Altoubat - Early Age Stresses and Creep-shrinkage Interaction of Restrained Concrete THESIS
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Transcript of 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
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UMI Number". 9989929
Copyright 2000 byAltoubat, Salah Ahmed
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© Copyright by Salah Ahmed Altoubat, 2000
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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.
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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.
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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
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This work is dedicated to
My wife, Ruba Abu-Kaf
And
To my parents and all ofmy family members
V
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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
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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
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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 ......................................................................
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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
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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
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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
7.5 Concluding Remarks.............................................................................................. .. 146
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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
8.9 Concluding Remarks.............................................................................................. .. 176
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
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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
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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
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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
Restrained shrinkage results for plain concrete, w/c=0.5, age at drying =12
hours, RH = 70% ....................................................................................... .. 198
Restrained shrinkage results for plain concrete, w/c=0.5, age at drying =12
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
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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
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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
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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
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Figure 4-22
Figure 4-23
Figure 4-24
Figure 5-1
Figure 5-2Figure 5-3
Figure 5-4
Figure 5-5
Figure 5-6Figure 5-7
Figure 5-8
Figure 5-9
Figure 5-10
Figure 5-11Figure 5-12
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
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Figure 5-14
Figure 5-15
Figure 5-16
Figure 5-17
Figure 5-18
Figure 6-1
Figure 6-2
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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
..
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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
...
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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
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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
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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
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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
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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,
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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,
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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.
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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
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(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.
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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
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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).
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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
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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
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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
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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,
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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
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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.
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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).
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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mm) A
(Mindess and Young, 1981)
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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
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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
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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
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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
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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
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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
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.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
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_ 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
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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
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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
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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
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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
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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
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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
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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
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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
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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_
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f‘,
;.._
Restrained Sample
Free Shrinkage Sample
Figure 3-2: Experimental device showing restrained and fiee shrinkage samples
53
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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,
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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
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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 drying- wetting 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-
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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).
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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
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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
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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
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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
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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
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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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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.
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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
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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%
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
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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
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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
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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
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§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
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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
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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
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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:
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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
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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
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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.
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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
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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
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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
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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:
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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,
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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
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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)
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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
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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.
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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.
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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
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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;
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.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:
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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.
7.5 Concluding Remarks
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
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dominates the creep ofplain concrete while it is more controlled in fiber reinforced
concrete.
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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
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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
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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
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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
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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
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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
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/'§
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
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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
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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
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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
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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
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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.
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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;
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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.
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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
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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
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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
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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
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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
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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
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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
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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:
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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
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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
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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.
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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:
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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.
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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
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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.
8.9 Concluding Remarks
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
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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
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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)
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(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,
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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
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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)
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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
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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
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—¢— 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)
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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)
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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
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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
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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.
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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
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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.
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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
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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
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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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Table A-8: Restrained shrinkage results for plain concretew/c = 0.32, age at drying = 14 hours, RH = 50 %
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Table A-10: Restrained shrinkage results for plain concretew/c = 0.32, age at drying = 14 hours, RH = 80 %
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table A-11: Restrained shrinkage results for plain concretew/c = 0.5, age at drying = 12 hours, RH = 70 %
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
Table A-12: Restrained shrinkage results for plain concretew/c = 0.5, age at drying = 12 hours, RH = 80 %
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B
RESULTS FOR CONCRETE HUMIDITY MEASUREMENT
201
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX C
ANALYTICAL RESULTS FOR BASIC CREEP
205
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(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
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| ) * ' - ' |
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
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(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
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l
2
3
4
5
6
7
8
9
l0.
ll.
12.
LIST OF REFERENCES
AC1 Committee 209,” Prediction ofcreep, shrinkage, and temperature efiects inconcrete structures,” ACI Std. No. 209R-92. ACI, 1992.
ACI Committee 207, “ Efiect ofRestraint, volume changes and reinforcement oncracking of massive concrete,” AC1 Std. No. 207.2R-90, reported by AC1Committee 207, AC1, 1990.
