Altoubat - Early Age Stresses and Creep-shrinkage Interaction of Restrained Concrete THESIS

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Early age stresses and creep-shrinkage interaction of restrained concreteAltoubat, Salah AhmedProQuest Dissertations and Theses; 2000; ProQuest Dissertations & Theses (PQDT)pg. n/a

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EARLY AGE STRESSES AND CREEP-SHRINKAGEINTERACTION OF RESTRAINED CONCRETE

BY

SALAH AHMED ALTOUBAT

B.Engr., Yarmouk University, I987M.S.. Jordan University of Science and Technology, 1990

THESIS

Submitted in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy in Civil Engineering

in the Graduate College of theUniversity of Illinois at Urbana-Champaign, 2000

Urbana, Hlinois


UMI Number". 9989929

Copyright 2000 byAltoubat, Salah Ahmed

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

2 THE GRADUATE COLLEGE

MARCH ZQO0j (date)

, \VE HEREBY RECOMMEND TH.-\T THE THESIS BY

i SALAH AHMED ALTOUBATl l

. S 1

EXTITLED EARLY AGE STRESSES AND CREEP—S,HRINKAGE __

l1l1 INTERACTION OF RESTRAINED CONCRETE

BE .~\L'CEP'[‘ED I.\' PARTI.-\L FL'LFILL.\IE.\'T OF Tl-IE REQL'IREME.\'TS FOR

' THE DEGREE OE no on or PHILOSOPHYl

l

. Director of Thesis Research

L9 PHead of Department ‘

l'l

: Lommittee on irnztl E. inationf7/, ~

l Chairperson ,I’ ‘4‘

I _' -l ’

1 li E‘ A — .4

i Required for doetor’s degree but not for master's.

0.11.


EARLY AGE STRESSES AND CREEP-SHRINKAGE INTERACTIONOF RESTRAINED CONCRETE

Salah Ahmed Altoubat, Ph.D.Department ofCivil Engineering

University of Illinois at Urbana-Champaign, 2000David A. Lange, Advisor

Experimental and numerical analyses were performed to characterize the early age

tensile creep and shrinkage behavior of normal and high performance concrete. A uniaxial,

computer controlled restrained shrinkage test was developed. The experiment tested two

identical specimens: restrained and unrestrained. The computer program controlling the test

checked shrinkage deformation continuously, and compared it to a threshold value of 5 um,

which when exceeded, triggered an increase in tensile load to recover the shrinkage strain

in the restrained specimen. Thus, a restrained condition is achieved and the stress generated

by shrinkage mechanisms was measurable. The experiment revealed how shrinkage

stresses developed and how creep mechanisms reduced shrinkage strain.

It was found that the early days of concrete life are characterized by a complex

interaction of intemal drying, extemal drying and thermal efiects. Restraining shrinkage in

the first days after casting generated significant tensile stresses, and these stresses led to

fi-acture of the concrete. The rate of stress evolution at early age is an important factor that

influences the time of cracking and stress at failure. The tensile creep of concrete at early

age formed a substantial part of the time dependent deformation and reduced the shrinkage

stresses by 50 %.

A method to separate drying creep mechanisms of concrete was developed. The

method combined experimental results of creep and shrinkage of concrete with numerical

analysis to separate the drying creep into two components: stress-induced shrinkage and

microcracking. The experiment measured the creep and shrinkage of concrete under drying,

sealed, and moist curing conditions. The test under moist curing condition gave the basic

creep; the test tmder sealed condition provided data on basic creep and stress-induced

shrinkage, and the drying test provided data on basic creep, stress-induced shrinkage and

microcracking.


A model based on the solidification theory was used to capture the characteristics of

the basic creep of concrete. The basic creep function of yotmg concrete was characterized

by a high inifial rate ofcreep in the initial 10-20 hours after loading. Then, the rate

decreased and the creep fiinction approached a stable value. The initial rate of creep was

sensitive to age at loading at an early age; and, after a few days, the tensile basic creep

became age-independent.

The combined numerical and experimental analysis revealed stress-induced

shrinkage as a major mechanism ofdrying creep ofplain and fiber reinforced concrete.

Microcracking forms a significant portion ofdrying tensile creep ofplain concrete, but it is

less significant in fiber reinforced concrete. Therefore, creep of PRC is dominated by real

mechanisms (basic and stress-reduced shrinkage), whereas apparent mechanisms induced

by microcracking form a significant part of the tensile creep ofplain concrete. The real

creep mechanisms are beneficial because they provide tensile stress relaxation, but the

apparent mechanisms are associated with microstructural damage and are detrimental.

Therefore, fiber reinforcement enhances stress relaxation and delays the time of shrinkage

cracking.

A damage-based model was used to demonstrate the relation between drying

microcracking and failure ofrestrained concrete. The model characterized the damage of

concrete as a degradation to the secant stifiiiess computed from a stress-strain diagram. The

model satisfactorily captured the features of failure, and quantitatively demonstrated the

contribution ofdrying microcracking to failure of restrained concrete.

iv


This work is dedicated to

My wife, Ruba Abu-Kaf

And

To my parents and all ofmy family members

V


ACKNOWLEDGEMENT

The author would like t_o express his deep gratitude and sincere appreciation to

Professor David A. Lange for his technical guidance, continuous support, and constructive

suggestions throughout the course ofthis research.

The research was supported by the Federal Aviation Administration (FAA) Center

of Excellence (COE) at the University of Illinois and by the National Science Foundation

(CAREER Award #CMS-9623467).

The author would like to extend his sincere thanks and appreciation to Professors J .

Francis Young, Neil M. Hawkins, and Emest J. Barenberg for their valuable comments and

helpful suggestions while serving on his advisory committee. Special thanks are due to Dr.

Greg Banas for his technical help and assistance throughout the experimental phase of this

research. Without his help and guidance, the experiment could not have been established

and completed.

The author would like to express his deep gratitude and sincere thanks to his wife.

Ruba Abu-Kaf for her unlimited patience, encouragement, and love during the five years of

study at the University of Illinois. The author is deeply indebted to her continuous support

and extraordinary efforts to share the bulk of responsibility at home and in raising our two

kids Mohammed and Maies. Without her efforts, this work could not have been completed.

Special thanks are due to the author’s parents and family members in Jordan for their

unwavering love, support and encouragement.

The author would also like to thank his friends Khalid Ghuzlan, Khaldoon Bani-

l-Iani. and Ghazi Alkhateeb for their help and support throughout this research. Finally. the

author extends a sincere thanks to his best colleagues, Nathan Rau, Anne Werner. Hak-

Chul Shin and all of the author’s colleagues in the Department ofCivil Engineering for

their fiiendship and support.

vi

~


TABLE OF CONTENTS

CHAPTER 1

INTRODUCTION................................................................................................................

...................... .. 1

3

4

1.1 Background ........................................................................................ ..

1.2 Research Objectives ............................................................................. ..

CHAPTER 2

LITERATURE REVIEW .............................................................................

....l. G€I1€l‘3.l ................................................................................................. ..

2.2 Driving Mechanisms for Cracking .................................................... ..

1.3 Scope ofWork ........................................................................................................ ..

..1

oooooooooooooooooooooo007

-------------------- --7

---------------------- --7

2.2.1 Autogenous Deformation (AD)........................................................................ .. 7

2.2.2 Thermal Dilation............................................................................................. ..

2.2.3 Drying Shrinkage (DS) ............................................................ ..

2.2.3.1 Influence of Shrinkage on Pavement............................. ..

2.2.3.2 Influence of Shrinkage on Material Performance ......... ..

2.3 Restrained Test Methods and Stress Measurement .......................... ..

2.4 Mechanical Properties..........................................................................

2.5 Creep of Concrete at Early Age............................................................................... ..

2.5.1 General Definitions......................................................................................... ..

2.5.2 Availability ofExperimental Data ................................................................. ..

2.5.3 Creep Mechanisms ................................................................... ..

2.5.4 Review ofAnalytical Models .....................................................

2.5.5 Tensile Creep at Early Age ............................................................................ ..

2.6 Creep of Concrete under Drying ............................................................................. ..

2.7 Efiect ofFiber Reinforcement on Creep and Shrinkage ........................................ ..

CHAPTER 3

EXPERIMENTAL TECHNIQUE AND TEST MATERLALS ........

3.1 Introduction ........................................................................................ ..

3.2 Experimental Technique ......................................................................

vii

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14

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17

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20

24

27

30

33

37

37

37


32.1 Design Considerations and Requirements ..................................................... .. 37

3.2.2 Uniaxial Creep-Shrinkage Test ...................................................................... .. 383.2.3 Mechanism ofthe Test ................................................................................... .. 40

3.2.4 Analytical Aspects of the Test ....................................................................... .. 41

3.3 Materials and Concrete Mix Compositions ............................................................ .. 43

3.3.1 Materials ......................................................................................................... .. 433.3.2 Concrete Mix Proportions .............................................................................. .. 44

3.3.3 Basic Tests on Aggregates ............................................................................. .. 45

3.3.4 Mixing Procedures .......................................................................................... .. 46

3.3.5 Hardened Concrete Characterization ............................................................. .. 46

3.4 Preliminary Stage ..................................................................................................... .. 47

3.4.1 Typical Results ............................................................................................... .. 48

3.4.2 Summary ofExperimental Observations ....................................................... .. 49

3.5 Final Research Plan.................................................................................................. .. 50

CHAPTER 4RESULTS OF DRYING CREEP-SHRTNKAGE TESTS .............................................. 60

4.1 General ..................................................................................................................... .. 60

4.2 Restrained Shrinkage Stress .................................................................................... .. 60

4.2.1 Failure ofRestrained Concrete ....................................................................... .. 61

4.2.2 Effect ofExtemal Relative Humidity ............................................................ .. 62

4.3 Free Shrinkage ......................................................................................................... .. 63

4.3.1 Eflect ofFiber Reinforcement on Shrinkage ................................................. .. 64

4.3.2 Efiect ofRelative Humidity on Shrinkage..................................................... .. 65

4.4 Total Tensile Creep .................................................................................................. .. 65

4.4.1 Efiect ofFiber Reinforcement on Total Tensile Creep ................................... 67

4.4.2 Total Creep Coefficient .................................................................................. .. 67

4.5 Shrinkage Stress-Strain Diagram ........................................................................... .. 684.6 Concrete Humidity and Temperature ...................................................................... .. 69

4.7 Efiect ofInitial Curing on Creep and Shrinkage .................................................... .. 70

4.8 Efiect ofAltemate Drying / Wetting on Creep and Shrinkage .............................. .. 72

4.9 Tensile Strength ......................................................................................................... 74

...


4.10 Concluding Remarks ............................................................................................. .. 75

CHAPTER 5RESULTS OF CREEP-SHRINKAGE TESTS UNDER SEALED AND WETCURING CONDITIONS .................................................................................................... 89

5.1 Introduction .............................................................................................................. .. 89

5.2 Sealed Condition ...................................................................................................... .. 905.2.1 Free Shrinkage (Autogenous Deformation)................................................... .. 91

5.2.2 Humidity Profile of Sealed Samples .............................................................. .. 92

52.3 Tensile Creep of Sealed concrete ................................................................... .. 93

5.2.4 Age at Which Sealing is Applied ................................................................... .. 94

5.2.5 Cumulative Stress versus Cumulative Elastic Strain..................................... .. 95

5.3 Wet Curing Condition.............................................................................................. .. 96

5.3.1 Effect ofWet Curing on Autogenous Shrinkage ........................................... .. 97

5.3.2 Does Wet Curing Afiect Mechanical Properties ........................................... .. 98

5.4 Identification of Basic Creep ................................................................................... .. 99

5.4.1 Efiect of Fiber Reinforcement on Basic Creep........................................... .. 100

5.4.2 Efiect ofW/C on Basic Creep ...................................................................... .. 102

5.5 Concluding Remarks.............................................................................................. .. 102

CHAPTER 6ANALYTICAL MODELS: BACKGROUND AND FORMULATION..................... 113

6.1 Introduction ............................................................................................................ .. 113

6.2 Basic Creep Constitutive Laws Formulation ........................................................ .. 113

6.2.1 Integral Formulation ..................................................................................... .. 113

6.2.2 Differential Formulation............................................................................... .. 1 15

6.2.2.1 Maxwell versus Kelvin Chain Model .................................................. 1 16

6.2.3 Aging Creep Based on Solidification Theory.............................................. .. 117

6.2.3.1 Qualitative Description ofAging ...................................................... .. 117

6.2.3.2 Micro-mechanics ofthe Creep Model ............................................... .. 118

6.2.3.3 Constitutive Relations .......................................................................... 119

6.2.3.4 Rate-Type Approximation ................................................................. .. 120

ix


6.3 Drying Creep Modeling and Mechanisms ............................................................ .. 121

6.3.1 General .......................................................................................................... .. 1216.32 Microcracking ............................................................................................... .. 122

6.3.3 Stress-induced Shrinkage ............................................................................. .. 1226.3.4 Formulation for Stress-induced Shrinkage .................................................. .. 123

6.3.5 Stress-Strain Relation for Microcracking .................................................... .. 125

6.4 Components and Sequence ofthe Analysis ............................................................ 126

6.5 Damage and Failure ofConcrete ............................................................................. 127

6.5.1 Basic Concepts.............................................................................................. .. 127

6.5.1.1 Damage Threshold ............................................................................. .. 128

6.5.1.2 Failure Criterion ................................................................................. .. 128

6.5.1.3 Evolution ofDamage ........................................................................... 129

CHAPTER 7ANALYSIS AND DISCUSSION OF BASIC CREEP TEST RESULTS ................... 133

7.1 Introduction ............................................................................................................ .. 133

7.2 Basic Creep Analysis ............................................................................................. .. 133

7.2.1 Review ofBasic Creep Model ..................................................................... .. 134

7.2.1.1 Important Comment on Flow Term................................................... .. 135

7.2.2 Identification ofModel Parameters .............................................................. .. 135

7.3 Incremental Approach............................................................................................ .. 136

7.3.1 Influence ofthe Flow Term on the Analysis ............................................... .. 137

7.3.2 Nonlinear Stress Factor ................................................................................ .. 138

7.3.3 Model Coefificients ....................................................................................... .. 139

7.3.4 Effective Volume Growth v(t)...................................................................... .. 140

7.4 Analysis Based on Principle of Superposition ...................................................... .. 141

7.4.1 Creep fimctions for Plain Concrete .............................................................. .. 143

7.4.2 Creep frmctions for Fiber Reinforced Concrete........................................... .. 144

7.4.3 Efiect ofWater-Cement Ratio...................................................................... .. 145


X


CHAPTER 8ANALYSIS AND DISCUSSION OF DRYING CREEP MECHANISMS ................ 157

8.1 Introduction ............................................................................................................ .. 157

8.2 A Technique to Separate the Pickett Efiect Mechanisms..................................... .. 157

8.2.1 Principal Assumptions .................................................................................. .. 158

8.2.2 Basic Concept of the Experiment................................................................. .. 158

8.2.3 Key Features ofthe Method and Analytical Procedures ............................. .. 159

8.3 Stress-Reduced Shrinkage ..................................................................................... .. 161

8.3.1 Influence of Stress on Restrained Shrinkage ............................................... .. 162

8.3.2 Influence ofFiber Reinforcement on Shrinkage Behavior under Load...... .. 163

8.4 Quantification ofMicrocrackingl Softening ........................................................ .. 163

8.4.1 Qualitative Analysis for Microcracking and Failure ................................... .. 1658.42 Stress-Strain Relation for Distributed Microcracking ................................. .. 166

8.4.3 Evolution ofMicrocracking ......................................................................... .. 168

8.5 Limitations of the Approach .................................................................................. .. 169

8.6 Significance of the Approach ................................................................................ .. 169

8.7 Validation of the Approach ................................................................................... .. 170

8.8 Damage-Based Analysis ofMicrocracking .......................................................... .. 171

8.8.1 Basic Damage Concepts ............................................................................... .. 171

8.8.2 Identification ofDamage Variables ............................................................. .. 172

82.2.1 Critical Damage Factor ...................................................................... .. 173

8.2.2.2 Damage Threshold ............................................................................. .. 173

8.2.2.3 Damage Strength Material Parameter S ............................................ .. 174

8.8.3 Quantitative Analysis for Microcracking and Failure ................................. .. 175


CHAPTER 9CONCLUSIONS AND RECOMMENDATIONS ......................................................... 186

9.1 Introduction ............................................................................................................ .. 186

9.2 Experimental Technique ........................................................................................ .. 186

9.3 Restrained Drying Concrete .................................................................................. .. 187

9.4 Sealed and Wet Cming Conditions ....................................................................... .. 188

xi


9.5 Basic Creep Behavior ................................................................................ ..

9.6 Drying Creep Mechanisms ........................................................................ ..

9.7 General Behavior at Early Age.................................................................. ..

9.8 Failure Analysis ......................................................................................... ..

APPENDIX AEXPERHVIENTAL RESULTS FOR RESTRAINED SHRINKAGE TESTSAPPENDIX BRESULTS FOR CONCRETE HUMIDITY MEASUREMENT .....................APPENDIX CANALYTICAL RESULTS FOR BASIC CREEP .............................................LIST OF REFERENCES......................................................................................VITA ........................................................................................................................

xii


Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

Table 4.1

Table 5.1

Table 7.1

Table 8.1

Table 8.2

Table 8.3

Table A-1

Table A-2

Table A-3

Table A-4

Table A-5

Table A-6

Table A-7

LIST OF TABLES

Concrete mix proportions (preliminary stage) ........................................... .. 44

Concrete mix proportions (final stage) ....................................................... .. 45

Aggregate properties ................................................................................... .. 46

28-day compressive suength and modulus ofelasticity ............................ .. 47

Test matrix for Phase I ................................................................................ .. 51

Test matrix for Phases H and HI ................................................................. .. 52Shrinkage stress and age at failure .............................................................. .. 61

Load profile applied on sealed and wet-cured concrete ............................. .. 90

Coefficients for linear and nonlinear models ofbasic creep .................... .. 139

Model parameters for stress-reduced shrinkage ....................................... .. 162

Parameters for strain softening of restrained drying concrete ................. .. 167

Parameters for microcracking evolution of restrained drying concrete..... 169

Restrained shrinkage results for plain concrete, w/c=0.5, sample #1. age at

drying =14 hours, RH = 50% .................................................................... .. 193Restrained shrinkage results for plain concrete, w/c=0.5, sample #2. age at

drying =14 hours, R1-I = 50% .................................................................... .. 193Restrained shrinkage results for steel fiber concrete, w/c=0.5, sample .=-*1,

age at drying=14 hours,RH=50% ......................................................... ..194

Restrained shrinkage results for steel fiber concrete, w/c=0.5, sample #2,

age at drying =14 hours, RH = 50% ......................................................... .. 194

Restrained shrinkage results for polypropylene fiber concrete, w/c=0 .5,

sample #1, age at drying =14 hours, RH = 50% ...................................... .. 195

Restrained shrinkage results for plain concrete, w/c=O.4, age at drying =15

hours, RH = 50% ....................................................................................... .. 195Restrained shrinkage results for steel fiber concrete, w/c=O.4, age at drying

=14 hours, RH = 50% ............................................................................... .. 196

...


Table A-8

Table A-9

Table A-10

Table A-11

Table A-12

Table A-13

Table A-14

Table A-15

Resuained shrinkage results for plain concrete, w/c=0.32, age at drying =14

hours, RH = 50% ....................................................................................... .. 196Resuained shrinkage results for steel fiber concrete, w/c=0.32, age at drying

=14 hours, RH = 50% ............................................................................... .. 197

Restrained shrinkage results for plain concrete, w/c=0.32, age at drying =14

hours, RH = 80% ....................................................................................... .. 197


hours, RH = 70% ....................................................................................... .. 198


hours, RH = 80% ....................................................................................... .. 198

Restrained shrinkage results for plain concrete, w/c=0.5, age at sealing =15

hours, sealed for 72 hours prior to drying at RH = 50% .......................... .. 199Restrained shrinkage results for steel fiber concrete, w/c=0.5, age at sealing

=15 hours, sealed for 72 hours prior to drying at RH = 50% ................... .. 199

Restrained shrinkage results for steel fiber concrete subjected to

drying/wetting cycle, w/c=0.5, age at drying =15 hours, RH = 50%, wetting

applied at age of 67 hours for 24 hours and then exposed to drying ....... .. 200

xiv


Figure 2-1

Figure 2-2

Figure 2-3

Figure 2-4

Figure 3-1

Figure 3-2

Figure 3-3

Figure 3-4

Figure 3-5

Figure 3-6

Figure 3-7

Figure 3-8

Figure 3-9

Figure 3-10

Figure 3-11

Figure 3-12

Figure 3-13

Figure 4-1

Figure 4-2

Figure 4-3

Figure 4-4

Figure 4-5

Figure 4-6

Figure 4-7

LIST OF FIGURES

Normalized tensile strength, compressive strength, and modulus of elasticity

vs. degee ofhydration ................................................................................ .. 34

Time dependent deformations in concrete subjected to sustain load......... .. 35

Schematic representation ofvarious models of C-S-H .............................. .. 36

Additional ftmctions G(t') and H(t,t_) for early age creep response shown

schematically ............................................................................................... .. 36

Companion specimens ................................................................................ .. 52

Experimental device showing restrained and fiee shrinkage samples ....... .. 53

Parts ofthe experimental setup ................................................................... .. 54

Schematic diagram ofthe test mechanism ................................................. .. 55

Aggregate gradation .................................................................................... .. 55

General view ofexperimental setup in the preliminary stage .................... .. 56

Effect of threshold on stress evolution ....................................................... .. 56

Free shrinkage and tensile creep of replicate samples with w/c=O.56 ....... .. 57

Shrinkage stress evolution with time of replicate samples ........................ .. 57

Shrinkage stress evolution with time of replicate samples w/c= 0.48 ....... .. 58

Stress-elastic strain diagrams for replicate samples w/c= 0.48 .................. .. 58

LVDT attachment method influences stress-strain evolution.................... .. 59

LVDT attachment method influences modulus ofelasticity ..................... .. 59

Shrinkage stress evolution ofdifferent plain concrete mixes .................... .. 77

Efiect ofsteel fiber reinforcement on shrinkage stress .............................. .. 77

Shrinkage stress evolution ofplain concrete under various

drying conditions ......................................................................................... .. 78

Free shrinkage strain for difierent plain concrete mixes ............................ .. 78

Typical temperature and humidity distribution .......................................... .. 79

Efiect offiber reinforcement on fiee shrinkage ......................................... .. 79

Efiect ofdrying condition on free shrinkage (W/c = 0.50) ......................... .. 80

XV


Figure 4-8

Figure 4-9

Figure 4-10

Figure 4-11

Figure 4-12

Figure 4-13

Figure 4-14

Figure 4-15

Figure 4-16

Figure 4-17

Figure 4-18

Figure 4-19

Figure 4-20

Figure 4-21

Figure 4-22

Figure 4-23

Figure 4-24

Figure 5-1

Figure 5-2Figure 5-3

Figure 5-4

Figure 5-5


Figure 5-8

Figure 5-9

Figure 5-10


Figure 5-13

Tensile creep for difierent plain concrete mixes ........................................ .. 80

Creep is proportional to fi'ee shrinkage (replicate samples)....................... .. 81

Creep/shrinkage ratio for difierent plain concrete mixes........................... .. 81

Efi‘ect of fiber reinforcement on tensile creep (W/c = 0.5) ......................... .. 82

Creep coefficient evo1u1:ion for various plain concrete mixes ................... .. 82

Shrinkage stress-elastic suain diagram for difierent plain concrete mixes . 83

General view ofhumidity measurement sample and device ..................... .. 83

Humidity profiles for NC-0.5 mix .............................................................. .. 84

Humidity profiles for concrete after 2 days ofdrying................................ .. 84

Efiect of initial cming on stress evolution ofplain concrete and FRC...... .. 85

Efiect of initial curing on fiee shrinkage ofplain concrete and FRC ........ .. 85

Efiect of initial curing on tensile creep ofplain concrete and FRC ........... .. 86

Shrinkage stress evolution ofFRC upon drying/wetting cycles ................ .. 86

Efiect of drying/wetting on free shrinkage and shrinkage

recovery ofFRC .......................................................................................... .. 87

Efiect ofdrying/wetting on tensile creep ofFRC ...................................... .. 87

Humidity profile upon drying/wetting cycle .............................................. .. 88

Evolution of splitting tensile strength (drying curing) .............................. .. 88

Stress profile applied on wet and sealed concrete samples ...................... .. 104

Free shrinkage of sealed concrete samples ............................................... .. 104

Free shrinkage of sealed and drying concrete .......................................... .. 105

Humidity profile in sealed concrete samples ............................................ .. 105

Free shrinkage and creep strains of replicate samples ............................. .. 106

Creep and shrinkage of sealed concrete with difierent w/c-ratios ........... .. 106

Free shrinkage and tensile creep of sealed FRC....................................... .. 107

Eflect ofage at sealing on fiee shrinkage and tensile creep .................... .. 107Stress -cumulative elastic strain diagrams at difierent curing conditions . 108

Eflect ofmoist curing on early age shrinkage (w/c=0.5) ........................... 108Effect ofmoist curing on early age shrinkage (w/c=0.4) ......................... .. 109

Stress-strain diagram of sealed and wet-cured concrete .......................... .. 109

Creep and shrinkage ofFRC tmder difierent curing conditions .............. .. 110

xvi


Figure 5-14

Figure 5-15

Figure 5-16

Figure 5-17

Figure 5-18

Figure 6-1

Figure 6-2

Figure 6-3

Figure 6-4

Figure 7-1

Figure 7-2

Figure 7-3

Figure 7-4

Figure 7-5

Figure 7-6

Figure 7-7

Figure 7-8

Figure 7-9

Figure 7-10

Figure 7-11

Figure 7-12

Figure 7-13

Figure 7-14

Figure 7-15

Figure 7-16

Figure 7-17

Figure 7-18

Figure 8-1

Figure 8-2

Figure 8-3

Figure 8-4

Creep and shrinkage ofplain concrete under difierent curing conditions. 110

Effect of fiber reinforcement on specific basic creep for NC-0.5 mix .... .. 111

Efi‘ect of fiber reinforcement on specific basic creep for NC-0.4 mix .... .. 111

Effect ofw/c-ratio on specific basic creep ofFRC .................................. .. 112

Efi'ect ofw/c-ratio on specific basic creep ofplain concrete ................... .. 112

Kelvin and Maxwell chain units ............................................................... .. 130

Solidification theory for basic creep ......................................................... .. 131

Strain softening curve................................................................................ .. 131

Damage evaluation from a uniaxial stress-strain diagram ....................... .. 132

Optimum fits and the flow term for plain concrete (w/c=0.4) ................. .. 148

Optimum fits and the flow term for plain concrete (w/c=0.5) ................. .. 148

Data fit ofbasic creep with and without stress nonlinearity .................... .. 149

Non-aging creep frmction obtained by fitting data for the NC-0.4 mix 149

Shift in efiective volmne fraction due to stress nonlinearity ................... .. 150

Efiect ofage on load bearing volume fraction growth ofFRC, w/c=0 .4 .. 150

Efi'ect of age on load bearing volume fiaction growth of FRC, w/c=0.5 .. 151

Effect of retardation times on the superposition-based analysis, w/c=0.4 151

Efi'ect of retardation times on the superposition-based analysis, w/c=0.5 152

Extracted creep functions at different ages at loading for NC-0.5 mix 152

Extracted creep functions at difierent ages at loading for NC-0.4 mix 153

Age dependency of the creep frmction for NC-0.5 mix ........................... .. 15 3

Age dependency of the creep function for NC-0.4 mix ........................... .. 154

Creep functions at different ages at loading for FRC (w/c=0.4).............. .. 154

Creep ftmctions at difierent ages at loading for FRC (w/c=0.5).............. .. 155

Age dependency ofthe creep function for FRC (w/c=0.4) ...................... .. 155

Age dependency ofthe creep ftmction for FRC (w/c=0.5) ...................... .. 156

Efiect of fiber reinforcement and w/c-ratio on creep function ................ .. 156

Stress-reduced shrinkage for plain concrete (w/c=0.5) ............................ .. 178

Stress-reduced shrinkage for fiber reinforced concrete (w/c=0.5)........... .. 178

Efiect oftensile stress on shrinkage (w/c=0.5) ........................................ .. 179

Components ofthe Pickett efiect (w/c=0.5) ............................................. .. 179

..


Figure 8-5

Figure 8-6

Figure 8-7

Figure 8-8

Figure 8-9

Figure 8-10

Figure 8-11

Figure 8-12

Figure 8-13

Figure 8- 14

Figure B-1

Figure B-2

Figure B-3

Figure B-4

Figure B-5

Figure B-6

Figure C-1

Figure C-2

Figure C-3

Figure C-4

Figure C-5

Figure C-6

Figure C-7

Figure C-8

Components ofthe Pickett efi'ect (w/c=0.4) ............................................. .. 180

Efi'ect ofmicrocracking on age at failure ofFRC samples (w/c=0.5) ..... .. 180

Typical stress-strain curves associated with microcracking (w/c=0.5) 181

Model for total creep ................................................................................. .. 182

Validation ofthe creep model for plain concrete (w/c=0.5) .................... .. 183

Validation ofthe creep model for FRC (w/c=0.5) ................................... .. 183

Crifical damage factors for plain and fiber reinforced concrete (w/c=0.5) 184

Damage threshold strain for plain and fiber reinforced

concrete (w/c=0.5)..................................................................................... .. 184

Damage evolution and failure ofplain concrete (w/c=0.5) ..................... .. 185

Damage evolution and failure ofFRC (w/c=0.5) ..................................... .. 185

Humidity profile ofHPC-0.32 mix, RH=50% ......................................... .. 202

Humidity profile for I-IPC-0.32 mix, RH=80% ......................................... . 202

Humidity fimctions ofNC-0.5 mix, RH=50% ......................................... .. 203Humidity profile ofNC-0.5 mix, RH=50% ............................................. .. 203Humidity profile ofNC-0.5 mix, RH=80% ............................................. .. 204Humidity profile ofNC-0.4 mix, RH=50% ............................................. .. 204

Incremental-based model for basic creep ofplain concrete (w/c=0.5) .... .. 206

Superposition-based model for basic creep ofplain concrete (w/c=0.5) .. 206

Incremental-based model for basic creep ofFRC (w/c=0.5) ................... .. 207

Superposition-based model for basic creep ofFRC (w/c=0.5) ................ .. 207

incremental-based model for basic creep ofplain concrete (w/c=0.4) .... .. 208

Superposition-based model for basic creep ofplain concrete (w/c=0.4) .. 208

Incremental-based model for basic creep ofFRC (w/c=0.4) ................... .. 209

Superposition-based model for basic creep ofFRC (w/c=0.4) .................. 209

...


GLOSSARY

Shrinkage Stress: Stress developed in the concrete sample by restraining its shrinkagedeformation

Drying Shrinkage: Deformation associated with drying ofconcrete

Autogenous Shrinkage: Deformation associated with intemal drying of concrete

Tensile Creep: Time dependent deformation of concrete under a sustained tensile load

Basic Creep: Creep ofconcrete when no shrinkage occurs

Drying Creep: The creep strain in excess to basic creep in specimens Lmdergoing drying

Total Creep: The summation of the basic creep and the drying creep

Creep Coeficient: Creep strain at any point in time divided by the elastic strain at thattime

Specific Creep: The creep strain per mit stress

Free Shrinkage: Shrinkage deformation when no extemal loads are applied on theconcrete specimen

Creep-Shrinkage Ratio: The ratio between the creep strain to the free shrinkage strain atany point in time

Stress-Reduced Shrinkage: Reduction in the shrinkage deformation when tensile load isapplied

Microcracking Strain: Strain associated with surface microcracking results from thegradient in drying ofthe concrete sample

Failure Stress: Stress at which the restrained concrete sample fails

Failure Strain: Summation ofelastic strains ofthe compensation cycles required tofracture the restrained concrete sample

Tensile Strength: Stress at failure in a direct tensile strength test

Damage: Degradation in the elastic stifiiess ofthe concrete material

Critical Damage Factor: A level ofdamage, which when reached, failure occurs suddenly

xix


CHAPTER 1

INTRODUCTION

1.1 Background

Concrete is generally unique among structural materials in that it interacts with its

environment undergoing unavoidable complex physical and chemical volume changes. The

process ofhydration and the molecular structure ofconcrete give certain characteristics to

this material such as aging, creep and shrinkage. These characteristics as a group are known

as time dependent deformation.

Early age deterioration of concrete is a persistent problem that arises because

concrete interacts with its environment and experiences complex physical and chemical

changes. Volume instability is detrimental to performance and durability of concrete

structures because structures are usually restrained. The induced stresses may cause

immediate cracking or linger as “residual stresses” that serve to limit capacity of the

concrete material. Such premature deterioration affects integrity, durability, and long-terrn

service life of concrete structures. This potential for damage depends on composition of

concrete, curing conditions, age and load condition.

Recent advances in rapid construction overlay techniques, high early strength

concrete technology, and new cement and admixture formulations have renewed concems

about volumetric stability ofconcrete. For example, High-performance concrete (I-IPC) and

fiber-reinforced concrete (FRC) have been introduced to meet the needs generated by the

continuous advancement in the technology ofaviation, transportation and other public

services; a new class ofplanes have entered the airways. Boeing for example, is currently

producing the new 777 plane. These planes are the first to use tr-idem wheel configurations

in the landing gear. The new landing gear configuration and large passenger capacity

produce wheel loads of 50,000 potmds that cause extremely high pavement stress due to

interaction of loads associated with the individual tires. The use of low w/c ratio,

superplasticizer, silica fume and fibers enables producing high perfonnance concrete with

mechanical properties adequate for the new loading. However, it aggravates the problem of

early age cracking due to autogenous shrinkage caused by the low w/c required for these

1


materials. Therefore, understanding the behavior at early age (first days afier placement) is

very important for the development ofthese novel materials.

Early days after casting is not only important for I-IPC, it also considers one ofthe

most critical periods in the life ofall types ofconcrete. The concrete at this age tmdergoes

rapid complex volume changes such as autogenous shrinkage, drying shrinkage and

thermal deformation that lead to a rapid build up of tensile stresses in the material. At the

same time, strength and stiffness of the material is relatively low, but increasing as

hydration proceeds. There is a competition inside the material between the development of

tensile stress and the development of strength— both ofwhich are evolving with time. At

stake in this competition is the potential for premature deterioration. The research

commrmity has realized the impact of early age damage on various concrete structures

particularly in flat structures such as pavements, slabs on grade, and parking garages. Early

age deterioration has become a hot issue at almost every conference on concrete. In fact,

entire intemational conferences have been devoted to early issues, [e.g. Intemational

RELEM Symposium” Thermal Cracking in Concrete at Early Age, “ 1994].

Tensile creep and shrinkage are two major mechanisms to consider in the

assessment of damage and performance. Shrinkage of restrained concrete components

causes stresses in the material whereas tensile creep counteracts the shrinkage as a stress

relaxing mechanism and reliefpart of the induced stress. Therefore, analysis of cracking

based solely on a motmt ofshrinkage is erroneous. Both creep and shrinkage are to be

considered for accurate stress analysis and crack prediction.

It has been long recognized that the role of tensile creep is of great importance

when the possibility ofcracking is to be considered. Shrinkage cracking has always been a

major concem for concrete technologists and engineers especially in flat structures such as

pavement, parking garages and slabs. This concem is usually addressed by specifying

conservative joint spacing. However, there is a high economic incentive to reduce the

number ofjoints in flat structures particularly highway and airport pavement without

compromising serviceability, durability and structural capacity ofthe structure due to

cracking. The advancement in concrete and construction technology has pushed the

envelope ofmaterial performance. For example, a 200 feet long by 75 feet wide continuous

rtmway slab without joints (or cracks) was made possible by using fiber concrete at the

2


Rockford, IL airport in 1993. The slab length is almost 10 times longer than possible with

conventional plain concrete, and it is an inspiring demonstration ofone material

performance for reducing joints. FAA is moving toward reducing number ofjoints in

airport pavement without compromising serviceability, durability and structural capacity of

the pavement due to cracking. The potential for early age shrinkage cracking increases

because shrinkage stresses are proportional to the length ofjoint spacing. Therefore, the

concem of cracking becomes a pressing factor toward tmderstanding tensile creep,

shrinkage and their interaction at early age because the key to prevention premature

cracking is to keep the built-up stress lower than the tensile strength ofconcrete at every

point in time. The role of tensile creep is extremely important in this regard.

In view ofconcrete microstructure, creep and shrinkage are not independent

phenomena. They are inter-related and afiected by a common process at the level of

microstructure. Although this interaction has been researched for many years, the focus has

been exclusively limited to compressive loading in matured concrete. Past research has

almost igrored tensile creep behavior at early age. Not only is experimental data on tensile

creep not available for early age, but also the current analytical models for stress analysis

and prediction of shrinkage cracking utilize creep formulas derived for compressive creep,

even though shrinkage involves tensile loading. The models assume similar creep behavior

in both compression and tension. This assumption, although inaccurate, is understandable

given the lack of data and models for tensile creep. Even ifthe creep mechanism is

assumed to be similar in both compression and tension, their interaction with shrinkage is

difi'erent because compressive creep adds to shrinkage while tensile creep works against it.

This research focused on early age shrinkage, tensile creep and their interaction for

fiber and plain concrete to characterize the behavior and provide experimental data that

help in establishing a model consistent with material behavior.

1.2 Research Objectives

The main objective ofthis research is to provide early age behavioral information

on fibrous and plain concrete that exposed to drying under restrained conditions. The

restrained condition simulates evolution ofcompressive and tensile stresses in real

3


structures due to thermal and shrinkage induced deformations. Therefore, the shrinkage

characteristics are required to assess potential for cracking and to perform correct stress

analysis. The subsequent stress development causes the material to creep that in tum plays

an important role as a stress relaxing mechanism. This interaction between shrinkage,

thermal and tensile creep is the main focus ofthis research. Complexity ofthe interaction is

augmented in the first days after casting due to concomitant physical and chemical changes

in the microstructure of concrete. These characteristics require special tesfing techniques to

be evaluated, and hence, one of the objectives in this research is to develop reliable testing

techniques and procedures that can be used to generate accurate and reproducible data on

tensile creep, shrinkage and their interaction at early age.

In addition to behavioral understanding, characterization ofvarious properties such

as tensile creep, shrinkage, shrinkage stress, and thermal strain is intended. Experimental

evaluation and separation of each property is therefore required. The stresses in the

experiment are self-generated by restraining shrinkage and these stresses are due to

combined efiect of creep and shrinkage, in other words, they are relaxed stresses. The

research put special emphasis on tensile creep and its various mechanisms. Basic tensile

creep and the effect of concurrent drying forms the bulk part of this research, the ptupose

ofwhich, is to characterize the role of tensile creep in relaxing stresses, particularly when

the concrete is subjected to high stresses that lead to failure. The efiect ofw/c ratio, fiber

reinforcement, and curing condition on these properties are investigated.

Formulation ofanalytical techniques for creep-shrinkage interaction based on

concrete micromechanics, established facts about concrete microstructure, and the

experimental data is another objective. The analytical technique provides means consistent

with material behavior, to tmderstand the creep and its interaction with shrinkage at early

age. It can be used in models existing in literature for stress analysis and prediction of

shrinkage cracking.

1.3 Scope of Work

A tmiaxial restrained test technique was utilized to generate basic experimental data

on early age shrinkage and creep. The test simulates evolution ofstress in real structures,

4


and most importantly, it quantifies shrinkage, tensile creep, shrinkage stress and elastic

moduli ofconcrete. Separation ofcreep fiom shrinkage was made possible by testing and

comparing two companion samples, one was restrained and the other was fi'ee. Stresses in

the restrained sample were self-induced by restraining shrinkage, which, with time,

increased and caused stress development that led to fiacture. Tensile creep tmder the

increased, self-induced stresses was evaluated. This condition is ofpractical interest for two

reasons. First, the load causing the creep is induced by shrinkage and the rate of shrinkagedetermines the level of stress. Hence, interaction between creep and shrinkage is more

pronounced. Second, the high stress promotes microcracking and non-linearity ofcreep

which are important features when cracking is to be evaluated. The testing system is one of

the most promising ideas in the field of restrained shrinkage and cracking at early age.

Since the testing technique is not a standard or conventional test, reliability of the collected

data on shrinkage and tensile creep must be ensured. Therefore, significant efibrts were

devoted in this research to develop and design a reliable experiment in terms of accuracy,

reproducibility and practicality.

To evaluate the efiect of concurrent drying on tensile creep, a separate test for basic

creep (no drying) was conducted. The basic creep test was conducted using the same

experimental setup by applying the load obtained in drying test onto sealed samples.

Sealing the sample however, suppresses extemal drying but may not eliminate intemal

drying which can not be ignored at early age, particularly for the low w/c-ratio mixes.

Therefore, a separate set ofbasic creep tests (similar to those on sealed samples) was

performed on samples subjected to continuous moist condition to minimize intemal drying

and the subsequent interaction with basic tensile creep. The three sets of tests under drying,

sealing, and moist curing conditions provide insight into the creep-shrinkage interaction

and enable quantification of the difierent tensile creep components.

Along with the uniaxial restrained test, the relative humidity and temperature ofconcrete and their gradients across the test specimen were measured in order to model their

effect on the creep-shrinkage interaction.

Normal and high performance concrete were tested to characterize their behavior.

Material parameters ofpractical interest such as water-cement ratio and the addition of

steel and polypropylene fibers were considered to study their influence on the tensile creep,

5


shrinkage and their interaction at early age. Literature review ofexisting mathematical

models and theories for the creep of concrete were explored. The best models that suit early

age behavior were chosen. Analytical techniques to model difierent components oftensile

creep and its interaction with shrinkage were developed accordingly.

6


CHAPTER 2

LITERATURE REVIEW

2.1 General

Early age cracking ofconcrete has been a persistent problem, and recent

development in construction practice has heightened attention on the issue. It has received

considerable attention, since l930’s for the construction of dams (ACI Committee 207).

Since then, tangible amount of research has been performed to tmderstand the nature of the

problem yet, its complexities are not fully tmderstood. Fmthermore, recent advances in

rapid construction, high early strength concrete technology and new cement and admixtures

formulation have renewed worldwide concems about the early age cracking (e.g. RILEM

1994). This literature study focuses on the driving mechanisms for cracking, relevant

material properties, and test techniques. Relevant material models are also discussed

particularly those pertaining to creep behavior and its interaction with shrinkage.

2.2 Driving Mechanisms for Cracking

Concrete in the hardening phase (afier setting) will generate stresses if volume

changes are restrained. Consequently, concrete may exhibit early age cracldng if the

stresses exceed tensile strength of the material. Volumetric instability ofconcrete has been

reported in literature as the main cause ofearly age cracking (e.g. ACI Committee 224,

Rolling (1986, 1993)). In the very early age (hydration period), there are primarily two

active mechanisms producing volume changes; autogenous deformation and thermal

dilation. At later stage when the concrete is exposed to drying, drying shrinkage acts as a

third active mechanism that produces tangible volume change. The following sections

discuss particulars of these mechanisms.

2.2.1 Autogenous Deformation (AD)

The autogenous volume change has been given a variety of labels in the Literature,

some ofwhich include autogenous shrinkage (Ziegeldorfet al., 1982), chemical shrinkage

7


(Tazawa and Kasai, 1995), autogenous deformation (Mejlhede and Freiesleben, 1996) and

selfdesiccation shrinkage (Paillere et al., 1989). In detailed analysis, it may be necessary to

further define and classify each term for consistency. However, for the purpose ofthe

current work, the term autogenous deformation is adopted. It is defined, as all the extemal

volume change that takes place regardless ofthe mechanism provided there is no exchange

ofmoisture with the smrotmding environment (constant mass). The above definition ofAD

is in accordance with the proposal given in the intemational workshop on AD held in

Japan, (Hammer et al., 1998) and adopted in recent work in this field (Bjcpntegaard, 1999).

The autogenous deformation has been considered of minor importance in traditional

concrete and has not been distinguished clearly fi'om the shrinkage caused by drying except

possibly for mass concrete (M.indess and Young, 1981, and Neville, 1996). However, these

phenomena seem to be an important cause ofthe observed cracking in modem high

strength and high performance concrete structures (Paillere et al., 1989, and Tazawa and

Miyazawa, 1993). It has been also reported that the autogenous deformation becomes equal

to the drying shrinkage for concrete with a very low w/c-ratio. For instance, Tazawa and

Miyazawa (1995) reported autogenous shrinkage that composed 40 % ofthe total drying

shrinkage magnitude at w/c-ratio of0.4, 50 % at w/c-ratio of 0.3, and 100% at w/c-ratio of

0.17.

Autogenous deformation is mainly generated during the first day, which increases

the risk of cracking (Markku and Erika, 1997). It may reach 500 — 800 microstrain during

the first week. The intemal ingredients and mix composition have the most significant

influence on the autogenous deformation as the phenomena itself results from the physical

and chemical changes afiiliated with the hydration ofcement particles. The exact

breakdowns ofthe influencing factors on the deformation magnitude are still disputed

(Markku and Erika, 1997). However, the w/c-ratio and silica fume has been found crucial

factors that affect the autogenous deformation. Lowering the w/c-ratio and/or increased the

dosage of silica firme has been fotmd to provide faster development ofAD. This is mainly

due to the denser cement microstructure and more refined pore structure that results as a

consequence of lowering the w/c-ratio and/or adding silica firme (Mejlede and Freiesleben,

1996, and Tazawa and Miyazawa, 1997). High capillary tension and low RH in the pore

structure is therefore expected.

8


The underlying driving force to the occurrence ofAD is chemical shrinkage.

