200290

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Control of Cracking in Reinforced Concrete Structures

Series Editor Jacky Mazars

Control of Cracking in Reinforced Concrete

Structures

Research Project CEOSfr

Francis Barre Philippe Bisch Daniegravele Chauvel Jacques Cortade

Jean-Franccedilois Coste Jean-Philippe Dubois Silvano Erlicher Etienne Gallitre

Pierre Labbeacute Jacky Mazars Claude Rospars Alain Sellier

Jean-Michel Torrenti Franccedilois Toutlemonde

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley amp Sons Inc

Apart from any fair dealing for the purposes of research or private study or criticism or review as permitted under the Copyright Designs and Patents Act 1988 this publication may only be reproduced stored or transmitted in any form or by any means with the prior permission in writing of the publishers or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address

ISTE Ltd John Wiley amp Sons Inc 27-37 St Georgersquos Road 111 River Street London SW19 4EU Hoboken NJ 07030 UK USA

wwwistecouk wwwwileycom

copy ISTE Ltd 2016 The rights of Research Project CEOSFr to be identified as the authors of this work have been asserted by them in accordance with the Copyright Designs and Patents Act 1988

Library of Congress Control Number 2016941705 British Library Cataloguing-in-Publication Data 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 CEOSfr Project Presentation 1

11 CEOSfr work program 1 12 Testing 2

121 Tests on prismatic full-scale blocks 2 122 Tests on 13-scale beams 10 123 Tests on 13-scale shear walls 13 124 Tests on ties 17

13 Modeling and simulation 21 131 MEFISTO research program 21 132 Benchmarks and workshops 23 133 Numerical experiments 24

14 Engineering 25 15 Database and specimen storage 26

151 Database CHEOPS 26 152 Specimen storage (Renardiegraveres site) 26

Chapter 2 Hydration Effects of Concrete at an Early Age and the Scale Effect 27

21 Hydration effects of concrete at an early age 27 211 Global heating and cooling of a concrete element 28

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Control of Cracking in Reinforced Concrete Structures

Series Editor Jacky Mazars

Control of Cracking in Reinforced Concrete

Structures

Research Project CEOSfr

Francis Barre Philippe Bisch Daniegravele Chauvel Jacques Cortade

Jean-Franccedilois Coste Jean-Philippe Dubois Silvano Erlicher Etienne Gallitre

Pierre Labbeacute Jacky Mazars Claude Rospars Alain Sellier

Jean-Michel Torrenti Franccedilois Toutlemonde

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley amp Sons Inc

Apart from any fair dealing for the purposes of research or private study or criticism or review as permitted under the Copyright Designs and Patents Act 1988 this publication may only be reproduced stored or transmitted in any form or by any means with the prior permission in writing of the publishers or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address

ISTE Ltd John Wiley amp Sons Inc 27-37 St Georgersquos Road 111 River Street London SW19 4EU Hoboken NJ 07030 UK USA

wwwistecouk wwwwileycom

copy ISTE Ltd 2016 The rights of Research Project CEOSFr to be identified as the authors of this work have been asserted by them in accordance with the Copyright Designs and Patents Act 1988

Library of Congress Control Number 2016941705 British Library Cataloguing-in-Publication Data 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 CEOSfr Project Presentation 1

11 CEOSfr work program 1 12 Testing 2

121 Tests on prismatic full-scale blocks 2 122 Tests on 13-scale beams 10 123 Tests on 13-scale shear walls 13 124 Tests on ties 17

13 Modeling and simulation 21 131 MEFISTO research program 21 132 Benchmarks and workshops 23 133 Numerical experiments 24

14 Engineering 25 15 Database and specimen storage 26

151 Database CHEOPS 26 152 Specimen storage (Renardiegraveres site) 26

Chapter 2 Hydration Effects of Concrete at an Early Age and the Scale Effect 27

21 Hydration effects of concrete at an early age 27 211 Global heating and cooling of a concrete element 28

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Series Editor Jacky Mazars

Control of Cracking in Reinforced Concrete

Structures

Research Project CEOSfr

Francis Barre Philippe Bisch Daniegravele Chauvel Jacques Cortade

Jean-Franccedilois Coste Jean-Philippe Dubois Silvano Erlicher Etienne Gallitre

Pierre Labbeacute Jacky Mazars Claude Rospars Alain Sellier

Jean-Michel Torrenti Franccedilois Toutlemonde

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley amp Sons Inc

Apart from any fair dealing for the purposes of research or private study or criticism or review as permitted under the Copyright Designs and Patents Act 1988 this publication may only be reproduced stored or transmitted in any form or by any means with the prior permission in writing of the publishers or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address

