<%BANNER%>

A Finite Element Model for the Prediction of Thermal Stresses in Mass Concrete

Permanent Link: http://ufdc.ufl.edu/UFE0041235/00001

Material Information

Title: A Finite Element Model for the Prediction of Thermal Stresses in Mass Concrete
Physical Description: 1 online resource (177 p.)
Language: english
Creator: Lawrence, Adrian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: concrete, element, finite, gradient, mass, stress, temperature, thermal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents the development of a finite element model for the prediction of the distribution of temperatures within a hydrating massive concrete element. The temperature distribution produced by the finite element thermal analysis of the model is used in the finite element structural analysis to quantify the maximum allowable thermal gradient before cracking will initiate in the concrete. Temperature differences within the concrete occur when the heat being generated by the concrete is dissipated to the surrounding environment causing the temperature at the surface of the concrete to be lower than the temperature at the interior of the concrete. At the same time the heat generated is a function of the temperature and time history of the concrete. Therefore, individual locations in the concrete will experience different levels of heat. The temperature difference between the concrete at the center of the element and the concrete in the outer region will create stresses. If the induced tensile stresses are larger than the early age tensile strength of the concrete, cracking will occur. The requirements for the control of heat generation and maximum allowable temperature difference in mass concrete vary on a state by state basis. Currently, there is no agreement on what should be the maximum allowable temperature differential between the center of a mass concrete element and its surface. How the various states arrive at their respective values is not clear. The development of an effective model for analysis of mass concrete behavior will enable the establishment of rational requirements for mass concrete to reduce cracking. To verify the results obtained in the finite element model, four different mixes of concrete, typical of use in mass concrete applications in Florida, were produced, and each mix used to make two large-scale 3.5ft x 3.5 ft x 3.5 ft (1.07 m x 1.07 m x 1.07 m) concrete blocks. In each mix, one block was insulated on all six sides to simulate a fully adiabatic process, while the other block was insulated on five of the faces with the top face left open and exposed to environmental conditions. Measurements of the temperature and strain at predetermined locations within the blocks were recorded until the equilibrium temperature was achieved. Using the developed model, a parametric analysis was performed to evaluate the effects of cement heat generation, concrete thermal properties, dimension of concrete structure, insulation of structure, convection of heat, etc. on the temperature distribution and induced stresses in mass concrete structures. Recommendations on methods for evaluating the potential performance of mass concrete structures are presented.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Adrian Lawrence.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Tia, Mang.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041235:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041235/00001

Material Information

Title: A Finite Element Model for the Prediction of Thermal Stresses in Mass Concrete
Physical Description: 1 online resource (177 p.)
Language: english
Creator: Lawrence, Adrian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: concrete, element, finite, gradient, mass, stress, temperature, thermal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents the development of a finite element model for the prediction of the distribution of temperatures within a hydrating massive concrete element. The temperature distribution produced by the finite element thermal analysis of the model is used in the finite element structural analysis to quantify the maximum allowable thermal gradient before cracking will initiate in the concrete. Temperature differences within the concrete occur when the heat being generated by the concrete is dissipated to the surrounding environment causing the temperature at the surface of the concrete to be lower than the temperature at the interior of the concrete. At the same time the heat generated is a function of the temperature and time history of the concrete. Therefore, individual locations in the concrete will experience different levels of heat. The temperature difference between the concrete at the center of the element and the concrete in the outer region will create stresses. If the induced tensile stresses are larger than the early age tensile strength of the concrete, cracking will occur. The requirements for the control of heat generation and maximum allowable temperature difference in mass concrete vary on a state by state basis. Currently, there is no agreement on what should be the maximum allowable temperature differential between the center of a mass concrete element and its surface. How the various states arrive at their respective values is not clear. The development of an effective model for analysis of mass concrete behavior will enable the establishment of rational requirements for mass concrete to reduce cracking. To verify the results obtained in the finite element model, four different mixes of concrete, typical of use in mass concrete applications in Florida, were produced, and each mix used to make two large-scale 3.5ft x 3.5 ft x 3.5 ft (1.07 m x 1.07 m x 1.07 m) concrete blocks. In each mix, one block was insulated on all six sides to simulate a fully adiabatic process, while the other block was insulated on five of the faces with the top face left open and exposed to environmental conditions. Measurements of the temperature and strain at predetermined locations within the blocks were recorded until the equilibrium temperature was achieved. Using the developed model, a parametric analysis was performed to evaluate the effects of cement heat generation, concrete thermal properties, dimension of concrete structure, insulation of structure, convection of heat, etc. on the temperature distribution and induced stresses in mass concrete structures. Recommendations on methods for evaluating the potential performance of mass concrete structures are presented.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Adrian Lawrence.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Tia, Mang.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041235:00001


This item has the following downloads:


Full Text

PAGE 1

A FINITE ELEMENT MODEL FOR THE PRED ICTION OF THERMAL STRESSES IN MASS CONCRETE By ADRIAN M. LAWRENCE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

PAGE 2

2009 Adrian M. Lawrence 2

PAGE 3

To my family 3

PAGE 4

ACKNOWLEDGMENTS I would first like to express my deepest gr atitude to Dr. Mang Tia for his help and guidance during the course of my study at The University of Fl orida. I would also like to thank the members of my supervisory committee: Dr. Reynaldo Roque, Dr. Fazil Najafi, Dr. John Lybas of the civil and coastal e ngineering department, and Dr. La rry Muszynski of the school of building construction, for their insi ghtful suggestions that aided in determining the main focus of this study. Special gratitude is extended to Dr Jonathan F. Earle for his encouragement and timely advice. Thanks also to my partner in this research and fellow doctoral student Christopher Ferraro, who led and conducted the research on th e physical input parameters needed for the finite element model. I would also like to acknowledge and thank the Florida Department of Transportation for funding this research. I would es pecially like to thank Mr. Michael Bergin and Mr. Charles Ishee of the FDOT Materials Laborat ory, Gainesville, for th eir invaluable support and contributions to this study. Si ncere thanks to Mr. Richard DeLorenzo, Mr. Joseph Fitzgerald, Mr. Craig Roberts, Mr. Toby Dillow, and all the staff in the laboratory for their help in the physical experiments on the material properties of the concrete used in th is study. Thanks to the students who also helped in this study: Carrie Ulm, Boris Hara nki, and Patrick Bekoe. Finally, I would like to thank my family. My wife Andr ea, daughter Gabrielle, parents Dr. Vincent and Beverley Lawrence, my sister Marilyn, and brothers Neil a nd Gregory for their support and motivation throughout my years of study. 4

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................8 LIST OF FIGURES .........................................................................................................................9 ABSTRACT ...................................................................................................................................16 CHAPTER 1 INTRODUCTION................................................................................................................. .18 Background .............................................................................................................................18 Mass Concrete .................................................................................................................20 Thermal Gradients ...........................................................................................................20 Research Needs .......................................................................................................................21 Objective of Study ..................................................................................................................21 Research Hypothesis ...............................................................................................................22 Research Approach .................................................................................................................22 Significance of Research ........................................................................................................23 Outline of Dissertation ............................................................................................................24 2 LITERATURE REVIEW.......................................................................................................28 Introduction .............................................................................................................................28 Supplementary Cementitious Materials ..................................................................................28 Long Spruce Dam Rehabilitation Project ...............................................................................29 Reinforced Concrete Wall on Basemat Concrete Slab Project ...............................................33 The James Bay Concrete Monolith Project ............................................................................35 3 FINITE ELEMENT THERMAL MODEL............................................................................42 Introduction .............................................................................................................................42 Element Selection ...................................................................................................................43 Input Parameters .....................................................................................................................44 Heat of Hydration ............................................................................................................44 Conductivity and Heat Capacity ......................................................................................46 Convection .......................................................................................................................49 Model Geometry .....................................................................................................................50 Boundary Conditions ..............................................................................................................50 4 FINITE ELEMENT ST RUCTURAL MODEL......................................................................58 Introduction .............................................................................................................................58 Element Selection ...................................................................................................................58 5