AC1 Committee 224, “Control ofcracking in concrete structures” AC1 Std. No.224. Reported by AC1 Committee 224, ACI, Detroit, 1990.
ACI Committee No. 318, “Building Code Requirements for Reinforced Concrete,”AC1, Detroit, 1989.
AC1 Committee 517: Accelerated curing of concrete at atmospheric pressure-stateof the art, ACI Journal, No. 77, 1980, pp. 429-4-48.
Al-Kubaisy, M. A., and Young, A. G. (1975), “ Failure of concrete imdersustained tension,” Magazine of Concrete Research, Vol. 27, No. 92, pp. 171-178.
Alvaredo, A., and Wittmann, F. H. (1993), “ Shrinkage as influenced by strainsoftening and crack formation,” Creep and Shrinkage of Concrete, Proc. of the FifthInternational RILEM Symposium, Z. P. Bazant and 1., Carol, ed., B & FN SPON,New York, 1993, pp. 103-113.
Ardoullie B., and I-Ienrix E. (1997), “ Chemical shrinkage ofcementitious pastesand mortars,” Diploma work, Katholieke Universiteit Leuven and NTNU-Trondheim, (Referred by Bjqmtegaard 1999).
Balaguru, P. N. and Shah, S. P. (1992),“ Fiber - reinforced cement composites”,McGraw-Hill, Inc. New York.
Banthia, N., Yan, C., and Mindess, S. (1996), “Restrained shrinkage cracking infiber reinforced concrete: a novel test technique,” Cement and Concrete Research,Vol. 26, N0. 1, pp. 9-14.
Banthia, N., Anabi, M., and Pigeon, M. (1993), “ Restrained shrinkage cracking infiber reinforced cementitious composites,” Materials and Structures, RILEM(Paris), Vol. 26, pp. 405-413.
Bazant, Z. P. (Editor), (1988), “Mathematical modeling ofcreep and shrinkage ofconcrete,” John Wiley and Sons Ltd.
210
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Bazant, Z. P. (1979), “ Thermodynamics ofsolidifying or melting viscoelasticmaterial,” Joumal ofengineering mechanics, ASCE, Vol. 105, pp. 933-952.
Bazant, Z. P. (1977), “ Viscoelasticity of solidifying porous material-concrete,"Journal of engineering mechanics, ASCE, Vol. 103, pp. 1049-1067.
Bazant, Z. P. (1972), “ Prediction of concrete creep efiects using age-adj ustedeffective modulus method,” ACI Joumal, Vol. 69, pp. 212-217.
Bazant, Z. P. (l972a), “ Numerical determination of long range stress history fromstrain history in concrete,” Materials and Structures, Vol. 5, No. 27. pp. 135-141 .
Bazant, Z. P., and Chem, J. C. ( 1987), “ Stress-induced thermal and shrinkagestrains in concrete,” J. of Eng. Mech., ASCE, 113 (10), pp. 1493-1511.
Bazant, Z. P., and Chem, J. C. (1985), “ Concrete creep at variable humidity:constitutive law and mechanism,” Materials and Structures, 18 (103), pp. 1-20.
Baza.nt, Z. P., and Chem, J. C. (1985a), “ Triple power law for concrete creep." J . otEngineering Mech. ASCE, Vol. 1 1 1, pp. 63-84.
Bazant, Z. P., and Chem, J. C. (l985b),”Strain softening with creep and exponentialalgorithim.‘ Journal ofEngineering Mechanics, Vol. 1 11, No. 3. pp. 391-415.
Bazant, Z. P., and Chem, J. C. (1978), Practical prediction of time dependentdeformations of concrete, Materials and Structures, Research and Testing (R[LEMParis), ll(65), 307-28, (66), 415-34; and l2(69), (1979), 169-83.
