR, normal water reducer) and Sika Visocrete PC HRF-2 (HWR, high-

range water reducer) were used in OPC concrete mixes.

Table 3.3: Trial mix designs of geopolymer and OPC concrete

Binder Trial

No.

Binder

content

(kg/m3)

Water

content

(kg/m3)

Aggregates (kg/m3) Measured

density

(kg/m3)

water/

binder

ratio

Slump

(mm)

Chemical

admixture

(ml/m3) 20

mm

10

mm

Coarse

sand

Fine

sand WR HWR

Geo

poly

mer

1a 365 155 738 433 620 136 2447 0.425 90

1b 366 153 739 434 621 136 2450 0.418 90 1350

2a 380 158 732 428 622 133 2453 0.416 100

2b 381 154 733 429 623 133 2454 0.404 110

1400

3a 400 162 723 422 613 132 2452 0.405 100

3b 401 158 724 423 614 133 2454 0.394 110

1450

4 420 163 713 436 601 118 2451 0.388 100

OPC 1 385 185 720 418 563 138 2411 0.481 90 1,600 660

2 415 186 716 413 554 132 2418 0.448 90 1,700 720

3 435 183 693 406 565 133 2418 0.421 100 1,750 760


81

Some photo images of the geopolymer concrete mixing process are shown in Figure

3.4. Photos show that geopolymer binder concrete looks physically similar to

conventional OPC concrete.

-

(a) (b)

Figure 3.4: Mixing of concrete (a) loading of materials (b) mixed geopolymer

concrete

The compressive strength development of geopolymer concrete of different trial mixes

are presented in Figure 3.5. Similar to conventional concrete, there was a gradual

increase in compressive strength of geopolymer concrete for all ages with a decrease in

water/binder ratio or an increase in binder content. Data points in Table 3.3 show that

there were no significant positive impacts in the workability of geopolymer concrete

with addition of superplasticizer except a very small decrease in water/binder ratio. The

addition of superplasticizer in geopolymer concrete, however, brought a small decrease

in the compressive strength of concrete in the later age as shown in Figure 3.5. Target

mean strength of OPC concrete, on the other hand, was achieved with three different

mix designs with a gradual decrease in water/binder ratios from 0.48 to 0.42. The

strength developments of OPC concrete are shown in Figure 3.6.

The trial mix design data can also be used to compare the amount of binder needed in

geopolymer and OPC concrete for comparable 28-days strength. Mix compositions in

Table 3.3 show that concrete from one-part geopolymer binder can be mix designed in


82

the similar way to OPC concrete with slightly less water/binder ratio and amount of

binder for comparable workability and 28-days compressive strength.

Figure 3.5: Compressive strength of geopolymer concrete trial mixes

Figure 3.6: Compressive strength of OPC concrete trial mixes

3.5 Final mix designs and casting of concrete specimens

As mentioned in Section 3.4, the mix design of geopolymer and OPC concrete were

based on comparable workability (slump) and 28 days compressive strength, not based

0

10

20

30

40

50

60

0 7 14 21 28

Com

pre

ssiv

e st

ren

gth

(M

Pa)

Age (day)

Geopolymer-Trial 1a

Geopolymer-Trial 1b

Geopolymer-Trial 2a

Geopolymer-Trial 2b

Geopolymer-Trial 3a

Geopolymer-Trial 3b

Geopolymer-Trial 4

0

10

20

30

40

50

60

0 7 14 21 28

Com

pre

ssiv

e st

ren

gth

(M

Pa)

Age (day)

OPC-Trial 2

OPC-Trial 3

OPC-Trial 1


83

on an equal amount of binder or water/binder ratio. Results from the trial mix works

showed that the use of chemical admixture was not effective in case of geopolymer

binder, and therefore the final mix of geopolymer concrete was produced without any

addition of admixture. OPC concrete, on the other hand, was produced with the same

chemical admixtures that were used in trial mix designs.

The final concrete mixes adopted in this study are shown in Table 3.4. This table shows

that geopolymer concrete needed slightly less amount of water and binder for a

comparable workability and strength grade to OPC concrete. Despite not having any

admixtures, geopolymer concrete showed sufficient cohesiveness and no observable

segregation.

Table 3.4: Mix compositions of Grade 50 MPa concrete

Binder type Binder content (kg/m3)

Water content (kg/m3)

Aggregates (kg/m3) water/ binder ratio

Slump (mm)

Chemical admixtures (ml/m3)

20 mm

10 mm

Coarse sand

Fine sand

WR HWR Geopolymer 420 162.4 713 436 600 118 0.386 110 0 0

OPC 440 182.9 691 407 565 132 0.419 100 1,750 760

Series of concrete cylinders with dimensions of 100 mm 200 mm (diameter height),

flexural beams with dimensions of 100 mm × 100 mm × 350 mm (width height

length), and shrinkage prisms with dimensions of 75 mm × 75 mm × 280 mm (width

height length), were cast to determine fresh, mechanical and serviceability properties

of both geopolymer and OPC concrete. A minimum of three specimens were made for

each test. Casting of concrete cylinders, flexural beams and shrinkage prisms were

done according to AS-1012.8.1 (2014), AS-1012.8.2 (2014) and AS-1012.8.4 (2015),

respectively. All the concrete specimens were compacted by vibrating. After casting,

concrete cylinders and prisms from both, geopolymer and OPC concrete were left in

their moulds in the laboratory at standard temperature (23± 2 °C) for 24 hours, whereas

flexural beams were left for 48 hours in the same temperature. Then, the specimens

were gently demolded and placed for curing at standard temperature (23± 2 °C). Photo

images of casting of geopolymer concrete cylinders, shrinkage prisms and flexural

beams are shown in Figure 3.7.


84

-

(a) (b)

(c)

Figure 3.7: Casting of concrete specimens (a) cylinders, (b) shrinkage prisms and (c)

flexural beams

3.6 Curing of concrete specimens

Specimens from both geopolymer and OPC concrete were cured at two different

conditions; ambient temperature and accelerated curing.


85

3.6.1 Curing at ambient (standard laboratory) temperature

The presence of moisture is necessary in the strength development of geopolymer

concrete because water is the medium of geopolymerisation reaction. As discussed in

Chapter 2, geopolymerisation process recovers water molecules. Therefore, the initial

moisture available in concrete may be sufficient for further geopolymerisation process.

Different curing methods were practiced in earlier studies for curing of geopolymer

concrete at ambient temperature; sealed curing by an impervious plastic sheet or

submerged curing in a water tank. However, submerging of geopolymer concrete

specimens in water at an early age can result in leaching of alkali activators from the

geopolymer system because they are easily soluble in water. Zhang et al. (2013)

reported leaching of alkali activators from geopolymer mortar when submerged in

water at early age with some efflorescence on the surface of specimens. Sakulich et al.

(2009) used sealed curing by impervious polythene sheet to cure geopolymer concrete

at ambient temperature. Collins and Sanjayan (1999) reported a higher compressive

strength results of sealed cured geopolymer concrete cylinders than immersed cured

ones for the same temperature (ambient) and period of curing. Generally, ambient

temperature refers to the average outdoor air temperature, which may be different from

place to place. In this study, ambient temperature has been referred to as standard

laboratory temperature (23 ±2 °C) as recommended by AS-1012.8.1 (2014).

In order to get a better result, geopolymer concrete specimens were sealed cured by an

impervious plastic sheet immediately after demolding. A piece of wet cloth was also

kept inside the plastic cover to provide additional moisture in concrete as shown in

Figure 3.8. Whereas, OPC concrete specimens were immersed cured in lime-saturated

water. All the concrete specimens were cured in standard laboratory temperature until

testing as specify by AS-1012.8.1 (2014).

After the initial curing (first 7 days after demolding), the drying shrinkage prisms and

cylinders for creep testing from both, geopolymer and OPC concrete were taken out

from curing. Immediately after exposing to air, they were taken for initial dimensional

readings and then stored in a room having a standard temperature of 23± 2 °C and 50%


86

relative humidity according to (AS-1012.13, 2015) and subsequent readings were taken

on a weekly basis.

_

(a) (b)

(c)

Figure 3.8: Sealed cured geopolymer concrete specimens (a) cylinders, (b) shrinkage

prisms and (c) flexural beam

3.6.2 Accelerated curing

Accelerated curing or heat curing is the process of curing of concrete at an early age at

a higher temperature than ambient conditions (above 50 °C) in order to develop high

early-age strength. The purpose of investigation of strength development at accelerated

curing was to investigate the suitability of geopolymer concrete for precast prestressed

concrete structures, such as bridge girders, precast beams and precast floor panels. AS-

1597.2 (2013) recommends a minimum 32 MPa compressive strength for releasing of

precast concrete elements from formworks and a maximum curing temperature of 70°C


87

which is also followed by Australian precast concrete industries. Due to unavailability

of steam curing facility in the laboratory, an oven curing was used in the experimental

work. In order to prevent the loss of moisture, the concrete cylinder moulds were

properly sealed while keeping inside the heating oven as shown in Figure 3.9.

Figure 3.9: Sealing of concrete cylinder for accelerated curing

The temperature profile of accelerated curing process of Grade 50 MPa concrete

adopted in this experiment is shown in Figure 3.10. In order to compare the

early age strength growth, specimens from both concrete were cured at a

maximum temperature of 70 °C for 6 hours as specified by AS-1597.2 (2013).

After the casting, concrete specimens were kept for an initial delay period of

around 1.5 hours at laboratory temperature to provide time for the initial setting

of concrete before exposing to temperature. Then, the oven temperature was

gradually increased at 24 °C/hour rate (ramping up) to a maximum curing

temperature of 70 °C. Concrete specimens were cured for 6 hours at the

maximum temperature and then taken out from the oven and left at laboratory

temperature for cooling down. Around after 1.5 hours of air cooling, concrete

cylinders were demolded and measured for compressive strength and indirect-

tensile strength. In addition, six of accelerated cured concrete cylinders from

each concrete were kept at laboratory temperature to measure compressive


88

strength and indirect tensile strength at 28 days. Every day, the concrete

cylinders were sprayed with some water to keep them moist.

Figure 3.10: Temperature profile for accelerated curing of concrete specimens

3.7 Investigation of engineering properties of concrete

In this study, the engineering properties of both, geopolymer and OPC concrete of

Grade 50MPa were measured in fresh concrete and hardened concrete states. Concrete

workability (slump) and density were measured as a property of fresh concrete. Under

mechanical properties of concrete, compressive strength, indirect tensile strength and

flexural strength were investigated. Modulus of elasticity and Poisson’s ratio were

measured as deformation properties of concrete. Drying shrinkage and creep strains of

concrete were measured as long-term serviceability properties up to one-year of period.

To date, there is not any separate specification for geopolymer concrete, hence standard

test methods designed for OPC concrete were followed to investigate the engineering

properties of both, geopolymer and OPC concrete in this study. The investigated

engineering properties of Grade 50MPa concrete and relevant standards for the method

of testing are shown in Table 3.5.

0

20

40

60

80

0 1 2 3 4 5 6 7 8 9 10 11

Tem

per

atu

re (

ºC)

Time (hour)

Heating period Curing period

Initial delay period

Cooling period


89

Table 3.5: Investigated concrete properties and relevant standards

Creep cylinders were loaded at 28 days, their dimensional measurements were taken

immediately before and after the loading. Two control cylinders were kept in the same

room without loading in order to measure the shrinkage creep.

3.8 Conclusions

This study used sodium hydroxide-free one-part geopolymer binder to produce

structural grade (grade 50 MPa) concrete. Sealed curing was adopted in geopolymer

concrete specimens to prevent the alkali activator from leaching out. The engineering

properties of both, geopolymer and OPC concrete were measured according to relevant

Australian standards. Following conclusions can be made based on this experiment.

Sodium carbonate (soda ash) can be a viable replacement for sodium hydroxide in

geopolymer binder to minimize the safety hazard posed by sodium hydroxide.

One-part geopolymer binder concrete can be mixed and handled in a similar way

to conventional OPC concrete.

Curing conditions

Properties Age Relevant standards

Ambient (standard temperature)

Fresh concrete Workability (slump) immediately AS-1012.3.1 (2014)

Wet density immediately AS-1012.5 (2014)

Mechanical Compressive strength 3,7, 14, 28,56 and 365 days

AS-1012.9 (2014)

Indirect-tensile strength

7, 14 and 28 days

AS-1012.10 (2014)

Flexural strength 14 and 28 days AS-1012.11 (2014)

Deformation Modulus of elasticity 28 days AS-1012.17 (2014)

Poisson’s ratio 28 days AS-1012.17 (2014)

Serviceability Shrinkage every week, up to 1 year

AS-1012.13 (2015)

Creep every week, up to 1 year

AS-1012.16 (2014)

Accelerated curing (70°C)

Mechanical Compressive strength 11 hours and 28 days

AS-1012.9 (2014)

Indirect-tensile strength 11 hours AS-1012.10 (2014)


90

Unlike OPC concrete, the addition of chemical admixture is not effective in

geopolymer binder concrete to improve the workability.

One-part geopolymer binder follows the general rule of concrete mix design i.e.

compressive strength of concrete increases with a decrease in water/binder ratio.

Chapter 4: Experimental results and discussions

91

CHAPTER 4

4. Experimental Results and Discussions 4.1 Preamble

The experimental results of fresh and hardened state properties of geopolymer concrete

of grade 50 MPa are discussed in this chapter with comparing the results of OPC

concrete of same grade. Workability and wet density of concrete were studied as fresh

concrete properties in this chapter with their influencing factors of concrete mix design.

Compressive strength, indirect-tensile strength and flexural strength are the major

mechanical strengths of concrete investigated in this study. The measured mechanical

properties of geopolymer concrete were compared against the models suggested in

concrete standards of current practice, such as AS-3600 (2018) and ACI 318 (2011) in

this chapter. Modulus of elasticity and Poisson’s ratio of geopolymer concrete are

discussed as deformation properties. Experimental results of these properties of

geopolymer concrete were compared with the results of previous studies as well as with

the recommended value suggested in AS-3600 (2018). Drying shrinkage and creep

strains of geopolymer and OPC concretes were studied for one-year period as long-term

serviceability properties of concrete. These measured data were compared with the

estimated values according to AS 3600 (2018). The influencing parameters, such as

water/binder ratio and binder content on drying shrinkage are also discussed.

In this experiment both, geopolymer and OPC concrete were produced from the same

sourced aggregates with similar sand proportions (around 38%) in concrete mix

designs. Therefore, the engineering properties of both concrete measured in this study

can be compared with each other. Each data point of test result represents an average

result from minimum of three concrete specimens.

4.2 Fresh concrete properties

Workability, wet density and air content are the important fresh concrete properties.

Photo images of measurement of fresh concrete properties, such as workability (slump)

and air content are shown in Figure 4.1 which were carried according to relevant

Australian Standards as shown in Table 3.5.


92

-

Figure 4.1: Measurement of fresh concrete properties (a) slump (b) air content

Concrete should have sufficient workability in order to achieve good compaction and

placement in the formworks. Some factors affecting concrete workability are discussed

in Chapter 2. The fresh concrete properties of Grade 50 MPa concrete are shown earlier

in Table 3.4. Data points show that geopolymer concrete needed around 20 kg less

water than OPC concrete for comparable workability of 100± 20 mm slump although

OPC concrete was produced with addition of high range water reducing admixtures

(HWR). As discussed earlier in Chapter 2, a higher proportion of fly ash in binder was

one of the reasons to decrease the water demand in geopolymer concrete when

compared to OPC concrete. Geopolymer concrete also had a slightly lower water/binder

ratio than OPC concrete in this experiment.

The amount of free water added in the geopolymer concrete mix in this experiment was

significantly lower compared to some past studies. Collins and Sanjayan (1999) added

180 kg/m3 of free water in GGBS based geopolymer concrete mixes to achieve 60 to

120 mm of slump. Fernandez-Jimenez et al. (2006b) used 186 kg/m3 and 255 kg/m3

of free water in two different fly-ash based geopolymer concrete mixes. The difference

in water demand in geopolymer concrete was because of the difference in binder

compositions (source materials and alkali activator) as well as the difference in

compositions of concrete itself.


93

Wet density of concrete mainly depends upon the property of aggregates. The

aggregates used in this experiment were igneous rock aggregates having a higher

density than sandstone and limestone rocks. The measured wet density of geopolymer

and OPC concrete were 2450 kg/m3 and 2420 kg/m3, respectively which were relatively

higher than density of the geopolymer concrete in previous studies (2300-2350 kg/m3)

(Diaz-Loya et al., 2011, Hardjito and Rangan, 2005). The higher density of concrete

may be due to the use of heavier and well-graded aggregates. Measured air contents

were 1.1% and 1.2%, respectively in geopolymer and OPC concrete.

A lower amount of water and lower air contents in concrete mix can contribute to a

dense concrete microstructure with lower porosity which is an indicator of higher

durability of geopolymer concrete than OPC concrete.

4.3 Mechanical properties

Mechanical properties of concrete are strength properties of hardened concrete which

were measured at different ages. Conventionally, concrete strengths are defined by

strengths measured at 28 days.

4.3.1 Comprehensive strength development

The compressive strength of concrete is the major mechanical property of concrete

because other mechanical properties, such as tensile strength and modulus of elasticity

can be estimated on the basis of its compressive strength. Both, OPC and geopolymer

concrete were tested in the same way according to AS-1012.9 (2014), an arrangement

of compressive strength testing of this experiment is shown in Figure 4.2.


94

Figure 4.2: Arrangement of compressive strength test

The compressive strength developments of Grade 50 MPa concrete up to one year

period are shown in Figure 4.3. In Figure 4.3, both geopolymer and OPC concretes

showed similar patterns of compressive strength development with time. The measured

28 days compressive strength of geopolymer and OPC concrete were 61 MPa and 59

MPa, respectively. Although having slightly lower strength (28.5 MPa) than OPC

concrete (30 MPa) at 3 days, geopolymer concrete developed higher compressive

strength (74 MPa) compared to OPC concrete (71 MPa) after one-year period. There

were continuous growths of strength until the one-year period in both concretes,

however, strength growths in later age were very small. The numeric values of

compressive strength developments at all ages are presented in Table A.2 with the

standard deviation data. Data points in Table A.2 show that geopolymer concrete

specimens showed relatively smaller standard deviations compared to OPC concrete

which were 1.58 MPa and 3.28 MPa, respectively at 28 days. Smaller value of standard

deviations generally represents uniformity of mixing of concrete ingredients and

consistency of strength development of concrete specimens.


95

Geopolymer concrete showed slightly higher binder strength than OPC concrete. As

shown in Table 3.4, the binder/aggregate ratios in geopolymer and OPC concrete were

0.22 and 0.25, respectively. This indicates sodium hydroxide-free one-part geopolymer

binder is slightly more efficient than OPC to produce structural grade concrete.

Figure 4.3: Compressive strength development of 50MPa concrete

As discussed earlier in Chapter 2, stress-strain graphs from previous studies suggested

that geopolymer concrete could be less brittle (ductile) than OPC concrete of same

grade. Generally, breaking of brittle material is characterised by more visual damage,

such as shattering of glass. Figure 4.4 shows a pair of concrete cylinders of same grade

crushed under compressive load. In this figure, OPC concrete cylinder apparently

suffered more damage at failure point than geopolymer concrete cylinder which

indicates its brittleness.

0

20

40

60

80

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Com

pre

ssiv

e st

ren

gth

(M

Pa)

Age (day)

OPC concrete

Geopolymer concrete


96

(a) (b)

Figure 4.4: Crushed concrete cylinders of grade 50 MPa (a) geopolymer (b) OPC

4.3.2 Indirect-tensile strength

By name, it is an indirect measurement of the tensile strength of concrete because

measurement of the direct axial tensile strength of concrete is a complicated procedure

due to axial alignment issues of concrete specimen (Neville, 1995). A test set-up of

indirect-tensile strength measurement is shown in Figure 4.5.


97

Figure 4.5: Test set of indirect-tensile strength measurement

The indirect-tensile strength development of geopolymer and OPC concrete of this

study are shown in Figure 4.6. This figure shows that geopolymer concrete attained

higher indirect-tensile strength than OPC concrete of the same grade for all ages. The

28 days indirect-tensile strength of geopolymer concrete was 5.1 which was 27.5%

higher than the strength of OPC concrete (4.0 MPa) at the same age. The error bars in

Figure 4.6 represent the standards deviations of the measured results. Geopolymer

concrete specimens showed relatively smaller standard deviations compared to OPC

concrete which were 0.22 MPa and 0.41 MPa respectively at 28 days.

There are some relationships suggested in concrete standards of current practice to

calculate the indirect-tensile strength of OPC concrete, as discussed earlier in Chapter

2. The calculated indirect-tensile strength for Grade 50 MPa concrete would be 2.83

MPa and 3.96 MPa, respectively using AS-3600 (2018) and ACI-318 (2011) which are

shown in Figure 4.6. The indirect-tensile strength of OPC concrete measured in this

study was very close to the predicted value using ACI-318 (2011).


98

Figure 4.6: Indirect tensile strength of Grade 50 MPa concrete

A Comparison of indirect-tensile strength of geopolymer and OPC concrete of this

study with some earlier results and relationship models are presented in Figure 4.7.

Data points in Figure 4.7 show that the indirect-tensile strength of geopolymer concrete

of this study was higher than estimated values using AS-3600 (2018) and ACI-318

(2011). Indirect-tensile strength results of geopolymer concrete in some previous

studies (Raijiwala and Patil, 2011, Hardjito and Rangan, 2005) were even higher than

the current results. Indirect-tensile strength results of this study were closer to the model

proposed by Albitar et al. (2014).

0

1

2

3

4

5

6

7

7 14 28

Ind

irec

t-te

nsi

le s

tren

gth

(M

Pa)

Age (day)

OPC concrete Geopolymer concrete

AS 3600 (2018) ACI 318 (2011)


99

Figure 4.7: Comparison of indirect-tensile strengths of concrete

4.3.3 Flexural strength

Flexural strength test of concrete is also called modulus of rupture test which is also an

indirect measurement of tensile strength of concrete. Generally, the flexural strength of

concrete is 20% to 40% higher than its indirect-tensile strength. An arrangement for

Flexural strength test of concrete is shown in Figure 4.8.

0

1

2

3

4

5

6

4 5 6 7 8 9

Ind

irec

t-te

nsi

le s

tren

tgh

(M

Pa

)

√f'c (MPa)1/2


AS 3600 (2018) ACI 318 (2011)

Hardjito and Rangan (2005) Sofi et al. (2007)

Raijiwala and Patil (2011) Albitar et al. (2014)


100

Figure 4.8: Arrangement for modulus of rupture test of concrete

The flexural strength results of geopolymer and OPC concrete of Grade 50MPa are

shown in Figure 4.9. Data points in Figure 4.9 show that geopolymer concrete attained

higher flexural strength than OPC concrete of the same grade in both ages; 7 days and

28 days. The measured 28 days flexural strength of geopolymer concrete was 7.1 which

was 26.8% higher than the flexural strength of OPC concrete (5.6 MPa) of the same

age. The error bars in Figure 4.9 represent the standard deviations of flexural strength

of concrete specimens. Geopolymer concrete specimens showed relatively smaller

standards deviations compared to OPC concrete which were 0.31 MPa and 0.49 MPa,

respectively at 28 days. The calculated flexural strength for Grade 50 MPa concrete

would be 4.24 MPa and 4.38 MPa, respectively using equations of AS-3600 (2018) and

ACI-318 (2011) which are shown in Figure 4.9. Hence, both concrete standards

predicted a smaller value of flexural strength when compared with experimental result

of OPC concrete of this study.