PAGE 6

Material Model .......................................................................................................................59 Input Parameters .....................................................................................................................59 Modulus of Elasticity ......................................................................................................59 Poissons Ratio ................................................................................................................60 Coefficient of Thermal Expansion ..................................................................................60 Tensile Strength ...............................................................................................................60 Symmetry and Boundary Conditions ......................................................................................61 5 BLOCK EXPERIMENT........................................................................................................63 Introduction .............................................................................................................................63 Concrete Mix Design..............................................................................................................63 Block Geometry ......................................................................................................................63 Instrumentation for Data Collection .......................................................................................64 Temperature Profiles ..............................................................................................................64 6 MATERIAL TESTS AND PROPERTIES.............................................................................73 Introduction .............................................................................................................................73 Heat of Hydration ...................................................................................................................73 Semi-Adiabatic Calorimetry ............................................................................................73 Isothermal Conduction Calorimetry ................................................................................74 Specific Heat Capacity ...........................................................................................................75 Thermal Diffusivity ................................................................................................................75 Flexural Strength ....................................................................................................................76 Splitting Tensile Strength .......................................................................................................77 Modulus of Elasticity an d Poissons Ratio Testing ................................................................78 Coefficient of Thermal Expansion Testing .............................................................................78 Summary of Material Properties .............................................................................................78 7 THERMAL ANALYSIS RESULTS......................................................................................91 Introduction .............................................................................................................................91 Semi-Adiabatic Calorimetry Finite Element Results .............................................................92 Isothermal Calorimetry Finite Element Results .....................................................................94 Summary of Findings .............................................................................................................96 8 STRUCTURAL ANALYSIS RESULTS.............................................................................113 Stress Results ........................................................................................................................113 Cracking Potential ................................................................................................................115 Temperature Difference and Cracking .................................................................................116 Summary of Findings ...........................................................................................................117 9 PARAMETRIC STUDY......................................................................................................131 Introduction ...........................................................................................................................131 Effect of Specimen Size ........................................................................................................131 6

PAGE 7

Effect of Insulation Thickness..............................................................................................132 Time of Formwork Removal Effect .....................................................................................135 Heat Generation Rate Effect .................................................................................................136 Summary of Findings ...........................................................................................................136 10 CONCLUSIONS AND RECOMMENDATIONS...............................................................152 Findings ................................................................................................................................152 Conclusions ...........................................................................................................................154 Recommendations for Future Research................................................................................154 APPENDIX A GRAPHICAL USER INTER FACE INPUT COMMANDS................................................155 B BATCH FILE INPUT COMMANDS..................................................................................159 C STAGGERED ANALYSIS COMMANDS.........................................................................168 D PHASED ANALYSIS COMMANDS.................................................................................171 LIST OF REFERENCES .............................................................................................................175 BIOGRAPHICAL SKETCH .......................................................................................................177 7

PAGE 8

LIST OF TABLES Table page 3-1 Example of direct input of concrete internal heat production ......................................51 3-2 Example of adiabatic temperature rise input .............................................................51 3-3 Cementitious content of each mixture ......................................................................51 5-1 Mix designs of concrete us ed in the large-scale blocks ..............................................67 6-1 Thermal properties of concrete ...............................................................................80 6-2 Thermal properties of plywood and polystyrene .......................................................80 6-3 Mechanical properties of concrete ...........................................................................80 6-4 Mechanical properties of concrete ...........................................................................81 8

PAGE 9

LIST OF FIGURES Figure page 1-1 Typical temperature characteris tics of a mass concrete element ..................................26 1-2 Stress vs. time plot show ing time of crack initiation ..................................................26 1-3 Temperature balance computed from te mperature difference di stribution for surface gradient analysis of lock wall .................................................................................27 2-1 Effect of substituting an Italian natural pozzolan on the heat of hydration of Portland cement. ................................................................................................................39 2-2 K and Values of adiabatic temperature rise ..........................................................39 2-3 Locations for temperature and stress meas urements in a reinforced concrete wall ........40 2-4 Thermocouple and strain gage locations in the James Bay concrete monolith ..............41 3-1 Elements used to model early age concrete behavior. ................................................52 3-2 Four-node Isoparametric Boundary Element BQ4HT ................................................52 3-3 Adiabatic temperature rise of each concrete mixture obtained from semi-adiabatic calorimetry testing ................................................................................................53 3-4 Hydration power of each cementitious mixture obtained from isothermal calorimetry testing ..................................................................................................................53 3-5 Adiabatic temperature rise of each concrete mixture calculated from the hydration power obtained in the isothermal calorim etry testing of cementitious mixtures ............54 3-6 One dimensional conduction heat transfer ................................................................54 3-7 Differential volume for a rectangular solid ...............................................................55 3-8 Convection heat transfer ........................................................................................55 3-9 Finite element model of c oncrete block with insulation .............................................56 3-10 Ambient temperatures during experimental block monitoring ....................................56 3-11 External temperatures imposed on fini te element model representing the ambient conditions of the laboratory ....................................................................................57 4-1 Twenty-node Isoparametric Solid Brick element CHX60 ..........................................62 4-2 Symmetry conditions and supports of model ............................................................62 9

PAGE 10

5-1 Experimental block geometry .................................................................................68 5-2 Uninsulated (left) and insulated (right) mass concrete block specimens .......................68 5-3 Thermocouple location (Plan) .................................................................................69 5-4 Thermocouple location (Section) ............................................................................69 5-5 Instrumentation layout for experimental block ..........................................................70 5-6 Temperatures along the center line of the uncovered concrete block mix 1 ..................70 5-7 Temperatures 2 from the side of the uncovered block in mix 1 .................................71 5-8 Temperatures along the center lin e of the uncovered block in mix 2 ...........................71 5-9 Temperatures along the center lin e of the uncovered block in Mix 3 ...........................72 5-10 Temperatures along the center line of the uncovered block in mix 4 ...........................72 6-1 Resultant semi-adiabatic calorimetric energy curve for mix 1 ....................................82 6-2 Resultant isothermal calorimetric curves with regard to energy versus time for mix 1 ...82 6-3 Resultant isothermal calorimetric curves w ith regard to energy ve rsus equivalent Age for mix 1 ..............................................................................................................83 6-4 Resultant isothermal calorimetric curves w ith regard to energy ve rsus equivalent Age for mix 2 ..............................................................................................................83 6-5 Resultant isothermal calorimetric curves w ith regard to energy ve rsus equivalent Age for mix 3 ..............................................................................................................84 6-6 Resultant isothermal calorimetric curves w ith regard to energy ve rsus equivalent Age for mix 4 ..............................................................................................................84 6-7 Schematic of the specific heat capacity calorimeter ...................................................85 6-8 Thermal diffusivity vs. age of the experimental blocks ..............................................85 6-9 Beam specimens for flexural strength testing ...........................................................86 6-10 Beam specimen undergoing flexural strength testing .................................................86 6-11 Theoretical stress and strain di stribution through b eam cross section ..........................87 6-12 The modulus of rupture of the beam specimens taken from mixtures 1, 2, 3 and 4 ........87 6-13 Diagrammatic arrangement of splitting tension test ASTM C496 ...............................88 10