ISTE Ltd John Wiley amp Sons Inc 27-37 St Georgersquos Road 111 River Street London SW19 4EU Hoboken NJ 07030 UK USA

wwwistecouk wwwwileycom

copy ISTE Ltd 2016 The rights of Research Project CEOSFr to be identified as the authors of this work have been asserted by them in accordance with the Copyright Designs and Patents Act 1988

Library of Congress Control Number 2016941705 British Library Cataloguing-in-Publication Data 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 CEOSfr Project Presentation 1

11 CEOSfr work program 1 12 Testing 2

121 Tests on prismatic full-scale blocks 2 122 Tests on 13-scale beams 10 123 Tests on 13-scale shear walls 13 124 Tests on ties 17

13 Modeling and simulation 21 131 MEFISTO research program 21 132 Benchmarks and workshops 23 133 Numerical experiments 24

14 Engineering 25 15 Database and specimen storage 26

151 Database CHEOPS 26 152 Specimen storage (Renardiegraveres site) 26

Chapter 2 Hydration Effects of Concrete at an Early Age and the Scale Effect 27

21 Hydration effects of concrete at an early age 27 211 Global heating and cooling of a concrete element 28

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley amp Sons Inc

Apart from any fair dealing for the purposes of research or private study or criticism or review as permitted under the Copyright Designs and Patents Act 1988 this publication may only be reproduced stored or transmitted in any form or by any means with the prior permission in writing of the publishers or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address

ISTE Ltd John Wiley amp Sons Inc 27-37 St Georgersquos Road 111 River Street London SW19 4EU Hoboken NJ 07030 UK USA

wwwistecouk wwwwileycom

copy ISTE Ltd 2016 The rights of Research Project CEOSFr to be identified as the authors of this work have been asserted by them in accordance with the Copyright Designs and Patents Act 1988

Library of Congress Control Number 2016941705 British Library Cataloguing-in-Publication Data 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 CEOSfr Project Presentation 1

11 CEOSfr work program 1 12 Testing 2

121 Tests on prismatic full-scale blocks 2 122 Tests on 13-scale beams 10 123 Tests on 13-scale shear walls 13 124 Tests on ties 17

13 Modeling and simulation 21 131 MEFISTO research program 21 132 Benchmarks and workshops 23 133 Numerical experiments 24

14 Engineering 25 15 Database and specimen storage 26

151 Database CHEOPS 26 152 Specimen storage (Renardiegraveres site) 26

Chapter 2 Hydration Effects of Concrete at an Early Age and the Scale Effect 27

21 Hydration effects of concrete at an early age 27 211 Global heating and cooling of a concrete element 28

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Contents

Foreword xi

Notations xv

Introduction xxi

Chapter 1 CEOSfr Project Presentation 1

11 CEOSfr work program 1 12 Testing 2

121 Tests on prismatic full-scale blocks 2 122 Tests on 13-scale beams 10 123 Tests on 13-scale shear walls 13 124 Tests on ties 17

13 Modeling and simulation 21 131 MEFISTO research program 21 132 Benchmarks and workshops 23 133 Numerical experiments 24

14 Engineering 25 15 Database and specimen storage 26

151 Database CHEOPS 26 152 Specimen storage (Renardiegraveres site) 26

Chapter 2 Hydration Effects of Concrete at an Early Age and the Scale Effect 27

21 Hydration effects of concrete at an early age 27 211 Global heating and cooling of a concrete element 28

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

vi Control of Cracking in Reinforced Concrete Structures

212 Differential temperature between concrete core and surface 29

22 Scale effect 32 221 Scale effect principle 32 222 Calculating scale effect according to Weibull theory 33 223 Worked examples of calculation with the scale effect according to the Weibull model 37 224 Application of Weibull integral in bending and in tension 44