Bazant, Z. P., and Najjar, L. J. (1971), “ Drying of concrete as nonlinear diffiisionproblem,” Cement and Concrete Research, Vol. 1, pp. 461-473.
Bazant, Z. P., and Osman, E. (1976), “ Double power law for basic creep ofconcrete,” Materials and Structures, Vol. 9, No.49, pp. 3-11.
Bazant, Z. P., and Prasannan, S. (l989a), “ Solidification theory for concrete creepI: Formulation,” Journal ofEngineering Mechanics, Vol. 115, No. 8, pp. 1691-1703.
Bazant, Z. P., and Prasarman, S. (1989b), “ Solidification theory for concrete creepll: Verification and Application,” Joumal ofEngineering Mechanics, Vol. 115. No8, P11 1704-1725.
Bazant, Z. P., and Raftshol, W. J. (1982), “ Effect ofcracking in drying andshrinkage specimens,” Cement and Concrete Research, Vol. 12, No. 2, pp. 209-226
211
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
28
29
30
31
32
33
34
35
36
37
38
39
Bazant, Z. P., and Wittmann, F. H., (Editors), (1982), “ Creep and shrinkage inconcrete structures,” John Wiley & Sons Ltd., New York.
Bazant, Z. P., and Wu, S. T., (1974), “ Rate type creep law ofaging concrete basedon Maxwell chain,” Materials and Structures, Vol. 7, No. 37, pp. 45-60.
Bazant, Z. P., and Xi, Y. (1994), “ Drying creep of concrete: constitutive model andexperiments separating its mechanisms,” Materials and Structures, Vol. 27, pp. 3-14.
Bentur, A., Berger, L., Lawrence, F. ‘v'., Milestone, N.V, Mindess, S., amd Young,F. Y. (1978), “ Creep and drying shrinkage oftricalcium silicate. IH. A hypothesisof irreversible strains,” Cement and Concrete Research, Vol. 8, pp. 721-73.
Bissonnette, B., and Pigeon, M. (1995), “ Tensile creep at early ages of ordinary,silica fume and fiber reinforced concretes,” Cement and Concrete Research, Vol.25, No. 5, PP- 1075-1085.
Bjcbntegaard O. (1999), “ Thermal dilation and autogenous deformation as drivingforces to self-induced stresses in high performance concrete,” Doctoral thesis,Division of Structural Eng., The Norwegian Univ. of Science and Technology,Trondheim, Dec. 256 p.
Bloom, R.. and Benture, A. (1995), “ Free and restrained shrinkage ofnormal andhigh strength concrete,” ACI Materials Joumal, Vol. 92, No.2, pp. 211-217.
Boumazel, J. P., and Martineau, J. P. (1993), “ A laboratory test to analyze creepimder tension of young concrete,” Creep and Shrinkage of Concrete, Proc. of theFifih lntemational RI[..EM Symposium, Z. P. Bazant and 1., Carol, ed., E & FNSPON, New York, 1993, pp. 57-62.
Bradbury, R. D. (1938), “ Reinforced concrete pavements,” Wire ReinforcementInstitute, Washington, D.C.
Brooks, J. J., and Neville, A. M. (1977), “ A comparison of creep, elasticity andstrength of concrete in tension and in compression,” Magazine of ConcreteResearch, Vol. 29, No. 100, pp. 131-141.
Byfors (1980),” Plain concrete at early ages,” Swedish Cement and ConcreteInstitute, Fo 3:80, Stockholm (Referred by RILEM 1998).
CEB-FIP Model Code 1990, Comite Euro-International Du Beton, Bulletine D’Information No. 203, 1991.
Chem, I. C., and Yotmg, C. H. (1989), “ Compressive creep and shrinkage ofsteel fiber reinforced concrete,” The intemational Joumal ofCement compositesand Light weight Concrete, Vol. ll, No. 4, pp. 205-214.