101

Figure 4.9: Flexural strength of Grade 50MPa concrete

4.3.4 Influence of aggregate-concrete bond on tensile strength of concrete

The mechanical strengths of concrete mainly depend on the strength of the bond

between aggregate and binder paste matrix (called interfacial transition zone) and the

strength of binder paste matrix itself. The strength of this interfacial transition zone is

governed by the adhesive property of the binder paste which is the function of its

molecular structures and chemical bonds. From the chemical perspective, geopolymer

binders are formed by the polymeric structure resulting from cross-linking of poly-

sialate chains having a strong covalent bond (Davidovits 1999) which makes

geopolymer paste more adhesive than OPC paste. Unlike to compressive strength, there

is no significant contribution of mechanical interlocking and friction between the

aggregates in case of tensile strength of concrete, which is more dependent on the

strength of the bond between aggregate and binder paste matrix. When the concrete has

a stronger bond between the aggregate and binder paste matrix, it can resist higher

tensile strength. As a result, geopolymer concrete possesses higher tensile and flexural

strength than OPC concrete for the same level of compressive strength.

0

1

2

3

4

5

6

7

8

9

14 28

Fle

xura

l st

ren

gth

(M

Pa

)

Age (day)


AS 3600 (2018) ACI 318 (2011)


102

The difference in tensile strength between geopolymer and OPC concrete can be

visually explained by their failure modes under tensile stress. Figure 4.10 shows photo

images of fracture surfaces of geopolymer and OPC concrete cylinders obtained from

indirect-tensile strength testing. In this figure, the fracture surface of geopolymer

concrete cylinder has an even surface containing the majority of aggregates split under

tensile stress rather than the failure of the interfacial transition zone. In case of OPC

concrete, the fracture surface is highly uneven and dominated by the failure of the

interfacial transition zone or bond failure. It indicates that the bond between aggregate

and binder paste matrix in geopolymer concrete was stronger compared to OPC

concrete of same compressive strength which resulted in higher tensile strength of


-

(a) (b)

Figure 4.10: Fracture surfaces (a) geopolymer concrete and (b) OPC concrete

4.4 Deformation properties

Modulus of elasticity and Poisson’s ratio of concrete were measured under this

category. Generally, the modulus of elasticity of concrete is measured within elastic


103

range of stress which is considered up to 40% of concrete strength (ASTM-C469, 2014,

AS-1012.17, 2014). Test set-up for the measurement of modulus of elasticity of

concrete is shown in Figure 4.11.

Figure 4.11: Test set-up of modulus of elasticity of concrete

The measured module of elasticity of geopolymer and OPC concrete of this study were

34.2 GPa (standard deviation 0.62 GPa) and 35.3 GPa, (standard deviation 1.35 GPa)

respectively. These results were very close to each other as well as close with the

estimated value of modulus of elasticity of concrete using AS-3600 (2018) for Grade

50 MPa as shown in Figure 4.12. This figure shows that the modulus of elasticity of

geopolymer and OPC concrete are plotted well inside the ±10% range of AS-3600

(2018). Hence, the current equation of modulus of elasticity suggested by AS-3600

(2018) can closely estimate the modulus of elasticity of geopolymer concrete. Whereas,

the modulus of elasticity of concrete estimated using ACI-318 (2011) seems to be

higher than measured values of both, geopolymer and OPC concrete of this study.


104

Figure 4.12: Modulus of elasticity of geopolymer concrete

The modulus of elasticity of geopolymer concrete measured in this study was higher

than modulus of elasticity of heat-cured geopolymer concrete in previous studies

(Hardjito and Rangan, 2005, Fernandez-Jimenez et al., 2006b, Tempest, 2010) which

are shown in Figure 4.12. As discussed in Chapter 2, density is an important factor;

higher concrete density results in higher modulus of elasticity. Generally, concrete

specimen cured at normal temperature has higher density than heat-cured one because

of relatively smaller pore volume. Hardened concrete density of geopolymer and OPC

concrete specimens measured in this study were 2480 kg/m3 and 2450 kg/m3,

respectively which were higher than the density of geopolymer concrete in previous

studies. Modulus of elasticity of ambient cured geopolymer concrete measured by

Douglas et al. (1992) was also close with the prediction of AS-3600 (2018) as shown

in Figure 4.12. Sofi et al. (2007) also suggested that the existing model of modulus of

elasticity of AS 3600 can be applied in geopolymer concrete (ambient cured).

Besides, the modulus of elasticity concrete is largely affected by the quality and

quantity of coarse aggregates used in concrete. Nikbin et al. (2014) suggested that an

increase in proportion of coarse aggregate in concrete mix increased modulus of

elasticity of concrete because aggregate rocks have a higher modulus of elasticity than

mortar or binder paste. Both, geopolymer and OPC concrete produced in this study

0

10

20

30

40

50

60

70

4 5 6 7 8 9

Mod

ulu

s of

ela

stic

ity

(G

Pa

)

√fcm (MPa)1/2


AS 3600 (2018) AS 3600 ±10%

ACI 318 (2011) Douglas et al. (1992)

Hardjito and Rangan (2005) Fernandez-Jimenez et al. (2006)

Diaz-Loya et al. (2011) Tempest (2010)


105

contained same proportions (around 60% of total) of coarse aggregate in the concrete

mix which was an optimum amount. In addition, coarse aggregates used in this study

were quality aggregates (granite rock) having high modulus of elasticity, which also

contributed to achieve higher modules of elasticity of concrete.

As discussed earlier in Chapter 2, Poisson's ratio of concrete can be considered as

independent from concrete strength grade. The measured Poisson's ratio of geopolymer

and OPC concrete were 0.207 and 0.203, respectively which were very close to the

recommended value (0.2) in concrete standards of current practice as well as in

literature (AS-3600, 2018, EN-1992.1.1, 2004, Neville, 1995).

4.5 Serviceability properties

Drying shrinkage and creep strains are the important serviceability properties of

concrete. They cause the contraction of the concrete member which leads to the

development of cracks over the service period of structure.

4.5.1 Drying shrinkage

The test set-up for measurement of drying shrinkage of a concrete specimen is shown

in Figure 4.14. Measurement of drying shrinkage is a non-destructive test procedure,

so same concrete specimen can be used for next measurement.

Figure 4.13: Drying shrinkage reading of concrete specimen


106

Measured drying shrinkage data of geopolymer and OPC concrete of grade 50 MPa are

presented in Figure 4.14. The estimated drying shrinkage of same grade concrete using

AS-3600 (2018) is also plotted in this figure as bench-marks. Data points in Figure

4.14 show that geopolymer concrete exhibited significantly lower drying shrinkage

strain than OPC concrete of same grade at ambient temperature.

Figure 4.14: Drying shrinkage of Grade 50 MPa concrete

The drying shrinkage strain of geopolymer concrete of this study was 455 microstrains

for one-year which was 30% less compared to OPC concrete (590 microstrains) for the

same period. The drying shrinkage of geopolymer concrete was lower than the

estimated strain using AS-3600 (2018) for initial as well as later age. OPC concrete

showed similar strains to the estimated value initially but exhibited higher shrinkage in

later age. These lower drying shrinkage strains in geopolymer concrete can make a

significant difference in the serviceability of concrete structures. Australian Standard

1379 (2017) has specified the 56 days drying shrinkage of normal class concrete (50

MPa or less) should be less than 1000 microstrain. Data points in Figure 4.14 show

that both, OPC and geopolymer concrete have not exceeded this limit. Drying shrinkage

in geopolymer concrete was therefore within the acceptable limits suggested in the

current code of practice.

0

100

200

300

400

500

600

0 28 56 84 112 140 168 196 224 252 280 308 336 364 392

Dry

ing

shri

nk

age

(M

icro

stra

in)

Age (days)

OPC concrete-50 MPa

Geopolymer concrete-50 MPa

AS 3600-50 MPa

Deb et al. (2015)

Wallah (2009)


107

The drying shrinkage strains of geopolymer and OPC concrete (482 and 562

microstrains, respectively for 6 months) measured by Deb et al. (2015) under ambient

temperature curing were very close to current experimental results. As discussed earlier

in Chapter 2, geopolymer concrete specimens that were cured at elevated temperature

exhibited very low drying shrinkage strains in previous studies (Wallah, 2009, Sagoe-

Crentsil et al., 2013, Tempest, 2010). Drying shrinkage results of this study were higher

than those previous results because this study adopted ambient temperature curing.

Drying shrinkage of concrete is affected by several factors of concrete mix, such as

amounts of binder and water, quality of aggregates and properties of the binder itself.

Concrete made from high-quality aggregates, such as quartzite, granite and basalt

generally exhibits less drying shrinkage than from inferior aggregates like sandstones.

In this study, geopolymer and OPC concrete were produced with the same sourced

granite aggregates with similar sand proportions, hence aggregate quality was not a

factor of difference. Water content and amount of binder (paste volume) of concrete

mix are the major factors to increase the drying shrinkage of concrete (Neville, 1995,

Leemann and Lura, 2014). In this study, the water content in geopolymer concrete

mixes were 162 kg/m3 and 183 kg/m3, respectively. In addition, OPC concrete

contained around 20 kg/m3 more binder than geopolymer concrete. The differences in

amounts of binder and water in geopolymer and OPC concrete mixes were the factors

to make difference in shrinkage results in this study. In addition, the difference in the

chemistry of OPC and geopolymer binder was also a factor to influence in drying

shrinkage properties of concrete made from these binders.

4.5.2 Creep strain

An arrangement of creep testing with loaded creep rigs which were kept in a shrinkage

room having controlled temperature and humidity are shown in Figure 4.15. The

deformation readings of loaded creep cylinders were taken on a weekly basis for one

year as a non-destructive testing method.


108

Figure 4.15: Arrangement of creep testing with loaded creep rigs

Generally, creep property of concrete is measured by creep coefficients, and then creep

strains can be calculated using Equation 2.9. The measured creep coefficients of

geopolymer and OPC concrete of grade 50 MPa for one-year period are shown in

Figure 4.16. The estimated creep coefficient of concrete of same grade using equation

of AS-3600 (2018) is also plotted in this figure for comparison. Data points in Figure

4.16 show that geopolymer concrete exhibited a significantly lower creep coefficient

than OPC concrete of same grade at ambient temperature for all ages. For one year, the

measured creep coefficient of OPC concrete was 2.75, which was 47% higher compared

to geopolymer concrete (1.87). The creep coefficient estimated using AS-3600 (2018)

was very close to the experimental results of OPC concrete in this study.


109

Figure 4.16: Creep coefficients of 50MPa concrete

Similar to drying shrinkage, the creep strain in concrete increases rapidly in the initial

period and slowdowns in later age because most of the deformation happens in the early

age of loading. In case of geopolymer concrete, there was not significant increment in

creep after 56 days. Creep coefficient of OPC concrete, on the other hand, increased

with a similar rate to estimated creep using AS-3600 (2018). As discussed in Chapter

2, accelerated curing or heat curing at an early age decreases the long-term creep strain

in conventional OPC concrete due to accelerated hydration of cement and moisture loss

at early age (Sennour and Carrasquillo, 1989). Similar phenomena can be applicable in

geopolymer concrete, hence there were differences in creep coefficient and specific

creep values of this study and results of previous studies. Therefore, the creep

coefficient of this study were higher than measured creep data of heat-cured

geopolymer concrete in previous studies (Wallah, 2010, Sagoe-Crentsil et al., 2013) as

shown in Figure 4.16.

Generally, the creep strain of concrete decreases with the increase in concrete strength

grade because higher grade concrete contains smaller pore volume and higher modulus

of elasticity to resist the deformation. The creep coefficient of heat-cured fly ash-based

geopolymer concrete (��= 35.6 MPa) measured by Gunasekera et al. (2019) seems

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Cre

ep c

off

icie

nt

Age (days)

OPC concrete-50MPa Geopolymer concrete-50MPa

AS 3600-50MPa Gunasekera et al. (2019)

Sagoe-Crentsil et al. (2013) Wallah (2010)


110

close to the creep coefficient of geopolymer concrete of this study as shown in Figure

4.16. However, it should be noted that, creep coefficient of the heat-cured geopolymer

concrete would be much smaller if the compressive strength was at the same level of

this study (��= 60 MPa).

Specific creeps of geopolymer and OPC concrete of this study are shown in Figure

4.17, which were 68 microstrain/MPa and 102 microstrain/MPa, respectively for one

year after loading. Specific creep of heat-cured geopolymer concrete measured by

Wallah (2010) was far less than results of this study as shown in Figure 4.17. For the

conventional OPC concrete, Warner et al. (1998) suggested that the specific creep of

60 MPa concrete would be 50 to 60 microstrain/MPa, after one-year period which was

close to the reading of geopolymer concrete of this study.

Figure 4.17: Measured specific creep of 50MPa concrete

The creep strain of concrete depends on several factors, such as amounts of binder and

water, quality of aggregates and properties of the binder itself. As explained earlier,

both, geopolymer and OPC concrete were produced with same sourced aggregates in

similar sand proportions, hence the quality of aggregates was not a contributing factor

here. Wallah (2010) suggested that the amount of aggregates is a major factor to affect

the creep behaviour of concrete because they are more compact and volumetrically

0

20

40

60

80

100

120

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Sp

ecif

ic c

reep

(m

icro

stra

in/M

Pa

)

Age (days)

OPC concrete-50MPa Geopolymer concrete-50MPa

Wallah (2010)


111

stable than concrete paste under load. The concrete mix designs data in Table 3.4 show

that geopolymer concrete contained a slightly higher amount of aggregates than OPC

concrete. In addition, geopolymer binder generally consists of a big amount of fly ash

which can work as ‘micro-aggregate’ and increases the creep resisting function of

geopolymer concrete which is not available in OPC concrete. A study by Arezoumandi

and Volz (2013) showed that OPC concrete with a high amount of fly ash (more than

50% by weight) exhibited around 20% less creep strain than OPC concrete without fly

ash. In the current study, geopolymer concrete contained 52% of fly ash in the binder

compared to 20% in OPC concrete which can make the difference in the creep property

of concrete.

The difference in the microstructure and pore size in geopolymer and OPC concrete

may also be differentiating factors in the creep strains. The microstructure of the

geopolymer matrix contains cross-linked tetrahedral structures, however, hydrated

OPC (i. e. C-S-H) does not contain such cross-linked structures (Richardson, 2008).

Therefore, the response of the binder pastes under sustained load would be different. In

addition, OPC concrete may have higher porosity in binder paste compared to

geopolymer concrete due to higher water/cement ratio in the concrete mix which was

also one of the reasons for higher creep strain in OPC concrete. Gunasekera et al. (2019)

suggested that the difference in pore volume between OPC and geopolymer concrete

may be one of the factors to make difference in their creep behaviour.

4.6 Development of strength at accelerated curing

The compressive strength and indirect-tensile strength development in geopolymer and

OPC concrete under accelerated curing at an early age are shown in Table 4.1. The

concrete specimens used for accelerated curing were made from a different concrete

batch but with the same mix design as shown in Table 3.4. Data points in Table 4.1

show that geopolymer concrete developed significantly higher early age strength at

accelerated (heat) curing compared to ambient-cured results. Compressive strength

developments of geopolymer and OPC concrete at 6 hours of accelerated curing were

33.5 MPa and 24 MPa, respectively. As shown in Table 4.1, geopolymer concrete

cured at 70ºC for 6 hours can develop around 54% of its 28-days compressive strength

(standard temperature cured) compared to 40% in OPC concrete of same grade for the


112

same duration of curing. This accelerated curing of geopolymer concrete for 6 hours

fulfilled the requirements of AS-1597.2 (2013) (i.e. minimum 32 MPa compressive

strength) for releasing of precast concrete elements from formworks.

Table 4.1: Strengths development at accelerated curing

Accelerated curing for 6 hours Standard

temperature curing

Compressive strength ratio:

6 hours accelerated cured/ 28

days standard temperature

cured

Tested immediately

after accelerated curing Tested at 28 days 28 days

Compressive strength (MPa)

Compressive

strength (MPa)

Indirect-tensile

strength (MPa)


Indirect-tensile

strength (MPa)

Geopolymer 33.5 3.8 56.5 5.0 62.0 54%

OPC 24.0 2.5 54.5 3.8 60.5 40%

Complying with the previous suggestion that early-age heat curing of OPC concrete

could bring adverse effects on long-term strength development of concrete (Higginson,

1961), the 28-days compressive strength of accelerated cured geopolymer concrete

specimens were relatively lower than the strength of standard temperature cured

specimens. For both, geopolymer and OPC concrete, 28-days compressive strength of

accelerated-cured specimens were around 6 MPa lower than strength of standard

temperature cured specimens for the same period.

In addition, the measured density of accelerated-cured concrete specimens was

relatively lower than the density of standard temperature cured specimens in both, OPC

and geopolymer concrete. As discussed earlier, it may be due to the higher pore volume

and loss of moisture from concrete microstructures in accelerated cured concrete

specimens. The average density of standard temperature cured geopolymer and OPC

concrete were around 2480 kg/m3 and 2450 kg/m3, respectively. However, the average

density of accelerated-cured concrete cylinders were 2390 kg/m3 and 2370 kg/m3,

respectively for geopolymer and OPC concrete.

Despite earlier suggestions about higher porosity in accelerated-cured concrete, the

ratio of indirect-tensile strength to compressive strength (��/√��) was similar for

both, ambient cured and accelerated cured geopolymer concrete. This ratio was 0.66


113

and 0.67, for ambient cured and accelerated cured geopolymer concrete specimens,

respectively. In case of OPC concrete, this ratio was 0.52 for both curing conditions.

Previous studies suggested that accelerated cured geopolymer concrete specimens

exhibited significantly lower drying shrinkage and creep strains when compared to

ambient curing results (Tempest, 2010, Wallah, 2009, Sagoe-Crentsil et al., 2013). This

can be considered as an advantage in precast applications. Lower drying shrinkage in

precast concrete elements after the installation can result in lower shrinkage stress

development.

4.7 Conclusions

Specimens of grade 50 MPa Geopolymer and OPC concrete were tested for their

engineering properties at fresh and hardened states according to relevant Australian

standards. Following conclusions can be made from the experimental results of this

study:

a) Geopolymer concrete needed around 13% less binder for comparable 28-day

compressive strength and workability to OPC concrete.

b) Geopolymer concrete showed around 27% higher indirect-tensile and flexural

strength than OPC concrete of same strength grade. Both, indirect-tensile and

flexural strength and flexural strength of geopolymer concrete were higher than

estimated values using AS-3600 (2018) and ACI-318 (2011).

c) Stronger bond between aggregate and binder paste matrix in geopolymer concrete

was the main reason for higher indirect-tensile and flexural strength of geopolymer

concrete than OPC concrete of same strength grade.

d) Measured modules of elasticity of geopolymer concrete was found to be close with

OPC concrete of same grade which can be closely estimated using equations

suggested in AS-3600 (2018).

e) Under ambient curing, Geopolymer concrete showed around 30% less drying

shrinkage and around 50% less creep strain than OPC concrete of same grade.

Both, drying shrinkage and creep coefficient of geopolymer concrete were lower

than estimated values using AS-3600 (2018).

Chapter 5: Finite element modelling

114

CHAPTER 5

5. Finite Element Modelling 5.1 Preamble

This chapter discusses the finite element modelling of reinforced concrete and

prestressed concrete beams using Abaqus programme (Abaqus-Inc., 2014). Concrete

damaged plasticity (CDP) model was adopted in this analysis to apply the progressive

damage behaviour of concrete under imposed load. The interaction between

prestressing steel tendon and surrounding concrete was studied using modelling of a

simple pull-out test. The applicability of CDP model and the interactions of steel (both,

prestressing steel and conventional steel) with surrounding concrete were validated by

comparing the experimental load-deflection responses taken from some published

studies with their finite element analysis results. Simply supported beams of different

cross-sections and spans were modelled to investigate the effects of the tensile strength

of concrete in load-deflection behaviours of both, conventional reinforced concrete

beams and prestressed concrete beams. The engineering properties of grade 50 MPa

concrete measured in this experimental programme were taken as input parameters

(material’s properties) for finite element modelling.

5.2 Model development

5.2.1 Material properties and constitutive models

The equation proposed by Hognestad (1951) was adopted in this study for the

modelling of compressive stress-strain behaviour both, geopolymer and OPC concrete.

However, considering the brittleness of high strength concrete (50 MPa), the

descending slope of softening branch was taken higher than suggested in the original

equation. The adopted equations can be written as follows:

�� = �� 2 �

�

�� − �

�

��

�

� when ɛ ≤ �� (5.1)

�� = �� 1 − 0.3 �

��

�� when ɛ < �� (5.2)


115

where, �� is stress in concrete to corresponding strain ɛ; ε� is the strain at the maximum

compressive stress (critical strain); and ε� is the ultimate strain at failure.

The stress-strain behaviour of concrete under flexural tensile stress was modelled using

Carreira and Chu (1986) equation as follows:

��

��=

�(� ��⁄ )

��(� ��⁄ )� (5.3)

where, �� is the flexural stress corresponding to strain ε; �′� is the flexural strength of

concrete; ε�� is the strain at the maximum tensile stress; value of β is taken as 1.85.

(a)

(b)

Figure 5.1: Stress-strain models of concrete a) compressive and b) tensile behaviours

0

5

10

15

20

25

30

35

40

45

0 0.001 0.002 0.003 0.004 0.005 0.006

Co

mp

ress

ive

stre

ss (

MP

a)

Compressive strain

Geopolymer concrete

OPC concrete

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

Fle

xu

ral

stre

ss (

MP

a)

Flexural strain

Geopolymer concrete

OPC concrete


116

The constitutive models adopted in this study are shown in Figure 5.1. Based on

previous studies, critical strain (��) and ultimate strain (��) of geopolymer concrete

were taken as slightly higher than OPC concrete for both; uniaxial compression and

flexural tensile stress.

The damage parameters of the constitutive models of concrete adopted in this study are

shown in Figure 5.2. Data points in this figure show that geopolymer concrete can

sustain relatively higher deformation than OPC concrete for the same level of damage

under both stresses; compression and tension. Complying with the constitutive models,

the damage parameter for compression is linear after critical strain whereas the damage

parameter for tension is represented by a curve line for both, geopolymer and OPC

concrete. All the calculated values of stress-strain behaviour and damage parameters of

both; geopolymer and OPC concrete of grade 50 MPa are presented in Appendices.

_

(a) (b)

Figure 5.2: Damage parameters of constitutive models of concrete at a) compression

and b) tension

On the other hand, reinforcing steel can be considered as isotropic material having a

similar stress-strain property in both, tension and compression. The yield strength of

conventional reinforcement was taken as 500 MPa (normal ductility class). In case of

prestressing steel, it was taken as 82% of characteristic breaking strength as

recommended by AS-3600 (2018). An idealised elastic and perfectly plastic model was

0.0

0.1

0.2

0.3

0.4

0 0.002 0.004 0.006

Dam

age

par

amet

er

Compressive strain

Geopolymer concrete

OPC concrete

0.0

0.2

0.4

0.6

0.8

1.0

0 0.001 0.002 0.003 0.004

Dam

age

par

amet

er

Tensile strain

Geopolymer concrete

OPC concrete


117

adopted in this study to define stress-strain behaviour of normal and prestressing steels

which are shown in Figure 5.3.

