Series Editor
Jacky Mazars
First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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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
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 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 CEOS.fr project (Comportement et Evaluation des Ouvrages Spéciaux – fissuration, retrait) covering the behavior and evaluation of special reinforced concrete (RC) works with regard to cracking and shrinkage. The CEOS.fr project took place between 2008 and 2015, involving 41 French Ministère de l’Environnement de l’Énergie et de la Mer (MEEM), clients and project managers. The project was funded jointly by the partners of the MEEM.
The CEOS.fr 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 CEOS.fr 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 CEOS.fr test report, titled “Results obtained in the understanding of cracking phenomena” [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.
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 appliquée et l’expérimentation en génie civil (IREX) for their administrative and logistical support.
Pierre LABBÉ, EDF
December 2015
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 – Tini |
Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature | °C | |
| Tadiab | Adiabatic temperature | °C | ||
| λ | Thermal conductivity | W–1.m–1.K–1 | ||
| Q∞ | Hydration heat per weight unit of cement | kJ.kg–1 | ||
| ρC | Heat capacity per weight unit of concrete | kJ.kg–1.°C–1 | ||
| a | Diffusivity | m2.s–1 | ||
| βT | Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions: |
(–) | ||
| σcm | Mean value of concrete compressive strength | MPa | ||
| fctm,scale | 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 | ||
| 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 | – | ||
 |
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 | ||
| γ | Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack | (–) | ||
| 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:  |
(–) | |
| α | Exponent of the bond–slip relationship given by Equation 6.1–1 of MC2010 | (–) | ||
| αe | Modular ratio Es/Ecm (see EC2 and MC2010) | (–) | ||
| Chapter 4 | ζ | Parameter reflecting the crack width, depending on σsr/σs (seeEC2 and MC2010) | (–) | |
| εI | The relative strain in the section considered un–cracked | (–) | ||
| εII | The relative strain in the cracked section. | (–) | ||
| Chapter 5 |  |
Stress tensor (Nxx, Nxy = Nyx, Nyy) derived from structural design | MPa | |
| Nr | Membrane force normal to the crack | kN/m | ||
| Tr | Membrane force tangential to the crack | kN/m | ||
| N// | Membrane force normal to a plan which is perpendicular to the crack | kN/m | ||
| 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 | ||
| θ° | Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010) | (°) | ||
| 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 | (–) | ||
| εsy | Mean steel bar strain along the y-direction | (–) | ||
| ρsx,eff | Percentage of steel reinforcement in the x-direction | % | ||
| ρsy,eff | Percentage of steel reinforcement in the y-direction | % | ||
| α | Local distortion | rad | ||
| ρ | As/Ac, 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 | (–) | ||
| Fct,scale | Concrete tensile stress at a given point along the reinforcing bar | MPa | ||
| Chapter 8 |  |
See Chapter 2 | °C | |
| Tmin | Minimum temperature up to time t | °C | ||
| α | Free coefficient of thermal expansion of concrete | K–1 | ||
| εca(t) | Basic creep at time t | (–) | ||
| R | Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) | (–) | ||
| 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 | (–) | ||
| Rbridage | Restraint factor including reduction | (–) | ||
| Mth,el | Elastic bending moment induced by a restrained deformation gradient (e.g. thermal gradient) | N.m | ||
| k | Reduction coefficient related to the elastic bending moment | (–) | ||
| Chapter 10 | θ | Temperature in Kelvin | °K | |
| ζ | Hydration degree of cement | (–) | ||
| w(t) | Water content at time t | Kg.m–3 | ||
| wζ∝∞ | Water quantity for cement hydration | Kg/m–3 | ||
| Dw | Global coefficient of water diffusion | m2.s–1 | ||
| Sr | Degree of concrete water saturation | (–) | ||
| HR∞ | Relative humidity of environment | (–) | ||
| Mw | Molar mass of water | g.mol–1 | ||
| ρw | Water density | g.m–3 | ||
| Q∞ | Hydration heat per volume unit of concrete | J.m–3 | ||
| ρc | Thermal capacity of concrete per volume unit | J.m–3 | ||
| w/c | Water–cement ratio | (–) | ||
| Φ | Concrete porosity (ratio of voids to the total volume) | (–) | ||
| ζ0 | Threshold of mechanical percolation (concrete change from liquid state to solid state) | (–) | ||
| S(ζ) | Rigidity matrix (Hook’s 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 temperature θref | s | ||
| Φpbc | Coefficient of basic permanent creep of concrete | (–) | ||
| Cc | Coefficient of creep stabilization | (–) | ||
| dεpbc | Increment of permanent basic creep | (–) | ||
| dεrbc | Increment of basic reversible creep | (–) | ||
| dεbc | Increment of basic creep | (–) | ||
| dεdc | Increment of intrinsic drying creep | (–) | ||
| εpbc | Permanent basic creep strain | (–) | ||
| εrbc | Basic reversible creep strain | (–) | ||
| εsh | Shrinkage strain | (–) | ||
| εash | Autogenous shrinkage strain | (–) | ||
| εkbc | Potential of basic creep | (–) | ||
| εpl | Plastic strain | (–) | ||
| εE | Instantaneous elastic strain | |||
| Cth | Reducing coefficient for characteristic times of creep according to temperature | (–) | ||
| Cdc | Reducing coefficient for characteristic time of drying creep | (–) | ||
| Ew | Activation energy of creep mechanisms | J/mol | ||
| Gf | Fracture energy | J/m2 | ||
| Φpbd | Creep coefficient | (–) | ||
| hw | Coefficient of water surface exchange | m.s–1 | ||
| m,n | Adjustment parameters of hydration model. Typical values: m=2.2; n=0.25 | (–) | ||
| Aw, Bw | Adjustment parameter of drying model | m.s–1 and m3.kg–1 | ||
| Chapter 11 | α | Coefficient of thermal expansion of concrete | K–1 | |
| w | Crack width | mm | ||
| Tsurface | Temperature measured on the concrete surface | |||
| Tambient | Temperature measured outside of the formwork |
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, CEOS.fr, 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 CEOS.fr project were threefold:
The CEOS.fr 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.
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 CEOS.fr 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 CEOS.fr project to address the difficult topic of concrete cracking control.
Chapter 2 examines two significant effects that were identified during the massive structure tests:
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 ≤ 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.
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.