PAGE 11

6-14 Splitting tensile strength of concre te used in mixtures 1, 2, 3 and 4 .............................88 6-15 Compressive modulus of elasticity versus time .........................................................89 6-16 Tensile modulus of elasticity versus time .................................................................89 6-17 Coefficient of thermal expansion versus time for each mixture ..................................90 7-1 Thermocouple location (Plan) .................................................................................98 7-2 Thermocouple location (Section) ............................................................................98 7-3 Degree of hydration at the center and top of the block in mixture 1 ............................99 7-4 Equivalent age at the center and top of the block in mixture 1 ....................................99 7-5 Concrete quarter block with insulation at time step 1 ..............................................100 7-6 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 2 below the exposed top surface of mixture 1 ....................................100 7-7 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 4 below the exposed top surface of mixture 1 ....................................101 7-8 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 21 below the exposed top surface of mixture 1 ...................................101 7-9 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 2 below the exposed top surface of mixture 2 ....................................102 7-10 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 4 below the exposed top surface of mixture 2 ....................................102 7-11 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 21 below the exposed top surface of mixture 2 ...................................103 7-12 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 2 below the exposed top surface of mixture 3 ....................................103 7-13 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 4 below the exposed top surface of mixture 3 ....................................104 7-14 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 21 below the exposed top surface of mixture 3 ...................................104 7-15 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 2 below the exposed top surface of mixture 4 ....................................105 11

PAGE 12

7-16 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 4 below the exposed top surface of mixture 4 ....................................105 7-17 Semi-adiabatic and experimentally measur ed temperature-time hi stories at the center of the block, 21 below the exposed top surface of mixture 4 ...................................106 7-18 Isothermal and experimentally measured te mperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 1 ........................................106 7-19 Isothermal and experimentally measured te mperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 1 ........................................107 7-20 Isothermal and experimentally measured te mperature-time histories at the center of the block, 21 below the exposed top surface of mixture 1 .......................................107 7-21 Isothermal and experimentally measured te mperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 2 ........................................108 7-22 Isothermal and experimentally measured te mperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 2 ........................................108 7-23 Isothermal and experimentally measured te mperature-time histories at the center of the block, 21 below the exposed top surface of mixture 2 .......................................109 7-24 Isothermal and experimentally measured te mperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 3 ........................................109 7-25 Isothermal and experimentally measured te mperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 3 ........................................110 7-26 Isothermal and experimentally measured te mperature-time histories at the center of the block, 21 below the exposed top surface of mixture 3 .......................................110 7-27 Isothermal and experimentally measured te mperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 4 ........................................111 7-28 Isothermal and experimentally measured te mperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 4 ........................................111 7-29 Isothermal and experimentally measured te mperature-time histories at the center of the block, 21 below the exposed top surface of mixture 4 .......................................112 8-1 Location of elements analyzed for stress ................................................................119 8-2 Stress state at the top center and center of the finite element concrete block with mixture 1 ............................................................................................................120 12

PAGE 13

8-3 Stress state at the top edge and center edge of the finite element concrete block with mixture 1 ............................................................................................................120 8-4 Stress state at the top center and center of the finite element concrete block with mixture 2 ............................................................................................................121 8-5 Stress state at the top edge and center edge of the finite element concrete block with mixture 2 ............................................................................................................121 8-6 Stress state at the top center and center of the finite element concrete block with mixture 3 ............................................................................................................122 8-7 Stress state at the top edge and center edge of the finite element concrete block with mixture 3 ............................................................................................................122 8-8 Stress state at the top center and center of the finite element concrete block with mixture 4 ............................................................................................................123 8-9 Stress state at the top edge and center edge of the finite element concrete block with mixture 4 ............................................................................................................123 8-10 Crack index for elements along the center line of block with mixture 1 .....................124 8-11 Crack index for elements along th e edge of block with mixture 1 .............................124 8-12 Crack index for elements along the center line of block with mixture 2 .....................125 8-13 Crack index for elements along th e edge of block with mixture 2 .............................125 8-14 Crack index for elements along the center line of block with mixture 3 .....................126 8-15 Crack index for elements along th e edge of block with mixture 3 .............................126 8-16 Crack index for elements along the center line of block with mixture 4 .....................127 8-17 Crack index for elements along th e edge of block with mixture 4 .............................127 8-18 Induced stress with re spect to temperature differential for mixture 1 .........................128 8-19 Induced stress with re spect to temperature differential for mixture 2 .........................128 8-20 Induced stress with Respect to te mperature differential for mixture 3 .......................129 8-21 Induced stress with re spect to temperature differential for mixture 4 .........................129 8-22 Top surface of experimental block containing mixture 1 showing numerous cracks along the edges ...................................................................................................130 9-1 Comparison of temperature profiles calculated at the center of each block ................138 13

PAGE 14

9-2 Calculated peak temperature va lues with respect to block size .................................138 9-3 Effect of concrete block size on the maximum internal temperature difference ..........139 9-4 Comparison of stresses at the cent er of the top surface of each block ........................139 9-5 Comparison of stresses at the top surface edge of each block ...................................140 9-6 Maximum induced stress with respect to maximum temperature differential as a result of increasing block size ...............................................................................140 9-7 Plot of maximum stress versus maximu m temperature difference with respect to block size and type of concrete used. .....................................................................141 9-8 Plot of maximum stress ve rsus maximum temperature gradient with respect to block size and type of concrete used...............................................................................141 9-9 Temperature profiles with respect to time 2 inches, 4 inches and 21 inches below the top surface of the block insu lated with a 1.5 inch thick layer of polystyrene foam ......142 9-10 Temperature profiles with respect to time 2 inches, 4 inches and 21 inches below the top surface of the block insu lated with a 6.0 inch thick layer of polystyrene foam ......142 9-11 Comparison of temperature profiles with respect to time 2 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation ...........143 9-12 Comparison of temperature profiles with respect to time 4 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation ...........143 9-13 Comparison of temperature profiles with respect to time 21 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation ...........144 9-14 Temperatures calculated at the side and cen ter of a concrete block with 1.5 inch thick insulation ...........................................................................................................144 9-15 Temperatures calculated at the side and cen ter of a concrete block with 3.0 inch thick insulation ...........................................................................................................145 9-16 Temperatures calculated at the side and cen ter of a concrete block with 6.0 inch thick insulation ...........................................................................................................145 9-17 Comparison of experimentally measured a nd calculated temperature profiles 2 inches below the top surface at the centerline of concrete block with 3.0 inch thick insulation ...........................................................................................................146 9-18 Comparison of experimentally measured a nd calculated temperature profiles 4 inches below the top surface at the centerline of concrete block with 3.0 inch thick insulation ...........................................................................................................146 14