Figure 5.3: Idealised stress-strain diagram of normal and prestressing steel

The adopted strength properties of concrete and steel in this study are summarised in

Table 5.1. The flexural strengths of both, geopolymer and OPC concrete were taken as

90% of the experimental values for modelling purposes, considering safety factors.

Table 5.1: Mechanical properties of concrete and steel

Properties Steel Concrete

Prestressing Conventional Geopolymer OPC

Characteristic strength (MPa) - - 50 50

Flexural strength (MPa) - - 6.4 5.04

Tensile strength (MPa) - - 5.1 4.0

Modulus of elasticity (MPa) 195,000 200,000 34,200 35,300

Poisson’s ratio 0.3 0.3 0.2 0.2

Yield strength (MPa) 1500 500 - -

In addition, the adopted parameters of the concrete damaged plasticity model with their

recommended default values are shown in Table 5.2. Parameters of CDP, such as

viscosity and dilation angle can make difference in convergence of numerical models

and its results (Demir et al., 2018, Hamoda et al., 2019) which are discussed in later

0

500

1000

1500

0 0.01 0.02 0.03 0.04 0.05

Ten

sile

str

ess

(MP

a)

Strain

Prestressing steel

Normal steel


118

section. In this study, both geopolymer and OPC concrete beams were modelled using

same values of these parameters such that the results can be compared.

Table 5.2: Adopted parameters of concrete damaged plasticity

Dilation angle, Shape factor Stress ratio,

fb0/fc0

Eccentricity Viscosity parameter,

μ

30° 0.667 1.16 0.1 0.0005

5.2.2 Modelling of elements

Concrete beams, support plates and end plates were modelled using three-dimensional

solid brick elements (8-nodes with reduced integration C3D8R). Normal reinforcing

steel bars were modelled using three-dimensional beam elements (B31) which have

bending stiffness. Prestressing tendons were also modelled using a three-dimensional

solid brick elements (C3D8R).

5.2.3 Modelling of steel-concrete interaction

The interaction between steel bars and concrete was considered as rigid bonding using

the embedded technique. In this method, the reinforcement bar is considered as an axial

member imbedded in the solid concrete element, such that its displacements are

consistent with the surrounding concrete. An equal number of nodes and same degrees

of freedom are applied in both, concrete and steel elements of contact. This type of

rigid or perfect bonding between reinforced steel and concrete has been applied in some

previous studies where results from finite element analysis of reinforced concrete (RC)

beams showed a good correlation with experimental results (Hamoda et al., 2019,

Wahalathantri et al., 2011)

However, the bond between prestressing steel tendon and concrete is different than

steel-concrete bond in conventional steel reinforcement, it gradually deteriorates with

the increase in shear stress in the steel tendon and concrete interface due to an increase

of imposed load. So, it needs a different assumption to model the interaction, such as

traction-separation law. The traction-separation law for elastic range can be shown in

Equation (5.4).


119

Ʈ = �

��

��

��

� = ��

��

��

� �

��

��

��

� = �� (5.4)

where, Ʈ is the traction vector having three-dimensional (normal, shear and transverse

directions) components ��, �� and �� ; � is the stiffness of cohesive surface having

three-dimensional components �� , �� and �� and ��, �� and �� are the displacement

components of separation vector � respectively.

Figure 5.4: Traction-separation of a cohesive bond

In traction- separation law, the bond between any two surfaces starts to deteriorate

when the shear stress reaches a maximum value Ʈ�� at critical separation (��) then

after, it gradually deteriorates towards the complete failure of bond when the separation

reaches the ultimate separation (��) as shown in Figure 5.4. The traction-separation

model generally assumes a linear elastic behaviour up to the maximum stress (Ʈ��)

followed by the initiation and evolution of damage. The elastic behaviour can be

written in terms of a constitutive matrix (Equation 5.4) that relates the normal and shear

stresses to the normal and shear separations across the steel-concrete interface. Damage

modelling simulates the degradation and eventual failure of the bond between two

cohesive surfaces which consists of two parts; damage initiation and damage evolution

criteria (Abaqus-Inc., 2014).


120

a) Damage initiation

Damage initiation is the beginning of the degradation of the stiffness of the interface.

Damage on the stiffness of the interface starts when the damage initiation criteria are

fulfilled. In traction-separation law, damage initiation criteria are based on normal

and/or shear stresses subjected to the interface or relative displacements between steel

tendon and concrete. Generally, a numeric value of 1 or higher is assumed to be fulfilled

the initiation criterion. Abaqus-Inc. (2014) adopts following damage initiation criteria

for cohesive surface behaviour:

a. Maximum stress criterion: damage initiates when the ratio between normal or

shear stress (��, �� and ��) and maximum stress in the corresponding direction

(��, ��

�� and ��) reaches a value of one.

b. Quadratic stress criterion: damage initiates when a sum of squares of the ratios

between each stress and maximum stress in the corresponding direction (e.g.

(��/��)�) reaches a value of one.

c. Maximum separation criterion: damage initiates when the ratio between each

displacement in each direction (��, �� and ��) and maximum displacement in the

corresponding direction (��, ��

�� and ��) reaches a value of one.

d. Quadratic separation criterion: damage initiates when a sum of squares of the

ratios between each stresses and maximum stress in the corresponding direction

(e.g. (��/��)�) reaches a value of one.

b) Damage evolution

It is assumed that damage evolution criteria do not have any effect on the adopted

damage initiation criteria. In surface-based cohesive behaviour, damage evolution

describes the degradation of the cohesive surface stiffness. The damage evolution

criterion describes the degradation rate of the stiffness of cohesive surface after

reaching the damage initiation criterion. The post-initiation response in traction-

separation curve (softening curve or descending branch) can be linear, expositional or

user defined (tabular) path. Damage evolution criteria can be based on specified

fracture energy (area under traction-separation curve) or separation at failure (��).


121

5.2.4 Bond strength of reinforcing steel and concrete

Strength of bond between reinforcing steel and concrete is the result of adhesion,

friction and mechanical interlocking between reinforcing steel and concrete surfaces.

The adhesion is attributed to the binding property of cement developed during

hydration and setting process, whereas friction and mechanical interlocking depend on

hardness and roughness of interacting surfaces i.e. reinforcing steel and concrete

surfaces. Bond strength of concrete depends on several factors, such as concrete

strength grade, size and quality of coarse aggregates and surface geometry of steel bar.

Generally, the bond strength between reinforcing steel and concrete increases with

strength grade of concrete due to higher adhesion with steel and stronger surface

provided by higher-grade concrete. Ribbed or deformed bars provide a significantly

stronger bond with concrete than plain bars due to higher mechanical interlocking and

friction provided by rough surface (Xing et al., 2015). Generally, the bond strength

between reinforcing steel and concrete is measured using simple pull-out test of

embedded steel bar according to ASTM-A944 (2015) or other standard methods.

During the pull-out, the external force (�) acting along the transfer length is expressed

as:

� = �� ∫ ��

�� (5.5)

The work done by an external force during the pulling-out of the embedded bar, which

is equivalent to the fracture energy can be written as:

� = �� ∫ � ��

��

�

�� (5.6)

where, � is the diameter of the bar, � is the bond strength between steel and concrete,

� is the embedded length and � is the slippage distance.

Several experimental studies were done in the past to determine the bond strength of

reinforcing steel and concrete using pull-out test. An experimental study of pull-out test

by de Almeida Filho et al. (2008) using 500 MPa deformed bar in different grades of

concrete reported that bond strength of steel concrete was between 10 MPa-14 MPa,


122

with critical separation (��) was less than 1.0 mm for all cases. The average maximum

slippage distance (��) was 4.0 mm in their study. Series of pull-out testing by Diab et

al. (2014) using 16 mm deformed bar in normal strength and high strength concrete

found bond strength of concrete was directly proportional to the compressive strength

of concrete which was ranged from 5.5 MPa to 10.5 MPa. In addition, their study

suggested that bond strength increases with an increase in concrete cover thickness and

quality of coarse aggregates used.

A study by Sarker (2011) showed that bond strength of fly ash-based geopolymer

concrete ranged from 11 MPa to 19 MPa which was relatively higher than OPC

concrete of similar compressive strength because of the higher tensile strength of

geopolymer concrete. In Sarker (2011) study, bond strength increases with an increase

in concrete cover thickness because the majority of test specimens failed by splitting

of the concrete cover in a brittle manner. Bond strength of fly ash and GGBS based

geopolymer concrete studied by Castel and Foster (2015) using pull-out testing of

deformed steel bar found geopolymer concrete has 24 MPa to 32 MPa bond strength

which was around 10% higher bond strength than OPC of same compressive strength

due to higher tensile strength. In their study, critical separation (��) was less than 1.0

mm for all cases and most specimens failed by splitting of concrete block, therefore,

the descending branch of the bond stress-slip curve did not appear. On the other hand,

the bond strength of the same concrete using plain bars was recorded only around 4.0

MPa which showed significant impacts of friction and mechanical interlocking

between reinforcing steel and concrete. An experimental study on bond strength of fly

ash and GGBS based geopolymer concrete by Doguparti (2015) reported that

geopolymer concrete has higher bond strength than OPC concrete which was around

12.0 MPa for concrete having 35 MPa compressive strength. Based on experimental

results, some models and equations are suggested to calculate bond strength between

reinforcing steel and OPC based concrete.

Orangun et al. (1977) proposed the following formula to calculate the bond strength:

� = 0.083045��′� �1.2 + 3 ��

�� + 50 �

��

�� (5.7)


123

where, � is the concrete cover, mm; �� is the bar diameter and �� is the development

length.

Hadi (2008) proposed a similar equation to Orangun et al. (1977) as following:

� = 0.083045��′� �22.8 − 0.208 ��

�� − 38.212 �

��

�� (5.8)

Esfahani and Rangan (1998) proposed an equation to calculate the bond strength of

reinforcing bar and concrete as following:

� = 8.6�/��.�

�/��·�� (5.9)

where, �� is tensile strength of concrete.

EN-1992.1.1 (2004) recommends following equation to calculate bond strength as

following:

�� = 2.25 �� (5.10)

where, �� is a coefficient related to the quality of the bond condition and the position

of the bar and �� is related to bar diameter (�� = 1.0 for bar diameter (φ) ≤32 mm).

Equations 5.7 and 5.8 show that bond strength between reinforcing bar and concrete is

directly related to strength grade of concrete due to the increase of adhesion and

frictional resistance with concrete quality. However, Equations 5.9 and 5.10 considered

tensile strength of concrete as the major factor to determine the bond strength between

reinforcing bar and concrete. For an embedded length of 150 mm and cover 40 mm the

calculated values of bond strength for grade 50 MPa concrete using the above equations

are presented in Table 5.3.

Table 5.3: Calculated bond strength

Orangun et al. (1977) Hadi (2008) Esfahani and Rangan (1998) EN-1992.1.1 (2004)

8.2 10.7 12.9 9.0


124

Some studies were done to simulate the pull-out testing of steel reinforcement using

finite element method. A finite element simulation of pull-out test by Lowes et al.

(2004) applying spring elements to generate a cohesive surface with critical separation

(��) less than 1.0 mm and ultimate separation (��) of 10.0 mm showed a good

correlation with the experimental results. Luna Molina et al. (2015) showed that finite

element simulation of pull-out test of deformed steel bar using Abaqus can make a good

correlation with test results. In their study, bond strength (τ) and critical separation

(��) were around 10 MPa mm and 2.0 mm, respectively for concrete having 27 MPa

compressive strength using both galvanised steel and non-galvanised steel bar. It also

reported that bond stress-slip curve of pull-out test using deformed steel bar showed

good agreement with traction-separation law.

5.2.5 Modelling of bond between prestressing steel tendon and concrete

Yapar et al. (2015) simulated the bond between the pre-tensioned strand and concrete

using a cohesive surface model. Their simulation was carried out using Abaqus

software applying a concrete damaged plasticity model. The cohesive surface model

included hard contact, friction, cohesion and damage model to define the interfacial

bond strength. In their study, finite element simulation showed good agreement with

experimental results in terms of load versus displacement plot.

Generally, the hollow duct area of the bonded post-tensioned concrete beam is filled

with pressured grout after the completion of the prestress transfer process. Generally,

grout contains cement, water and sand but no coarse aggregates, which weakens its

interaction with reinforced steel because of small frictional resistance and less

mechanical interlocking. In addition, prestressing steel tendons can provide less surface

roughness than deformed steel bars. These factors influence the bond between

prestressing steel tendons and concrete to make it relatively weaker than the bond

between normal steel reinforcement and concrete.

The interaction between prestressing tendon and surrounding concrete in the post-

tensioned concrete beam can be modelled using a pull-out test of reinforcement bar

with smaller values of bond strength (�), critical separation (��) and maximum slippage


125

distance (��) compared to normal reinforced steel. The modelling of cohesive surface

interaction depends on several user-defined parameters, such as stiffness of cohesive

surface (�), damage initiation and damage evolution criteria. The objective of this

modelling was to find out the optimum value of stiffness of cohesive surface (�) such

that it can satisfy the given values of bond strength (�), critical separation (��) and final

slippage (��). The cohesive surface parameters and their values used in this simulation

are presented in Table 5.4. The material constitutive models used in this simulation are

presented in Table 5.1.

Table 5.4: Parameters of pull-out test modelling

Parameters values

Bond strength (�) 10-12 MPa

Stiffness of cohesive surface (�) 1-200 N/mm

Normal behaviour hard contact

Coefficient of friction 0.1

Critical separation (��) <1.0 mm

Maximum slippage (��) 3.0 mm

Damage initiation criteria maximum nominal stress

Damage evolution criteria energy

Softening path exponential

Nominal fracture energy 15-18 N.mm

A concrete block of 200 mm width, 200 mm breadth and 200 mm depth was modelled

with a centrally embedded steel bar of 16 mm diameter having 150 mm of contact

length with the concrete block as shown in Figure 5.5. Enough contact length (��>

5d�) was provided such that maximum bond strength would develop within the contact

length. The concrete block was laterally reinforced by 4 stirrups of 6 mm diameter

placed at 50 mm of spacing supported by 8 mm diameter reinforcement bars in each

corners in order to prevent the block from splitting. The reinforcement schedule of

modelled block is shown in Figure A.10. A full restraint was applied on the back

surface of the block to fix it against any movement. Average mesh sizes of 12.5 mm

were applied to all elements. As the objective of this simulation was to model the

interfacial bond between prestressing tendon and concrete, the steel bar was modelled


126

using a solid element (C3D8R) having strength properties equivalent to prestressing

tendon (i.e. yield strength 1500 MPa).

Figure 5.5: A finite element modelling of pull-out test

Pulling force was applied on the free end of the bar using the displacement control

method until the bond failed. The bond stress can be calculated from the pull-out test

using following equation:

� = �/(��) (5.11)

where, P is the axial force exerted in an embedded bar while pulling-out.

Different values of stiffness coefficients of cohesion (1 N/mm to 200 N/mm) were used

to define the cohesive surface behaviour of steel concrete interfacial bond. Bond stress

versus slippage graphs obtained from the simulation of pull-out test using different

stiffness coefficients are presented in Figure 5.6. This figure shows that �� or bond

strength increased with the increase in stiffness coefficient due to higher resistance of

bond against deformation. The distance of critical separation (��) decreased with an

increase in stiffness coefficient as expected. A value of 25 N/mm3 of stiffness

coefficient of cohesion (�� or ��) can give the optimum result of bond strength in


127

modelling of prestressing steel and concrete interfacial bond (i.e. bond strength was

around 10 MPa). It is assumed that, degradation of bond strength in a pull-out test is

mainly due to shear stress, therefore stiffness coefficient of cohesion in normal

direction (��) was not considered as an important factor in this simulation. In Figure

5.6, bond stress of stiffness coefficients from 1 N/mm to 100 N/mm3 have followed the

traction-separation law. However, a higher value of stiffness coefficients (200 N/mm3)

may result in rupture of concrete due to very high pulling stress before reaching

maximum bond stress and does not follow traction-separation law.

Figure 5.6: Bond stress-slippage curves for different stiffness coefficients

Using the equation of traction-separation, the approximate value of critical separation

can be expressed as follows.

�� = �� = ��

�� (5.12)

The estimated value of critical separation (��) from the maximum traction obtained

from the simulation of pull-out testing is calculated in Table 5.5. This table shows the

calculated values of critical separation (��) for different stiffness coefficients were very

close to that obtained from the bond stress-slippage curve as shown in Figure 5.6.

0

4

8

12

16

20

24

28

0 1 2 3 4 5 6 7 8 9 10 11 12

Bo

nd

str

ess

(MP

a)

Slippage (mm)

kss = 1

kss = 5

kss = 10

kss=25

kss=50

kss= 100

kss=200


128

Table 5.5: Calculated values of critical separation

�� = �� (N/mm3) �� (MPa) �� =��

�� (mm)

1 7.1 7.11

5 8.2 1.63

10 8.9 0.89

25 10.3 0.41

50 13.4 0.27

100 17.5 0.17

The maximum stress levels in steel bar and concrete (for �� = �� = 25 N/mm3) are

shown in Figure 5.7. This figure shows that stress level in the steel bar gradually

increased along the direction of pull and reached the peak value within the contact

length. There was not any apparent damage in the concrete until this stress level.

Figure 5.7: Stress level on steel bar and concrete during pulling-out

The profiles of stress subjected in the steel bar, as well as bond stress developed along

the embedded length of bar (for �� = �� = 25 N/mm3) are shown in Figure 5.8. This

figure shows that both stresses gradually increased along the length of the bar and reach

the maximum values within the contact length. The maximum stress was less than the

yield strength of steel bar (1500 MPa), therefore no yielding of steel was expected.


129

Figure 5.8: Profile of stress along the reinforcement bar

5.3 Finite element analysis of reinforced concrete (RC) beams

Before doing the finite element analysis of prestressed concrete beams, it is necessary

to investigate the effect of tensile or flexural strength of concrete on the flexural

capacity of reinforced concrete beam. Generally, tensile or flexural strength of concrete

is ignored in the design of flexural reinforced concrete structures, such as beam and

slab because plain concrete possesses very low tensile strength. However, it can be an

import factor in design of flexural concrete members where a crack-free section is

desired because cracking of concrete is directly related to its flexural strength.

5.3.1 Validation of CDP in RC beam

In order to validate the applicability of concrete damaged plasticity model in flexural

concrete member, a finite element model of a reinforced concrete beam was analysed

for a similar cross-section and loading arrangement with a published experimental

work. A reinforced concrete beam having a cross-section of 150 mm × 200 mm and

1600 mm effective span with four-point loading arrangement tested by Esfahani et al.

(2007) was selected in this modelling. Concrete beam and support plates were modelled

using three-dimensional solid brick elements (C3D8R) whereas, conventional steel

reinforcement bars were modelled as three-dimensional beam elements (B31). A

0

2

4

6

8

10

12

0

50

100

150

200

250

300

350

400

0 25 50 75 100 125 150 175 200 225 250

Bo

nd

str

ess

(MP

a)

Ba

r st

ress

(M

Pa

)

Bar axis (mm)

Bar stress

Bond stress


130

perfect bond between steel bars and concrete was applied using the embedded

techniques. The strength grade of concrete was taken as 25 MPa, whereas yield strength

and ultimate strength of tensile reinforcement were taken as 400 MPa and 575 MPa,

respectively as specified in the paper. The stress-strain behaviours of concrete under

compression and tension (flexural) were modelled using Hognestad (1951) and

Carreira and Chu (1986) models, respectively. In case of reinforcing steel, two different

models were used to define stress-strain behaviours of steel; idealised elastic and

perfect plastic model and trilinear strain-hardening model which are discussed earlier

in Chapter 2. The concrete damage parameter values were taken as their default values

as shown in Table 5.2. In this modelling, an average mesh size of 25 mm was used to

model all the elements parts.

Figure 5.9: Load-deflection responses of RC concrete beam

Load-deflection response of experimental results and numerical simulations of the test

beam are shown in Figure 5.9. In this figure, finite element simulations using a

concrete damaged plasticity model showed a good correlation with experimental load-

deflection response of reinforced concrete beam. Both stress-strain models (elastic and

perfect plastic model and strain-hardening model) of reinforcing steel predicted similar

yield load of the beam. However, the strain-hardening model closely captured the

increment of imposed load after the yielding of the beam because it allows the

0

10

20

30

40

50

60

0 10 20 30 40

Imp

osed

loa

d (

kN

)

Mid-span deflection (mm)

Esfahani et a. (2007) B1-12 beam: Experimental

Simulated B1-12 beam: FE simulation (strain hardening)

Simulated B1-12 beam: FE simulation (Elastic and perfectly plastic)


131

increment of stress in steel reinforcements after the yield point, hence closely predicted

ultimate load.

In addition, some more experimental results of reinforced concrete beams from publish

literature were also simulated to validate the applicability of CDP model to predict

load-deflection behaviours of flexural concrete members. All the RC beams simulated

in this study failed in a flexural failure mode. The amount of reinforcement in these

beams varied from under-reinforced to over-reinforced, such that the finite element

simulation would cover all types of reinforced beams. The reinforced beams tested by

Mertol et al. (2015) have under-reinforced (CC0.81) and balanced (CC1.60) designs.

Whereas light-weight concrete reinforced beam tested by Dias-da-Costa et al. (2014)

has over-reinforced design. The details of simulated reinforced concrete beams are

shown in Table 5.6. The modelling parts (concrete beams, support plates and steel

reinforcements) was done using similar elements to earlier modelling. The stress-strain

behaviours of concrete were also modelled using Hognestad (1951) and Carreira and

Chu (1986) models, for compression and tension respectively. In order to comply with

stress-strain behaviour of steel material, steel reinforcements were modelled with

strain-hardening concept for all cases.

Table 5.6: Details of simulated reinforced concrete beams

Reference Beam ID Beam

size (mm2)

Eff. span (mm)

fcm (MPa

Steel ratio

(��)*%

Steel yield strength (fsy)

MPa

Mertol et al. (2015) CC0.81 180 × 250 3300 31.4 0.81 420

Mertol et al. (2015) CC1.60 180 × 250 3300 36.7 1.6 420

Dias-da-Costa et al. (2014)

3T 120 × 270 2800 57.0 2.96 545

* �� = ��/��, where � is the effective depth of beam cross-section.

The finite element analysis results of modelled RC beams are plotted in Figure 5.10

with their experimental results. The simulated load-deflection responses of these beams

showed very close agreements with the corresponding experimental results as shown

in Figure 5.10. The differences between predicted and experimental ultimate loads were

2.7%, 2.9% and 2.4% for beam CC0.81, beam CC1.60 and beam 3T, respectively. The

3T beam tested by Dias-da-Costa et al. (2014) was a light weight concrete. Thus, it can


132

be concluded that concrete damaged plasticity model can closely predict the load-

deflection behaviour of a flexural member having concrete of any strength grade and

types. However, finite element analysis gives smooth load-deflection curves, although

there were sudden increments in imposed load values in some experimental load-

deflection responses.