Chemical shrinkage develops continuously from the point ofcement-water contact as a

result ofthe loss ofvolume due to hydration (volume ofreactions products is smaller than

the volume ofthe reactants). Chemical shrinkage has been measured in literature by

measuring the water suction ofwater-cured cement paste samples “Dilatometry method”

and by weight changes “Gravimetry method” (Tazawa and Kasai, 1995, and Geiker, 1983).

Powers (1948) found that the chemical shrinkage could be approximated by assuming that

the reacting water looses 25 % of its volume. Ardoullie and Henrix (1997) have measured

the volumetric AD offiesh mortar using the condom method. The condom method was

developed in Norway, and it measures the volume change of cement paste contained in a

rubber membrane, which is submerged into a water bath at constant temperature. The

volume change is recorded as the change in the buoyancy. Their results have shown that

the chemical shrinkage is equal to the volumetric AD as long as the paste is liquid. Once a

certain rigidity of the system ofhydrating cement paste has developed, the measured AD is

much smaller than the chemical shrinkage because solid structure start to resist the

contraction forces set up by the chemical shrinkage. Hence, arotmd the time of setting, the

AD changes character, a solid skeleton is formed allowing empty pores to form. The

consequence ofthis is development of intemal water menisci in the capillary pore system

which means increase in capillary tension in the pore water and a lowering of the relative

humidity (RH) in the empty part of the pores. From that point on, the stresses developed

due to self-desiccation drive the autogenous deformation. The period around this point is

also believed to be sensitive in terms of cracking since the paste (or concrete) is able to pick

up stresses but has very low capacity to withstand them. The difierence between the

chemical shrinkage and the AD is because major part of chemical shrinkage is tinned into

intrinsic voids (self-desiccation).

AD in the first day can be in the form of expansion, particularly for w/c-ratio higher

than 0.4. The origin ofthis expansion is not fully tmderstood. Formation of ettringite has

been proposed as a possible cause of early age expansion but this has not been verified by

special experiments. Recently Bjqantegaard (1999) has demonstrated the reabsorption of

bleed water as a possible cause for this expansion. The above discussion suggests that the

autogenous deformation is a complex phenomena yet, one ofthe important driving

9


mechanisms for cracking of restrained concrete particularly at early age, and it should be

carefully considered when the sensitivity for cracking is investigated.

2.2.2 Thermal Dilation (TD)

Thermal stresses at early age have been a major cause for early age cracking of

concrete since the beginning ofthis century. The importance oftemperature effects in

hardening concrete has inspired extensive research worldwide in recent years. In 1989

RILEM has established a Technical Committee TC 119, on “The Avoidance ofThermal

Cracking in Concrete at Early Age”. The committee has organized intemational

symposiums to firrther expand the existing knowledge ofthe problem (RJLEM, 1994 and

RILEM, 1998). Theoretical and experimental studies and worldwide experience were

discussed in these symposiums. The key parameter that converts the temperature change

into suain in concrete is the thermal dilation coefficient (TDC).

Thermal dilation coefficient (TDC) ofmanned cement paste and concrete has been

extensively investigated in literature. The general agreement on the TDC is that it depends

on the moisture state of the pore system (Neville, 1996). Several researchers haveinvestigated the topic in pure cement paste with the conclusion that fully samrated pore

system and empty (dried) pore system give much lower TDC values i.e. around 10-l2xl0'°;'

°C, than a partly saturated pore system, with a maximum values in the range of 18-25x10*"’

°C. The high value in partly saturated pore system is believed to be due to some kind of

hygrothermal effect (redistribution ofpore water and change in capillary tension) which

add to the true thermal movement (Power and Brownyard, 1947, Wittmann and Lukas,

1974, and Neville, 1996). The TDC of concrete, on the other hand, is very dependent on the

type of aggregate (which constitutes 65-75% ofthe concrete volume) used in the mix since

the TDC ofdifierent minerals are found to vary over a wide range. Limestone aggregate

has been found to have a very low TDC (down to 1x10*5/ °C ) (Neville, 1996). Measuring

the TDC of cement paste and concrete have sometimes been observed to be complicated

because of so-called “ delayed deformations” which is caused by a temperature induced

shrinkage and swelling. The delayed deformations are probably a relatively slow

redistribution ofwater which state has come out ofequilibrium after a temperature change.

(Wittrnann and Lukas, 1974).

10


The amotmt ofwork reported in literature on the TDC ofyotmg concrete is quite

limited and hence, no conclusive behavior of the TDC ofyoung concrete can be given

today. The general finding is that the TDC starts at very high value (20xl06/ °C ) and drops

significantly during setting; i.e. from a few hours and up to 12-14 hours (ACI Committee

517, RILEM, 1998, and Miao et al., 1993). This feature, in the fi'esh state, has been

attributed to the dominance of water phase that has high TDC as compared to solids. When

skeleton is formed, solid behavior can be expected with a much lower TDC. The

development of the TDC fi'om setting and further on (up to 1-2 weeks) is even more

uncertain since very few and also contradictory results have been reported. For example,

Mitchell et al. (1998) tested the TDC ofnormal strength, medium strength and high

strength concrete at early ages (in the first 36 hours). Their results have indicated TDC

values that are relatively independent of age and typically in the order of9.5xl0'6/ °C.

Similar conclusions were reported by other researchers (LaPlante and Boulay, 1994, and

Miao et al., 1993). TDC values that are increasing with time were also reported by

Wittmann and Lukas (1974) and even decreasing TDC values with time was reported

(Emborg, 1989) with no systematic relation to curing conditions or concrete quality.

2.2.3 Drying Shrinkage (DS)

Drying shrinkage (DS) ofconcrete is defined as the time dependent deformation

due to loss of water at constant temperature and relative humidity (RH). It is a

characteristic property ofportland cement paste and concrete. Extensive research has been

conducted in literature to characterize the drying shrinkage of concrete in terms of

mechanisms and influencing factors. The results were summarized by several authors

(Bazant and Wittrnann, 1982, Mindess and Yotmg, 1981 and Neville, 1996). The four most

prominent shrinkage mechanisms that have been proposed in literature are surface fiee

energy, capillary tension, movement of interlayer water, and disjoining pressure. These

mechanisms are discussed and summarized by Young et al. (chapter 1, physical

mechanisms and their mathematical description, in Bazant, 1988). However, mechanisms

ofreversible and irreversible shrinkage behavior are not quite understood. It has been

indicated that irreversibility of shrinkage occurs only during the first drying and that

shrinkage on subsequent wetting and drying cycles are essentially reversible (Mindess and

ll


Yoimg, 1981). It is generally perceived that more than one mechanism is involved. Hansen,

(1987) have identified two distinctive shrinkage mechanisms upon first drying. They are

the Gibbs-Bangham (surface free energy) and the capillary tension mechanisms, ofwhich

Gibbs-Bangham is the major component offirst drying shrinkage. Gibbs-Bangham isactive between 100% and 0% of relative humidity whereas, the capillary stress mechanism

is active in the RH range above 25%. The surface fi'ee energy stress-induced mechanism

forms 67 % and 85 % ofthe shrinkage measured by Hansen for cement paste with w/c-ratio

of 0.6 and 0.4, respectively. He also calculated the “true” Gibbs-Bangham shrinkage using

the elastic modulus ofthe hydration product and f0lIl1d it to be 33 %. The rest of

deformation, as per Hansen seems to be due to decrease in interlayer spacing, which is not

entirely a reversible mechanism in concrete. This is probably explaining the significant

irreversible component of first drying shrinkage, which has also been reported by other

researchers (Helmuth and Turk, 1967). Therefore, the first drying shrinkage is ofparticular

importance especially for restrained concrete subjected to drying at early age. It influences

the stress generation and the residual stresses in restrained concrete.

The extent of shrinkage depends on many factors, including the properties of the

material, temperature and relative humidity of the environment, the age when concrete is

subjected to drying, and the size of the structure (Neville, 1996). The w/c-ratio of the mix

and the aggregate content are the most influenced factors on concrete shrinkage. The w/c-

ratio determines the extent of shrinkage of the cement paste; shrinkage is larger the higher

the w/c-ratio. The aggregate restrains the amount of shrinkage that can actually be realized.

The drying shrinkage of concrete at can be estimated fiom that ofcement paste e P having

the same w/c-ratio and degree ofhydration by the following formula (Pickett, 1956)

at =e,(l—V,)" 2.1

where Va is the aggregate content and n varies between 1.2 and 1.7. The drying shrinkage

ofnormal concrete is therefore much smaller than the drying shrinkage ofthe paste because

ofthe restraining efi'ect provided by the aggregates. It is typically between 10% to 20 % of

the paste shrinkage. Drying shrinkage is clearly a major cause ofvolume change ofconcrete, which influences the stress generation and cracking of restrained structures. The

12


importance ofdrying shrinkage can be clearly perceived in pavements and slabs on grade

as will be discussed in the following section

2.2.3.1 Influence of Shrinkage on Pavement

The risk of shrinkage cracking is more pronounced in flat structures such as

pavements and slabs on grades. Inadequate allowances for effects ofdrying shrinkage in

concrete design and construction can lead to cracking and warping ofpavement. The most

obvious example is the necessity ofproviding shrinkage control joints in pavements and

slabs on grade. The joint spacing highly influences the slab curling and the suess

development (Rolling, 1986, 1993). Warping of slabs results from differential shrinkage

between the top and the bottom concrete layers. Curling stresses are normally viewed as a

result of temperature gradient through the slab. However, difl'erential shrinkage can also

cause warping particularly at early age. The curl stress can be calculated by the following

equation (Westergaard and Bradbury, 1926,1938)

0' = EaAr 2.23(1 - #1‘ )

where 0' is the curl stress; c, ,c, are curl stress coefficients that depend on slab dimensions

and 1'3diI.B of relative stiffness; a is the coefficient ofthermal dilation; E is the elastic

modulus; p is the Poisson’s ratio and Ar is the maximum temperature difference between

the top and bottom of the slab.

Warping stresses that are caused by shrinkage gradient through the slab can be

calculated using the same concept of Westergaard for temperature if the shrinkage gradient

is known. Shrinkage strain of lab and full-size concrete slabs has been measured in the

literature. For example, Nagataki (1970) has measured shrinkage strain in pavement and

calculated shrinkage stresses based on the distribution ofstrains. He indicated that the

stresses due to restraint ofwarping are more important than those induced due to restraint

of imiform movement ofthe slab by friction. The study also indicated that the efiect of

shrinkage is not small and must be considered in the design ofpavement for thermal cycles.

However, the traditional practices in pavement thickness design is to neglect the warping

stresses due to shrinkage gradient (Huang, 1993). The philosophy that govems the design

as per Yoder and Witczak (1975) states that “joints and steel are used to relieve and/or take

l3


care ofwarping stresses, and the design is then based upon load alone when considering

thickness”.

The above discussion indicates the importance of shrinkage on determining joint

spacing in concrete pavement and the need to include the shrinkage in the stress analysis

and design ofpavement. This influence is more critical at early age because a combination

ofhigh rate of shrinkage and low tensile strength ofconcrete often exits.

2.2.3.2 influence of Shrinkage on Material Performance

Drying of concrete is govemed by a nonlinear diffusion ofmoisture with coefficient

ofdiffusivity depending on pore humidity, concrete maturity, and temperature (Bazant and

Najjar, 1971). Gradient ofmoisture and the associated shrinkage in drying concrete is

therefore inevitable. Surface cracking occurs when the induced tensile stress in the outer

zones exceeds tensile strength of concrete. The characteristics ofsurface cracking are

difierent from those of continuous cracking and fracture. The microcracking density is

quite low (Hwang and Young, 1984) and the cracking produced by drying are more likely

fine, densely distributed, discontinuous and can be appropriately modeled as tensilenonlinearity with strain softening as shown by Bazant and Rafishol (1982).

Although the drying microcracking are fine and discontinuous, they profoundly

influence the material performance, particularly at early age. For example, the flexural

strength or modulus of rupture of concrete specimens with no shrinkage cracks was found

to be more than twice that with dry shrinkage cracks (Planas and Elices, 1993). The first

crack strength and the efiective modulus ofhigh performance fiber concrete at early age

were significantly influenced by surface microcracking as shown by Lim et al. (1999).

Planas and Elices (1992) have also shown significant influence ofthe shrinkage stress on

the size efi'ect in concrete, which plays a paramotmt role in the interpretation of laboratory

experiments and in their extrapolation to full-scale structures. Total time dependent

deformation is also influenced by the surface cracking (Wittrnann and Roelfstra, 1980, and

Alvaredo and Wittmann, 1993).

The above discussion shows the importance ofrestrained shrinkage ofconcrete. Its

impact is not necessarily a failure in the form ofcon1:inuous cracldng, but it also changes

the mechanical behavior by the finely distributed microcracking. Therefore,

14


characterization of restrained shrinkage is essential to understand and to correctly predict

the material performance particularly at early age.

2.3 Restrained Test Methods and Stress Measurement

The cracking tendency and ability ofmaterial to resist shrinkage cracking can only

be judged on the basis of restrained shrinkage test. There is no standard method for testing

restrained shrinkage of concrete. However, several methods have been tried and reported in

literature. Many researchers have used concrete ring specimens cast around a rigid steel

ring. The steel ring provides restraint to the concrete when it shrinks, tensile stresses are

induced, and cracking may occur. This method has been primarily used to investigate

concrete cracking and the effectiveness of different types and volume fiactions of fibers in

controlling cracking of concrete and mortars (Grzybowski and Shah, 1990, Swamy and

Stavrides, 1979, Malmberg and Skarendahl, 1978, Sarigaphuti et al., 1993, and Krenchel

and Shah, 1987). Calculation of tensile stresses is conceptually possible with this test and

attempts to calculate stresses for shrinkage crack prediction have been pursued by

Grzybowski and Shah (1990, 1989). However, the stress analysis was based on theory of

elasticity whereas concrete is inelastic particularly at early age. A modified ring test in

which a concrete ring is cast arormd a Perspex core having a high coefficient ofexpansion

has been also used to provide cracking sensitivity within a short time (Kovler et al., 1993).

Raising the temperature of the core material increases the stress in concrete ring. This test

provides an efiective way to get useful data on cracking within few days. However, this test

does not provide actual stress in the shrinking material and does not allow relaxation of

stress due to creep. Nonetheless, it could be considered as a qualitative test that serves to

compare difierent formulations by determining the time ofcrack appearance and the width

ofcrack.

Doubly restrained plate specimens have been also used to determine cracking

potential for concrete subjected to drying conditions (Kraai, 1985). The specimen is

restrained at its perimeter by means of stirrups attached to a rigid steel frame. The primary

difficulty with this test is to determine the extent of restraint. Complex distribution of stress

at the restrained ends causes difficulties in stress analysis. The shrinkage stress can not be

15


calculated because it is dependent upon the geometry of specimen. To avoid these

difficulties, researchers have used uniaxial shrinkage tests.

Uniaxial restrained shrinkage tests have been performed in difierent ways. One

way is by transferring tensile stresses through an epoxy interface between concrete

specimen and pre-compressed steel box (Ong and Paramsivam, 1989). Another way is by

gripping specimen with flared ends in a rigid frame (Paillere et al., 1989). Linear specimen

that is anchored at both ends was also used in literature (Banthia et al., 1993). In these tests

shrinkage stress can be measured. The idea ofuniaxial restrained beam test has been

originally developed in German (Cracking frame) back in 1960s for thermal stress

measurement. A concrete specimen is connected to a restraining steel frame by increasing

the cross section at both ends in steel “crossheads”. The restraining force was calculated by

using strain gages fixed to the surrounding steel frame. The cracking frame provides high

but unknown degree of restraint. The frame was improved to provide 100% restraint by

controlling the movement ofthe crossheads in 1980s. The new frame has been called

"Temperature-Stress Testing Machine”. Frill restraint is achieved by computer controlled

step motor which moves one of the crossheads in order to compensate for any length

change of the specimen. Details of these thermal test devices are described in

Springenschrnid et al. (1995).

Many researchers have exploited the idea of a test frame with adjustable crossheads

and used it for early age restrained shrinkage. For example, Bloom and Bentur (1994) have

developed a uniaxial restrained shrinkage test. The system allows testing of concrete at

early age using a specimen laid in a horizontal position and gripped at both ends. One of

the grips is fixed and the other is movable. The movement of the free grip is monitored by a

displacement gage and periodically recovered by applying tensile load to the specimen.

Thus, stresses imder fully restrained conditions can be measured. Kovler (1994) has

developed similar system with a closed-loop computer control. Twin specimens are used;

one is restrained and the other is free to shrink. A variety ofmechanical properties can be

obtained, and more important is that, comparison of results from the two specimens allows

for quantification ofcreep as a relaxation mechanism. This method has the merit of

measuring creep strain in addition to shrinkage strains and stresses.

16


Another experimental technique to assess the cracking potential of cement-base

materials when used as a bonded overlay was developed by Banthia et al (1996). The

system provides resuaining to shrinkage at the base ofthe specimen by natural bonding to a

rough pre-cast concrete substrate. This system provides a more realistic restraint to bonded

overlays. Although crack assessment is possible with this test, it does not provide any

quantitative data about shrinkage stresses.

The above discussion described a variety oftesting systems that allow the

measurement of stresses and assessment ofthe potential for cracking at early age. In such

restraining laboratory tests the overall behavior of the concrete can only be investigated.

They are suitable tools to optimize the concrete mix as to a high cracking resistance. The

experimental data can also be as valuable information for checking theoretical models.

Thus the models may be calibrated for concrete qualities, cement type, admixtures etc.

2.4 Mechanical Properties

The accuracy of stress analysis of restrained shrinkage depends primarily on how

the required mechanical properties are described. The key mechanical properties requiredfor the stress analysis at early age are modulus of elasticity, tensile strength and the

viscoelastic behavior ofthe material. These properties are rapidly changing at early age

especially when the concrete changes from a liquid state to a solid state. Therefore, the

development of these properties is extremely important at early age. For instance, the E-

modulus reaches measurable values around the time of setting and any length change in the

concrete afterward becomes stress inducing if the movement is restraint. Bjrpntegaard

(1999) has shown that stresses start to develop as early as 7 hours for restrained concrete

with w/c-ratio of0.4. Laube (1990) foimd that for concrete with w/c-ratio of0.58, the

degree ofhydration was around 20 % when the concrete started to achieve mechanical

properties (typically arormd 8-10 hours). He formd that the E-modulus develops relatively

fast compared to the tensile strength which illustrates the crack sensitivity ofyormg

concrete-an early build-up of stresses is possible with a low capacity to withstand them.Figure 2-1 depicted the relationship between mechanical properties and degree ofhydration

as reported in Gutsch and Rostasy (1995). It has been shown that the concrete has the

lowest tensile strain capacity in these early hours (Kasai et al., 1974).

17


Early age tensile strength has not been examined to the same extent as the

compressive strength. Several investigations report test results and theoretical models for

the tensile strength e.g. Kasai (1974) and Khan et al. (1996). It has been seen for many of

the tests that the tensile strength at early age tends to grow faster than the compressive

strength. As uniaxial tensile tests are complicated to carry out, other methods are used to

determine the tensile strength by relating it to the splitting, flexural and compressive

strengths. Several models are available in literature and good survey for these models are

available in RILEM (1998). However, a high scatter between these relations has been

observed and one must be therefore careful when using formulas for tensile strength gain

fotuid in literature and codes. The expression must be calibrated to actual concrete mixtures

RILEM (1998).A number of test results compiled by Byfors (1980) has shown that the E-modulus

of young concrete grows more rapidly than the compressive strength. It has also shown that

the stress-strain relation at early ages marks nonlinear shape even at low stress levels.

Further, it has shown that the E-modulus determined at lower rate of loading is lower than

the E-modulus determined by means ofdynamic testing due to creep phenomenon in the

tests, an effect which probably is very strong at early ages. Many expressions relating the

E-modulus to compressive strength is available in literature, (e.g. the AC1-318-89

expression, E, = 4730,/I which has also shown by Oluoktm et al. (1991) to besatisfactory for yoimg concrete). Good survey ofsome ofthe expressions is given in

RILEM (1998). A multiphase model for concrete has also been developed to describe the

stifiiess fonnation of concrete and has been verified against tests (Paulini and Gratl, 1995).

The most important parameter in the early age stress analysis and crack tendency

evaluation is the viscoelastic behavior. The validity and reliability of such analysis depends

mainly on how well the viscoelastic model used describes the real behavior of the young

concrete. In engineering practices, creep is mainly used to denote the time dependent

deformation under load. It relaxes part of the stress induced and hence influences the time

and tendency for cracking. Viscoelastic behavior for young and hardened concrete will bediscussed in the next section. However, the rapid change in concrete properties at early ageand the uncertainty of the existing expression that describes these properties, require actual

18


stress measurement of restrained concrete to calibrate the various models available in

literature. The experimental part ofthis study attempts to provide some data for this matter.

2.5 Creep of Concrete at Early Age

2.5.1 General Definitions

Creep is generally defined as the total strain in a loaded specimen minus the initial

elastic strain and the shrinkage in an unloaded companion specimen subjected to a similar

environment. This definition assumes that creep and shrinkage are phenomena which do

not interact, and hence the total strain can be obtained by summing the elastic, the creep,

and shrinkage strains (shrinkage and creep are additive). Although, this assumption has

been generally accepted, some researchers have found it to underestimate the total strain

(see Bazant, 1988). In the literature, creep is commonly divided into two components: basic

creep and drying creep (see Neville, 1996). Basic creep is defined as the creep tmder

conditions when concrete is loaded in sealed condition (no moisture exchange with the

environment). Drying creep (which is sometimes also referred to as Pickett efiect) is the

additional creep in excess of basic creep when concrete is allowed to dry while under load.

Accordingly, the total creep is the sum of the basic creep and drying creep, although this

distinction is not always made. Total creep is assumed in the compliance firnction. Figure

2-2 shows schematically the terms and definitions involved. Only small proportion of creep

strain is reversible upon unloading ofconcrete. This creep recovery depends strongly on

load duration, temperature, and relative humidity (Mindess and Young, 1981).

2.5.2 Availability of Experimental Data

Extensive research has been conducted to study the phenomena of creep in

hardened concrete. These investigations have been summarized by Neville et al. (1983),

Bazant and Wittrnann (1982), ACI committee 209 (1992), and Bazant (1988). However,

when confining the scope to behavior at early ages (< 5 days after casting) and in

particular, at very early ages (< 1-2 days after casting), available experimental data andtheoretical approaches become more scarce because ofthe complexity of the material at

early age. The scatter in reported creep test data for earlier ages is considerable (see

RILEM, 1998). It appears that testing and modeling creep in very yotmg concrete is

19


dificult and only few attempts are found in literature. Mitchell et al. (1998) reported

compressive creep data for yormg concrete. Normal and high strength concrete were

considered and the results ofcompressive creep for high strength concrete have indicated

sensitivity to age at loading in the same way as the normal concrete. At the RILEM

Conference (1994) on thermal cracking in concrete at early ages, several authors presented

test results and models for viscoelastic behavior ofyoung concrete. For example, Umehara

and Uehara (1995) demonstrated the influence oftemperature on creep of young concrete,

the higher the temperature the higher the compressive creep. Westrnan (1995) reported and

modeled compressive creep of young normal concrete (w/c= 0.4) and high performance

concrete (w/c= 0.3) with silica fume. The age at loading ranges from 13 hrs to 7 days. I-lis

results indicated high creep disposition at early age for high strength concrete which,

however, rapidly turns into a stiffer response. His results indicated almost no change in

response at age of loading beyond 48 hours for the two concrete mixes considered.

Morimoto and Koyanagi (1995) have shown compressive and tensile relaxation data of

young concrete (w/c= 0.5 and 0.59). Their results demonstrated the influence of age at

loading and the initial level of stress on relaxation capacity and time. The results alsoindicated that the tensile relaxation is smaller and terminates in a shorter time than the

compressive relaxation. Shutter and Taerwe (1997) have generated compressive creep data

for a concrete mix with w/c-ratio of 0.5 at difierent ages of loading (12 hr, 13hr, l6.5hr,

lday, 2days, 3 days, 7days and 14 days) at stress/strength ratio of 20 % and 40%. Their

experimental results indicated that the very early age creep strain at the stress level of 40%

is markedly higher than the creep strain at 20% which demonstrates the high nonlinearity

of creep at early age.

2.5.3 Creep Mechanisms

The mechanism of creep is of utmost important in arriving at an understanding of

the creep phenomena. Several theories have been proposed over the years to explain the

creep mechanism, but non of these theories has adequately explained all the observed

information regarding creep ofconcrete. On phenomenological basis, several broad

mechanisms can be distinguished. Ofthese the prevalent theories are viscous flow theory,

plastic flow theory, and seepage of gel water. These theories are summarized in a book by

20


Neville et al. (1983). It is important however, to between real and apparent

mechanisms ofcreep. Real mechanisms are associated with the hydrated cement paste and

can be considered to be material properties. Apparent mechanisms are caused by other

factors (e.g. microcracking), which modify the anticipated strain. Only real mechanisms

will be discussed here and apparent mechanism will be discussed later in section 2.6.

Viscous flow theories postulate that creep occurs within the hydrated cement paste

Under sustained load, the cement paste undergoes viscous flow causing creep. Plastic

theories suggest that the creep of concrete may be in the nature of crystalline flow, i.e., a

result of slippage along planes within the crystal lattice. Seepage of gel water theory

postulates that hydrated cement paste is a rigid gel. In such gels, application of load causes

expulsion of the viscous components from the voids in the elastic skeleton. Thus creep

occurs due to seepage of gel water under pressure.

Since no one ofthe previous mechanisms can account for all the observed

phenomena, several hypotheses that ascribe creep to more than one mechanism have been

proposed. According to AC1 Committee 209, the main mechanisms that describe creep are

1) Viscous flow of the cement paste caused by sliding or shear of the gel particleslubricated by layers ofadsorbed water;

2) Consolidation due to seepage in the form of adsorbed water or the decomposition of

interlayer hydrate water;

3) Delayed elasticity due to the cement paste acting as a restraint on the elastic

deformation of the skeleton formed by the aggregate and gel crystals;

4) Permanent deformation caused by microcracking as well as recrystalization and

formation ofnew physical bonds.

It is generally agreed that viscous flow and seepage contribute to the bulk ofcreep (ACI-

209). The main disagreement revolves arotmd the role ofwater in the cement paste. This

can be better understood by considering the structure ofC-S-H. Several models for the C-

S-H microsuucture have been proposed in literature ofwhich the three most prominent

models are: a) the Powers-Brunauer model, b) the Feldman-Sereda model, and c) the

Munich model. These models are described in Mindess and Young (1981) and briefly

discussed herein. Schematic representation ofthese models is shown in Figure 2-3. In the

Powers-Bmnauer model, C-S-H consists ofcolloidal particles with short- range order over

21


a few layers; not enough to consider the material crystalline. The C-S-H is made of random

arrangement ofthese particles bonded together by surface forces and occasional ionic-

covalent bonds that links the adjacent particles. The evaporable water held between the

sheets is lost irreversibly only at low relative humidity (see Yotmg et al., 1988). Feldman

and Sereda envision the structure ofC-S-H as a completely irregular array ofsingle layers

which may come together randomly to create interlayer space. In contrast to Powers and

Brunauer. they consider that water can move reversibly in and out of the interlayer space.

The interlayer regions also vary randomly in thiclcness. Bonding between layers is through

solid-solid contacts formed during drying and disrupted on wetting as per Mindess and

Young (1981). In the Munich model, the C-S-H structure is a three dimensional network of

colloidal size particles. The binding energy between adjacent particles is dominated by

interfacial energies. The influence of adsorbed water on the surface free energy is important

and plays a role on expansion /contraction upon wetting/drying. In light of these models

several hypothesis that relate creep with the microstructure ofhardened cement paste have

been suggested. Of these the prevalent creep hypothesis are seepage theory, interlayer

theory, and thermally activated creep. However, no single hypothesis can fully explain the

property of creep. A good review ofthese hypothesis are presented by Hansen and Young

(1991). Reversible and irreversible mechanisms of creep are discussed.

Reversible Creep Mechanisms

a) Powers Model- Seepage Theory: The basic assumption is that only water in

micropores (adsorbed water) within the C-S-H layers is load bearing. When extemal stress

is applied, the intemal stress on the water in micropores is increased beyond the existing

disjoining pressure. Consequently, the thickness of the adsorbed film ofwater is changed to

maintain equihbrium and water diffuses from the micropores to the capillary pores. This

process is associated with reduction in the interlayer spacing that leads to bulk reduction in

volume (creep). This theory view creep as a result ofwater diffusion under stress from the

micropores to the larger, capillary pores.

b) Feldman-Sereda Model- Interlayer Theory: They postulated that, in contrast to the

seepage concept ofadsorbed water, the main mechanism ofcreep involves a structural

change at the entrances to the interlayer spaces. Under compressive stress, specific regions

22


ofthe entrances to the interlayer surface contact or separate to form new interlayer spaces.

Only water in the limited regions ofthe interlayer entances is influenced by stess. The

interlayer water is perceived to be part ofC-S-H and is not influenced by stress. "llre theory

view creep as a result of deformation and ordering ofthe assembly of C-S-H particles.

c) Munich Model-Thermal Activation Approach: The basic assumption -of this

hypothesis is that time dependent strains are the result ofthermally activated processes that

can be described by the rate process theory. Creep stains will originate through

deformation of a microvolume ofpaste, designated as “creep center”. Extemal stress and/or

temperature provide exta energy to the material and consequently, the creep center

deforms to attain a lower state ofenergy. The energy provided must overcome the energy

barrier of the creep center for the deformation to occur. This method applies to reversible

and irreversible creep, and it is the only model that has been defined in mathematical terms.

The creep stain is given by empirical equationV

ac = act” exp(5)sinh(i) 2.3RT RT

Where, ac is the total creep stain, r is the load duration, E, is the apparent activation energy

ofthe creep centers, Va is activation volume, av is the number of creep centers at the time

of loading, R is the gas constant, Tis the absolute temperature, and n is a modeling

constant.Irreversible Mechanisms: various processes have been proposed to explain the

irreversibility of creep strain. Powers related the irreversibility of creep to the formation of

new bonds when the gel particles come into close proximity for the first time. According to

Feldman and Sereda, irreversible creep is due to gradual redistribution ofwater which

results in a densification and ordering ofC-S-H with a net increase in the layer volume.

The net result is a more stable C-S-H structure. In addition, they proposed other processes

of shear slippage, microcracking, breaking of and re-forming ofbonds to explain the

irreversible creep. The Munich model of thermally activated creep has irreversibilityincluded through deformation of creep centers. Creep centers are viewed as areas of slipbetween adjacent particles. Aging of the paste decreases the potential number ofcreep

centers and the activation volume. The activation energy increases with time and hence, it

23


reduces the creep rate. Benture et al. (1978) related irreversible creep to silicate

polymerization ofthe C-S-H.

The above mechanisms for creep have been inspired and proposed for matured

concrete. Yormg concrete however may include difl'erent and/or additional mechanisms.

For example, Tanabe and Ishikawa (1993) have foimd strong effect ofpore water pressure

on the creep behavior ofyoung concrete. Their model considers the efi'ect ofpore water

migration on the creep and relaxation behavior ofyormg concrete which seems to be a

stong factor. At this point, however, more works are needed on concrete at early age to

develop SOl1I1(l. understanding of the creep behavior.

2.5.4 Review of Analytical Models

Two terms are ofien used to model the creep behavior of concrete: creep coefficient

and creep compliance. The creep coefficient implies that the deformation at time t induced

by a loading at time r’ is subdivided into two parts: the instantaneous deformation (elastic)

and the creep. The total deformation can be written as

60') .s(r, r’) = ——[1 + ¢(r,r )] 2.4E(z ’)

where o"(t') is the stess applied at time t’ ; E(t') is the modulus of elasticity at time 1" :

¢(t,t’) is the creep coeficient at t for a loading at t’ .

In contrast to creep coefificient, the creep compliance J(t,t') combines the elastic and the

creep deformation into one function. The total time dependent stain is expressed ase(r,r’) = ./(r,r’)o-(r') 2.5

Several models have been formulated for the creep coefiicient of concrete at early age of

which the vast majority was originally formulated for hardened concrete. Some ofthese

models are adopted by the contemporary codes such as ACI-209 (1992) and CEB/FIP

MC90 (1991). A good survey for the early age models is available in RILEM (1998). For

example the AC1 model predict creep coeficient from the following expression(t _ I 0.6

¢<m=—’%,-¢..<o 2.610+(r-r)

46,, (t,t') = 2.35k,'k§k§k§k§k§k; 2.7

24


where kl’ —-> k; are coeficient to coimt for the eflect of age and concrete mixture. The

CEB/FIP MC90 predict creep coefficient by the following expression

¢(r.r')=¢.fi.(r-r’) 2-8where ¢a is notional creep that include the efi'ect ofage and shrinkage (see the code) and

,8, (r — t’) is the development of creep with time after loading. The efiect ofhumidity,

concrete mixture, and temperature can be modeled. The earliest age at which this

expression could be applied is 12 hours. A primary question remains however regarding the

accuracy of these models at early age and only limited investigations available in literature

to verify the applicability ofthese models at early age. For example, Guenot et al. (1996)

have shown that the creep coefficient by CEB/FIP MC90 gives quite good results when

compared to their early age data on concrete with w/c-ratio of0.5, and high performance

concrete with w/c-ratio of 0.3. Similar conclusion was reached by Mitchell et al. (1998) for

normal and medium stength concrete but not for high stength concrete (w/c=0.3) for

which the CEB/FIP MC90 model fotmd to be underestimating the creep at very early age.

For the creep compliance, perhaps the most well known compliance firnction for

hardened concrete is the Double-Power Law by Bazant and Panula (1978) and its extension

to the Triple Power Law (Bazant and Chem, 1985a) in which the long time creep is better

described. However these laws are not valid for basic creep at very early ages. Emborg

(1989) has modified the Triple Power Law to predict creep at very early age by adding two

additional functions G(t’) and H(t,t') ofexponential type and the expression becomes

J(r,r') = El#1?‘-(r'""' +a)[(t - r')” - B(r,r',n)]+%_'l +%") 2.9

Where E0 , go, , m, oz and n are material parameters. G(t') models the stong age-

dependence of the instantaneous deformation (load duration 1.4 minutes) and

H(r,t') models the increase ofearly age creep when the load has been applied (see Figure

2-4). Westrnan (1995) has used the extended Triple Power Law (with modified early age

functions for high stength concrete, see the reference) for early age basic creep and good

agreement with test results for high stength concrete (w/c = 0.3) was achieved.

Another method to model the creep is to convert the response of the material into

difierential forms of equations which can be described by rheological models (see Bazant

25


and Wittrnann, 1982). This approach simplifies the numerical computation and better

allows the modeling of creep nonlinearity. It is also called rate-type creep method. Some of

the researchers who presented experimental results and models for early age creep at

RILEM Conference on thermal craclcing at early age in 1994 have used this method in the

analysis.

New approach that starts firom the microstuctural development of the concrete was

used to model creep of young concrete (e.g. Lokhorst and van Breugel, 1995). According

to this approach the degree ofhydration proves to be a very fundamental parameter. In the

literature, a degree ofhydration based creep formulation was developed by Rostasy et al.

(1993), yielding the following specific creep firnction .

, r-t’ PMT)C(t—t,ro)=P,(ro) T 2.10I:

Where I, = lhour and 1-’, (re ) and P, (re) are parameters depending on the degree of

hydration r, at the time t’ . Good agreement with tensile creep data of concrete mix with

w/c-ratio of 0.65 has been demonstrated at high r, values (>0.52). However, at low ra it

seems that the model results in poor prediction of creep as demonstated by Shutter and

Taerwe (1997). The latter view the poor prediction at low ro as to the fact that Equation

2.10 provides a linear creep formulation, whereas the very early age creep behavior

definitely is nonlinear. Shutter and Taerwe (1997) generated early age compressive creep

data for a concrete mix with w/c-ratio of 0.5 at difl’ererit ages of loading (12 hr-7days) at

stress/strength ratio of20 % and 40%. (Their experimental results demonstated the high

nonlinearity ofcreep at early age, and then'they developed a new nonlinear basic creep

model for early age concrete in compression based on degree ofhydration re and stress

level aas fundamental parameters. The expression for the specific creep has the following

form -I 0.35

C(t —t',r,,a) = yo (ra,a)(-it] 2.11,u,(r,)+t —t

This model has demonstated the ftmdamental influence o_f the degree ofhydration. The

end value of the creep as wellas the creep evolutionhas formd_to be influenced by the

.26


degree ofhydration at time of loading. Although the model fit their results, the validity of

the proposed model still has to be checked.

The above discussion indicated the current movement of the research commtmity

toward understanding and modeling early age creep behavior. However, the vast majority

of research in area has been focussing on early age creep of concrete in compression

though tensile creep is equally important for accurate stess analysis and crack prediction.

Nevertheless, the next section is devoted to discuss literature available on tensile creep

behavior.

2.5.5 Tensile Creep at Early Age

As mentioned earlier the vast majority ofpast work on the creep of concrete has

been concemed with compression creep behavior. Creep in tension however, is of great

importance when potential for cracking is to be determined. It is important in estimating the

possibility of cracking due to shrinkage and thermal stresses at early age. It is also

important in calculation of tensile stresses in prestressed concrete and in the design of

water-retaining stucture. Although the importance of tensile creep has been firlly realizedfor long time, tests on tensile creep ofhardened concrete that are available in the literature

are very limited and the studies becomes more scarce when confining the scope to early

age.Most of the work on tensile creep of manned hardened concrete emphasizes the

comparison with the behavior under compression, either in terms of magnitude and rate, or

in terms ofthe mechanisms involved (Brooks and Neville, 1977, Domone, 1974, Ward and

Cook 1969, and lllston, 1965). For example Brooks and Neville (1977) reported test results

for tensile and compressive creep of concrete with w/c-ratio of 0.5 at ages of loading of 28

and 56 days. Their results indicated similar initial rate ofbasic creep in tension and in

compression, but in contrast to compression case, the rate ofbasic tensile creep does not

decrease with time. On the contary, the rate ofcreep under drying at 60 % RH was found

to be higher in tension than in compression. They noticed also that the basic creep in

tension is not appreciably reduced as in compression when age at loading is increased. The

basic tensile creep in their study was found to be irrecoverable when tmloading was

imposed at the age of56 days, whereas a recovery of40 % in compressive creep was

27


observed. Another reported study in literature is by Illston (1965) in which, the influence of

stess level, age at loading, and humidity ofthe environment on tensile and compressive

creep were investigated for a concrete with w/c-ratio of0.4. His results indicated

similarities and differences between tensile and compressive creep. The tensile creep is

similar to compressive creep in some aspects such as proportionality to stess level rmtil 50

% and the reduction in creep rate as age of the concrete is increased. It dififers fi'om

compressive creep in that, the initial rate of creep is higher in tension than in compression,

and the influence ofdrying at 65 % RH on tensile creep is not significant as in

compression.

The existing studies on matured tensile creep are not only limited but also the

results are conflicting. The following remarks are illustating the scarcity and conflicts of

existing results.

9 Some researchers have found equal total creep in compression and tension at the same

stess level (see Neville et al., 1983). However, Hlston (1965) and Brooks and Neville

(1977) have found higher initial rate ofcreep in tension than in compression.

9 The influence of age at application of load appears to be similar in compression andtension as found by Illston (1965). Brooks and Neville (1977) on the contary observed

insignificant reduction in basic tensile creep with the increase in age at loading as

compared to compression.

9 Tests by Illston (1965) suggested that the presence or absence ofdrying at 65% RH has

practically no influence on the magnitude of creep in tension. This is not the case in

tests reported by Ruetz (1968) and tests by Brooks and Neville (1977), which indicated

increase in tensile creep under simultaneous drying. Domone (1974) also found that

tensile creep increases for both gain and loss of moisture.

The influence ofmix proportions on creep in tension is similar to that on creep in

compression. However, absorption ofwater is likely more influential on creep in tension.

Tests by Ward and Cook (1969) indicated for example rapid acceleration of creep rate upon

re-saturation under loading. Brooks and Neville (1977) findings reveals that the total creep

in tension of already dried samples is less than the total creep in compression.

28


Microcracking has an important role in creep in tension. The time dependent

microcracking creep at high stess/stength level may lead to failure. Al-kubaisy and Yormg

(1975) have demonstated the existence ofa fracture limit envelope beyond which tertiary

creep and time dependent failure is induced. Microcracking efiect is not only significant at

high stess/stength-ratio but also at low stress/stength-ratio as suggested by Ward and

Cook (1969).When confining the scope to early age concrete only very few studies on tensile

creep are detected in literature. These studies are even limited in scope and intended to

either emphasize the effect ofmix parameters on tensile creep (e.g. Bissonnette and Pigeon,

(1995), Kovler et al. (1999)) or to explain and model the drying creep in tension (Kovler,

1995,1999). For example Bissonnette and Pigeon (1995) have shown that the w/c ratio and

age at loading are significant parameters for tensile creep. They have demonstated this by

tensile creep tests on microconcrete (max. agg. Size of 10mm) with w/c-ratio of 0.35 and

0.55. Prismatic samples (50x50mm in cross section) were loaded by constant stess at ages

of 2 days and 8 days and measurement ofcreep and shrinkage were taken for 45 days in

environmental condition of23 °C and 50 % RH. Their results indicated higher specificcreep when w/c-ratio increases. However, this is based on the assumption that creep is

proportional to stess regardless ofw/c-ratio which may not be true for comparison at early

age particularly when normal and high strength concrete are to be compared. They fixed

the stress in the test but not the stess/strength ratio. Kovler et al. (1999) reported the

influence of silica fume on early age tensile creep ofhigh stength concrete, and

microconcrete (max agg. size of7 mm) with w/c-ratio of 0.33 was only tested. Their tests

included only sealed samples (40x 40 mm in x-section) loaded at the age of 1 day. The

results showed that the tensile creep of silica fume concrete is greater than of a plain

concrete with similar w/b-ratio. In RILEM Conference on Thermal Cracking at Early Age

in 1994, only two papers on early age tensile creep were presented. One demonstrated the

influence oftemperature on early age tensile creep (Umehara and Uehara, 1995) and the

other reported the influence of stess/stength- ratio on tensile creep at early age (Gutsch

and Rostasy, 1995). The later showed that the initial stess/stength-ratio does not exert a

very significant influence on tensile creep at early age. In addition to that, no creep failure

occurred during a period of 168 hours for samples loaded at age of24 hours even rmder

29


stess/strength of0.9. This contradicts the existence of fracture limit (0.6-0.8) observed by

Al-kubaisy and Young (1975) for hardened concrete. Kovler (1995) presented a

phenomenological approach describing the drying creep in tension as a sum of shrinkage-

induced creep and creep-induced shrinkage. However, interpretation ofthe experimental

data that inspired the model has been changed and revised in Kovler (1999) which negates

the applicability of the proposed model. He pointed out that the mechanisms of drying

compressive creep might not be valid for tension. The drying creep will be discussed in the

next section.

The above discussion reveals the scarcity of comprehensive data on tensile creep at

early age. Apparently there is a need for more work on tensile creep ofconcrete in general

and in particular at early age. This research intended to investigate some of the issues

pertaining to tensile creep behavior at early age.

2.6 Creep of Concrete under Drying

At simultaneous drying, the deformation of a concrete specimen under sustained

load is larger than the sum of the drying shrinkage deformation ofthe specimen at no load

and ofthe deformation of the specimen that does not dry (i.e. sealed). The excess

deformation is called Pickett efi'ect (Pickett, 1942) after the man who first clearly

documented it. L’Hermite (1959) suggested an empirical linear relation between creep and

shrinkage in which the drying creep is considered functions ofboth basic creep and free

shrinkage. Gamble and Parrot (1978) used similar approach in which the drying creep is

dependent on basic creep and free shrinkage and they suggested empirical formulas for

drying creep. Bazant and Pannula (1978) proposed a model for estimating total creep,

which includes empirical formula for drying creep as a firnction ofdrying shrinkage and

mix properties. Thus, all the main known formulas for predicting time-dependent

deformation of drying concrete under compressive loading link drying creep with free

shrinkage and some ofthem with basic creep. Apparently, drying creep is dependent on

both fiee shrinkage and basic creep in a complex manner.

The interpretation of the excess deformation and its mechanisms is still a matter of

major controversy among researchers. Two major views exist in the literature regarding the

Pickett efiect. One is saying that the excess deformation is basically due to the division of

30


total deformation of loaded drying sample into creep and shrinkage components, where in

fact, only the total deformation is a well defined quantity. The total deformation does not

depend on the internal state of stess and extemal load separately but only on the composite

state of stress. Supporters of this view tied to explain the excess deformation by apparent

mechanisms related to shrinkage-induced stresses and associated cracldng (e.g. Wittnann

and Roelfsta, 1980, and Wittnann, 1993). The second view considers a real mechanism

related to material property to explain the excess deformation. This real mechanism of

excess deformation has been shown by experiments (Bazant and Xi, 1994, and Reid, 1993).

In this regard researchers are divided also into two groups. One group considers the rate of

creep to increase as a consequence ofdrying process (see Bazant, 1988 for list) and in this

context generally the term drying creep is used. Another group maintains that creep is

unaffected by drying, but the shrinkage is altered rmder load. The shrinkage will be

increased under compressive load as noticed by Wittmann and Roelfsta (1980) and far

decreased under tensile loads as shown by Wittrnann (1993). In this regard, the term stress-

induced shrinkage is used in the literature (e.g. Bazant and Chem, 1985).

It has been admitted that neither of the views can alone explain the excess

deformation. Meanwhile, a combination of the two views is more acceptable in the research

commrmity (Bazant, 1988). Drying creep is now admitted to be the sum of at least two

components; an intrinsic drying creep with its own mechanisms and a stuctural drying

creep resulting from micro-cracking efiect due to the non-uniformity of the free drying

shrinkage in the concrete specimen. Accordingly, it now appears that there are two major

mechanisms causing the Pickett effect: microcracking and stess-induced shrinkage.

