Francis Barre, Géodynamique et Structure.Philippe Bisch, Egis Industries.Danièle Chauvel, EDF SEPTEN.Jacques Cortade, Consultant.Jean-François Coste, IESF.Jean-Philippe Dubois, Consultant.Silvano Erlicher, Egis.Etienne Gallitre, EDF SEPTEN.Pierre Labbé, EDF.Jacky Mazars, University of Grenoble.Claude Rospars, IFSTTAR - EDF SEPTEN.Alain Sellier, LMDC, University of Toulouse.Jean-Michel Torrenti, IFSTTAR.

• Foreword xiNotations xvIntroduction xxiChapter 1. CEOS.fr Project Presentation  11.1. CEOS.fr work program 11.2. Testing 21.2.1. Tests on prismatic full-scale blocks 21.2.2. Tests on 1/3-scale beams 101.2.3. Tests on 1/3-scale shear walls 131.2.4. Tests on ties 171.3. Modeling and simulation 211.3.1. MEFISTO research program 211.3.2. Benchmarks and workshops 231.3.3. Numerical experiments 241.4. Engineering 251.5. Database and specimen storage 261.5.1. Database CHEOPS 261.5.2. Specimen storage (Renardières site) 26Chapter 2. Hydration Effects of Concrete at an Early Age and the Scale Effect 272.1. Hydration effects of concrete at an early age 272.1.1. Global heating and cooling of a concrete element 282.1.2. Differential temperature between concrete core and surface 292.2. Scale effect 322.2.1. Scale effect principle 322.2.2. Calculating scale effect according to Weibull theory 332.2.3. Worked examples of calculation with the scale effect according to the Weibull model 372.2.4. Application of Weibull integral in bending and in tension 44Chapter 3. Cracking of Ties 473.1. Design values and limit values 473.2. Adjusting the design value for verification purposes 473.3. Crack spacing equation 483.3.1. Linear equation 483.3.2. Relationship between the maximum spacing Sr,max and the mean spacing Sr,m 493.3.3. Equation based on the MC2010 bond-slip relationship 493.4. Equation for the mean differential strain 503.5. Model accuracy when calculating the strain and crack width 513.6. Example of the application of the cracking equations to a concrete tie in tension 53Chapter 4. Cracking of Beams Under Mechanical Flexural Loading 594.1. Crack spacing 594.2. Crack width 604.2.1. Tensile stress–strain curve 604.2.2. Calculating the crack width from the relative strain 614.2.3. Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 624.3. Examples 694.3.1. Example 1: calculation of crack spacing and crack width in a thick concrete slab under heavy loads 694.3.2. Example 2: calculation of crack spacing and crack width in a double thick beam 71Chapter 5. Cracking in Walls 755.1. Current status of the reference texts 755.2. Validity of the physical model and calculating of the crack angle 775.3. Calculation model 785.4. Crack spacing and slippage length 795.5. Mean differential strain 825.6. Calculating the crack width from reinforcing bar strains 875.7. Calculating the crack width in accordance with the strut and tie model 895.8. Recommendations for evaluating the cracking in walls subject to earthquake situations 915.9. Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 925.9.1. Example 1 945.9.2. Example 2 1025.9.3. Example 3 103Chapter 6. Minimum Reinforcement of Thick Concrete Elements 1056.1. Reinforcement of reinforced concrete ties 1066.1.1. Detailed calculation from a 3D approach 1066.1.2. Simplified methodology for calculating concrete reinforcement 1066.2. Reinforcement of prestressed concrete ties 1116.2.1. Crack formation in an element in tension 1126.2.2. Stabilized cracking stage in an element in tension 1136.2.3. Conclusion 1146.3. Reinforcement of beams 1156.3.1. Beams under monotonic mechanical loading 1156.3.2. Beams under imposed deformation and monotonic mechanical loading 1156.4. Reinforcement