Figure 5.10: Load-deflection response of simulated RC beams

5.3.2 Modelling of test RC beams

Simply supported beams of three different effective spans, 2.8 m, 5 m and 10 m from

geopolymer and OPC concrete of grades 50 MPa were modelled and simulated in this

study. For each span, two identical (cross-section) beams from geopolymer and OPC

concretes were considered. Load-deflection response of the reinforced concrete beam

at flexural mode of failure was the focus of this study, and therefore only long-span

beams (span/depth>10) were considered. Each span beam had different tensile steel

reinforcement; ranging from nearly-balanced to under-reinforced sections. A concrete

section is said to be under-reinforced when it has a smaller amount of steel than

required for a balanced failure. The degree of under-reinforcement increases with the

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90

Loa

d (

KN

)

Mid-span defelection (mm)

Dias-da-Costa et al. (2014): 3T beam-Experimental

Dias-da-Costa et al. (2014): 3T beam-FE simulation

Mertol et al. (2015)-CC1.60 beam-Experimental

Mertol et al. (2015)-CC1.60 beam-FE Simulation

Mertol et al. (2015)-CC0.81 beam-Experimental

Mertol et al. (2015)-CC0.81 beam-EF sumulation


133

decrease in the amount of tensile reinforcement in the concrete section. The design

details of concrete sections and reinforcements are shown in Table 5.7. Adequate

numbers of vertical stirrups were provided in the shear span of the test beams, such that

the beams should fail under flexure in the middle span (not a shear failure). The spacing

of stirrups were taken smaller than calculated spacing using AS-3600 (2018) to be on

the safe side. The middle spans have only the minimum required numbers of vertical

stirrups. The reinforcement schedule in a 5 m long RC beam is shown in Figure A.11

(in the Appendices).

The element types, stress-strain models of concrete and bond between steel

reinforcement and concrete were adopted as described in the earlier section. In case of

reinforcing steel, idealised elastic and perfect plastic model (see Figure 5.3) was

adopted in this modelling due to its simplicity and correlation with analytical

calculations. An average 25 mm of mesh size was applied in all the modelled beams.

All beams were subjected to a 4-point symmetrical loading system with displacement

control methods until failure.

Table 5.7: Design details of the test RC beams

Effective span (mm)

Shear span (mm)

Depth (D) mm

Width (�) mm

Tensile

steel (��)

Compressive steel

Vertical stirrups in shear span

Steel ratio (��)*

2,800 1,000 250 150 3 × Φ20 mm

2 × Φ12 mm Φ 8 mm @90 mm

2.9%

5,000 1,750 400 300 4 × Φ24 mm

2 × Φ12 mm Φ 8 mm @100 mm

1.7%

10,000 3,800 750 350 5 × Φ32 mm

3 × Φ12 mm Φ10 mm @200 mm

1.6%

*�� = ��/��; where, � is the effective depth of beam cross-section.

5.3.3 Parametric study using finite element modelling

The finite element analysis process and its outcome can be affected by the adopted

constitutive parameters. Viscosity (μ) is one of the parameters to effect in finite element

analysis. Demir et al. (2018) suggested that an increase in value of this parameter

increases the ability of model convergence and decreases the time for analysis by

decreasing the total number of iterations required. However, increasing the numeric

value of this parameter can affect in load-deflection behaviour of flexural members by


134

increasing the stiffness of concrete section. Their study suggested the value of this

parameter can be in a range from 0.00005 to 0.001 with an optimum value as 0.0005

for realistic load-displacement response in modelling of the reinforced concrete beam.

This value (0.0005) of the viscosity parameter was also adopted in this study. Dilation

angle, which represents the vector direction of plastic strain increment in concrete can

also affect the outcome of the finite element analysis (Hamoda et al., 2019). The

recommended value of dilation angle range between 25° to 50°, Sümer and Aktaş

(2015) suggested its value as 30° to predict more realistic response of the concrete

beam.

Mesh size is an important parameter to affect the finite element results and the

convergence capacity of the model. Generally, a smaller mesh size gives more accurate

result than coarser one, however, it takes longer times to solve the finite element modes

due to the higher number of elements (Sümer and Aktaş, 2015, Tahmasebinia et al.,

2012). Sometimes finer mesh can also cause convergence issue of finite element

analysis due to the large number of connecting points in the model and equations. In

order to study the mesh sensitivity, three different mesh sizes; fine (12.5 mm), medium

(25 mm), and coarse (50 mm) were applied in the 2.8 m long RC beam as shown in

Figure 5.11.


135

(a)

(b)

(c)

Figure 5.11: Modelled beams with different mesh sizes (a) fine, (b) medium (c)

coarse

The load-deflection responses of 2.8 m long reinforced geopolymer concrete beam with

different mesh sizes are presented in Figure 5.12. Increasing the mesh size generally

gives a rough approximation of numeric results with a shorter time for analysis. It also

shows a slightly higher bending stiffness of concrete beam and higher value of ultimate

load (��). Figure 5.12 shows an uneven line of load-deflection response obtained from

50 mm mesh size which resulted in around 4% higher value of ultimate load than from

medium (25mm) mesh size. Finer mesh generally size gives a very smooth load-

deflection curve, but it may not show the descending curve after failure. In this study,

mesh size of 25 mm showed a complete prediction of load-deflection response

representing by a smooth line. Sümer and Aktaş (2015) also reported that 25 mm of

mesh size showed a good correlation with the experimental result of reinforced

concrete beam rather than 50 mm and 10 mm mesh sizes. This mesh size (25 mm) was

also adopted in modelling of both, conventional reinforced and prestressed concrete


136

beams in this study. The finite element model with medium (25mm) mesh size can be

solved in a reasonable time. The ultimate load values obtained from 12.5 mm and 25

mm mesh sizes were very close to each other. Therefore, a 25 mm mesh size seemed a

practicable option in terms of analysis time and numeric result.

Figure 5.12: Load-deflection response of 2.8 m long beam with different mesh sizes

5.3.4 Results and analysis of RC beams

The load-deflection responses of reinforced concrete beams of different sizes obtained

from finite element analysis are presented in Figure 5.13. This figure shows that

geopolymer concrete beams performed better than OPC concrete beam of same span

in terms of load-carrying capacity and vertical deflection. For all cases, geopolymer

concrete showed higher first-crack as well as ultimate load capacity than OPC beam of

same span. The differences in ultimate capacity between geopolymer and OPC

concrete beams increased with the degree of under-reinforcement (decrease in density

of tensile reinforcement) which were 4.6%, 6.0% and 6.5% for the spans 2.8 m, 5 m

and 10 m respectively. The difference in first-crack load capacity, however, remained

almost constant (around 28% higher in geopolymer concrete beam) for all cases

because it was directly dependent on second moment of beam section and the flexural

strength of the concrete. Load-deflection curves show that a geopolymer concrete beam

0

50

100

150

200

0 10 20 30 40 50 60 70

Imp

osed

loa

d (

kN

)


Geopolymer 3m RC beam-Fine

Geopolymer 3m RC beam-Medium

Geopolymer 3m RC beam-Coarse


137

can sustain slightly more ultimate vertical deflection (hence, higher plastic deformation

and ductility) than OPC concrete of same span at failure. This could be due to the

difference in stress-strain behaviours of geopolymer and OPC concrete. As shown in

Figure 5.1, geopolymer concrete can undergo higher deformation (strain) than OPC

concrete before failure under both, compressive and tensile stress. Before yielding, the

geopolymer concrete beam showed slightly higher bending stiffness than OPC concrete

beam, as a result it experienced slightly less deflection for the same value of imposed

load. Tensile damages (cracks) in 2.8 m long RC beam in Figure 5.14 suggest its

flexural mode of failure under imposed load.

Figure 5.13: Load-deflection responses of modelled RC beams

Figure 5.14: Flexural damage in 2.8 m long geopolymer RC beam

0

200

400

600

800

0 40 80 120 160 200 240 280 320

Imp

osed

loa

d (

kN

)


Geopolymer 3m small RC beam

OPC 3m small RC beam

Geopolymer 5m RC beam

OPC 5m RC beam

Geopolymer 10 m RC beam

OPC 10m RC beam


138

5.3.5 Effect of tensile strength in flexural capacity of reinforced concrete beam

a) First-crack load When tensile stress in the extreme tensile fibre of concrete beam exceeds the flexural

strength of concrete, concrete starts to crack. Moment due to imposed load which

initiates the first crack in concrete section is called cracking moment (��) and

corresponding load called first-crack load or cracking load. In flexural concrete

members, such as beam the cracking moment can be directly calculated as following:

�� = ��. ��/��.�� (5.13)

where, �� is the second moment of area of uncracked concrete section and ��.�� is the

vertical distance of extreme tensile fibre from neutral axis (N-A) at cracking moment

as shown in Figure 5.15.

Therefore, for a similar cross-section, the geopolymer concrete beam had around 28%

higher first-crack load than OPC concrete beam of same span due to higher flexural

strength. Higher first-crack load can also contribute to increase the ultimate load

capacity of the concrete beam by maintaining an uncracked section for a higher

imposed load. Obviously, an uncracked section can resist a higher imposed load than a

cracked section due to its higher bending stiffness.

b) Ultimate load capacity

After the first-crack load, concrete below the neutral axis (tensile zone) starts to

develop vertical cracks under the increment of imposed load. When the concrete

section below the neutral axis fully cracks, its contribution to the bending stiffness of

the beam ceases. As a result, tensile steel reinforcement starts to yield, hence this stage

is called the yield point. Because of the increase in crack depth due to imposed load,

the neutral axis of concrete section also moves upward to a depth of ��.� (Figure 5.15).

Upon further increase of imposed load, the flexural crack depth of concrete also

increases from ��.� to ��.�. As a result, the neutral axis of beam section shifts further

upward, and a large portion of the concrete section below the neutral axis remains

cracked under tensile stress as shown in Figure 5.15.


139

Figure 5.15: A typical stress profiles on concrete (a) concrete section, (b) cracking

load, (c) yield load and (d) ultimate load

Conventionally, the flexural capacity of the reinforced concrete beam is calculated by

considering the contributions of compressive concrete block and steel reinforcement.

The ultimate moment capacity (��) of the reinforced concrete section can be

calculated as follows:

�� = �(� −�.��.�

�) + ɛ��. ��. ��(� − ��) (5.14)

where, � is the compressive stress block factor which can be calculated using AS-3600

(2018) or other concrete standards; � is the effective depth of concrete cross-section;

��.� is the depth of neutral axis at ultimate load which can be estimated by equating

the total compressive force and tensile force applying in the concrete section; �� is the

area of compressive steel reinforcement; ɛ�� strain in the compressive reinforcement

bar (maximum value 0.0025) and � is the compressive force acting on concrete section

which can be estimated as follows:

� = 0.85��

�. �. ��.�. � (5.15)

Then, the ultimate load capacity (��) of flexural members can be calculated using

conventional flexural equations. Equation (5.14) shows that the contribution of


140

concrete below the neutral axis has not been considered in calculating the ultimate

moment capacity of reinforced concrete member using conventional design practice.

While concrete section below the neural axis undergoes cracking, it needs a lot of

fracture energy to form the flexural cracks which is equivalent to the work done by the

imposed load. Fracture energy is defined as the energy required per unit new-formed

area of crack surface in concrete section, which depends on the properties of materials

not the on size of structure. Cracking behaviour of concrete is governed by tensile

strength of concrete (Marzouk and Chen, 1995). A study of Hillerborg et al. (1976) and

Marzouk and Chen (1995), suggested that the fracture energy absorbed per unit crack

area (��) can be calculated by integrating the complete stress-displacement curve as

following:

��= ∫ ��.

��

�� = ��

�. ��/2 (5.16)

where, �� is the maximum tensile displacement (cracking) when flexural stress ��

reaches zero.

Then, the net fracture energy required (��) per unit crack for this stage can be calculted

as:

�� = ��. � · ��.� (5.17)

where, ��.� is flexural crack depth or vertical distance between neutral axis and

bottommost tensile fibre of concrete section at ultimate load.

The fracture energy required to form the cracks should be equivalent to the work done

by an additional imposed load (��.��) in the concrete tensile zone. The actual ultimate

load capacity of the section should be the summation of ��.�� and ��. Equation (5.17)

shows that amount of fracture energy required per unit crack is directly proportional to

the depth of ��.� which is governed by the degree of reinforcement of the beam section.

Obviously, an under-reinforced section has a larger value of ��.� than a balanced or

over reinforced section because it needs only a small depth of concrete compressive

block to counterbalance the stress on tensile reinforcement. Nowadays, most of the


141

reinforced concrete structures are designed as under-reinforced sections because under-

reinforcement allows a significant yielding of tensile reinforcement before failure,

hence a ductile failure of structure will occur (Warner et al., 1998). Considering the

contribution of concrete below the neutral axis, an under-reinforced section can

withstand a higher imposed load than calculated from the conventional method.

However, it is difficult to calculate the amount of ��.�� because of the difficulties to

predict the exact number of cracks in the tensile zone along the longitudinal axis of

concrete beam.

Some previous studies of under-reinforced concrete beam showed that there were

noticeable differences in the ultimate load capacity between analytically calculated and

experimentally measured imposed load values. A set of reinforced concrete beams

(control OPC beams) with different reinforcement ratios tested by Esfahani et al.

(2007) found that an under-reinforced concrete beam (B1-12) can withstand around 8%

higher imposed load than analytically calculated imposed load. Whereas, other

reinforced beams having nearly-balanced and over-reinforced sections withstood equal

or lower imposed load than corresponding calculated loads. A study of flexural capacity

of reinforced concrete beams from OPC concrete of different grades by Pam et al.

(2001) also reported that the experimental ultimate moment was around 15% higher

than the corresponding theoretical ultimate moment. In case of grade 37 MPa concrete,

there was an obvious trend that the difference between experimental and theoretical

values increased with the degree of under-reinforcement. A study on under-reinforced

geopolymer concrete beams by Nguyen et al. (2016) showed that the experimental

ultimate load capacity of geopolymer concrete beams was around 12% higher than

analytically calculated values which were very close with the results from finite

element analysis using Abaqus program. In this current study also, the difference

between ultimate load capacity obtained from analytical calculation and finite element

analysis increases with the degree of under-reinforcement of concrete (both,

geopolymer and OPC) beams. For geopolymer concrete beams, the differences are 9%,

12 % and 13% for 2.8 m, 5 m and 10 m span beams, respectively. Another study by

Kumaravel and Thirugnanasambandam (2013) showed that fly ash-based reinforced

geopolymer concrete beam (3000 mm span) can bear around 8% higher first-crack and

6% higher ultimate load than OPC concrete beam of an identical section with slightly


142

higher ultimate deflection. The experiential load-deflection responses of both,

geopolymer and OPC concrete beams complied with the prediction of finite element

analysis.

As geopolymer concrete has higher flexural strength, it requires relatively higher

fracture energy than OPC concrete for the same area of crack to be formed. As an

indirect measurement of fracture energy, it can be seen that the area under the stress-

strain curve in Figure 5.1 for geopolymer concrete is bigger than that of OPC concrete.

Therefore, the additional load (P�.��) of geopolymer concrete beam should be higher

compared to OPC concrete for a similar cross-section and same concrete grade. Thus,

fracture energy may be a hidden factor to differentiate between the ultimate load

capacities of geopolymer and OPC reinforced concrete beams which increases with the

increase in degree of under-reinforcement of concrete beams.

c) Tension stiffening

After the initiation of the first-crack, reinforced concrete section suffers rapid

development of cracks under increment of imposed load. In this stage, concrete

continues to carry tensile stress between the cracks due to the transfer of forces from

the tensile reinforcement to the concrete through a bond called tension stiffening which

is a function of concrete tensile strength. The tension stiffening is a mechanism in

reinforced concrete member, by which concrete provides a bond with steel

reinforcement and keeps carrying tensile stress even after starting of crack under

imposed load (Gilbert, 2007). This mechanism prevents the concrete beam from a

sudden loss of bending stiffness due to the tensile stress carried by the concrete between

cracks (Bischoff, 2007). A tension stiffening model for concrete purposed by Al-

Manaseer and Phillips (1987) is presented earlier in Chapter 2 (Figure 2.21). The

tension stiffening effect is applicable between the first-crack load (uncracked section)

and the yield load (fully-cracked section) of the beam. ACI-318 (2011) suggests an

equation to estimate the effective moment of inertia of concrete section (��) after

starting of cracking; between first-crack load and yield load as follows:

�� = ��

��

�� + �1 − �

��

��

�

� �� ≤ �� (5.18)


143

where, �� is the second moment of area of fully cracked section and �� is bending

moment due to imposed load at that point.

Equation (5.18) suggests that the effective moment of inertia of reinforced concrete

beam at any point is dependent on the cracking moment of the beam section. Whereas,

cracking moment itself is the function of flexural strength of concrete. Obviously, a

beam section with higher moment of inertia has higher bending stiffness. This implies,

reinforced concrete beam with geopolymer concrete can maintain relatively lower

vertical deflection than OPC concrete beam after the first-crack load because of having

higher bending stiffness. However, this phenomenon does not explain about the effects

of tensile strength of concrete on the ultimate load capacity of reinforced concrete

beam.

d) Analogous of fibre reinforced concrete beam

The effect of higher tensile strength of concrete into load-deflection behaviour of

flexural concrete member is similar to the effect of fibre reinforcing in concrete.

Several studies showed that addition of macro-synthetic or steel fibres in concrete

significantly increases the toughness (area under stress-strain curve) of concrete as well

as tensile and flexural strength of concrete with very small effects in compressive

strength (Teng et al., 2018, Pająk and Ponikiewski, 2013). The improved flexural

properties of concrete can significantly increase flexural load capacity (yield load and

ultimate load) as well as ultimate deflection (ductility) of the reinforced concrete beam

because of absorption of higher fracture energy by concrete before failure (Altun et al.,

2007, Campione and Mangiavillano, 2008). The stress-strain curves in Figure 5.1 show

that geopolymer concrete also has higher flexural strength as well as higher flexural

toughness than OPC concrete, which is analogous to the effect of fibre reinforced

concrete in flexural load capacity of the beam. Therefore, a geopolymer concrete beam

can resist higher flexural load before failure as well as higher ultimate vertical

deformation than OPC concrete beam of same span.


144

5.4 Finite element modelling of prestresses concrete beams

The load-deflection behaviours of prestressed concrete beams of different spans and

cross-sections were investigated using finite element analysis in Abaqus program.

Prestressed concrete beams from OPC (control) concrete of same grade were also

modelled and analysed in order to compare the results with geopolymer concrete

beams.

5.4.1 Validation of steel-concrete interaction in prestressed concrete beam

In order to validate the applicability of concrete damaged plasticity model and cohesive

interaction between prestressing steel and concrete, a 4500 mm long post-tensioned

beam tested by Moawad et al. (2018) was simulated using Abaqus program with

identical geometry and loading arrangement. Concrete beam, endplate and support

plates were modelled using three-dimensional solid brick elements (C3D8R). The

prestressing tendon was also modelled using three-dimensional solid brick element.

The conventional steel bars were modelled using three-dimensional beam elements

(B31) with a perfect bond with the surrounding concrete. The strength properties of

steel and concrete were taken as specified in the paper. This beam was made from grade

40 MPa OPC concrete. The stress-strain behaviours of concrete under compression and

tension (flexural) were modelled using Hognestad (1951) and Carreira and Chu (1986)

models, respectively. In case of reinforcing steel, the trilinear model was adopted in

order to comply with the strain hardening behaviour of steel.

A prestressing steel cable (tendon) is a flexible element made from several wires

helically laid together having very small bending stiffness (HSI, 2013). In order to

apply cohesive surface interaction between prestressing steel tendon and concrete, the

steel tendon should be modelled using solid elements. As defined in the material library

of Abaqus (Abaqus-Inc., 2014), a solid element possesses a defined surface for

applying interaction properties but it also has bending stiffness which is an undesirable

property for a prestressing tendon. And therefore, the circular section of prestressing

tendon was replaced by a thin rectangular section with an equivalent area but having a

small second moment of inertia to decrease the bending stiffness of the section. Two

more identical models of the prestressed concrete beams were also prepared using


145

circular (original) solid section with cohesive interaction and a truss element (T3D2)

with a perfect bond in order to compare the results. The original and modified

prestressed beam sections are shown in Figure 5.16. In order to comply with the

experimental result (zero deflection at beginning of imposed load), the finite element

analysis was carried out in two steps only; initial step and step 1 (imposed load).

(a) (b)

Figure 5.16: Prestressed beam sections (a) original (b) adopted in FE model

(dimensions are in mm)

Load-deflection responses of simulated prestressed concrete beam with different

modelling approaches are shown in Figure 5.17. Results show that the finite element

simulation using a concrete damaged plasticity model can closely predict the load-

deflection behaviour of prestressed concrete beam. Among all, finite element model

using thin rectangular solid section of steel tendon and cohesive surface interaction

predicted the closest load-deflection behaviour of prestressed concrete beam with

experimental results. Finite element model using solid circular section predicts slightly

higher value of imposed load for a similar vertical deflection due to additional stiffness

provided by solid section of prestressing tendon. Whereas, using a truss element for

prestressing tendon and applying of perfect bond with surrounding concrete showed

relatively larger displacement and bigger load than using solid section because of the

rigid bond of steel tendon and surrounding concrete until failure point.


146

Figure 5.17: Load-deflection responses of modelled prestressed concrete beam

In addition, two more partially prestressed concrete beams tested by Abdelrahman et

al. (2011) were also simulated to validate the applicability of concrete damage plasticity

model and interaction of prestressing steel-concrete interface in partially prestressed

condition. Both beams had effective spans of 4000 mm and shear spans of 1000 mm.

The details of test beams are shown in Table 5.8.

Table 5.8: Details of simulated partially prestressed concrete beams

Beam ID Beam size

(mm2)

fcm (MPa) Strand

diameter

(mm)

Ast Eq. area of

strand

(mm2)

B.40-P-25-NE 340 × 160 39 12.7 2×Φ10 mm 5×19.72

B.80.P-25-NE 340 × 160 89 12.7 2×Φ10 mm 5×19.72

Modelling of parts (beam, support plate, conventional reinforcements and end plates)

were done using same elements used in validation of prestressed beam tested by

Moawad et al. (2018). Considering the results of finite element analysis of prestressed

beam tested by Moawad et al. (2018), prestressing steel tendon was transferred in thin

rectangular steel section of equivalent area and modelled using solid elements. The

prestressing steel-concrete interface was modelled using a cohesive surface interaction.

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

Imp

osed

loa

d (

kN

)


Experimental result (Beam 3)

FE- Rectangular solid tendon

FE-Truss element tendon

FE- Circular solid tendon


147

The load-deflection responses achieved from finite element simulations of these

prestressed beams are shown in Figure 5.18. Data points in this figure show that

application of concrete damaged plasticity model and cohesive surface interaction can

closely predict the load-deflection behaviour of prestressed concrete beams of having

any both, normal strength and high strength grade concrete. Unlike to sudden increase

in imposed load value in some experimental results, finite element analysis gives a

smooth load-deflection curve (Figure 5.18 b).

(a)

(b)

Figure 5.18: Load-deflection responses of prestressed beams (a) B.40-P-25-NE, and

(b) B.80-P-25-NE

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100 110

Loa

d (

KN

)


Abdelrahman et al. (2011): B.40-P-25-NE beam-Experimental

Abdelrahman et al. (2011): B.40-P-25-NE beam-FE simulation

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100

Loa

d (

KN

)


Adbelrahman et al. (2011)-B.80-P-25-NE beam-Experimental

Adbelrahman et al. (2011)-B.80-P-25-NE beam-FE Simulation


148

5.4.2 Modelling of test beams

To investigate the effect of geopolymer concrete on prestressed concrete beams, 5 m,

10 m, and 15 m long beams were modelled and analysed. Test specimens used for finite

element analyses were simply supported post-tensioned concrete beams with

application of prestress after 28 days. Prestressed concrete beams are generally

designed to bear load in longer spans because they may not be feasible for a shorter

span due to the complicity associated with their design and construction process when

compared to conventional reinforced concrete beams. In this study, all modelled

prestressed concrete beams were relatively longer in span and their span to depth ratios

(L/D) were higher than 10, such that they will experience a flexural mode of failure.