PAGE 15

9-19 Variation in maximum temp erature differential within the concrete with respect to insulation thickness fo r each block size .................................................................147 9-20 Effect of reduction of temperature differential caused by increasing insulation thickness on the maximum induced stress ..............................................................147 9-21 Effect of insulation thickness on the maximum induced stress in each block size .......148 9-22 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 12 hours after casting ..................................................148 9-23 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 1 day after casting .......................................................149 9-24 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 2 days after casting .....................................................149 9-25 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 3 days after casting .....................................................150 9-26 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 4 days after casting .....................................................150 9-27 Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 6 days after casting .....................................................151 9-28 Temperature profiles with respect to time at the center of a concrete block with varying heat generation rates. ...............................................................................151 15

PAGE 16

Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A FINITE ELEMENT MODEL FOR THE PRED ICTION OF THERMAL STRESSES IN MASS CONCRETE By Adrian Lawrence December 2009 Chair: Mang Tia Major: Civil Engineering This dissertation presents the development of a finite element model for the prediction of the distribution of temperatures within a hydrat ing massive concrete element. The temperature distribution produced by the finite element thermal analysis of the model is used in the finite element structural analysis to quantify the maxi mum allowable thermal gradient before cracking will initiate in the concrete. Temperature differences within the concrete occur when the heat being generated by the concrete is dissipated to the surrounding environment causing the temperature at the surface of the concrete to be lower than the temperature at the interior of th e concrete. At the same time the heat generated is a function of the temperature and time history of th e concrete. Therefore, individual locations in the concrete will experi ence different levels of heat. The temperature difference between the concrete at the center of the element and the concrete in the outer region will create stresses. If the induced tensile stresses are larger than th e early age tensile strength of the concrete, cracking will occur. The requirements for the cont rol of heat generation and ma ximum allowable temperature difference in mass concrete vary on a state by st ate basis. Currently, there is no agreement on 16

PAGE 17

what should be the maximum allowable temperatur e differential between the center of a mass concrete element and its surface. How the various st ates arrive at their re spective values is not clear. The development of an effective model for analysis of mass concrete behavior will enable the establishment of rational requirements for mass concrete to reduce cracking. To verify the results obtained in the finite element model, four different mixes of concrete, typical of use in mass concrete appli cations in Florida, were produced, and each mix used to make two large-scale 3.5ft x 3.5 ft x 3.5 ft (1.07 m x 1.07 m x 1.07 m) concrete blocks. In each mix, one block was insulated on all six side s to simulate a fully adiabatic process, while the other block was insulated on five of the faces with the top face left open and exposed to environmental conditions. Measur ements of the temperature a nd strain at predetermined locations within the blocks were recorded until the equilibrium temperature was achieved. Using the developed model, a parametric anal ysis was performed to evaluate the effects of cement heat generation, concrete thermal properties, dimension of concrete structure, insulation of structure, convection of heat, etc. on the temperature distribution and induced stresses in mass concrete stru ctures. Recommendations on met hods for evaluating the potential performance of mass concrete st ructures are presented. 17

PAGE 18

CHAPTER 1 INTRODUCTION Background Whenever fresh concrete is used in the c onstruction of large homogeneous structures such as foundations and dams, cons ideration is always given to th e amount of heat that will be generated and the resulting volume change. Volu me changes occur due to temperature changes in the structure which initially in crease as the concrete hydrates and decrease as the reaction is exhausted. Temperature difference per unit distance between one point and another in a structure is called a thermal gradient. Temperature gradie nts are produced when th e heat being generated in the concrete is dissipated to the surr ounding environment causing the temperature at the surface of the concrete to be lower than the temp erature at the interior of the concrete. This temperature drop at the surface result s in the contraction of the conc rete. With the interior of the concrete being more mature than the surface, it acts as a restraint against th e contraction, creating tensile stresses in the surface. Since the concrete is still in its early age, it s full tensile strength is not developed, and if the tensile stresses are larger than the earl y age tensile strength, cracking will occur. The behavior of concrete at early age is influenced by the heat generated, which, by extension, dictates the temperat ure distribution during hydration. The temperature profile of a concrete element is further affected by the sp ecific heat capacity, thermal diffusivity, and emissivity of the concrete. At the same time, the rate of development of mechanical strength of concretes at early age increases with increasi ng temperature and hence can be expressed as a function of temperature and time. Past research leading to the creation of numerical models for the prediction of temperature distribution in mass concrete has ma inly focused on using generic heat generation 18

PAGE 19

functions for the calculation of adiabatic temper ature rise. The use of actual measured heat of hydration results from calorimetry testing of the concrete paste has been mo stly neglected. At the same time, attempts at modeling hydrating mass concrete (Radovanic (20 04)) have treated the heat generated by the reacting cement as being uniform throughout the concrete mass, whereas, in reality, the heat generation is a function of th e temperature and time history of the concrete at individual locations in the concrete mass. Diffe rent locations in a mass concrete element have different time-temperature conditions. This research is aimed at formulating a fin ite element model, taking into consideration the non-homogeneity of heat generation within concrete, to accurately predict the distribution of temperature in a hydrating concrete mass, the re sulting thermal gradients and associated thermal stresses and strains. Knowledge of these phenomena will allow for a reasonably accurate prediction of the location and poten tial for cracking of concrete. The thermal stresses that occur during the hardening of mass concrete are extremely complex and difficult to assess. This is due to se veral factors, chief among which is the complex distribution of temperature changes thr oughout the volume of the mass concrete. As depicted in Figure 1-1, the central region of the mass concrete at early age experiences high but uniform temperatures while the temperat ure in the outer region decreases as we move closer to the surface. Since the maturity of conc rete and strength are functions of temperature, the central region of the mass concrete structure will be more mature and stronger than the outer region. As the concrete hydrates faster in the middl e, large thermal gradients are produced, and strength and maturity decreases moving outwards towards the surface. Since the concrete in the outer region of mass concrete is being cooled by the atmospheric environment, contraction will 19

PAGE 20

occur. Restraint against this contraction will cause tensile stresses and strains to develop, creating the possibility that cracks will occur at or close to the surface of the concrete. These cracks will initiate when the tensile stresses ex ceed the low tensile strength at the surface as depicted in Figure 1-2. The magnitude of the tensile stresses are dependent on the thermal differential in the mass concrete, the coefficien t of thermal expansion, modulus of elasticity, creep or relaxation of the concre te, and the degree of restraint in the concrete. If cracking does occur, it will ultimately affect the ability of the concrete to withstand its design load, and allow the infiltration of deleterious materials which undermine durability. Mass Concrete Research has shown that the inner core of massive concrete elements experience compressive stresses as it tries to expand but is restricted by the slower hydrating and hence less mature outer region. Conversely, moving out towards the surface, the outer region of the hydrating concrete element acts in tension as it is being pushed against by the expanding inner core. Figure 1-3 shows a graph of temperature balance computed from temperature differences distributed across a typical mass concrete lock wall (U.S. Army Corps of Engineers 1997). Tension is induced along the su rface, while the central interior portion experiences compressive stresses. Since concrete is str ong in compression but weak in tens ion, this suggests that cracking will initiate close to the su rface and towards the edges and corners of a structure. Thermal Gradients Temperature differences per uni t distance along a particular path in a structure are called thermal gradients. These gradients result from the surface of a mass concrete element being cooled by the ambient environment while the inte rnal concrete temperature remains high due to the exothermic reaction of hydration. This causes the surface concrete to be restrained by the interior concrete. This may resu lt in the cracking of the surfac e concrete. For this reason, many 20