of walls 1166.4.1. Walls without specific requirements for cracking 1166.4.2. Walls with specific requirements for cracking 117Chapter 7. Shrinkage, Creep and Other Concrete Properties 1197.1. Introduction 1197.2. Strain 1217.2.1. Definition 1217.2.2. Range of applicability 1217.2.3. Initial strain at loading 1227.3. Shrinkage 1247.3.1. Autogenous shrinkage 1257.3.2. Drying shrinkage 1257.4. Creep 1297.4.1. Assumptions and related basic equation 1297.4.2. Basic creep 1317.4.3. Drying creep 1317.5. Experimental identification procedures 1337.5.1. Initial strain at loading time 1347.5.2. Shrinkage 1347.5.3. Basic creep 1347.5.4. Drying creep 1347.5.5. Estimation of long-term delayed strain 1347.6. Temperature effects on concrete properties 1357.6.1. Temperature effects on instantaneous concrete characteristics 1367.6.2. Maturity 1367.6.3. Thermal expansion 1367.6.4. Compressive strength 1377.6.5. Tensile strength 1377.6.6. Fracture energy 1387.6.7. Elasticity modulus 1387.6.8. Temperature effects on the delayed deformations 1397.6.9. Autogenous shrinkage 1417.6.10. Drying shrinkage 141Chapter 8. Cracking of Beams and Walls Subject to Restrained Deformations at SLS 1438.1. Evaluation of shrinkage with bulk heating and cooling of concrete 1448.2. Estimating and limiting crack widths 1458.3. Estimating restraints at SLS 1468.3.1. Approximate calculation of external restraint 1468.3.2. Detailed calculation of a restraint on a wall 1478.4. Estimation of stiffness 1528.4.1. General comments 1528.4.2. Simplified method 1538.4.3. Principles of the detailed method 1548.4.4. Worked example of a massive element thermal gradient 158Chapter 9. Effects of Various Phenomena in Combination 1639.1. Estimating crack width 1639.2. Combining effects due to imposed deformations and deformations resulting from in-service loadings 1649.2.1. Structures with water or air tightness requirements 1659.2.2. Structures with durability requirements 1679.2.3. Minimum reinforcement 169Chapter 10. Numerical Modeling: a Methodological Approach 17110.1. Scope 17110.2. Methodology 17210.3. Thermal and hydration effects 17310.4. Drying 17510.5. Mechanics 17710.5.1. Hydration 17710.5.2. Permanent basic creep 17810.5.3. Reversible basic creep 18010.5.4. Influence of temperature on the creep velocity 18110.5.5. Shrinkage 18210.5.6. Drying creep 18210.5.7. Steel-concrete composite modeling 18310.5.8. Statistical scale effect 18410.6. Example simulation 18510.6.1. Thermal and hydration simulation 185Chapter 11. Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 18911.1. General methodology of the measurements 19011.1.1. Preliminary general approach 19211.1.2. Selection and choice of measuring devices 19311.1.3. Method of measurement selection 19411.1.4. Measurement data-mining and analysis 19411.2. Mock-up measurements 19611.2.1. Measurement of parameters 19711.2.2. Data acquisition and storage 20711.3. Measurement of structures 20811.3.1. Preliminary measurements 21011.3.2. Parameters to be measured 21011.3.3. Equipment of the measurements 21111.3.4. Formwork 21211.4. Example of measurement instrumentation on massive structures 21211.5. Example of mock-up test instrumentation 21311.6. Conclusion 216Bibliography 217Index 225

Francis Barre, Géodynamique et Structure.Philippe Bisch, Egis Industries.Danièle Chauvel, EDF SEPTEN.Jacques Cortade, Consultant.Jean-François Coste, IESF.Jean-Philippe Dubois, Consultant.Silvano Erlicher, Egis.Etienne Gallitre, EDF SEPTEN.Pierre Labbé, EDF.Jacky Mazars, University of Grenoble.Claude Rospars, IFSTTAR - EDF SEPTEN.Alain Sellier, LMDC, University of Toulouse.Jean-Michel Torrenti, IFSTTAR.