All beams were subjected to 4 points loading with 100 mm support distance from the

ends. The shear reinforcement contained 10 mm vertical stirrups for all beams. The

centre-to-centre spacing of vertical stirrups was 225 mm in the middle and 175 mm in

either shear lengths for 5 m beam and 240 mm in the middle and 200 mm in either

shear lengths for 10 m and 15 m beams. All top reinforcement and side-reinforcement

bars were 12 mm size. For each span, two identical beams were modelled from

geopolymer and OPC concrete. The circular cross-sections of prestressing tendons

were replaced by a thin rectangular steel section of equivalent areas in order to reduce

the bending stiffness as described earlier. The test set up of a 5 m long modelled

prestressed beam is shown in Figure 5.19. The cross-sections and reinforcement details

of modelled geopolymer prestressed beams of different spans are presented in Figure

5.20. This figure shows that concrete cross-sections and the amount of steel

reinforcements were in increasing order with the span of beams. The reinforcement

arrangements of 5 m and 10 m prestressed concrete beams are shown in Figure 5.21

and Figure 5.22, respectively


149

Figure 5.19: Elevation of 5000 mm modelled prestressed concrete beam (dimensions

are in mm)

(a) (b) (c)

Figure 5.20: Cross-sections of modelled prestressed beams (a) 5 m (b) 10 m (c) 15 m

(dimensions are in mm)

Figure 5.21: Reinforcement arrangement in 5 m prestressed concrete beam

Figure 5.22: Reinforcement arrangement in 10 m prestressed concrete beam


150

The concrete beams, end plates, prestressing tendons and support plates were modelled

using solid C3D8R element as described in Section 5.1. The conventional steel bars

and stirrups were modelled using beam B31 elements with a perfect bond with the

surrounding concrete. The interaction between prestressing steel tendon and concrete

was modelled using cohesive surface interaction parameters as shown in Table 5.4.

The stress-strain behaviours of concrete under compression and tension were modelled

using Hognestad (1951) and Carreira and Chu (1986) models, respectively. An

idealised elastic and perfect plastic model was adopted for stress-strain behaviours of

both, normal and prestressing steels. Elements and parts of all test beams were

modelled using an average of 25 mm of mesh size. The modelled 5 m long prestressed

beam and rectangular prestressing tendon with meshing elements are shown in and

Figure 5.23 and Figure 5.24, respectively.

Figure 5.23: Modelled 5 m prestressed concrete beam with 25 mm mesh size

Figure 5.24: Modelled rectangular prestressing tendon with mesh elements

5.4.3 Application of initial prestressing stress

The maximum allowable effective prestressing force (��) for each beam was

calculated using Equation (2.23) according to the recommendation of ACI-318 (2011).

Using the experimental results of concrete strengths of this study, the calculated

permissible tensile stress in extreme fibre would be around 0.33√�� (equals to 0.4��)

for geopolymer concrete. Whereas, this value would be around 0.26√�� (equals to

0.4��) in OPC concrete.


151

Having a straight tendon profile, prestress loss due to friction would be small and

therefore it can be ignored. Prestress loss due to anchorage slip was also negligible and

was not included in the analyses. Whereas, loss of prestressing stress due to the elastic

shortening of concrete beam during prestress transfer was taken into account and

calculated using Equation 2.14. The geometries of the test beams, arrangement of

conventional and prestressing reinforcements and applied effective prestressing loads

are shown in Table 5.9. The difference of prestressing loads between geopolymer and

OPC concrete beams varied according to the length to depth (L/D) ratios of beams,

which were 19.6%, 13.5% and 10% for 5 m, 10 m and 15 m beams, respectively. In

this study, prestressing tendons in both, geopolymer and OPC concrete beams were

subjected to the same level of prestressing stress, such that they would experience same

level of strain before application of imposed load. An initial strain could make

difference in their further deformation available before yielding under imposed load.

Table 5.9: Geometries, reinforcement details and applied prestress of test beams Effective

span

(mm)

Shear

span

(mm)

Concrete

type

Cross-

section

(mm2)

Tensile steel

reinforcement

Area of

prestressing

tendons (mm2)

Effective prestress

Stress

(MPa)

Load (kN)

5,000 1750 Geopolymer 300 × 400 3×ϕ 16 mm 6 × 147.1 1234.5 1089.58

OPC 300 × 400 3×ϕ 16 mm 6 × 123 1234.5 911.08

10,000 3800 Geopolymer 350 × 700 4×ϕ 24 mm 8 × 131.1 1236.6 1296.96

OPC 350 × 700 4×ϕ 24 mm 8 × 115 1236.4 1142.43

15,000 5200 Geopolymer 400 × 900 4×ϕ 28 mm 10 ×189.6 1233.5 2,338.62

OPC 400 × 900 4×ϕ 28 mm 10 ×172.5 1233.8 2,128.39

5.4.4 Application of load

The modelled beams were tested under a uniformly increasing static loading

(displacement control) until failure. Generally, a finite element analysis is carried out

in two different steps; initial step and analysis step (loading step). Depending upon the

nature of loading, the analysis step can have one or more steps. Each analysis step is

associated with a specific procedure that defines the types of loading and analysis; such

as linearly increasing load or instantaneous load, linear or non-linear analysis and a


152

maximum number of iterations. Finite element analysis of general structures, such as

reinforced concrete beams, steel beams and box culverts can be carried out in two steps;

initial step and step 1 (analysis step). However, finite element analysis of prestressed

concrete structure needs to be carried out in three different steps because the application

of loads in prestressed concrete beam occurs in two different stages; prestress transfer

and imposed loads. The steps adopted in finite element analysis of prestressed concrete

beams in this study are following:

Initial step: It is the pre-loading stage in Abaqus/standard. In this step, steel-

concrete interactions and boundary conditions, such as support conditions are

defined.

Step 1 (prestress transfer) is the first analysis step in which self-loads and

prestressing stress are applied in the system. Axial shortening and upward

deflection of prestressed concrete beam happen in this step as a result of prestress

transfer.

All the applicable imposed loads act in step 2 (imposed load). Vertical deflection

of concrete beam in the direction of imposed load (downward) and failure of

beam happen in this step. Results from the previous step (step 1) are taken as

initial conditions in this step. And therefore, the measurement of vertical

deflection is taken from the mid-span of deformed (hogging shape) beam. All the

results (field output variables) can be obtained from this step.

5.5 Conclusions

Finite element modelling and analysis of reinforced and prestressed concrete beams of

different spans and cross-sections were carried out in this study using concrete

damaged plasticity model. The interaction between prestressing steel tendon and

surrounding concrete (in post-tensioned concrete) was studied using modelling of a

simple pull-out test. Following conclusion can be made based on the finite element

modelling.


153

Stress-strain behaviour of both, geopolymer and OPC concrete can be modelled

using mathematical equations suggested in the literature, however, a slightly

higher deformation was considered in geopolymer concrete compared to OPC

concrete of same strength grade.

The interactions of prestressing tendon and concrete can be modelled using

traction-separation law. A cohesive stiffness value (��or ��) of 25 N/mm3

showed a good correlation with the bond strength (��) of this interface (around

10 MPa).

Reinforced concrete beam from geopolymer concrete can bear 28% higher first-

crack load and around 6% higher ultimate load geopolymer concrete.

Higher fracture energy of geopolymer concrete is one of major reasons for higher

flexural load capacity of geopolymer concrete beam.

The allowable prestressing load in geopolymer prestressed concrete beams was

around 15% higher compared to OPC prestressed concrete beam of same span and

cross-section due to the higher flexural strength of geopolymer concrete. The

calculated permissible tensile stress in extreme fibre in a geopolymer prestressed

concrete beam would be around 0.33√�� (equals to 0.4��) for geopolymer

concrete. Whereas, this value would be around 0.26√�� for OPC concrete, close

to the ACI-318 (2011) recommendation (0.25√��).

Chapter 6: Results of finite element analysis

154

CHAPTER: 6

6. Results of Finite Element Analysis

6.1 Preamble

This chapter discusses the load-deflection behaviours of prestressed concrete beams

from geopolymer and OPC concrete of same strength grade using the finite element

models developed in Chapter 5. The effect of tensile strength of concrete in load-

deflection behaviours of prestressed concrete beam is analysed in this chapter on the

basis of finite element analysis results. The load-deflection behaviours of geopolymer

prestressed concrete beams have been discussed in two stages; (a) short-term loading,

and (b) long-term behaviour. The short-term loading result was achieved by applying

the imposed load shortly after the post-tensioning or prestress transfer of the beam (at

28 days). However, long-term behaviour refers to the load-deflection response of

prestressed concrete beam when the imposed load is applied a long time after the post-

tensioning process. Time-dependent losses of prestressing stress due to creep and

shrinkage strains in geopolymer and OPC concrete and their effects on long-term (up

to 10 years) load-deflection behaviours of prestressed concrete beams are studied in this

chapter.

6.2 Short-term performance

The load-deflection responses of six different prestressed concrete beams obtained from

finite element analysis are shown in Figure 6.1. Each load-deflection curve in this

figure shows three stages of deformation; linear elastic, inelastic and plastic stages. The

load-deflection response of a flexural concrete member is assumed to be linear elastic

until the first-crack load, then it shows inelastic behaviour due to cracking of concrete

below the neutral axis and it becomes fully plastic after the yield load. Load-deflection

responses in Figure 6.1 demonstrate that geopolymer prestressed concrete beams

exhibited better structural performance, such as higher load carrying capacity and

higher bending stiffness than OPC concrete beams of same spans. Geopolymer

prestressed concrete beams can bear around 20% higher first-crack load and around

14% higher ultimate load than OPC concrete beams of same spans and cross-sections.


155

Both, geopolymer and OPC concrete beams showed similar vertical deflection patterns

until the first-crack load. Then, OPC concrete beams exhibit a rapid increase in vertical

deflection due to higher developing cracks in tensile zone than geopolymer concrete

beams. As a result, OPC concrete beams experienced relatively higher vertical

deflection than geopolymer concrete beams for an equal amount of imposed load and

showed smaller ultimate load capacity. In this study, geopolymer concrete exhibited

around 27% higher flexural strength than OPC concrete of same grade. In addition,

geopolymer prestressed concrete beams were subjected to a higher prestressing load

(around 15%) than OPC concrete beams of same spans. These two factors can influence

the load-carrying capacity of geopolymer concrete beams. Besides, geopolymer

concrete beams showed slightly larger ultimate deflection than OPC concrete beams of

same spans.

Figure 6.1: Load- deflection curves of prestressed concrete beams

0

200

400

600

800

1000

1200

-25 25 75 125 175 225 275 325 375 425 475 525

Imp

osed

loa

d (

kN

)


Geopolymer 15m beam

OPC 15m beam

Geopolymer 10m beam

OPC 10m beam

Geopolymer 5m beam

OPC 5m beam


156

The deformed shapes and flexural stress profiles of 5 m long geopolymer prestressed

concrete beam at different stages are shown in Figure 6.2 to Figure 6.6. Figure 6.2

shows the flexural stress generated in the geopolymer prestressed beam immediately

after the prestress transfer (no imposed condition). The flexural stress value in the

topmost concrete fibre shown in this figure (2.6 MPa) was close to the calculated stress

(2.54 MPa) for this beam. The maximum tensile stress exerted in the prestressing

tendon (1235.9 MPa) is shown in Figure 6.3 which showed a good correlation with the

calculated effective prestress value (1234.5 MPa) (see Table 5.9). Figure 6.4 and

Figure 6.5 show the flexural stress developed along the longitudinal axis of prestressed

concrete beam due to the imposed load in the first-crack load and ultimate failure point,

respectively. In the first-crack load, the tensile stress level in the bottommost fibre has

just reached the maximum flexural stress (flexural strength) of concrete zone which is

represented by the red zone. In the ultimate failure point, the flexural stress in concrete

below the neutral axis already decreased from maximum value because of the concrete

damage due to flexural cracks. The tensile stress exerted in prestressing tendon and its

deformed shape at the ultimate failure point is shown in Figure 6.6. The maximum

stress is represented by red colour located in its mid-span which is just above the yield

strength of prestressing steel.

Figure 6.2: Flexural stress in geopolymer prestressed 5 m beam at prestress-transfer


157

Figure 6.3: Stress on prestressing steel tendon at prestress transfer (no-load

condition)

Figure 6.4: Flexural stress in 5 m prestressed beam at first-crack load

Figure 6.5: Flexural stress in 5 m prestressed beam at failure


158

Figure 6.6: Flexural stress in prestressing tendon of 5 m beam at failure

Finite element analysis can capture the damage of concrete in reinforced or prestressed

concrete members under imposed load. Figure 6.7 shows the initiation of tensile

damage (cracking) in the concrete below the neutral axis of 5 m long prestressed

geopolymer concrete beam after the first-crack load. This tensile damage propagates up

to the neutral axis of concrete section at yielding load when concrete below the neutral

axis cracks completely as shown in Figure 6.8. Similar damages at yielding load of 10

m long geopolymer prestressed beam is shown in Figure 6.9. The damage in

prestressed concrete beam at ultimate failure point is shown in Figure 6.10, that shows

a complete tensile damage in the bottom portion of concrete section and some

compressive damage on the top (under the loading points). The images of finite element

analysis suggest the flexural failure mode of prestressed beams.

Figure 6.7: Damage initiation after first-crack load on 5 m long prestressed beam


159

Figure 6.8: Progress of damage at yielding load on 5 m long prestressed beam

Figure 6.9: Progress of damage at yielding load on 10 m long prestressed beam

Figure 6.10: Damages on concrete at failure point on 5 m long prestressed beam

The tensile stress exerted in the normal steel reinforcements and vertical stirrups in 5

m long prestressed concrete beam at the ultimate failure point is shown in Figure 6.11.

The tensile stress in the label shows that both tensile and compressive reinforcement


160

reached their maximum stress level (yield strength) at the mid-span of beam. The

failure of beam may be associated with the rupture of steel reinforcements. Some other

relevant images of finite element analysis of prestressed beams are presented in

Appendices.

Figure 6.11: Tensile stress in normal reinforcements at ultimate failure

6.2.1 First crack load

The load-deflection behaviour of both, conventional reinforced and prestressed

concrete beam is assumed to be linear-elastic until the first-crack load which is

represented by ending of initial straight portion (line) of the load-deflection curve. In

conventional reinforced concrete beams, it is widely accepted that higher flexural

strength of concrete results in higher the first-crack load. Calculation of first-crack load

in prestressed concrete beam can be done using flexural equation of cracking moment

as following.

��

�= �

��.�

�+

��

�� − ��.�� + �′� (6.1)

In Equation (6.1), flexural strength of concrete (�′�) and initial prestressing load (��)

are the two factors which make the difference between OPC and geopolymer

prestressed beams. In this study, geopolymer prestressed concrete beams were

subjected to higher (around 15%) prestressing load than OPC concrete beams of same


161

spans and geopolymer concrete exhibited around 28% higher flexural strength than

OPC concrete. Therefore, geopolymer prestressed concrete beams should exhibit higher

first-crack load than OPC concrete beams of same span. Prestressed concrete structures

are typically designed to remain uncracked under the service loads (Gilbert et al., 2016),

hence the first-crack load can be considered as the maximum designed imposed load of

prestressed concrete beams. In this study, geopolymer prestressed concrete beams

exhibited 22.5%, 19.6% and 17% higher first-crack loads than OPC concrete for the

spans of 5 m, 10 m and 15 m, respectively.

Unlike conventional reinforced beam, the stress level in the cross-section of prestressed

concrete beam changes significantly from no-load (prestress-transfer) condition to first-

crack load stage. The profiles of flexural stress in the cross-section (at mid-span) of 5

m long geopolymer and OPC prestressed concrete beams are shown in Figure 6.12 for

the prestress-transfer condition and first-crack load. The stress profiles in Figure 6.12

(a) and (b) show that geopolymer concrete beams experienced relatively higher stress

than OPC concrete beam for both, prestress transfer condition and first-crack load.

-

(a) (b)

Figure 6.12: Stress profiles of prestressed concrete beams at (a) prestress transfer and

(b) first-crack load

-400

-300

-200

-100

0

100

-4 0 4 8 12 16 20

Bea

m c

ross

-sec

tion

(m

m)

Flexural stress (MPa)

Geopolmer 5 m beam

OPC 5 m beam

-100

0

100

200

300

400

-8 -4 0 4 8 12 16 20 24

Bea

m c

ross

-sec

tion

(m

m)

Flexural stress (MPa)

Geopolmer 5 m beam

OPC 5 m beam


162

When an external load (can be in the form of prestressing load or imposed load) is

applied into a prestressed concrete beam, it transfers into the strain energy (internal

work done) of the beam which changes the magnitude and direction of flexural stress

in the beam cross-section. The elastic strain energy transferred from an external load

can be expressed as follows:

� = �

��

��

�� (6.2)

where, �� is the modulus of elasticity of concrete and �� is the vertical distance from

neutral axis to the bottommost fibre of beam.

Equation (6.2) shows that strain energy in the prestressed beam is directly proportional

to the square of maximum flexural stress in the concrete cross-section. This indicates a

small increment in stress can make a significant difference in the elastic energy

absorbed. Therefore, higher flexural stress in geopolymer concrete beam results in a

higher first-crack load of the prestressed beam.

6.2.2 Ultimate load

Similar to conventional RC beam, geopolymer prestressed concrete beams showed

higher ultimate load capacities than OPC concrete beams of same span. Both,

conventional RC beams and prestressed concrete beams simulated in this study were

under-reinforced flexural members with long spans (�/� > 10). Therefore, they can

experience similar failure modes, i.e. flexural cracking of concrete. The effects of

higher flexural strength of concrete into the ultimate load capacity of RC concrete

beams are discussed in the earlier section. A similar effect of higher flexural strength

of concrete into ultimate load capacity of prestressed concrete beams can be assumed.

This higher load-carrying capacity of geopolymer prestressed concrete maybe the

combined effects of higher first-crack load and higher fracture energy absorbed by


A study of prestressed concrete beams using carbon fibre reinforced polymer bar as

prestressing tendon by El-Hacha and Gaafar (2011) also showed that the load-carrying

capacity of a prestressed beam (for all stage; first-crack, yielding and ultimate)


163

increased with the increase of prestressing load in the tendon. A study of externally

prestressed continuous concrete beams by Ghallab (2014) also showed that increasing

the prestressing load resulted in increase of load-carrying capacity of beams but a

decrease in ultimate deformation.

In this study, prestressing tendons in both, geopolymer and OPC concrete beams were

subjected to a same level of prestressing stress. In addition, the stress-strain behaviour

of geopolymer concrete shows that it can resist more deformation than OPC concrete

before failure, in both, compression and tension, hence able to absorb more energy. The

load-deflection diagram of a flexural member represents its ability to absorb external

energy before failure; higher absorbed energy results in higher ultimate deformation.

Therefore, geopolymer prestressed concrete beams in this study showed slightly higher

ultimate plastic deformation at failure compared to OPC concrete of same span due to

the difference in stress-strain behaviour of geopolymer and OPC concrete.

6.2.3 Effects of self-weight

As prestressed concrete beams are generally designed for longer span, they are

associated with large self-weight which can reduce their load-carrying capacity

significantly. The imposed load values of load-deflection responses shown in Figure

6.1 are the combination of self-weight and live loads. Considering the live load capacity

only, the difference in first-crack load capacity between geopolymer and OPC beams

would be 24.5%, 26% and 25.5% for the spans of 5 m, 10 m and 15 m, respectively.

Similarly, the difference in ultimate load capacity between geopolymer and OPC beams

would be 18.2%, 14.5% and 13.5% for the spans of 5 m, 10 m and 15 m, respectively.

6.3 Long term performance

In this study, the long-term behaviour (serviceability) of prestressed concrete beams

were evaluated by their load-deflection responses after one-year from the application

of prestressing load. A gradual loss of prestress in the steel tendon with time is one of

the major serviceability issues of prestressed concrete structures which can decrease

their load-carrying capacity. The major causes of time-dependent losses of prestress are

shrinkage and creep strains in concrete and relaxation of steel tendons which gradually


164

increase with the age of structures. The measured serviceability properties of concrete

discussed in Chapter 4 showed that geopolymer concrete experienced significantly less

drying shrinkage and creep strains than OPC concrete of same grade. The time-

dependent losses of prestress due to shrinkage and creep strains were estimated using

the strain data from experimental results and loss due to relaxation of steel tendon was

estimated according to AS-3600 (2018). The prestressed concrete beams have different

sizes than standard specimens for the measurements of drying shrinkage and creep of

concrete. In addition, they could remain in the ambient conditions after 28 days

(prestress transfer) which could be different than standard laboratory conditions

(temperature and humidity). In this case, the measured creep coefficients and drying

shrinkage strains should be modified by the suitable modification factors "ϒ��" and

"ϒ��", respectively to estimate the shrinkage strains and creep coefficient of prestressed

concrete beams according to the recommendation of ACI-209.2R (2008).

The different types of time-dependent losses of prestress; shrinkage loss, creep loss and

relaxation loss are shown in Figure 6.13. For all the cases, loss of prestress due to creep

strain was significantly higher than other losses; which contributes around 73% of total

losses of prestress. Geopolymer prestressed concrete beams showed relatively small

cumulative (total) prestress losses compared to OPC concrete beams of same spans as

shown in Figure 6.13 because they experienced lower shrinkage and creep strains. In

10 m span, geopolymer and OPC concrete beams lose 9% and 11% of initial prestress,

respectively after one year. For 15 m span, this loss will be 10% and 12.5% for

geopolymer and OPC concrete beams, respectively for the same period. Losses in

prestress are directly proportional to the initial prestressing load, hence 15 m long beam

experiences more reduction in prestress than 10 m long beam from same concrete.


165

-

(a) (b)

-

(c) (d)

Figure 6.13: Losses of prestress in concrete beams (a) geopolymer 10 m, (b) OPC 10 m, (c) geopolymer 15 m and (d) OPC 15 m

0

40

80

120

160

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Pre

stre

ss l

osse

s (M

Pa)

Time (days)

Shrinkage loss Creep loss

Relaxation loss Total lossess

0

40

80

120

160

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Pre

stre

ss l

oss

es (

MP

a)

Time (days)

Shrinkage loss Creep lossRelaxation loss Total lossess

0

40

80

120

160

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Pre

stre

ss l

osse

s (M

Pa)

Time (days)



0

40

80

120

160

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Pre

stre

ss l

osse

s (M

Pa

)

Time (days)




166

Similar to the growth of shrinkage and creep strains in concrete, the time-dependent

losses of prestress also increase rapidly in the early days (first 3 months) then slow down

gradually with time. However, there was a small difference in the trends in geopolymer

and OPC concrete beams in the later age (after 6 months). Geopolymer concrete showed

a relatively small rate of prestress loss in the later age because the growth of shrinkage

and creep strains in geopolymer concrete were relatively smaller compared to OPC

concrete. In average, the total loss of prestress in geopolymer concrete after 6 months

was increased by 0.4% whereas this increment was 0.7% for OPC concrete beams. This

difference could be significant for the longer service of structures (for example after 10

years), because of the difference in the pattern of loss of prestress in the later age.