PAGE 21

state Departments of Transporta tion incorporate into their spec ifications a limit on the maximum allowable temperature differential between the ex terior and interior por tions of mass concrete elements during curing. The magnitude of the thermal gradients expe rienced by concrete depends on the initial placing temperature, the thermal properties (specific heat, ther mal conductivity), environmental temperature, wind speed, and precipitation. Research Needs The high amount of heat that develops during the hydra tion of massive concrete structures produces very high temp eratures throughout the structure. The variation in the rate of heat production at different locations within the concrete results in temp erature gradients that have the potential to cause microcracking as some sections cool down towards ambient temperature while others are st ill being heated. Though the effects thermal gradients have on concrete is well known, there is no agreement on what the maximum allowable temperature differential between the cente r of a mass concrete element and its surface should be. Some researchers have modeled the therma l behavior of hydrating mass concrete with some degree of success. However, none have stud ied the effects of the variation in hydration rates on the distribution of temperatures, the th ermal gradients, and resulting stresses. This research focuses on the development of a fin ite element analysis model that takes into consideration these factors. Objective of Study The goal of the research is to develop a fin ite element model of mass concrete, which is based on the input of measured thermal and mechanical characteristics, and which can predict the temperature distribution duri ng hydration and the thermal stre sses that result from the thermal gradients within the structure. Prev ious attempts at predicting the temperature 21

PAGE 22

distribution in mass concrete by way of finite element models has mainly focused on using generic heat generation functions for the calculation of adiaba tic temperature rise. The heat generated by hydrating mass concrete has also been widely modele d as being uniform throughout the concrete mass, whereas in reality the heat generation is a function of the temperature and time history of i ndividual locations in the concre te mass. The developed finite element model will take into consideration th e time-temperature conditions of individual locations within a hydrating mass concrete structure. A stress analysis util izing changing strength properties of the concrete will also be c onducted and the results compared with the experimentally measured strain data as a means of validation. Research Hypothesis The hydration reaction between cement and wa ter in a mass concrete structure does not occur uniformly. It is driven in part by the temperature conditions under which the reaction is taking place. Since the temperature within a mass concrete element is not homogeneous, the heat generation will also not be homogeneous. To properl y model the behavior of mass concrete at an early age, the temperature-time condition at indi vidual points within the concrete needs to be considered. Research Approach The modeling of the large scale concrete blocks is done with the aid of the commercially available TNO DIANA software. The analysis is done in two parts, first a thermal analysis, in which the thermal properties are modeled, the h ydration process simulated, and the resulting temperature distribution obtained. Th e second part of the analysis is a stress analysis in which the physical properties such as elas tic modulus and coefficient of thermal expansion are used along with the temperature histories obtained in the thermal analysis to calculate the stresses and strains produced by the ther mal gradients. The cracking potential is then assessed. 22

PAGE 23

As a means of validation, four different mixes of concrete, typical of use in mass concrete applications in Florida, were produced, and each mix used to make two 3.5ft x 3.5 ft x 3.5 ft (1.07m x 1.07m x 1.07m) concrete blocks. For each mix, one block was insulated on all six sides to simulate a fully adiabatic process, while the ot her block was insulated on five of the faces with the top face left open and exposed to envir onmental conditions. Measurements of the temperature and strain at pred etermined locations within the blocks were recorded until the equilibrium temperature was achieved. At the time of casting the blocks, concrete taken from the same mix were used to perform the evaluation of small-scale sample s which are then stored at 73F 2F and 100% relative humidity until the time of testing for the mechani cal properties at ages of 1 day, 2 days, 3 days, 7days, 14 days, and 28days. Tests for the thermal properties, heat of hydration, specific heat capacity, and thermal diffusivity were also done at these ages. Finally, a parametric analysis was conducted to determine what effects the size of the concrete structure, amount of insulation used, specific heat cap acity and diffusivity, would have on the temperature distribution, indu ced stresses and the cracking risk. Significance of Research The requirements for the control of heat ge neration and temperature distribution in mass concrete vary on a state by state basis. Current ly there is no agreement on what should be the maximum allowable temperature differential between the center of a mass concrete element and its surface. The states of Florida, Iowa, Virginia, and West Virginia De partments of Transportations specification requirements currently include a requ irement that the temperature differential in 23

PAGE 24

elements designated as mass concrete be controll ed to a maximum of 35 degrees Fahrenheit (20 degrees Celcius). Colorados specification states that the temp erature differential be tween the midpoint and a point 2 inches inside the exposed face of all mass concrete elements shall not exceed 45 degrees Fahrenheit as measured between temperatur e sensors. It further states that the maximum peak curing temperature of all mass concrete el ements shall not exceed 165 degrees Fahrenheit. The state of Delawares specification cal ls for a range of maximum differential temperatures based on the number of hours af ter casting of the concrete as follows: First 48 hours 40 F Next 2 to 7 days 50 F Next 8 to 14 days 60 F North Dakotas Department of Transportation specifies that measures and procedures should be taken to maintain, monitor and cont rol the temperature differential of 50 degrees Fahrenheit or less between the interior a nd exterior of the mass concrete element. Considering the inconsistencies in the maxi mum allowable temperature differential in mass concrete structures, how the various states arrive at their respective va lues is not clear. Therefore, the determination of a maximum temper ature gradient limit base d on the analysis of a finite element model that accurately predicts th e behavior of a hydrating mass concrete element would constitute a substantial contri bution to this area of engineering. Outline of Dissertation Chapter 2 is a review of the literature ci ting specifications curr ently in use and other attempts at modeling the behavior of mass concrete. Chapters 3 and 4 discuss the finite element model input parameters, material model, elem ent type and boundary conditions used in the thermal and stress analyses respectively. 24

PAGE 25

Chapter 5 discusses the mix proportions of the concrete used in the experimental blocks as well as the types and location of the monitoring instruments used. Chapter 6 describes the test procedures carried out on concrete specimens sampled directly from the concrete used in the construction of the experimental blocks. Chapters 7 and 8 present and discuss the results obtained from the finite element analyses, with comparisons of the analytical re sults of the temperature distribution and stress state with those measured in the experimental blocks. Chapter 9 presents a parametric study of mass concrete elements of varying sizes and levels of insulation in order to determine the limiting temperature gradient to prevent thermal cracking. Chapter 10 provides discussion, conclusi ons and recommendations for future research efforts. 25

PAGE 26

Higher Uniform Temperature Lower Variable Temperatures Heat Diss ipation Figure 1-1. Typical temperature charact eristics of a mass concrete element Tensile Stren g th Induced Tensile Stress Stress (p si ) Time ( hr ) Plastic Elastic Cracking will occur at this point Figure 1-2. Stress vs. time plot showing time of crack initiation 26

PAGE 27

Figure 1-3. Temperature balance computed from temperature difference distribution for surface gradient analysis of lock wall (U.S. Army Corps of Engineers 1997) 27

