Control of Cracking in Reinforced Concrete Structures

245 Pages·2016·14.169 MB·English

by  Barre, Francis

Control of Cracking in Reinforced Concrete Structures
Series Editor
Jacky Mazars
Control of Cracking in
Reinforced Concrete
Structures

Research Project CEOS.fr

Francis Barre, Philippe Bisch,
Danièle Chauvel, Jacques Cortade,
Jean-François Coste, Jean-Philippe Dubois,
Silvano Erlicher, Etienne Gallitre,
Pierre Labbé, Jacky Mazars,
Claude Rospars, Alain Sellier,
Jean-Michel Torrenti, François Toutlemonde
First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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© ISTE Ltd 2016
The rights of Research Project CEOS.Fr to be identified as the authors of this work have been asserted by
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Library of Congress Control Number: 2016941705

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A CIP record for this book is available from the British Library
ISBN 978-1-78630-052-2
Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Chapter 1. CEOS.fr Project Presentation . . . . . . . . . . . . . . . . . . . 1
1.1. CEOS.fr work program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1. Tests on prismatic full-scale blocks . . . . . . . . . . . . . . . . . . . 2
1.2.2. Tests on 1/3-scale beams . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3. Tests on 1/3-scale shear walls . . . . . . . . . . . . . . . . . . . . . . 13
1.2.4. Tests on ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3. Modeling and simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.1. MEFISTO research program . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.2. Benchmarks and workshops . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.3. Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.4. Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5. Database and specimen storage . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.1. Database CHEOPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.2. Specimen storage (Renardières site) . . . . . . . . . . . . . . . . . . . 26
Chapter 2. Hydration Effects of Concrete at
an Early Age and the Scale Effect . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1. Hydration effects of concrete at an early age . . . . . . . . . . . . . . . . 27
2.1.1. Global heating and cooling of a concrete element . . . . . . . . . . . 28
vi Control of Cracking in Reinforced Concrete Structures
2.1.2. Differential temperature between
concrete core and surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2. Scale effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1. Scale effect principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2. Calculating scale effect according to Weibull theory . . . . . . . . . 33
2.2.3. Worked examples of calculation with the
scale effect according to the Weibull model . . . . . . . . . . . . . . . . . . 37
2.2.4. Application of Weibull integral in
bending and in tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 3. Cracking of Ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1. Design values and limit values . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2. Adjusting the design value for verification purposes . . . . . . . . . . . 47
3.3. Crack spacing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.1. Linear equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.2. Relationship between the maximum spacing
S and the mean spacing S . . . . . . . . . . . . . . . . . . . . . . . . . 49
r,max r,m
3.3.3. Equation based on the MC2010 bond-slip
relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4. Equation for the mean differential strain . . . . . . . . . . . . . . . . . . . 50
3.5. Model accuracy when calculating the strain
and crack width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6. Example of the application of the cracking equations
to a concrete tie in tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 4. Cracking of Beams Under
Mechanical Flexural Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1. Crack spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2. Crack width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1. Tensile stress–strain curve . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.2. Calculating the crack width from the relative strain . . . . . . . . . 61
4.2.3. Calculating the crack width by interpolation
between uncracked and fully cracked conditions (the ζ method) . . . . . . 62
4.3. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.1. Example 1: calculation of crack spacing and
crack width in a thick concrete slab under heavy loads . . . . . . . . . . . 69
4.3.2. Example 2: calculation of crack spacing and
crack width in a double thick beam . . . . . . . . . . . . . . . . . . . . . . . 71
Contents vii
Chapter 5. Cracking in Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1. Current status of the reference texts . . . . . . . . . . . . . . . . . . . . . 75
5.2. Validity of the physical model and calculating
of the crack angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3. Calculation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4. Crack spacing and slippage length . . . . . . . . . . . . . . . . . . . . . . 79
5.5. Mean differential strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.6. Calculating the crack width from
reinforcing bar strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.7. Calculating the crack width in accordance
with the strut and tie model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.8. Recommendations for evaluating the cracking
in walls subject to earthquake situations . . . . . . . . . . . . . . . . . . . . . 91
5.9. Examples of application of cracking equations
in a wall subjected to a shear stress in the plane of the wall . . . . . . . . . . 92
5.9.1. Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.9.2. Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.9.3. Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Chapter 6. Minimum Reinforcement of
Thick Concrete Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1. Reinforcement of reinforced concrete ties . . . . . . . . . . . . . . . . . . 106
6.1.1. Detailed calculation from a 3D approach . . . . . . . . . . . . . . . . 106
6.1.2. Simplified methodology for calculating
concrete reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.2. Reinforcement of prestressed concrete ties . . . . . . . . . . . . . . . . . 111
6.2.1. Crack formation in an element in tension . . . . . . . . . . . . . . . . 112
6.2.2. Stabilized cracking stage in an element in tension . . . . . . . . . . 113
6.2.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3. Reinforcement of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.3.1. Beams under monotonic mechanical loading . . . . . . . . . . . . . 115
6.3.2. Beams under imposed deformation and monotonic
mechanical loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.4. Reinforcement of walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4.1. Walls without specific requirements for cracking . . . . . . . . . . . 116
6.4.2. Walls with specific requirements for cracking . . . . . . . . . . . . . 117
Chapter 7. Shrinkage, Creep and Other Concrete Properties . . . . . 119
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2. Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
viii Control of Cracking in Reinforced Concrete Structures