Chapter 3 Cracking of Ties 47

31 Design values and limit values 47 32 Adjusting the design value for verification purposes 47 33 Crack spacing equation 48

331 Linear equation 48 332 Relationship between the maximum spacing Srmax and the mean spacing Srm 49 333 Equation based on the MC2010 bond-slip relationship 49

34 Equation for the mean differential strain 50 35 Model accuracy when calculating the strain and crack width 51 36 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

41 Crack spacing 59 42 Crack width 60

421 Tensile stressndashstrain curve 60 422 Calculating the crack width from the relative strain 61 423 Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 62

43 Examples 69 431 Example 1 calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 432 Example 2 calculation of crack spacing and crack width in a double thick beam 71

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Contents vii

Chapter 5 Cracking in Walls 75

51 Current status of the reference texts 75 52 Validity of the physical model and calculating of the crack angle 77 53 Calculation model 78 54 Crack spacing and slippage length 79 55 Mean differential strain 82 56 Calculating the crack width from reinforcing bar strains 87 57 Calculating the crack width in accordance with the strut and tie model 89 58 Recommendations for evaluating the cracking in walls subject to earthquake situations 91 59 Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92

591 Example 1 94 592 Example 2 102 593 Example 3 103

Chapter 6 Minimum Reinforcement of Thick Concrete Elements 105

61 Reinforcement of reinforced concrete ties 106 611 Detailed calculation from a 3D approach 106 612 Simplified methodology for calculating concrete reinforcement 106

62 Reinforcement of prestressed concrete ties 111 621 Crack formation in an element in tension 112 622 Stabilized cracking stage in an element in tension 113 623 Conclusion 114

63 Reinforcement of beams 115 631 Beams under monotonic mechanical loading 115 632 Beams under imposed deformation and monotonic mechanical loading 115

64 Reinforcement of walls 116 641 Walls without specific requirements for cracking 116 642 Walls with specific requirements for cracking 117

Chapter 7 Shrinkage Creep and Other Concrete Properties 119

71 Introduction 119 72 Strain 121

721 Definition 121

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

viii Control of Cracking in Reinforced Concrete Structures

722 Range of applicability 121 723 Initial strain at loading 122

73 Shrinkage 124 731 Autogenous shrinkage 125 732 Drying shrinkage 125

74 Creep 129 741 Assumptions and related basic equation 129 742 Basic creep 131 743 Drying creep 131

75 Experimental identification procedures 133 751 Initial strain at loading time 134 752 Shrinkage 134 753 Basic creep 134 754 Drying creep 134 755 Estimation of long-term delayed strain 134

76 Temperature effects on concrete properties 135 761 Temperature effects on instantaneous concrete characteristics 136 762 Maturity 136 763 Thermal expansion 136 764 Compressive strength 137 765 Tensile strength 137 766 Fracture energy 138 767 Elasticity modulus 138 768 Temperature effects on the delayed deformations 139 769 Autogenous shrinkage 141 7610 Drying shrinkage 141

Chapter 8 Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143

81 Evaluation of shrinkage with bulk heating and cooling of concrete 144 82 Estimating and limiting crack widths 145 83 Estimating restraints at SLS 146

831 Approximate calculation of external restraint 146 832 Detailed calculation of a restraint on a wall 147

84 Estimation of stiffness 152 841 General comments 152 842 Simplified method 153 843 Principles of the detailed method 154 844 Worked example of a massive element thermal gradient 158

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Contents ix

Chapter 9 Effects of Various Phenomena in Combination 163

91 Estimating crack width 163 92 Combining effects due to imposed deformations and deformations resulting from in-service loadings 164

921 Structures with water or air tightness requirements 165 922 Structures with durability requirements 167 923 Minimum reinforcement 169

Chapter 10 Numerical Modeling a Methodological Approach 171

101 Scope 171 102 Methodology 172 103 Thermal and hydration effects 173 104 Drying 175 105 Mechanics 177

1051 Hydration 177 1052 Permanent basic creep 178 1053 Reversible basic creep 180 1054 Influence of temperature on the creep velocity 181 1055 Shrinkage 182 1056 Drying creep 182 1057 Steel-concrete composite modeling 183 1058 Statistical scale effect 184