PAGE 28

CHAPTER 2 LITERATURE REVIEW Introduction Mass concrete is defined by the Ameri can Concrete Institute (ACI) as any volume of concrete with dimensions large e nough to require that m easures be taken to cope with generation of heat from hydration from cement and attendant volume change to minimize cracking (ACI 207.1-R96). Increasingl y, this definition refers to a larger spectrum of structures, but most importantly ap plies to concrete dams and large concrete foundations, the failure of which can have di sastrous consequences to human life and property. For this reason th e study and understanding of ma ss concrete has been of interest to engineers for the last 70 years. Methods of controlling mass concrete temperatures range from simple to complex, and from inexpensive to costly. Some of the methods commonly used are: lowheat generating concrete mixes that cont ain pozzolans; precooling of concrete; post cooling of concrete with cooling pipes; insu lation or insulated formwork; and aggregates with low-thermal-expansion aggregates. Past studies on mass concrete have focused on methods to control the heat generated during cement hydration, modeling ad iabatic temperature rise, and predicting thermally induced internal stre sses. The studies vary in th e environmental conditions in which the mass concrete is poured, purpose of the mass concrete st ructure, duration, and placement of thermocouples and strain gages. Three such field studies are presented here. Supplementary Cementitious Materials The temperature rise in the centers of la rge concrete sections is approximately proportional to the cement content used in the mix design of the concrete. This 28

PAGE 29

temperature rise is affected by the rate at which heat is developed due to the hydration of the cement. The rate and quantity of heat gene rated is further affected by the fineness and chemical composition of the Portland cement. Cements with high Tricalcium Aluminate (C 3 A) content tend to hydrate rapidly producing high adiaba tic temperature rises. The most direct way of reducing the temp erature rise in concrete is by lowering the cement content in the concrete mix desi gn. However this cannot always be done due to strength and durability restrictions, he nce the use of supplementary cementitious materials such as Fly Ash (FA) and Ground Gra nulated Blast-Furnace Slag (GGBF) is an effective way of reducing the temperature in the concrete without compromising the strength and durability. This reduction in the temperature rise is due to the slower rate of hydration reaction that occurs in concretes with these materials. Figure 2-1 shows the effect of increasing the percent content of these supplementary cementitious materials on the heat of hydration There is however a negative to replacing a percentage of Portland cement with fly ash and or blast-furnace slag in concrete. It has been observed that for a given strength, blended cement concretes tend to be less duct ile, resulting in a higher elastic modulus, lower creep, and a reduced stra in capacity (Bamforth 1984). It is important therefore to ensure that the percentage of replacement will result in temperatures low enough to compensate for the loss of ductility. Long Spruce Dam Rehabilitation Project The Long Spruce Dam in northern Manitoba, Canada, was found to have a crack that runs from the downstream side to the ups tream side of the structure. In order to perform an effective rehabilitation procedur e, an in-depth analysis to understand the stresses involved in the failure of the cr ack was undertaken. A Tw o-Dimensional Finite 29

PAGE 30

Element Analysis with the aid the comme rcial software ANSYS was conducted to achieve this goal. Two theoretical models, namely a transient thermal model and a transient stress model were developed to predic t the early stage behavior of the concrete used in the construction of the dam. The finite element analysis sought to i nvestigate whether the residual thermal stresses caused by the heat of hydration of the massive concrete pour were responsible for the apparent loss of strength in the construction joints. The early thermal behavior of a 0.6m x 0.6m laborator y concrete specimen and a dam structure model consisting of an upper and lower bl ock cast 102 hours apart were modeled and observed. The thermal qualities of interest we re the temperature field, thermal flux and thermal gradient. The thermal properties of the concrete in the laboratory specimen model were assumed to be independent of time and temperature during hydration. The thermal conductivity was assigned a cons tant value of 4.1 KJ/m-hrC, and the specific heat 1971 KJ/m 3 C, obtained from literature. The ambient temperature in the laboratory analysis was also kept constant at 23 C to represent a controlled environment. For the dam structure model, the thermal properties were slightly different to reflect the use of larger aggregate. The ini tial temperature of the concrete was set at 10 C because of the use of ice water to pre-c ool the large blocks. The boundary condition of convection is imposed on all sides except the bottom where a prescribed temperature is described. For the stress analysis, the botto m surface is constrained in all directions, representing the contact friction of the block resting on the floor. 30

PAGE 31

The analysis for the labo ratory specimen model was conducted in six hour load steps. The beginning of thermal process in the dam structure model was analyzed every six hours, and then increased to every 12 hours, then finally every 24 hours. The adiabatic temperature ri se resulting from the heat of hydration was calculated using the expression developed and pres ented by Tanabe, T., Kawasumi, M., and Yamashita, Y., in Seminar Proceedings for Finite Element Analysis of Reinforced Structured, Tokyo, Japan (1985), and publishe d by the American Society of Civil Engineers (ASCE) in 1986: T(t) = K(1e a t ) Where, T = temperature ( C) t = time (days) K = constant based on casting temperature ( C) = constant based on casting temperature The values for K and are obtained from the plots in Figure 2-2. The total amount of heat generated was th en calculated by the following equation: Q(t) = C p r T (t) = KC p r (1e a t ) Where, C p = specific heat capacity of the concrete J/gC r T = density of the concrete g/m 3 t = time (days) K = constant based on casting temperature ( C) = constant based on casting temperature And the rate of heat ge neration calculated as: R(t) = KC p r e a t 31

PAGE 32

Where, C p = specific heat capacity of the concrete J/gC r T = density of the concrete g/m 3 t = time (days) K = constant based on casting temperature ( C) = constant based on casting temperature The highest temperature was found to occur in the middle section of the specimen and decreased as it got closer to the sides of the model. This conf irms the theory that the outer section of the concrete loses heat more qui ckly than the middle because of its greater exposure to the atmospheric conditions. Radovanic (2004) found that the 0.6m x 0.6 m laboratory specimen was too small to realistically predict the behavior of ma ssive concrete structures. This led to the enlargement of the FE model by the two, five and ten orders of magnitude. The size that came closest to a realistic characterization of the behavior of the Long Spruce Dam was the 6m x 6m model. However the maximum temperature for this size model was much higher than the dam specimen. The reason gi ven by Radovanic (2004) was that the dam specimen was cast in September, when the out side temperature was much lower than the initial temperature used for the laborator y specimen. Radovanic ( 2004) concluded that assumptions made in the calculation of the h eat generation rates, ma terial properties and boundary conditions were reasonable and that the finite element algorithm was accurate enough to predict the early age thermal behavi or of the laboratory concrete specimen and dam. A finite element stress analysis of th e laboratory specimen and the dam were conducted. As a worse case scenario, the maxi mum stress occurring in the models were considered as the residual stress. The process of hardening was implemented by 32