7.2.2. Range of applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.3. Initial strain at loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3. Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.1. Autogenous shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.3.2. Drying shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.4. Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4.1. Assumptions and related basic equation . . . . . . . . . . . . . . . . 129
7.4.2. Basic creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4.3. Drying creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.5. Experimental identification procedures . . . . . . . . . . . . . . . . . . . 133
7.5.1. Initial strain at loading time . . . . . . . . . . . . . . . . . . . . . . . . 134
7.5.2. Shrinkage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.5.3. Basic creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.5.4. Drying creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.5.5. Estimation of long-term delayed strain . . . . . . . . . . . . . . . . . 134
7.6. Temperature effects on concrete properties . . . . . . . . . . . . . . . . . 135
7.6.1. Temperature effects on instantaneous
concrete characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.6.2. Maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.6.3. Thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.6.4. Compressive strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.6.5. Tensile strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.6.6. Fracture energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.6.7. Elasticity modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.6.8. Temperature effects on the delayed deformations . . . . . . . . . . . 139
7.6.9. Autogenous shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.6.10. Drying shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Chapter 8. Cracking of Beams and Walls Subject
to Restrained Deformations at SLS . . . . . . . . . . . . . . . . . . . . . . . 143
8.1. Evaluation of shrinkage with bulk heating and
cooling of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.2. Estimating and limiting crack widths . . . . . . . . . . . . . . . . . . . . . 145
8.3. Estimating restraints at SLS . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.3.1. Approximate calculation of external restraint . . . . . . . . . . . . . 146
8.3.2. Detailed calculation of a restraint on a wall . . . . . . . . . . . . . . 147
8.4. Estimation of stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.4.1. General comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.4.2. Simplified method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.4.3. Principles of the detailed method . . . . . . . . . . . . . . . . . . . . 154
8.4.4. Worked example of a massive
element thermal gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Contents ix
Chapter 9. Effects of Various Phenomena in Combination . . . . . . 163
9.1. Estimating crack width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.2. Combining effects due to imposed deformations
and deformations resulting from in-service loadings . . . . . . . . . . . . . . 164
9.2.1. Structures with water or air tightness requirements . . . . . . . . . . 165
9.2.2. Structures with durability requirements . . . . . . . . . . . . . . . . . 167
9.2.3. Minimum reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Chapter 10. Numerical Modeling:
a Methodological Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
10.1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
10.2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
10.3. Thermal and hydration effects . . . . . . . . . . . . . . . . . . . . . . . . 173
10.4. Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.5. Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.5.1. Hydration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.5.2. Permanent basic creep . . . . . . . . . . . . . . . . . . . . . . . . . . 178
10.5.3. Reversible basic creep . . . . . . . . . . . . . . . . . . . . . . . . . . 180
10.5.4. Influence of temperature on the creep velocity . . . . . . . . . . . . 181
10.5.5. Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
10.5.6. Drying creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
10.5.7. Steel-concrete composite modeling . . . . . . . . . . . . . . . . . . 183
10.5.8. Statistical scale effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10.6. Example simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
10.6.1. Thermal and hydration simulation . . . . . . . . . . . . . . . . . . . 185
Chapter 11. Recommendations for the use of Measurements
on Mock-up Test Facilities and Structures . . . . . . . . . . . . . . . . . . 189
11.1. General methodology of the measurements . . . . . . . . . . . . . . . . 190
11.1.1. Preliminary general approach . . . . . . . . . . . . . . . . . . . . . . 192
11.1.2. Selection and choice of measuring devices . . . . . . . . . . . . . . 193
11.1.3. Method of measurement selection . . . . . . . . . . . . . . . . . . . 194
11.1.4. Measurement data-mining and analysis . . . . . . . . . . . . . . . . 194
11.2. Mock-up measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
11.2.1. Measurement of parameters . . . . . . . . . . . . . . . . . . . . . . . 197
11.2.2. Data acquisition and storage . . . . . . . . . . . . . . . . . . . . . . . 207
11.3. Measurement of structures . . . . . . . . . . . . . . . . . . . . . . . . . . 208
11.3.1. Preliminary measurements . . . . . . . . . . . . . . . . . . . . . . . . 210
11.3.2. Parameters to be measured. . . . . . . . . . . . . . . . . . . . . . . . 210
11.3.3. Equipment of the measurements . . . . . . . . . . . . . . . . . . . . 211
11.3.4. Formwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
x Control of Cracking in Reinforced Concrete Structures
11.4. Example of measurement instrumentation
on massive structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.5. Example of mock-up test instrumentation . . . . . . . . . . . . . . . . . 213
11.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Foreword
The control of cracking in reinforced and prestressed concrete is an
essential factor in ensuring the reliability and durability of structures,
together with many other important properties including water-tightness and
air-tightness.
Eurocode 2 (EC2) and, more recently, fib Model Code 2010 (MC2010)
address the durability of structures and contain guidelines and rules for
estimating and limiting cracking as a function of the characteristics of
concrete and its reinforcement, and the exposure classifications of the works.
However, these rules are normally only intended to be applied to the most
common design situations. As a result, they do not take sufficient account of
the behaviour of works containing massive reinforced and prestressed
concrete structures, nor works which are subject to special service
requirements in terms of water-tightness and air-tightness or service life and
so forth. These rules are also inadequate for works requiring enhanced load
protection against natural hazards or external attack. In these works, thermo-
hydro-mechanical (THM) effects, scale effects and structural effects can all
result in specific cracking behavior. In the case of thick rafts and walls,
shrinkage and creep shall be taken into account, both in early-age concrete
and in the long-term.
The purpose of this book is to provide further guidelines which can
extend the existing standards and codes to cover these types of special
works, especially those which are massive in nature, taking account of their