• Foreword xiNotations xvIntroduction xxiChapter 1. CEOS.fr Project Presentation  11.1. CEOS.fr work program 11.2. Testing 21.2.1. Tests on prismatic full-scale blocks 21.2.2. Tests on 1/3-scale beams 101.2.3. Tests on 1/3-scale shear walls 131.2.4. Tests on ties 171.3. Modeling and simulation 211.3.1. MEFISTO research program 211.3.2. Benchmarks and workshops 231.3.3. Numerical experiments 241.4. Engineering 251.5. Database and specimen storage 261.5.1. Database CHEOPS 261.5.2. Specimen storage (Renardières site) 26Chapter 2. Hydration Effects of Concrete at an Early Age and the Scale Effect 272.1. Hydration effects of concrete at an early age 272.1.1. Global heating and cooling of a concrete element 282.1.2. Differential temperature between concrete core and surface 292.2. Scale effect 322.2.1. Scale effect principle 322.2.2. Calculating scale effect according to Weibull theory 332.2.3. Worked examples of calculation with the scale effect according to the Weibull model 372.2.4. Application of Weibull integral in bending and in tension 44Chapter 3. Cracking of Ties 473.1. Design values and limit values 473.2. Adjusting the design value for verification purposes 473.3. Crack spacing equation 483.3.1. Linear equation 483.3.2. Relationship between the maximum spacing Sr,max and the mean spacing Sr,m 493.3.3. Equation based on the MC2010 bond-slip relationship 493.4. Equation for the mean differential strain 503.5. Model accuracy when calculating the strain and crack width 513.6. Example of the application of the cracking equations to a concrete tie in tension 53Chapter 4. Cracking of Beams Under Mechanical Flexural Loading 594.1. Crack spacing 594.2. Crack width 604.2.1. Tensile stress–strain curve 604.2.2. Calculating the crack width from the relative strain 614.2.3. Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 624.3. Examples 694.3.1. Example 1: calculation of crack spacing and crack width in a thick concrete slab under heavy loads 694.3.2. Example 2: calculation of crack spacing and crack width in a double thick beam 71Chapter 5. Cracking in Walls 755.1. Current status of the reference texts 755.2. Validity of the physical model and calculating of the crack angle 775.3. Calculation model 785.4. Crack spacing and slippage length 795.5. Mean differential strain 825.6. Calculating the crack width from reinforcing bar strains 875.7. Calculating the crack width in accordance with the strut and tie model 895.8. Recommendations for evaluating the cracking in walls subject to earthquake situations 915.9. Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 925.9.1. Example 1 945.9.2. Example 2 1025.9.3. Example 3 103Chapter 6. Minimum Reinforcement of Thick Concrete Elements 1056.1. Reinforcement of reinforced concrete ties 1066.1.1. Detailed calculation from a 3D approach 1066.1.2. Simplified methodology for calculating concrete reinforcement 1066.2. Reinforcement of prestressed concrete ties 1116.2.1. Crack formation in an element in tension 1126.2.2. Stabilized cracking stage in an element in tension 1136.2.3. Conclusion 1146.3. Reinforcement of beams 1156.3.1. Beams under monotonic mechanical loading 1156.3.2. Beams under imposed deformation and monotonic mechanical loading 1156.4. Reinforcement of walls 1166.4.1. Walls without specific requirements for cracking 1166.4.2. Walls with specific requirements for cracking 117Chapter 7. Shrinkage, Creep and Other Concrete Properties 1197.1. Introduction 1197.2. Strain 1217.2.1. Definition 1217.2.2. Range of applicability 1217.2.3. Initial strain at loading 1227.3. Shrinkage 1247.3.1. Autogenous shrinkage 1257.3.2. Drying shrinkage 1257.4. Creep 1297.4.1. Assumptions and related basic equation 1297.4.2. Basic creep 1317.4.3. Drying creep 1317.5. Experimental identification procedures 1337.5.1. Initial strain at loading time 1347.5.2. Shrinkage 1347.5.3. Basic creep 1347.5.4. Drying creep 1347.5.5. Estimation of long-term delayed strain 1347.6. Temperature effects on concrete properties 1357.6.1. Temperature effects on instantaneous concrete characteristics 1367.6.2. Maturity 1367.6.3. Thermal expansion 1367.6.4. Compressive strength 1377.6.5. Tensile strength 1377.6.6. Fracture energy 1387.6.7. Elasticity modulus 1387.6.8. Temperature effects on the delayed deformations 1397.6.9. Autogenous shrinkage 1417.6.10. Drying shrinkage 141Chapter 8. Cracking of Beams and Walls Subject to Restrained Deformations at SLS 1438.1. Evaluation of shrinkage with bulk heating