PAGE 33

calculating the development of the modulus of elasticity of the conc rete with time based on the ACI charts. Radovanic (2004) concluded that the results of the analysis showed that the stresses produced by the thermal gr adients were signifi cant enough to cause cracking in the early age concrete. Reinforced Concrete Wall on Ba semat Concrete Slab Project As part of a field study (Machida; Ueha ra, 1987), a wall structure consisting of reinforced concrete measuring 1.0m thick, va rying height of 3.9 4.73m, and 15.0m long was cast on a 1.5m thick basemat concrete slab. The wall was instrumented with thermocouples, effective stress meters, mold type strain gages, and non-stress strain gages, to capture the temperatures, strain and stress responses at different locations within the wall, as shown in Figure 2-3. The meas urement time interval used for this instrumentation setup was 1 hour in the first three days, 3 hours until the seventh day, and 6 hours until the thirtieth day, la st day of the experiment. The concrete stress and strain condition immediately after placing was unstable, with recordings becoming stable after 6 hour s. The tensile strength was measured using the cleavage test, and the elastic modulus take n as the secant modulus of one-third the collapse strength. The stress-strain relation of one of the non-stress gages was used to calculate the coefficient of thermal expansi on which was then assumed to be a constant value throughout the experiment. A finite element model of half of the concrete wall, basemat slab, and the soil beneath was created to evaluate and forecas t cracking in the concrete wall. This was achieved by conducting a heat transfer analysis of the cements heat of hydration, and the phenomena of heat conduction and convection, followed by a thermal stress analysis for the mechanical characteristics. 33

PAGE 34

Although the atmospheric temperature of th e actual structure varied day by day, a fixed temperature of 22 C was assumed for this analysis. The heat generation rate for the concrete used in the wall was calculated by differentiating with respect to time the equation for adiabatic temperature rise developed by Tanabe et al. q = 1/24 KC p r e a t/24 (kcal/m 3 h) Where, C p = specific heat capacity of the concrete cal/gC r T = density of the concrete g/m 3 t = time (hours) K = constant based on casting temperature ( C) = constant based on casting temperature A comparison of the thermal analysis results with the experimental results revealed that the maximum measured temper ature occurred along the mid-length of the wall and was 2.1 C higher than the maximum analytical temperature which also occurred along the mid-length of the wall model. Afte r the peak temperature was obtained, the analytical temperature decrease was larger than the experimental, but after 12 days the temperature of the structure equaled the am bient temperature. The difference in the estimation of temperature decrease was attributed to the difference in the assumed heat convectivity in the model a nd the actual convection, and th e variance in atmospheric temperature of the experimental wall instead of the assumed constant temperature in the model. The stress analysis model was similar to the one used in the thermal analysis. It was assumed that no sliding took place between the basemat and the subsoil. The degrees of freedom were constrained in the directi on perpendicular to the structural symmetry plane and perpendicular to the subsoils outside surface plane. The compressive and 34

PAGE 35

tensile strengths and elastic modulus of the wall were calculated usi ng empirical formulas that related their development with the temp erature of the hydrating concrete. Constant values for the Poissons ratio and coefficien t of thermal expansion were also assumed. The results showed that the maximum expansion in the structure was recorded after 24 hours. The maximum compressive stress occurred in the mid-length one day after concrete placement in both the experiment and finite element analysis. The compressive stress became a tension stress in the middle and bottom of the wall as the concrete aged. The experiment showed that the upper mi d-length of the structure experienced a small compression peak at 18 hours which then became a tensile stress, peaking after about 2 days becoming a compressive stress again peaking at 8 days after placement. On the other hand, the finite element analysis results showed no clear compressive stress peak, but a tensile peak at 60 hours, after whic h it began to decrease but remained in the tensile stress region. Again, the difference in the measured a nd analytical results for the mid-length point close to the surface was attri buted to the real atmospheric conditions of the structure being different than the assumed constant values assigned in the finite element model. The James Bay Concrete Monolith Project The James Bay concrete monolith project (Ayotte et al., 1997), a joint effort between the Societe dEnergie de la Baie Ja mes (SEBJ) and the Ecole Polytechnique de Montreal, focused on developing a methodology, ba sed on finite elements, that could be used to predict the heat gene rated and resulting thermal st resses in mass concrete. The project included both an experimental component and a modeling component. Three concrete monoliths were built dire ctly on bedrock in the St. James Bay Territory in Northern Quebec Canada, on the site of a major hydroe lectric project. The 35

PAGE 36

dimensions of the monoliths were 2 meters wide, 10 meters long, and 2 to 3 meters high, with the height depending on the bedrock prof ile. Each monolith was instrumented with 26 T-type (Copper-Constantan alloy) thermoc ouples to monitor temperature distribution with time, and 8 pairs of mechanical strain targets on the skin reinforcement to measure the induced strain (See Figure 2-4). To obser ve the performance of the concrete when subjected to severe freeze thaw cycles, the monoliths were cast in February inside large individual heated shelters in which the temperature was maintained at 30 to 32 C during the construction phase. Two and three dimensional modeling of the concrete thermal behavior was conducted using the finite element software ADINA-T while the mechanical response, stresses and strains, were obtained using ADINA. To accommodate simultaneous changes of temperature and mechanical pr operty, a modeling technique which employed a step-by-step incremental approach of cal culating the thermally induced strains was developed to bypass the link between ADINA-T and ADINA. The cement type used was Portland cement Type 20M which was specially made for Hydro-Quebec, so a generic function for th e heat of hydration as a function of time was obtained by interpolati ng between the known functions of Type 20 and Type 50 cements, which was then calibrated by compar ing the calculated temperatures with the temperatures measured by the thermocouples The values for other concrete thermal properties, which included specific heat the thermal conductivity and convection coefficient, were obtained from various liter ature sources. Radiation was not considered because the monoliths were bui lt inside shelters which blocked the heat radiation. Convection boundary conditions were used to model the heat loss to the ambient air, 36

PAGE 37

while rock elements were added below the concrete elements for the heat dissipation through the rock foundation. The structural model for the monolith was identical to the three-dimensional model used in the thermal analysis. Displacements were restricted in the directions of the planes of symmetry, and in all directions at the bottom of the rock elements. The mechanical properties, which included elas tic modulus, compressive and tensile strength, were modeled as varying with time, while th e coefficient of thermal expansion was given a constant value of 10 / C. To include creep and relaxation, an effective reduced elastic modulus that accounts for the reduction in st resses was adopted. The computation of the incremental stresses was done by modifying the ADINA file containing the temperatures from the thermal analysis by calculating the incremental temperature T i = T i T i-1 Then computing the incremental stresses in which the current Youngs Modulus E i at each step is used = E i = E i ( T i 0) Then finally the total stresses were obtained using the previous time step ( i-1 ) i = i-1 + i Ayotte et al. (1997) found that the calcul ated temperature at the center of the monolith model followed almost perfectly th e temperatures measured experimentally. However there was a gap between the temperatur es calculated at a point near the top of the monolith and those experimentally measur ed. In the structural analysis, they found that the largest strains were located at the top of the monolith where there was the least restraint, while the strains at the base we re very small due to the restraint of the 37

PAGE 38

foundation. It was also observed that the stress variation on the top surface of the monolith was in tension while compressive stresses were computed on the vertical faces due to the insulating effect of the formwork which limited the temperature difference between this surface and the core. 38

PAGE 39

Figure 2-1. Effect of substitu ting an Italian natural pozzola n on the heat of hydration of Portland cement. (Massazza and Costa, 1979) Figure 2-2. K and Values of adiabatic temper ature rise (Radovanic, 1998) 39

PAGE 40

Figure 2-3. Locations for temp erature and stress measurements in a reinforced concrete wall (Machida and Uehara, 1987) 40

PAGE 41

Figure 2-4. Thermocouple and strain gage lo cations in the James Bay concrete monolith (Ayotte, Massicotte, Houde, and Gocevski, 1997) 41