212
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
41
42
43
44
45
46
47
48
49
50
51
Domone, P. L. (1974), “ Uniaxial tensile creep and failure of concrete,” MagazineofConcrete Research, Vol. 26, No. 88, pp. 14-4-152.
Edgington, J., Hannant, D. J., and Williams, R 1. T. (1974), “ Steel fiberreinforced concrete,” Current paper CP 69/74, Building Research Establishment,pp. 17.
Emborg M. (1989), “ Thermal stresses in concrete structures at early ages,”Doctoral thesis, Lulea Univ. ofTechnology, Division of structural engineering,1989, (Referred by Bjrbntegaard 0., 1999 and RILEM 1998).
Gamble, B. R, and Parrot, L. J. (1978), “ Creep of concrete in compressionduring drying and wetting,” Magazine. of Concrete Research, 30 (104), pp. 129-138.
Geiker M. (1983), “ Studies ofPortland cement hydration,” Doctoral thesis,Technical University ofDenmark, (Referred by Bjqantegaard 1999).
Gilbert, R. I. (1988), “ Time efiects in concrete structures,” Elsevier, Amsterdam,(Referred by Kovler, 1994).
Goran, H (1997), “ Measurement ofmoisture in high performance concrete,” LundInstitute ofTechnology, Division ofBuilding Materials, Lund, Sweden
Grzybowski, M., and Shah, S. P. (1990), “Shrinkage cracking of fiber reinforcedconcrete,” AC1 Material Joumal, Vol.87, No. 2, pp. 138-148.
Grzybowski, M., and Shah, S. P. (1989), “Model to predict cracking in fiberreinforced concrete due to restrained shrinkage,” Magazine ofConcrete Research(London), Vol. 41, No. 148, pp. 125-135.
Guenot, 1., Torrenti, J-M., and Laplante, P. (1996), “ Stresses in early age concrete:comparison ofdifierent creep models,” AC1 Materials Joumal, Vol. 93, No. 3, pp.254-259.
Gutsch, A., and Rostasy, F. S. (1995 ),” Young concrete under high tensile stresses-creep, relaxation and cracking,” In Thermal Craclcing In Concrete at Early Age,Proceedings ofthe intemational RILEM Symposium, Ed. by R Springenschmid,Munich, 1994 pp. 111-118.
Hansen, W., and Young, J. F. (1991), “Creep mechanisms in concrete,” MaterialsScience ofConcrete 11, Edited by Jan Skalny and Sidney Mindess, Published byAmerican Ceramic Society, INC, pp. 185-199.
213
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52.
53
54
55
56
57
58
59
60
61
62.
Hansen, W. (1987), “ Drying shrinkage mechanisms in portland cement paste,”Journal ofAmerican Ceramic Society, Vol. 70, No. 5, pp. 323-328.
Hammer T. A., Justnes H., Bjontegaard 0., and Sellevold E. J. (1998), “Suggestions on the terminology and test methods proposed by JCI,” In the Int.Workshop: “Autogenous Shrinkage of Concrete” Organized by the JCI (JapanConcrete Institute), Hiroshima, Jime 13-14,l998/ Ed. By Ei-ichi Tazawa, pp. 397-98. (Referred by Bjtbntegaard 1999).
Helmuth, R. A., and Turk, D. H. (1967), “ The reversible and irreversible dryingshrinkage ofhardened portland cement and tricalcium silicate paste,” J. PCA Res.Dev. Lab., Vol. 9, No.2, pp. 8-21.
Huang, Y. H. (1993), “ Pavement analysis and design,” Printice Hall Inc.,Englewood cliffs, New Jersey.
Hwang, C. L., and Yotmg, J. F. (1984), “ Drying shrinkage ofportalnd cementpastes, I, microcracking during drying,” Cement and Concrete Research, Vol. 16,pp. 584-594.
Illston, J. M. (1965), “ The creep ofconcrete under uniaxial tension,” Magazine ofConcrete Research, Vol. 17, No. 51, pp. 77-84.
