Contents

Preface i About the Author v

1 Introduction 1

1.1 The Significance of Thermal Stress in Mass Concrete 1

1.2 The Features of Thermal Stresses in Concrete Structures 3

1.3 The Variation of Temperature and Thermal Stress of Mass Concrete with Time 4

1.3.1 The Variation of Temperature of Mass Concrete with Time 4

1.3.2 The Variation of the Thermal Stress in Mass Concrete 5

1.4 Kinds of Thermal Stress 6

1.5 Analysis of Thermal Stress of a Massive Concrete Structure 6

1.6 Thermal Stress—The Cause of Crack 7

1.7 Technical Measures for Control of Thermal Stress and Prevention of Cracking 8

1.8 The Experience of the Temperature Control and Crack Prevention

2 ConductionofHeatinMassConcrete,BoundaryConditions,andMethodsofSolution11

2.1 DifferentialEquationofHeatConduction,InitialandBoundaryConditions11

2.1.1 DifferentialEquationofHeatConduction11

2.1.2 InitialCondition12

2.1.3 BoundaryConditions13

2.1.4 TheApproximateTreatmentoftheThirdKindofBoundaryCondition14

2.2 SurfaceConductanceandComputationofSuperficialThermalInsulation16

2.2.1 SurfaceConductanceβ16

2.2.2 ComputationoftheEffectofSuperficialThermalInsulation17

2.3 AirTemperature19

2.3.1 AnnualVariationofAirTemperature19

2.3.2 ColdWave19

2.4 TemperatureIncrementsduetoSunshine20

2.4.1 SunRadiationonHorizontalSurface20

2.4.2 TemperatureIncrementoftheDamSurfaceduetoSunshine22

2.4.3 InfluenceofSunshineontheTemperatureofHorizontalLiftSurface22

2.5 EstimationofWaterTemperatureinReservoir25

2.6 NumericalComputationofWaterTemperatureinReservoir28

2.7 ThermalPropertiesofConcrete29

2.8 HeatofHydrationofCementandtheAdiabaticTemperatureRiseofConcrete31

2.8.1 HeatofHydrationofCement31

2.8.2 AdiabaticTemperatureRiseofConcrete32

2.9 TemperatureontheSurfaceofDam35

2.10 TheAutogenousDeformationofConcrete36

2.11 Semi-MatureAgeofConcrete36

2.11.1 MethodforDeterminingtheSemi-MatureAgeofConcrete37

2.11.2 FormulasforComputingtheSemi-MatureAgeofConcrete38

2.11.3 MeaningofSemi-MatureAgeinEngineering40

2.11.4 ExampleoftheInfluenceofSemi-MatureAge40

2.11.5 MeasuresforAdjustingtheSemi-MatureAgesofConcrete41

2.11.6 Conclusions42

2.12 DeformationofConcreteCausedbyChangeofHumidity42

2.13 CoefficientsofThermalExpansionofConcrete43

2.14 SolutionofTemperatureFieldbyFiniteDifferenceMethod44

3 TemperatureFieldintheOperationPeriodofaMassiveConcreteStructure49

3.1 DepthofInfluenceoftheVariationofExteriorTemperatureintheOperationPeriod49

3.1.1 DepthofInfluenceofVariationofWaterTemperature49

3.1.2 DepthofInfluenceofVariationofAirTemperature50

3.2 VariationofConcreteTemperaturefromtheBeginningofConstructiontothePeriodofOperation53

3.3 SteadyTemperatureFieldofConcreteDams54

4 PlacingTemperatureandTemperatureRiseofConcreteLiftduetoHydrationHeatofCement57

4.1 MixingTemperatureofConcrete—T057

4.2 TheFormingTemperatureofConcreteT158

4.3 PlacingTemperatureofConcreteTp60

4.4 TheoreticalSolutionofTemperatureRiseofConcreteLiftduetoHydrationHeatofCement62

4.4.1TemperatureRiseduetoHydrationHeatinConcrete

LiftwithFirstKindofBoundaryCondition4.4.2TemperatureRiseduetoHydrationHeatinConcrete