and cooling of concrete 1448.2. Estimating and limiting crack widths 1458.3. Estimating restraints at SLS 1468.3.1. Approximate calculation of external restraint 1468.3.2. Detailed calculation of a restraint on a wall 1478.4. Estimation of stiffness 1528.4.1. General comments 1528.4.2. Simplified method 1538.4.3. Principles of the detailed method 1548.4.4. Worked example of a massive element thermal gradient 158Chapter 9. Effects of Various Phenomena in Combination 1639.1. Estimating crack width 1639.2. Combining effects due to imposed deformations and deformations resulting from in-service loadings 1649.2.1. Structures with water or air tightness requirements 1659.2.2. Structures with durability requirements 1679.2.3. Minimum reinforcement 169Chapter 10. Numerical Modeling: a Methodological Approach 17110.1. Scope 17110.2. Methodology 17210.3. Thermal and hydration effects 17310.4. Drying 17510.5. Mechanics 17710.5.1. Hydration 17710.5.2. Permanent basic creep 17810.5.3. Reversible basic creep 18010.5.4. Influence of temperature on the creep velocity 18110.5.5. Shrinkage 18210.5.6. Drying creep 18210.5.7. Steel-concrete composite modeling 18310.5.8. Statistical scale effect 18410.6. Example simulation 18510.6.1. Thermal and hydration simulation 185Chapter 11. Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 18911.1. General methodology of the measurements 19011.1.1. Preliminary general approach 19211.1.2. Selection and choice of measuring devices 19311.1.3. Method of measurement selection 19411.1.4. Measurement data-mining and analysis 19411.2. Mock-up measurements 19611.2.1. Measurement of parameters 19711.2.2. Data acquisition and storage 20711.3. Measurement of structures 20811.3.1. Preliminary measurements 21011.3.2. Parameters to be measured 21011.3.3. Equipment of the measurements 21111.3.4. Formwork 21211.4. Example of measurement instrumentation on massive structures 21211.5. Example of mock-up test instrumentation 21311.6. Conclusion 216Bibliography 217Index 225

Francis Barre, Géodynamique et Structure.Philippe Bisch, Egis Industries.Danièle Chauvel, EDF SEPTEN.Jacques Cortade, Consultant.Jean-François Coste, IESF.Jean-Philippe Dubois, Consultant.Silvano Erlicher, Egis.Etienne Gallitre, EDF SEPTEN.Pierre Labbé, EDF.Jacky Mazars, University of Grenoble.Claude Rospars, IFSTTAR - EDF SEPTEN.Alain Sellier, LMDC, University of Toulouse.Jean-Michel Torrenti, IFSTTAR.

• Foreword xiNotations xvIntroduction xxiChapter 1. CEOS.fr Project Presentation  11.1. CEOS.fr work program 11.2. Testing 21.2.1. Tests on prismatic full-scale blocks 21.2.2. Tests on 1/3-scale beams 101.2.3. Tests on 1/3-scale shear walls 131.2.4. Tests on ties 171.3. Modeling and simulation 211.3.1. MEFISTO research program 211.3.2. Benchmarks and workshops 231.3.3. Numerical experiments 241.4. Engineering 251.5. Database and specimen storage 261.5.1. Database CHEOPS 261.5.2. Specimen storage (Renardières site) 26Chapter 2. Hydration Effects of Concrete at an Early Age and the Scale Effect 272.1. Hydration effects of concrete at an early age 272.1.1. Global heating and cooling of a concrete element 282.1.2. Differential temperature between concrete core and surface 292.2. Scale effect 322.2.1. Scale effect principle 322.2.2. Calculating scale effect according to Weibull theory 332.2.3. Worked examples of calculation with the scale effect according to the Weibull model 372.2.4. Application of Weibull integral in bending and in tension 44Chapter 3. Cracking of Ties 473.1. Design values and limit values 473.2. Adjusting the design value for verification purposes 473.3. Crack spacing equation 483.3.1. Linear equation 483.3.2. Relationship between the maximum spacing Sr,max and the mean spacing Sr,m 493.3.3. Equation based on the MC2010 bond-slip relationship 493.4. Equation for the mean differential strain 503.5. Model accuracy when calculating the strain and crack width 513.6. Example of the application of the cracking equations to a concrete tie in tension 53Chapter 4. Cracking of Beams Under Mechanical Flexural Loading 594.1. Crack spacing 594.2. Crack width 604.2.1. Tensile stress–strain curve 604.2.2. Calculating the crack width from the relative strain 614.2.3. Calculating the crack width by interpolation between uncracked and fully cracked conditions (the ζ method) 624.3. Examples 694.3.1. Example 1: calculation of crack spacing and crack width in a thick concrete slab under heavy loads 694.3.2. Example 2: calculation of crack spacing and crack width in a double thick beam 71Chapter 5. Cracking in Walls 755.1. Current status of the reference texts 755.2. Validity of the physical model and calculating of the crack angle 775.3. Calculation model 785.4. Crack spacing and slippage length 795.5. Mean differential strain 825.6. Calculating the crack width from reinforcing bar strains 875.7. Calculating the crack width in accordance with the strut and tie model 895.8. Recommendations for evaluating the cracking in walls subject to earthquake situations 915.9. Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 925.9.1. Example 1 945.9.2. Example 2 1025.9.3. Example 3 103Chapter 6. Minimum Reinforcement of Thick Concrete Elements 1056.1. Reinforcement of reinforced concrete ties 1066.1.1. Detailed calculation from a 3D approach 1066.1.2. Simplified methodology for calculating concrete reinforcement 1066.2. Reinforcement of prestressed concrete ties 1116.2.1. Crack formation in an element in tension 1126.2.2. Stabilized cracking stage in an element in tension 1136.2.3. Conclusion 1146.3. Reinforcement of beams 1156.3.1. Beams under monotonic mechanical loading 1156.3.2. Beams under imposed deformation and monotonic mechanical loading 1156.4. Reinforcement of walls 1166.4.1. Walls without specific requirements for cracking 1166.4.2. Walls with specific requirements for cracking 117Chapter 7. Shrinkage, Creep and Other Concrete Properties 1197.1. Introduction 1197.2. Strain 1217.2.1. Definition 1217.2.2. Range of applicability 1217.2.3. Initial strain at loading 1227.3. Shrinkage 1247.3.1. Autogenous shrinkage 1257.3.2. Drying shrinkage 1257.4. Creep 1297.4.1. Assumptions and related basic equation 1297.4.2. Basic creep 1317.4.3. Drying creep 1317.5. Experimental identification procedures 1337.5.1. Initial strain at loading time 1347.5.2. Shrinkage 1347.5.3. Basic creep 1347.5.4. Drying creep 1347.5.5. Estimation of long-term delayed strain 1347.6. Temperature effects on concrete properties 1357.6.1. Temperature effects on instantaneous concrete characteristics 1367.6.2. Maturity 1367.6.3. Thermal expansion 1367.6.4. Compressive strength 1377.6.5. Tensile strength 1377.6.6. Fracture energy 1387.6.7. Elasticity modulus 1387.6.8. Temperature effects on the delayed deformations 1397.6.9. Autogenous shrinkage 1417.6.10. Drying shrinkage 141Chapter 8. Cracking of Beams and Walls Subject to Restrained Deformations at SLS 1438.1. Evaluation of shrinkage with bulk heating and cooling of concrete 1448.2. Estimating and limiting crack widths 1458.3. Estimating restraints at SLS 1468.3.1. Approximate calculation of external restraint 1468.3.2. Detailed calculation of a restraint on a wall 1478.4. Estimation of stiffness 1528.4.1. General comments 1528.4.2. Simplified method 1538.4.3. Principles of the detailed method 1548.4.4. Worked example of a massive element thermal gradient 158Chapter 9. Effects of Various Phenomena in Combination 1639.1. Estimating crack width 1639.2. Combining effects due to imposed deformations and deformations resulting from in-service loadings 1649.2.1. Structures with water or air tightness requirements 1659.2.2. Structures with durability requirements 1679.2.3. Minimum reinforcement 169Chapter 10. Numerical Modeling: a Methodological Approach 17110.1. Scope 17110.2. Methodology 17210.3. Thermal and hydration effects 17310.4. Drying 17510.5. Mechanics 17710.5.1. Hydration 17710.5.2. Permanent basic creep 17810.5.3. Reversible basic creep 18010.5.4. Influence of temperature on the creep velocity 18110.5.5. Shrinkage 18210.5.6. Drying creep 18210.5.7. Steel-concrete composite modeling 18310.5.8. Statistical scale effect 18410.6. Example simulation 18510.6.1. Thermal and hydration simulation 185Chapter 11. Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 18911.1. General methodology of the measurements 19011.1.1. Preliminary general approach 19211.1.2. Selection and choice of measuring devices 19311.1.3. Method of measurement selection 19411.1.4. Measurement data-mining and analysis 19411.2. Mock-up measurements 19611.2.1. Measurement of parameters 19711.2.2. Data acquisition and storage 20711.3. Measurement of structures 20811.3.1. Preliminary measurements 21011.3.2. Parameters to be measured 21011.3.3. Equipment of the measurements 21111.3.4. Formwork 21211.4. Example of measurement instrumentation on massive structures 21211.5. Example of mock-up test instrumentation 21311.6. Conclusion 216Bibliography 217Index 225