106 Example simulation 185 1061 Thermal and hydration simulation 185

Chapter 11 Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189

111 General methodology of the measurements 190 1111 Preliminary general approach 192 1112 Selection and choice of measuring devices 193 1113 Method of measurement selection 194 1114 Measurement data-mining and analysis 194

112 Mock-up measurements 196 1121 Measurement of parameters 197 1122 Data acquisition and storage 207

113 Measurement of structures 208 1131 Preliminary measurements 210 1132 Parameters to be measured 210 1133 Equipment of the measurements 211 1134 Formwork 212

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

x Control of Cracking in Reinforced Concrete Structures

114 Example of measurement instrumentation on massive structures 212 115 Example of mock-up test instrumentation 213 116 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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

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

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

xii Control of Cracking in Reinforced Concrete Structures

specific behavior in terms of cracking and shrinkage together with other important properties such as water- and air-tightness

The proposed rules and guidelines given in this book are based on the results of the French CEOSfr project (Comportement et Evaluation des Ouvrages Speacuteciaux ndash fissuration retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage The CEOSfr project took place between 2008 and 2015 involving 41 French Ministegravere de lrsquoEnvironnement de lrsquoEacutenergie et de la Mer (MEEM) clients and project managers The project was funded jointly by the partners of the MEEM

The CEOSfr project consisted partly of tests some using full-scale solid concrete blocks and others performed on a smaller scale using laboratory models together with the development of simulation models in collaboration with the MEFISTO project1 under the auspices of the French Agence Nationale pour la Recherche (ANR) The experimental results were presented to the international scientific community and a panel of experts in these complex and rapidly changing fields assessed the simulation models The CEOSfr project also took account of experimental results and actual experience feedback of concrete works from the various partners

These guidelines are addressed primarily to designers and civil engineers responsible for construction projects Engineering rules and recommendations are illustrated at the end of each chapter using examples of design calculations commentary on the use of models or applicable measurement methods Further supporting details of the basis for these guidelines may be found in the CEOSfr test report titled ldquoResults obtained in the understanding of cracking phenomenardquo [PN 13b] which describes the results of the associated tests the interpretation of these results and the justifications for each proposed modification to EC2 and MC2010

The guidelines given herein reflect the latest state of the art understanding at the time of going to press They are therefore subject to expansion and modification as new experimental data becomes available further experience is gained and new technologies are used in future projects

1 Maicirctrise durablE de la Fissuration des InfraSTructures en beacutetOn

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Foreword xiii

We would like to express our sincere thanks to all those who have contributed to the publication of this document its English version and to the Institut pour la recherche appliqueacutee et lrsquoexpeacuterimentation en geacutenie civil (IREX) for their administrative and logistical support

Pierre LABBEacute EDF December 2015

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Notations

Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04 NF 06a NF 06b] and fib model code 2010 (MC2010) [CEB 12] However some symbols used less in these codes are also quoted The units refer to the International System (IS)

Chapter Symbol Description Unit

Chapter 2

Tmax ndash

Tini

Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature

degC

Tadiab Adiabatic temperature degC

λ Thermal conductivity Wndash1mndash1Kndash1

Qinfin Hydration heat per weight unit of cement kJkgndash1

ρC Heat capacity per weight unit of concrete kJkgndash1degCndash1

a Diffusivity m2sndash1

βT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions ∆ = ∙ ∆

(ndash)

σcm Mean value of concrete compressive strength MPa

Mean value of concrete axial tensile strength taking account of scale effect MPa

Mean value of concrete axial strength taking account of scale effect calculated according to Weibull approach

MPa

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

xvi Control of Cracking in Reinforced Concrete Structures

Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3

Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume

m3

k Weibull exponent ndash

5 fractile of the tensile strength including scale effect according to Weibull approach MPa

95 fractile of the tensile strength with scale effect according to Weibull approach MPa

r Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (ndash)

hceff Effective height of the considered cross section m

Chapter 3

γ Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section =

(ndash)