LiftwithThirdKindofBoundaryCondition 64

4.4.3 TemperatureRiseduetoHydrationHeatwithAdiabaticTemperatureRiseExpressedbyCompoundExponentials66

4.5 TheoreticalSolutionofTemperatureFieldofConcreteLiftduetoSimultaneousActionofNaturalCoolingandPipeCooling67

4.6 TemperatureFieldinConcreteLiftComputedbyFiniteDifferenceMethod69

4.6.1 TemperatureFieldinConcreteLiftduetoHydrationHeatComputedbyFiniteDifferenceMethod69

4.6.2 TemperatureFieldduetoHydrationHeatinConcreteLiftwithCoolingPipeComputedbyFiniteDifferenceMethod70

4.7 PracticalMethodforComputingTemperatureFieldinConstructionPeriodofConcreteDams72

4.7.1 PracticalMethodforComputingTemperatureFieldinConcreteLiftwithoutPipeCooling74

4.7.2 InfluenceofthePlacingTemperatureTpoftheNewConcrete75

4.7.3 PracticalMethodforComputingTemperatureinConcreteLiftwithoutPipeCooling77

4.7.4 PracticalMethodforComputingTemperatureFieldinConcreteLiftwithPipeCooling77

4.7.5 PracticalTreatmentofBoundaryConditionontheTopSurface80

5 NaturalCoolingofMassConcrete83

5.1 CoolingofSemi-InfiniteSolid,ThirdKindofBoundaryCondition83

5.2 CoolingofaSlabwithFirstKindofBoundaryCondition85

5.3 CoolingofaSlabwithThirdKindofBoundaryCondition89

5.4 TemperatureinaConcreteSlabwithHarmonicSurfaceTemperature91

5.4.1 ConcreteSlabwithZeroInitialTemperatureandHarmonicSurfaceTemperature91

5.4.2 ConcreteSlab,InitialTemperatureT0,HarmonicSurfaceTemperature94

5.5 TemperatureinaSlabwithArbitraryExternalTemperature98

5.6 CoolingofMassConcreteinTwoandThreeDirections,TheoremofProduct101

6 Stress-StrainRelationandAnalysisofViscoelasticStressofMassConcrete105

6.1 Stress-StrainRelationofConcrete105

6.1.1 StrainofConcreteduetoConstantStress105

6.1.2 StrainofConcreteduetoVariableStress107

6.1.3 ModulusofElasticityandCreepofConcrete107

6.1.4 LateralStrainandPoisson’sRatioofConcrete110

6.2 StressRelaxationofConcrete111

6.2.1 StressRelaxationofConcreteSubjectedtoConstantStrain111

6.2.2 MethodforComputingtheRelaxationCoefficientfromCreepofConcrete112

6.2.3 FormulasforRelaxationCoefficient114

6.3 ModulusofElasticity,UnitCreep,andRelaxationCoefficientofConcreteforPreliminaryAnalysis115

6.4 TwoTheoremsAbouttheInfluenceofCreepontheStressesandDeformationsofConcreteStructures115

6.5 ClassificationofMassiveConcreteStructuresandMethodofAnalysis117

6.6 MethodofEquivalentModulusforAnalyzingStressesinMaturedConcreteduetoHarmonicVariationofTemperature117

7 ThermalStressesinFixedSlaborFreeSlab121

7.1 ThermalStressesinFixedSlab121

7.1.1 ComputationoftheTemperatureField121

7.1.2 TheElasticThermalStress121

7.1.3 TheViscoelasticThermalStresses123

7.1.4 TheThermalStressesinFixedSlabDuetoHydrationHeatofCement123

7.2 MethodforComputingThermalStressesinaFreeSlab126

7.2.1 ElasticThermalStressinaFreeSlabWhentheModulusofElasticityisConstant126

7.2.2 ViscoelasticThermalStressinaFreeSlabConsideringtheInfluenceofAge128 2100433B