Kasai, Y., Yokoyama, K., Matsui, I., and Tobinai, K. (1974), “ Tensile properties ofEarly age concrete,” Mechanical Behavior ofMaterials, The Society ofMaterialsScience, Japan, Vol.2, pp. 433-441.
Khan, A. A., Cook, W. D., and Mitchell, D. (1996), “ Tensile strength of low,medium, and high strength concretes at early age,” ACI Materials Joumal, Vol. 93,No. 5, PP- 487-493.
Kovler, K. (1999), “ A new look at the problem ofdrying creep of concrete undertension,” Joumal ofMaterials in Civil Engineering, Vol. 11, No. 1, Feb, 1999, pp.84-87.
Kovler, K. (1996), “Why sealed concrete swells,” AC1 Materials Joumal, Vol. 93,No. 4, pp. 334-340.
Kovler, K. (1995), “ Interdependence of creep and shrinkage for concrete undertension,” AC1 Materials Joumal, Vol. 7, No. 2, pp. 96-101.
214
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
64
65
66
67
68
69
70
71
72
73
74
¢
Kovler, K. (1995a), “Shock of evaporative cooling of concrete in hot dry climates,”Concrete intemational, No. 10, pp. 65-69.
Kovler, K. (1994), “Testing system for detennining the mechanical behavior ofearly age concrete under restrained and fiee tmiaxial shrinkage,” Materials andStructures, Vol. 27, pp. 324-330.
Kovler. K., Igarashi, S., and Benture, A. (1999), “ Tensile creep behavior ofhighstrength concretes at early ages,” Materials and Structures, Vol. 32, pp. 383-3 87.
Kovler, K., Sikuier, J., and Bentur, A. (1993), “ Restrained shrinkage tests offiber-reinforced concrete ring specimens: efiect ofcore thermal expansion,”Materials and Stmctures, Vol. 26, pp. 231-237.
Kraai, P. P. (1985), “A proposed test to determine the cracking potential due todrying shrinkage ofconcrete,” Concrete Construction, Vol. 30, No. 9, pp. 775-778.
Krenchel, H., and Shah, S. P. (1987), “ Restrained shrinkage tests with PP-fiberreinforced concrete,” Fiber reinforced concrete properties and applications, SP-105,AC1, Detroit, Michigan, pp. 141-158. _
LaPlante, P., and Boulay C. (1994), “ Evolution du coefficient de dilationthermique du beton en fonction de sa maturite aux tout premiers ages,” Materialsand Structures, Vol. 2, pp.596-605 (in french), (Referred by Bjontegaard 0., 1999).
Laube, M. (1990), “ Werkstofinodell Zur Berechnung von Temperatursparmungenin massigen Betonbauteilen immjungen Alter,” Doctoral Thesis, TUBraunschweig. (Referred by Bj¢ntegaarc1 0., 1999).
Lemaitre, J. (1992), “ A course on damage mechanics,” 2“ edition, Published bySpringer-Verlag, New York.
L’Hermite, R. (1959), “ What do we know about the plastic deformation andcreep of concrete?,” RILEM Bull., No. 1, Paris, France, pp. 21-51.
Lim, Y. M., Wu, H. -C., and Li, V. C. (1999), “ Development offlexural compositeproperties and dry shrinkage behavior ofhigh performance fiber reinforcedcementitious composites at early age,” AC1 Materials Joumal, Vol. 96, No., 1, pp.20-26.
Lokhorst, S. J., and Breugel, K. van. (1995), “ From microstructural developmenttowards prediction ofmacro stresses in hardening concrete,” In Thermal CrackingIn Concrete at Early Age, Proceedings of the International RILEM Symposium, Ed.by R. Springenschmid, Munich, 1994 pp. 71-78.
215
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
76
77
78
79
80
81
82.