Microcracking eflect was used by many models to explain the Pickett efiect (e.g.

Pickett, 1942, and Wittnann and Roelfsta, 1980). The explanation is based on the skin

cracking occurred due to nonunifonnity ofmoisture distibution in a drying specimen. The

surface layer ofthe specimen shrinks more than the inner layers at the initial stage of

drying. As a result, the surface layer is in tension while the inner layer is in compression.

The tensile stess causes microcracking in the surface layer. Due to the nonlinear inelasticbehavior and irrecoverable creep of concrete caused by the tensile stess, the microcrackscannot fully close when the moisture distibution finally approaches a uniform state. As a

result, the measured shrinkage ofthe unrestained specimen is always smaller than the true

31


shrinkage. For drying creep specimen, ifthe whole cross section is in compression, there

can be no microcracking efiect. Therefore a larger shrinkage will occur in the compressed

specimen than in the fiee shrinkage specimen which may falsely appear as creep in the

traditional definition of creep. Wittnann and Reolfstam (1980) have shown higher

shrinkage in specimens loaded in compression than that for the fiee of load specimens. The

increase in shrinkage stain is proportional to the compressive stess as it minimizes the

microcracking to different extents. This led Wittnann to suggest that tensile cracking might

perhaps explain all of the excess deformation at drying.

The stess-induced shrinkage has a difierent explanation, which is as follows: two

moisture-diflirsion processes can exist: macrodifiirsion and microdiffusion. The

macrodiffusion consists ofwater transport through large pores and has no measurable

efiect on deformation. The microdiffusion transports water locally between the capillary

pores (macropores) and gel pores (micropores), and because it occurs in far smaller pores

ofmolecular size, it affects the deformation rate of the solid fiamework ofthe cement gel.

The movement of water through the gel pores, which are only a few molecules in size,

promotes the breakage ofbonds that are the source of creep, and thus intensifies creep. This

mechanism was used by Bazant and Chem (1985, 1987).

However, the contribution of each mechanism is not yet agreed upon and remains

to be a matter for further research. There was no experimental data in literature that clearly

distinguishes between the difierent mechanisms ofdrying creep until the study ofBazant

and Xi was published in 1994. The basic idea was to compare the curvature creep of beams

subjected to the same bending moment but very difierent axial forces. The authors found

that drying creep has two different sources: microcracking and stress-induced shrinkage.

The later was found to increase continuously whereas the former, first increase and then

decrease. The basic principle ofthe experiment limited its applicability to compression.

However, for tensile creep, there are no available experimental data on the difierent

mechanisms ofdrying. The explanation for the drying creep mechanisms and the suggested

empirical formulas for its quanti.fication were all based on compressive creep results. For

tensile creep there is almost no experimental data on the various mechanisms. Furthermore,

the mechanisms discussed above may not be valid in tension. For example, the role of

microcracking becomes ambiguous in tension, because the tensile load intensifies

32


microcracking and will lead to smaller shrinkage than in the fiee of load specimen as found

by Wittnann (1993). Kovler (1995 , 1999) questioned the role ofmicrocracking and stress-

induced shrinkage as mechanisms to explain the drying creep in tension. This research

intended to clarify some ofthese matters.

2.7 Effect of Fiber Reinforcement on Creep and Shrinkage

Studies on creep and shrinkage of fiber reinforced concrete (FRC) are limited in

literature. Balaguru and Shah (1992) summarized some of these studies. The addition of

steel fiber to concrete seems in general to reduce the shrinkage of concrete to a limited

extent. However, the extent of reduction is still debatable. For example, Grzybowski and

Shah (1990) have shown that the addition of one percent by volume of steel fibers does not

substantially reduce the drying shrinkage. On the other hand, Swamy and Stavrides (1979)

have reported 15-20 % reduction in shrinkage when 1% (by volume) of steel fiber is added.

Magnat and Azari (1988) have also reported significant reduction of shrinkage due to

addition of steel fibers up to 3 % by volume. On the contary, Edgington er al. (1974) have

reported that the shrinkage of concrete is tmafiected by the presence of steel fibers.The efi'ect ofsize and age on shrinkage of fiber concrete is similar to that on plain

concrete as shown by Chem and Young (1989). Their study also indicated that the

reduction in shrinkage is increased with the increase of fiber volume fiaction up to a certain

percentage beyond which no more reduction is attained. It seems that shrinkage reduction

is optimal when volume fraction of steel fibers is arotmd 2%. The restaining effect

becomes more efi'ective at later ages, and is increased as fiber aspect ratio is increased.

Accordingly, the efiect offiber on shrinkage at early age may be negligible, although it is

not conclusive at this point.

Only very limited studies are available on creep of fiber reinforced concrete. The

available studies showed conflicting results on the efiect offiber on creep. The general

tend based on matured samples, is to increase compressive creep when fiber volume

fiaction is less than 1 % (Balaguru and Shah, 1992). Tensile creep ofFRC is almost

neglected in the literature and no conclusive remarks can be made today. As a

consequence, researchers have been using formulas derived for plain concrete in

compression, to analyze tensile problems offiber concrete. For example, several models

33


have been formulated in the literature to predict shrinkage craclcing offiber concrete (e g

Grzybowsld and Shah, 1989, and Yang et al., 1996). These models utilized creep formulas

derived for plain concrete in compression due to the lack ofcreep data / models for fiber

concrete in tension. This studyis also intended to provide some data on early age tensile

creep and shrinkage offiber concretei , H , . D

ULl.l

"aLL.

'uU

LL

Figure 2-1 Normalized tensile stength, compressive stength, and modulus of elasticity vs

- 1 -I

II

I1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , > . . - - - - ~ . . . , . . . > - . . . . . o . A . < 4 i . . - . . . . . ..,. . . . . . . . ..u—

I

_ I 0I

0 .E .» I ~ICI’ 1 -o’ 1_.... .............................. .. . .._

.' I-. '. ’ <

I. F Ict,’ FmI_........................................ .., ..................... .. .._.

I_ ’ -Q I -

I_ I -

I... . . . . . . . . . . . . . . . . . . , . . . . . . . . ..,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , , . . .._

1- I -I- , __

- : ' -Yv I l- 1

0 0.2 0.4 0.6 0.8 1

Degree of Hydration, or

degree ofhydration (Gutsch and Rostasy, 1995)

34


Stmn

Figure 2-2 Time dependent deformations in concrete subjected to sustain load

Stran

Stran

Stron

® Shrinkagefrom to

to Timecl) Shrinkage or an Unloaded Specimen

Creep on Basis@ or Additive

Definition

_ oTrue Elastic Strain

Shrinkage olan UnloadedSpecimenNominal ElasticSlJ'OlI‘\

/

to Time

bl Change in Strain ol Loaded andDrying Specimen

@ Creep

Nominal EKISUCStr‘cm

‘9 Timec) Creep ol a Loaded Specimen In Hygrol

Equilibrium with the Ambient Medium

Drying Creep

® BOSIC Creep

Shrinkage

NOfl’1Il'10l ElasticStrain

‘° Timed) Change in Strain ol a Loaded and Dl’ylflQ Specimen

(Neville, 1996)

35


OQ O

Og°0°°x z 0°04. ‘

I009000 g O

1*

O O~¥~

O0°°‘°,_,_1~ *

090° ‘_I +°°

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+10 k ‘L O

O Q0 O09'0 0-ffO

Off01-’

00,

‘F O

°~%?,»i~ oz/*<"-_ ~-

:§°° °° ‘-

Q00 O O O 8///! @§§(cl l

1 Wllerinimnlzyerregiom i C-S-Hslveeu

0

6‘I O 0 og‘

O ‘- O ‘ ,40° . _ - ‘$0,.0° -v‘1,"5°O°9,,° '°o0* °°°°o0 ~° 0°‘ °°o*

0 ,0 ¢I ~¢ .

0I °0 °o' °°o o0o ° O1° *' 0o :‘o 4;

la)

°;\;\\\\\\\\\\\\§\:- ,00'.00--Q§ kiaqooooo “-lo

oO.\,O +0

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0000°8000000 .00

=9

O

°\\\\\\\\\\\\\§‘>"2§‘*

. I ° _. _ g O0Q 4‘ ° oggqg + a

++°+° ,_, 0°. . v ,_

9 - - .' °°° - O 0°°°o° . 0 +O - 0 - go "0 E’, °o °o °oO0 C 0° °o°oo .1i, 9000090 O '_

°°°o0oO° *"‘ool 00°

ooo 0 Q 0 °°oooooiéq°°°0q ‘ °

lbl

09° I

0 Water odsovbed on nullzu 7/////,j C-S-H cuticle:C Cloilluy new (BO dtiiwlltd ilruflurel

Figure 2-3 Schematic representation ofvarious models of C-S-H

mm) A

(Mindess and Young, 1981)

om>34

‘In //// 171%Y

° l|,_ IGH )--'.'.'.-_;:_;_:,_ \\ 1?

U

l l P

Figure 2-4 Additional fimctions G(t') and H(t,t.) for early age creep response shown

schematically (Emborg, 1989, graph taken from RILEM, 1998)

‘o :' 1 :

36

' nus


CHAPTER 3

EXPERIMENTAL TECHNIQUE AND TEST MATERIALS

3.1 Introduction

This chapter describes two major pans: experimental techniques and materials. The

first part presents particulars ofthe testing system. It provides detailed description of the

various aspects of the experiment, its mechanism, and the analytical aspects of the test

technique. The second part presents the material tested in the experiment, mix

compositions, and basic tests conducted on concrete and its ingredients. It also details the

test matrix, and the plan and difierent phases adopted in the research. In addition, results

and experimental observations during the preliminary stage are briefly discussed.

3.2 Experimental Technique

The research utilizes a uniaxial restrained shrinkage test to provide basic

information needed for characterization of restrained shrinkage, shrinkage stress, tensile

creep and its interaction with shrinkage of concrete at early age. A Lmiaxial creep-shrinkage

test in which restrained and unrestrained samples can be tested simultaneously was

designed primarily for the purpose ofthis research. The test is not a standard or

conventional test. Therefore, significant efforts were made during the design and

implementation ofthe system to ensure a reliable experiment. The following sections

discuss the various aspects ofthe testing system.

3.2.1 Design Considerations and Requirements

Since this test is not a standard test, details and complexities ofthe system were studiedduring this project. In addition to the problems encotmtered in conventional tensile test of

concrete such as alignment and end effects, the complexity ofthe system is augmented by

the testing of early age concrete, which requires special consideration. Several aspects

pertaining to the testing system, material behavior, and age must be carefully considered to

design a reliable experimental setup. These aspects can be summarized as follows:

37


Specimen geometry must be chosen such that interference between specimen geometry

and material response is For example, stress calculated in a plate~type

specimen is not a pure material property, but depends on specimen size and aspect

ratio. A uniaxial test can eliminate geometrical efifects on measurements of material

properties ifproperly designed to maintain uniform state of stress in the cross section of

the specimen.

Stable and controllable restraint is required in a restrained shrinkage test. The degree

and stability of restraint is extremely important for characterizing restrained shrinkage

because it determines the level of generated sness and the subsequent relaxation. In this

respect the connection between specimen and restraining source must be adequately

designed to maintain a stable restraint while at the same time, avoiding slippage and

premature failure due to stress concentration.

The loading system must be accurate and suficient to provide a firlly restrained test. It

must also provide gentle and smooth application of loads without irregularities to avoid

load shocks that may cause premature failure, particularly of the young concrete

samples.

Size and layout of the testing setup must be adequate to test real concrete and allow the

test to start as early as possible. A horizontal layout is preferable to allow for testing a

few hours after casting.

The system must be able to discriminate creep strain from shrinkage and thermal

induced strains. This requirement is the key feature of the experiment that enable

quantification oftensile creep and its interaction with shrinkage and thermal strain.

Restrained and unrestrained samples must therefore be tested. The experiment must

also allow measurement of shrinkage loads. High accuracy displacement and load

measurement devices are required.

These aspects and requirements were compiled into the design of the experiment.

Details of the setup are presented in the following section.

3 2.2 Uniaxial Creep-Shrinkage Test

The experimental apparatus was developed based on a uniaxial system suggested

by Bloom and Bentur (1994) and upgraded by Kovler (1994). It was modified to carry out

38


tests on concrete containing coarse aggregate with a maximum size of25.4mm. The basic

idea of this system is to test two identical “dog-bone” samples; one is restrained where load

developed by drying shrinkage is measured, and the other is free to shrink where

deformation is measured as shown in Figure 3-1. Each specimen is 1000 mm long and

76.6x76.6 mm in cross-section. The specimen cross section is gradually enlarged at both

ends to fit into the grips. The grips were designed to provide full restraint and to avoid

stress concentration. so that a imiform state of stress could be achieved within the

specimen.

The two samples were laid horizontally in a controlled environmental chamber. The

restrained sample was motmted on a W36 steel I-beam, one end ofthe restrained sample

was fixed to a reaction block attached to the I-beam and the other end was movable and

connected to a hydraulic actuator through a load cell. The system was stiflf enough to

provide a fully restrained test. A general view of the experimental device is shown in

Figure 3-2.

The longitudinal shrinkage was measured by a linearly variable displacement

transducer (LVDT); .—'= 2.54 mm AC-AC. Each measurement was an average value of 100

readings per second of the LVDT. Such a procedure permitted very high accuracy and

reproducibility of linear displacement measurement of less than : 0.1 um.

To avoid inducing premature failure ofthe young concrete specimens, three things

were considered in the design ofthis setup. First, the grip at both ends was of special shape,

characterized by gradual widening ofthe intemal section to reduce stress concentrations.

Second, swivel-joints were installed at the connection between the grips and both the load

cell and the reaction block (fixed end) to substitute for possible misalignment of the load.

Third, deformation was recovered gently and at a rate of 0.5 um/second to avoid irregular

compensation of deformation. Measures to reduce fiictional resistance were taken by using

a Teflon plate with a low coefficient offiiction tmderneath the concrete sample in addition

to the use of lubricating oil. The measured value of friction force did not exceed 15 N, and

was therefore neglected at data analysis.

A computer-controlled hydraulic actuator loaded the restrained specimen according

to a special program. The load was measured by a load cell, and the test was controlled by a

39


computer via Labview. Various components ofthe experimental device are shown in

Figure 3-3 and summarized as follows:

1) The concrete beam (1000 mm long and 762x76.2 mm in cross-section) flared at both

ends to fit into the grips;

2) The specimen grip characterized by gradual increase of the intemal section to fully fit

end of specimen and to eliminate stress concentration;

3) A Hydraulic servo-actuator (MTS) with a load capacity of 114 ICN and a stroke of:

76.2 mm. A servo-valve of 10 gpm and nominal pressure of 20 MPa delivered by l0

gpm hydraulic power supply;

4) An [NSTRON 8500 Plus Controller with a GPIB 24-pin standard (IEEE-488) computer

interface;

5) A computer (Apple CENTRIS 650) with Labview Software custom-developed for this

test. The Hardware is NB-MIO-l6XH-18 A/D Board and NB-GPIBFINT board;

6) A modified Trans-Tek LVDT extensometer (i 2.54mm) instrumented through the

strain channel of INSTRON 8500 Plus.

3.2.3 Mechanism of the Test

The test is characterized by a fiilly automated closed loop control, a high accuracy

of measurements, and a sofi and smooth loading. The restrained condition is simulated in

the test by maintaining the total defonnation of the restrained sample within a threshold

value of 5 um. This was achieved by applying extemal loads to recover the deformation

when exceeded the assigned threshold value. A computer program was written to control

the test via Labview and record the measured data. The longitudinal shrinkage was

measured by LVDT, each measurement was the average of 100 readings in 1 second. The

computer- controlled test checked shrinkage deformation continuously and compared it to

the threshold value, which when exceeded, triggered an increase in tensile load by the

actuator to recover the shrinkage strain and restore the specimen to its original length. In

this way, a restrained condition was achieved and the stress generated by shrinkage

mechanism was measurable. The small threshold value was required to capture the gradual

evolution of tensile stress and to avoid large, sudden, and irregular compensation of

deformation, which may cause premature failure ofthe specimen. Hence, the first recovery

40


cycle began when the absolute value ofthe total restrained shrinkage exceeded 5 um. Load

was then applied to recover the strain elastically and the load was recorded and maintained

constant until further compensation deemed necessary. The computer also recorded

measurement of shrinkage deformation of the unrestrained sample.

Comparison of the fiee shrinkage results with the shrinkage ofthe restrained

specimen revealed the contribution of creep as a relaxation mechanism and enabled

discrimination ofcreep strain fi'om shrinkage strain. The discrimination between creep and

shrinkage strain is essential in characterization ofmaterial properties for input into models

for material response to early age drying. Figure 3-4 shows schematically how creep strain

can be calculated fi'om the restrained and fiee shrinkage test. The fiee shrinkage was

measured fi'om the free shrinkage specimen and the restrained shrinkage was based on the

recovery cycles in which the specimen was brought to its original position by the applied

tensile load. Each recovery cycle consisted of shrinkage and creep strain recovered by

instantaneous elastic strain that was induced by incremental tensile load applied by the

actuator. Therefore, the sum of the elastic strain at any time is equal to the combined

shrinkage and creep strains. Knowing the fi'ee shrinkage component, the creep strain can bequantified.

A variety of mechanical properties of concrete at early age such as components of

strain, shrinkage stress, moduli ofelasticity and creep coeficient were determined in this

experiment. The following section details the analytical aspects ofthe test that allow the

measurement of these properties.

3.2.4 Analytical Aspects of the Test

As mentioned in the previous section, the deformation of the restrained sample was

maintained close to zero all the time. Consequently, the total concrete strain is close to

zero. However, the individual elastic, creep, and shrinkage components of strain have finite

values. Equation 3.1 govems the test and explains various components of strain.

80‘) =8.(r)+8.(r)+8.,.(r) = 0 3.1where 8(t) is the total strain at time t. The elastic strain can be expressed as:

4 I


.52)— Em 3.2

where E(t) is the elastic (secant) modulus ofconcrete. The creep strain can be related to

ac (t

elastic strain through creep coefficient by Equation 3.3:

U) U)am=%%mnwhere ¢(r) is the creep coefficient, defined as the ratio between the creep and elastic

strain. ifthe elastic and creep components ofstrain are combined, a reduced (efiective)

modulus can be obtained as in Equation 3.5:

an=g%0+uo%*no 34r

where E,_,,(r) = l%§;f(—)t)- 3.5

Since stress in this test is increasing gradually, creep ofconcrete progresses more slowly

than under a constant stress 0' applied from the beginning of the test (Bazant, 1972). Areduced creep coefficient r7(r)¢(r) must be therefore used in Equation 3.5, where r;(r) is

aging coefficient and its magnitude generally falls between 0.6 and 0.9 for ordinary

hardened concrete and between 0.9 and 1.0 for young concrete (Gilbert, 1988). In this

research this coeflicient is assumed to be 1.0 since only young concrete is considered. For

the restrained test, Equation 3.4 may be written as:

Egg!-) = -55}, (I) 3.6

The tangent modulus ofconcrete can also be calculated in this test as a result of

incremental application of load during cycle compensation in which deformation is

recovered elastically by increasing the load to keep the specimen at zero strain. The tangent

modulus E,(r) can be calculated fiom the following equation:

._¢m .“am

The creep coefiicient ¢(t) can be calculated as:

42

5.7


_ Q2 _ ‘U) _"(')‘”(') ' 8.0) ' -..<r>h+ 8.0) 1 3'8

It is necessary to emphasize that the creep coefficient defined in Equation 3.8 is different

from the classical definition in the literature, which is usually defined at a certain age, as

the ratio ofcreep strain determined at that age to the elastic strain at the time of load

application. In this research, the elastic strain varies with time and the creep coefficient is

defined as the ratio of creep snain to the corresponding elastic strain at the time considered.

3.3 Materials and Concrete Mix Compositions

The research was conducted in two phases; the preliminary phase in which the main

focus was to develop a reliable experiment and the final phase in which the main focus was

to characterize the material behavior. Normal concrete (NC) was only used in the

preliminary phase, whereas normal and high performance concrete (HPC) were used in the

final phase. Plain and fiber reinforced concrete (FRC) mixes were tested for each type of

concrete. The mix proportion and parameters are relatively different in each phase. In this

section, type and properties of the material used in the experiment along with theexperimental techniques are presented. The concrete mix proportions for the two phases are

also presented.

3.3.1 Materials

Materials used are Type I Portland cement (Manufactured by Saylor), crushed

limestone aggregate with a maximum size of25 mm, and natural sand. The gradation of

coarse and fine aggregates satisfied ASTM C33 requirement and the fine aggregate had a

fineness modulus of 2.2. Silica fume was used in the HPC mix (microsilica controlled

density EMS 956 supplied by Elkem Materials Inc.), Superplasticizer (product ofW. R

Grace Co.) and tap water. Two types of fibers were used in the FRC mix; steel fiber 30mm

long and 0.4mm in diameter (manufactured by NOVACON) and multiple design

polypropylene fiber MD (Fibermesh fibers).

43


3.3.2 Concrete Mix Proportions

Typical normal and high performance concrete mixes were tested. A typical normalconcrete mix for pavement was tested since the main motive driving this study was the

application in airport pavement. The concrete mix proportions used in the construction of

Roclcford Airport (1993) was used as a control mix design in this study. In the early stage

ofthis research (preliminary stage), when the main focus was to develop a reliable

experimental setup and procedures, three normal concrete mixes with w/c ratio of 0.48,

0.51, and 0.56 were tested to study the reliability and sensitivity of the test. Steel fiber with

a volume fiaction of 0.6 % was only used in FRC mixes. Mix proportions ofthe concrete

tested in this stage are presented in Table 3.1.

In the final stage when the main focus was to characterize the material behavior,

I-IPC mix with w/c of 0.32 and two normal concrete mixes with w/c of 0.4 and 0.5 were

tested. Steel and polypropylene fibers with volume fraction of 0.5 % were used in this

stage. For normal concrete, paste volume fiaction was held constant at 35 % throughout the

whole experiment. Mix proportions of the concrete considered in the final stage are

presented in Table 3.2.

Table 3.1: Concrete mix proportions (preliminary stage)

Component Mix # 1 Mix # 2 Mix # 3

‘ 925.8 925.8 925.8 lli Coarse Agg. kg/m’

741.8 741.8 741.8i Fine Agg.kg/ms =

421.4 421.4Cement kg/mi 421.4 4

214.9 71') 7-.~~a_ Water kg/mi 210.0lI Steel Fiber kg/m’ 46.8 46.8 46.8

I Paste volume 0.349 0.349 0.349

W/C ratio 0.51 0.56 0.48

44


Table 3.2: Concrete mix proportions (final stage)

HPC- 0.32 NC-0.5 NC-0.4 lPC SF PC SF PP PC SF PP‘

Coarse Agg.kgm3 974.1 974.1 925.8 925.8 925.8 925.8 925 .8 925.8

Fine Agg.1<g/m‘ p 622.8 622.8 741.8 741.8 741.8 741.8 741.8 7411

.8

Cementkg/m3 i 533.1 533.1 421.4 421.4 421.4 480 480 ‘480

117.0 117.0Silica fume kg/ms A lWaterkg/m3 208.0 208.0 ‘210.7 210.7 210.7 192.0 192.0 192.0

‘--- l -- 565.1=Superplasticizermll 954.8 954.8 —- l i 565.

m3 . , t

1

11-~ 39.2 ’ 'Fiber kg/mi 1 39.2 1 ‘ 4.55--- 4.55

565.

_- 39.20.344 I 0.344 10.344Paste volume 0.4 0.4 0.344 0.344 0.344

W/C ratio 0.32 0.32 l 0.5 0.5 0.5 0.4 0.4 I 0.41l

HPC: High Performance Mix NC-0.5: Normal Concrete with w/c of0.5 I

PC: Plain concrete SF: Steel Fiber Mix PP: Polypropylene Fiber Mix

3.3.3 Basic Tests on Aggregates

The batched concrete included both fine and coarse aggregate. Sieve analysis,

specific gravity and moisture content tests were conducted for fine and coarse aggregates.

Sieve analysis ofall aggregates were conducted according to ASTM C 136, Standard Test

Method for Sieve Analysis ofFine and Coarse Aggregate. The results are given in Figure

3-5. In addition, coarse and fine aggregate tests were performed according to ASTM C 127,

Standard Test Method for Specific Gravity and Absorption of Coarse Aggregate, and

ASTM C 128, Standard Test Method for Specific Gravity and Absorption ofFine

Aggregate, respectively. Aggregate properties are Qven in Table 3.3.

45


Table 3.3: Aggregate properties

(SSD) % % iAggregate Type ‘ 7 Specific Gravity Absorption Capacity Moisture Content

Coarse Aggregate ‘ 2.636 ‘ 1.73 -1.71 3 1 1 3I NaturalSand 1 2.642 . -. i

3.3.4 Mixing Procedures

Concrete mixtures were mechanically mixed in a Lancaster pan mixer. It tumed out

however, that standard mixing procedures ofplain concrete are not the most proper

procedures when fibers are added, at least for the mixes considered in this study. Several

trials of FRC were made using difierent method ofmixing. The optimum method that

produced homogenous fiber distribution with minimal fiber balling will be described. The

process was initiated by mixing the dry ingredients for 3 minutes. Part of the water was

then added and the material mixed for another two minutes. The mixed material was then

reblended manually and another part of the water with superplasticizer was then added and

mixed for 1 minute. The fibers were then added in two doses, at each time, the material

mixed for one minute and finally the rest of the water was added and mixed for two

minutes. These procedures were consistently used throughout the whole research.

3.3.5 Hardened Concrete Characterization

Compressive strength and modulus ofelasticity of the nonnal concrete were

determined. The compressive strength was determined in accordance with ASTM C 39,

Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. The

modulus ofelasticity was determined in accordance with ASTM C 469, Standard Test

Method for Static Modulus ofElasticity and Poisson’s Ratio of Concrete in Compression.

The results at 28 days for the mixes used in the final stage are presented in Table 3.4

46


Table 3.4: 28-day compressive strength and modulus of elasticity

NC - 0.5 NC — 0.4 I HPC - 0.32

Compressive Strength 36.6 43.6 56.4

12" (MP4)U) 2"‘0Modulus ofElasticity 28.0 35.6*

(GPa)

* calculated from AC1 formula

3.4 Preliminary Stage

This section explains the early stage of research in which the main focus was to

establish a reliable experiment and test procedures for early age creep and shrinkage. A

vertical layout of the experimental set-up was designed in which the test specimens were

mounted vertically in a 114 ICN Universal Testing Machine. The bottom grip of the

restrained specimen was rigidly attached to the base of the machine, whereas the top grip

was movable and was connected to the machine through a load cell. A swivel-joint was

installed between the grip and the load cell to minimize eccentric loading. The free

shrinkage specimen was mounted on the base of the machine. A general view for the

experimental set-up in the early stage is presented in Figure 3-6.

The deformation measuring devices (LVDTs) were attached to the surface of the

grip, hence the measured deformation encompassed whatever happened between the two

grips. Several runs were carried out to tune the machine and the controller for the proper

loop parameters that ensured smooth, gentle and stable test.

Concrete specimens were cast, covered with plastic sheets and stored in a humidity

chamber for 18 hours, the earliest possible time at which specimens were installed in the

machine. At this age, it was possible to handle the specimens with the vertical layout of the

experiment. Specimens were left unrestrained for l-2 hours after exposure to minimize the

efi'ect of thermal shock that may cause premature failure as described by Kovler (l995a).

The relative humidity and temperature of the drying environment were recorded at every

shrinkage-measurement time interval (10 minutes). The environment was not well

47


controlled, the relative humidity (RH) varied between 40 % and 55 %; the temperature

varied between 21 and 23 degrees C.

3.4.1 Typical Results

To decide on the proper threshold value for the test, several nms were conducted

with difierent threshold values ranges between 10 and 20 microstrain. The results indicated

that the smaller the threshold value. the more uniform the stress evolution. Figure 3-7

presents two stress curves for difierent threshold values. The threshold snain adopted in the

preliminary experiment was l0 microstrain

To evaluate reproducibility of the experiment, replicate samples were tested at

different times. Replicate samples were initially prepared from the normal concrete mix

with w/c ratio of 0.56. Typical results of the shrinkage and creep are presented in Figure 3-

8. The results indicated a reasonable consistency of the experiment and the resolved creep

strain was almost halfof the shrinkage strain. Evolution ofthe shrinkage stress for the same

samples indicated satisfactory reproducibility as shown in Figure 3-9. Similar sample to

sample variation in the stress evolution and stress-strain cu.rves was obtained with a

concrete mix with w/c ratio of 0.48 as indicated in Figures 3-10 and 3-l l.

Despite the consistency of the stress-strain relation fiom one sample to another, it

was noticed that the stress — strain relation of the test samples did not agree with literature

values at this age. It is known that the modulus of elasticity ofconcrete may reach 20 MPa

in 24 hours, however the calculated values from the test results ranged between 8 and l2

MPa. The experimental procedures and methods ofmeasurement were re-examined and it

tumed out that the attachment of the LVDT on the surface of the grip resulted in errant

measurement of the elastic strain due to grip-specimen interaction (slippage between the

grip and the specimen). The error was substantiated by the very small measurement the

experiment was dealing with. As a result, a partially- restrained test was induced and false

measurements of elastic modulus were obtained. Subsequently, the resolved creep strain

was also including the slip error that was tmknown in the experiment. The problem was

then corrected by attaching the LVDTs to the concrete specimen directly. The shrinkage

stress measured in the experiment was subsequently increased which indicated a fully

restrained condition. The calculated modulus ofelasticity agreed reasonably with normal

48


values for concrete as shown in Figures 3-12 and 3-13, respectively. Reproducibility of the

test was maintained with the new attachment ofthe LVDTs and will be addressed in the

results obtained using the new configuration ofthe experimental set up adopted in the final

stage.

3.4.2 Summary of Experimental Observations

Based on the results fiom the preliminary stage and performance of the experiment,

the following observations can be made:

9 The experiment is reliable and can be used to produce reliable data on restrained

shrinkage and tensile creep of concrete at early age. Reproducibility of data is

acceptable and falls within the normal scatter ofmaterial properties.

9 Tensile stresses generated by restraining shrinkage are significant within the first days

and the role of tensile creep in relaxing shrinkage stress is substantial, and it reduces the

stresses by 50 %. The test is able to detect the sensitivity of creep and shrinkage to

various material parameters such as w/c ratio and cement paste content.

9 To ensure realistic strains measurement, the LVDT must measure the deformation of

concrete sample free from erroneous deformation due to interaction with the test

machine and end grips. The LVDTs must therefore be attached directly to concrete

sample.

9 As the case in every tensile test, alignment is important to avoid eccentric loading. The

rigid attachment of the specimen to the base of the machine was not proper. Swivel

joints must be installed at both ends to minimize eccentric loading.

9 Vertical alignment of the test impedes restraining the sample earlier than 18 hours.

Horizontal layout overcomes this problem and enables testing to start as earlier as the

time set of the concrete.

The above observations and remarks drove the adoption ofthe experiment to

characterize the early age tensile creep and shrinkage of concrete. The research movedtoward designing a horizontal layout of the system in which the above mentioned

shortcomings were improved in the new experimental set up. The following section

descnbes the final research plan

49


3.5 Final Research Plan

The final research plan included designing a new horizontal layout of the

experiment, which could be installed in a controlled environmental chamber. The

horizontal lay out system described in Section 3.2 was adopted in the final stage. In this

stage, the testing suategy was primarily divided into three phases as described below

Phase I: A series of restrained shrinkage-creep tests were conducted under drying

condition of 50% RH and 23° C. Plain and fiber reinforced concrete samples were prepared

from normal concrete and HPC and tests were replicated as needed. Results fiom this part

enabled characterization of total tensile creep, shrinkage, and their interaction. Tests under

combinations of sealing/drying and drying/wetting were conducted on some samples to

provide further insight of the behavior. Shrinkage loads measured on the tests conducted in

this stage were used as the load profile for tests in Phase II and Phase I11.

Phase H: Similar samples as in phase I were tested under sealed condition, in which

samples were prepared and sealed prior to testing. Loads obtained in phase I were imposed

on the sealed samples in the same pattem as obtained in drying test. Extemal drying of

concrete samples was suppressed by sealing but intemal drying was not eliminated in this

part particularly at early age. Therefore, the results for creep included part of the interaction

with shrinkage due to intemal drying. Only samples fiom nonnal concrete with w/c of 0.4

and 0.5 were considered in this part to demonstrate the test methodology and its validity.

Phase III: Tests in phase H were repeated on similar samples and subjected to the same

load profiles, but the sealing condition was replaced by continuous moist curing. Instead of

sealing the test sample, it was covered with moist cloths that remained moist during the test

duration. Extemal and intemal drying were suppressed in this case and subsequently the

measured creep tumed out to be pure material characteristic that had no interaction with

shrinkage.

The testing strategy adopted in the final stage provided basic data that were

required to characterize early age creep and shrinkage of concrete. It also allowed

50


separation and identification ofthe difierent mechanisms of creep and its interaction with

shrinkage. Along with the creep-shrinkage tests, humidity and temperature ofthe concrete

were measured. In addition, split tensile strength tests on 6x12 in cylinders and direct

tensile strength tests were performed to determine the tensile strength evolution with time.

The same experimental setup was used to conduct the direct tensile strength ofconcrete. At

the end of the creep-shrinkage test, the sample if intact, was unloaded and then loaded to

failure to determine the tensile strength at the end of the test. The test matrix for the final

stage is summarized in Tables 3.5 and 3.6. The outcome ofthis stage was used to

characterize the early age behavior and modeling ofcreep-shrinkage interaction. Analysis

and presentation of test results in the following chapters consider only the outcome of these

phase.

Table 3.5: Test matrix for Phase I

1

Mix { Drying Test @ RH V Htunidity/ Tensile Combined Curing

Identification Temp Strength Additional Tests50 % 1 80 %

i l :I X X Sealing / Drying

1NC-0.5 X 1 X

I X X 1) Sealing / Drying1 I 2) Drying / Wetting

l

NC-0.5-SI-' X E

NC-0.5-PP‘ X 1 X X 1

1

1 INC-0.4 X f X

1

I X

NC-0.4-SF X XXI-[PC-0.32 Y X X ‘ X X

C-0.32-SF X | X 'E X

51


Table 3.6: Test matrix for Phases II and III

Mix Identification I Sealed condition Wet condition Humidity / TempNC-0.5 X X

NC-0.5-SF X X XNC-0.4 X X X

NC-0.4-SF X XI

IR X

I XI

Restrained FIGS ShrinkageSpecimen Specimen

fP P=0-z Z e__"° 51 i—Uj1-

76.2X76.2 mm ‘T’ ‘T’

l:lL:l

Figure 3-1: Companion specimens

52

1000 mm

_Y_


f‘,

;.._

Restrained Sample

Free Shrinkage Sample

Figure 3-2: Experimental device showing restrained and fiee shrinkage samples

53


LVDT-—

HydraulicigActuator

RestrainedSample

GageLength

/\

24.5 1n

3x3 111 —

.'.. ,

:1 _ ',.

v

. .-. r._. a . I.

Free ShrinkageSample

8in

Controller

Figure 3-3: Parts of the experimental setup

54

INSTRON 8500

Computer


Strain

100

(°/9)

CummuatvePassng

-40

80

60

20

0

A

Free Shrinkage \

Creep

Recovery cycle

+ Shrinkage

Threshold/

Drying Time

Figure 3-4: Schematic diagram of the test mechanism

no90

-I.|.l

un1. . _ ,...

n

Natural Sand. . . .‘.

0|r0u

F.

1 21

_,-a-

Coarse Aggregate

0.001 0.01 0.1 1 "0

Sieve Size (inch)

Figure 3-5: Aggregate gradation

55


kageStress(MPa)

Shr'n

Q_3 _____.;:. . . . . . . . . . . . . . . . . . . . . . . . . .. -

Figure 3-6: General view of experimental setup ir1 the preliminary stage

1.2 . . 4

W/C = 0.511 . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. _

'----

- -_l 1

0.6 ------------------------- --. .............................................. 41

QQJ

0.4 - - » ~ - ~ » - - - - - - -- i --------- -8 -—-—Thresho|d = 10 migrgstrain -

i’ 7 7 - - - - -Threshold = 20 microstrainQ2 _ . . . . . . ._! ................. ._ _

II

0 1 l l 1 1

0 50 100 150 20

Drying Time (hrs)

Figure 3-7: Effect ofThreshold on Stress Evolution

56


Stran(|1tm)

300__-0

4"J»41'1

-_200 ~ _,4-_¢

,0’‘f

0

100 , ' —-I—- Free shrinkage (spec. 1)—-*—'Creep strain (spec. 1)- - 9 - - Free shrinkage (spec. 2)

0 - - 9 - - Creep strain (spec. 2)

1-100 ‘

-200O

ShrnkageStress(MPa)

50 100 150 200Drying Time (hrs)

Figure 3-8: Free shrinkage and tensile creep of replicate samples with w/c = 0.56

1.4W/C = 0.56

1.2

1 ........................................................ .. -1..,_,,._ . . . . . . . . . . . . . . . ..___-r.----0.8 ,

44............ ..

, -----Spec.2. . . . . ..l .................._......-..................... ...............................

I

0.6

0.4

IQ2 . ........................................... ..

00 50 100 150 200

Drying Time (hrs)

Figure 3-9: Shrinkage Stress evolution with time of replicate samples

57


nkageStress(MPa)Shr

kageStress(MPa)

Shrn

1.6

1.2 -

0.8 —- -

Q_4 _.............................................. .. . ........ ..

....................Q

a0

0a

""""""....... ..,f ..-.:r:.t;Spec..2.

I.....; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

I

I.‘ . . . . . . . - ~ . . - . . . - . - . _ - - - - - - - . . . . . . . - - ~ > - - - . . . . . . - . . - - .-

P1 .

0 50 1 00 1 50 200

Drying Time (hrs)

Figure 3-10: Shrinkage stress evolution of replicate samples w/c = 0.48

j w/c = 0.48T A

.................................................... ..,.-+.'....A"

"' I._ I

II

I

- —*— Spec- 1- --'1--Spec.2

' I1

' I__ 1

0 I

O 40 80 120 160 200

Elastic Strain (um)

Figure 3-11: Stress — elastic strain diagrams for replicate samples w/c = 0.48

58


ShrnkageStress(MPa)¢

S(MPa)

EastcModuu—-

2.510‘

-5 .

1.6

1.2 --

0.8 --

F1.

0.4

0

W/C = 0.56

. . . . . - . . . . . . . . ~ . . . . . . . . . . . . . . . . - , . . . . . . . . . . . . . . . . . . . . . . . . . . . V . . . ..

;‘I

4” -§

f

‘R. . t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7..............-.......-...................->....

CI

I

IL’

----- -- -----;»‘~-I------------------ -- -'—LVDT on concreteI

" ‘I’ -----LVDTongrip

0 40 80 120 160 200

Figure 3-12: LVDT attachment method influences stress - strain evolunon

Elastic Strain (nm)

4 _210

510‘ ~

110‘ - h“---__

W/C = 0.56

—-I-— LVDT on concrete

- -* - - LVDT on grip

-___-1--__

_‘_-“—-.------1

50000 50 1 00 1 50 200

Figure 3-13: LVDT attachment method influences modulus ofelasticity

Drying Time (hrs)

59


CHAPTER 4

RESULTS OF DRYING CREEP-SHRINKAGE TESTS

4.1 General

This chapter presents and briefly discusses the results of creep-shrinkage testing on

concrete samples subjected to drying in the first days after casting. The results include

restrained shrinkage stress, fiee shrinkage, total tensile creep, creep coefficient, elastic

response with time, humidity, and temperature measurements. Typical data is illustrated by

figures in this chapter, and additional test results are documented in Appendices.

The effect offiber inclusion, w/c ratio, drying condition, and initial curing condition on

early age behavior under a restrained condition are also discussed.

4.2 Retrained Shrinkage Stress

The tensile load required to restrain shrinkage deformation of the test sample was

measured in the experiment. Mean shrinkage sness was then calculated by dividing the

measured load by the cross section of the test sample. Typical results are presented in

Figures 4-1 and 4-2, and additional data are presented in Appendix A. Figure 4~1 shows the

efiect ofw/c-ratio on stress development. The shrinkage stress at any given time is

inversely related to the w/c-ratio of the concrete mix. For example, the induced stress at the

age of 70 hours was 1.76 MPa, 1.7 MPa, and 1.1 MPa for the control (plain) concrete

mixes with w/c-ratio of 0.32, 0.4, and 0.5, respectively. The tensile stress developed in the

restrained sample was high enough to fiacture the test sample for all mixes tested; however,

the time to fiacture was different from one mix to another. The mix with a low w/c-ratio

tended to fracture at earlier time than the mix with a high w/c-ratio as seen in Figure 4-1.

This behavior was primarily due to a high rate of early age shrinkage for the low w/c-ratio

mix, which led to a rapid stress development. Typical values for the calculated failure stress

and the age at failure are presented in Table 4.1.

60


The influence ofadding 0.5 % by volume ofsteel fibers to the concrete mix on

shrinkage stress is shown in Figure 4-2. The steel fiber reinforcement delayed the fi'act"ure

time, and the delay was more pronounced in mixes with low w/c-ratio as presented in Table

4.1. The delay in fracture time, as compared to the control mix, was 4-4.6 %, 20.8 %, and

13.5 % for the mixes with w/c-ratio of0.32, 0.4 and 0.5, respectively. However, the

shrinkage stress at failure is not significantly influenced by the addition of fibers. It is

almost of the same order of magnitude as the control mix. The delay in fracture of fiber

concrete may therefore be attributed to the fibers enhancing relaxation by creep. or

improving the ability to distribute stresses and reduce damage at the micro-level.

Table 4.1: Shrinkage stress and age at failure

Mix

Identification

Direct Tensile DelaStress (MPa) Age (hrs) StreStrength (MPa) ss/Stre

‘<

ngth factor

I-[PC-0.32-PC 1.759 69.5 2.325 0.757 NAl

I-[PC-0.32-SF 1.898 100.5 2.465 0.770 1 .446

NC-0.4-PC 2.130 144.7 2.649 0.804 NA

NC-0.4-SF 2.221 174.8 2.790 0.796 1 .208

NC-0.5-PC 1.782 159.5 2.214 0.805 'NANC-0.5-SF 1.767 181.0 2.307 0.766 I 1.135NC-0.5-PP 1.887 134.5 2.083 0.906 0.843

I-IPC: High Performance Mix NC-0.5: Normal Concrete with w/c = 0.5PC: Plain concrete SF: Steel Fiber Mix PP: Polypropylene Fiber Mix

Delay factor = FRC fracture time / PC fracture time

4.2.1 Failure of Restrained Concrete

Tensile stress is not the only factor goveming the failure of restrained concrete. It

can be seen from Figure 4-1 that, at the age of 70 hrs, the difference between the mean

stress of the 1-[PC-0.32-PC mix and of the NC-0.4-PC mix is almost negligible. However,

the 1-{PC mix failed at that age while the mix with w/c-ratio of 0.4 sustained the stress for a

longer period of time. Therefore, cracking criteria based on mere comparison ofthe tensile


stress with the tensile strength at every point in time is deceptive in the case of restrained

conditions. For example, the tensile strength ofthe HPC mix is higher than the tensile

strength of the NC-0.4 mix at the age of70 hrs, yet the former failed despite the almost

equal stresses at that age. This discrepancy can not be explained solely by strength factor,

and other mechanisms must be involved. The other important factor that must be

considered to predict shrinkage cracking time is the stress history, particularly at the very

early age. Examining the results in Figure 4-1 reveals a high rate of stress evolution in the

HPC mix in the first 24 hours. A tensile stress of 1.0 MPa was induced in the HPC mix at

the age of 24 hours, whereas the stress developed in the NC-0.4 mix was aroimd 0.3 MPa.

The high stress at this early age suggests that permanent damage at the micro-level reduces

the integrity of the material and leads to failure sooner than what the strength criterion

theoretically requires. Therefore, the stress history at the very early ages is a critical factor

that influences the performance and durability of the material in the long rim, even if the

material sustains these stresses without fracture. The early age damage caused by rapid

development of stresses may be responsible for the poor performance at later ages as seen

in the early age failure of the HPC samples. The contribution of fibers in this scenario is to

reduce the rate of stress evolution by improving relaxation characteristics, redistributing the

intemal stresses and hence, minimizing the subsequent damage.

Another important behavior observed in res1:rained experiments is that the failure

stress was significantly lower than the nominal tensile strength ofthe material. The results

in Table 4.1 indicate that the ratio between failure stress to direct tensile strength at the

corresponding age is approximately 0.75 to 0.8. The explanation is related to static fatigue

and intemal damage accumulation under sustained loads. The static fatigue represents a

slow crack growth under sustained load that eventually leads to failure. This experimental

observation is important because strength alone is often considered as a criterion for

cracking.

4.2.2 Effect of Extemal Relative HumidityTwo sets of test were conducted under drying condition of 50 % RH and 80 % RH

to examine the efiect ofrelative humidity of the drying environment on restrained

shrinkage characteristics. Typical shrinkage stress obtained for normal concrete and HPC

62


under different drying conditions is given in Figure 4-3. The stress evolution at early age

was not very sensitive to the drying conditions considered in this work. The failure stress in

the case of 80 % RH was higher than that in the case of 50 % RH. This may be attributed to

the positive influence ofhigh RH on elastic modulus and strength The high RH reduces

skin microcracking and improves hydration. Fracture ofthe normal concrete samples was

delayed under the 80 % RH by around 14 % whereas the HPC samples failed at almost the

same age as that under 50 % RH. Despite the higher failure stress exhibited by the samples

tested imder 80 % RH, the rate of early age stress evolution was not significantly altered.