(a)

(b)

Figure 6.14: Residual prestress in steel tendon (a) 10 m beams (b) 15 m beams

1000

1050

1100

1150

1200

1250

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Res

idu

al p

rest

ress

(M

Pa

)

Time (days)

OPC 10m prestressed beam

Geopolymer 10m prestressed beam

1000

1050

1100

1150

1200

1250

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Res

idu

al

pre

stre

ss (

MP

a)

Time (days)




167

The residual prestressing stress in steel tendons in 10 m and 15 m long prestressed

concrete beams for one-year period are shown in Figure 6.14. After one year, there

would be 91% and 89% of residual prestress in 10 m long geopolymer and OPC concrete

beams, respectively. In case of 15 m span, the residual prestresses were 90% and 87.5%

for geopolymer and OPC concrete beams, respectively for the same period. This residual

prestress has been used to investigate the load-deflection responses of prestressed

concrete beams.

Long-term serviceability of prestressed concrete beams was evaluated on the basis of

reduction in load-carrying capacity after 6 months and one-year durations. Figure 6.15

compares the load-deflection behaviours of 10 m and 15 m prestressed concrete beams

up to one year obtained from finite element analysis. This figure shows that OPC

concrete beams suffered more reduction in load-carrying capacity than geopolymer

concrete beams of same span due to higher loss in prestress. After one-year, the

reductions in the first-crack load capacity of geopolymer concrete beams were 7% and

9% for 10 m and 15 m beams, respectively. Whereas, first-crack load capacity of OPC

concrete beams decreased by 9% and 12% for 10 m and 15 m beams, respectively for

this period. Due to the smaller loss in prestress between 6 months to one-year period in

both geopolymer and OPC concrete beams, only a marginal difference in load-deflection

behaviours can be seen for these periods. The reduction in ultimate load capacity was

smaller than the reduction in first-crack loads for all cases because ultimate load capacity

mainly depends on compressive strength of concrete and amount of steel

reinforcements. In average, there were 3.3% and 4.3% losses in ultimate load capacity

in geopolymer and OPC concrete beams, respectively for one year. As discussed earlier,

a decrease in first-crack load can be regarded as the reduction in load capacity of

prestressed concrete beams because they are designed for crack-free section under

service loads. For both geopolymer and OPC concrete beams, the of load-deflection

response patterns remained similar to the initial one despite the losses in load-carrying

capacities.


168

(a)

(b)

Figure 6.15: Long-term load-deflection responses (a) 10 m beams, and (b) 15 m

beams

0

200

400

600

800

-25 25 75 125 175 225 275 325

Imp

osed

loa

d (

kN

)


Geopolymer 10m beam

OPC 10m beam

Geopolymer 10m beam-6 months

OPC 10m beam-6 months

OPC 10m beam- 1 year

Geopolymer 10m beam-1 year

0

200

400

600

800

1000

1200

-25 25 75 125 175 225 275 325 375 425 475 525

Imp

osed

loa

d (

kN

)


Geopolymer 15m beam

OPC 15m beam

Geopolymer 15m beam-6 months

OPC 15m beam-6 months

Geopolymer 15m beam-1 year

OPC 15m beam-1 year

Geopolymer 15m beam-10 years

OPC 15m-10 years


169

6.4 Serviceability after 10 years

Concrete structures are generally designed for a long service life (more than 50 years).

Drying shrinkage and creep strains are the two major factors that cause negative impacts

on the serviceability of concrete structures. In case of prestressed concrete beams,

reduction in first-crack load carrying capacity is one of the major serviceability issues

because they are designed for crack-free sections. Experimental results showed that

drying shrinkage and creep strains of concrete did not increase significantly after first

six months. It is also difficult to get experimental data of drying shrinkage and creep

strains for a very long time. ACI-209.2R (2008) suggests some equations to predict

long-term shrinkage and creep strains from the available data. For the standard 7 days

moist curing conditions, the ultimate shrinkage value can be estimated by rewriting the

Equation (2.6) as following:

�� = ��

�� . �� (6.3)

Similarly, the ultimate creep coefficient can be estimated by rewriting the Equation

(2.11) as following:

�� = ��.��

�� . �� (6.4)

After calculating the ultimate values, drying shrinkage and creep coefficient values up

to 10 years of period from the prestress transfer can be estimated using Equations (2.6)

and (2.11), respectively. The estimated long-term serviceably properties of concrete;

drying shrinkage and creep coefficient up to 10 years are shown in Figure 6.16. Data

points in Figure 6.16 show that increments in drying shrinkage strain and creep

coefficient were not significant at the later age. The increments in drying shrinkage and

creep coefficient from 1 year to 10 years period were around 12 % and 9%, respectively.

Both, geopolymer and OPC concrete showed similar patterns of growth of drying

shrinkage strain and creep coefficient.


170

(a)

(b)

Figure 6.16: Long-term serviceably (a) drying shrinkage (b) creep coefficient

Using these calculated drying shrinkage and creep coefficient values, the time-

dependent losses on prestress and residual prestress for 15 m long prestressed concrete

beams were estimated for 10 years period. The remaining prestress in 15 m long

prestressed concrete beams for up to 10 years period are shown in Figure 6.17. Since

the long-term losses on prestress are dependent on increases of drying shrinkage and

creep strains, only a small reduction can happen in residual prestress in the later age. As

0

100

200

300

400

500

600

700

0 365 730 1095 1460 1825 2190 2555 2920 3285 3650

Dry

ing

shri

nk

age

(mic

rost

rain

)

Time (days)

OPC concrete

Geopolymer concrete

0

1

2

3

0 365 730 1095 1460 1825 2190 2555 2920 3285 3650

Cre

ep c

oef

fici

ent

Time (days)

OPC concrete

Geopolymer concrete


171

shown in Figure 6.17, the loss of prestress from one year to 10 years of period were

1.3% and 1.6% for geopolymer and OPC prestressed concrete beams, respectively.

Therefore, an experimental study of serviceability properties of concrete (drying

shrinkage and creep strains) up to one year is sufficient to evaluate the long-term

serviceability of a prestressed concrete beam.

Figure 6.17: Residual prestress in 15 m long prestressed beam

The effects of loss of prestress in the load-deflection responses of prestressed concrete

beams after a long time (10 years) for 15 m long beams are shown in Figure 6.15 (b).

This figure shows that there was apparently no significant loss in load-carrying

capacities of prestressed concrete beams after one year. The reduction in load-carrying

capacities obtained from the finite element analysis of 15 m long prestressed concrete

beams with different prestressing stress values are shown in Figure 6.18 for up to 10

years of period. Data points in in Figure 6.18 show that there was only a small decrease

in load-carrying capacities of prestressed concrete beams after one year. From one year

to 10 years period, the reductions in first-crack load capacity were 1.7% and 2.1% for

geopolymer and OPC concrete beams, respectively. Whereas, reductions in ultimate

load capacity were less than one percent for both concrete beams.

1000

1050

1100

1150

1200

1250

0 365 730 1095 1460 1825 2190 2555 2920 3285 3650

Res

idu

al p

rest

ress

(M

Pa)

Time (days)




172

Figure 6.18: Reduction in load capacity of 15 m long prestressed concrete beams

6.5 Research outcomes

This study investigated the effects of higher tensile (or flexural) strength of geopolymer

concrete into flexural (load-deflection) behaviours of prestressed concrete beams using

finite element analysis method.

ACI-318 (2011) limits the allowable prestressing load in a prestressed concrete member

such that, the tensile stress on the extreme tensile fibre should not exceed 0.25√f�� which

is equivalent to 0.4f�� in case of OPC concrete. Since geopolymer concrete has 25% to

40% higher tensile strength than OPC concrete of same strength grade, this allowable

stress in extreme tensile fibre could be higher than 0.25√f��. Therefore, it can be

suggested that the maximum tensile stress on the extreme tensile fibre should be based

on tensile or flexural strength of concrete at that stage i.e. 0.4f��. Taking 25% higher

tensile strength, allowable stress in extreme tensile fibre in geopolymer concrete could

be around 0.32√f��.

The First-crack load of conventional reinforced or prestressed concrete beams can be

estimated from flexural strength of concrete using conventional equations of flexure.

However, the effect of the tensile strength of concrete on ultimate load capacity could

0

4

8

12

16

0 1 2 3 4 5 6 7 8 9 10

Los

s of

loa

d c

ap

acit

y (

%)

Time (years)

OPC 15m beam- first crack load Geopolymer 15m beam- first crack load

OPC 15m beam- ultimate load Geopolymer 15m beam- ultimate load


173

not be calculated using conventional equations. In case of geopolymer concrete, it could

be taken around 10% higher than OPC concrete beams of same grade.

Drying shrinkage and creep strains of geopolymer concrete were found significantly

lower than OPC concrete of same grade as well as calculated values using AS-3600

(2018) at ambient curing. Therefore, a reduction factor (30% -40%) can be applied in

case of geopolymer concrete to estimate drying shrinkage and creep coefficient using

AS-3600 (2018) at ambient temperature curing.

6.6 Conclusions

Load-deflection behaviours of prestressed concrete beams of different spans and cross-

sections made from grade 50 MPa geopolymer concrete were studied using finite

element analysis results for short-term and long-term durations in this chapter. These

results were compared to identical prestressed concrete beams from OPC concrete of

same strength grade. Effect of shrinkage and creep strains of concrete on long-term

serviceability of prestressed concrete beam were also investigated in this chapter. The

serviceability of prestressed concrete beams for up to 10 years was evaluated using

predicted values of drying shrinkage and creep coefficient according to ACI-209.2R

(2008). Following conclusions can be made based on finite element analysis results.

Geopolymer prestressed concrete beam can carry around 20% higher first-crack

load and 13% higher ultimate load than identical OPC concrete beams.

For a similar span and cross-section, a geopolymer reinforced concrete beam can

resist slightly more ultimate plastic deflection before failure compared to OPC

concrete beam because of the difference in their stress-strain behaviours.

Smaller shrinkage and creep strains of geopolymer concrete contribute to

relatively smaller time-dependent losses of prestress in geopolymer prestressed

concrete beams compared to OPC concrete beams of same span. After one-year,

there were around 90% and 87.5% residual prestresses in geopolymer and OPC

concrete beams, respectively in 15 m span beams. Geopolymer and OPC concrete

beams lost 9% and 12% first-crack load capacity in 15 m spans, respectively after

1 year. Reduction in ultimate load capacity due to loss of prestress was smaller


174

than first-crack load which was 3.3% and 4.3% in geopolymer and OPC concrete

beams, respectively for one-year. Therefore, a geopolymer prestressed concrete

beam can maintain better serviceability than prestressed beam from OPC concrete

of same strength grade.

The increments in drying shrinkage and creep coefficient from 1 year to 10 years

period were found to be 12 % and 9% respectively for both, geopolymer and OPC.

For this period, reductions in first-crack load capacity were 1.7% and 2.1% for

geopolymer and OPC concrete beams, respectively. Whereas, reductions in

ultimate load capacity were less than one percent for both concrete beams.

Chapter 7: Environmental sustainability of geopolymer concrete

175

CHAPTER 7

7. Environmental Sustainability of Geopolymer Concrete 7.1 Preamble

The production of Portland cement generates significant amounts of carbon dioxide gas

which poses a big threat to global climate change because of its greenhouse effects. The

recent advent of geopolymer technology shows great potential to reduce carbon

footprints by utilising industrial by-products, such as fly ash and GGBS and convert

them into effective binding material. One of the reasons for the growing worldwide

interest in geopolymer binder is its environmental sustainability over Portland cement.

Environmental sustainability of any materials is generally evaluated based on its carbon

footprints (amount of CO2 gas produced during the production of a unit mass of the

material) and embodied energy (amount of energy required to produced unit mass of

the material). This chapter compares the carbon footprints and embodied energy of

geopolymer and OPC concrete produced in this study. Besides, the environmental

sustainability of geopolymer concrete produced in some previous studies is also

compared with the geopolymer concrete produced in the current study.

7.2 Carbon footprint of Portland cement

Production of Portland cement is a highly carbon-intensive process, which generates

significant amounts of greenhouse gases by consuming a huge amount of fossil fuels

during the manufacturing process. Nowadays, dry process is more popular than wet

process to produce Portland cement because it requires relatively less fuel than the wet

process (PCA, 2019). However, both manufacturing processes include grinding of raw

materials and heating up them at very high temperature (above 1450 °C) inside the

rotating kiln which requires a huge amount of energy. Besides, thermal decomposition

of limestone directly emits CO2 into the atmosphere during the manufacturing of

cement, which is around 0.5 kg of CO2 per kg of cement clinker produced (Hendriks et

al., 1998). Some other toxic and greenhouse gases, such as nitrogen dioxide (NO2)

and sulphur dioxide (SO2) are also released to the atmosphere in a small amount during

this production process. Depending upon the process, 1 kg of Portland cement generates

0.8 to 0.9 kg of CO2 during its production (Huntzinger and Eatmon, 2009). Overall,

cement industries are responsible for around 7 % of global CO2 emissions (Meyer,


176

2009, Turner and Collins, 2013). Due to the growing demand of concrete for

infrastructures and housings, production of Portland cement is increasing day by day.

The worldwide cement production for the year of 2018 was around 4,100 million metric

tonnes (ICR, 2019). The substantial amount of CO2 generated from the production of

OPC creates a potential threat to the global climate because of its greenhouse effects.

Geopolymer binder, on the other hand, utilises industrial by-products, such as fly ash

and GGBS, while only the production of alkali activators generates a small amount of

greenhouse gases. In Australia alone, 12.2 million metric tonnes of coal combustion

products were generated for the year 2016 with only 43.5% were utilised (Harris et al.,

2019). Coal combustion products primarily contain fly ash (Over 70%). More than 50%

of them are dumped in stockpiles every year. Those stockpiles can be the source of

several toxic materials and heavy metals which can contaminate groundwater of

surrounding environment (Gottlieb et al., 2010). Thus, geopolymer technology can

offer a sustainable solution by utilisation of industrial wastes and reducing the emission

of greenhouse gases.

7.3 Carbon footprint of concrete production

Concrete is a composite material, mainly contains binding materials (cement),

aggregates, sands, and water. Production of concrete structures includes different

stages, from the collection of raw materials to curing of end products. Every step of

concrete production is energy consuming and responsible for CO2 emission as well.

Figure 7.1 shows the life cycle stages for the production of a concrete structure. Not

all the stages are equally responsible for generating carbon footprints. For example,

mixing and batching works of concrete consumes significantly less energy than the

production of binding materials.


177

Figure 7.1: Life cycle stages of concrete production

Figure 7.2 shows the carbon footprint of a typical precast reinforced concrete element.

A structural grade concrete generally contains 15% -25% of Portland cement by mass;

however, Portland cement dominates other ingredients in the total carbon footprint of

the end product. In conventional concrete, Portland cement is the major ingredient to

contribute for carbon footprint due to its carbon-intensive manufacturing process which

is responsible for 74% to 81% of total CO2 emissions of concrete (Flower and Sanjayan,

2007). Partial replacement of Portland cement by SCMs, such as fly ash and GGBS can

reduce the carbon footprints to some extent, however, OPC concrete still remains

responsible for a significant amount of CO2 emissions as shown in Figure 7.2.

Collection of

raw materials

Processing or manufacturing

of materials

Transportation

of materials

Mixing and batching

of concrete

Transportation of

concrete to site

Placement and

compaction work

Curing of concrete

structure


178

Figure 7.2: Embodied carbon in a precast reinforced concrete member (Circular-

Ecology, 2020)

7.4 Carbon footprint and embodied energy of concrete ingredients

In order to estimate the carbon emission of geopolymer binder and Portland cement,

carbon footprint and embodied energy data of individual ingredients were taken from

various published papers. Different values for the carbon footprint of ingredients

materials of geopolymer binder are suggested in the literature. For example, the CO2

emission for the production of one kg of sodium silicate liquid (excluding

transportation) is suggested as 1.222 kg and 0.445 kg by Turner and Collins (2013) and

Heath et al. (2014), respectively. Davidovits (2015) warned that some of the literature

have unrealistically reported higher values of carbon emission for the production of

alkali activators.


179

The average carbon footprint and embodied energy of individual materials and

production process of concrete are presented in Table 7.1. This table shows that

Portland cement, chemical admixtures (superplasticizers) and alkali activators emit a

higher amount of CO2 gas per unit mass of production. However, chemical admixtures

are used in very small amounts in a concrete mix compared to other ingredients, such

as binder and aggregates, hence their contributions are not significant.

Table 7.1: Carbon footprint of concrete ingredients and production process

Ingredients Embodied energy

(MJ/kg)

Carbon emission

(tonne CO2-e/tonne) References

Portland cement 5.6 0.860 (Hendriks et al., 1998, MPA,

2018)

GGBS 0.33 0.143 (ASA, 2012)

Fly ash 0.1 0.027 (Flower and Sanjayan, 2007)

Sodium hydroxide

(solid)

10.8 0.625 (Thannimalay et al., 2013,

NEDO, 2011)

Sodium silicate solution 5.37 0.445 (Heath et al., 2014, Fawer et al.,

1999)

Sodium silicate dry

powder (80% solid)

17.9 0.892 (Fawer et al., 1999)

Sodium carbonate 1.35 0.250 (TFEIP, 2009)

Coarse aggregate 0.22 0.036 (ASA, 2012)

Fine aggregate 0.02 0.014 (ASA, 2012)

Tap water 0.00091 (Botto, 2009)

Superplasticizer (HWR) 11.4 0.720 (Flower and Sanjayan, 2007,

Sonebi et al., 2016) Water reducer (WR) 5.3 0.35

Concrete batching 0.003* (ASA, 2012)

Concrete transport 0.009* (ASA, 2012)

Concrete placement 0.009* (ASA, 2012)

Heat curing @60 °C for

24 hours

146* 39.97* (Turner and Collins, 2013,

Salas et al., 2018)

* Embodied energy or carbon emission per m3 of concrete

Table 7.1 shows that there is a big difference in sustainability between sodium

hydroxide and sodium carbonate in terms of both, carbon footprint and their embodied

energy. Nowadays, the Solvay process or ammonia-soda process is the major industrial

process adopted for the production of sodium carbonate. This process is carbon-

efficient because it can recapture CO2 gas from the industrial exhaust or flue gases and

utilises it into the production process (Mohammad et al., 2016). Therefore, the


180

replacement of sodium hydroxide by sodium carbonate in the geopolymer binder

further reduces its carbon footprint.

The proportions (by mass) of ingredients; fly ash, GGBS, sodium carbonate and sodium

silicate powder in one-part geopolymer binder used in this study were 50%, 32%, 9%

and 9%, respectively. Using the information of Table 7.1, the carbon footprint and

embodied energy of individual ingredients of geopolymer binder were estimated by

multiplying their proportions with carbon footprint and embodied energy of the unit

mass. The calculated carbon footprint and embodied energy of geopolymer binder (sum

of individual ingredients) and Portland cement of unit mass are compared in Figure

7.3. This figure shows that the production of geopolymer binder is more carbon efficient

than production of Portland cement. For the same mass of production, geopolymer

binder emits 5 times less CO2 than Portland cement and consumes 3 times less energy.

Figure 7.3: Carbon footprint of geopolymer and Portland cement used in this study

The contributions of individual ingredients of geopolymer binder for carbon emission

are shown in Figure 7.4. This figure shows that alkali activators are the major sources

of carbon emission in geopolymer binder which contribute around two-thirds of the

total volume of carbon emission. Sodium silicate is the prominent one, which is

responsible for 50% of the total carbon emission of the binder. Despite having the

0

1

2

3

4

5

6

Carbon emission (kg CO2 -e/kg) Embodied energy (MJ/kg)

Geopolymer binder OPC


181

highest amount (50% by weight) in the binder, fly ash contributes only around 8% of

total CO2 emission.

Figure 7.4: Contributions of ingredients to carbon footprints of geopolymer binder

7.5 Carbonation and CO2 uptake by OPC concrete

Carbonation of concrete is a process by which CO2 from the air penetrates into the

concrete through pores and reacts with calcium hydroxide to form calcium carbonates

(CaCO3). Carbonation is an undesirable process in OPC concrete because it results in

the reduction of concrete alkalinity and deterioration of the corrosion protective layer

of steel reinforcement. The depth of carbonation of concrete largely depends upon the

porosity of the concrete. Generally, higher strength grade concrete has a dense

microstructure and lower porosity, hence it is less susceptible to carbonation than lower

strength grade concrete. The depth of carbonation may be very small compared to the

thickness of the concrete member. Cho et al. (2016) suggested an average 30 mm depth

of carbonation in 30 to 40 years in building structures made from normal strength grade

concrete. Whereas, Malhotra et al. (2000) reported less than 1 mm of carbonation depth

in high strength grade concrete for 10 years of outdoor exposures. Obviously, the

carbonation of OPC concrete leads to the absorption of some of CO2 from the air,

however, this happens in a very small quantity because of the small depth of

carbonation. Yang et al. (2014) concluded that the CO2 uptake of concrete by

GGBS

Sodium siliacate

Sodiumcarbonate

Fly ash


182

carbonation during the service life of the concrete structures is expected to range

between 5.5% and 6.0% of the emission during the concrete production. Therefore, CO2

uptake by OPC concrete during the carbonation process can not compensate the large

amount of carbon emission during the production process of Porcemt cement. Thus, the

effect of carbonation in OPC concrete is not considered in this study for the evaluation

of the sustainability of concrete.

7.6 Evaluation of environmental sustainability of geopolymer concrete

In order to evaluate the environmental sustainability of geopolymer concrete, a

comparison of carbon footprint and energy consumption by unit volume (m3) of

concrete produced in different studies have been made. This comparison is carried out

for concrete with similar 28 days compressive strengths. The mix compositions of

geopolymer and OPC concrete produced in different studies taken into consideration

are shown in Table 7.2. Two trial mixes for concrete used in this study are also included

in the comparison. This comparison covers a wide range of geopolymer concrete; fly

ash only based (Diaz-Loya et al., 2011, Hardjito and Rangan, 2005), fly ash and GGBS

based (Fang et al., 2018, Deb et al., 2014) and GGBS only based (Farhan et al., 2019).

In addition, different proportions of activating materials and curing methods were used

in these studies. Generally, fly ash only based geopolymer concrete was cured at a

higher temperature because of its slow reaction rate at ambient temperature. Whereas,

geopolymer concrete containing GGBS can be cured at ambient temperature.

According to their 28 days compressive strengths, concrete specimens are divided into

two groups; grade 50 MPa and grade 40 MPa. Obviously, higher grade concrete

contains higher amount of binder, therefore it generates more carbon footprint than

lower grade concrete.