α Exponent of the bondndashslip relationship given by Equation 61ndash1 of MC2010 (ndash)

αe Modular ratio EsEcm (seeEC2 and MC2010) (ndash)

Chapter 4

ζ Parameter reflecting the crack width depending on σsrσs (seeEC2 and MC2010) (ndash)

εI The relative strain in the section considered unndashcracked (ndash)

εII The relative strain in the cracked section (ndash)

Chapter 5

Stress tensor (Nxx Nxy= Nyx Nyy) derived from structural design MPa

Nr Membrane force normal to the crack kNm

Tr Membrane force tangential to the crack kNm

N Membrane force normal to a plan which is perpendicular to the crack kNm

Fsx Effort component on reinforcing bars along Ox kN

Fsy Effort component on reinforcing bars along Oy kN

heff Effective depth evaluated for the total shear wall thickness depending on concrete cover to reinforcement

m

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Notations xvii

θdeg Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010)

(deg)

σsx Mean steel bar stress along the x-direction MPa

σsy Mean steel bar stress along the y-direction MPa

εsx Mean steel bar strain along the x-direction (ndash)

εsy Mean steel bar strain along the y-direction (ndash)

Percentage of steel reinforcement in the x-direction

Percentage of steel reinforcement in the y-direction

α Local distortion rad

ρ AsAc percentage of steel reinforcement As based on the area Ac of concrete in tension

Chapter 6

Asmin Minimum cross sectional area of reinforcement m2

ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle

m

εc (t) Total strain of a concrete element at time t (ndash)

Fctscale Concrete tensile stress at a given point along the reinforcing bar MPa

Chapter 8

Tmax ndashTini

See Chapter 2 degC

Tmin Minimum temperature up to time t degC

α Free coefficient of thermal expansion of concrete Kndash1 ( ) Basic creep at time t (ndash)

R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (ndash)

H L Height and length of a wall m

h Distance from the given point to the base m

Reduction coefficient of restraint factor R (ndash)

Rbridage Restraint factor including reduction (ndash)

Mthel Elastic bending moment induced by a restrained deformation gradient (eg thermal gradient) Nm

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

xviii Control of Cracking in Reinforced Concrete Structures

k Reduction coefficient related to the elastic bending moment (ndash)

Chapter 10

θ Temperature in Kelvin degK

ζ Hydration degree of cement (ndash)

w(t) Water content at time t Kgmndash3

propinfin Water quantity for cement hydration Kgmndash3

Dw Global coefficient of water diffusion m2sndash1

Sr Degree of concrete water saturation (ndash)

HRinfin Relative humidity of environment (ndash)

Mw Molar mass of water gmolndash1

Water density gmndash3

Qinfin Hydration heat per volume unit of concrete Jmndash3

Thermal capacity of concrete per volume unit Jmndash3

wc Waterndashcement ratio (ndash)

Φ Concrete porosity (ratio of voids to the total volume) (ndash)

ζ0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (ndash)

S(ζ) Rigidity matrix (Hookrsquos law) MPa

τS Bond stress MPa

τM Time constant of permanent creep s

τrbc Time constant of reversible basic creep s

τpbd Characteristic time of creep at temperatureθref s

Φ Coefficient of basic permanent creep of concrete (ndash)

Cc Coefficient of creep stabilization (ndash)

Increment of permanent basic creep (ndash)

Increment of basic reversible creep (ndash)

Increment of basic creep (ndash)

Increment of intrinsic drying creep (ndash)

εpbc Permanent basic creep strain (ndash)

εrbc Basic reversible creep strain (ndash)

εsh Shrinkage strain (ndash)

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Notations xix

εash Autogenous shrinkage strain (ndash)

εkbc Potential of basic creep (ndash)

εpl Plastic strain (ndash)

εE Instantaneous elastic strain

Cth Reducing coefficient for characteristic times of creep according to temperature (ndash)

Cdc Reducing coefficient for characteristic time of drying creep (ndash)

Ew Activation energy of creep mechanisms Jmol

Gf Fracture energy Jm2

Φpbd Creep coefficient (ndash)

hw Coefficient of water surface exchange msndash1

mn Adjustment parameters of hydration model Typical values m=22 n=025 (ndash)