83
84
85
86
87
Malmberg, B., and Skarendahl, A. (1978), “ Method of studying cracking of fiberconcrete under restrained shrinkage,” Testing and Test Methods ofFiber CementComposites. RILEM, Paris, pp. 173-179.
Mangat, P. S., and Azari, M. M. (1988), “ Shrinkage of steel fiber reinforcedcement composites,” Materials and Structures, RILEM, Vol. 21, pp. 163-171.
Markku, L., and Erika, H. (1997), “ Autogenous volume changes at early ages,”Proceedings of the International Research Seminar: “ Self-desiccation and ItsImportance in Concrete Technology,” Ltmd, Sweden, pp. 88-98.
The MathWorks, INC (l997),” MATLAB,” Natick, Massachusetts.
Mejlhed Jensen, O., and Freieslebeb Hansen, P. (1996), “ Autogenous deformationand change ofthe relative humidity in silica fume-modified cement paste,” ACIMaterials Journal, Vol. 93, No. 6, pp. 539-543.
Miao, B., Chaallal, O., Perraton, D., and Aitcin, P. C. (1993), “ On-site early agemonitoring ofhigh performance concrete columns,” AC1 Materials Journal, No. 90pp. 415-420.
Mindess, S., and Young, J. F. (1981) , “ Concrete,” Prentice-Hall Inc., New Jersey,USA.
Mitchell, D., Khan, A. A., and Cook, W. D. (1998), “ Early age properties forthermal and stress analyses during hydration,” In Material Science of Concrete V,Ed. by Jan Skalny and Sidney Mindess, Published by The American CeramicSociety, pp. 265-305.
Morimoto, H., and Koyanagi, W. (1995), “ Estimation of stress relaxation inconcrete at early ages,” In Thermal Cracking In Concrete at Early Age, Proceedingsofthe Intemational RILEM Symposium, Ed. by R Springenschmid, Munich, 1994pp. 95-102.
Nagataki, S. (1970), “ Shrinkage and shrinkage restraints in concrete pavements,”Proceedings, ASCE, V. 96, ST7, pp. 1333-1358.
Neville, A. M. (1996), “ Properties of concrete,” 4'“ edition, John Wiley & Sons,Inc. New York, USA.
Neville, A. M., Dilger, W. H., and Brooks, J. J. (1983), “Creep ofplain andstructural concrete,” Construction Press, London and New-York.
Oluokun, F. A., Burdette, E. G., Deatherage, J. H. (1991),” Elastic modulus,Poisson’s ratio, and compressive strength relationships at early ages,” ACIMaterials Jomnal, Vol. 88, No. 1, pp. 487-493.
216
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
89
90
91
92
93
94
95
96
97
98
Ong, K. C. G., and Paramsivam, P. (1989), “Cracking of steel fiber reinforcedmortar due to restrained shrinkage,” In Fiber Reinforced Cements and Concretes -Recent Developments, edited by R. N. Swamy and B. Barr (Elsevier, London), pp.179-187.
Paillere, A. M., Buil, M., and Serrano, J. J. (1989), “Efiect offiber addition on theautogenous shrinkage of silica fume concrete,” ACI Mater. J., Vol. 86, No. 2, pp.139-144.
Paulini, P., and Gratl, N. (1995), “ Stiffiiess formation ofearly age concrete,” InThermal Cracking In Concrete at Early Age, Proceedings ofthe IntemationalRILEM Symposium, Ed by R Springenschmid, Munich, 1994 pp. 63-70.
Pickett, G. (1956), “ Effect ofaggregate on shrinkage ofconcrete and hypothesisconcerning shrinkage,” J. American Concrete Inst. Vol. 52, pp. 581-590.
Picket, C. (1942), “ The efi'ect of change in moisture-content on the creep ofconcrete imder a sustained load,” ACI J., Vol. 38, pp. 333-356.
Pijaudier-Cabot, G. (1995), “ Damage in discrete and continuum models,” InFractures Mechanics of Concrete Structures FRAMCOS-2, edited by Wittmann,F. H., pp. 981-989.