Thus, the contribution ofdrying is not dominating the behavior at the very early age,

particularly for the HPC. Stress evolution at early ages seems to be driven mainly by

autogenous deformation and thermal efiects.

4.3 Free Shrinkage

The free shrinkage was determined from the unrestrained specimen by measuring

deformation over a concrete gage length of24.5 inches. The measured values of the free

shrinkage represent mean values over the cross section. Figure 4-4 shows typical results of

fiee shrinkage for the tested concrete mixes, and more data are documented in Appendix A.

In the early hours of exposure; the normal concrete samples experienced either no

shrinkage or minimal expansion. This period varied between 0 hours, in the case of HPC

samples, and 7 hours for a mix with w/c-ratio of 0.5. The reason behind this dormant period

is probably the disturbance ofthermal and moisture equilibrium upon exposure. There is no

definite answer why this behavior was experienced, and the behavior is not widely

discussed in the literature. However, Kovler (l995a) has also observed this behavior, and

he has called it “thermal shock”, an abrupt cooling associated with removal cf formwork.

The rapid evaporation ofwater from the surface causes cooling of the sample and rapid

reduction in temperature of 3 to 5 degrees C within the first few hours of exposure. In this

experiment, the sample at this time is still tmrestrained to avoid stresses from the thermal

shock. Afier the sample reaches thermodynamic equilibrium with the environment, the

temperature retums to room temperature. This increase in temperature causes the expansion

observed in the beginning ofthe test. The deformation in the first 10 hours is primarily

63


driven by a combination ofthermal and drying (intemal and extemal) efiects. Ifthe thermal

effect dominates this period (e.g. the case ofw/c-ratio of0.5), expansion is observed, but if

drying dominates the period (e.g. the HPC sample) shrinkage is observed. Measurement of

concrete temperature and relative humidity indicates that the thermal efi'ect influences the

first two days. Figure 4-5 presents typical results of intemal humidity and temperature

measurement. The temperature variation is apparent, and this variation is accompanied by

relative humidity changes. The relative humidity starts to decrease after the cooling period

until it reaches a Then, it recovers back to nearly its original value in 24 hours.

The reduction in humidity is partially associated with the increase in temperature (e.g.

when temperature increases by 1 °C, the RH decreases by approximately 2 %). The

reduction in humidity may also be attributed in part to the rapid diflirsion ofcapillary water

in the first hours of exposure. Initially, the diffusion occurs through a water-solid media

that promotes the drying. After that, diffusivity of concrete reduces by several orders of

magiitude when the difliision becomes through a vapor-solid media. Consequently,

redistribution of water occurs in the pore structure and the humidity starts to increase.

After the very early ambiguous period, the shrinkage occurred at a rapid rate until

the age of 50 hours when the thermal effect became negligible and the rate of shrinkage

decreased afierward. At the age of 50 hours the shrinkage strain reached 100, 125, and 160

microstrain, which corresponds to 46.8 %, 50.4 %, and 76.2 % ofthe shrinkage at failure

for the mixes with w/c-ratio of 0.5, 0.4 and 0.32, respectively. The shrinkage during the

critical first 50 hours may be attributed to the combined efiect of autogenous and drying

shrinkage. The HPC samples experienced 76 % of the failure shrinkage strain in the first 50

hours. The high rate of initial shrinkage in HPC was promoted by self-desiccation, a

chemical process ofien occurs in concrete with low w/c-ratio. Clearly, the fiee shrinkage at

early ages is inversely related to w/c-ratio, which is expected for concrete.

4.3.1 Effect of Fiber Reinforcement on Shrinkage

The addition ofsteel fibers to the concrete mixture did not alter the shrinkagebehavior of the mixes. Typical free shrinkage curves offiber and plain concrete mixes are

presented in Figure 4-6. The addition of0.5 % by volume of steel fibers (SF) to the

64


concrete mix did not influence the shrinkage ofconcrete, and the variation between

shrinkage of steel fiber mixes and conuol mixes can be considered to be within the intrinsic

scatter of the measurement. However, it seems that the addition of 0.5 % by volume of

polypropylene fiber (PP) increases the free shrinkage ofthe concrete in early age. This

increase may be linked to the ability ofpolypropylene fiber to control plastic shrinkage

cracking and the associated localized damage in concrete sample. The initial micro-damage

intensity (prior to loading) ofPP is therefore lower than that in plain concrete. As a result,

more intact material per unit volume is expected and higher shrinkage strain is reflected on

macro-level. The explanation ofthis phenomenon is related to the fact that PP have a much

smaller cross-section than steel fibers, and are therefore more numerous and have closer

fiber spacing for a given volume fraction. Consequently, the stiffness ofthe PP concrete

material at early age is less influenced by the initial micro-damage as compared to plain

concrete. This explains the high modulus ofPP samples, which leads to the high stress

development. Accordingly, the early failure of the PP sample and the higher failure stress

as compared to the control mix in Table 4.1 is explainable.

4.3.2 Effect of Relative Humidity (RH) on Shrinkage

The effect of relative humidity of the drying environment on free shrinkage can be

seen in Figure 4-7. Slight variation in the free shrinkage for samples subjected to drying

environment in the range between 50 % and 80 % RH was observed. However, the

difierence was not significant in the very early age (first two days). Despite the slight

reduction in fi'ee shrinkage with the increase in the RH, the overall behavior is not

significantly altered for the range adopted in the experiment. Therefore, extemal drying

alone does not explain the early age free shrinkage behavior even for normal concrete, and

other mechanisms must exist. The free shrinkage at early age is controlled by a complex

interaction between intemal drying, thermal eflects and extemal drying.

4.4 Total Tensile Creep

Typical results of early age tensile creep for the three concrete mixes tested in this

study are presented in Figure 4-8. Test results for various mixes are available in Appendix

65


A. The test results reveal the creep strain as a significant part ofthe concrete deformation at

early age. The resolved creep strains at the time offailure reached 100, 150 and 110

microstra.in for the concrete mixes with w/c-ratio of 0.32, 0.40 and 0.50, respectively. The

corresponding cumulative elastic strains at failure for the same mixes were 110, 100, and

106 microstrain (see section 4.5). Clearly, the tensile creep strain was at least of the same

order ofmagnitude as the elastic strain. Tensile creep, therefore, was able to enhance the

cracking strain capacity of drying restrained concrete by a factor of two.

The tensile creep induced by drying stresses is proportional to the free shrinkage

strain. Figure 4-9 presents typical results of the creep and shrinkage and the reproducibility

ofreplicate samples. Comparison ofthe results fiom replicate samples revealed the

interaction of creep with shrinkage; the resolved creep was larger in samples exhibited

greater shrinkage strain. Therefore, drying increases tensile creep at early age, a behavior

consistent with the concept of drying creep, also called “Pickett effect” (Pickett, 1942).

Interaction of creep with shrinkage at early age is an important element in the deformation

analysis of restrained concrete, and it can be expressed as the ratio between the tensile

creep to free shrinkage. This ratio is a meaningful index as it reflects the reduction of the

build up of tensile strain in the restrained concrete and, consequently, the degree of stress

relaxation. The results of this research indicated ratios in the order of 0.5 to 0.6 at failure

for all mixes. However, the rate of evolufion with time was typically high in the first two

days of exposure and then decreased afierward to asymptotically approach a stable value.

Typical results ofthe creep/shrinkage ratio for the three concrete mixes are presented in

Figure 4-10. It can be generally stated that the ratio of creep to shrinkage (around cracking

time) for concrete in restrained condition is 0.5 regardless of the material. Therefore, the

tensile creep serves to reduce the build up of stress by 50 %. Given the elastic failure strain

mentioned above for the tested concrete mixes, an analysis based on free shrinkage strain

alone would predict failure at 35, 45, and 50 hotus for the mixes with w/c-ratio of 0.32, 0.4,

and 0.5, respectively. However, since the creep reduced stresses far below tensile strength

at those ages, the failure time was extended to 70, 145 and 160 hours, respectively. The

failure time was doubled for the HPC mix and tripled for the other mixes solely due to

creep. The role and importance oftensile creep as a relaxation mechanism is clear from the

results, and it must be considered in the analysis of shrinkage stresses and prediction of

66


shrinkage craclcing. Neglecting tensile creep would result in severe loss ofaccuracy in the

analysis. The ratio of creep to shrinkage in the restrained test is probably the best parameter

to accotmt for creep in a coupled creep-shrinkage analysis.

4.4.1 Effect of Fiber Reinforcement on Total Tensile Creep

A slight increase in total creep due to steel fiber reinforcement was observed in the

tests. However, this increase was only observed when the stress exceeded halfofthe tensile

stength (nonlinear range). This suggests that steel fiber reinforcement successfully

distributes load, and thus engages a great volume ofthe matrix in carrying tensile load,

particularly in the nonlinear range. On the other hand, similar creep behavior was observed

in the polypropylene fiber and plain concrete mixes. This suggests that polypropylene fiber

reinforcement does not enhance the creep behaviorl relaxation ofconcrete at early age.

Figure 4-ll presents typical results of total tensile creep for fiber and plain concrete mixes

(w/c = 0.5). Clearly, the fiber influence on total creep was minimal for the volume fiaction

used in the experiment.

Despite the slight increase in total creep due to steel fiber reinforcement, it can be

generally stated that the fiber reinforcement with a volume fraction of 0.5 % does not

substantially influence the total tensile creep. However, a significant delay in fracture was

observed when steel fibers were included. Thus, the delay in fracture observed in the steel

fiber concrete cannot be explained solely by relaxation due to creep, and other mechanisms

must exist to count for this delay. This suggests that fibers may influence the results of

creep by influencing the creep mechanisms that are related to damage and microcracking.

The influence of fiber on creep mechanisms will be discussed in Chapter 8.

4.4.2 Total Creep Coefficient

Creep coeficient is another important parameter to describe creep behavior of

concrete rmder restrained conditions. The coeficient is defined as the creep stain divided

by the corresponding cumulative elastic stain at the specified time. This definition, as

mentioned in Chapter 3, is different from the classical definition in the literature, which is

defined as the creep stain at any time divided by the elastic stain at the time of load

67


application. The creep coeficient, as defined in this study, is useful for the prediction of

shrinkage cracldng at early age because the elastic modulus ofconcrete changes

significantly in the early days after casting. This parameter more realistically describes the

behavior of a restained test that is characterized by a gradual increase ofthe tensile load,

since creep progresses more slowly rmder a gradually increasing load than that tmder a

constant load (Bazant, 1972). It also eliminates the history dependence in the analysis as

the creep coeficient at any point in 1:ime includes the contribution ofall previous stess and

time steps. Typical results ofcreep coeficient for the tested mixes are presented in Figure

4-12. The creep contribution increased rapidly in the very early age (within the first two

days). This is attibuted to the high rate ofshrinkage and the consequent stess development

observed in the very early age. The creep coefficient continued to increase after the first

two days but at lower rates and reached a value of 0.9, 1.5 and 1.0 at failure for mixes with

w/c-ratio of 0.32, 0.4 and 0.5, respectively. The creep coefificient at failure indicates that

the tensile creep doubles the failure stain capacity of the material irrespective of the w/c

ratio and the failure time.

4.5 Shrinkage Stress-Strain Diagram

The shrinkage-induced stess obtained in the experiment was plotted against the

cumulative elastic stain results fiom the compensation cycles. Typical results are presented

in Figure 4-13. These curves cannot be interpreted as the instantaneous stess-stain

diagram because of the time and drying efiects on these curves. However, they can be used

to characterize the damage caused to the material by drying and sustained loads. The

degradation of the stiffness caused by the drying and sustained stess may be used to

quantify the damage and its impact on fiacture time.

The secant modulus of elasticity calculated fiom the cumulative stain and the

cumulative stress is a good index of either degradation due to damage or stifiening due to

aging. It is well established in the literature that the modulus ofelasticity ofconcrete

increases with time due to aging effects. However, the results of elastic modulus resolved

from the creep-shrinkage test were not following this trend. The reasons for the difference

are related to drying/damage/aging interaction. The results in Figure 4-13 roughly indicate

68


this interaction for the tested mixes. For example, the curve ofthe HPC mix is

characterized by a continuous degradation ofthe secant modulus, in other words, damage

and drying efi'ects are dominating over the aging effect. This is mainly due to the early

rapid development ofstesses caused by the high rate of shrinkage explained earlier. The

efi'ect of extemal drying is also sigrificant since the HPC included silica firme as a

constituent, which needs moisture to hydrate. The drying also causes skin microcracking

that soften the response of the material. For these reasons, a degradation in modulus was

seen in the HPC samples. The mix with w/c of 0.4 indicated almost linear behavior of the

stess-stain curve (constant E). This suggests that the degradation ofmodulus by

microcracking cormteracted the stifiening due to increased mattn-ity. Thus, the elastic

modulus remained almost the same. The mix with w/c of 0.5 exhibited the greatest

degradation of modulus until the age of 85 hours, when the aging efl'ect seemed to

dominate the behavior. As will be presented in the next chapter, the sealed concrete

samples always exhibited stifiening because the effect ofextemal drying was eliminated. A

main point to consider here is that the secant modulus can be used as an index for the

damage caused by drying.

4.6 Concrete Humidity and Temperature

Relative humidity and temperature ofthe concrete were measured during the

experiment. A separate specimen with the same cross section as the one used for the

restained shrinkage test was used to monitor the concrete temperature and humidity.

Several PVC tubes were installed at difierent depths across the sample thickness and filled

with plastic filler before casting. The filler was taken out before starting the measurement

and the pipe was sealed with a rubber stopper. The main purpose ofthe tube was to provide

a liner against water vapor emission from the side ofthe hole and hence permitted

measurement ofRH ofthe material at the specified depth. This approach has been used

successfully as reported in the literature and recommended by some researchers (e.g.

Goran, 1997). An Omega R.H30 humidity meter with RH30-2 probe was used to measure

the humidity. The accuracy ofthe RH30 meter was -J: 3 %. The probe was inserted in the

PVC tube at the time ofmeasurement. An O-ring was attached to the probe in order to seal

69


the pipe after insertion. The temperature was measured by inserting thermocouples in the

concrete sample. The humidity specimen was subjected to drying from the sides only; the

top and bottom sides ofthe specimen were sealed to provide symmetical drying as in the

restrained shrinkage sample. General view ofthe humidity sample is shown in Figure 4-14.

The results ofhumidity measurement ofvarious mixes are presented in Appendix

B. A typical humidity profile ofthe NC-0.5 mix is presented in Figure 4-15. Due to

symmetry in drying, the humidity profile over only halfofthe specimen thickness is shown

in Figure 4-15. To view the profile over the whole thiclmess ofthe sample, a mirror image

can be assumed. The results indicate a drying gradient across the sample.

The exterior 1-inch was subjected to substantial gradient in drying in the first 7

days. However, the gradient was not significant in the first 24 hours. This may explain the

similar shrinkage behavior exhibited during this period by samples subjected to 50%, 70%

and 80% RH. As mentioned earlier, the free shrinkage ofNC-0.5 samples subjected to

these drying environments exhibited similar behavior tmtil the age of 50 hrs which

corresponds to 36 hrs (1.5 days) of exposure, and the humidity measurements support this

finding.

As mentioned earlier, autogenous deformation due to intemal drying was the major

source of shrinkage in the first 48 hours ofdrying, particularly for the HPC mix. The

intemal drying was reflected in the RH measurement. Typical profiles ofRH after 48 hours

of exposure are presented in Figure 4-16 for the three mixes. Clearly, the RH in concrete is

proportional to the w/c-ratio. For example, the HPC-0.32 mix exhibited intemal RH profile

after two days ofdrying that is 5 % less than the NC-0.4 mix and 10 % less than the RH

profile for NC-0.5 mix. The difierence in the RH values in concrete reflects the degree of

intemal drying exhibited by these mixes.

4.7 Effect of Initial Curing on Creep and Shrinkage

The insignificant effect offiber addition on total tensile creep and shrinkage rmder

drying condition may be attributed in part to the bond characteristics between fibers and

cement matrix. Debonding and low bond stength may result as a consequence of early age

exposure to drying and thus hinder the influence offibers. To examine this hypothesis,

70


initial curing period was adopted to improve bond stength characteristics. The curing

method adopted was the sealing ofthe concrete samples to promote hydration for a period

of 3 days before exposure to drying conditions. For this purpose, plain and steel fiber

concrete samples were cast and restained rmder this condition. At the age of 14 hours, the

samples were sealed and restained through the following three days. The samples were

then tmsealed and exposed to extemal drying while restaint was maintained tmfil failure.

Typical stess evolution for these tests is presented in Figure 4-17. The shrinkage stess

during the sealed period was low compared to the rmsealed tests, but was not eliminated, as

sealing could not suppress the intemal drying. Despite the low evolution of shrinkage stess

during the first three days, the samples subjected to initial sealing surprisingly failed earlier

than the corresponding drying samples with no initial curing. The failure stess however,

was similar in all cases. This trend was observed in both plain and fiber reinforced

concrete.The stess evolution immediately afier exposure increases rapidly for two possible

reasons. First, initial sealing increases maturity and elastic modulus of the sample by

improving the hydration ofcement and, subsequently, the restraining stess. Second, theexposure shock seems to accelerate the shrinkage regardless of the age at exposure as

shown in Figure 4-18 for fiee shrinkage. Therefore, the initial curing improves the stength

and the stiffness of the material and reduces the shrinkage. On the other hand, it increases

the magnitude of stess and the potential of early cracking. The balance between these two

aspects must be considered to optimize the strength and reduce the risk ofearly cracking.

The initial sealing of the samples reduced the initial free shrinkage as compared to

drying samples. However, it did not eliminate the shrinkage totally because intemal drying

was not eliminated. The autogenous shrinkage after the first three days composed at least

30 % ofthe total shrinkage for the NC-0.5 mix, as seen in Figure 4-18. This means that

sealing concrete in the field alone (e.g. protective curing compounds) would not eliminate

the development of shrinkage stresses in the very early age.

The total tensile creep of initially sealed samples was smaller in magnitude than the

creep ofdrying samples as shown in Figure 4-19. For example, the tensile creep at failure

for the initially sealed plain concrete sample was 80 microstain compared to 110

microstain for the drying sample. Similarly, the total tensile creep at failure ofpre-sealed

71


FRC sample was 99 microstain compared to 134 microstain for the drying sample. This

difierence in creep may not be attributed to real mechanisms but rather to apparent tensile

creep mechanisms such as drying microcracking. Furthermore, the difierence in the

accumulated elastic stain at failure between the pre-sealed and drying samples was ofthe

same order ofmagitude (arormd 30 microstain) as the difierence in tensile creep. For

instance, the elastic stain at failure ofpre-sealed samples was 75 and 76 microstain for the

plain and the fiber concrete mixes. respectively. The corresponding elastic stain at failure

of the drying samples was 106 and 108 microstain. This indicates that the higher total

creep tmder the drying condition can be attibuted to the efiect ofdrying on microcracking.

The contibution offibers to the increase in tensile creep was not altered by the

initial sealing period. In both cases (pre-sealed and drying) the FRC mix exhibited similar

level of increase in total tensile creep. The effect offiber on delaying fiacture was also

similar; the delay factor defined in Table 4-1 ofthe initially sealed FRC was 1.12 compared

to 1.135 for drying FRC. Based on these observations, the hypothesis stated above

regarding the possible enhancement of creep characteristics ofFRC by initial curing is not

justified, at least for the sealing condition and duration considered in this study.

4.8 Effect of Altemate Dryinglwetting on Shrinkage and Creep

Concrete in the field may be subjected to altemate dryingwetting cycles. The

restained shrinkage of concrete subjected to this condition is therefore, ofpractical

interest. To examine the behavior, a sample from the NC-0.5-SF mix was restained while

subjected to drying in the first 3 days. The sample was then covered with wet cloths for the

following 24 hours and then uncovered and exposed to drying for the rest ofthe test

duration. The stess evolution is presented in Figure 4-20. In the first three days, the

shrinkage stess developed as usual in the drying test and reached a value of 1.44 MPa.

Upon wetting, the stess relaxed at a high rate to 0.08 MPa in 23 hours. The shrinkage

stess however, started to increase upon re-drying but at a lower rate than in the initial

drying. For example, it took the sample only 50 hours to develop a stess of 1.4 MPa in theinitial stage, whereas, it took 72 hours to reach that level of stress once again upon re-

72


drying. The reduction in the rate of stess development is attributed to the low rate of

shrinkage evolution.

Figure 4-21 presents the result of free shrinkage upon the drying-wetting cycle. The

initial rate of shrinkage is high. However, the free shrinkage sample exhibited swelling at a

high rate upon the wetting, which reduced the shrinkage stain fi'om 142 microstain to 69

microstain in 23 hours (51.4 % ofthe initial shrinkage was recovered upon wetting). This

indicates a significant recovery ofearly age initial shrinkage upon wetting, which caused

the stess to drop off significantly. Upon re-drying however, the sample shrunk at a rate

much lower than initially observed in the first drying. For example, the free shrinkage

increased fiom 69 microstain to 126 microstain in 72 hours upon re-drying, whereas it

increased fiom 0 to 142 microstain in 54 hours in the initial drying. Clearly, the first

drying shrinkage in the very early age is critical and the potential for cracking can be

reduced if it is controlled.

The total tensile creep was also afiected by wetting. Figure 4-22 indicates reduction

ofthe total tensile creep fiom 75 microstain to 45 microstain upon wetting (40 % of the

total creep). This reduction is attibuted to the decrease in tensile load and the associated

recovery of tensile creep. It seems that the recovery in creep upon first wetting is also

significant. Thus, drying/wetting cycles influenced the restained shrinkage and creep

behavior at early age. However, no conclusive remarks can be drawn fiom the results

because ofthe limited tests conducted and the multitude ofparameters involved such as

time of application, duration and number of cycles.

Along with the measurement of creep and shrinkage, the internal humidity of the

concrete was measured. Figure 4-23 presents the humidity measurement with time. It can

be seen that the wetting caused the humidity to decrease, which is cormterintuitive.

Furthermore, this reduction in humidity was associated with expansion (swelling). This

behavior was replicated in other samples. The explanation may be related to the alterafion

of intemal thermodynamic equilibrium upon wetting. It is possible that, wetting of the

concrete surface alters the equilibrium between capillary water and the stessed micro-pore

water. For equilibrium to re-establish, water moves from the capillary pores to micro-pores.

This movement ofwater reduces the relative humidity and causes the micro-pore to open

up (expansion).

73


4.9 Tensile Strength

To determine the tensile stength ofthe creep samples, splitting tensile stength

tests were conducted at difierent ages for all concrete mixes considered in the study. The

evolution of splitting tensile stength was then established. The efi'ect offiber on splitting

tensile stength was found insignificant. Therefore, the fiber and plain concrete stength test

results were combined to establish the time evolution curve of the splitting tensile stength

by data fit. A logarithmic relation was found to fit the data reasonably well as shown in

Figure 4-24. The following relations were determined for the mixes considered in thisstudy

w/c = 0.5 0'“ = 2.1151 logr - 2.027 4.1w/c = 0.4 5,, = 2.1443logt -1.320s 4.2w/c = 0.32 6,, = 0.8706logr +1.3516 4.3

Where 0'“ is the splitting tensile stength in MPa and t is the age in hours. in addition to

splitting tensile stength, direct tensile stength tests were conducted for the mix with w/c-

ratio of0.5. The direct tensile stength test was performed using the experimental setup

used for creep test. It tumed out that the difierence between the direct tensile stength

behavior and splitting behavior is significant, particularly in the first days after casting.

Therefore, the use of splitting stength as the tensile strength for creep analysis in the very

early age leads to false relations between creep and stess/stength ratio. A relation between

the splitting stength and direct stength must be established for accurate creep analysis. It

was formd that the direct tensile stength ofdrying samples can be realted to the splitting

tensile stength by the following equation

illdl) =1.377 -0.00571 1 5 room6,, (dry) 4.4£15-Yl= 0.2 1 2100hrs<Y,,(dry)

74


Where 0', is the direct tensile stength in MPa. In addition to the inherent difierences

between splitting and direct tensile stength tests, the discrepancy is probably augmented

by the specimen size and geomety (l50x300 mm cylinders were used for splitting test and

a rmiaxial specimen with a cross section of 76x76 mm for direct tensile test). The specimen

srze and geomety influence the drying behavior and the associated cracking, particularly at

early age. For a realistic representation oftensile stength for creep analysis at early age,

the direct tensile stength must be evaluated for all creep tests.

4 10 Concluding Remarks

The shrinkage stess evolution at early age is substantial. It has significant impact on

material performance and can lead to fiacture ofthe material. The stength criterion,

which is usually implemented for estimating time of first crack, is erroneous if

considered alone. Static fatigue and damage accumulation seems to promote failure at

stess level less than the theoretical tensile stength. The rate and history of stess

evolution are two important factors that influence the time of cracking and the failure

stess. These parameters must be considered in the analysis for accurate prediction of

shrinkage cracking.

The very early days of concrete life are characterized by a complex interaction of

intemal drying, extemal drying and thermal effects. The free shrinkage ofnormal

concrete and HPC in the first two days forms a significant portion of the early age

shrinkage, and it is also driven by a complex combination of internal and extemal

drying. Extemal drying alone cannot explain the free shrinkage in the first two days and

other mechanisms must exist. The addition of fibers (0.5 % by volume) does not afiect

the free shrinkage at early age.

Total tensile creep at early age forms substantial portion ofthe time dependent

deformation. Its cross-dependence with the fiee shrinkage can be expressed as the ratio

oftotal creep to free shrinkage. This ratio is important and can be roughly taken as 0.5,

which indicates that the creep relaxes the shrinkage stess by 50 % for normal and high

performance concrete.

75


Although the addition ofsteel fibers slightly increases the total tensile creep, stress

relaxation caused by total tensile creep cannot solely explain the delay in fracture time

when fibers are included. However, it seems that the fiber addition influences certain

creep mechanisms that afiect the fracture behavior as the fiber samples last more than

plain concrete samples before failure.

Initial cming of concrete does not change the restrained shrinkage behavior ofFRC as

compared to plain concrete. However, the potential for cracking of concrete generally

increases as the initial curing improves stifiiess. The balance between improving

strength and stifiiess ofconcrete and the risk of cracking must be therefore considered

Alternate drying and wetting significantly afiects the creep and shrinkage behavior at

early age. The shrinkage stress relaxes rapidly upon the first wetting and developed

once again but at a lower rate upon drying. Creep and shrinkage recovery of restrainedconcrete is also influenced by wetting/drying application.

76


hr'nkageStress(MPa)S

nkageStress(MPa)

Shr

2.5 —

2 ................................................................................ ..

1.5 ------------------------------------------------------------------------------ --

1 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ‘ ' ' ' " ' ' ' ' ' ' ' ' ' ‘ ' ' ' ' ' ' ' ' ' ‘ ' ‘ ' ' ' ' ' " - =

_""'—' W/C = Q40

0.5 ------------------------------------------------ -- --— W/C = Q_5Q

O0 50 100 150 200

Age (hrs)

Figure 4-1 Shrinkage stress evolution of different plain concrete mixes

2.5

2 ................................................................................ ..

1_5 .......................................................................... ..

1 """"""""""""""""""" "" —-—-w/c=o.3o—-—w/c =0.s2 SF-—-—w/c =o.so s|=

7 ——~—w/c=0.soQ_5 .................................... ..

i . . _ \0O 50 100 150 200

Age (hrs)

Figure 4-2 Efiect of steel fiber reinforcement on shrinkage stress

77


ShrnkageStress(MPa)

Figure 4-3 Shrinkage stress evolution ofplain concrete under various drying conditions

FreeShrnkage(pm/m)

2.5

1.5

O0.5 _,- 3'

-100

-150

-290 ...................................................................... ..

-250

2 . , n4"’._.

0’.-o"- '-

, - ‘ ' . . . ' ' ‘i. - ' . ". .-0,0 __.-

-'._¢ ’..'_,-

I _..'. _,-0"

1" . '1 _ . t ,!.x. . .0' ' —-—-w/c= .2RH=50%

—-—w/c = 2 RH = so %--------w/c = 0 RH = so %----~---w/c = . 0 RH = so %GOOD O1U'lOJ(.|O

It ‘.-

' -'0

P.’0

100 150Age (hrs)

‘O

0 Q

0 50

50

Q .................................... .. W/C=0_32

_50 _ _ _ , . . . . . . . . . . _ _ _ _ _ . . . _ . . . . . . . . . . , . . . . . . . . . .. = .

—~—w/c = 0.50

300 ‘

. . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 50 100 150 200Age (hrs)

Figure 4-4 Free shrinkage strain for difierent plain concrete mixes

78


e(;mlm)-0

nkag

FreeShr

ConcreteTemperature(C°)

50

O

'-..-...___

~___

~

0II

-____

J

—-- Relative Humidity- - - - - Temperature

96

92

88

84

0 20 40 60 80 100 120 1

Figure 4-5 Typical temperature and humidity distribution

Drying Time (hrs)

4

'—"'-W/C = 0.32 SF—"—W/C = 0.32

-50 —°-W/C = 0.50 SF-"—" W/C = 0.50

-100 ———w/c = o.so PP-150

-200

-250

-300

350O 50 100 150

Age (hrs)

Figure 4-6 Efi'ect of fiber reinforcement on fiee shrinkage

79

200

100

80

tveHum'dly%)

xr

._

ConcreteRea


nkage(pm/m)

FreeShr

mlm)--n.sr

Creep

Tense

50

0

-50

100

-150

200

-250

160

140

120

100

80

60

40

20

0

or —-—RH=so%—-——RH =10 %

-- —'—-RH=80%

-50 o so 100 150 200Drying Time (hrs)

Figure 4-7 Effect of drying condition on free shrinkage (w/c = 0.50)

—'-‘W/C = 0.32—"—W/C = 0.40—'°"—WlC = 0.50

0 20 40 60 80 100 120 140 160

Age (hrs)

Figure 4-8 Tensile Creep for different plain concrete mixes

80


lm)_¢

n(im

Stra

nkage

Creep/Shr

200

100

0

-100

-200

-300

0.6

0.5

0.4

0.3

0.2

0.1

O

-0.1

—o4g_ ‘

A.’ -4+

_.'*4I*

4}

—'—Creep Spec. 1—-—-Shrinkage. Spec. 1-°—Creep Spec.2—°—Shrinkage Spec. 2

0 50 100 150 200

Age (hrs)

Figure 4-9 Creep is proportional to free shrinkage (replicate samples)

4,4_.*

' 40*i

_ 1<1’

l .

; “_'_W/C

T —°—W/C

0.320.500.40

0 20 40 so so 100 120 140 160Age (hrs)

Figure 4-10 Creep/shrinkage ratio for difierent plain concrete mixes

81


140

pm/m)

100 —-—Steel Fiber30 "—°— Polypropylene

Creepstran(

._ 5Q .

40

20

O

-20

—'— Plain Concrete

-0.2 0 0.2 0.4 0 6 0 8 1

Stress I Strength

Figure 4-11 Effect of fiber reinforcement on tensile creep (w/c = 0.5)

1.5

cent 1

CreepCoeff0.5

O

44»_,o—

_* T

—-—w/c = 0.32 1—-— w/c = 0.40—-——vv/c = 0.50

0 20 40 60 so 100 120 140 160

Age (hrs)

Figure 4-12 Creep coefficient evolution for various plain concrete mixes

82


ikageStress(MPa)

Shr

Figure 4-I3 Shrinkage stress-elastic strain diagram for different plain concrete mixes

2.5

il1.5 —

1

0.5 [

lQ ,

—-——w/c = 0.32—-—w/c = 0.40

; —-—w/c = 0.500.5

-20 0 20 40 60 80 100 120

Elastic Strain (um / m)

Figure 4-14 General view ofhumidity measurement sample and device

83


ty%

Hum'd

atveRe

ly°/0

tveHum'd

Rea

100

4*93 . . . . . . . . . . . T . . . .,--._'_,---

96 .. ___,,-.-4‘.-_.

- .1

¢ @—V ¢. .' '

92

90

88

86

..,- .........._......__,»<-

’._/."?z<.:'," _'.»' -—'-—1day

, '

i»/ /' RH = so % "*" 3daY$_ /- . --°- 4day$

E '1' Age at Exposure = 14 hrs -ll/

a

¢ - - - - ' """.

_,-0"__ ._ -- "’__¢ _

’ V .. ,’ _} _ .1, mi __i=

.--v--_. --Q’

‘—-~_\l

--------- --

__¢--_-¢ I

, '-1' "'

,-"’

F58

r1

..... --_ , . . - . - --->---¢-0.-.-.'.‘.'.T . . . . . . . . , . . . ._

-Q__ --¢ ----- -¢- -, ------

_-Q-_ —._,__

-----" 2days

Sdays- 6days

~-*- 7days

--q

@.

84 T0.25 0.5 0.75 1 1.25 15

Depth (inch)

Figure 4-15 Humidity profiles for NC-0.5 mix

100Age at Exposure = 14 hrs

98 _k4

96

94

92

90

88 -

4! .

-I I

' I

—-—w/c = 0.32—-—w/c = o.so—-—w/c = 0.40

RH=50%as

0.25 0.5 0.75 1 1.25Depth (inch)

15

Figure 4-16 Humidity profiles for concrete after 2 days ofdrying

84


kageStress(MPa)

Shr'n

E§

kageStran

FreeShr'n

2j fi

..9 ,0' 0¢ ¢

.' Q.. ..4~--‘I. ._ .

.

Q;1 . ..;;..,, . . . . . V . ..

0,‘.

-"-'8.,.

1.5

. ..._..':..-’ . '4 ., 440' " x4' ' —-I--PC-0.5-drying

"' —*—SF-0.5-dryingY » ~' - ~ » - "--°----PC-initially sealed '

Sealing period SF-initially sealed

0.5

O

-0.50 50 100 150 200

Age (hrs)

Figure 4-17 Efiect of initial curing on stress evolution ofplain concrete and PRC

50

Sealing —-'-— SF-initially sealed_ ""~"" PC-initially sealed’ , _ _ _ _ - - --'--" SF-0.5-drying

“‘""" ——'- PC-0.5-drying

O

-50A

-1DQ\

-150 1\\

Q 1

O.0-200 ~--__.

.."‘\““-

-250o so 1oo 150 200

Age (hrs)

Figure 4-18 Effect of initial ciuing on free shrinkage ofplain concrete and FRC

85


CreepStran(pm/m)

150

100 ~ ~ _,~

50 ' ,',

I¢¢¢_.v0

Q‘,

_./'1.’It.0-.¢

' I4,»I —-— PC-0.5-drying

__.-»-_’_jIIII....--" -—*- SF-0.5-drying° 1 =~' ' ' ' - - PC-initially sealed

Sealing period ""'--" SF-initially sealed

0 50 100 150 200

Age (hrs)

Figure 4-19 Effect of initial curing on tensile creep of plain concrete and FRC

/'\

StressMPa

%/

kage

Shrn

2~ Drying i 1 Re-Drying, < ¢ >

7 tting

1:.

0.5-

‘ WIC = 0.500 _

0 30 60 90 120 150 180

Ag e (h rs)

Figure 4-20 Shrinkage stress evolution of FRC upon drying/wetting cycles

86


FreeShrnkage(pmIm)

Figure 4-21 Efi'ect of dryingwetting on fiee shrinkage and shrinkage recovery of FRC

mlm)--A.

&r

CreepStran

-150

50

-50

100

80

60

40

20

E

<( )>D rying L L Re-Drying

LnflztlingW/C = 0.50

O 30 60 90 120 150 180

Age (hrs)

0

W/C = 0.50

Wetting

DI'Vin9 i i L Re-Drying<( +' )>

30 60 90 120 150 180

Age (hrs)

Figure 4-22 Effect of drying/wetting on tensile creep ofFRC

87


ty%

Reat'veHum'd

Strength(MPa)

tngTense

Spt

_'t==Ii‘*-

‘ Re-d rying 'K > H

Initial Drying Wetting -so 1 Y -»

T 1_ t Depth = 0.5 inch f

j w/c = 0.5 1J

Drying Time (hrs)

Figure 4-23 Humidity profile upon drying/wetting cycle

750 50 100 150

-~"‘.

_¢

.;A-__.»"' - -a.’

. . . . . . . . , . . . . . . . . . . . _ . . . . . . .._.’._._,_»........;-A ,'

__.lQt’_-,

a." I .

4' I‘ 4‘ Q

I. . . . . . . . . . . . . . . . . . . . . . . ..,......‘..................

I, O

O

....;. . . . . . . . _ . . . . . . . . . . . . _ . . ..

'6A

O

O

"""""" W/C = 0.32-----w/c=o.4 '—'— W/C = 0.5

Age (hrs)

Figure 4-24 Evolution of splitting tensile strength (drying curing)

88

0 50 100 150 200


CHAPTER 5

RESULTS OF CREEP-SHRINKAGE TESTS UNDER SEALED ANDWET CURING CONDITIONS

5.1 Introduction

Knowledge of basic tensile creep is essential to characterize the behavior of early

age tensile creep of concrete and its interaction with shrinkage. The basic creep is a

material property that is defined as the creep ofconcrete when moisture content is held

constant. However, Intemal drying at early age is in most cases unavoidable, and it

complicates the measurement ofearly age basic creep ofconcrete. Therefore, two curing

conditions were used in this study to quantify the basic creep: sealed conditions and wet

conditions. In the sealed condition, the sample was sealed using a self-stick aluminum foil,

while in the moist condition, the sample was covered with moist cloths throughout the test

duration.

The experimental set-up described in section 3.2.2 was used to measure the creep

and shrinkage of sealed and wet samples. Unlike the drying test in which loads were self-

induced, the loads applied in the sealed and wet tests were pre-deterrnined. The loading

profile with time was based on the loading history recorded during tests tmder drying

conditions. The magnitude and pattem ofthe load induced in drying condition was applied

to the sealed and wet samples. This chapter presents and briefly discusses results of early

age creep-shrinkage tests on concrete samples subjected to sealed and wet curing

conditions. The results include free shrinkage, total tensile creep, creep coeficient, elastic

response with time, humidity, and temperature measurements. Typical results are only

presented in this chapter. Additional test results are documented in appendices. Two mixes

were tested in this part: NC-0.5 and NC-0.4. Steel fiber reinforcement with a volume

fiaction of 0.5 % was used in FRC mixes. The efiects offiber reinforcement and w/c ratio

on the creep and shrinkage behavior under sealed and wet curing conditions are discussed.

89


5.2 Sealed Condition

The significance ofthe behavior of concrete rmder sealed conditions lies in its

relation to the basic creep and the interaction between creep and shrinkage. The common

practice for many years was to consider the deformation to cease because no shrinkage

occurs when moisture exchange with the ambient medium is not allowed. However, this

assumption may not hold when young concrete is considered because drying of concrete at

early age is driven by other than extemal factors only. Therefore, firrther investigation is

required to validate the behavior at early age. For this purpose, samples were cast and

sealed with aluminum foil in order to eliminate moisture exchange with the environment.

Creep and free shrinkage tests were carried out simultaneously using the same

experimental procedures described in Chapter 3, except that the samples were sealed and

the load was applied in the same pattern and magnitude as those induced in drying test. The

load applied for the various concrete mixes are presented in Table 5.1 and the load pattems

are shown in Figure 5-1.

Table 5.1: Load Profile Applied on Sealed and Wet-Cured Concrete

NC-0.5 & NC-0.5-SF NC-0.4-PC NC-0.4-SF

Age (hrs) Load (KN) Age (hrs) Load (KN) Age (hrs) Load (KN)27.50 1.00 22.67 1.03 26.33 1.2030.50 1.65 27.17 2.01 30.83 2.3933.17 2.60 30.50 3.05 34.50 3.5836.50 3.39 33.50 4.13 38.00 4.7040.50 4.41 36.50 5.18 41.17 5.4547.67 5.19 39.83 6.12 44.83 6.5256.08 6.13 43.83 7.16 51.67 7.5071.25 6.84 50.33 8.31 62.00 8.5887.25 7.28 62.33 9.23 79.17 9.64

101.33 7.69 81.83 10.05 105.67 10.73121.67 8.35 108.17 11.20 139.83 11.80143.25 8.90 144.67 12.37 174.83 12.90155.84 9.53180.95 10.25

90


5.2.1 Free Shrinkage (Autogenous Defonnation)

Despite the fact that test samples were sealed against extemal drying, significant

fiee shrinkage was measured in the test. Figure 5-2 presents typical results of free

shrinkage for the two mixes tested in this study. The results revealed higher shrinkage of

the NC-0.4 mix than that exhibited by the NC-0.5 mix. The shrinkage strain at the age of 7

days reached 120 microstrain for the NC-0.4 mix and 82 microstrain for the NC-0.5 mix. lt

is well known that concrete with w/c-ratio less than 0.42 will exhibit shrinkage under a

sealed condition because of intemal drying (self-desiccation). However, it is less

understood that the mix with w/c-ratio of 0.5 will exhibit measurable autogenous shrinkage

because intemal structure presumably contains enough capillary water to avoid self-

desiccation. This phenomenon may be explained in part, by chemical shrinkage afiliated

with cement hydration at early age contributing to the observed deformation. The chemical

shrinkage develops continuously fi'om the point of cement-water contact as a result of the

loss ofvolume due to hydration (volume of reactions products is smaller than the volume

ofthe reactants). Clearly, sealing the samples alone will not eliminate the early age

shrinkage, even for normal concrete because ofthe intemal drying and chemical shrinkage.

This has an impact on understanding and determination ofbasic creep ofconcrete at early

age.The early age shrinkage of sealed concrete forms a significant portion of the total

drying shrinkage. The exact proportion of these two factors (drying and autogenous) in the

total shrinkage, however, is still disputed, especially at early age. Figure 5-3 shows the

sealed and drying shrinkage for two mixes: NC-0.4 and NC-0.5. The total drying shrinkage

at the age of 7 days is shown in Figure 5-3 as 260 and 230 microstrain, whereas the

corresponding shrinkage of sealed samples is 120 and 82 microstrain, respectively.

Accordingly, the sealed shrinkage at the age of 7 days is 46.1 % and 35.6 % of the

corresponding total drying shrinkage for the two mixes. However, at the age of 2 days, the

sealed shrinkage composes 72.7 % and 31.5 % ofthe corresponding total drying shrinkage

for the mixes NC-0.4 and NC-0.5, respectively. Hence, at very early ages shrinkage is

primarily driven by intemal drying, particularly for the concrete with low w/c-ratio. The

91


observed minor effect ofextemal relative humidity on very early age fiee shrinkage, as

explained in Chapter 4, also supports this finding.

These results provoke a question: Can the shrinkage of sealed concrete be

considered to be primarily due to autogenous shrinkage, or may there be other mechanisms

related to sealing condition? Kovler (I996) showed that sealing ofdrying concrete causes

some swelling. He explained the swelling by the release of the surface tension of capillary

water due to the change ofvapor pressure above water menisci. When concrete is sealed,

the vapor pressure increases quickly and changes the meniscus curvature so that the level of

water becomes flatter, and the average radius of meniscus increases. This releases the

capillary surface tension and leads to consequent swelling. In this study, the sealing

commenced at the age of 12-14 hours when only minimal drying had occurred and the

intemal vapor pressure would not have been significantly altered by sealing. The observed

swelling in the tests was minimal and can therefore be neglected. The early age shrinkage

ofsealed samples can be primarily considered as autogenous shrinkage. It is a significant

contributor to the total shrinkage measured in early age, particularly for the concrete with

low w/c- ratio.

5.2.2 Humidity Profile of Sealed Samples

The measurement of intemal relative humidity in sealed samples indicated some

internal drying. The relative humidity ofconcrete dropped by 6-10 % over a period of

drying for 7 days. Figure 5-4 shows typical profile of the relative humidity of sealed

concrete for the NC-0.4 and NC-0.5 mixes. The results showed reduction in the relative

humidity, which is mainly due to the continuing hydration. The relative humidity at depth

of 0.25 inch (maximum drying) for drying concrete samples was only 5-7 percent higher

than that for sealed concrete samples. This indicates the significance of intemal drying at

early age. One major difference between sealed and drying conditions, however, is that the

relative humidity across the sealed specimen is almost tmiform at any given time as shown

in Figure 5-4. In contrast, a relative difierence in humidity across the drying sample was

quite obvious in Figure 4-15. In other words, no significant drying gradient occurred tmder

the sealed condition. This observation has a substantial influence on the analysis as will be

92


discussed in Chapter 8. The uniform drying eliminates the gradient in the intemal stress and

thus impedes the occurrence ofmicrocracking in the outer skin ofthe specimen. The

phenomena ofmicrocracking on exterior surfaces result when the outer layer of concrete

dries out at a higher rate than the inner layers. As a result, the outer layer rmdergoes tensile

stress which when exceeds the tensile strength of the material causes the surface cracking.

The microcracking caused by drying gradient has a profound impact on the overall

response of material as will be discussed in Chapter 8.

5.2.3 Tensile Creep of Sealed Concrete

Since the sealing of concrete, as discussed in section 2.2.1, does not eliminate

autogenous shrinkage at early age, the tensile creep of sealed concrete cannot be resolved

from the deformation of a loaded sample alone. Two samples must be tested

simultaneously; one must be fiee of load to account for autogenous shrinkage and the other

loaded as in the drying test. As with the drying test, reproducibility of test results was

established first. Creep tests for the same material, and same load pattem and magnitude

were replicated at different times for various mixes. The results were then compared.

Typical test results of replicate samples are presented in Figure 5-5. The results indicated

that both the fiee shrinkage and tensile creep were consistently reproduced. The variation in

the autogenous shrinkage, for example, was around 10 microstrain, which lies within the

intrinsic variation ofthe material. The experimental set up and procedures were shown to

be consistent, and the data on creep and autogenous shrinkage at early age was reliable.