183

Table 7.2: Concrete from different studies considered for evaluation

Concrete ingredients (kg/m3)

28-day strength (MPa)

Source references Portland cement

Fly ash

GGBS Sodium silicate

Sodium hydroxide

Sodium carbonate

Coarse aggregate

Fine aggregate

WR HWR Curing

Gra

de

50

MP

a

61.0 Current study-Geopolymer

0 210 134.4 37.8 0 37.8 1149 718 0 0 ambient

59.0 Current study-OPC 352 88 0 0 0 0 1098 697 1.91 0.9 ambient

57.0 Hardjito and Rangan (2005)- Geopolymer

0 476 0 120.0 12.6 0 1294 554 0 0 24 h @ 60 °C

57.0 Fang et al. (2018)- Geopolymer

0 280 120 107.0 16.6 0 1210 652 0 4 ambient

59.5 Diaz-Loya et al. (2011)- Geopolymer

0 494 0 111.2 44.9 0 858 691 0 15 72 h @ 60 °C

66.1 Farhan et al. (2019)-Geopolymer

0 0 450 106.0 21.4 0 1154 625 12.5 ambient

Gra

de

50

MP

a

47.5 Current study-Geopolymer

0 182.5 116.8 32.9 0 32.9 1171 756 0 0 ambient

48.0 Current study-OPC 308 77 0 0 0 0 1138 701 1.74 0.77 ambient

48.0 Hardjito and Rangan (2005)-Geopolymer

0 476 0 48.0 48.5 0 1294 554 0 0 24 h @ 60 °C

48.0 Fang et al. (2018)-Geopolymer

0 300 100 93.0 14.8 0 1246 671 0 4 ambient

47.0 Deb et al. (2014)-Geopolymer

0 320 80 114.3 18.5 0 1209 651 0 0 ambient

48.0 Deb et al. (2014)-OPC

446 0 0 0.0 0 0 1054 768 0 0 ambient

47.4 Diaz-Loya et al. (2011)-Geopolymer

0 494 0 123.5 49.9 0 858 691 0 15 72 h @ 60 °C


184

As shown in Table 7.1, processing of unit mass of water emits a very small amount of CO2

when compared to other concrete ingredients, such as Portland cement and aggregates,

therefore its contribution is not considered here. Carbon emission due to transportation of

raw materials was also considered as a significant issue in the sustainability of concrete in

some studies (Turner and Collins, 2013). McLellan et al. (2011) suggested that long

transporting distance of alkali activators, such as sodium hydroxide and sodium silicate

may emit a significant amount of CO2 due to their unavailability in local markets. However,

due to their growing demands in the industrial sector, such as cleaning and laundry

materials and glass industry, nowadays, sodium-based alkali materials are manufactured in

various places around the world. They are readily available in Australian local market at a

competitive price. Therefore, carbon emission due to the transportation of materials is also

excluded in this calculation.

The carbon footprints and embodied energy for individual ingredients of concrete were

calculated by multiplying their amount in the unit volume of concrete (m3) with

corresponding carbon emission and embodied energy data in Table 7.1. The carbon

emission and embodied energy of unit volume of concrete of different studies were

estimated by cumulating their ingredients’ contributions as presented in Figure 7.5 and

Figure 7.6, respectively. For example, carbon footprint of the production of one m3 of

grade 50 MPa OPC concrete (of this study) was estimated by combining the carbon

footprint of 352 kg of Portland cement, 88 kg of fly ash, 1098 kg of coarse aggregate, 697

kg of fine aggregate, 1.91 kg of water reducer and 0.9 kg of superplasticiser (required for

one m3 of concrete). The calcualted numeric values of carbon footprints and embodied

energy of individual ingredients of different concrete are shown in the Appendices (Table

A.18 and Table A.19, respectively).


185

Figure 7.5: Carbon footprints of manufacturing of unit volume of concrete

0

100

200

300

400

500C

arb

on e

mis

sion

(k

g C

O2-e

/m3

of c

oncr

ete)

HWR WR

Steam curing @60 °C Fine aggregate

Coarse aggreagte Sodium carbonate

Sodium hydroxide Sodium silicate

GGBS Fly ash

Portland cement


186

Figure 7.6: Energy consumptions of manufacturing of unit volume of concrete

0

400

800

1200

1600

2000

2400

2800E

mb

odie

d e

ner

gy

(MJ/

m3

of c

oncr

ete)

HWR WRSteam curing @60 °C Fine aggregateCoarse aggreagte Sodium carbonateSodium hydroxide Sodium silicateGGBS Fly ashPortland cement


187

As shown in Figure 7.5 and Figure 7.6, conventional OPC concrete shows a significantly

higher amount of carbon emission as well as higher embodied energy than geopolymer

concrete of same grade because of the carbon footprint and embodied energy associated

with Portland cement. Partial replacement of Portland cement by fly ash can reduce the

total carbon footprint of OPC concrete, however, it still has a significantly higher carbon

footprint than geopolymer concrete of same grade. Comparing OPC and geopolymer

concrete produced in this study, geopolymer concrete generates around 66% less CO2 than

OPC concrete (with 20% fly ash) of same grade. Whereas, comparing with OPC concrete

without SCMs (Deb et al., 2014), geopolymer concrete of this study has around 74% lower

carbon emission than OPC concrete of same grade. Davidovits (2015) suggested that

geopolymer concrete could have 70% to 90% less carbon footprint than OPC concrete of

same strength grade. Which was a close estimation with this study. In case of embodied

energy, the production of geopolymer concrete (cured at normal temperature) consumes

around 53% less energy than OPC concrete of same grade. For both, geopolymer and OPC

concrete, binders (geopolymer binder or Portland cement) are the major ingredients to

contribute to carbon footprints of concrete mix. Portland cement contributions around 86%

of total carbon footprints of concrete mix, whereas geopolymer binder is responsible for

around 52% of total carbon footprints of geopolymer concrete.

Despite very small carbon footprint of fly ash, fly ash only based geopolymer concrete has

some sustainability issue because it needs to be cured at high temperature and leads to the

consumption of a significant amount of energy. Data points in Figure 7.5 and Figure 7.6

show that fly based geopolymer concrete produced by Diaz-Loya et al. (2011) have a

significantly higher carbon footprint and higher embodied energy than geopolymer

concrete cured at normal temperature. In geopolymer concrete, sodium silicate, sodium

hydroxide and coarse aggregates are the major ingredients responsible for higher carbon

footprint and embodied energy of concrete. Comparing between geopolymer concrete of

same strength grade, geopolymer concrete having a combination of fly ash and GGBS in

source materials show higher sustainability than fly ash only or GGBS only based


188

geopolymer concrete because it contains more than 50% of fly ash (by mass) in the binder

and it does not need high temperature curing.

Among all, the geopolymer concrete of this study shows the smallest carbon footprint than

same grade geopolymer concrete of previous studies because it contains less amount of

binder than others and sodium hydroxide was replaced by sodium carbonate in alkali

activator. Figure 7.7 shows a comparison between carbon footprint of geopolymer

concrete of same strength grade and same source materials. Considering only the binder

ingredients and chemical admixtures used in concrete production, the geopolymer concrete

of this study emits around 22% less CO2 than geopolymer concrete of same grade produced

in previous studies. This evaluation shows that one-part geopolymer binder used in this

study was significantly more environmentally sustainable than the Portland cement and

two-part geopolymer binder used in previous studies as well.

Figure 7.7: Carbon footprint of ambient cured geopolymer concrete

0

25

50

75

100

Current study-61 MPa

Fang et al.(2018)-57.5

MPa

Current study-47.5 MPa

Fang et al.(2018)-48 MPa

Deb et al.(2014)-47 MPa

Car

bon

em

issi

on

(k

g C

O2

-e/

m3

of c

oncr

ete)

Fly ash GGBS Sodium silicate

Sodium hydroxide Sodium carbonate HWR


189

7.7 Conclusions

This study evaluated the environmental sustainability of OPC and geopolymer concrete of

different types based on their mixed compositions. In order to estimate the carbon emission

of geopolymer and OPC concrete, carbon footprints and embodied energy data of

individual ingredients were taken from various published papers. Following conclusions

can be made from this evaluation.

For both, geopolymer and OPC concrete, binders (geopolymer binder or Portland

cement) are the major ingredients to contribute to total carbon footprints of concrete

mix whose contributions are around 86% and 52%, respectively for OPC and


alkali activators are the major sources of carbon emission in geopolymer binder

which contribute around two-thirds of the total volume of carbon emission of the

binder.

Geopolymer binder used in this study was significantly carbon-efficient than

Portland cement. Production of geopolymer binder emits around 5 times less CO2

than the production of Portland cement and consumes around 3 times less energy.

For the same volume of production, geopolymer concrete generates around 65% less

CO2 and consumes 52% less energy than OPC concrete of same strength grade.

Geopolymer concrete produced in this study emits around 22% less CO2 than

geopolymer concrete of same strength grade produced in previous studies because it

needed a smaller amount of binder and sodium hydroxide was replaced by sodium

carbonate in the alkali activator.

Chapter 8: Conclusions and recommendations for further study

190

CHAPTER 8

8. Conclusions and Recommendations for Future Study

8.1 Conclusions of this study

Geopolymer binder offers a sustainable alternative to Portland cement to produce

structural as well as non-structural grade concrete by reducing carbon footprint from

cement production. Geopolymer technology not only reduces the embodied energy by

utilizing the industrial by-products but also reduces the stockpiles of coal combustion

products. One-part geopolymer binder having fly ash and GGBS in source materials

was used in this study to produce grade 50 MPa geopolymer concrete. A series of

experiments were carried out to investigate the engineering properties of geopolymer

concrete at ambient curing conditions according to relevant Austrian Standards. In

addition, early age strength development of geopolymer concrete under accelerated

curing was measured to investigate its potential application in the precast concrete

sector. The investigated engineering properties were compared with control (OPC)

concrete of same grade. Prestressed concrete structures are the most suitable

applications of geopolymer concrete because the tensile strength of concrete can

influence their structural behaviour. In order to evaluate the suitability of geopolymer

concrete in prestressed concrete structures, load-deflection behaviour of prestressed

concrete beams of different spans made from geopolymer and OPC concrete of same

grade were studied using finite element analysis method. The environmental

sustainability of geopolymer and OPC concrete were evaluated by calculating their

carbon footprints for a unit volume of production of same grade concrete. Based on the

experimental and analytical results, the following conclusions can be made as the

outcomes of this research study:

Unlike the liquid-activated geopolymer binder used in previous studies, the

geopolymer binder used in this study was one-part (powder) binder and free from

sodium hydroxide. Therefore, it posed a minimum safety hazard.

Mixing and handling of one-part geopolymer binder was found to be similar to

conventional Portland cement. Geopolymer binder needed a relatively lower


191

amount of binder and water than OPC to produce concrete of the same strength

grade and workability despite the addition of no chemical admixtures.

Geopolymer concrete specimens can be cast and cured according to the

conventional methods under ambient conditions. Having GGBS in the source

materials, this geopolymer concrete set and hardened at ambient conditions and

attained comparable early age strength to OPC concrete of the same grade.

Measured 28 days indirect-tensile and flexural strengths of geopolymer concrete

were 5.1 MPa and 7.1 MPa, respectively. These were around 27% higher

compared to OPC concrete of same strength grade as well as higher than estimated

values using concrete standards of current practice. The higher tensile strength of

geopolymer concrete was due to the stronger bond between aggregate and binder

paste. The fractured surface of geopolymer concrete under tensile load was

dominated by splitting of aggregates rather than the failure of bonds between

aggregates and binder paste.

Grade 50 MPa geopolymer concrete attained 33.5 MPa compressive strength

under accelerated curing at 70ºC for 6 hours which was 54% of its 28 days

compressive strength. This fulfilled the requirements of AS-1597.2 (2013) for

releasing of precast concrete elements from formworks. Whereas, OPC concrete

of same grade developed only 24 MPa for the same period of curing.

Measured modulus of elasticity of geopolymer and OPC concrete were 34.2 GPa

and 35.3 GPa, respectively which were very close to the estimated value using

AS-3600 (2018). Hence, existing model for calculating the modulus of elasticity

of OPC concrete can also be used for geopolymer concrete. The modulus of

elasticity of geopolymer concrete measured in this study was higher than previous

results of heat-cured geopolymer concrete.

Geopolymer concrete showed better serviceability properties than OPC concrete

at ambient curing. The drying shrinkage of geopolymer concrete was 450

microstrain for one-year period, which was 30% lower compared to OPC concrete

of same strength grade. The creep coefficient of geopolymer concrete was found


192

to be 1.87 for one-year, which was 47% lower compared to OPC concrete for the

same period. Whereas, measured specific creep of geopolymer concrete was 68

microstrain/MPa for one-year, which was 50% lower compared to OPC concrete

of same grade.

The interaction between concrete and prestressing steel tendon can be modelled

using a cohesive surface interactions which follows the traction-separation law.

The allowable prestressing load in geopolymer prestressed concrete beams was

around 15% higher compared to OPC prestressed concrete beam of same span

and cross-section due to the higher flexural strength of geopolymer concrete. The

calculated permissible tensile stress in extreme fibre in a geopolymer prestressed

concrete beam would be around 0.33√�� (equals to 0.4��) for geopolymer

concrete. Whereas, this value would be around 0.26√�� for OPC concrete, close

to the ACI-318 (2011) recommendation (0.25√��).

Load–deflection response obtained from finite element analysis of conventional

RC beams of different spans showed that geopolymer concrete beam can

withstand around 28% higher first-crack load than OPC concrete beam of same

span and cross-section due to the higher flexural strength of the geopolymer

concrete. Whereas, the ultimate load capacity of geopolymer RC beam was

around 5.5% higher than OPC concrete beams of same span. The difference in

ultimate load capacity increased with the degree of under-reinforcement (decrease

in density of tensile reinforcement) of the beam section. Geopolymer prestressed

concrete beam can carry around 20% higher first-crack load and 13% higher

ultimate load than identical OPC concrete beams.

Concrete below the neutral-axis of RC beam needs a significant amount of

fracture energy to form flexural cracks due to imposed load. The amount of

fracture energy required to form a unit crack area is the function of the tensile

strength of concrete. As geopolymer concrete has higher flexural strength, it

requires relatively higher fracture energy than OPC concrete for the same area of

crack to be formed. Thus, fracture energy may be a factor to differentiate between


193

the ultimate load capacities of geopolymer and OPC concrete beams which

increases with the increase in the degree of under-reinforcement of concrete

beams. This phenomenon is applicable to both conventional reinforced and

prestressed concrete beams.

For a similar span and cross-section, a geopolymer reinforced concrete beam can

resist slightly more ultimate plastic deflection before failure (hence, higher

ductility) than OPC concrete beam because of the difference in stress-strain

behaviours of concrete.

Smaller shrinkage and creep strains of geopolymer concrete contribute to

relatively smaller time-dependent losses of prestress in geopolymer prestressed

concrete beams than OPC concrete beams of same span. After one-year, there

were around 90% and 87.5% residual prestresses in geopolymer and OPC

concrete beams, respectively in 15 m span beams. Geopolymer concrete beams

lost 7% and 9% first-crack load capacity for 10 m and 15 m spans, respectively

after 1 year. Whereas, the first-crack load capacity of OPC concrete beams

decreased by 9% and 12% for 10 m and 15 m spans, respectively for this period.

Reduction in ultimate load capacity due to loss of prestress was smaller than first-

crack load which was 3.3% and 4.3% in geopolymer and OPC concrete beams,

respectively for one-year. Therefore, a geopolymer prestressed concrete beam can

maintain better serviceability compared to prestressed beam from OPC concrete

of same strength grade.

The serviceability of prestressed concrete beams for up to 10 years was evaluated

using predicted values of drying shrinkage and creep coefficient according to

ACI-209.2R (2008). The increments in drying shrinkage and creep coefficient

from 1 year to 10 years period were found to be 12 % and 9% respectively. Both,

geopolymer and OPC concrete showed similar patterns of growth of drying

shrinkage and creep strains. For this period, reductions in first-crack load capacity

were 1.7% and 2.1% for geopolymer and OPC concrete beams, respectively.

Whereas, reductions in ultimate load capacity were less than one percent for both

concrete beams. Therefore, the study of serviceability properties of concrete


194

(drying shrinkage and creep strains) up to one year was sufficient to evaluate the

long-term serviceability of a prestressed concrete beam.

The geopolymer binder used in this study was significantly carbon-efficient than

Portland cement. Production of geopolymer binder emits around 5 times less CO2

than the production of Portland cement and consumes around 3 times less energy.

For the same volume of production, geopolymer concrete generates around 65%

less CO2 and consumes 52% less energy than OPC concrete of same strength

grade.

Geopolymer concrete produced in this study emits around 22% less CO2 than

geopolymer concrete of same strength grade produced in previous studies because

it needed a smaller amount of binder and sodium hydroxide was replaced by

sodium carbonate in alkali activator.


195

8.2 Recommendation for further study

This study is based on finite element analysis of prestressed concrete beams. Finite

element analysis can be regarded as an alternative to experimental load testing of

structures. Appropriate finite element analysis methods were followed in this study in

order to achieve realistic load-deflection responses. The author suggests to carry out

load testing of prestressed concrete beams for short-term (after 28 days) and long-term

(after six months and one year) to compare the results from finite element analysis. It

would be interesting to see the effect of creep and shrinkage strains in the long-term

load-deflection responses of prestressed concrete beam.

Bridge girders and multi-span prestressed concrete beams are some other applications

of geopolymer concrete in the prestressed concrete sector. As geopolymer has higher

flexural strength than OPC concrete, the load-carrying capacity of these structures may

be significantly improved with the application of geopolymer concrete. An

experimental study of these structures could be a milestone in the application of

geopolymer concrete in prestressed concrete sector. The current study evaluates the

structural performance of geopolymer and OPC prestressed concrete beams applying

static load. Study of structural behaviours under dynamic load is also important for

some prestressed concrete structures, such as bridge girders.

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Appendices

209

A. Appendices

Some Figures and Tables which are relevant to this study but not included in the body

of the thesis are presented in these appendices.

Table A.1: Sieve analysis of aggregates used for concrete production

Percentage passing

Sieve size (mm)

Fine sand

Medium sand

10mm aggregate

20mm aggregate

26.5 100

19 98

13.2 100 52

9.5 93 11

6.7 100 50 3

4.75 99 12 2

2.36 81 4 1

1.18 100 57 2 0

0.6 98 38 0 0.425 87 31 0.3 47 24 0.15 2 12 0.075 0 4 0.03 0 0

Appendices

210

Figure A.1: Compositions of fly ash

Appendices

211

Figure A.2: Compositions of GGBS

Appendices

212

Figure A.3: Compositions of sodium silicate

Appendices

213

Figure A.4: Geopolymer concrete being mixed

Appendices

214

Figure A.5: Concrete cylinders being cast and vibrated

Appendices

215

Figure A.6: Measurement of concrete wert density

Appendices

216

Figure A.7: Immersed curing of OPC concrete specimens

Appendices

217

Figure A.8: Storage of shrinkage prisms in the control room

Appendices

218

Figure A.9: Indirect-tensile testing frame

Table A.2: Compressive strength developments of 50 MPa concrete


Days Compressive strength (MPa)

Standard deviation


Standard deviation

3 30.0 2.78 28.5 1.32

7 41.5 2.52 42.0 1.61

14 52.0 2.93 54.0 1.53

28 59.0 3.28 61.0 1.58

56 64.0 3.12 66.5 1.8

90 66.0 2.93 69.0 1.89

365 71.0 2.9 74.0 1.82

Table A.3: Indirect-tensile strength developments 50 MPa concrete


Days Indirect-tensile strength (MPa)

Standard deviation

Indirect-tensile strength (MPa)

Standard deviation

7 3.2 0.32 4.1 0.21

14 3.6 0.36 4.6 0.25

28 4.0 0.41 5.1 0.22

Appendices

219

Table A.4: Flexural strength developments 50 MPa concrete


Days Indirect-tensile strength (MPa)

Standard deviation

Indirect-tensile strength (MPa)

Standard deviation

14 5.0 0.4 6.3 0.31

28 5.6 0.49 7.1 0.321

Appendices

220

Table A.5: Shrinkage measurement of geopolymer and OPC concrete 50 MPa

Drying shrinkage (Microstrain)

Concrete age (day) Effective days OPC Geopolymer AS 3600

7 0 0 0 0

14 7 240 160 256.2

21 14 320 240 333.1

28 21 370 290 375.2

35 28 410 320 402.5

42 35 440 340 421.9

49 42 460 350 436.5

56 49 480 360 448.0

63 56 490 370 457.3

70 63 500 375 464.9

77 70 510 380 471.4

84 77 520 390 476.9

91 84 525 395 481.7

98 91 525 400 485.9

105 98 530 405 489.7

112 105 535 410 493.0

119 112 540 410 496.0

126 119 545 415 498.7

133 126 550 415 501.1

140 133 550 420 503.4

154 147 555 425 507.3

168 161 555 425 510.7

189 182 560 430 514.9

210 203 565 435 518.4

231 224 565 435 521.3

252 245 570 440 523.8

280 273 575 440 526.7

308 301 580 445 529.0

336 329 585 450 531.0

372 365 585 450 533.2

393 386 590 455 534.4

Appendices

221

Table A.6: Creep measurement of geopolymer concrete of 50 MPa

�� = 51.5 MPa, 40% �� = 20.6 MPa

Microstrain

Age (day)

Effective day

Shrinkage strain

Total loaded strain

Act. Creep

Creep coefficient

Specific creep (Microstrain/MPa)

28 0 0.0 752.7 0.0 0.00 0.0

28 0 0.0 851.5 0.0 0.00 0.0

29 1 7.2 982.6 222.6 0.30 10.8

30 2 11.6 1079.1 314.8 0.42 15.3

31 3 21.3 1194.1 420.0 0.56 20.4

33 5 28.5 1341.6 560.4 0.74 27.2 35 7 36.9 1448.0 658.3 0.87 32.0

42 14 52.6 1633.8 828.5 1.10 40.2

49 21 62.5 1776.3 961.2 1.28 46.7

56 28 70.6 1886.8 1063.4 1.41 51.6

63 35 78.3 1961.8 1130.8 1.50 54.9

70 42 80.4 2006.2 1173.1 1.56 56.9

77 49 85.84 2034.5 1196.0 1.59 58.1

84 56 88.8 2069.6 1228.0 1.63 59.6

91 63 89.6 2083.4 1241.1 1.65 60.2

98 70 90.14 2094.7 1251.8 1.66 60.8

105 77 90.72 2106.4 1263.0 1.68 61.3

112 84 91.04 2116.4 1272.6 1.69 61.8

119 91 91.6 2123.9 1279.6 1.70 62.1

126 98 93.14 2130.7 1284.8 1.71 62.4

133 105 95.06 2141.6 1293.9 1.72 62.8

140 112 96.1 2149.0 1300.3 1.73 63.1

154 126 97.3 2160.3 1310.3 1.74 63.6

168 140 98.8 2171.0 1319.4 1.75 64.0

196 168 102.2 2191.1 1336.2 1.78 64.9 210 182 103.8 2197.5 1341.0 1.78 65.1

231 203 104.1 2207.6 1350.7 1.79 65.6

252 224 104.8 2218.7 1361.1 1.81 66.1

280 252 105.4 2233.6 1375.4 1.83 66.8

308 280 107.4 2237.7 1377.6 1.83 66.9

336 308 108.3 2254.8 1393.8 1.85 67.7

372 344 109.5 2265.8 1403.5 1.86 68.1

393 365 110.3 2273.5 1410.5 1.87 68.5

Appendices

222

Table A.7: Creep measurement of OPC concrete of 50 MPa

�� = 50.5 MPa, 40% �� = 20.2 MPa

Microstrain

Age (day)

Effective day

Shrinkage strain

Total loaded

Act. Creep

Creep coefficient

Specific creep (Microstrain/MPa)

28 0 0.0 743.6 0.0 0.00 0.0 28 0 0.0 848.5 0.0 0.00 0.0 29 1 9.0 1026.1 273.4 0.36 13.5