Planas, J., and Elices, M. (1993), “Drying shrinkage effect on the modulus ofrupture,” Creep and Shrinkage of Concrete, Proc. ofthe Fifth Intemational RILEMSymposium, Z. P. Bazant and 1., Carol, ed., E & FN SPON, New York, 1993, pp.357-368.
Planas, J., and Elices, M. (1992), “ Dry shrinkage eigenstresses and structural sizeeffect,” Fracture Mechanics of Concrete Structures, Z. P., Bazant, ed., ElsevierApplied Science, New York, 1992, pp. 939-950.
Powers, T. C. (1966), “ Some observations on the interpretation of creep data,”RILEM Bulletine, Paris, No. 33, pp. 381-391.
Powers, T. C., and Brownyard, T. L. (1947), “ Studies ofthe physical properties ofhardened portland cement paste-part 4: The thermodynamics ofadsorption ofwateron hardened paste,” Jomnal ofAm. Concr. Inst., Vol. 18, No. 5, Jan., 1947, pp.549-595.
Powers T. C and Brownyard T. L. (1948), “ Studies ofthe physical properties ofhardened Portland cement paste,” Research Department Bulletine #22, Chicago:Portland Cement Association.
217
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99.
100
101
102
103
104
105
106
107
108
109
Reid, S. G. (1993), “ Deformation of concrete due to drying creep, “Creep andShrinkage ofConcrete, Proc. ofthe Fifih Intemational RILEM Symposium, Z. P.Bazant and I., Carol, ed., E & FN SPON, New York, 1993, pp. 39-44.
RILEM report 15 (1998): Prevention of thermal cracking in concrete at early ages,State-of-the-art report prepared by RILEM technical Committee 119,” AvoidanceofThermal Cracking in Concrete at Early Ages,” Ed. by R. Springenschmid, 1998.
RILEM, (1994) “ Thermal cracking in concrete at early age,” Proceedings of theIntemational RII.EM Symposium, Ed. by R. Springenschmid, Munich, 1994.
Rolling, R. S. (1993), “ Curling failures of steel fiber reinforced concrete slabs,”Joumal of Performance of Constructed Facilities, ASCE, Vol. 7, No. 1, pp. 3-19.
Rolling, R. S. (1986), “ Field performance of fiber reinforced concrete airfieldpavements,” DOT/FAA/PM-86/26, Federal Aviation Administration,Washington, D.C., 1986.
Rostasy, F. S., Gutsch, A., and Laube, M., (1993), “ Creep and relaxation ofconcrete at early ages-experiments and mathematical modeling,” Creep andShrinkage ofConcrete, Proc. of the Fifth Intemational RILEM Symposium. Z. P.Bazant and 1., Carol, ed., E & FN SPON, New York, 1993, pp. 453-458.
Ruetz, W. (1968), " A hypothesis for the creep of hardened cement paste and theinfluence of simultaneous shrinkage,” Proc. Int. Conf. on the Structures ofConcrete, Cement and Concrete Association: London, pp.365-87.
Sarigaphuti, M., Shah, S. P., and Vinson, K. D. (1993), “ shrinkage cracking anddurability characteristics of cellulose fiber reinforced concrete,” AC1 MaterialsJoumal, Vol. 90, No. 4, pp. 309-318.
De Schutter, G., and Taerwe, L. (1997), “ Towards a more fundamental non-linearbasic creep model for early age concrete,”, Magazine ofConcrete Research, Vol.49, No. 180, PP. 195-200.
Springenschmid, R., Breitenbucher, R, and Mangold, M. (1995), “ Development ofthermal cracking frame and the temperature-stress testing machine,” In ThermalCracking In Concrete at Early Age, Proceedings of the Intemational RILEMSymposium, Ed. by R. Springenschmid, Munich, 1994 pp. 137-144.