The sealed tensile creep, as in the case ofdrying, was proportional to the

autogenous shrinkage; the high values oftensile creep were observed on specimens

exhibiting high autogenous shrinkage. This experimental observation reveals the

interrelation between tensile creep and autogenous shrinkage. The tensile creep is,

therefore, increased by concurrent drying irrespective ofthe source ofdrying; i.e. the

Pickett efiect is not only limited to extemal drying. The tensile creep - autogenous

shrinkage interrelation suggests that creep is influenced by a common mechanism upon

drying. However, the magnitude of increase in tensile creep depends on whether the drying

is extemal or intemal. For example, the tensile creep resolved in the sealed experiment was

93


almost equal to the autogenous shrinkage of the material at the age of 7 days as seen in

Figure 5-6. The same concrete mixes on the other hand, exhibited total creep strain equal to

halfof the shrinkage strain in the case of drying. The difference was probably related to the

intemal stress distribution and the drying gradient that influenced the drying creep

mechanisms. The difierence in the ratio ofcreep to shrinkage between sealed and drying

tests is a general indication to the existence ofdifferent creep mechanisms related to drying

gradient and true stress distribution. Further discussion of this matter and the possible

mechanisms will be presented in chapter 8. The lower creep in sealed samples is also

supported by Powers hypothesis (Powers, 1966) which says that there should be some

differences in the creep of sealed and unsealed samples. The difierence according to

Powers is arising from the fact that in the sealed sample, the ultimate expulsion ofwater to

the ambient environment is not possible, and hence, the creep is lower than in an rmsealed

sample. However, Neville (Neville et al., 1983) doubts whether the efiect suggested by

Powers is significant.

Steel fiber reinforced concrete was tested under sealed conditions to investigate the

effect of fiber reinforcement on the early age creep and shrinkage. The results ofautogenous shrinkage for FRC and plain concrete mixes were quite similar; thus, the effect

of fiber on autogenous shrinkage was negligible. Likewise, the tensile creep was not

significantly altered by the addition of steel fibers. Figure 5-7 presents creep and shrinkage

results of sealed FRC and plain concrete with a w/c-ratio of 0.4. Similar behavior was also

observed in the concrete mix with w/c-ratio of 0.5. It must be noted that for the samples

tested in this research, there was a slight increase in tensile creep when steel fibers are

added to the concrete mix. However, the magnitude of increase of tensile creep was not

conclusive as it always lied within normal scatter of the material. Nevertheless, the fact that

it happened in most specimens indicated a general trend that was related to material

behavior.

5.2.4 Age at which Sealing is Applied

The age of concrete at which sealing is applied is a primary factor that afiects the

level ofsubsequent swelling and shrinkage. Sealing the concrete, particularly at early age,

94


disturbs temporarily its thermodynamic equilibrium with the environment, and subsequent

deformation ofconcrete is expected to reflect this disturbance. The level of disturbance is

mainly influenced by the age ofconcrete and its moisture content at the onset of sealing.

Concrete samples sealed at difierent ages were tested to examine the efl“ect of sealing time

on creep and shrinkage. One set of tests was sealed at the age of 14 hours and another set

was sealed at the age of27 hours. The age at the onset of load application was 27.5 hours

and same load pattem and magnitude was applied for the two sets.

Figure 5-8 presents typical results of fiee shrinkage and tensile creep for both tests.

The results indicated variation in the magnitude of free shrinkage from the onset of load

application. The samples that were sealed at 14 hours exhibited less swelling and more

shrinkage than that for the samples sealed at 27 hours. The variation can be explained as

follows: when the initial drying period increases, the volume of emptied capillary pores

will increase. Hence, the potential formation ofwater meniscus will be promoted because

the intemal vapor pressure decreases upon drying. However, upon sealing, the vapor

pressure increases and causes reduction of the capillary surface tension, and consequent

swelling. The degree of swelling depends on the intemal vapor pressure at the time of

sealing and volume and size ofempty pores.

Accordingly, the impact of sealing on changing the vapor pressure in concrete

samples remaining uncured for 27 hours will be more pronounced than in samples sealed at

the age of 14 hours. Swelling will be promoted, which means less shrinkage in the samples

sealed at the age of 27 hours. As a result, the resolved total tensile creep will be influenced.

Therefore, characterization ofdrying creep by testing sealed and drying samples will be

influenced by the time of sealing, particularly at early age. Hence, it must be specified

consistently in the experiment to avoid misinterpretation of the data. Sealing at the age of

12-14 hours was adopted as a standard time in this research.

5.2.5 Cumulative Stress versus Cumulative Elastic Strain

As mentioned in Chapter 4, restrained shrinkage test samples were all failed duringthe drying test. However, the sealed samples were able to sustain the same loads that

caused failure in the drying test. Sealing seems to improve strength and stifiress of

95


concrete due to improved hydration of cement and hence, the stifiress of sealed concrete

should increase at a rmique rate. The applied stress was plotted against the elastic strain

induced in the concrete. The resulting diagram for sealed concrete was dramatically

changed as compared to drying concrete. Figure 5-9 presents typical results for the mix

NC-0.5. The secant modulus can serve as an index of either damage (degradation in

modulus) due to drying and sustained load efiects or stifiening due to increased maturity.

The shape of the diagram is controlled by the combined efi‘ect ofthese two factors. For

example, the secant modulus exhibits degradation with time if the drying effect dominates

the aging effect, whereas it increases with time when the aging effect is dominant.

The results for sealed concrete exhibited increases in the secant modulus with time

while drying caused softening (or at best constant modulus) with time. The difierence in

the elastic strain between sealed and drying concrete could be related to the drying gradient

and the associated microcracking. Moreover, the ratio between the secant modulus of the

drying sample to the sealed sample could also serve as a state variable for drying-related

damage. Chapter 8 sheds more light on these observations to better understand the drying

creep behavior and the relation between drying microcracking and fracture.

5.3 Wet Curing Condition

Since the sealed curing condition did not eliminate autogenous shrinkage of

concrete at early age, the measured tensile creep was not equivalent to basic creep. To

evaluate the basic creep, shrinkage must be essentially zero. This research has adopted a

moist curing technique to suppress the early age shrinkage. The moist curing method

adopted consisted of covering the concrete with wet cloths throughout the test duration.

The cloth was kept wet by frequently adding water, and the water temperature was held

constant at 23 °C (the temperature of the environmental chamber). Creep and shrinkage

were measured on samples prepared fiom two mixes: NC-0.4 and NC-0.5. Tensile loads

and ages at load application were the same as that for sealed tests. The only difference was

the curing method in which the samples were covered by wet cloths right after demolding

and are maintained wet throughout the test duration. This section presents the test results of

creep, shrinkage, and stress-strain response.

96


5.3.1 Effect of Wet Curing on Autogenous Shrinkage

The moist curing technique successfully suppressed the early age autogenous

shrinkage as shown in Figures 5-10 and 5-ll for plain and fiber reinforced concrete. The

results clearly indicate substantial reduction in the fiee shrinkage ofmoist concrete as

compared to sealed concrete. For example, the magnitude ofthe fiee shrinkage afier 7 days

for the mix NC-0.5 as shown in Figure 5-l0 was substantially reduced from 83 and 98

microstrain (sealed condition) to 7 and 17 microstrain (moist condition) for fiber and plain

concrete, respectively. Similarly, the shrinkage ofthe mix NC-0.4 is reduced from 121

microstrain to 4 microstrain for plain concrete, and for fiber concrete the wet curing

counteracted the shrinkage and induced minor expansion of l7 microstrain as shown in

Figure 5-11.The moist curing not only reduced the absolute shrinkage but also reduced the rate

of shrinkage afier the first 24 hours. Unlike for the sealed conditions, the shrinkage under

moist conditions reached a stable value within 24 hours and remained almost unchanged

throughout the rest of the test duration. The stability of shrinkage for most of the test period

eliminated the efi'ect of shrinkage on the measured creep. The elimination of shrinkage by

wet curing was probably due to two factors. One factor is related to the increase of the

intemal vapor pressure and the associated swelling following the covering of the sample.

This swelling oflsets the autogenous shrinkage fiom hydration. The other factor is the

replenishment ofmoisture to the internal system by capillary suction and difiirsion, which

compensates for the consumed moisture by continuing hydration. The first mechanism is

probably working in the initial period following the covering with wet cloths and may

continue for a day or so; the second mechanism plays its role at later stage because

difiusion ofmoisture from the surface to the inner material takes some time. The combined

efiect of the two mechanisms was responsible for the elimination of shrinkage.

The suppression ofshrinkage by wet curing was confirmed by measurement of the

intemal relative humidity. The measurements indicated almost constancy ofthe relativehumidity throughout the test duration. This does not mean that self desiccation was totally

eliminated because the error of the RI-I measurement is within 3 %. The constancy ofthe

97


measured RH explains, at least in part, the observed minimal shrinkage. In addition to that,

rmiform distribution ofrelative humidity across the thickness ofthe sample was observed

similar to that for sealed concrete. The consequences of constancy and uniformity of

intemal humidity on the analysis of creep data and mechanisms are important for

discussion in section 5.4 and in chapter 8.

5.3.2 Does Wet Curing Affect Mechanical Properties?

As mentioned in the previous section, the wet curing reduced concrete shrinkage by

providing extra moisture to the system. The consequences on creep measurement were

profotmd because the interaction with shrinkage was eliminated. On the other hand, adding

water to hardened concrete may result in changes ofthe microstructure, which in turn may

afl'ect mechanical behavior of concrete including creep. It was desired to examine the

influence ofwet curing on mechanical behavior despite the absence ofmicrostructure

examination ofthe tested concrete. The elastic response ofthe material was used as an

index for evaluating the effect ofwet curing on mechanical behavior ofconcrete. Since the

sealed and wet samples were subjected to the same stress history, comparison of their

responses to stress can be used to qualitatively identify the impact ofwet curing on elastic

response. Similar impact on both creep and elastic response can be reasonably expected.

and hence, the wet curing must afiect both of them if it has a real influence on mechanical

behavior. Ifthe wet condition does not alter the elastic response of concrete as compared to

that for sealed concrete, it is unlikely that the basic creep behavior be altered. Another

possible way to examine the influence ofwet-curing on mechanical behavior is to compare

the elastic response upon loading to failure for sealed and wet samples that are pre-loaded

by the same stress history and then unloaded prior to the test. In this case the efiect of

damage accumulation would be encompassed in the response.

Either ofthe above approaches could be used to qualitatively examine the

influence ofwet curing on mechanical behavior, and data on both was available in this

study. The available data on both methods gives the same conclusions however, the second

approach is only presented herein. At the end ofbasic creep test, the sample was unloaded

and then loaded to failure. Figure 5-l2 presents typical stress-strain results of sealed and

98


wet cured concrete for the two mixes: NC-0.4 and NC-0.5. The diagrams indicate similar

shape and inclination for both sealed and wet cured concrete. The stress-strain diagram is

almost bilinear with the pivot point corresponding to the pre-applied stress prior to

unloading. Two major points can be seen in the diagrams. First, the modulus of elasticity of

sealed and wet-cured samples was almost identical, which means that the influence ofwet

curing on elastic modulus is not significant. Second, the tensile strength ofwet-cured

concrete only slightly exceeds that of the sealed concrete. Therefore. the difierence in

mechanical properties between sealed and wet-cured concrete was minor. Likewise, the

basic creep behavior was most likely be rmafiected by wet ctuing condition. It seems that

the wet curing suppresses the shrinkage of concrete without altering the mechanical

behavior of the material.

5.4 Identification of Basic Creep

The measurement of tensile creep under the three different curing conditions

provided valuable information on the total creep, basic creep, and drying creep. For

example, the drying condition provided data on total tensile creep; the sealed condition

provided data on basic creep and its interaction with autogenous shrinkage; and the wet

condition provided data on the basic creep. The stress history applied in the test of each

mix was identical for the three curing conditions. Typical results ofcreep and shrinkage

under the three curing conditions are shown in Figures 5-13 and 5-14 for the mixes NC-

0.5-SF and NC-0.4, respectively. Three major points can be seen in these results. First, the

resolved tensile creep was directly proportional to the associated free shrinkage. This is

primarily due to the interaction between tensile creep and the accompanied shrinkage; the

greater tensile creep was observed in specimens exhibited high shrinkage. Tensile creep of

concrete was therefore greatest under drying condition and smallest under wet condition.

Second, the sealed condition reduced the fi'ee shrinkage but the reduction is not substantial

for the purpose ofbasic creep measurement. Consequently the measured tensile creep of

sealed concrete was not totally related to basic creep because it included the interaction

with autogenous shrinkage. Third, the wet curing suppressed the free shrinkage

substantially and maintained it at a minimum level throughout the test duration.

99


Consequently, the measured tensile creep ofwet concrete was not influenced by shrinkage,

and it could be called the basic creep ofthe material. In this research, the basic creep as a

material property was extracted from the test under wet condition.

5.4.1 Effect of Fiber Reinforcement on Basic Creep

The efiect of fiber reinforcement on creep behavior of concrete is subtle. In general

it seems that the curing condition influences the effect of fiber on creep. In the case of

drying, for example, the addition offibers slightly increased the total tensile creep of

concrete particularly at high range of stress (o'/ 0', 2 0.6) as mentioned in Chapter 4.

However, from material point ofview, the real effect on creep due to fiber reinforcement

can be judged fiom the basic creep results.

Figures 5-15 and 5-16 present typical results of specific basic creep for fiber and

plain concrete for the mixes NC-0.5 and NC-0 .4, respectively. The stress profile and age at

loading were identical for fiber and plain concrete of the mix NC-0.5. For the mix NC-0.4,

the stress profile and age at loading were not identical for fiber and plain concrete but close

enough (as shown in Figure 5-l) to compare results. The two mixes exhibited similar

behavior at early age. The addition offibers tended to reduce the specific creep in the very

early age. The results showed higher rate ofcreep evolution ofplain concrete than that of

fiber concrete in the very early age. This behavior continued for the first 6 days before the

rate of creep evolution was surpassed by the fiber reinforced concrete for the NC-0.4 mix.

However, creep measurements beyond seven days were not available to draw conclusions

on the rate ofcreep afier that period.

On the contrary, the total tensile creep (drying case) offiber concrete exhibited a

rate ofevolution similar to plain concrete in the first two days, and afterward the fiber

concrete exhibited more tensile creep than plain concrete as shown in Chapter 4. The

efiects of fiber reinforcement on basic and total tensile creep at early age are somewhat

conflicting, which is primarily due to the type ofcuring adopted. Difierent curing

conditions seemed to invoke difierent creep mechanisms. It is therefore required to define

the curing condition when the efiect offibers on early age creep is examined.

100

7


The reduction in basic creep rate offiber concrete at early age can be hypothetically

attributed to the ability of fiber to control initial (prior to loading) microcracking density in

the concrete. Concrete generally exhibits some level ofmicrocracking in the first l2-24

hours. At the onset of loading, which was arotmd 24 hours in this research, the fiber

concrete probably included less uncontrolled microcracking density than the plain concrete.

As a result, the initial load could be distributed more tmiformly in fiber concrete which led

to lower intemal true stresses than that in plain concrete where no distribution of stresses

had occurred. The difierence in intemal stress intensity drives the difierence in the rate of

early age creep between FRC and plain concrete.

The impact of fiber addition on creep seems to depend on the curing condition and

the microcracking density. Wet curing reduced the microcracking density, at least in the

early age, and less creep was exhibited. However, the drying condition promoted

microcracking density in fiber concrete (debonding offibers due to simultaneous shrinkage

and load), and more creep was exhibited at high stress range. In other words, part of the

tensile creep was contributed by cracking. This hypothesis, however, opposes the role of

fiber on controlling cracking and the ability to distribute intemal stresses. The net efiect oncreep is probably govemed by the combination of both phenomena, which is a rather

complex interaction and many parameters are involved. This complexity may explain the

conflicting results of the fiber effect on creep that are available from the limited studies in

literature and the lack of conclusive results regarding the effect of fiber on creep (Shah

l992).The data generated in this research suggested that fiber reinforcement generally

reduces creep as long as the cracking density is below a critical value. When the cracking

density exceeds the critical value, the rate of creep increases. This hypothesis explains why

fiber concrete exhibited lower basic creep, but slightly higher total tensile creep at high

stress ranges as compared to plain concrete. It also explains results in the literature that

showed reduction of compressive creep when the fiber volmne fraction exceeds l % and

increase in creep when the fiber volume fiaction is below l % (Shah 1992). The critical

cracking density depends primarily on fiber’s volume fiaction, aspect ratio, geometry, and

the quality ofconcrete matrix. Testing the stated hypothesis needs further research, but at

101


this point it is a reasonable interpretation to explain the results of this research. Further

discussion ofthe contribution ofcracking to tensile creep will be discussed in Chapter 8.

5.4.2 Effect of WIC on Basic Creep

It is generally known that the w/c-ratio of the concrete mix influences its creep

capacity. However, the efi'ect ofw/c-ratio on creep at early age, particularly on tensile

creep, is less conclusive. Creep is generally lcnown to increase as the w/c-ratio increases;

however, in the early age the results ofthe tested mixes exhibited the opposite under

restrained condition. The creep ofthe NC-0.4 mix (w/c = 0.4) was more than that of the

NC-0.5 mix (w/c = 0.5) as shown in Figtues 4-17 and 4-18 for fiber and plain concrete,

respectively. Consequently the stress relaxation capacity prior to failure was higher in the

concrete mix with a low w/c-ratio. This result was evident not only from basic creep test

results, but also fi'om the total tensile creep under drying conditions as explained in Chapter

4. The NC-0.4 mix exhibited not only higher drying shrinkage and autogenous shrinkage,

but also higher tensile creep capacity as compared to the NC-0.5 mix.

5.5 Concluding Remarks

0 Sealing against drying alone does not eliminate the early age shrinkage even for normal

concrete, because of intemal drying. Therefore, the common pracfice of considering the

shrinkage deformation to cease by sealing the sample is inaccurate for early age

concrete. The tensile creep of sealed concrete at early age is not equivalent to the basic

creep because it includes part of the autogenous shrinkage.

0 The autogenous shrinkage of concrete is a significant contributor to the total concrete

shrinkage measured in early age, particularly for the concrete with low w/c- ratio. It

forms a major part ofthe total shrinkage in the very early days.

I The creep/shrinkage ratio ofconcrete under the sealed condition difi'ers fiom that under

the drying condition. This suggests that the drying gradient and associated cracking

influence the creep and shrinkage of concrete. The sealed and wet-curing conditions

provide a uniform distribution of intemal humidity in concrete, which eliminates the

102


surface cracking and impacts the creep analysis, particularly the drying creep

mechanisms.

The age ofconcrete at the onset of sealing influences its shrinkage and creep behavior.

Thus, the experimental procedures must specify the age at which sealing is applied to

avoid misinterpretation ofthe collected data.

Moist curing can be successfully adopted to suppress early age shrinkage. Its influence

on mechanical properties of concrete as compared to the sealed curing condition is

negligible. Therefore, the creep measured tmder the wet curing condition is equivalent

to the material basic creep because shrinkage is eliminated fiom the measurement.

Steel fiber reinforcement alters the rate and magnitude ofbasic tensile creep in very

early ages. However, whether real or apparent creep mechanisms are influenced is not

immediately obvious. Nevertheless, it seems that the microcracking component of the

creep of concrete is influenced by the fiber reinforcement. A hypothesis of the

existence of a critical crack density is suggested to explain the creep behavior of fiber

concrete. When microcracking is below the critical density, fibers distribute intemal

stresses more rmiformly and reduces the intemal stress intensity, which subsequently

lower the creep. However, when crack density exceeds the critical value, the

microcracking contribution becomes dominant and the creep of fiber reinforced

concrete increases.

The water-cement ratio of the concrete mix influences the early age shrinkage and

creep behavior ofconcrete. The early age creep is inversely related to the w/c-ratio of

the restrained concrete.

103


Stress(MPa)

(rm/m)-4

kage

FreeShr'n

2.5 .

O5 . . . . . . . . . . . . ..

,-1 ............... . .,-..r

F’ - .1, 4

, - _ - - ~ - - - - - - » . - - » - .4. . . . . . . . . . -...-........---.....‘-. ._..._..............

Y n‘I'D IOOOIOOIIQCOOIIII‘

. I| - ¢ - . - - Q cf.-' ‘---__J

-15 ..__._._._._;;_. . . _ _ . . . . _; . . . . . . . . . . . . . . . . . ..v.?.-. . . . . . . . . . . . . . . . ..- -----4

I1-..--

—— no-0.4"""""""""""""""""""""""""""""" -- NC-0.4-SF

_,~' - - - - - NC-0.5

Age (hrs)

Figure 5-1 Stress profile applied on wet and sealed concrete samples

20

-20

-40

-60

-80

-100

-120

-14

0 1o so 1oo 150 200

—"—W/C = 0.40

-'"'—W/C = 0.50

00 50 100 150

Age (hrs)

Figure 5-2 Free shrinkage of sealed concrete samples

104

200


FreeShrnkage(pmIm)

ty%(w/c=0.4)

atveHum'd‘-

.1

Re

50

O

-50

-100

-150

-200

-250

-300

102

100

98

96

94

92

90

—-— Sealed - 0.4—-— Sealed - 0.5—°— Drying - 0.5—°— Drying - 0.4

&"_‘.T Em

0 50 100 150

Age (hrs)

Figure 5-3 Free shrinkage of sealed and drying concrete

No gradient W/C = Q_5 3F__ £155. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - ..,;. ......................._...._~ '___-er

‘ ._¢,,_.z_>.... .-\ ."- A .-'\ .,'. . . . . . . . . . . . . . . . . - . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

,2?.~' —-0-— Depth = 0.50 inch

-', Depth = 0.75 inch‘W,’ """""""""""" ” "-5- Depth=1.00inch. /' _ - - - - - Depth = 0.25 inch-------------------- --x-_- ---- -- —-— Depth = 0,50 inch

-5 1- Depth = 0.75 inchNo gradient

W/C = 0.4 SF ~

F 1020 50 100 150 200

Drying Time (hrs)

Figure 5-4 Humidity profile in sealed concrete samples

l05

200

90

92

94

96

98

- 100

Areea

/\1.P.W"H-9

(90=9//V\l%


Stran(pmIm)-—,

1-s

(pm/m

Stran

150 . ,

-1 ' ' ' ' ' ' ‘ ' ' ' ‘ ' ‘ ' ' ' ‘ ' "_'.'.:::-5""'"-'-".'.:;;;;______U"; ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' " ' ' ' ' ' ' ' ' ' ‘ " ' ‘ '

Shrinkage """""""""-150 - ' * ' I ‘ 10 50 100 150 200

Cfeep w/c = 0-4. steel fiber‘ ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ";"'"""""'"';::;_1i;'.€"”“*':’::i." ’ ' ' ' ‘ ' ' ' ‘ "

5Q . . . . . . . . . . . . . . ....‘_.',..j-.-'f.’:- ..................................... ..i .................... ..

" A ------- ~- Free shr.-Spec.20 ------------------------------------- ~- Creep-$pe¢_2 ------------ --

_ -—— Creep-Spec.1_5O Hi _________ ___________ __ —i Free shr.- Spec. 1 ____________ __

Age (hrs)

Figure 5-5 Free shrinkage and creep strain of replicate samples

1soCreep Steel Fiber

n... --------- ~--4, .—(100 ________,

.f’fl'507 -------" Free shr. - WIC = 0.4

0 -------" Creep - W/C = 0.4—-— Free shr. - W/C = 0.5——-Creep - W/C = 0.5

-__~

-100 j _____________________________________ __

V Shrinkage-150

o so 100 150 zooDrying Time (hrs)

Figure 5-6 Creep and shrinkage of sealed concrete with diflerent w/c-ratios

106


um/m)‘y

.1

Stran

/\

n(um/m

Stra

150

100

-50

-100

100

0 \ "

El...... ............................ ., —oreei>sF-<14

150

Creep ;__..

-------..I..

O.- :

_ ------- -- Free shr.-PC-0.4. . . . . . . . -.---.... C‘-eep_pC_0_4

—-— Free shr.-SF-0.4

Shrinkage

O 50 100 150 200

Age (hrs)

Figure 5-7 Free shrinkage and tensile creep of sealed FRC

- A

' ‘ C'eeP Sealed at 14 hrsO

_ ...¢ao--1''_‘"-‘uvO0I'-.'4""‘_. . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."..Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

¢§""

- ,..x.--*"’ Sealed at 21 hrs i4. ‘.‘I"‘.

_,..¢' W/C = 0.5is-. x . - - - - ..‘ - . - - . , . . . . - > - - - . . - . . - . - - - ~ . > - r - - - - r - - . . . x . _ ~ - - - - - . . . . . . . - ~ - . . . . . . . - Y - -.

- "\. .-a“'°‘“1.

. W‘.-

_ ""“\._ Sealed at 27 hrs;_ i \Qr"""%.'§¢'-'.;;-‘"13-I-'8‘-lib;-'-’e'.'.L'¢'-'-li' ' '

~ Shmkage Sealed5at 14 hrs ‘- Y

._.... ............................... .

0 50 100 150 200

Age (hrs)

Figure 5-8 Efiect of age at sealing on fiee shrinkage and tensile creep

107


Stress(MPa)

kage(um/m)

FreeShr'n

Figure 5-9 Stress-cumulative elastic strain diagrams at difierent curing conditions

1.5

0.5

2

O ‘O

I‘. I,

.9 9.., -0 _e

.* If I

0’ ‘~ a

1 I "-"r .'.'5"L - ¢

.',‘P'5?‘ -r"-Dwms-PC—--—Drying - SF

Q ----'--"Sealed - PC -' ""'"--Sealed - SF 0" Oo.o,O u1'q1°‘°1

00 20 40 60 80 100 120

Cumulative Elastic Strain (um /m )

20

5‘. I-Q T‘ —y_.¢¢ F‘-T B £_r% ‘

.'k\| '_

-.3. . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- .-..-.. --------""""'.-.-l"‘-.- .----' .. I.v¢"-. 1.. "1 ~.C""

-20 A

lsO

2222 99999.0.9.0 °“."°“.“(I)(D‘Tl"Tl

_60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .'-1:‘;. . . . . . . . . . . . . . . . . .L".

Sealed ""1. 1-8Q .......................................... .- P. .._‘............................... ..

s.,_' °"'-Q.... ___. . g._____‘ _

100 ' ’ ' "o so 100 150 zoo

Age (hrs)

Figure 5-10 Effect ofmoist curing on early age shrinkage (W/C = 0.5)

I08


f\

kage(pmlm

FreeShrn

Stress(MPa)

100

150

1.5

0.5

50

0

50

3

l l

_.__:.----.-------0--"'t¢......-0--i‘~~'¢--" --0 has _ —

_. . . . . . . . . . . . . . . . - ............................ .._-,___,...¢--' ; T‘ *"'—-c-. .

_............ ..................................... .. —-—Nc-0.4 . '

L............................. ..... .......................... .. J

Wet ~ I—-— no-0.4 -

NC-0.4-SF -NC-0.4-SF -Sealed

' --A---....,_ -

O 50 100 150 200

Age (hrs)

Figure 5-ll Effect of moist curing on early age shrinkage (W/C = 0.4)

4'.

.-'25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...F ...,-erf .......... ..

2 ....................................... ..f ................................ ..I

- - eal- et

ealetl312222 coco0.00.0 ‘."‘r“'P*“E”’E"'

Q 10 20 40 60 80 100 120 140 160

Elastic Strain (umlm)

Figure 5-12 Stress-strain diagram for sealed and wet cured concrete

109


§Basic Creep 5 5w-LU1 @ P

8O >5 Cr§ee 3 . __----1j _pn--

,--n -

50 ................... -..-.=§.~..'.f.?.'.TT.SeaIed.,,,........... ..... ..."- - - ‘ ' ' ..-..---------'-"'0 Wet' . ...QI-II:

on.-3",". l 1

Stran(um/m)nkage 22:‘ E,'E5'5

0 ' ‘ noanaq;,;.‘.'.‘.'-';-'—“¢iiii’pa.-|_' ‘ ‘ ‘ ' '-“.'ji'¢-h1nnln-nanny--q--—-—.---_.‘

~ -_ _, Wet-so ------- - _

Sealed. --------------- - -" -1oo

FreeShr

-1so ----- -»y Dry w/c = o.s

-200 ----- --

-2500 50 100 150 200

Age (hrs)

Figure 5-13 Creep and shrinkage of FRC under difierent curing conditions

200

> Creep

DBasic Creep F!

1QQ .. . ... . . . _ . . . . . . -..-.-Q n ~ ~0|........ .. .----_--‘P

______ ‘D cnnnqonuun'-' ___;-.-I.-.,,.uuuu--pa, an

(um/m)

Q . IIIC i.‘-.- > - - . _ . . - . . . _ . _ _ . . _ . . . . .

‘ Wet._ ‘~__ Seal

""""‘?‘?'~°“'-'é';';§I;;';';‘;';:;';' ' ' " ' ' ' ' ' ' ‘ ' ' ' ‘ ' ' ' ' ' ' ' ' "

....- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

Stran

< FreeShrnkage

-300 *0 50 100 150 200

Age (hrs)

Figure 5-14 Creep and shrinkage ofplain concrete under difierent curing conditions

110


cCreep(pmlmlMPa)

Spec'f'

f'cCreep(um/m/MPa)

Spec

40Load increment W/C = 0-5

35

30

25

20 . . . . . . . . . . . . . . - . ..0I0

2;;:_ ..;.--.--_15

. I

_..\*,..,.-_,.-_.\_

.10

5 . . . . . . . . . . . . . ..

In|an

,0

i

. . . . . . . . . . . . . . _ . .._._.,..................... ....... ...-., ,I .-I005’|' I

II r

..o! 1 . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . ..0-

......................................... , . ..' 3_,..,-~_.... g

1 .

""""""""-—"“"‘"'srasl"n'ss"r'"“...............iitiii1ti.Elai.I1Qqnqtete

00 50 100 1 50 200

Figure 5-15 Efi'ect of fiber reinforcement on specific basic creep for NC 0 5 mix

Age (hrs)

50

.':'7::\~..-

W/C = 0.4Load increment40 5:

--_-,.._,,,;-...

\\ _ E

.-q.._ ...._.{~..,... ..;.30

0 v\ ‘x

2o ;--------- Plain Concrete—— Steel Fiber

10

O0 50 100 150 200

Figure 5-16 Effect of fiber reinforcement on specific basic creep for NC 0 4 mix

1 .

Age (hrs)

lll


cCreep(umlmlMPa)

Spec'f'

Creep(pm/mlMPa)

Spec'f'c

40

30

20 ---------;;;;_-;;r;-.~-'r= ---------------------------------------- ~-

19 .......... . .;,-:..'.................................................................... ..

0 I . l . 1

0 50 100 150 200

50

40 ................................................................................. ..

30 .. ............. ................. ..

20 . . . . . . .._.q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . _ . . . . . . . . ..

10

0 r . .

0 50 100 150 200

riNC-0.4-SF"""""" NC-0.5-SF

..... --. . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . .._.,:.......i.......-1

__ __(.' r ------ ' ‘

I‘.

4

\-,'\1,‘ '

. -f

0|HpI

Age (hrs)

Figure 5-17 Efifect of w/c-ratio on specific basic creep of FRC

I -"'..‘_______ -',,_.-.-.,.-- Q,' >

~--"r; .... --,-, .' I

M. .‘I

-.:-e\,.$ .-___-_.1-_._,',_\ .'~ _-—v;_ I -

' ------- -- no-o.s—-— NC-0.4

Age (hrs)

Figure 5-18 Efiect ofw/c-ratio on specific basic creep ofplain concrete

l 12


CHAPTER 6

ANALYTICAL MODELS: BACKGROUND AND FORMULATION

6.1 Introduction

Analytical models are required to characterize the interaction between tensile creep

and shrinkage at early ages, because direct experimental measurement is not yet possible.

This chapter presents and discusses the analytical models implemented in the analysis.

Literature backgrotmd and formulation ofthese models are presented. Models for basic and

drying creep, basic concepts of damage, and a method to characterize the damage in

restrained concrete are discussed in this chapter

6.2 Basic Creep Constitutive Laws Formulation

Basic creep is a material property defined as the creep when no exchange of

moisture between the test sample and the surroimding environment occurs. Mechanisms ofthe basic creep and its modeling have been a matter of research since the beginning of this

century and a great deal of imderstanding to the phenomena has been achieved. It is

generally assumed that the basic creep can be predicted with a reasonable accuracy by the

linear viscoelastic theory (Bazant 1988). However, there are two general approaches in the

linear viscoelasticity: integral formulation and difierential formulation. Particulars ofeach

approach are briefly discussed in the following sections.

6.2.1 Integral Formulation

The integral representation of linear viscoelastic stress-strain relations for agng

materials was given by Voltera using Boltzmann’s superposition principle (see Bazant,

1988). The constitutive relation is expressed in terms ofa superposition integral. The

kemels in the integral fonnulation are either the creep or relaxation fimction, which

represents the response ofthe material to imit step ftmction. For a tmiaxial state of stress

and an aging material the constitutive relationship can be written according to Voltera as:

I13


I

2(2) = ]'J(r,r')do-(r') + 8" (r) 6.10

Where a(t) is the strain at time t, 6° (t) is the stress-independent strain (shrinkage and

thermal) and J(t,t') is the creep compliance ftmction which is expressed as a sum of the

elastic strain at time of load application t’ and the creep strain at any time t; r >- r’ , i.e.

J(r,r') = H1:,§+C(r,r') 6.2

Where E(r') is the elastic modulus characterizing the instantaneous deformation at age

1' and C(r, r’) is the specific creep, and ¢(t,t’) is the creep coefficient defined as the ratio of

the creep deformation to the initial elastic deformation.

Equation 6.1 is a general uniaxial constitutive relation defining concrete as an aging

viscoelastic material, based on applying the principle ofsuperposition. It basically states

that the response to a sum oftwo stress histories is the sum ofthe responses to each of them

taken separately. This principle of superposition facilitates the calculation of creep caused

by variable stress, and its use in design is permitted by contemporary design codes and

recommendations of engineering societies. However, the use of the principle of

superposition yields accurate prediction only when the stress lies within the service limits

(i.e. less than 50% ofthe strength).

The principle of superposition may be equivalently expressed in terms of the

relaxation function, R(r, I’) which represents the uniaxial stress 0' at time t caused by a unit

constant axial strain imposed at time r’ and held constant afierwards. This yields the

constitutive relation of aging viscoelasticity in the following form:l’

0'(t) = IR(t,r')[de(r') - dr:° (r)] 6.30

In this research, the integral formulation was not used for the analysis because of

the computational dificulties associated with this approach and the limitations of the

principle of superposition. It is likely that the li.nearity of creep, on which superposition is

based, be violated at early age for at least two reasons. First, early age concrete exhibits

deviation from linearity in the constitutive stress-strain relation. Second, the generated

stresses in a restrained test exceed the service stress limit in most cases, which put the creep

114


law in the non-linear range. Therefore, the superposition principle will not be the most

accurate analysis, and a crude estimation of the creep fimction is only possible.

6.2.2 Differential Fomiulation

In this approach, the creep behavior is represented by rheological models composed

ofelastic (spring) and viscous (dash-pot) elements placed together in a series and/or

parallel coupling. The difierential formulation, also called “rate — type formulation”

eliminates history dependency in the analysis of creep. It requires only the current values of

stresses, strains, and a few hidden state variables to be stored. Therefore, the number of

arithmetic operations is significantly reduced (Bazant, 1972a, Bazant, 1988, and Bazant

and Wu, 1974).The rate-type formulation ofthe aging creep law of concrete results in a system of

first or second-order differential equations- with the actual time as an independent variable.

It can be based on either Maxwell chain model or Kelvin chain model (Figure 6-l).

The Maxwell chain model represent the stress-strain relation as follows:

0' = Z01, 6.4

Where 0",, is the stress in the ,urh Maxwell tmit. The strain rate in the aging spring is

6'“ / Eu (t) , and that in the dash-pot is of“ / r7/J (t) , where r1“ represents the age-dependent

viscosity of the nth dash-pot. Summing these strains results in the following equation:

. 5,. . . -0'“ +-;7—o'“ =E“(s—so) 6.5

Where, so is the stress-independent inelastic strain. A unique characterization of the model

requires some relationship between 17,, and E/J to be assumed. A parameter r“ has been

introduced to relate dash-pot viscosity to spring modulus, the simplest fonn of it is

2'” = 17” / Ey and has been used in most works (see Bazant, 1988). This parameter is called

relaxation time, and also called retardation time.

A similar conversion to a difierential —type form can be achieved based on Kelvin

chain model. The rate ofstress in the ,urh spring is Eu (t)s'j“ , while the rate of stress in

ll5


the prh dash-pot is 17,, (t)s"# . Setting the sum ofthese two stress rates equal to 6' , The

following difierential constitutive law is obtained:E ' 'é.y+ ,,(f)+'7,,(l‘)éfl= 0' 65

'l,,(f) T7,.(I)

6.2.2.1 Maxwell versus Kelvin Chain Model

The above discussion reveals that either the Maxwell chain or the Kelvin chain can

approximate the integral-type creep law of linear aging viscoelastic material. Thus, these

models are mutually equivalent, but each has different analytical features. The primary

characteristics of the two models can be pointed out as follows:

0 The difierential equation for Kelvin chain model (Eq. 6.6) is ofthe second order, while

for a non-aging material it is of the first order. The difierence in the order of the

goveming differential equation basically results because the stress for the aging spring

must be written as 0"“ = EH (t)é,, , not as 0"“ = EH (t)a“ for the non-aging material, to

satisfy thermodynamic restrictions on the solidifying process (agi.ng) (Bazant, 1988). In

contrast to the aging Kelvin chain model, the difierential equation for the aging

Maxwell chain model (Eq. 6.5) is of the first order. This is one advantageous property

ofMaxwell chains over the Kelvin chains as it simplifies the computational aspects of

the creep law.

Q The Kelvin model formulation is based on the creep compliance fimction whereas, the

Maxwell model formulation is based on the relaxation function. Identification of

material parameters by optimizing the difierence between the model and the test data

requires creep data for Kelvin model and relaxation data for Maxwell model. Kelvin

model in this regard is more convenient since the creep test is much easier to perform

than the relaxation test and is more common in literature. The simplicity and

straightforwardness of the material identification in Kelvin chain model is a great

advantageous property over the Maxwell model.

Apparently, it is possible to approximate creep law by either Maxwell or Kelvin model.

However, these models are not completely equivalent for aging material such as concrete.

116


The main difificulty in these models arises fi'om aging. In this study, the problem ofaging

was dealt with separately as will be discussed in the next section. Nevertheless, the Kelvin

chain model motivated by simplicity ofmaterial identi.fication was adopted in the analysis

ofbasic creep in this study.

6.2.3 Aging Creep Based on Solidification Theory

The aging aspect ofbasic creep ofconcrete can be mathematically handled by two

difierent approaches. First, the classical, direct approach that treats the material parameters

involved in the creep model as empirical fimctions ofage as explained in the previous

section. Second, the approach based on solidification theory (Bazant and Prasannan, 1989

a, l989b), in which the creep function ofthe viscoelastic material is considered age-

independent but the volume fiaction ofthis material is increased with time. This approach

has a solid foimdation fiom the viewpoint ofchemical thermodynamics. It also has an

important practical advantage, namely, the characterization of creep by a non-ag'ng model

which is much simpler. The aging in the solidification theory is introduced separately by

means of a variation of the volume fraction of the solidifying viscoelastic material

constituent as will be discussed in the next section.

6.2.3.1 Qualitative Description of Aging

The main idea in this formulation is that the aging aspect of concrete is considered

to be due to growth ofthe volume fraction v(t) of the load —bearing portion of the

solidified matter, the properties ofwhich are age-independent as required by equilibrium

thermodynamics. The model portrays aging as a consequence of the growth of the volume

fiactions v and h associated with viscoelastic and viscous suains, respectively as shown in

Figure 6-2. Generally, thermodynamic analysis can be perfoirned only for systems of

substances that have time-invariant properties. As known from chemical thermodynamics,

a time-dependent chemical system is obtained as a consequence of a time-varyingcomposition of the substances in the system. The hydration ofcement is a chemical

reaction, and so it must be treated similarly as proposed by Bazant (1977, 1979). Thevolume v(t) represents the increase ofboth the volume fiaction ofthe hydrated cement and

117

7


the load-bearing solid fiaction, which is growing due to formation offiirther bonds or

polymerization ofthe calcium silicates hydrates. The principal advantage ofthis theory is

that the load-bearing matters are age-independent. This makes possible, the application of

the conventional theory ofnon-aging viscoelasticity.

6.2.3.2 Micro-Mechanics of the Creep Model

The micromechanics ofthe model described in this section was formulated by

Bazant and Prasannan (1989a). The creep strain is assumed to be composed oftwo

components as shown in Figure 6-2: viscoelastic strains" and viscous strains’ . At high

stresses, 2" and sf represent the viscoelastic-plastic strain and the viscoplastic strain.

Micromechanical analysis ofthe solidifying process has been used by Bazant (1977) to

model the aging as a growth of the volume fraction of load-bearing solidified matter. The

basic hypothesis illustrated by this model is that the volume elements dv(t) solidified at

various times are all subjected to the same strain, which is equal to the overall macroscopic

creep strain s"(t) . This hypothesis implies the coupling of all these volume elements to be

in parallel (Figure 6-2). More complicated combinations ofparallel and series coupling

should be more realistic. However, the parallel coupling generally gives upper bounds on

the stiffiiess of composites, and for concrete it gives good estimates. So it should be also

acceptable for creep as a simple approximation. The model introduces a microstress

0'8 (v,z) in the solidified matter at time r, which is defined as the stress at the location where

the solidification occurs when the volume of all the solidified matter is v (Figure 6-2). A

layer of thickness, dv(r) , is assumed to solidify and bind with the previously solidified

matter at time 2' , at which the volume ofall the solidified matter is */(2') . Now an essential

point is that, at the moment it solidifies, the layer dv must be in a stress- fi'ee state,

i.e. o'g[v(r), z']= 0. This assumption is applicable only to solidification at a solid-solution

interface, as shown in Figure 6-2. Conceivably, the solidification process could also occur

at a solid-solid interface, in which case a pressure across the interface could happen (crystal

growth pressure). However, consideration ofthis phenomenon has no significant influence

118


on the age-dependence ofcreep and would require a model that is more complex than the

parallel coupling of elements dv(t).

Equilibrium condition ofthe macroscopic applied stress O’ with the intemal

microscopic stress leads to the following equation:I

Io‘: [v(z'),t]dv(r) = o'(t) 6.7r=O

The solidifying material on the microscale is considered to be non-aging and linearly

viscoelastic. So the stress-strain relation for the layer solidified at time r is given as:I

@"(¢)-5(1) = I¢(t—t')o'g[v(z'), 41'] 6.2

in which it is assumed that cg [v(r),dt'] = 0 for r’ -< r; s"(t) - e"(r)= viscoelastic strain

actually sufiered by the element that solidified at time r , and ¢(t - t’) = microscopic creep

compliance function of the solidified matter, representing the creep strain at time r, caused

by a unit microstress (08 = 1 ) applied at time r . Note that the compliance fimction is

written in terms ofonly one variable: - t’ , the load duration, rather than two independentvariables t and r as required for the compliance function on the macroscale. This is a great

simplification that eliminates the eflect of age at the rnicroscale.

6.2.3.3 Constitutive Relations

Equations (6.7) and (6.8) represent a system of two coupled- integral equations

relating the variables o'(t) , e"(r) and o'g(v,t) . The assumption of layer deposition

(solidification) at a stress-free state eliminates the microstress 0': from the system as shown

by Bazant, (1977). The result is a macroscopic stress-strain relation of the following fonn:

a" (r) =L !I¢5(r - r')do-(:3 6.9v(r) ,where, 4z5(t - t’) = 6¢(t - t’)/ 6t . A generalization for nonlinear behavior is introduced by

multiplying the strain rate by a non-dimensional factor F(o'(t)) . By introducing a

viscoelastic microstrain y(t)which represents the strain of the binder whose volume grows

119


with time, the creep strain rate ofthe solid é" (t) can be expressed as the product of the age-

independent strain rate of solid 7(t), and the increase of the volume fraction v(t) of the solid

as follows:

5(1) = 1‘-’(L))y'(r) ;> = ]'¢(z -t’)do-(r') 6.10v(r) OFor the viscous strain sf (t), the efiect ofvolume growth ftmction h(t) of the solidified

matter is mathematically analogous. So the results must be as:

sf (I) = %‘.z% ].,;(¢ - z’)do-(2') 6.11

Where, 1;/(r -t’) is the corresponding microscopic compliance function of the solidified

matter that is non-aging. Since the strains’-(t) is viscous, the strain rate at time t caused by

microstress 0'], acting at time t is éf (r) = 0' / 17, where 27, = constant =efl‘ective viscosity of

the solidified matter. So zfl(r — r’) =1/no , 1;/(t — r’) = (r -1’)/170 . Then Eq. (6.11) can

be integrated to yield

5(1) = 6(t) 6.12

Where r7(t) = r7,,h(t) is the apparent (effective) macroscopic viscosity, which is not constant

but increase with time. Equation (6.12) can be written analogously to Equation (6.10) by

introducing a constant in the equation as follows:

sf (1) = q,f%)@6-(1) 6.13v t

Where q, is empirical constant depends on the composition of concrete.