30 2 14.9 1172.5 414.0 0.55 20.5

31 3 21.6 1301.4 536.2 0.71 26.5

33 5 29.8 1475.6 702.2 0.93 34.8

35 7 37.2 1622.1 841.3 1.12 41.6

42 14 53.0 1956.0 1159.5 1.54 57.4

49 21 64.9 2147.2 1338.7 1.78 66.3

56 28 73.7 2264.6 1447.3 1.92 71.6

63 35 80.1 2348.1 1524.4 2.03 75.5

70 42 85.2 2408.5 1579.7 2.10 78.2 77 49 89.6 2462.3 1629.1 2.16 80.6

84 56 93.4 2524.8 1687.7 2.24 83.6

91 63 95.6 2568.6 1729.4 2.30 85.6

98 70 97.1 2597.6 1756.8 2.33 87.0

105 77 98.8 2619.5 1777.1 2.36 88.0

112 84 99.6 2648.6 1805.4 2.40 89.4

119 91 101.1 2672.5 1827.8 2.43 90.5

126 98 103.25 2685.62 1838.8 2.44 91.0

133 105 104.86 2697.36 1848.9 2.46 91.5

140 112 106.3 2706.2 1856.3 2.47 91.9

154 126 108.66 2731.69 1879.4 2.50 93.0

168 140 110.4 2754.8 1900.7 2.53 94.1

189 161 113.4 2797.5 1940.5 2.58 96.1

210 182 115.1 2814.5 1955.8 2.60 96.8

231 203 117.2 2836.3 1975.5 2.6 97.8

252 224 119.5 2854.3 1991.3 2.65 98.6

280 252 121.8 2878.6 2013.1 2.67 99.7

308 280 123.4 2897.8 2030.8 2.70 100.5

336 308 124.7 2918.2 2049.8 2.72 101.5

372 344 126.4 2934.3 2064.3 2.74 102.2

393 365 128.1 2944.6 2073.0 2.75 102.6

Appendices

223

Table A.8: Compressive stress-strain model of geopolymer concrete of 50 MPa

ɛ ɛo ɛ/ɛo Stress (MPa) Damage Parameter

0 0.0027 0.00 0.000 0

0.00025 0.0027 0.093 7.506 0

0.0005 0.0027 0.185 14.283 0

0.00075 0.0027 0.278 20.332 0

0.001 0.0027 0.370 25.652 0

0.00125 0.0027 0.463 30.243 0

0.0015 0.0027 0.556 34.105 0

0.00175 0.0027 0.648 37.239 0 Inelastic strain

0.002 0.0027 0.741 39.643 0.0000 0

0.00225 0.0027 0.833 41.319 0.0000 0.00025

0.0025 0.0027 0.926 42.267 0.0000 0.0005

0.0027 0.0027 1.000 42.500 0.0000 0.0007

0.003 0.0027 1.111 41.341 0.0273 0.001

0.0035 0.0027 1.296 39.409 0.0727 0.0015

0.00375 0.0027 1.389 38.443 0.0955 0.00175

0.00425 0.0027 1.574 36.511 0.1409 0.00225

0.006 0.0027 2.222 29.750 0.3000 0.004

Table A.9: Compressive stress-strain model of OPC concrete of 50 MPa

ɛ ɛo ɛ/ɛo Stress (MPa) Damage Parameter

0 0.0025 0.00 0.000 0

0.00025 0.0025 0.1 8.075 0

0.0005 0.0025 0.2 15.300 0

0.00075 0.0025 0.3 21.675 0

0.001 0.0025 0.4 27.200 0

0.00125 0.0025 0.5 31.875 0

0.0015 0.0025 0.6 35.700 0

0.00175 0.0025 0.7 38.675 0 Inelastic strain

0.002 0.0025 0.8 40.800 0.000 0

0.00225 0.0025 0.9 42.075 0.000 0.00025

0.0025 0.0025 1.0 42.500 0.000 0.0005

0.00275 0.0025 1.1 41.225 0.030 0.00075

0.003 0.0025 1.2 39.950 0.060 0.001

0.0035 0.0025 1.4 37.400 0.120 0.0015

0.005 0.0025 2.0 29.750 0.300 0.003

Appendices

224

Table A.10: Tensile stress-strain model of geopolymer concrete of 50 MPa

ɛ f't ɛ't ɛ/ɛ't Stress (MPa) Damage Parameter

0 6.4 0.00025 0.00 0.000 0.0

0.00002 6.4 0.00025 0.08 1.102 0.0

0.00004 6.4 0.00025 0.16 2.144 0.0

0.00006 6.4 0.00025 0.24 3.084 0.0

0.00008 6.4 0.00025 0.32 3.900 0.0

0.0001 6.4 0.00025 0.40 4.582 0.0

0.00012 6.4 0.00025 0.48 5.133 0.0

0.00014 6.4 0.00025 0.56 5.562 0.0

0.00018 6.4 0.00025 0.72 6.113 0.0

0.0002 6.4 0.00025 0.80 6.265 0.0 Cracking strain

0.00025 6.4 0.00025 1.00 6.400 0.0000 0

0.0004 6.4 0.00025 1.60 5.855 0.0852 0.00015

0.0006 6.4 0.00025 2.40 4.815 0.2476 0.00035

0.0008 6.4 0.00025 3.20 4.009 0.3736 0.00055

0.001 6.4 0.00025 4.00 3.420 0.4656 0.00075

0.0012 6.4 0.00025 4.80 2.982 0.5341 0.00095

0.0014 6.4 0.00025 5.60 2.645 0.5867 0.00115

0.0016 6.4 0.00025 6.40 2.379 0.6283 0.00135

0.0018 6.4 0.00025 7.20 2.163 0.6620 0.00155

0.002 6.4 0.00025 8.00 1.986 0.6897 0.00175

0.0025 6.4 0.00025 10.00 1.653 0.7418 0.00225

0.0032 6.4 0.00025 12.80 1.346 0.7897 0.00295

Appendices

225

Table A.11: Tensile stress-strain model of OPC concrete of 50 MPa

ɛ f't ɛ't ɛ/ɛ't Yield stress (ft) Damage Parameter

0 5.04 0.0002 0.00 0.000 0

0.00002 5.04 0.0002 0.10 1.079 0

0.00004 5.04 0.0002 0.20 2.070 0

0.00006 5.04 0.0002 0.30 2.920 0

0.00008 5.04 0.0002 0.40 3.608 0

0.0001 5.04 0.0002 0.50 4.135 0

0.00012 5.04 0.0002 0.60 4.516 0

0.00014 5.04 0.0002 0.70 4.775 0

0.00016 5.04 0.0002 0.80 4.934 0

0.00018 5.04 0.0002 0.90 5.016 0 Cracking strain

0.0002 5.04 0.0002 1.00 5.040 0.000 0

0.00025 5.04 0.0002 1.25 4.936 0.021 0.00005

0.0004 5.04 0.0002 2.00 4.186 0.169 0.0002

0.0006 5.04 0.0002 3.00 3.298 0.346 0.0004

0.0008 5.04 0.0002 4.00 2.694 0.466 0.0006

0.001 5.04 0.0002 5.00 2.275 0.549 0.0008

0.0012 5.04 0.0002 6.00 1.972 0.609 0.001

0.0014 5.04 0.0002 7.00 1.743 0.654 0.0012

0.0016 5.04 0.0002 8.00 1.564 0.690 0.0014

0.0018 5.04 0.0002 9.00 1.420 0.718 0.0016

0.002 5.04 0.0002 10.00 1.301 0.742 0.0018

0.0026 5.04 0.0002 13.00 1.046 0.792 0.0024

Appendices

226

Figure A.10: Reinforcements schedule of modelled pull-out block (not in scale)

Figure A.11: Reinforcements schedule of modelled 5 m long RC beam (not in scale)

Figure A.12: Prestressed 10 m long beam with mesh elements

Appendices

227


Figure A.14: Flexural stress on 10 m long prestressed beam at zero vertical

deflection

Figure A.15: Flexural stress on 10 m long prestressed beam at first-crack load

Appendices

228

Figure A.16: Tensile damage initiation in prestressed 10 m beam

Figure A.17: Tensile stress at geopolymer 10 m prestressed beam at ultimate failure

Appendices

229

Table A.12: Loss of prestress in geopolymer 10 m long concrete beam

Effective days

Shrinkage loss (MPa)

Creep loss

(MPa)

Relaxation loss (MPa)

Σ Time-dependent

losses (MPa)

Residual Pre-stress

(MPa)

% loss Residual prestress

% 0 0.0 0.0 0.0 0.0 1236.6 0.0% 100.0%

7 2.1 36.0 17.3 55.4 1181.2 4.5% 95.5%

14 3.6 45.2 18.3 67.1 1169.5 5.4% 94.6%

21 4.3 52.5 18.9 75.6 1161.0 6.1% 93.9%

28 5.0 58.1 19.3 82.3 1154.3 6.7% 93.3%

35 5.7 61.8 19.6 87.0 1149.6 7.0% 93.0%

42 6.0 64.1 19.9 90.0 1146.6 7.3% 92.7%

49 6.4 65.3 20.1 91.8 1144.8 7.4% 92.6%

56 7.1 67.1 20.3 94.5 1142.1 7.6% 92.4%

63 7.5 67.8 20.5 95.7 1140.9 7.7% 92.3%

70 7.8 68.4 20.7 96.8 1139.8 7.8% 92.2%

77 8.2 69.0 20.8 98.0 1138.6 7.9% 92.1%

84 8.5 69.5 21.0 99.0 1137.6 8.0% 92.0%

91 8.5 69.9 21.1 99.5 1137.1 8.0% 92.0%

98 8.9 70.2 21.2 100.3 1136.3 8.1% 91.9%

105 8.9 70.7 21.3 100.9 1135.7 8.2% 91.8%

112 9.2 71.0 21.4 101.7 1134.9 8.2% 91.8%

126 9.6 71.6 21.6 102.8 1133.8 8.3% 91.7%

140 9.6 72.1 21.8 103.4 1133.2 8.4% 91.6%

161 9.9 73.0 21.8 104.7 1131.9 8.5% 91.5%

182 10.3 73.2 21.9 105.5 1131.1 8.5% 91.5%

203 10.3 73.8 22.1 106.2 1130.4 8.6% 91.4%

224 10.7 74.3 22.2 107.2 1129.4 8.7% 91.3%

252 10.7 75.1 22.4 108.2 1128.4 8.7% 91.3%

280 11.0 75.2 22.6 108.8 1127.8 8.8% 91.2%

308 11.4 76.1 22.7 110.2 1126.4 8.9% 91.1%

344 11.4 76.7 22.9 110.9 1125.7 9.0% 91.0%

365 11.7 77.0 22.9 111.7 1124.9 9.0% 91.0%

Appendices

230

Table A.13: Loss of prestress in OPC 10 m long concrete beam

Age (days)


Creep loss (MPa)


Σ Time-dependent losses (MPa)

Residual Pre-stress (MPa)

% loss

Residual prestress %

0 0.0 0.0 0.0 0.0 1236.4 0.0% 100.0%

7 2.8 38.7 17.3 58.8 1177.6 4.8% 95.2%

14 4.8 53.4 18.3 76.5 1159.9 6.2% 93.8%

21 6.2 61.7 18.8 86.7 1149.7 7.0% 93.0%

28 7.6 66.7 19.3 93.5 1142.9 7.6% 92.4%

35 8.3 70.2 19.6 98.1 1138.3 7.9% 92.1%

42 9.0 72.8 19.9 101.6 1134.8 8.2% 91.8%

49 9.7 75.0 20.1 104.8 1131.6 8.5% 91.5%

56 10.4 77.7 20.3 108.4 1128.0 8.8% 91.2%

63 10.7 79.6 20.5 110.9 1125.5 9.0% 91.0%

70 10.7 80.9 20.7 112.3 1124.1 9.1% 90.9%

77 11.1 81.8 20.8 113.7 1122.7 9.2% 90.8%

84 11.4 83.1 21.0 115.5 1120.9 9.3% 90.7%

91 11.8 84.2 21.1 117.0 1119.4 9.5% 90.5%

98 12.1 84.7 21.2 118.0 1118.4 9.5% 90.5%

105 12.5 85.1 21.3 118.9 1117.5 9.6% 90.4%

112 12.5 85.5 21.4 119.4 1117.0 9.7% 90.3%

126 12.8 86.6 21.6 121.0 1115.4 9.8% 90.2%

140 12.8 87.5 21.8 122.1 1114.3 9.9% 90.1%

161 13.2 89.4 21.8 124.3 1112.1 10.1% 89.9%

182 13.5 90.1 21.9 125.5 1110.9 10.2% 89.8%

203 13.5 91.0 22.1 126.6 1109.8 10.2% 89.8%

224 13.8 91.7 22.2 127.8 1108.6 10.3% 89.7%

252 14.2 92.7 22.4 129.3 1107.1 10.5% 89.5%

280 14.5 93.5 22.6 130.6 1105.8 10.6% 89.4%

308 14.9 94.4 22.7 132.0 1104.4 10.7% 89.3%

344 14.9 95.1 22.9 132.8 1103.6 10.7% 89.3%

365 15.2 95.5 22.9 133.6 1102.8 10.8% 89.2%

Appendices

231

Table A.14: Loss of prestress in geopolymer 15 m long concrete beam

Age (days)


Creep loss (MPa)




% loss

Residual prestress %

0 0.0 0.0 0.0 0.0 1233.5 0.0% 100.0%

7 1.9 42.9 17.2 62.1 1171.4 5.0% 95.0%

14 3.2 54.0 18.2 75.5 1158.0 6.1% 93.9%

21 3.8 62.7 18.8 85.4 1148.1 6.9% 93.1%

28 4.5 69.4 19.2 93.1 1140.4 7.5% 92.5%

35 5.1 73.8 19.5 98.4 1135.1 8.0% 92.0%

42 5.5 76.5 19.8 101.8 1131.7 8.3% 91.7%

49 5.8 78.0 20.0 103.8 1129.7 8.4% 91.6%

56 6.4 80.1 20.2 106.7 1126.8 8.7% 91.3%

63 6.7 81.0 20.4 108.1 1125.4 8.8% 91.2%

70 7.1 81.7 20.5 109.2 1124.3 8.9% 91.1%

77 7.4 82.4 20.7 110.4 1123.1 9.0% 91.0%

84 7.7 83.0 20.8 111.5 1122.0 9.0% 91.0%

91 7.7 83.5 20.9 112.1 1121.4 9.1% 90.9%

98 8.0 83.8 21.0 112.8 1120.7 9.1% 90.9%

105 8.0 84.4 21.1 113.5 1120.0 9.2% 90.8%

112 8.3 84.8 21.2 114.4 1119.1 9.3% 90.7%

126 8.7 85.5 21.4 115.5 1118.0 9.4% 90.6%

140 8.7 86.1 21.5 116.2 1117.3 9.4% 90.6%

161 9.0 87.2 21.7 117.9 1115.6 9.6% 90.4%

182 9.3 87.5 21.9 118.7 1114.8 9.6% 90.4%

203 9.3 88.1 22.0 119.5 1114.0 9.7% 90.3%

224 9.6 88.8 22.2 120.6 1112.9 9.8% 90.2%

252 9.6 89.7 22.4 121.7 1111.8 9.9% 90.1%

280 9.9 89.9 22.5 122.3 1111.2 9.9% 90.1%

308 10.3 90.9 22.6 123.8 1109.7 10.0% 90.0%

344 10.3 91.6 22.8 124.6 1108.9 10.1% 89.9%

365 10.6 92.0 22.9 125.5 1108.0 10.2% 89.8%

Appendices

232

Table A.15: Loss of prestress in OPC 15 m long concrete beam

Age (days)


Creep loss (MPa)




% loss Residual %

0 0.0 0.0 0.0 0.0 1233.8 0.0% 100.0%

7 2.5 47.8 17.2 67.6 1166.2 5.5% 94.5%

14 4.4 65.9 18.2 88.5 1145.3 7.2% 92.8%

21 5.6 76.1 18.8 100.5 1133.3 8.1% 91.9%

28 6.9 82.3 19.2 108.4 1125.4 8.8% 91.2%

35 7.5 86.6 19.5 113.7 1120.1 9.2% 90.8%

42 8.1 89.8 19.8 117.7 1116.1 9.5% 90.5%

49 8.8 92.6 20.0 121.4 1112.4 9.8% 90.2%

56 9.4 95.9 20.2 125.5 1108.3 10.2% 89.8%

63 9.7 98.3 20.4 128.4 1105.4 10.4% 89.6%

70 9.7 99.8 20.5 130.1 1103.7 10.5% 89.5%

77 10.0 101.0 20.7 131.7 1102.1 10.7% 89.3%

84 10.3 102.6 20.8 133.7 1100.1 10.8% 89.2%

91 10.6 103.9 20.9 135.4 1098.4 11.0% 89.0%

98 10.9 104.5 21.0 136.5 1097.3 11.1% 88.9%

105 11.3 105.1 21.1 137.4 1096.4 11.1% 88.9%

112 11.3 105.5 21.2 138.0 1095.8 11.2% 88.8%

126 11.6 106.8 21.4 139.7 1094.1 11.3% 88.7%

140 11.6 108.0 21.5 141.1 1092.7 11.4% 88.6%

161 11.9 110.3 21.7 143.9 1089.9 11.7% 88.3%

182 12.2 111.2 21.9 145.2 1088.6 11.8% 88.2%

203 12.2 112.3 22.1 146.5 1087.3 11.9% 88.1%

224 12.5 113.2 22.2 147.9 1085.9 12.0% 88.0%

252 12.8 114.4 22.4 149.6 1084.2 12.1% 87.9%

280 13.1 115.4 22.5 151.1 1082.7 12.2% 87.8%

308 13.4 116.5 22.6 152.6 1081.2 12.4% 87.6%

344 13.4 117.3 22.8 153.6 1080.2 12.4% 87.6%

365 13.8 117.8 22.9 154.5 1079.3 12.5% 87.5%

Appendices

233

Table A.16: Long-term drying shrinkage of 50 MPa concrete

Drying shrinkage (microstrain)


Effective age Measured �� Estimated Measured �� Estimated

0 0 0

3 months 540 410

1/2 year 565 435

1 year 590 643.5 455 496.3

2 years 613.2 472.9

5 years 630.8 486.5

10 years 637.1 491.3

Table A.17: Long-term creep coefficient of 50 MPa concrete

Creep coefficients

Geopolymer concrete OPC concrete

Effective age Measured �� Estimated Measured �� Estimated

0 0

0

3 months 1.70 2.43

1/2 year 1.78 2.60

1 year 1.87 2.06 2.75 3.03

2 years 1.96 2.89

5 years 2.02 2.97

10 years 2.04 3.00

Appendices

234

Table A.18: Calculated carbon emission of different concrete (kg CO2-e/kg)

Carbon footprint of concrete ingredients ((kg CO2-e) Source reference Portland

cement Fly ash GGBS Sodium

silicate Sodium hydroxide

Sodium carbonate

Coarse aggregate

Fine aggregate

Steam curing @60 °C

WR HWR Total (kg CO2-e/m3)

Current study-Geopolymer (61 MPa)

0.0 5.7 19.2 33.7 0.0 9.5 41.4 10.1 0 0.0 0.0 119.5

Current study-OPC (59 MPa) 302.7 2.4 0.0 0.0 0.0 0 39.5 9.8 0 0.7 0.6 355.7

Hardjito and Rangan (2005)-Geopolymer (57 MPa)

0.0 12.9 0.0 53.4 7.9 0 46.6 7.8 39.97 0.0 0.0 168.4

Fang et al. (2018)-Geopolymer (57.5 MPa)

0.0 7.6 17.2 47.6 10.4 0 43.6 9.1 0 0.0 2.9 138.3

Diaz-Loya et al. (2011)-Geopolymer (59.5 MPa)

0.0 13.3 0.0 49.5 28.1 0 30.9 9.7 119.91 0.0 10.8 262.1

Farhan et al. (2019)-Geopolymer (66.1 MPa)

0.0 0.0 64.4 47.2 13.4 0 41.5 8.8 0.0 0.0 9.0 184.2

Current study-Geopolymer (47.5 MPa)

0.0 4.9 16.7 29.3 0.0 8.2 42.2 10.6 0 0.0 0.0 111.9

Current study-OPC (48 MPa) 264.9 2.1 0.0 0.0 0.0 0 41.0 9.8 0 0.6 0.6 318.9


0.0 12.9 0.0 21.4 30.3 0 46.6 7.8 39.97 0.0 0.0 158.8

Fang et al. (2018)-Geopolymer (48 MPa)

0.0 8.1 14.3 41.4 9.2 0 44.9 9.4 0 0.0 2.9 130.1

Deb et al. (2014)-Geopolymer (47 MPa)

0.0 8.6 11.4 50.9 11.5 0 43.5 9.1 0 0.0 0.0 135.1

Deb et al. (2014)-OPC (48 MPa)

383.6 0.0 0.0 0.0 0.0 0 37.9 10.8 0 0.0 0.0 432.3


0.0 13.3 0.0 55.0 31.2 0 30.9 9.7 119.91 0.0 10.8 270.8

Appendices

235

Table A.19: Calculated embodied energy of different concrete

Embodied energy of concrete ingredients (MJ) Source reference Portland

cement Fly ash

GGBS Sodium silicate

Sodium hydroxide

Sodium carbonate

Coarse aggregate

Fine aggregate

Steam curing @60 °C

WR HWR Total (MJ/m3)

Current study-Geopolymer (61 MPa)

0 21.0 44.4 676.6 0.0 51.0 252.8 14.4 0.0 0 0 1060.1

Current study-OPC (59 MPa) 1971.2 8.8 0.0 0.0 0.0 0.0 241.6 13.9 0.0 10.1 10.3 2251.4


0 47.6 0.0 644.4 135.8 0.0 284.7 11.1 146.0 0 0.0 1269.6

Fang et al. (2018)-Geopolymer (57.5 MPa)

0 28.0 39.6 574.6 179.7 0.0 266.2 13.0 0.0 0 45.6 1146.8


0 49.4 0.0 596.9 485.0 0.0 188.8 13.8 438.0 0 171.0 1942.8

Farhan et al. (2019)-Geopolymer (66.1 MPa)

0.0 0.0 148.5 569.2 231.2 0.0 253.9 12.5 0.0 0.0 142.5 1357.8

Current study-Geopolymer (47.5 MPa)

0 18.3 38.5 588.0 0.0 44.3 257.6 15.1 0.0 0.0 0.0 961.9

Current study-OPC (48 MPa) 1724.8 7.7 0.0 0.0 0.0 0.0 250.4 14.0 0.0 9.2 8.8 2011.1


0 47.6 0.0 257.8 523.6 0.0 284.7 11.1 146.0 0 0.0 1270.7

Fang et al. (2018)-Geopolymer (48 MPa)

0 30.0 33.0 499.4 159.4 0.0 274.1 13.4 0.0 0 45.6 1054.9

Deb et al. (2014)-Geopolymer (47 MPa)

0 32.0 26.4 613.8 199.4 0.0 266.0 13.0 0.0 0 0 1150.6

Deb et al. (2014)-OPC (48 MPa)

2497.6 0.0 0.0 0.0 0.0 0.0 231.9 15.4 0.0 0 0 2744.8


0 49.4 0.0 663.2 538.9 0.0 188.8 13.8 438.0 0 171 2063.0

Documents

Investigation of Structural Behaviour of Geopolymer