Swamy, R. N., and Stavrides, H. (1979), “Influence of fiber reinforcement onrestrained shrinkage and cracking,” ACI Joumal, Vol. 76, pp. 443-459.
218
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
111
112
113
114
115
116
117
118
119
120
121
Tanabe, T., and Ishikawa, Y. (1993), “ Time-dependent behavior of concrete atearly ages and its modeling,” Creep and Shrinkage of Concrete, Proc. of the FifthIntemational RILEM Symposium, Z. P. Bazant and 1., Carol, ed., E & FN SPON,New York. 1993, pp. 435-452.
Tazawa, E., and Miyazawa, S. (1997), “Influence ofConstituents and Compositionon autogenous shrinkage ofcementitious materials,” Magafine of ConcreteResearch, Vol.49, No. 178, pp. 15-22.
Tazawa, E., and Kasai, T. (1995), “ Chemical shrinkage and autogenous shrinkageofhydrating cement paste,” Cement and Concrete Research, Vol. 25, No. 2, pp.288-292.
Tazawa, E., and Miyazawa, S. (1995), “Experimental study on mechanisms ofautogenous shrinkage of concrete,” Cement and Concrete Research, Vol. 25, No. 8.pp. 1633-1638.
Tazawa, E., and Miyazawa, S. (1993), “ Autogenous shrinkage of concrete and itsimportance in concrete technology,” Creep and Shrinkage of Concrete. Proceedingsof the Fifth International RH.EM Symposium, Barcelona, Spain, pp. 159-168.
Umehara, H., and Uehara, T. (1995),” Effect of creep in concrete at early ages onthermal stress.” In Thermal Cracking In Concrete at Early Age, Proceedings of theIntemational RILEM Symposium, Ed. by R. Springenschmid, Munich, 1994 pp.79-86.
Ward, M. A., and Cook, D. J. (1969), “ The mechanism of tensile creep inconcrete,” Magazine of Concrete Research, Vol. 21, No. 68, pp. 151-158.
Westergaard, H. M. (1926), “ analysis of stresses in concrete pavements due tovariation of temperature,” Proceedings, Highway Research Board.
Westrnan, G. (1995), “Basic creep and relaxation of young concrete," In ThermalCracking In Concrete at Early Age, Proceedings of the International RILEMSymposium, Ed. by R. Springenschmid, Munich, 1994 pp. 87-94.
Wittmann, F. H. (1993), “ On the influence of stress on shrinkage of concrete.”Creep and Shrinkage of Concrete, Z. Bazant and I. Carol, eds., RII.EM Proc. No.22, E&FN SPON Publ., London, England, pp. 151-157.
Wittmann F. and Lukas J. (1974), “Experimental study ofthermal expansion ofhardened cement paste,” Materials and Structures, No. 40, pp.247-252.
Wittmann, F. H., and Roelfstra, P. E. (1980), “ Total deformation of loaded dryingconcrete,” Cement and Concrete Res., Vol. 10, pp. 601-610.
219
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
123
124
125
Yang, W., Wang, K, and Shah, S. P. (1996), “Prediction of concrete crackingimder coupled shrinkage and creep conditions,” Proc. ofthe 4“ MaterialsConference, “Materials for the new millennium”, ASCE, Vol. 1, Nov. 10-14,Washington, D. C, pp. 564-573.
Yoder, E. J. and Witczak, M. W. (1975), “ Principles ofpavement design,” 2“edition, John Wiley 7& Sons, New York.
Young, J. F. (1988), “ Physical mechanisms and their mathematical descriptions,”Ch. 1 in Mathematical Modeling of Creep and Shrinkage of Concrete, Edited byBazant, Z. P, Wiley & Sons, New York.
Ziegeldorf, S., Muller, H. S., Plohn, J., and Hilsdorf, H. K. (1982), “ Autogenousshrinkage and crack formation in young concrete,” Intemational Conference onConcrete ofEarly Ages, RILEM, Vol. 1, pp.83.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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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