6.2.3.4 Rate - Type Approximation

The main practical advantage of the above formulation is that it can be reduced to a

rate-type creep law based on rheological models with non-aging properties. In this

formulation, the viscoelastic microstrain 7(t) is represented by a Kelvin chain with age-

independent elastic moduli Eg and viscosities r1” . This leads to the relation:

120


N

r];j”+Euy“=o' 7=Z}’,, 6.14u=l

The solution of the above equation for a constant stress tr applied at age t’ yields

qil"1'< ‘l‘*1/L>--

ya) = _e*(r-1’)/av) T“ =2

Where, ru are constants called the retardation times and must be chosen upfiront as

§I\ I\) l\)mentioned in section Constantsl/' Eu may, in general, be found by the method of

least squares. The response of the Kelvin chain is approximately equivalent for variable

stress, because 7(1) due to variable stress is obtained from ¢(t — t’) by principle of

superposition. Having identified }'(t) , the macroscopic viscoelastic strain and viscous

strain can be determined by numerical integration. Identification ofthe four major

parameters v(r), F(o'(t)) ,1/ Ep and qs is required to calibrate the model as will be

discussed in Chapter 7.

6.3 Drying Creep Modeling and Mechanisms

6.3.1 General

At simultaneous drying, the deformation of a concrete specimen under sustained

load is larger than the sum of the drying shrinkage of the specimen at no load and of the

deformation of the specimen that does not dry. The excess deformation is called Pickett

efl'ect (Pickett, 1942) after the man who first clearly documented it. The interpretation of

the excess deformation and its mechanisms is still a matter ofmajor controversy as detailed

in Chapter 2.

As explained in Chapter 2, two major views exist in the literature regarding thePickett effect. One relates the excess deformation to apparent mechanisms related to

microcracking associated with drying, and the other relates the excess deformation to real

mechanisms related to stress-induced shrinkage. It is generally stated that, neither ofthe

views can alone explain the excess deformation, and a combination ofthem is more

acceptable (Bazant 1988). However, there are no experimental data currently in the

literature that distinguish clearly among the two proposed mechanisms at early age,

121


particularly for tension. In this research, it is assumed that the excess deformation was

caused by two mechanisms: microcracking and stress-induced shrinkage. The following

sections describe these mechanisms and their mathematical formulation.

6.3.2 Micro-cracking

It is well known that drying of concrete causes cracking because ofthe non-

unifonnity ofmoisture distribution in a drying concrete specimen. The surface layer of the

specimen dries and shrinks first, while the inner layer remains wet and does not shrink. As

a result, the surface layer undergoes tension that causes local microcracking or tensile strain

softening. Due to the nonlinear inelastic behavior and unrecoverable creep of concrete

caused by the tensile stress, the micro-cracks cannot close fully when the moisture

approaches a uniform state. As a result, the measured shrinkage ofthe concrete specimen is

always less than the true shrinkage.

When the loaded specimen is under compression, the surface cracking is

eliminated. As a result, the surface cracking does not reduce the shrinkage. This conn-ibutes

in part to the excess deformation of the drying specimen tmder a compressive load. In

connast to the compressive case, when the specimen is tmder tension, the tensile load

promotes the surface cracking and reduces the shrinkage below that of the load-fiee

specimen (Bazant and Wittrnann, 1982). However, since tensile creep and shrinkage are

opposite to each other in direction, a further reduction in the shrinkage of the drying tension

specimen reflects as an additional tensile drying creep. The fact that tensile load promotes

microcracking led Kovler (1995) to question the efiect ofmicrocracking as a mechanism

for drying creep under tension. Nevertheless, it seems that whether tensile or compressive

loads are applied the effect ofmicrocracking on drying creep remains explainable.

6.3.3 Stress-induced shrinkage

The stress-induced shrinkage has been concluded in the literature as a result ofdetailed finite element analysis ofnumerous test data (Bazant and Chem 1985). In this

mechanism, the shrinkage and thermal dilation coeficients are dependent upon the stress.

For example, shrinkage has been shown to increase under compressive load and to decrease

122


under tensile load (Wittmann and Roelfstra, 1980, and Wittmann, 1993). The physical

mechanism that causes this stress dependency has been related to the existence oftwo

difliusion processes in concrete: macrodiffusion and microdifihsion. The macrodiffiision

transports water in large pores (capillary pores), and affects the macroscopic water

nansport, i.e. drying and wetting. The microdiffusion transports water locally between the

capillary pores and the gel pores. Thermodynamic equilibrium between water in the

macropores and the micropores must be maintained, and the thermodynamic imbalance is

the driving force of the microdifiusion. The movement ofwater molecules through the gel

pores promotes the debonding and rebonding process that is the source of creep.

6.3.4 Fonnulation for Stress-Induced Shrinkage

Two hypotheses have been considered in the literature to formulate a mathematical

model for stress-induced shrinkage. First, creep rate or creep viscosity depends on the

magnitude of the microdiffusion flux ofwater j which is driven by the difierence in the

chemical potential between capillary water and gel water; i.e. r; = r;(j) . This hypothesis

seems physically justified as movement of water through the micropores enhances the

process ofbond ruptures and reformation (creep source). Second, the microdifiiusion is

infinitely fast. Based on the second hypothesis, Bazant and Chem (1985) have shown the

dependence of r7 on microdiflusion flux as equivalent to its dependency on efiective pore

htunidity I? = a,H + a2T . From hypothesis I and the fact that only the absolute value of

flux is what really matter, the creep viscosity can be written as a function ofefiective pore

humidity; as a first order approximation it takes the following form:

:1-_=_—.1.-=-1-+/<'l1=7l 6.1611(1) '7 (H. T) '7

Where, r; is the viscosity without microdifliision, H is the pore humidity rate, T is the pore

temperature rate and k’ is a constant. For a single Maxwell unit, the following equation can

be written:

—-+:——.——.—=€_€:h’$TE n(H.T)

123


Where fi(H,T') is the creep viscosity imder drying; 6",, and é, is the shrinkage strain rate

and thermal strain rate; 6‘, = a,.T , wherea, is the coeficient ofthermal expansion; and

6,, = k,,,H , where /c,,, is the shrinkage coefficient.

Equation 6.16 represents the drying-induced creep since the viscosity is modified by the

variation ofhumidity. However ifEquation 6.16 is substituted in Equation 6.17 and

rearranged gives:

%+3 = .6 - (16,, +a,k'o'signFI_)H - (a, +a,k'<m'gnH)T 6.1811

Where signH is the sigi ofH , Rearranging terms in Eq. 6.18 lead to the following

%.+£=é—k,,,(l+ro'signF)H-aT(l +po'sign§)T 6.19'1

It can be seen fiom Equation 6.19 that the shrinkage coefficient km is modified by a stress

coefficient. That is why the associated deformation is called the stress-induced shrinkage.

Furthermore, the themial coeficient 0:, is also modified by the applied stress. The

corresponding increase of thermal deformation is called sness-induced thermal. This

conclusion is a consequence of the fact that the chemical potential ofwater is not only a

function ofhumidity but also of temperature. It is interesting to note that Equations 6.17

and 6.19 are mathematically equivalent. However, the efi"ect ofhumidity variation in

Equation 6.17 reflects on creep viscosity causing the drying-induced creep, whereas the

drying efiect in Equation 6.19 reflects on shrinkage and thermal coefficients which

represent the stress-induced shrinkage and the stress-induced thermal. Therefore, the

concepts of drying-induced creep and the stress-induced shrinkage are mathematically

equivalent.

Equation 6.19 can be rearranged such that the shrinkage and thermal strain rates are

directly appeared rather than the rate ofhumidity and temperature as follows:

= a - (1 + r,6szgnH).e,, - (1 + p,6.<ignH)e, 6.20

Either ofEquations 6.19 and 6.20 can be used in this study. However, The stress-induced

shrinkage in the form ofEquation 6.20 was used in the analysis and modeling of test

results. The strain rate was preferred to appear in the equation because the experiment

124


measured shrinkage strain more accurately than pore humidity. Furthermore, the pore

humidity was sensitive to the method ofmeasurement and to temperature variations. The

error in the humidity measurement was t 3 % (controlled by the accuracy ofthe humidity

meter). This error was substantial for the purpose ofthe analysis because the humidity

change was in the range of 10 % to 15 % during the first week ofdrying.

6.3.5 Stress-Strain Relation for Microcracking

It is generally known that, microcracking causes tensile strain sofiening. It has been

described in the literature as a stress-strain relation in continuum manner. Bazant and Chem

(l985b) have developed a constitutive relation that describes the tensile strain softening. A

basic hypothesis to establish the relation is that microcracking is permitted to take place

only within orthogonal planes. This simplifies the mathematics because orthogonal cracks

do not interact and cracks in one direction contribute only to the overall deformation in that

direction. This allows the description of strain sofiening by independent algebraic relations

for each of the orthogonal directions.

The same approach was adopted in this research. The stress-strain relation

goveming the strain softening part of response is additive to the strain due to creep,

shrinkage and elastic defomration as follows:

e=s,+e,+a,,,+§ 6.21

in which e, 6', , at , 6,, ,g' = column matrices of the Cartesian components of the tensors of

total strain, ofstrain due to elastic deformation, of strain due to creep, of strain due to

shrinkage, and of strain associated with microcracking. The relation between 0' and

g" must be algebraic (for monotonic loading) as mentioned earlier, and so

0' = C(5)5 6.22

in which C represents Cartesian components ofthe secant modulus tensor; C is a function

of 5 . Strain softening curve shown in Figure 6-3 was typically considered for the analysis.

This curve is characterized by infinite initial tangent, which means no elastic response was

included in this curve. The chosen curve characterized only the strain softening part of

response, which was reasonable since the elastic response was evaluated separately.

125


The above formulation is for monotonic loading and the experiment in this study

dealt with time-dependent loading. Hence, to capture the time dependency of

microcracking and effect of aging on strength, the strain-sofiening curve was normalized to

the tensile strength ofconcrete. The above stress-strain relation associated with drying

microcracking was a crude approximation to the behavior because the mean stress was only

considered in the analysis.

Since a uniaxial experiment was conducted in this research, only cracking normal to

x-direction were assumed to contribute to the overall deformation (hypothesis of crack

orthogonality). The uniaxial strain-sofiening diagram (Figure 6-3) can be described as

0' = A5‘ exp(-bi‘) 6.23

For this expression, the secant modulus is

C({;') = /15"" exp(—b§‘) (0 < q <1) 6.24

Where, A,q,b,s are empirical constants, and will be determined by fitting the

microcracking data resolved in the analysis.

6.4 Components and Sequence of the Analysis

The analysis performed in this research consisted of four major parts: Basic creep

analysis, stress-induced shrinkage, microcracking analysis, and damage analysis. These

components are briefly summarized as follows. Detailed analysis and discussion of results

will be presented in Chapters 7 and 8.

Part I: Basic Creep: Basic creep data extracted from tests of concrete under wet

conditions were used to identify the model parameters described in section 6.2, Equations

6.12-6.15. The calibrated model was used to characterize the basic creep behavior of

concrete at early age, and to predict the basic creep of concrete tested under sealed and

drying cming conditions.

Part II: Stress-Induced shrinkage: Creep data generated under sealed conditions were

used to quantify the stress-induced shrinkage strain and to calibrate the model formulated

in section 6.3.4. Equation 6.20 was used to model the stress-induced shrinkage.

126


Part HI: Microcracking: After determining the basic creep and stress-induced shrinkage

for drying concrete using their predictive models, the strain associated with drying

microcracking was estimated. Equation 6.23 was used to model the microcracking in the

drying test. The influence ofmicrocracldng on failure was determined based on a damage

model, the basic concepts ofwhich are discussed in the following section.

6.5 Damage and Failure of Concrete

Failure in quasi-brittle materials like concrete occurs first progressively and then

suddenly when micro cracks localize into a macro crack. The time-dependent

microcracking arises from drying is therefore connibuting to the fracture process of

restrained concrete. In this section, the efiect of drying microcracking on failure is

quantitatively examined by using basic principles ofdamage mechanics. From the

continuum point ofview, Damage models are well suited to capture the essential features

of the failure of concrete.

6.5.1 Basic Concepts

In phenomenological damage models, the damage is very often understood as a

degradation of the elastic stifiress of the material (Lemaitre 1992). Pijaudier-Cabot (1995)

demonstrated that, the pertinent variable that characterizes damage for quasi-brittle material

is the variation of secant stiffiress modulus. This concept was used in this study to predict

failure of restrained concrete. Therefore, the state coupling between strain and damage

must be established. The influence ofdamage on elasticity can be described through a state

coupling between the strain and the damage (Lemaitre 1992) and hence, a uniaxial law of

elasticity of damaged material can be written as follows:

8, =-L 6.25E(l - D)where D is a damage state variable. In this study the damage state variable was indirectly

approximated from the stress-strain diagram obtained in a uniaxial tensile strength test,

using the concept of secant stiffness degradation as a measure ofdamage. A schematic

127


diagram showing this process is presented in Figure 6-4. The damage variable D is defined

as follows:

E0 =1-— 6.26E0

where E is the efiective secant modulus ofthe damaged material and E, is the initial

modulus of the virgin material. The most accurate measurement ofE is during imloading,

however, the secant modulus obtained fi'om a loading suess-strain diagram tinned out to be

a good approximation to the stifiress

6.5.1.1 Damage Threshold

Before the microcracks are initiated, creating the damage modeled by D, they must

nucleate by the accumulation ofmicrostresses accompanying incompatibilities of

microstrains. This corresponds in pure tension case to a certain value of strain spa

(threshold) below which no damage by microcracking occurs:

s < spa —> D = 0

The damage tlueshold for concrete corresponds approximately to the end of linear portion

of the stress-strain diagram. When concrete strained to the nonlinear range, damage of

some sort to the material is expected. The damage threshold suain can be roughly taken as

the elastic suain corresponds to a tensile sn-ess ofaround 0.48-0.5 of the tensile strength as

shown in Figure 6-4.

6.5.1.2 Failure Criterion

Failure in concrete occurs first progressively and then suddenly when micro cracks

localize into a macro crack. It corresponds to a critical value ofdamage D, , which depends

upon the material and the conditions of loading. The final decohesion of atoms however, is

characterized by a critical value ofthe effective stress acting on the resisting area. This

critical efiective stress can be practically approximated by ultimate stress that is a material

characteristic. Then;

128


.0, =1-1 6.27all

gives the critical value of the damage at a macro crack initiation occmring for the

imidimentional stress 0'. The ultimate stress 0', being identified as a material characteristic,

D, may vary between D, == 0 for pure brittle fiacture to DC = l for pure ductile fiacture

but usually remains of the order of 0.2 to 0.5.

6.5.1.3 Evolution of Damage

Kinetic law ofdamage evolution which describes the kinetic coupling between the

plastic strain and the damage have been applied for several classical cases of loading giving

rise to difi'erent kinds of damage such as brittle, quasi-brittle, ductile, and low cycle fatigue

or high cycle fatigue (Lemaitre 1992). The common main feature is the proportionality of

the damage rate to the strain energy density release rate and to the accumulated plastic

strain rate beyond a plastic strain threshold and up to a critical value of the damage

variable. The general form of the law is as follows:

D=%p if pzpo 6.28

where Y is the strain energy density release rate, S is the damage strength material

parameter, pD is the damage threshold, D is the damage rate and p is the accumulated

plastic strain rate. The accumulated plastic strain that govems the damage is defined on the

mesoscale for materials such as metals and at the microscale when the damage is very

localized such as for concrete. For quasi-brittle material, the kinetic damage evolution can

be approximated as follows:‘I

. of’ _ _D=52_-§Re,q if a,q2p,_,ando',,,2o'f 6.29

D=0 U" o',q<o'f

where 0;, is the von Mises equivalent stress, 0', is the fatigue limit of the material, 6,, is

the rate oftotal equivalent strain, E is the elastic modulus, S is the material damage strength

parameter and R is the traixiality ratio defined as follows:

129


R = 3(1+ v) + 3(1- 2v)(“—" )= 6.303 0',

Where, v is the Poisson’s ratio and 0'H is the hydrostatic stress. The above law for damage

evolution was used to predict the damage caused by microcracldng that led to failure of

drying concrete.

WW hm

WW

0' T 0'

11. E1._ Maxwell

K<"=1Y"1 _ chain unitscham tmrts

'71‘

16' it

Figure 6-1: Kelvin and Maxwell chain units

130


0' 0'

WW F1S‘ 1.)1

E5277: 7: y

vvw 3.“

.

'7.v__\'_L.

¢(r —r’)

l—>¢(r -1’)

___i__,__

Z ElastiEV0-,(v.r> J -:-

014;—:—__—__ Vicscoelastic

::=?@gi¢i§ — F‘ __' e"PA* -.< " '— — - '-1 — — — -

¥ Creep

.\\"~- \r\r'rj"414ataw);$3.3‘.

‘ 4

ii.

I1‘;AVA 1, _rhrn_ 8 ,1‘ ‘ ~ _ __ _ Viscous

1<1 \'~"91' >‘v at6'r~$V*§‘,~'4‘9.0.;6')‘~".‘I{I/2?»-#6!IVIYV_ {.-‘$§51 .1IQ

A

47>> _Y_

A

8° Shrinkage111/(I —r’)

1

'76

[' t I’ I

Figure 6-2: Solidification theory for basic creep

0'/0',

0.8

0 = C(¢§)~§

0' = A?“ ¢XP(-bi’)

5Figure 6-3: Strain Softening Curve

131


GA

Gt ...-_. .

E3’ D3

E2, D2

5,1: \‘ ‘ E..D.E0

Di=l-E1/E9

(Sf ~ 0']: (0.48 — 0.5)o',

Di = Damage factor at point i

D¢= Critical damage factor

>and e, 8

a) Tensile stress-strain diagram and damage calculation from secant stiffiress

A

Dc ........s..._......2....................................................._.........................._......................._._...z.._................_....._..._........_._...

Damage Threshold dD

1 di’ >sad 2,,

b) Damage accumulation cm've

Figure 6-4 Damage evaluation fiom a tmiaxial stress-strain diagram

132


CHAPTER 7

ANALYSIS AND DISCUSSION OF BASIC CREEP TEST RESULTS

7.1 Introduction

This chapter presents the analysis ofbasic creep test results generated in this

research. Basic creep is a material property defined as the creep when no exchange of

moisture between the test sample and the surrounding environment occurs. Mechanisms of

basic creep and its modeling have been a matter ofresearch since the beginning ofthis

century, and a great deal ofunderstanding ofthe phenomena has been achieved. However,

the behavior oftensile creep at early age is not well understood, particularly for fiber

reinforced concrete.

The basic creep was determined fiom the creep measurement under wet curing

conditions. A model based on solidification theory, as presented in Chapter 6, was used to

analyze the basic creep test results, and various behavioral aspects are discussed in this

chapter.

7.2 Basic Creep Analysis

This section presents the analysis of basic creep data and discusses the test results.

Numerical analysis was performed to characterize the basic creep behavior ofplain and

fiber concrete at early age. Two approaches were used in the ntunerical analysis: step-by-

step method (incremental approach) and superposition method.

The step-by- step method divides the time domain into time increments. At each

time increment, the analysis considers the current value ofthe creep and updates the model

parameters accordingly. Thus, the time history is eliminated in the analysis. The outcome

fi:om this analysis is a predictive model, calibrated for the concrete tested in this study, to

predict the creep of restrained concrete at early age.

The superposition method adopts the principle ofsuperposition in the analysis. Itconsiders the response to varying stress as the sum ofthe responses to each stress taken

133


separately. In contrast to the step-by-step method, the time history in the superposition

analysis ofbasic creep is required. However, the outcome provides more behavioral

information such as the effect ofage at loading and fiber reinforcement on basic creep

behavior of concrete at early age.

7.2.1 Review of Basic Creep Model

The analytical model for basic creep was described in the previous chapter. It views

the basic creep as composed oftwo components: viscoelastic component 6:" (t) and viscous

(flow) component sf (t) . Mathematical equations for these components were formulated in

the previous chapter and summarized herein. The creep strain rate of the solid .é"(r) is

expressed as the product of the age-independent strain rate of solid ?(r) , and the increase

of the volume fi'action, v(r) , of the solid as follows:

é"(r) =%7(1) 7.1

Where function F(o'(t)) is introduced to reflect nonlinear behavior at high stress. The

viscoelastic microstrain y(t) is represented by a Kelvin chain model with N Kelvin units.

Each unit consists of a spring with age-independent elastic modulus Eu and a dashpot with

age-independent viscosity r)” . The solution for this spring-dashpot system is of the

following fonn:

Qi["1'< ‘D1/LI—I ‘L .31

;/(t) = — e"""’)"') 2', = '74 7.2

Where ry is a constant, called the retardation time, and must be chosen upfront. The viscous

strain term is given by the following equation:

e’(r1=q.lit()'l<r(r> 7-3V

Where q, is an empirical constant and depends on the composition of concrete. It is

apparent from Equations 7.1-7.3 that four main parameters are required to describe the

134


model: v(t), F(o'(t)) ,1/ E,1 and q, . For a constant stress, the basic creep strain according

to the model can be given as follows

8.. = a[A,(1 - e*'"'~>”~ ) + A, (1 - e*"‘~>’ ) + ...A_ (1 - e'<"'~>”~ ) + q, (r - 1, )] 7.4

Where t is the age ofconcrete, I, is the age at loading, A,~=I/E, and ti are constants for the 1""

Kelvin chain unit. Equation 7.4 was used as the primary analytical fimction for basic creep,

and the model parameters were identified from the experimental data. Identification of

these parameters is discussed in section 7.2.2.

7.2.1.1 Important comment on Flow Tenn

The flow term q, (1 - to) in Equation 7.4 has been introduced into the solidification-

based compressive creep model because it was found that fitting a large number of creep

data required this term (Bazant 1988). However, in the case of tensile creep this

requirement has not yet been confirmed since data on tensile creep is scarce in the

literature. Confirmation ofthis aspect requires tensile creep data tmder constant load and at

various ages, which is not available in this research. However, some of the available data

on basic tensile creep in the literature indicated a stability of the creep function after a

certain time under load (Kovler 1999, Benoit and Michel 1995). It is also indicated in the

literature that the tensile creep function stabilizes earlier than the compressive creep does as

discussed in Chapter 2. These observations question the necessity of the flow term in

modeling the basic tensile creep. In fact, Bazant, who is one of the prominent developers of

the theory, has neglected this term in one ofhis recent papers (Bazant and Xi, 1994).

7.2.2 Identification of Model Parameters

The model parameters were identified by optimization. In view ofthe aging law

known fiom the double power law (Bazant and Osman, 1976), the volume fiaction growth

can be introduced as follows:II‘!

L= -1- a 7.5v(t) t

135


Where m anda are empirical constants. The nonlinear dependence is introduced as follows:

(Bazant and Prasannan, 1989a)

F(o-(1)) = S = 7.6

Where Q represents damage at high stress and is taken as Q = s'° , and _/I’ is the direct

tensile strength ofconcrete. Numerical analysis in time domain was performed to identify

the model parameters. g

Linear and nonlinear optimization requires a response ftmction io evaluate the predicted

model values. Based on the basic creep model, Equation 7.4 forms the response fimction

for a constant stress applied at time to. In such a form, the optimization problem is

nonlinear. Nonlinear models are difficult to fir, and require iterative methods that start with

an initial guess of the tmknown parameters. Each iterafion step alters the current guess until

the algorithm converges. Statistics Toolbox built in computational MATLAB sofiware was

used for the optimization. It basically finds the parameters that minimize the sum of the

squared difierences between the observed responses and their fitted values. It uses the

Gauss-Newton algorithm with Levenberg-Marquardt modifications for global convergence(MathWorks, 1997). The optimization problem requires the following input parameters:

1 Response function in the form of equation 7.4;

0 Experimental data including, stress, time, age at loading, and the corresponding basic

creep;

0 Direct tensile strength data in time;

0 Initial guess of the model parameters;

0 Retardation times which must be chosen upfront as mentioned in Chapter 6.

A computer program was written in MATLAB to take the above input parameters and to

perform the nonlinear optimization accordingly. The outcome is the model parameters that

best fit the experimental data. - _nO6.

7.3 Incremental Approach --

Analysis based on a step-by-step method was used to optimize the parameters of

the basic creep model (Equation 7.4). The analysis divides the time domain into time

136


increments. This approach considers the current time step only and updates the parameters

accordingly. Thus, it simplifies the computations, particularly when the stress changes

frequently as in the case of restrained shrinkage.

In the initial stage of analysis, all parameters in Equations 7.4 and 7.5 wereincluded, and the following retardation times (in hours) were considered.

r=(0.01 0.1 1.0 10 100) 7.7

However, the results revealed that the parameter /lo in Equation 7.5 could be fixed m

24 hours once and for all. This value was also fixed as 1 day by Bazant and Prasannan

(1989b) in their fitting ofa large number of creep data.

7.3.1 Influence of the Flow Term on the Analysis

Analysis with and without the flow term was performed in this research. The

analysis with the flow term included, revealed that two exponential series with retardation

times of 0.1 and 1.0 hour provide a reasonable fit of the data. Therefore, Equation 7.4 and

7.5 are reduced to the following:

5:, = o'[A, (l — e"°""°)) + A, (1 — e""'"’ ) + qs (r — to )I 7.8V

and L = + a 7.9v(r) 1 ,

Where r is the age ofconcrete in hours, and to is the age of concrete at load application. The

parameters; Al, A, ,q,, m,a are identified by fitting the above nonlinear fimctions to basic

creep data.

Combinations of retardation times of (1.0 hr, l0hrs) and (0.1hr, 1.0hr, l0hrs),

(l.Ohr. 10hrs, 100hrs) and (10hrs, 100hrs) were tried using the incremental approach with

the flow term excluded. All these combinations could fit the data reasonably well.

However, the best combination of retardation times tumed out to be (l.0hr, l0hrs). This

combination seems reasonable as it covers the time domain between load increments, and

fits all the tests obtained in this research. Figures 7-1 and 7-2 present typical fits ofbasic

creep data with and without consideration ofthe flow term. Apparently, both models fitted

137


the data reasonably well and were able to capture the disconti.nuities in the applied stress

and consequent changes ofthe tensile creep.

Since either ofthe analysis methods, with-flow and without-flow, can predict the

basic creep using this approach, only material parameters identified based on with-flow

method were considered for further analysis.

7.3.2 Nonlinear Stress Factor

The effect ofhigh stress on tensile creep was included by the factor F(cr(t)) as defined

in Equation 7.6. To calculate the stress factor, tensile strength ofconcrete is required. The

direct tensile strength of concrete was determined from a split tensile test based on relations

established for the tested concrete as discussed in Chapter 4. Those relations were used to

calculate the direct tensile strength ofconcrete fiom the dry split test as follows:

a) For sealed samples .

-O-1'85-1le—(1l = 1.565 - 0.00718t r 5 80hrs6,. (dry)

—-—“(Sealed) = 0.99 1 2 so/11$6.. (do)

b) For drying samples

7.10

5’:_(5“1’l’l =-1.377 - 0.00571 1 510071116 (do)SI

3-'5‘-‘-{Tl = 0.8 1210071“ n6,. (dry)

The above relations were established for the concrete mix with w/c-ratio of 0.5. Due to the

lack of direct tensile strength tests on the NC-0.4 mix, similar relations were assumed for

the concrete mix with w/c-ratio of0.4. The split tensile strength (in MPa) is given by the

following relations

W/C = 0.5 0",, = 2.l75llogr—2.027 7.12

W/C = 0.4 0'“ = 2.1443 logt —l.3208 7.13

138


7.3.3 Model Coefficients

The model coeficients obtained from the analysis for plain and fiber concrete are

summarized in Table 7.1. Appendix C presents the outcome of the model versusexperimental data for basic creep for the various mixes. Table 7.1 includes parameters

obtained fi'om two difierent analyses: linear and nonlinear. The linear analysis did not

consider the effect of high stress (i.e. F(a'(r))=l), whereas the nonlinear analysis

considered this factor. Results fiom the two methods are presented because the

stress/strength ratio for the basic creep test was less than 0.6.

Table 7.1: Coeflicients for linear and nonlinear models of basic creep

NC-0.5 l A, 11 lLinear 3.3215 6.2640 0.8658 1.4817 0.0460

Nonlinear 3 .6551 6.3228 1.0159 1.8236 0.0405 IiINC-0.5-SF l

Linear I 0.9517 2.3686 0.0677 2.8961 0.7909 I1

I 0.1072 2.8498 0.408411611116661 i 1.2967 3.4575 INC-0.4 I

Linear 17.7616 47.2365 1.6868 7.1837 0.0496

Nonlinear 18.2495 47.7311 I 1.2671 7.0374 0.0400I

. I2n :53"11 l10.3687 7.5460 I 2.6800 5.0059Linear 0.0948

I1|I Nonlinear 10.4414 I 9.3661 2.5244 4.9269 ‘ 0.0732

The results revealed that including the high stress factor in the analysis did not

affect the fit of the data. Figure 7-3 shows the model results with high stress factor

(nonlinear) and without stress factor (linear) of the NC-0.4 mix. It is clear that both models

fitted the data satisfactorily, in fact, no discemible difference between the two models couldbe seen. Though, the model parameters were altered. When the stress factor was

considered, v(t) was shifted up to substitute for the efiect of the stress factor i.e. the stress

factor scaled up the parameter v(t). The non-aging creep ftmction, which was totally

139


characterized by the two exponential terms in Equation 7.8 and the two coeflicients, A1,

and A2 was also shifted accordingly. Figures 7-4 and 7-5 present typical non-aging creep

functions and v(t) for linear and nonlinear basic creep analysis for the NC-0.4 mix.

The linear and nonlinear models could be equivalently used to predict the basic

creep of concrete. The linear model required no tensile strength data, and hence it was

convenient for the analysis of the NC-04 mix because accurate direct tensile strength data

were not available. The relation between split tensile and direct tensile strengths was not

established for this mix and the assumption of a similar relation as of that for the NC-0.5

mix may be a crude estimation. For this reason the linear model could serve to predict the

basic creep of sealed and drying concrete for the NC-0.4 mix. The difierence between the

linear and nonlinear model would be noticeable when used to predict the basic creep for the

restrained drying concrete test since the stress/strength ratio reached 0.8. However, the

analysis revealed a difference of less than 10%, which could be acceptable in the absence

ofaccurate stress/strength data.

The coeficients in Table 7.1 were based on incremental analysis. Therefore, they

can be used only to predict basic creep of similar materials and load conditions. For

example, the basic tensile creep of sealed and drying concrete can be predicted using the

above parameters since the same load profile was applied. It can be also used to predict

basic creep for coupled creep-shrinkage analyses of restrained concrete using the step-by-

step approach. Ifthe loading condition is drastically difierent from that of the restrained

shrinkage test, the above model coefficients cannot be used to predict creep. Moreover, the

early age basic creep behavior cannot be easily characterized fiom this model because the

effect of age at loading on creep is not directly clear.

7.3.4 Effective Volume Growth v(t)

Aging properties as reflected from the model parameterv(t) depend on the w/c of

the mix as the coeflicients in Table 7.1 indicated. Figures 7-6 and 7-7 present aging as the

growth ofv(t) at different ages for the mixes NC-0.4-SF and NC-0.5-SF, respectively. The

absolute value of v(r) is immaterial, what really matters is the order ofmagnitudes and the

relative values between different ages. A strong age dependency ofthe volume growth is

140


seen in the concrete with low w/c-ratio. The volume fraction for the NC-0.4~SF mix at the

age of 72 hours is ten times greater than that at the age of24 hours, while it is only two

times greater for the mix NC-0.5-SF. In other words, the efl'ect ofage on creep at early age

is more pronounced for a low w/c-ratio mix.

The curves of v(t) at difierent ages indicated a substantial aging ofcreep when

concrete is loaded at the age ofone day. It becomes less significant as the age at loading

increases. The effect of aging on creep in the first two days of loading is quite obvious as

the v(t) increases at a high rate. Then it tends to level off and approaches almost a constant

value afterward. The fact that v(t) stabilizes after a certain age means that tensile creep

becomes age-independent afler that age.

The parameter v(r) is not a direct material property in a quantitative sense.

However, it is physically related to the hydration of cement and solidification of the C-S-H.

It may have potential as an index to hydration. The high rate of aging expressed in Figures

7-6 and 7-7 in the first two days is related to the high rate ofhydration of cement. The

hydration process slows down aflerward and the aging becomes less significant. Relating

the volume growth to the hydration of concrete is beyond the scope of this work. Though, it

does seem to be an interesting area for further research.

7.4 Analysis Based on Principle of Superposition

As mentioned in section 7.3.3, the incremental-based model can be used only if

loading conditions are similar to those adopted in this research. Furthermore, the behavioral

information provided by that model on the effect of aging and the influence of fibers on

creep are limited. To better understand the creep behavior at early age and to provide

information on creep fimctions at difierent ages, analysis based on the principle of

superposition was performed. The principle of superposition at early age may not be as

accurate for matured concrete because of the possible nonlinear stress-strain relations for

yotmg concrete. However, since the stress/strength ratio is less than 0.6 for the basic creep

tests conducted in this research, the superposition analysis can approximate the creep

behavior.

141


The approach requires a creep function to be established first, and the problem of

age dependency for that creep fimction must be addressed. The principle of solidification

theory was used to introduce the effect of aging. The best choice ofthe creep function can

be determined from tests of creep tmder a constant load and at different ages at loading, and

such data are not available in this research. However, the creep fimction can be analytically

extracted.Creep functions at different ages were analytically extracted from the basic creep

data. This was achieved by finding the best fit of the creep data based on permissible creep

ftmctions. A permissible creep ftmction must reflect the general behavior of tensile creep of

concrete, and the behavioral observations at early age such as the issues discussed in

section 7.2.1.1 regarding the flow term and stability of tensile creep. The creep function

adopted in the analysis did not include the flow term in Equation. 7.4 as the tensile basic

creep at early age stabilized after a certain time. This observation would be violated if the

flow term was included. The creep function used in this analysis has the following form for

a constant stress:

8,, = 3-[a, (1 - e""")"‘ )+ a, (1 - e'“"~”’= ) + ....a (1- e'*'-'~>”- )] 7.14v(t) ‘

Several choices for retardation times were tried in the analysis. The results

indicated that reasonable fits of the creep data could be achieved by considering two terms

in the exponential series with retardation times of l0 hrs and l00hrs. The function that

needs to be optimized was therefore reduced to the following:

0' —0.0l(!—! ) -O.l'(r-r , - -=—-—- 1- " + , 1- " /.1:st, V0) [a,( e ) a_( e )1

Where v(t) is given by the same form as Equation 7.5. Adding more terms to the

exponential series did not enhance the data fit. Therefore, only two exponential terms

corresponding to the above retardation times were used. This choice of retardation times

covers most of the time domain in the experiment. Figures 7-8 and 7-9 present typical fits

of the creep data using the principle of superposition and different retardation times for the

mixes NC-0.4-SF, and NC-0.5-PC. Reasonable fits of the creep data were achieved with

the above creep function and the retardation times. Fits ofthe various concrete mixes, and

information on model coefficients are presented in Appendix C.

142


7.4.1 Creep Functions for Plain Concrete

The model coeficients established in the previous section were used to generate

data on specific basic creep fimctions at different ages. The data were generated using

Equations 7.5 for aging and 7.15 for the creep fimction under a constant stress of 1 imit. A

spreadsheet was used to generate these data by inputting the model coefficients and age at

loading. The resulting fimction is the specific creep at the corresponding age at loading.

Figures 7-10 and 7-11 present the age-dependent, specific basic creep fimction for plain

concrete mixes NC-0.5 and NC-0.4, respectively. The resulting tensile creep fimction is

characterized by a high rate of creep during the first 10-20 hours of loading. This shows

that a major portion of the tensile creep ofplain concrete occurs during the first 20 hours

after loading while the rate decreases substantially afterward and asymptotically

approaches a stable value.

The initial rate of creep for plain concrete is not only high, but also is sensitive to

the age at loading, particularly in the very early ages. The initial rate of creep is

significantly changed when the age of loading is increased as shown in Figures 7-10 and 7-

11; the earlier the age at loading the higher the initial rate of creep. This suggests that stress

relaxation be faster at early age than at later ages. For example, the creep during the first 20

hours forms 85 % ofthe creep value afier 150 hours when the age of loading is 24 hours

and forms 60 % when the age of loading is 72 hours for the mix with w/c of 0.5.

The eflect ofaging on tensile creep at early age seems to cease after a few days.

The NC-0.5 mix exhibited similar specific creep functions when the age at loading

exceeded 96 hours as shown in Figure 7-10. This means that the basic tensile creep

becomes age-independent afier four to five days. Likewise, the NC-0.4 mix exhibited

similar creep behavior when the age at loading exceeded 72 hours. This means that the

tensile creep ofNC-0.4 mix becomes age-independent after three days. It seems that the

efiect of aging on basic tensile creep is only substantial in the first few days, and more

pronounced in concrete with low w/c-ratio. In fact, the creep fimction of the mix NC-0.4

exhibited a decrease in the creep at the ages of loading of24 hours and 27 hours. Thisdecrease in creep ofyoimg concrete was due to the strong efiect of aging. A decrease in

143


creep has also been reported in a paper published by Bournazel and Martineau (1993) in

which they referred to the decrease in creep as a maturation creep induced by aging.

The aging behavior is also reflected on the efiective load-bearing volume

fraction v(t) . Figures 7-12 and 7-14 present results ofthe growth ofthe eflective load-

bearing volume fiaction extracted from the analysis for the mixes NC-0.4 and NC-0.5. The

results indicate almost constant v(t) afler the ages of72 hours and 120 hours for the mixes

NC-0.4 and NC-0.5, respectively. This supports the age-independence ofbasic tensile creep

afier the first few days. Experimental results reported by Westman (1995) and Morimoto

and Koyangagi (1995) support this finding. For example, Westrnan observed an unchanged

response ofcompressive creep after the age of48 hours, and Horimoto and Koyangagi

observed that tensile relaxation ofyoung concrete terminates in a shorter period than

compressive relaxation and the half-relaxation time was not influenced by age at loading

afier 3 days. However, such observations are not directly documented in the literature.

Unlike compressive creep, the aging effect on basic tensile creep seems to become

less significant after a certain time that is arotmd 5 days as revealed by the analysis.

However, the cut ofiage for early age concrete does need more and separate tests to

characterize it. These observations are useful for designing tensile creep experiments and

modeling of general behavior.

7.4.2 Creep Functions for Fiber Reinforced Concrete

As for plain concrete. creep functions at difierent ages for fiber reinforced concrete

were generated using the model coeflicients established in section 7.4. The resulting

specific creep functions are presented in Figures 7-l4 and 7-15 for the fiber reinforced

concrete mixes NC-0.4-SF and NC-0.5-SF, respectively. As for plain concrete, the fiber

reinforced concrete exhibited a high initial rate of creep in the first 20 hours of loading, and

this rate was sensitive to age at loading. The sensitivity to age at loading was more

pronounced at a very early age as seen in Figures 7-14 and 7-15. For example, the initial

rate of creep for the age at loading of24 hours was much higher than that for the age at

loading of 30 hours. This age-sensitivity ceased with time and became age-independent

144


afier a few days. Therefore, stresses developed at a very early age relax faster than the

stresses developed at later ages.

Similar to plain concrete, the tensile creep offiber concrete became age-

independent after the first few days. This age-independence was also illustrated by the

efiective load-bearing volume growth, which exhibited approximately no change after 6

days as shown in Figures 7-16 and 7-17. It seems that the basic tensile creep becomes age-

independent at the age ofnearly 5 to 6 days.

The fiber reinforcement altered the creep behavior as shown in Figure 7-18. The

initial rate oftensile creep offiber reinforced concrete was much lower than the

corresponding rate ofplain concrete. The plain concrete was characterized by a rapid

increase of creep in the first 24 hours after loading and then died out to approach a constant

value. On the contrary, the fiber reinforced concrete exhibited a lower rate of creep in the

first 24 hours after loading, but the dying rate was lower. Consequently, the tensile creep of

plain concrete was surpassed by fiber reinforced concrete. This -is illustrated by comparing

the creep after 24 hours to the creep after 150 hours of loading for the results presented in

Figure 7-18. The ratio reaches 81 % and 71% for plain concrete mixes with w/c-ratio of 0.4and 0.5, respectively, whereas it reaches 36 % and 37 % for fiber reinforced concrete.

Therefore, relaxation by creep mechanism in fiber concrete continues for a longer time than

plain concrete. This behavior was exhibited by both concrete mixes, and was more

pronounced in the mix with low w/c- ratio. This explains the significant delay in fiacture

exhibited by fiber reinforced concrete with a low w/c- ratio as reported in Chapter 4.

The above discussion supports the hypothesis stated in Chapter 5 that related the

tensile creep of fiber concrete to a critical microcracking density. Upon loading, the rate of

creep of fiber concrete is smaller than that for plain concrete because microcracking

dominates the creep ofplain concrete while it is still controlled in FRC. With time the

ability of fiber to control microcracking ceases when it reaches a critical density. Afier this

the creep of fiber concrete surpasses the plain concrete.

7.4.3 Effect of Water-Cement Ratio

The efiect ofw/c-ratio ofconcrete on tensile creep is seen in Figure 7-18. The

results revealed higher basic tensile creep in concrete with lower w/c-ratio. This

145


observation contradicts the general behavior reported in the literature about the influence of

w/c-ratio on creep ofmatured concrete. The creep behavior at early age seems therefore to

be different fi'om that ofmatured concrete and in particular for tensile creep.

Similar influence ofw/c-ratio on tensile creep was exhibited in plain and fiber

concrete mixes. However, the fiber reinforced concrete seems to be more sensifive to the

water-cement ratio than plain concrete. For example, the results presented in Figure 7-18

indicate that the tensile creep after 150 hours of loading is increased by 57 % when the w/c-

ratio decreased from 0.5 to 0.4 for FRC mix, whereas it increases by 10% for plain

concrete. This suggests a difierent sensitivity of fiber reinforced concrete to w/c-ratio. It is

important to understand this sensitivity for optimal design offiber concrete to control

shrinkage cracking.


I The basic creep model based on solidification theory satisfactorily describes the tensile

creep behavior at early age. The model can be used to capture the various

characteristics of basic creep and provides valuable information on aging behavior.

Q The analysis of basic creep test results reveals that the tensile basic creep becomes age-

independent after a few days (typically 5 days for the concrete tested in this research).

This finding is useful for the characterization of tensile basic creep behavior and for the

design ofexperiments. However, generalization ofthis finding for early age concrete

requires more comprehensive investigations.

Q The basic creep fimction ofyoimg concrete is characterized by a high initial rate in the

first 10-20 hours. This rate dies out over time and the creep fimction tends to approach

a stable value. This behavior was observed for both plain and fiber reinforced concrete.

The dying rate is faster in plain concrete, and hence, the creep ofplain concrete

stabilizes earlier than that ofFRC.

0 The initial rate of creep is very sensitive to age at loading in the first two days, and

becomes less sensitive after that. The initial rate ofcreep ofplain concrete is higher

than that offiber reinforced concrete. This suggests that microcracking initially

146


dominates the creep ofplain concrete while it is more controlled in fiber reinforced

concrete.

147


CreepStran(pm/m)

CreepStran(pm/m)

' ' 1 ‘ ' ' l I I

: KW/C = -80 _....................... ..I ........................................................... .._

,0 1.................................... ............................................ ..;- -

I. = Basic creep 1“ —-— Model with flow tL ......................................" Model without flow

40

20

O-""" ‘l ' 720 40 60 80 100 120 140 160

Age (hrs)

Figure 7-1 Optimum fits and the flow term for plain concrete (w/c = 0.4)

70

W/C = 0.560

50

40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..f.a..=.i‘l'.i . . . . . . . . . . . . . . . . . . . . . ..an i

3Q ......................... ..

= Basic creep_ ----------------------------------- ~- —-— Model with flow

------" Model without flow20

10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

0 i .0 50

Age (hrs)

Figure 7-2 Optimum fits and the flow term for plain concrete (w/c =0.5)

148

100 150 200


100. ,

- W/C = 0.14 -80 _. . . . . . . . - - - . - - - . - - - - - - - - - - - - - - - - - - - - _ - - - - - - . - - _ . . . . . . . . . . . . . . . . . . . . . . . . . . - - _ - . . . . . . .._.

'n(um/m)3

ea” °' -- q -

- as B -

:_. . as . _ . ’

F 1" L . _l

CreepSt"a

-IiO - = Basic creep -- —-— Model-linear -

20 _........................................... "Model-nonlinear ...... .._'- f -

020 40 60 80 100 120 140 160

Age (hrs)

Figure 7-3 Data fit of basic creep with and without stress nonlinearity

350

(im/m). . . . . . _ . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . .

W/C = 0.4250 _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . _ . , _ _ . ._

-0

agngCreepFunctoné

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

—-I-— Linear .... ..-— —-— Nonlinear

50 . . . . . . . . . . . . . . _ . . _ . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . ..

Non-0 .

0 20 40 60 80 100 120 140 160

Time (t-to) (hrs)

Figure 7-4 Non-aging creep fimction obtained by fitting data for the NC-0.4 mix

149


eVoumev(t)

Effectv

25.‘ [III I I

20 . . . . . . . . . . . . . . . . . .. . . . . . . . ..8. . . . . . . . . . . . . . ..£...

nv(t). . . . . . . 1 . . . . . - . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . .._ 15

V0umefract0

—@— Linear

--'— Nonlinear10

5 . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . .

Age=24 hoursi0 . - . . l . .

0 20 40 60 80 100 120 140 160

Time (t-to) (hrs)

Figure 7-5 Shift in efiective volume fi'action due to stress nonlinearity

12

- - — — - —- I I I10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

_., /.