Aw Bw Adjustment parameter of drying model msndash1 and m3kgndash1

Chapter 11

α Coefficient of thermal expansion of concrete Kndash1

w Crack width mm

Tsurface Temperature measured on the concrete surface

Tambient Temperature measured outside of the formwork

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Introduction

Most concrete structures in Europe are currently designed according to Eurocode 2 (EC2) However feedback has shown that EC2 rules do not fully reflect the complete behavior of massive concrete structures such as thick slabs or thick walls throughout time These structures are subjected to THM effects scale effects and structural effects that induce specific cracking patterns related to crack spacing and crack width

To address concerns of the sustainability and durability of structures in 2008 the French Civil Engineering Community decided to launch a joint national research project CEOSfr with the aim of taking a step forward in engineering capabilities for predicting the crack pattern of special structures mainly massive structures

The aims of CEOSfr project were threefold

ndash to provide experimental data representative of massive test specimens

ndash to develop numerical nonlinear models and damage models to simulate concrete behavior under load and imposed deformation in accordance with the test results

ndash to propose engineering rules for crack width and space assessment of possible cracking patterns in massive structures in addition to the EC2 and fib Model Code (MC2010) standards

The CEOSfr project was carried out from 2008 up to mid-2015 around three axes modeling and simulation in parallel with MEFISTO research project testing on large-scale models and engineering rules

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

xxii Control of Cracking in Reinforced Concrete Structures

The guidelines for the control of cracking phenomena in reinforced concrete structures are mainly dedicated to the proposed rules based on the outcomes of the CEOSfr project and feedbacks from operated structures These rules aim to supplement those presented in EC2 and MC2010 These guidelines were presented to a panel of experts within the framework of the Concrack4 seminar held at Ispra (Italy) in March 2014 following meetings of the EC2 Committee in charge of reviewing this standard

The structure of this book is as follows

Chapter 1 gives a general overview of various tests and modeling approaches which were performed in the framework of CEOSfr project to address the difficult topic of concrete cracking control

Chapter 2 examines two significant effects that were identified during the massive structure tests

ndash section 21 hydration effects of concrete at an early age (increase of temperature due to cement hydration followed by temperature decrease) and over time (high level of moisture retention) which lead to non-uniform concrete strains in the structural cross section of the considered element

ndash section 22 scale effect which results in the decrease of the tensile strength at an early age as observed in massive elements compared to the strength measured on laboratory test specimens the probability to meet extreme values in the massive element volume being higher than in small size specimens

Chapter 3 deals in particular with the 3D effect which is characterized mainly by the non-uniform concrete stresses close to concrete cracks in the cross-section of the element This effect is taken into account by using the γ0 le 1 coefficient

Chapter 4 proposes two methods for concrete crack width assessment in the case of massive beams or elements assimilated to massive beams

Chapter 5 proposes an operational method for applying the rod-tie model as described in MC2010 and the calculation of the crack width derived from the reinforcing bar deformations

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters

Introduction xxiii

Chapter 6 applies to each type of concrete elements tie beam and shear walls according to whether the functioning of the concrete element is assimilated to a tie or to a shear wall

Chapter 7 outlines the related equations presented in MC2010 and proposes some adaptations to massive elements

Chapter 8 analyzes the relations used for the crack width calculation as given by MC2010 and proposes a method to assess the external restraints then the stiffness under the internal strains due to thermal efforts shrinkage and creep and under external imposed deformations such as settlement

Chapter 9 proposes an approach for calculating the concrete cracking by distinguishing the structures with waterproofing requirements from structures with sustainability requirements

Chapter 10 describes the methodology based on the project MEFISTO results supported by the French Agence Nationale de la Recherches (ANR) and describes how to simulate the thermal and hydration effects and how to take into account those effects during the drying phase of concrete

Chapter 11 provides recommendations on parameters measurement measurement devices test protocols in order to facilitate the use of measurements performed on structures mainly on massive structures under THM effects and the use of the feedback of experience related to this domain

Worked examples are presented at the end of each chapter

At the end of the book a Bibliography gives the references of all articles referred to in the chapters