8 _.............................................................. .., " W/C = 0.4

6 ' ------------------------------------------ -~ —e—— age=24 hrs' —-— Age=27 hrs

4 ' _ ___________________________________________ __ —~—Age=30 hrs,;" —*— Age=35 hrs

2 II. —'-— Age=40 hrs

- I - ~ _ . . - - - . . - - - . . - - - - ~ . » - - - . - - - - - - - - - - - - _ ~ » - - - - - . -- —-E-—Age=48 hrs .-7 —=— Age=72 hrs

00 20 40 60 80 100 120 140 160

Time (t-to) (hrs)

Figure 7-6 Efiect of age on load-bearing volume fiaction growth ofFRC, w/c =0 .4

150


1.4‘--1-~»;---| | 1 |

EffectveVoumev(t)

.¢>9 O7W—* 225‘.\\ 122\\\W/(3 = Q5 —="—Age=24 hrs.... ................... .. —'—Age=27 hrs

-- —'—Age=3O hrsO 4 ___________________________________________________ __ -*-—Age=35 hrs

' —"—Age=40 hrs—<@'--Age=48 hrs

0.2 ------------------------------------------------- '" _=,_Age=72 hrs

O ‘ 1 ' ' ‘ 'O 20 40 60 80 100 120 140 160

Time (t-to) (hrs)

Figure 7-7 Effect of age on load-bearing volume fraction growth ofFRC, w/c =0.5

100- 3 5

I W/C = 0.4 ,.. I80 _. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._

I Steel Fiber ' ------------- -- 1- _ . o ~ ~" 4

60 .... . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..__.(pm/m)

Stran ,0 ;.................................................................................. ..-Creep - - ‘ " creep -

20 — --------------------------- -- —-Retardation times (10,100) -' ------- " Retardation times (1.10) j

0 .

0 50 100 150 200Age (hrs)

Figure 7-8 Effect of retardation times on the superposition-based analysis, w/c=0.4

15 l


CreepStran(um/m)

f'cCreep(pm/m)

Spec

70 . I 1 . . . I I

2 w/c =o.s ;60

Plain Concrete - ----"............................................................ ..so , __1 _-*°° '

40 ................... .4 ............... .._..,.-:l.;"...if'. ............................... ..y Q

30 . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

20 . . . _ . . . . . . . . . . . . . . . . . . . . . . . .. = creep—-— Retardation times (10,100)

"""""""""""""""" Retardation times (1 ,10)10

O _

0 50 100 150 200Age (hrs)

Figure 7-9 Effect of retardation times on the superposition-based analysis, w/c=0.5

40 1 ' '-—'“ C

-=i?,?§/. ’ I. . . . . . . . . . . . . . . . ..

fir —~—Age=24 hrs, . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..

,;'// —~—Age=3o hrs

.’/

/H - i -—-—-Age=35 hrs T’1rll'[_,/ —'— Age=40 hrs

15 E " - ' ' ' ' ' " " * ' ' ‘ ' ‘ " " ‘ ' ' ' ' ' ' ' ' ' ' ' ‘ ' ' ' ' ' ' " ' ' ' ' ' ' " —eiAge=48 hrs "

10 /

35

30

25

20

—-=—- Age=72 hrs'1"""""""" " -—-*—Age=96 hrs "

W/C ‘ 0-5 —<>—Age=120 hrs-In-up-I

1 - t | r r

.'.

O 20 40 60 80 100 120 140 160

Time (t-to) (hours)

Figure 7-10 Extracted creep functions at difierent ages at loading for NC-0.5 mix

152


c'f'cCreep(pm/m)Spe

Voumevt

/§

\-/

1

Effectve

70

60

50

AO

O0O

20

10

00 20 40 60 80 100 120 140 160

Time (t-to) (hours)

Figure 7-11 Extracted creep functions at different ages at loading for NC-0 4 mix

1.8

1.6

1.4

1.2

1

0.8

0.6

\.j?"'“s;'——‘==.

2‘\. I

I"

1'

I l

I--..4 . - . ~ - . - - - - - - - - . . - - - -,1--1} '.. - . . . . . ..T‘ - - - - - . . . . .,......

-7 I g —-—Age=24 hrs

w/c i= 0.4

—'— Age=27 hrs—-*—- Age=30 hrs—-— Age=35 hrs—'— Age=40 hrs-6- Age=48 hrs—=~— Age=72 hrs

.,»- A

0 20 40 60 80 100 120

1, "‘1 I.-I..-1.

\\5\\§‘\\\\,ll‘1:\\\\,. IX*-,..-/_._,.r'—_;:’

-—@—— Age=24 hrs-1* Age=27 hrs—-~—- Age=30 hrs—=-— Age=35 hrs—'— Age=40 hrs-—~—- Age=48 hrs—*— Age=72 hrs

W/C = Q_5 -—~— Age=96 hrs—'-- Age=120 hrs

Figure 7-12 Age dependency ofthe creep fimction for NC-0.5 mix

Time, t-to (hours)

I53

140 160


/'§

Voumev(t

Effectve

c'f'cCreep(um/m)Spe

12 .. | . . A I

In-r -. IA

4 '1 '- . . . . . . . . . _ . . . . . . . . . . . . . . . ..

I I l I I I

ff-»;_j_?'— ' ' ' ' ' - ' ' ' '" ' ~ ' ' ' ' ' ' ' - - ' - - ~ -

—@— Age=24 hrs—E— Age=27 hrs—'—Age=30 hrs g—~=—Age=35 hrs—'—Age=40 hrs _

w/c =o.4 —‘_A9e=48 his-n

It tn2 ,_ ,, ............................. ..'1

I"'1

1.

Z ................ -—'—Age=72 hrs _

0 . r r 1 1 r

0 20 40 60 80Time, t-to (hours)

100 120 140 160

Figure 7-13 Age dependency of the creep function for NC-0.4 mix

60 ._

50 W/C = 0.4, Steel Fiber _ /A/‘

40 . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . ..

30 . l , . . . . . . . .

. ',7/20 ’ /. - . . . . . . . . . . . . . . . . . . . . . . . ..

ii / ll! '//'

10 |,,' ,/, ‘ ' ' ' ' ' ' ' ‘ ' ' ' "

—°-Age=120 hrs A

\

-1Cr‘ -

/

\ \\\\\\\\\ —-- Age=24 hrs—-— Age=27 hrs—°—Age=30 hrs i—-— Age=35 hrs-—'—Age=40 hrs .+AgeM8 hrs A—=—Age=72 hrs—~*—Age=96 hrs 1

0 20 40 60 80 100 120 140 160

Time, t-to (hours)

Figure 7-14 Creep fimctions at difierent ages at loading for FRC (w/c = 0.4)

154


Spec'f'cCreep(pm/m)

EffectveV0umev(t)

1

~—I

40

35

30

25

20

1 5

._s Q

U1

0. 1 .l- . 1

0 20 40 60 80

Figure 7-15 Creep fimctions at difierent ages at loading for FRC (w/c = 0.5)

25

20

15

10

5

O

. ‘.1-ll--|~.=|r i - . r . . tr‘

........ -i-W/C-€-0.5,-St;eelF-iher%---~

. . . - . . . . . , . . . . . . . . . . ¢ . . . _ . . . . . ..:...........~._.._

. ' . /' /‘

2\

---qr‘.

--:-=_0'3\~4— l‘.q_.‘~L_\,“~q3.~. -\ . . . v

...t

. . ._.. ,.

.......... ....... ... - 1

-°-Age=24 hrs—'— Age=27 hrs—*—Age=30 hrs—-— Age=35 hrs

Age-40 hrs--=*-Age=48 hrs-1‘-—Age=72 hrs—-°-—Age=96 hrs—°—Age=12O hrs

Time, t-to (h100 120 140

ours)

l

___,,. W/C =0 4 Steel Fiber

’,,,---'— ** ;-=;.- l, '1 —-* Age=24 hrs. / —=—Age=27 hrs

. . / . . . . . . . . . . . . . . . . . . . . . . . ..

. f I ' —--Age=35 hrs. , i —'—Age=40 hrs

. _ ------------- --‘-------- ------- -- —~—Age=48 hrs—I-— Age=72 hrs-—'— Age=96 hrs—'—Age=120 hrs

0 20 40 60 80 100 120 140 160

Time, t-to (hours)

Figure 7-16 Age dependency ofthe creep function for FRC (w/c = 0.4)

155

160


EffectveVoumev(t)

i

.1

f'cCreep(pmlm)

Spec

60

12"l"‘l"'l"l"‘l“i"'i';____~ -" -———;_7;—-—-—-——i""

mi

10 $""'-F /-/' -6- e=24 hrs

é-—Age=27 hrst ; , —-— Age=30 hrs

6 . ............................. .. -=-Age=35 hrs_ - ' § -‘.—Age=40 hrs

- " i —~—Age=48 hrs

~ 5 § —-—-Age=96 hrs2 I 1 —-'——Age=120 hrs

t‘£_\'.:\\\\\\l -\\lil

4 ‘ r. _________ .; ............................ .. _-_.Age=72 hrs

’ "" ' "" ' WIC '*’0'.'5' '.'St'e'el' “F-'ihé'r' i1 1 . . . I 1 . . ! . . . rO . . . l - .

0 20 40 60 80 100 120 140 160Time, t-to (hours)

Figure 7-17 Age dependency of the creep fimction for FRC (w/c = 0.5)

so . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..v .

40 2., 12. . . . . . . . . . . . . . . . . .‘ - ‘ - - - - I - . . - I _ _ - I D ’ ‘ _ . D D ‘ . - - _ . . - _ D I -4-""nu __._-_..-Q

. . . . . . _ _,*--.----.--c

.. ..--A-""" l .........".* O‘.A- __.-'30 .. .. . ...‘.._.‘._.,.-.r.. .. .. . . . . . . . . . . . . . . . _ . ..

A’ .-- "-‘ . ___,.9"’

L’ _,"’20 . _;_- _ _ _ _ _ _ . . . . . -.;;;,,.:'.......... _SF_o.4_48 .. ..

it ,..~-"' —-—-PC-0.4-48. ..:f ....................................... SF-0.5-481Q ‘ to

1' PC-0.5-48O . .

0 20 40Time, t-to (hours)

Figure 7-18 Effect offiber reinforcement and w/c-ratio on creep functions

156

60 80 1 00 120 140 160


CHAPTER 8

ANALYSIS AND DISCUSSION OF DRYING CREEP MECHANISMS

8.1 Introduction

Drying creep, also called the Pickett efl‘ect afler the man who was first to clearly

document this effect and to analyze it (Pickett 1942), is the increase in creep observed in

specimens undergoing drying. Over the last 50 years, several hypotheses have been

presented to explain the mechanisms ofthis effect. Unlike basic creep, its physico-chemical

origins are still not fully understood and there are uncertainties conceming the contribution

ofa real mechanism by which creep and drying interact, and an apparent mechanism

related to shrinkage induced stresses and associated cracking. Meanwhile, it is now

generally believed that drying creep is the sum of at least two components; an intrinsic

drying creep with its own mechanisms and a structural drying creep resulting from a micro-

cracking effect due to the non-uniformity of the free drying shrinkage in the concrete

specimen. These mechanisms were discussed in Chapter 6. However, the contribution of

the two components is still a matter of research and currently no experimental data in the

literature distinguishes clearly between the two proposed mechanisms. in this chapter. a

technique that separates and highlights the significance ofeach part of drying creep is

presented. Furthermore, the results are analyzed to provide behavioral information on early

age creep and the interaction with shrinkage. The influence of drying creep on mechanical

behavior, particularly the fracture of concrete, is discussed and a model that relates surface

microcracking to failure ofconcrete is demonstrated.

8.2 A Technique to Separate the Pickett Effect Mechanisms

In this study, a technique that separates and quantifies mechanisms of the Pickett

effect at early age was developed. It requires experimental data and analytical analysis.

This section presents the basic assumptions of the technique and describes the basic

experimental and analytical concepts ofthe approach.

157


8.2.1 Principal Assumptions

Two basic assumptions were made; one is related to the experimental technique

and the other is related to the analytical approach, and summarized as follows:

a) Experimental Technique: It is assumed that creep is additive to shrinkage. This is a

general assumption that enables measurement of creep from a loaded sample and a

companion free-of-load sample. This assumption is not entirely correct, but it is

essential for the measurement ofcreep at simultaneous drying. This assumption has

been widely accepted among experimentalists and researchers. It was incorporated in

the basic equation that govems the test as presented in Chapter 3.

b) Analytical assumptions: Two major assumptions were made:

l) The Pickett eflect was assumed to be primarily composed oftwo components:

stress-induced shrinkage and microcracking as detailed in section 6.3. This

assumption considers the major mechanisms of the Pickett efi'ect, however there

are other but less significant mechanisms such as the effect of irreversibility of

unloading after tensile cracking and the increase of material S1iffi1CSS with age

(Bazant, 1988). The two mechanisms are generally accepted to explain the

efi'ect of drying on creep as mentioned in section 6.3.

2) Deformations fiom each mechanism of creep were assumed to be additive.

This entailed that the total creep can be considered as the algebraic summation

ofbasic creep and drying creep components. The drying component was

obtained by adding the deformation from each ofthe two mechanisms

mentioned above.

8.2.2 Basic Concept of the Experiment

The basic idea consists ofmeasuring tensile creep and shrinkage of concrete

specimens subjected to similar loading but difierent curing conditions. Creep and shrinkage

tests imder drying, sealed and wet curing conditions are required. The test under drying

condition is a restrained shrinkage test that produces data on shrinkage stress, free

shrinkage and total tensile creep. The loads obtained fiom the restrained drying shrinkage

158


tests are to be applied on similar concrete samples subjected to sealed and wet curing

conditions. The results ofcreep and shrinkage imder these conditions were previously

reported and discussed in Chapters 4 and 5. Comparison ofthe test results oftensile creep

and shrinkage under these curing conditions provides fiindamental data required to separate

the Pickett efiect mechanisms.

The test under wet conditions provided basic tensile creep as no shrinkage was

experienced. The purpose ofthis test was to characterize the basic tensile creep of concrete

at early age. Therefore, the results were used to calibrate parameters for a predictive basic

creep model as discussed in Chapter 7. Another important aspect of this test was the

elimination of the Pickett effect because shrinkage was substantially suppressed as reported

in Chapter 5. On the other hand, the Pickett efi'ect was observed rmder both sealed and

drying curing conditions as discussed in Chapters 4 and 5. However, the particulars of

drying are difierent in sealed and drying tests. For example, intemal drying occurred in

sealed samples, whereas intemal and extemal drying was exhibited by drying concrete

samples. The difierent causes ofdrying influence the induced mechanisms ofPickett effect.

These features were exploited to separate the Pickett efiect mechanisms as discussed

below.

8.2.3 Key Features of the Method and Analytical Procedures

As mentioned in Chapter 5, sealing the concrete at early age did not eliminate the

shrinkage due to intemal drying, even for normal concrete with w/c of 0.5. Consequently,

measurement of tensile creep ofsealed concrete at early age included in addition to basic

creep, a component related to the Pickett effect caused by intemal drying. The intemal

drying was accompanied by reduction in relative humidity ofthe sealed concrete. However,

the distribution ofhumidity across the sealed sample was uniform, as measurement of

relative humidity at clifierent depths across the sample thickness has shown. Results of

shrinkage and intemal humidity distribution were presented in Chapter 5. The uniform

distribution ofhumidity impedes the surface cracking caused by drying gradient; a

phenomenon that is induced by extemal drying of concrete.

159


Early age shrinkage and the elimination of surface microcracldng of sealed concrete

were the key features that enabled separation ofPickett effect mechanisms. They provided

information on interaction of creep with shrinkage when no surface microcracking

occurred. Having assumed only two mechanisms ofthe Pickett efi'ect, microcracking and

stress-induced shrinkage, an argument supported by experimental observations can be

established. The argument states that the excess deformation over the basic creep of sealed

concrete at early age is primarily related to stress-induced shrinkage.

Knowing basic tensile creep from the predictive model formulated in Chapter 7,

experimental data on stress-induced shrinkage could be generated by subtracting the basic

creep from the total tensile creep measured on sealed samples. The data was used to

calibrate parameters ofthe stress-induced shrinkage model presented in section 6.3.4.

However, since the tensile load reduces shrinkage, the term stress-induced shrinkage is

replaced by stress-reduced shrinkage.

Unlike the sealed curing condition, the drying condition promotes stuface

microcracking due to the drying gradient (discussed in Chapter 4). Consequently, tensile

creep tmder drying condition includes all components: basic creep, stress-reduced

shrinkage and microcracking. Having identified basic creep and stress-reduced shrinkage,

microcracking can be quantified. This requires predictive models for basic creep and stress-

reduced shrinkage. The sequence of analysis to quantify the Pickett effect mechanisms is

summarized as follows:

0 The basic creep model that was identified in Chapter 7 is used to predict basic creep of

sealed and drying concrete;

v Stress-reduced shrinkage data is then generated from the sealed concrete test by

subtracting the predicted basic creep fiom the total creep;

0 The data generated in the previous step is used to calibrate a model for stress-reduced

shrinkage. The model was described in section 6.3.4 in Chapter 6;

0 The calibrated models for basic creep and stress-reduced shrinkage are used to predict

the basic creep and stress-reduced shrinkage ofdrying concrete;

0 Microcracking ofdrying concrete is then quantified by subtracting the basic creep and

st.ress-reduced shrinkage components fi'om the total creep ofdrying concrete;

160


0 This process requires data on temperature, free shrinkage, and stress evolution with

time.

8.3 Stress-Reduced Shrinkage

Data on stress-reduced shrinkage were generated for the mixes NC-0.4 and NC-0.5

from the results ofcreep imder sealed and wet curing conditions as explained in the

previous section. Typical data are presented in Figures 8-1 and 8-2. The data reflect the

reduction in the free shrinkage by the tensile load with time, and were used to calibrate a

model for stress-reduced shrinkage.

The model adopted for stress-reduced shrinkage was presented in section 6.3 .4. The

basic mathematical equation of this model is as follows:

0' 0' . . - . . -E+-5-5- (l+r,o' szgnH)e,,,— (1 +p,o'szgnH)é, 8.1

where $3,, and 8, are the fiee shrinkage strain rate and free thermal strain rate; 6', = a,T ,

where ar is the coeficient of thermal expansion; and a,, = /c,,,H , where km is shrinkage

coeficient, signl? is the sig ofif , and r_, , pr are empirical constants.

However, since data were resolved in the form of reduction in shrinkage rather than

the total shrinkage under load, Equation 8.1 needs to be rewritten accordingly. Fitting the

data indicated that the stress-induced thermal term must include signT that is equal to 1

for temperature increases (expansion), and -1 for temperature decreases (contraction). The

value ofthe term sign}? is equal to -l for drying conditions. Thus, the reduction in

shrinkage by tensile load becomes:

As“, = —o'(r,.a'",,, + p,signTé,) 8.2

The model parameters ofEquation 8.2 were calibrated by fitting the data generated

for stress-reduced shrinkage. The results for the concrete mixes NC-0.4 and NC-0.5 are

presented in Table 8.1. Figures 8-1 and 8-2 show the stress-reduced shrinkage data and the

model fit for the concrete mixes NC-0.5 and NC-0.5-SF, respectively. The results show

reasonable fits of the data by the analytical model.

161


The temperature seems to affect the stress-reduced shrinkage in the first two days

and becomes less significant afierward. This was reflected in the high initial rate of

reduction in shrinkage until the age of 50 hours due to synergistic effect of thermal and

shrinkage in that period. The change in temperature in that period however was not

significant (in the order of 1 degree C), but the initial rate of stress-reduced shrinkage was

captured more accurately when temperature efi'ect was included. However, a constancy in

temperature was the prevailing condition for the NC-0.4 mix.

Table 8.1 Model parameters for stress-reduced shrinkage

I Mix Identification p,-J."

I NC-0.5 -O 1.93bi so

NC-0.5-SF 4 4.79I9 )-4

NC-0.4 .45 -I@

NC-0.4-SF -0.30 -

The above results of the model coeficients indicate significant reduction in theshrinkage (40-60 %) imder tensile stress. This suggests a significant contribution of the

stress-reduced shrinkage mechanism to the observed Pickett efiect. Therefore, the tensile

load influences the shrinkage as will be discussed in the following section.

8.3.1 Influence of Stress on Restrained Shrinkage

Shrinkage under tensile load of the restrained drying concrete was predicted using

the model parameters identified in Table 8.1. Typical results for the concrete mix with w/c

of 0.5 are shown in Figure 8-3. The results indicate that the tensile stress substantially

reduces the shrinkage ofconcrete, and assuming equivalent shrinkage for restrained and

tmrestrained concrete is responsible at least in part, for the observed extra creep

deformation (Pickett effect). Wittrnann (1993) has stated that the influence of stress on

shrinkage of concrete is most likely sufficient to explain quantitatively the difi'erence

between shrinkage and creep when taking place separately, and shrinkage and creep when

162


taking place simultaneously. In fact, he among others has concluded that shrinkage is not a

material property but it depends strongly on the state ofstress tmder which it takes place.

The analytical results of this research indicated that the efl'ect of stress on shrinkage

explains a major part ofthe Pickett efl'ect, but not all deformation. This negates the notion

ofconsidering the influence of stress on shrinkage as the only mechanism to explain the

Pickett effect. Therefore, stress-reduced shrinkage is a mechanism, but not the only

mechanism that explains the excess creep deformation imder drying conditions.

8.3.2 Influence of Fiber Reinforcement on Shrinkage Behavior under Load

The results shown in Figure 8-3 reveal a difierence in behavior between plain and

fiber reinforced concrete. The shrinkage under stress ofboth fiber and plain concrete is

clearly different, although their fiee shrinkage is quite similar. The fiber reinforced

concrete exhibited more shrinkage under tensile load than that of the plain concrete. The

intuitive explanation to this behavior is related to the ability of fibers to conu-ol

microcracking/softening. Steel fibers seem to improve stress transfer in micro-cracked

concrete, which in tum reflects in greater macroscopic shrinkage under stress. Another

clear point in Figure 8-3 is the flatness of the shrinkage curve tmder tensile load for plain

concrete while it continues to increase for fiber concrete. This behavior suggests the ability

of fiber to control the sofiening ofconcrete, which influences the resulting shrinkage.

Therefore, shrinkage does not depend only on the moisture difiiision and state ofstress, but

also on the strain softening. Several researchers, among them Bazant and Raftshol (1982)

and Alvaredo and Wittmann (1993), have pointed out the influence of strain sofiening

phenomenon and fracture energy on shrinkage deformation. The softening due to drying

microcracking influences the fracture time ofrestrained concrete as will be discussed later

in this chapter.

8.4 Quantification of MicrocrackingISoftening

The microcracking that occurs in the outer layer ofdrying concrete is normally fine

and densely distributed. It causes material strain softening and influences its response to

stress. It is possible to descfibe it by a stress-strain relation in a continuum manner (see

163


Bazant and Chem, 1985b). It is assumed that the strain associated with microcracking be

additive to creep, shrinkage and elastic strains. Thus, it becomes possible to quantify the

strain associated with smface microcracldng. We must keep in mind, that the evaluated

strain softening in this case is an overall property (smeared value) ofa finite representative

volume ofheterogeneous material, not a point property ofhomogenized continuum.

The strain associated with surface microcracking ofdrying concrete was quantified

as follows. First. basic creep and stress-reduced shrinkage ofthe drying concrete were

predicted using their respective calibrated models. Second, microcracldng strain was

calculated such that the stress-reduced shrinkage and microcracking added up to the

measured drying creep in the experiment.

A sign convention adopted in the analysis expressed creep as a positive strain in

tension, and shrinkage as a negative strain. The drying creep and microcracking strain in

the tension case are of the same sign (positive) since they occurred in the same direction,

whereas the sign of the stress-reduced shrinkage is negative because it occurred in the

opposite direction to creep. For a restrained test, it can be written as follows:

Drying Creep + Stress-reduced shrinkage + Strain sofiening = 0 8.3

Typical analytical results of the drying creep (Pickett efi'ect) components are

presented in Figures 8-4 and 8-5 for concrete mixes with w/c-ratio of 0.5 and 0.4,

respectively. The results indicate that the stress-reduced shrinkage is a major contribution

to the Pickett efi'ect at early age for plain and fiber reinforced concrete. However,

microcracking component is quite obvious in plain concrete, but less significant in fiber

reinforced concrete as shown in Figures 8-4 and 8-5. Therefore, the stress-reduced

shrinkage in fiber reinforced concrete explains a major part ofthe drying creep. This

indicates that, the tensile creep ofFRC is dominated by real mechanisms related to

material, whereas for plain concrete a substantial amount ofcracking creep (apparent

mechanism) is involved. Moreover, considering only real mechanisms (i.e. excluding

microcracking) indicates that tensile creep offiber concrete is greater than that for plain

concrete. However, when all mechanisms ofcreep are considered, only a slight increase in

tensile creep of fiber concrete is observed. This explains the results ofcreep ofdrying

164


concrete discussed in Chapter 4, which revealed insignificant increases in the creep of fiber

concrete. Clearly, fiber reinforcement influences the apparent creep mechanism

substantially (the mechanism ofmicrocracking).

The above discussion suggests difierent stress relaxation mechanisms in plain and

fiber reinforced concrete. Real creep mechanisms are beneficial because they provide

tensile stress relaxation. But apparent creep mechanisms (microcracking), cannot be

viewed as beneficial because there is microstructural damage associated with the

deformation. Therefore, fiber reinforcement enhances stress relaxation because tensile

creep ofFRC is mainly dominated by real mechanisms. On the other hand, the

microcracking forms a substantial part of the tensile creep ofplain concrete. Therefore,

only part of tensile creep ofthe plain concrete contributes to beneficial stress relaxation

while the other part dominated by microcracking is detrimental as will be discussed later in

this chapter. The advantageous role offiber in modifying the creep behavior of concrete

and enhancing stress relaxation becomes more obvious when the difierent mechanisms of

creep are separated.

8.4.1 Qualitative Analysis for Microcracking and Failure

As shown in Figure 8-4, the strain associated with microcracking for fiber concrete

is substantially less than that for plain concrete. Consequently, the steel fiber reinforcement

controls the strain softening ofthe material. The less microcracking for fiber concrete

agrees with the general behavior ofFRC. Moreover, it explains the observed delay in

fracture ofdrying FRC samples under restrained conditions as mentioned in Chapter 4. The

impact ofmicrocracking on failure will be analytically demonstrated in section 8.8.4.

However, experimental observations supporting the link between the drying microcracking

and failure of restrained concrete are required.

For this purpose, replicate samples ofplain and fiber reinforced concrete were

tested imder restrained conditions. It was noticed that, similar restrained concrete samplesexhibited failure at difierent ages. For example, two samples offiber reinforced concretewith a w/c-ratio of0.5 failed at difierent ages: 145 hours and 181 hours. The fiee shrinkage

ofboth samples was quite similar but they failed at difierent ages. The analysis revealed

165


difierent levels of drying microcracking in these samples as shown in Figure 8-6. The first

concrete sample exhibited more microcraclcing than the second one. This diflerence is

possible because microcracking is localized in natlne and may occur faster at regions where

the fiber distribution density is low. Since fibers are randomly distributed, local regions

with low fiber density are fairly expected. Therefore, evolution ofmicrocracking in the first

sample was faster than the second sample as revealed by the analysis, and hence, the first

concrete sample failed earlier. Furthermore, when the resolved microcracking strain is

added to the measured elastic strain in the restrained test, the resulting strain at failure is

equivalent for both samples. Moreover, this strain was equal to the failure strain for that

concrete mix when monotonically loaded to failure. This experimental observation

validates the relation between the analytically resolved microcracking and fracture of

restrained concrete.

8.4.2 Stress-Strain Relation for Distributed Microcracking

As mentioned in section 8.4, the suain associated with microcracking can be

described in a stress-strain relation. Based on the strain softening model described in

Chapter 6, the softening part of response was assumed to be algebraic and additive to the

strain due to creep, shrinkage and elastic deformation as follows:

s=e,+ec+e,,,+.§ 8.4

Where a, 2, , er, 2,, ,5 = column matrices ofthe Cartesian components of the tensors of total

strain, of strain due to elastic deformation, of strain due to creep, of strain due to shrinkage,

and of strain associated with strain softening. The relation of 0' -af diagram can be

described as follows:

0' = (?(§)€ 3-5Where C represents Cartesian components ofthe secant modulus tensor; C is a fimction in

§ . The particulars of the model and its relevancy to the current analysis were discussed in

Chapter 6. The uniaxial strain-softening diagram is given by:

0' = A5” exp(—b§’) 8.6

For this expression, the secant modulus is

166


C(§) = 4-5”" ¢XP(-bi’) (0 < q <1) 3-7In which A, q,b,s are empirical constants. These parameters were determined by fitting the

data resolved for microcracking. Typical values ofthese parameters for fiber and plain

concrete are presented in Table 8.2.

Table 8.2 Parameters for strain softening of restrained drying concrete

Mix I .4 : q I B I s

NC-0.5-PC 103.17 0.4230 78.48 0.4747

‘P .¢>N 5-SF 77 10 0.3531 63.78 0.408

NC-0.4-PC 52.5 0.4045 21.11 I 0.4629

Figure 8-7 shows typical analytical results of strain soflening associated with

microcracking ofplain and fiber reinforced concrete with a w/c-ratio of 0.5. A significant

strain softening ofplain concrete is evident and started at a lowo-/ cr, , but FRC exhibited

less softening. However, 0 / 0', at failure is similar for plain and fiber reinforced concrete,

which was approximately 0.8. This is an important result indicating that concrete under

restrained condition failed at a stress level lower than its nominal value obtained by

conventional tensile strength test. The reduction in strength is primarily related to static

fatigue and accumulation ofdamage in the material under sustained load. Therefore, a

reduction strength factor must be considered for accurate prediction of shrinkage cracking

when strength is considered the criteria for failure. A factor of 0.8 was typically obtained in

this research.

The fact that fiber and plain concrete failed at the same o'/ 0', questions the

accuracy of strength-based failure analysis offiber concrete. For example, the tensile

strength of concrete was not improved by the fiber reinforcement while the age at failure

was delayed significantly as shown in Chapter 4. Thus, strength-based analytical models

would not capture the observed delay in fiacture. Therefore, fracture mechanics-based

analysis is probably more appropriate for the shrinkage craclcing of fiber concrete, because

167


it considers fi'acture toughness of concrete and mechanisms ofcrack propagation on which

fibers have a great influence.

8.4.3 Evolution of Microcracking

The previous analysis demonstrated the microcracldng as a contributor to tensile

creep ofdrying concrete. However, for the analysis ofshrinkage cracking in restrained

concrete, it is required to lmow the evolution ofdrying microcracking. This can be

achieved ifthe real stress distribution across the drying concrete is measured or calculated

by finite element analysis. Non ofthese were considered, and the mean stress was the only

form of stress obtained in the experiment. Having this restriction, empirical approach was

used to establish the evolution of smeared microcracking ofthe drying concrete.

Microcracking depends on the real stress and strength evolution (o'/ 0', ). A

phenomenological approach was used to establish the evolution ofmicrocracking. The

approach considers the evolution fimction as the product oftwo functions; one is a function

of 0' / 0', at the time of load application, and the other is a function of the time of exposure

to drying under load. The first fimction determines the location on the stress-strain

softening diagram established in the previous section, and the second describes the

progression ofmicrocracking in time due to continued drying. The choice ofthese

functions was based on experimental observations. The first fimction is of exponential type

because microcracking progress more rapidly as the o'/ 0', increases and the second is a

negative exponential fimction as drying generates stresses that follow a similar pattem. The

predictive fimction used in this study for the strain associated with microcracking (g' in

microstrain) has the following form:

:0) =A.e><p<a<%l)>‘>*<B. —e><p<-be-r.>>> 8.8Where r is the age of concrete, and to is the age at load application in hours;

A, , a, s, B, , b are empirical constants and determined by data fit; o'(t,, ), 0', (to ) are the mean

tensile stress and the tensile strength of concrete at time to . The suggested formula fitted the

168


resolved microcracking strains reasonably well, and the fitting coefficients for drying plain

and fiber concrete are presented in Table 8.3

Table 8.3 Parameters for microcracking evolution of restrained drying concrete

Mix I ,4, a s I B,NC-0.5-PCI 0.044 6.075 0.8805 I 2.611 6.037NC-0.5-SF ' 5.006 l 1.970 1.500 0.001 8.187

NC-0.4-PC I 0.164 I 5.410 I 0.2841 1.093 0.037 I

8.5 Limitations of the Approach

The technique implemented in this research separates and quantifies the

components of Pickett efl'ect. However, the implementation of the approach can not be

widely generalized at this point since it has been validated for certain concrete mixes under

specific conditions. As discussed in section 8.2.3, the key feature of the approach is the

condition of uniform drying of sealed samples. It provides infonnation on interaction of

creep with shrinkage at no surface microcracking. This condition was achieved under

sealed ctuing condition and validated only at early age for normal concrete with w/c-ratio

of 0.4 and 0.5. lt may not be guaranteed, however, to achieve this condition in old concrete

or in high performance concrete with a lower w/c-ratio. Validation of the approach for old

concrete is beyond the scope of this research. For these reasons, the approach described and

implemented in this research is applicable only to early age normal concrete, but may also

be applicable for old concrete. However, further research is clearly needed for validation.

8.6 Significance of the Approach

The approach developed in this research for separating the Pickett effect mechanisms is

very advantageous as it provides an avenue to tmderstand and explore the tensile creep-

shrinkage interaction particularly at early age. [ts significance can be seen as follows:

169


Q It provides a test technique to generate experimental data on the mechanisms ofthe

Pickett efi'ect on concrete in tension. Such data is not available in the literature, yet

required for better tmderstanding and modeling of the behavior ofconcrete.

0 Data on mechanisms ofthe Pickett effect allows modeling ofthe various mechanisms

and characterizing the contribution ofeach one to the overall deformation of concrete.

0 To study details and particulars of the interaction such as the identification of real

versus apparent creep mechanisms and their influence on the overall behavior. Micro-

mechanics based models can be developed accordingly.

0 It provides behavioral information and the effect ofvarious material parameters on the

creep of concrete and the overall mechanical behavior. For example, the explanation of

the delay in fracture of restrained drying FRC was only possible through the

quantification ofmicrocracking and its relation to material softening

8.7 Validation of the Approach

The experimental results indicate that the deformations from each mechanism of

tensile creep are additive. So the model for each mechanism can also be superposed to

describe total tensile creep. Based upon such considerations, a series-coupling model

(‘Figure 8-8) can be used to predict the total creep of restrained concrete. The basic creep is

represented by Kelvin chain model with aging modeled according to solidification theory

(Chapter 7, Equations 7.8-7.9). The stress- reduced shrinkage and stress -induced thermal is

from Equations 8.1-8.2. The microcracking is form Equation 8.8.

To validate the model oftotal creep, plain and fiber concrete samples with w/c-ratio of 0.5

were subjected to two difierent regimes of ctning during the restrained test: sealing and

drying curing conditions. The samples were initially sealed while restrained for 72 hours,

and exposed to dying afterward. Therefore, difierent mechanisms of creep were involved in

each stage.

In the sealed stage, only basic creep and stress-reduced shrinkage were assumed to

exist, whereas the microcracking mechanism was additionally induced upon drying. The

coefficients identified for basic creep, stress-reduced shrinkage, and microcracking of the

concrete with w/c-ratio of0.5 were used in the validation. Experimental and analytical

170


results for plain and fiber reinforced concrete are shown in Figures 8-9 and 8-10,

respectively. The results show a good agreement between the model and the experimental

data. Clearly, the model captures the discontinuity and the rapid change in the total creep

upon drying. This strong correlafion supports and strengthens the analytical approach and

the modeling of the various creep mechanisms at early age.

8.8 Damage-based Analysis of Microcracking

It is known that failure in quasi-brittle materials like concrete occurs first

progressively and then suddenly when micro cracks localize into a macro crack. The time-

dependent microcracking arises from drying is therefore contributing to the fracture process

of resnained concrete. In this section, the efl'ect of drying microcracking on failure is

quantitatively examined by using the basic principles of damage mechanics. From the

continuum point ofview, damage models are well suited to capture the essential features of

the failure of concrete. The basic damage concepts relevant to the current analysis were

described in Chapter 6, and a method to estimate damage in concrete was formulated.

However, a brief review ofthe method and its basic parameters is presented in thefollowing sections.

8.8.1 Basic Damage Concepts

Three basic parameters required for the analysis are briefly presented in this

section: damage factor, damage threshold, and damage evolution.

Damage Factor: The damage factor D was approximated from the tmiaxial tensile stress-

snain diagram using the concept of secant stiffness degradation as a measure of damage. A

skematic diagram showing this process was presented in Figure 6-4. The damage variable

D is defined as follows:

En=1-- 89E.

Where E is the efiective secant modulus of the damaged material and E0 is the initial

modulus of the virgin material. The failure is defined when the damage ofthe material

171


reaches a critical value Dc . The Dc may vary between DC =1 0 for pure brittle fi'acture

to DC = l for pure ductile fiacture but usually remains ofthe order of02 to 0.5.

Damage Threshold: The damage threshold PD is defined as the strain level below which

no damage by microcracking occurs. The damage threshold for concrete corresponds

approximately to the end of linear portion of the stress-strain diagram. It was approxiamted

on the stress-strain diagram as the elastic strain corresponding to a tensile stress of around

0.48-0.5 of the tensile strength (see Figure 6-4). However, for more accurate prediction of

the damage threshold, a series of load-unload stress-strain cmves are required, which were

not performed in this research.

Damage Evolution: Kinetic law of damage evolution was used to determine the evolution

ofdamage in restrained drying concrete. For quasi-brittle material, the kinetic damage

evolution can be approximated as follows (see Lemaitre, 1992):2. 0"_ f - -D - ;—Re,q zf an 2 PD andoyq 2 o'_,

__E$ 8.10

D=0 if o',q<crf

Where 0",, is the von Mises equivalent stress, 0' , is the fatigue limit of the material, an is

the rate oftotal equivalent strain, E is the elastic modulus, S is the material damage strength

factor, and R is the traixiality ratio defined as follows:

R=3(1+v)+3(1-2v)("—” )1 8.113 o'_,

Where, v is the poisson’s ratio and 0",, is the hydrostatic stress.

8.8.2 Identification of Damage Variables

The basic damage parameters described above were identified in the analysis from

the stress-strain diagrams obtained fiom uniaxial tensile strength tests for a concrete mix

with w/c-ratio of 0.5 as described in the following sections.

172


8.8.2.1 Critical Damage Factor

The pure monotonic tension test was considered a reference to characterize the

critical damage as a material property, and was defined as the damage factor at the

imminent of failure. Several tensile strength tests were conducted at difierent ages for plain

and fiber concrete with a w/c-ratio of 0.5. The obtained stress-strain diagrams were used to

calculate the crifical damage factor. The results for fiber and plain concrete are shown in

Figure 8-1 1. Clearly, the critical damage factor for plain and fiber concrete is increasing

with age, but it is reduced by fiber reinforcement, which suggests less damage at failure

when fibers are added to concrete. The critical damage factor at the age of 180 hours is

nearly 0.23 and 0.37 for fiber and plain concrete, respectively.

The evolution of critical damage factor with age is probably related to the aging of

concrete, and the subsequent changes in its fiacture characteristics. The exact form of

evolution requires large number of tests to characterize. However, with the limited number

of tests conducted in this research, a linear approximation is assumed as shown in Figure 8-

12 and is given by the following equations:

Dc = 0.243 + 0.00064 * t (Plain concrete) 8.12

Dc = 0.175 + 0.000278 *1 (Fiber Concrete) 8.13

Where t is the age of concrete in hours. So, at any point in time, if the damage caused to the

material exceeds the critical value, unstable crack propagation that leads to failure of

concrete is expected. The approach used to predict failure of restrained concrete is

empirical and approximate yet is simple and serves its purpose for this analysis. For more

sophisticated analysis of failure, fiacture-based finite element analysis is most likely

required.

8.8.2.2 Damage Threshold

Damage threshold strain was estimated as the strain corresponds to the end of linear

portion of the stress-strain diagram. The evolution of the threshold strain for plain and fiberconcrete was approximated by a power function as shown in Figure 8-12 and is given by

the following empirical equations:

173


8,, = 3.4127 * r°-"°’ (for plain concrete) 8.14and 5,, = 3.7309 *:°-“B (for fiber concrete) 8.15

8.8.2.3 Damage Strength Material Parameter, S

To identify the coefficient S, it is required to obtain data on damage accumulation.

Damages versus strain curves were constructed from the stress-strain diagrams using the

principle ofsecant stifiress degradation described in section 6.5.1. To construct such

curves, damage factors at different accumulated strain levels were calculated for each test

using Equation 8.9. The coeficient S was then determined fiom the slope of the curve:

damage D versus the accumulated equivalent strain, as shown in Figure 6-4b and is given

as follows (Based on damage evolution law, Equation 8.10):2

S =id—D—R if an 2 pp andoyq 20'; 8.162E——

dc“,

At each point of the curve, D is known (Equation 8.9), of is known from the tensile stress-

strain curve and is approximately equal to (0.48 — 0.5) * 0', for the tested concrete, :2 is8,,

estimated, E is the initial modulus, and R is the traixiality ratio which is known at each

point. Several points were considered in order to obtain S as the best average which when

used ir1 the kinetic damage evolution law (Equation 8.10) could reasonably predict the

critical damage factor for the material at that age.

The same stress-strain diagrams used for critical damage evaluation were used to

identify the parameter S at different ages. Linear approximation ofthe evolution is given by

the following empirical equation for the concrete mix with a w/c-ratio of 0.5:

s = 2.0188X10‘° + 4.338X10'“ *r 6.58Where t is the age ofconcrete in hours. So, at any point in time, the damage strength

parameter can be estimated to evaluate the damage by the kinetic law ofdamage evolution.

174


8.8.3 Quantitative Analysis for Microcracking and Failure

As discussed in Chapters 4 and 5, the restrained drying concrete samples were all

failed during the test. However, when the same loads were applied on concrete tmder wet

and sealed conditions, the concrete samples did not fail. The explanation to this observation

was primarily related to drying microcracking as demonstrated in section 8.4. To

demonstrate this relation quantitatively, the damage-based model described above was

used.

In a restrained shrinkage test, the accumulated elastic strain and the strain

associated with microcracking are primarily the damaging strains that lead to failure.

Therefore, these two components must be added for failure analysis of drying concrete. The

elastic component of strain (in time) was determined form the tests under wet curing

condition, and the strain associated with drying microcracking was calculated according to

the approach suggested in this study (see section 8.4). Thus, the two components were

added to construct a combined stress-strain diagram for damage analysis.

The kinetic law of damage evolution and the identified damage parameters for the

concrete under consideration were used to evaluate the evolution ofdamage factor and to

predict failure ofplain and fiber reinforced concrete. Figures 8-l3 and 8-14 presents

accumulation of the calculated damage and the critical damage in restrained plain and fiber

reinforced concrete, respectively. The accumulated damage only exceeds the critical

damage factor at a time that corresponds to the measured failure time for the tested

concrete i.e. the damage approach predicts the failure of the restrained concrete. Figure 8-

14 also presents the damage evolution for the replicate fiber concrete samples that failed at

dilferent ages due to the induced drying microcracking as discussed in section 8.4.1. The

CllSCL1:SlOIl initiated in section 8.4.1 qualitatively linked the microcracking strain to the

failure time. However, the damage analysis quantitatively demonstrates the contribution of

microcracking to the induced failure. Figure 8-14 shows the damage in the first sample

reaching a critical value (failure) earlier than in the second sample.

The damage-based analysis captures the features of failure for drying concrete,

particularly the influence offiber reinforcement. The suggested approach that characterizes

the damage ofconcrete using secant stiffness degradation is simple and sufiiciently

175


accurate. Moreover, it identifies all basic damage parameters from a tmiaxial stress-strain

diagram. Therefore, it can be used to predict shrinkage cracking ofdrying concrete with

suficient accuracy. Furthermore, the reasonable agreement between the failure time of

concrete in the experiment and the predicted failure time demonstrates the contribution of

microcracking to failure, and supports the suggested technique that resolves them.


0 The implemented experimental technique and the analytical approach satisfactorily

separate the early age drying tensile creep mechanisms into stress-reduced shrinkage

and microcracking. The combined experimental and analytical analysis provides

valuable behavioral information on the mechanisms of creep for fiber and plain

concrete. The experimental technique requires creep measurement under wet, sealed,

and drying curing conditions.

0 Stress-reduced shrinkage is a major mechanism of drying creep in plain and fiber

reinforced concrete, but not the only mechanism as demonstrated by the analysis. The

results reveal reduction of shrinkage under tensile load by 40 to 60 %.

0 Microcracking forms a significant portion ofdrying tensile creep in plain concrete, but

it is less significant in fiber concrete. Thus, fiber reinforcement controls the softening of

drying concrete, which in tum influences the shrinkage and stress-strain behavior.

v Real mechanisms of creep (basic and stress-reduced shrinkage) dominate the creep

behavior of fiber reinforced concrete, whereas apparent creep mechanism induced by

microcracking forms a significant part of the tensile creep ofplain concrete. Real

mechanisms are only beneficial for stress relaxation while apparent mechanisms are

detrimental. Therefore, fiber reinforcement influences the creep mechanisms and

enhances stress relaxation.

v The implemented analytical models for basic creep, stress-reduced shrinkage and

microcracking analysis are reliable and satisfactorily predict the behavior.

0 The microcracldng clearly influences the failure time ofrestained drying concrete. The

qualitative and quantitative analysis demonstrates the relation between drying

176


microcracking and failure. Drying microcracking profotmdly afl‘ects the mechanical

behavior and failure ofdrying concrete.

The method of secant stifiress degradation is appropriate to characterize damage

parameters. It requires only a imiaxial stress-strain diagram to identify various damage

parameters such as the damage factor, the damage threshold, the critical damage, and

the material damage strength factor.

The damage-based approach satisfactorily captures the features of failure ofdrying

concrete. It predicts the failure time, and demonstrates quantitatively the contribution of

microcracking to failure. Thus, a damage-based model is more appropriate for fiber

reinforced concrete than strength -based model because it predicts the time of failure

more accurately. For example, fiber reinforced and plain concrete failed at the same

stress/strength ratio (0.8) while the time to failure substantially increased by fiberreinforcement.

l77


kage(pm/m)

Stress-ReducedShrn

e(rm/rn)-9

nkag

Stress-ReducedShr

50----1---1._.r-

. °Model Parameters , _,,---* *

50 , , ._»rs= - 0.5910 I.

4° pT= 1.9340 730 7" L

20 6 = Data

—-— Model10

0 . . , .0 50 100 150 200

Age (hrs)

Figure 8-1 Stress-reduced shrinkage for plain concrete (w/c = 0.5)

50 .

Model Parameters

rS= - 0.4119 dpT= 4.7895 Q

40

30

20 = DataiModel

10

O _ . .0 50 100 150 200

Age (hrs)

Figure 8-2 Stress-reduced shrinkage for fiber reinforced concrete (w/c = 0.5)

178


(pm/m)

hr'nkageStranS

-so

-100

' “ ‘ ‘ ‘ ‘ ‘ ‘ ' ‘ ‘ ' ' ‘ ' ' ‘ ' ‘ ' * ‘ ' ' ' ‘ ' ' ’ ‘ ‘ ‘ ‘ ‘ ' ' ' ‘ ' ' ' ‘ ' ‘ ' ' ' ’ ’ ’ ' ‘ ‘ "

0 ' y

~~ __ Shrinkage under load. . v. -0 ..... _-__._

................................. ._ '..fitlffffifffiffffifffi.Eq.-..SF

Free Shrinkage ' __. ‘>1... .

q . . . . . . . . . . . . . . . ... . - - . . . . . . . . . . . . . . . . . ‘=1 . . . . . . . . . . . . . _ . ._‘~

. . . . . . . . . . . . . . . . . . .

' '_"l

Stran(pm/m)

100

""'""""“'"""""""“"""""""'“""" """"'“"" "-'-'_'_'_'_.

a SF250

0 50 100 150 200

Age (hrs)

Figure 8-3 Efiect of tensile stress on shrinkage (w/c = 0.5)

A Microcracking PC

0 . . ..frrr.-:9.-.--,.__,___.._,_.___-___--.,.....-.-.-¢.-9. . . . . . . . . . . . , ..

‘I ~' .

_50 . _ . . . . . . . . . . . . . . . . . . _ . . . . . .\._.‘.’ . . . . . .-___._

~,_.,._

Q,‘

Stress-induced shrinkage PCI r

1500 50 100 150 200

Age (hrs)

Figure 8-4 Components ofthe Pickett eflect (w/c = 0.5)

179

SF,


Stran(um/m)»-

(pm/m)

Stran

100

so

-100 '

-1500

100

-199 ..' ................... ................................... ..-2. . . . . . . . . . . . . . . _ ..

-150

__,__....-___._.._..__._..,__>. . . . . . . . I . . I . . . . .

<:_____

r 1 -. r 1 . . I

Microcracking

,[email protected]."" ..-......'::.-.-.->.-¢.-::f ................................. ..4.99.... ...... ..

Q..‘‘at

- '0. _9 ... .,; . - - . . . . . - - - - - - - - - - --

PC

' . ,-OA s1=‘___; ------ -'1 u .. ¢¢'. 0"’.

SF 2. _l_ .___ .. "0-._- '.“~.. ~-__.

..... '..............................Z:Q . . . . . . ..

Stress-induced shrinkage PC

50 100 150 200Age (hrs)

Figure 8-5 Components of the Pickett efi'ect ' (w/c = 0.4)

Microcracking j 1 i Failure

. . . . . . . . . . . . . . . . . . . .¢

Shrinkage

so A _..!.' 1 Samrgli?-__1... ------- 1j1_n1QI§.2-YQ .....'fo'-.':¥.'.'.'.°";" , , _ . . . . . . . . . _ . . . . . . . . , . . . . . _ . ..

Stress-induced shrinkage

----- __ Free shrinkage.1". _.299 ........................................................ ............ ..

-2500 50 100 150

Figure 8-6 Effect ofmicrocracking on age at failure ofFRC samples (w/c = 0 5)

Age (hrs)

180

2O0


0.8 . . J . ,» 4%E............................................................................... .1

0.6 . . . . . . . , _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

. . . . . . . . , . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .

" —*— Plain concreteQ 0_4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

Q3 ...................................... .. -'— Steel-fiber ...... ..

0_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . ..

. _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

0O 10 20 30 40 50 60 70 80

Microcracking Strain (mulm)

Figure 8-7 Typical stress-strain curves associated with microcracking (w/c = 0.5)

181


WW P1

WW F"

WW _l“'1“al.<

A A

Microcrackingstrain1

7:

ii

_‘__.

Basic creep .ya 7 (Kelvin chain model) M°?h““°a‘L.%__.

7’.v

X Y

Viscous flow

Y rStress-reducedshrinkage

V

Figure 8-8: Model for total creep

l 82


TotaCreep(pm/m)

TotaCreep(pm/m)

ao-

eo-

40- 1 -

20-

0 . . ‘ 1 .

20 40 60 80 100 120 140

100

so -

so - -

40 -

20 - -

O . 1 . _ . r . "

140 160

' l ‘ ‘ ‘ l ‘ l

_ ——Model ' T- I Experiment I -

- Sealed 1 _ -- 4 I

- 8 - _

- I A , T_ I ; Drying _- ——Z—————-> _

Age(hrs)

Figure 8-9 Validation of the creep model for plain concrete (w/c = 0.5)

- I Experiment -- —— Model T

_ Sealed i- qi-i . -

V -

- 4 Drying _

20 40 60 80 100 120

Age(hrs)

Figure 8-10 Validation of the creep model for FRC (w/c = 0.5)

183


—¢— Plain Concrete i ' 'O

amageFactor,D

t'caDCr’

Figure 8-ll Critical damage factors for plain and fiber reinforced concrete (w/c = 0 5)

apn(|.l|Tl/ITI)

DamageThreshod

Figure 8-12 Damage threshold strain for plain and fiber reinforced concrete (w/c = 0 5)

0-4 -'1"‘1‘""|"'1 r""i"*|

0.35 ----- ~ ——I—— Fiber Cgncrete --------------------------

. . . . . . . . . . . . . . . . . . . . ~ - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . _ . . . ..0.3

0.25 ----------------------------------------------------------------------------%"

02 ................... .............................................. ..

0.15 ' ' ‘ ’ ' ’ ‘ 1 ' ' ' I '40 60 80 100 120 140 160 18

Age (hours)

50

40 . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

30 . . . . . . . . . . . . . . . . . . . . . ..

20

—¢- Plain Concrete—l— Fiber Concrete

10 _ _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

1 . ,

0 50 100 150 200

Age (hrs)

184


DamageFactor

DamageFactor

0.4. , ,....,.0.35

0.3

0.25

0.2

F3 .4.U1 E................... ............ .. Calculated Damage

0-1 """ """""" """""" " —'—critica| damageQ95 ............... . ............................................................... ..

0 50 100 150 ZQQ

Z Failure ———,>~ - - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - ~ - - ~ - ' -7--~--~------------>--~.~‘-------------~~

I , 4? .' W f

7 , , - , , _ , , , , , , _ - _ , _ _ _ _I 1 - -

» » 1 | 1 1 I - 1 t I

...,

¢ - I 8 | 1 v I v ~ | 1 ~ 1 v v

.__i

Age (hrs)

Figure 8-13 Damage evolution and failure ofplain concrete (w/c = 0.5)

0.25

0.2

0.15

0.1

0.05

0O 50

.i> 'Failure4% —$*

-4*..............

Failure

-'— damage-sample # 1—I— damage-sample # 2 _—r— critiml-damage

100 150 200Age (hrs)

Figure 8-14 Damage evolution and failure ofFRC (w/c = 0.5)

185


CHAPTER 9

CONCLUSIONS AND RECOMMENDATIONS

9.1 Introduction

This chapter presents a summary ofthe findings and conclusions based on the

experimental and analytical results obtained in this research. The chapter summarizes the

findings ofthe difierent phases ofthis research, including experimental technique,

restrained behavior ofdrying concrete, sealed and wet curing at early age, basic creep

behavior, drying creep mechanisms, and the general behavior ofplain concrete and fiber

reinforced concrete (FRC).

9.2 Experimental Technique

The uniaxial, restrained shrinkage test developed in the experimental phase reveals how

shrinkage stresses develop and how creep mechanisms reduce shrinkage strain in the

restrained specimen. The following remarks can be made regarding the experimental

technique and procedures

0 The experimental setup developed in this study is reliable and can be used to

characterize tensile creep and restrained shrinkage ofconcrete in the early age. The

reproducibility of shrinkage stress, shrinkage strain and creep strain is acceptable and

falls within the inherent scatter ofmaterial properties. The test sufficiently detects the

sensitivity of creep and shrinkage to various material parameters.0 The experiment requires LVDT’s with high resolution to capture the small

deformations. The LVDT’s must be attached directly to the concrete sample to exclude

the effect oftest machine and end grips on the measurements. The test also requires a

closed-loop control system with a high resolution to avoid a rough application ofthe

load that may cause premature failure ofconcrete, particularly at early age.

I The end grips must be designed to avoid premature failure ofthe sample. Therefore, the

cross-section ofthe grips must be gradually increasing to minimize stress concentration

at the contact surfaces. Rigid attachment of the grips to the actuator and the end

186


reaction block is inappropriate and causes erroneous measurement due to possible

misalignment; instead, swivel joints must be installed at both ends to

eccentric loads.

9 3 Restrained Drying Concrete

Shrinkage Stress and Failure ofDrying Concrete

Tensile stresses generated by restraining shrinkage of concrete are significant in the

first days after casting, and lead to fracture of the material. The role of tensile creep in

relaxing shrinkage stress is substantial and reduces the stresses by 50 %.

The rate and history of shrinkage stress evolution at early age are two important factors

that influence the time ofcracking and stress at failure. These parameters must be

considered in the analysis for accurate prediction of shrinkage cracking because under

sustained loads, static fatigue and damage accumulation promote failure at a stress less

than the tensile strength. The static fatigue represents a slow crack growth under

sustained load that eventually leads to failure. A typical value of 0.8 for stress/strengthratio at failure is obtained for restrained concrete. Therefore, a reduction strength factor

of 0.8 can be applied in a strength-based analysis for shrinkage cracking.

b) Free Shrinkage and Tensile Creep

The very early days of concrete life are characterized by a complex interaction of

intemal drying, extemal drying and thermal effects. A major portion of the shrinkage of

normal and HPC occurs in the first two days afier casting, and is driven by a complex

combination of intemal and extemal drying. Extemal drying alone cannot explain the

fiee shrinkage in the first two days, and other mechanisms, such as autogenous and

chemical shrinkage must be considered.

Total tensile creep at early age forms a substantial part of the time dependent

deformation. The ratio between tensile creep and fiee shrinkage can be used to express

their interaction. This ratio is important and can be roughly considered in the vicinity of

187


failure as 0.5 for concrete irrespective ofw/c-ratio. This indicates that the creep relaxes

the shrinkage stress by 50 %.

Influence ofFiber Reinforcement

The addition of fibers (0.5 % by volume) does not affect fiee shrinkage at early age.

However, it slightly increases the total tensile creep.

Steel fiber reinforcement substantially delays the time of shrinkage cracking,

particularly in concrete mixes with low w/c-ratios. The delay in fracture seems

unexplainable solely by the slight improvement of total tensile creep. However, the

apparent creep associated with microcracking is substantially reduced by fiber

reinforcement. This part of the creep promotes failure in tension case, and hence, it is

detrimental. The reduction ofmicrocracking creep in FRC explains the delay ir1

fiacture.

9 4 Sealed and Wet Curing Conditions

The sealing ofconcrete against drying does not eliminate the early age shrinkage

because ofthe intemal drying, even for normal concrete. Therefore, tensile creep of

sealed concrete at early age includes the interaction with the autogenous shrinkage and

cannot be considered as a basic creep.

Autogenous shrinkage of concrete is a significant component of total shrinkage of

concrete measured in the early age, particularly for the concrete with low w/c- ratio.

The autogenous shrinkage forms a major part ofthe total shrinkage in the very early

days.

The sealed and wet-curing conditions used in this study provide imiform distribution of

intemal humidity in concrete. The uniform drying ofconcrete eliminates the potential

for surface microcracking.

188


The age at which sealing is applied influences the shrinkage and creep behavior. Thus,

the experimental procedures must specify the time at which sealing is applied to avoid

misinterpretation of the collected data.

Moist curing can be successfully used to suppress early age shrinkage ofnormal

concrete. Its influence on mechanical properties as compared to sealed curing is

negligible. Therefore, the creep measured under wet curing condition can be taken as a

basic creep ofthe material because shrinkage is eliminated from the measurement.

9 5 Basic Creep Behavior

The basic creep model based on solidification theory satisfactorily describes the tensile

creep behavior at early age. The model captures the various characteristics ofbasic

creep and provides valuable information on the aging behavior of concrete.

The analysis of basic creep test results reveal that the tensile basic creep becomes age-

independent after a few days, typically after five days for the concrete tested in this

research. This finding is useful for the characterization of tensile basic creep behavior

and for the design of its experiment. However, generalization of this finding for early

age concrete requires more comprehensive investigations.

The basic creep fimction ofyoung concrete is characterized by a high rate of creep in

the ir1itial 10-20 hours after loading, after which the rate decreases and the creep

function tends to approach a stable value. This behavior was observed ir1 the plain and

fiber reinforced concrete. However, the basic creep of the plain concrete stabilizes

earlier than that ofthe fiber concrete.

The initial rate ofbasic creep is very sensitive to age at loading in the first two days,

and becomes less sensitive afier that. The initial rate of creep ofplain concrete is higher

than that of fiber concrete. This suggests that microcracking initially dominates the

creep ofplain concrete while it is more controlled in fiber reinforced concrete.

9 6 Drying Creep Mechanisms

0 The experimental approach oftesting concrete under drying, sealed and wet curing

conditions enables the separation ofthe two mechanisms ofdrying creep at early age

189


stress-reduced shrinkage and microcracking. The separation ofdrying creep

mechanisms explains the diflerence in behavior between plain and fiber reinforced

concrete.

The implemented analytical models for basic creep, stress-reduced shrinkage and

microcracking analysis are reliable and satisfactorily predict the behavior ofconcrete.

Stress-reduced shrinkage is a major mechanism ofdrying creep ofplain and fiber

reinforced concrete, but not the only mechanism as demonstrated by the analysis. The

results reveal reduction of shrinkage under tensile load by 40 to 60 %.

Microcracking forms a significant portion ofdrying tensile creep ofplain concrete, but

it is less significant in fiber concrete. Fiber reinforcement controls the sofiening of

drying concrete, which in tum influences the shrinkage and stress-strain behavior.

9 7 General Behavior at Early Age

Real mechanisms of creep (basic and stress-reduced shrinkage) dominate the tensile

creep behavior of fiber reinforced concrete, whereas apparent creep mechanism

induced by microcracking forms a significant part of the tensile creep of plain concrete.

The real mechanisms are beneficial for stress relaxation, but apparent mechanisms

involve microcracking and are detrimental. Therefore, fiber reinforcement influences

the creep mechanisms and enhances stress relaxation.

Sofiening due to microcracking influences shrinkage behavior under tensile load.

Therefore, fiber reinforced concrete exhibited greater shrinkage under tensile load than

the plain concrete, because of the less softening associated with drying microcracking.

The drying microcracking profotmdly influences the failure time and mechanical

behavior ofrestrained concrete. The qualitative and quantitative analysis demonstrates

the relation between drying microcracking and failure of restrained concrete.

The basic creep fimction ofplain concrete is characterized by a high initial rate of creep

that does not last long before the creep function stabilizes. On the contrary, the initial

rate ofcreep ofFRC is not as high as ofplain concrete, but it lasts longer before the

creep fimction stabilizes. This implies that stress relaxation capacity of FRC is more

than that ofplain concrete because it continues for a longer duration.

190


0 The early age creep is inversely proportional to the w/c-ratio ofthe concrete mix.

9.8 Failure Analysis

0 The damage-based approach satisfactorily captures the features of failure ofdrying

concrete. It predicts the failure time satisfactorily, and demonstrates quantitatively the

contribution ofmicrocracldng to failure. Damage-based models capture the failure

characteristics of fiber reinforced concrete in a more appropriate way than strength-

based models. For example, fiber reinforced and plain concrete failed at the same

stress/strength ratio (0.8) while the time to failure substantially increased by fiber

reinforcement.

0 The method of secant stiffiiess degradation is appropriate to characterize damage

parameters. It requires only a uniaxial stress-strain diagram to identify various damage

parameters: damage factor, damage threshold, critical damage, and material damage

strength factor.

l9l


APPENDIX A

EXPERIMENTAL RESULTS FOR RESTRAINED SHRINKAGETESTS

Notes:

A) Creep, shrinkage, and elastic strains are reported in microstrain

B) Reported humidity values represent average humidity over the cross-section

192


Table A-1: Restrained shrinkage results forage at drying =14 hours, RH = 50 %

plain concrete, w/c = 0.5, sample # 1

Age(hrs) Stress,MPa Elastics Shrinkage Creep Creep coef. Humidity creeplshnnk32.00 0.05 8.24 -8.20 -0.21 0.00 97.98 0.0334.17 0.21 17.16 -15.35 -1.81 0.00 97.74 0.12

, 36.87 0.36 26.59 -26.07 -0.36 0.00 97.47 0.0139.50 0.52 36.19 ' -40.87 4.67 0.13 97.16 0.1142.17 0.68 45.03 -57.54 12.51 0.28 96.88 0.2246.00 0.85 53.78 -81.36 27.74 0.52 96.48 0.3452.00 1.00 62.19 -108.92 46.72 0.75 95.86 0.4361.33 1.13 69.75 -136.64 67.06 0.96 94.94 0.4974.00 1.25 78.16 -160.12 81.70 1.04 93.75 0.5193.67 1.38 86.75 -184.96 98.38 1.14 92.05 0.53116.83 1.49 95.07 -208.69 113.87 1.20 90.27 0.55135.67 1.55 102.80 -228.17 125.36 1.22 89.02 0.55154.33 1.67 111.30 -244.84 133.54 1.20 87.93 0.55179.00 1.75 119.12 -265.60 146.65 1.23 86.74 0.55

Table A-2: Restrained shrinkage results for plain concrete, w/c = 0.5, sample # 2age at drying =14 hours, RH = 50 %

Age (hrs) Stress,MPa, Elastic: Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 99.50 0.0026.00 0.22 8.08 -8.09 0.01 0.00 99.50 0.0028.67 0.33 16.25 -19.01 2.59 0.16 99.40 0.1430.83 0.45 24.50 -29.75 5.25 0.21 99.30 0.1833.00 0.57 32.58 -42.37 10.13 0.31 99.20 0.2436.33 0.67 40.92 -59.60 18.85 0.46 99.10 0.3240.67 0.76 48.96 -76.48 27.18 0.55 98.90 0.3646.17 0.87 57.38 -91.49 34.45 0.60 98.60 0.3854.33 0.98 65.42 -109.57 44.15 0.67 98.20 0.4066.17 1.10 73.58 -127.98 54.74 0.75 97.70 0.4384.67 1 .21 81.58 -149.82 68.24 0.84 96.80 0.46105.83 1.41 89.87 -169.26

179.39 0.88 95.80 0.47

131.83 1.57 97.95 I -192.45 94.50 0.96 94.60 0.49159.50 1.78 106.12 -215.65 1 09.53 1.03 93.30 0.51


Table A-3: Restrained shrinkage results for steel fiber concrete, w/c = 0.5, sample #1, age at drying =14 hours, RH = 50 %

Age (hrs) Stress,MPa Elastica Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 99.50 0.0027.50 0.13 8.16 -8.66 0.50 0.06 99.10 0.0629.83 0.27 16.65 -17.50 1.02 0.06 98.90 0.06

I 32.83 0.44 l1 25.75 -30.60 4.86 0.19 98.70 0.16

36.17 0.60 34.58 -47.44 12.69 0.37 98.40 0.2740.50 0.76 43.25 -65.99 23.08 0.54 98.00 0.3546.67 0.92 51 .66 -85.04 33.72 0.66 97.50 0.4055.50 1.06 59.82 -105.46 45.89 0.77 96.80 0.4467.50 1.21 68.91 -125.87 56.96 0.83 95.90 0.4584.17 1.31 77.66 -146.29 68.63 0.88 94.70 0.47101.33 1.45 86.07 -163.38 77.40 0.90 93.50 0.47123.67145.17

1.531.67

94.23 -183.89102.39 -203.06

89.65100.68

0.950.98

92.2091.10

0.490.50

Table A-4: Restrained shrinkage results for steel fiber concrete, w/c = 0.5 sample #2, age at drying =14hours, RH = 50 %

Age (hrs) Stress.MPa Elastica Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 99.50 0.0027.50 0.20 12.40 -8.08 0.00 -0.35 98.80 0.0031.17 0.30 19.63 -24.41 4.95 0.25 98.60 0.2033.50 0.46 29.57 -36.49 6.92 0.23 98.50 0.1936.83 0.57 37.72 -53.50 15.78 0.42 98.30 0.2940.50 0.76 46.73 -69.15 22.42 0.48 98.10 0.3248.67 0.87 54.46 -93.99 39.53 0.73 97.70 0.4256.67 1.05 62.62 -111.69 49.06 0.78 97.30 0.4475.00 1.15 70.01 -140.95 70.93 1.01 96.40 0.5090.34 1 .20 76.60 -158.64 83.14 1.10 95.70 0.52

1 19.68 1.35 85.01 -1 87.90 1 02.89 1.21 94.50 0.55141.34 1 .40 92.07 -208.32 1 16.25 1 .26 93.80 0.56155.84 1.62 101.58 -221.16 1 19.49 1.18 93.30 0.54181.01 1.77 108.38 -242.34 133.96 1 .24 92.50 0.55


Table A-5: Restrained shrinkage results for polypropylene fiber concretew/c = 0.5 sample # 2, age at drying =14hours, RH = 50 %

Age (hrs) Stress,MPa Elastic: Shrinkage Creep Creep coef. Humidity creeplshnnk13.00 0.00 0.00 0.00 0.00 0.00 99.50 0.0025.83 0.14 8.17 -8.20 0.03 0.00 99.24 0.0028.17 0.26 17.18 -18.43 1.42 0.08 99.11 0.08

1 .. .._1 30.01 0.41 25.35 -30.03 4.68 0.18 98.97 II 0.16

33.67 0.55 33.52 -45.38 11.86 0.35 98.80 0.2637.67 0.72 42.02 -62.77 20.75 0.49 98.57 0.3343.00 0.88 50.53 -83.24 33.05 0.66 98.27 0.4050.17 1.04 58.53 -104.73 46.20 0.79 97.85 0.4460.00 1.21 66.69 -127.92 61.40 0.92 97.27 0.4874.83 1.38 74.86 -154.19 79.33 1.06 96.38 0.5190.83 1.56 83.37 -177.38 94.01 1.13 95.38 0.53

1 14.67 1.72 91.53 -202.62 111.43 1.22 93.85 0.55134.50 1.89 100.38 -226.33 125.78 1 .25 92.51 0.56

Table A-6: Restrained shrinkage results for plain concretew/c = 0.4, age at drying = 15 hours, RH = 50 %

Age (hrs) Stress.MPa Elastic: Shrinkage Creep Creep coef. Humidity creeplshnnk15.00 0.00 0.00 0.00 0.00 0.00 0.0022.67 0.18 8.10 -8.17 0.24 0.03 95.77 0.0327.17 0.35 16.62 -17.88 1 .26 0.08 95.47 0.0730.50 0.53 25.23 -29.46 4.23 0.17 95.25 0.1433.50 0.71 33.84 -43.42 9.41 0.28 95.05 0.2236.50 0.89 42.20 -58.75 16.55 0.39 94.85 0.2839.83 1.05 50.64 -77.83 27.19 0.54 94.64 0.3543.83 1.23 59.08 -100.99 41 .91 0.71 94.38 0.4250.33 1 .43 67.26 -128.92 61.83 0.92 93.96 0.4862.3381 .83

1.591.73

75.3683.97

-158.21-187.50

82.85103.53

1.101.23

93.2092.00

0.520.55

108.17 1.93 92.32 -21 5.43 123.11 1.33 90.43 0.57144.67 2.13 100.56 -250.68 1 50.29 1.50 88.37 0.60


Table A-7: Restrained shrinkage results for steel fiber concretew/c = 0.4, age at drying = 14 hours, RH = 50 %

Age (hrs) Stress,MP Elastica Shrinkage Creep Creep coef. Humidity creeplshnnkaw14.00 0.00 0.00 0.00 0.00 0.00 0.0026.33 0.21 8.35 -8.37 0.01 0.00 0.00

} 30.83 0.41 ii 16.71 I

I -21.57 4.94 0.30 I I1 | 0.2334.50 0.62 25.06 -36.72 11.75 0.47 0.3238.00 0.81 33.41 -53.84 20.51 0.62 0.3841.17 0.94 41.85 -70.78 29.02 0.69 0.4144.83 1.12 50.55 -89.77 39.31 0.78 0.4451.67 1.29 58.81 -116.00 57.18 0.97 0.4962.00 1.48 67.34 -141.89 74.55 1.11 0.5379.17 1.66 75.52 -169.05 93.61 1 .24 0.55105.67 1.85 83.70 -199.11 1 15.40 1.38 0.58139.83 2.03 91.80 -233.17 141.37 1.54 0.61174.83 2.22 99.89 -265.52 165.98 1.67 0.63


Age (hrs) Stress.MPa] Elastics Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 0.0014.67 0.25 10.04 -1 1.43 1.39 0.14 0.1215.67 0.41 18.55 -24. 1 3 5.59 0.30 0.2317.50 0.58 26.88 -38.29 11.41 0.42 0.3020.33 0.75 35.47 -53.21 17.74 0.50 0.3323.67 0.93 44.32 -68.13 23.81 0.54 0.3528.00 1.09 52.91 -85.87 32.96 0.62 0.3832.50 1.20 61.08 -102.92 41.85 0.69 0.4137.50 1.30 69.41 -120.49 51.08 0.74 0.4242.50 1.39 77.41 -137.04 59.63 0.77 0.4447.83 1 .49 85.57 -153.47 67.90 0.79 0.4454.00 1.59 93.74 -171 .27 77.53 0.83 0.4560.67 1.68 101.90 -188.73 86.83 0.85 0.4669.50 1.76 109.98 -209.30 99.32 0.90 0.47


Table A-9: Restrained shrinkage results for steel fiber concretew/c = 0.32, age at drying = 14 hours, RH = 50 %

Age (hrs) Stress.MPa Elastice Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 0.0014.92 0.07 8.59 -1.33 0.00 0.00 0.1716.50 0.17 1 6.59 -16.80 0.21 0.01 0.01

i 122.61 0.30 24.84 -30.02 5.18 0.21 0.1721.17 0.46 32.83 -44.17 11.34 0.35 0.2624.50 0.63 40.83 -60.20 19.37 0.47 0.3228.75 0.80 48.83 -77.09 28.26 0.58 0.3733.00 0.90 57.08 -92.27 35.19 0.62 0.3837.33 1.05 65.16 -106.76 41 .60 0.64 0.3943.50 1.17 73.15 -125.86 52.71 0.72 0.4248.58 1 .23 81 .07 -140.87 59.81 0.74 0.4254.17 1 .40 89.23 -156.39 67.16 0.75 0.4363.00 1.53 97.40 -178.73 81.34 0.84 0.4673.08 1.66 105.65 -201.59 95.94 0.91 0.4885.58 1.79 1 13.82 -226.32 1 12.50 0.99 0.50100.58 1.90 122.07 -252.75 130.68 1.07 0.52


j Age (hrs) Stress,MPa Elastice Shrinkage Creep Creep coef. Humidity creeplshnnk14.50 0.00 0.00 0.00 0.00 0.00 0.0015.33 0.05 6.76 -10.32 3.56 0.53 0.3416.00 0.16 15.31 -16.80 1 .49 0.10 0.0917.67 0.25 23.09 -32.40 9.31 0.40 0.2919.50 0.38 31.60 -48.09 16.49 0.52 0.3421.00 0.56 40.45 -60.20 19.76 0.49 0.3323.83 0.73 49.34 -79.30 29.97 0.61 0.3827.17 0.92 59.03 -96.87 37.84 0.64 0.3932.00 1.07 68.01 -117.51 49.50 0.73 0.4236.67 1.18 76.51 -135.92 59.41 0.78 0.4441.50 1.36 85.78 -153.24 67.45 0.79 0.4447.33 1.45 93.44 -172.08 78.64 0.84 0.4651.83 1.60 101 .95 -185.73 83.78 0.82 0.4557.50 1.73 1 10.67 -201.50 90.84 0.82 0.4564.17 1.82 118.15 -219.15 101.00 0.85 0.4669.67 2.01 127.34 -232.80 1 05.46 0.83 0.45



Age (hrs) Stress,MPa] Elastice Shrinkage Creep Creep coef. Humidity creeplshnnk12.00 0.00 0.00 0.00 0.00 0.00 0.00

. 22.67 0.18 9.74 -8.93 0.00 0.00 99.50 0.0826.00 0.34 18.16 -19.17 1.09 0.06 99.30 0.06

i 2s.aa 0.50 26.28 -29.48 3.20 0.12 99.20 0.1132.00 0.69 34.88 -41.93 7.06 0.20 99.00 0.1736.17 0.88 43.08 -57.62 14.88 0.35 98.90 0.2641.33 1 .07 51.21 -75.70 24.50 0.48 98.70 0.3249.33 1.26 59.25 -95.66 36.41 0.61 98.30 0.3864.50 1 .40 67.92 -122.77 54.93 0.81 97.70 0.4587.67 1.58 75.96 -148.06 72.10 0.95 96.90 0.49121.67 1.79 83.96 -175.35 91.43 1 .09 95.90 0.52158.33 1.97 92.00 -202.55 110.47 1 .20 95.00 0.55


Age (hrs) Stress,MPa] Elastic: Shrinkage Creep Creep coef. Humidity creeplshnnk14.00 0.00 0.00 0.00 0.00 0.00 0.0027.50 0.07 8.85 -8.81 0.30 0.04 100.00 0.0330.00 0.18 17.01 -19.72 2.71 0.16 99.90 0.1433.67 0.30 25.18 -32.43 7.30 0.29 99.90 0.2237.33 0.45 33.35 -45.61 12.43 0.37 99.80 0.2742.00 0.61 41.60 -60.36 18.81 0.45 99.80 0.3148.17 0.79 50.10 -77. 1 6 27.06 0.54 99.70 0.3555.83 0.97 58.52 -95.24 36.71 0.63 99.50 0.3965.00 1.13 67.28 -113.14 45.86 0.68 99.40 0.4178.17102.67

1.321.53

75.4583.79

-132.76-158.85

57.3975.06

0.760.90

99.2098.70

0.430.47

138.00 1.72 92.04 -186.82 94.87 1.03 97.90 0.51169.33 1.92 100.71 -210.61 109.90 1 .09 97.10 0.52183.00 2.00 1 04.63 -220.42 1 15.79 1.11 96.80 0.53


Table A-13: Restrained shrinkage results of plain concrete w/c = 0.5, age at sealing =15 hours, sealed for 72 hours prior to drying at RH = 50 %

Age (hrs) Stress.MPa] Elastice Shrinkage Creep Creep coef. Humidity creeplshnnk15.00 0.00 0.00 0.00 0.00 0.00 0.0027.67 0.22 8.18 -8.25 0.06 0.01 0.01

1 48.50 0.42 16.36 -27.75 11.38 0.70I 1

0.4171.83 0.66 24.38 -41.80 17.42 0.71 0.4285.67 0.89 33.24 -61.81 27.97 0.83 0.4589.50 1.11 41.60 -78.42 36.82 0.89 0.4796.17 1.39 50.12 -98.00 47.88 0.96 0.49105.00 1.56 58.65 -117.08 58.43 1.00 0.50115.83 1.70 66.83 -134.79 67.96 1.02 0.50130.83 1.87 75.01 -154.54 79.53 1.06 0.51

Table A-14: Restrained shrinkage results for steel fiber concrete w/c = 0.5, age atsealing = 15 hours, sealed for 72 hours prior to drying at RH = 50 %

Age (hrs) Stress,MPa Elastica Shrinkage Creep Creep coef. Humidity creeplshnnk15.00 0.00 0.00 0.00 0.00 0.00 0.0036.33 0.19 8.18 -8.15 -0.04 0.00 0.0051.67 0.38 16.37 -21.09 4.55 0.28 0.2272.17 0.58 24.55 -34.71 10.17 0.41 0.2986.00 0.69 27.79 -44.59 16.81 0.60 0.3888.51 0.92 36.31 -58.43 22.12 0.61 0.3893.68 1.13 44.58 -78.01 33.43 0.75 0.43100.34 1.35 52.85 -97.60 44.92 0.85 0.46111.68 1 .49 59.38 -121.61 63.76 1.10 0.52126.52 1.69 67.91 -147.84 79.85 1.17 0.54146.18 1.88 76.09 -175.09 99.00 1.30 0.57


Table A-15: Restrained shrinkage results for steel fiber concrete subjected to drymg/ wetting cycle: w/c = 0.5, age at drying = 15 hours, RH = 50 %, wetting applied atage of 67 hours for 24 hours and then exposed to drying

Age (hrs) Stress,MPa‘ Elastice Shrinkage Creep Creep coef.creep/shnnk13.50 0.00 0.00 0.00 0.00 0.00 0.00

} 25.83 0.11 8.17 -8.17 0.34 0.04 0.0428.50 0.24 16.59 -18.40 1.81 0.11 0.1031.00 0.40 25.35 -30.00 4.65 0.18 0.1533.50 0.56 33.43 -43.98 10.55 0.32 0.2436.50 0.73 41.43 -60.35 19.10 0.46 0.3241.00 0.91 49.85 -80.48 30.81 0.62 0.3847.17 1.12 58.01 -101.03 43.10 0.74 0.4356.67 1.32 66.18 -123.63 57.45 0.87 0.4667.50 1.44 71.79 -142.22 70.42 0.98 0.5068.01 1.13 60.90 -136.08 75.00 1.23 0.5568.51 1.01 55.80 -128.57 72.69 1.30 0.5769.17 0.86 49.51 -121.07 71.48 1.44 0.5970.01 0.72 43.72 -113.23 69.50 1.59 0.6170.84 0.59 38.28 -106.66 68.46 1.79 0.6472.34 0.46 32.84 -97.88 64.87 1.97 0.6673.84 0.35 27.73 -91.40 63.66 2.30 0.7076.1784.18

0.230.13

22.2916.85

-84.57-73.49

62.2856.64

2.793.36

0.740.77

91.18 0.09 15.15 -69.48 54.33 3.59 0.78115.68 0.28 23.31 -68.71 45.49 1.96 0.66125.02 0.48 31.31 -77.50 46.19 1 .48 0.601.34.52 0.70 39.47 -88.24 48.77 1.24 0.55143.35 0.91 47.64 -99.84 52.20 1.10 0.52152.52 1.15 55.63 -112.46 56.82 1.02 0.51162.52 1.39 63.63 -126.61 62.90 0.99 0.50

200


APPENDIX B

RESULTS FOR CONCRETE HUMIDITY MEASUREMENT

201


eHumd'ty%atvRe

eHum'dty%3

Retv

90‘k _ - - . - - - - - - - - - - - --Q

- . - — ' - -‘---"

£7‘,r4 . . ~ . . --Q,P _. . . . . . . - . .-

¢ _--‘I ‘.0G —-¢ _.-

.--" 0 .......................... --4I ' ' _ -‘

85 .. . ' ,¢ ",-- -----Q-Q‘--------------.,1 v ,a v’¢

’-OO

."' ¢".' p_¢ '4

_,.-"M —-'—1 day.~"' A __ --~--2 days

80 A * ' '3 daysAge at Exposure = 14 hrs -~--'----4 days

"-1-" 5 daysRH = 50 % -——=-6 days

15- i0.25 0.5 0.75 1 1.25 1.5

Depth (inch)

Figure B-1 Humidity profile of HPC-0.32, RH = 50 °/0

Q6 1 I4

-I l

92 ” »

0 _ , - - . - -- ‘---_,_---------------------------- "'_,-" -

_ ’/'___ ——|—-1 day

88 " _-' —-— 2 days/' —*—- 3 days

Age at Exposure = 14 hrs """""‘ days5 da s""" YT: = O/0 iI———-6 days

840.25 0.5 0.75 1 1.25 1 .5

Depth (inch)

Figure B-2 Humidity profile for HPC-0.32, RH = 80 %

202


umd'ty%

ve-I

Reat

ty°/0

ReatveHum'd

100

95l-

90,-L

85-

:31'1 :7-\ -‘J_ V, --§§

~:\~- '~

E 0-' ‘ "-2 45 “€_‘~ J"-\._ >A ‘_ 7 “ _'_ . ' .

an5' 0

v._~_. -. 9 ‘= . . .. p Q. p_ _ _. —__% ._______~

: _"__'-- ‘*8 .- _~- __- '9:-..,;.*~_= = _ . -_. ... ‘ A

E AL

—-=-"Depth =—-—Depth =--°--Depth =--*--Depth =------"Depth =

0.25 "0.50 "0.75 "1.00 "1.50 "

800 50 100 150

100

98

96

94

92

Drying Time (hrs)

Figure B-3 Humidity functions ofNC-0.5, RH = 50 %

200

-a- - - _ . _ _ . . . _ __‘Q --_-_“44pp_

‘_ _ _ _ _ _ . ..._: ' . ’ _ _-o- . _ . _ . _ . _ _ _ __fI

1’ --"0 a." Qff ’

t’ . ’ 0 ---"""-/ __,--/ _-»

Q’?I 0"

O.‘_.

____,.o"'

< > __---‘Qt; - _ _ _ _ __

-—--..‘

O

—-'-2 days--' "3 days--° - 4 days

' 5 days----" 6 days

RH = O/0 ——I——7 days

I

0

900.25 0.5 0.75 1 1.25

Depth (inch)

Figure B-4 Humidity profile ofNC-0.5 , RH = 70 %

203

1.5


ty0/0

tveHum'd

Rea

atveHumdty%Re

100 —l—

99 _, ______ ..-0O ...... -- ‘___-------------------

-"

98

ao97 —

96

_ Q_Q¢‘__- -____- . .

' Q" — ..__- H¢' "0a¢o4n .44o4

If 4.fi ‘—-—; _ _ _ - - - _ - — - - - - - — --l

--'-.'-'-____, . . - - . ’_,_ . _ . _ . _ . _ . _ . _ . _ . ...-0_- ’__

_.,o"'.. __,.- . .. ,',.— ,¢................................. --¢

_@' _ _ . - "_@ _,-—

.4 ._--'

-'-»" ,-’

—I—1day _V --P-2days

--'- 3daysAge = 14 hrs """"°4 days-"-r" 5 days

_ O --E-6 daysRH - 80 /0 __;__7 days

95 E0.25 0.5 0.75 1 1.25 1.5

Depth (inch)

Figure B-5 Humidity profile ofNC-0.5, RH = 80 %

96n—

Q2 -' .. - - - ' ’ ' ' ' ' . ' , .-0 -------------- -—---------------------------------- --4

84)

i Ias / +1....31’ ._

-.— -nil I Z L

_..._—. -—-_- __-_ _-is -11- --i —-i-Q

4-P’ —I’’ _,. . - . . . . . . . . . . . . .... -- - . . . - . . . - . . . . - . - . . - . - - . - . . . . . . . .-Q} ..-

-’ 0’. -- --_. _,.- Q - -----.._-. ----__-_.' -" -"¢ ._-- ’-¢

4?-

-~— 2 days-----"3 days----*----4 days---- -- 5 d

Age = 14 hrs __;__6 dz:

RH = so % -'1-7 days80'

0.25 0.5 0.75 1 1.25 1.5

Depth (inch)

Figure B-6 Humidity profile ofNC- 0.4, RH = 50 %

204


APPENDIX C

ANALYTICAL RESULTS FOR BASIC CREEP

205


70 , ,

6° . . . . . . . - . . . . . . - - . - - - - - - - - - - - . - - . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

1W/C = 0.5 2

n(pm/m)

50 . . . . . . . . . . . - - . - - . - - -.I . - - - - - - . - ~ . . . . . . . . . . . . - . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

........................................ IF §66

30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ _ . . . . . . . . .

= Basic creep2Q . . . . . . . . . . . . . . . . . . - - . . . . . . . - . . . . . . . . . . . . . . . . . . . . _ . .

—-— Model-linear10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 . . . . . . . . . . . . . . . . . . . . . . . . . . . _ _ . . . . . . . . . . . ..

40

CreepStra

0 . IO 50 100 150 200

Age (hrs)

Figure C-1 Incremental-based model for basic creep of plain concrete (w/c =0.5)

70

60 Model coefficients

'~ 50 A1= 43.757 ,A = 32.193 "“"‘

40 2 "am= 1.8888 r *._- G3,;

q= Q5573 " Experiment3° . -—- Model

CreepStran(pm/m20

10 Plain Concrete W/C = 0.5

Q 1

0 50 100 150 200Age (hrs)

Figure C-2 Superpositi0n- based model for basic creep ofplain concrete (w/c = 0.5)

206


(pm/m)‘-

CreepStran

(um/m)

CreepStran

60

50

40

20

10

‘ l I

' 0. . _ . . . . . . . . . . . . . . . _ . . . . . .,.a>°..... .....

"""""""""""" Q

8 1so e

. . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . -. _ Basic Creep

. . . . . . . . . . . . . . . . . . . .- . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .

0 50 100 150 200Age (hrs)

0

Figure C-3 Incremental-based model for basic creep of FRC (w/c =0.5)

60Model coefficients _

50A1= 511.561 ="'A2= - 5.005 8

5m= 3.0702ot= 0.0883

40

30

= = Experiment2o " ” —— Model

10Steel Fiber W/C = 0-5

O | . . .

0 50 100 150 200Age (hrs)

Figure C-4 Superposition- based model for basic creep ofFRC (w/c = 0.5)

207


| ) * ' - ' |

an ----------------------- --;-------- --

(um/m) 8

pStran -hO

ECree20

020

Figure C-5 Incremental-based model for basic creep ofplain concrete (w/c =0.4)

80

70

(pm/m)

60

50

"' 40

CreepStran

30

20

10

020 40 60 80 100 120 140 160

Figure C-6 Superposition- based model for basic creep ofplain concrete (w/c = 0 4)

' i/v/c = 0;4 iQQ

= Basic creep

_ -iModel-linear ____________ ,__‘

1 r. l 1 . . . .

40 60 80 100 120 140 160

Age (hrs)

= Experiment—-— Model

3

Model coefficients

A1= 103.451

A2= 357.069

m= 5.5276ot= 0.0952

Plain Concrete W/C = 0.4

2

Age (hrs)

08


(Pm/ml

CreepStran

(pm/m)

CreepStran

100. ..

80 _. . . . . . . . - - - - - . . - - - - - -Q - - - - - - - - - - - - - - - - - - - - --- ~ - - - - - - - - - - - - - . ..e _ . - - - . . . . . - . . - . . . . . .._

_ ‘ _ 6 8 _

I 5 VVK:==(l4 I a, ' :

60 _. . . . . . . . . . - . . . . . . . . . J . - - . . . . . . . . . - - . . . . . . . . I>a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40 _ . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . _ . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._

F 0

L P’ . "I° Basic creep 1

20 T""""""""""""""""""""""""""" M -i'Model-linear 1'.

00

Figure C-7 lncremental- based model for basic creep of FRC (w/c = 0.4)

100

50 100 150 200

Age (hrs)

80;

60i-

20?

0

Model Coefficients

A1= 1618.67

A2= - 80.04

m= 3.4074ot= 0.04579

Steel Fiber W/C=O.4 -

5 -

' ..

= Experiment _—-—Model -

0 50 100 150 200

Figure C-8 Superposition- based model for basic creep of I-‘RC (w/c = 0.4)

Age (hrs)

209


l

2

3

4

5

6

7

8

9

l0.

ll.

12.

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VITA

Salah Ahmed Altoubat was bom in Dier-Essieneh, Irbid, Jordan in April 1, 1964.

He graduated fi'om Al-Taibah High School in June 1982 and pursued his undergraduate

study at Yarmouk University where he received his Bachelor of Science degree in Civil

Engineering (major in structures) in May 1987. After he received his B.S degree, he joined

the graduate program at Jordan University of Science and Technology in Irbid-Jordan

where he received his Master of Science degree in Civil Engineering (major in materials

and structures) in May 1990. During his study, he worked as a teaching assistant in the

Department of Civil Engineering in which he taught courses in analysis of structures,

behavior of concrete structures and design ofmetal and concrete structures. The master

thesis was to study accelerated curing methods ofconcrete in Jordan.

From July 1990 to July 1994, Salah Altoubat worked as materials and structural

engineer in the Arab Center for Engineering Studies, a regional consulting firm in the

Middle East. head quarter in Amman. Jordan. I-Iis work in the Arab Center provided him

with a valuable insight and experience on materials and evaluation/rehabilitation of existingstructures and pavements. He worked on a variety ofprojects including joint projects with

intemational contacts such as ERES Intemational, Inc., United Nations Development

Program, and some other regional firms.

In 1994, Salah Altoubat was admitted to the Department ofCivil Engineering at the

University of Illinois for his Ph.D. He worked as a research assistant and participated in

developing a research program for early age behavior of concrete. He researched in early

age creep and shrinkage ofnormal and high performance concrete and their implications on

early age cracking ofconcrete structures. His research interest is in the areas of early age

deterioration of concrete and its impact on long-term performance and durability, material

modeling of creep, shrinkage, and stress relaxation in high performance concrete and fiber

composites, and in evaluation and repair ofdamaged structures.

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Altoubat - Early Age Stresses and Creep-shrinkage Interaction of Restrained Concrete THESIS

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