PAGE 42

CHAPTER 3 FINITE ELEMENT THERMAL MODEL Introduction The modeling of the early age thermal behavior of concrete was conducted with the aid of the commercially available TNO DIANA soft ware package. This software package was chosen because it offers a wide range of material models for the analysis of non-linear concrete material behavior including the behavior of young hardening concrete. It can make the assessment of the temperature development due to the cement hydration and the computation of the associated stress development within the conc rete mass. Main modeling features utilized are : Equivalent age calculation Temperature and time dependent material properties Crack index calculation to assess risk of cracking The finite element analysis utilized DIANAs staggered flow-stress analysis feature, in which the thermal analysis is combined with a subsequent structural analysis. The model comprises two domains: one for the thermal flow analysis and one for the structural analysis. These domains overlap for a considerable part of the analysis and so reside in a domain called the flow-stress domain. Formwork used in the constr uction of massive concrete st ructures including plywood and polystyrene foam was explicitly modeled. Since we were only interested in their effects on the transfer of the thermal energy generated by the c oncrete, these materials were modeled with flow elements, and thus are only active in the thermal analysis. The concrete however is active in both the thermal analysis and structural analysis and therefore lies in the flow-stress domain. For this reason, the concrete is modeled w ith a quadratically interpolated structural element that is converted during the thermal analysis to a linearly interpolated flow element. 42

PAGE 43

Element Selection As stated above, the concrete in this analys is is active in the flow-stress domain and therefore is modeled with a structural element. For this, we selected the structural element CHX60, a three dimensional twenty-node brick element that is converted to the three dimensional eight-node HX8HT isoparametric brick element for the thermal analysis. Both types of elements, shown in Figure 3-1, have coinciding corner nodes. However, because the structural CHX60 element is quadratically interpolated and element HX8HT is a linearly interpolated element, the mid-nodes of the CHX60 are disregar ded in the thermal anal ysis. The basic theory and required material properties needed for the structural analysis with element CHX60 will be discussed in further detail in Chapter 4. Element HX8HT is effective in simulating the phenomenon of convection-diffusion, and is especially useful for the analys is of heat transfer problems. It utilizes linear interpolation and Gauss integration with a 2 x 2 x 2 integration sc heme. Heat transfer is modeled by assigning the thermal conductivity and heat capac ity of the concrete, where the conductivity can be modeled as isotropic, orthotropic or anisot ropic, while the heat capacity is always isotropic. Both the conductivity and capacitance may be constant or depend on temperature, or time or both. For the model described in this paper, both the conductivity and heat capacity were modeled as constant. Additional properties used to model the intern al heat generation of the concrete are the Arrhenius constant (activation energy divided by the universal gas c onstant), and the heat generation function, which can either be a table th at provides a direct description of the heat production rate with respect to the degree of hydration as shown in Table 3-1, or a table that describes the adiabatic temperatur e rise, in degrees Celsius (C), with respect to time shown in Table 3-2. 43

PAGE 44

The plywood and polystyrene were directly m odeled with element HX8HT, using each of its conductivity and heat capacity to describe the way the heat would be transferred between the concrete, plywood and polystyrene. The boundary convection was modeled using th e BQ4HT element, shown in Figure 3-2, which is a four-node isoparametric quadrilateral el ement specially used to describe boundaries in three-dimensional thermal analyses. It uses lin ear interpolation and Gauss integration in its computational scheme. The four nodes in this elem ent were modeled to coincide with the corner nodes of the surface of the brick elements they lie on. Input Parameters Heat of Hydration To properly model the behavior of hydrat ing concrete, knowledge of the heat produced during the hydration reaction as well as both the material properties of the concrete itself and the environmental conditions in which it is placed are needed. As previously stated the heat produced duri ng hydration is a function of the temperature history of the concrete. The momentary heat production rate is defined as )()(),( TqrqTrqvT r (3-1) Where: r = the degree of reaction T = the temperature C = the maximum value of the heat production rate (J/m 3 -hr) q r = the degree of reaction dependent heat production (J/m 3 -hr) q T = the temperature depe ndent heat production (J/m 3 -hr) and, 273 ),()(T Tr R E TaeTq (3-2) In which, E a = the activation energy of the concrete J/mol 44

PAGE 45

R = the universal gas constant, 8.3144 J/mol-C The heat production rate which is dependent on degree of reaction, q r can also be determined by DIANA using preprocessing. The te mperature history produced under adiabatic hydration conditions is used as the input in this case. DIANA derives th e heat production q(t) from t T rTctq ),()( (3-3) Where c(T,r) = the capacitance dependent on te mperature and degree of reaction DIANA then approximates the degree of reaction and the temperature de pendent heat production n m mQ Q r (3-4) m i iii mTrTcQ1 **),( (3-5) Where, n = specified time points m = 1,,n and, (3-6) 1 iiTTT 21 ii irr r (3-7) 21 ii iTT T (3-8) Finally, DIANA approximates t T numerically at m = 1,,n points and uses equations (3-1) and (3-2) to calculate the co rresponding degree of reaction de pendent heat production rate q r,m 11 11 mm m m mmtt TT c t T cq (3-9) mT m mrq q q, (3-10) 45

PAGE 46

The preprocessing method was utilized in this research. This method was chosen because the adiabatic temperature rise with respect to tim e, which is the output obtained from the semiadiabatic calorimetry test (shown in Figure 33), could be conveniently input into DIANA directly. Power data obtained from isothermal calorim etry testing on cementitious mixtures, shown in Figure 3-4, can be integrated with re spect to time to obtain the energy rise, t tdtPQ0 (3-11) which is then approximated to th e energy rise of the hydrating conc rete that is being represented by the mixture by multiplying by the percent cementi tious content. The cementitious content of concretes mixtures that will be used to validate the model are presented in Table 3-3. Finally, the adiabatic temperature rise, presente d in Figure 3-5, is calculated from the energy using the relationship described by the first law of thermodynamics and expressed in Equation 312. This method was used to maintain consistency in the type of input used to describe the concrete hydration. TCmQp or pCm Q T (3-12) Where: Q = energy rise (J) m = mass of concrete (g) C p = specific heat capacity (J/g-C) T = the change in temperature or temperature rise (C) Conductivity and Heat Capacity Heat energy transferred by way of conduction is caused by the physical interaction between adjacent molecules that have different temperatures. Experimental observations have shown that in the one dimensional plane, the rate of heat transfer through a finite area can be 46

PAGE 47

expressed by what is known as the Fourier la w of conduction, expresse d by Equation (3-13), and illustrated in Figure 3-6. x T kAqx x (3-13) where, q x = Heat Flow, J k = the thermal conductivity, J/m-hr-C A = The surface area, m 2 T = Temperature, -C x = coordinate, m The thermal conductivity of a solid is its ability or the ease wi th which it transmits heat. The minus sign denotes a negative temperature gradient reflecting the fact that the heat flows in the direction of decreasing temperature. Expanded to the three-dimensional case, as shown in Figure 3-7, the Fourier equation for heat transfer becomes z T k y T j x T ikTkqn (3-14) Where, x, y, z = the axes of the coordinate system i, j, k = the vectors directi ons in the coordinate system Consider the case of a heat-c onducting solid such as mass c oncrete which also has an internal source of heat generation. If q* is used to denote the rate at which heat is being internally generated per unit volume, then total heat generated = q*( dx dy dz ) (3-15) 47

PAGE 48

The law of conservation of energy th en states that energies in e quations (3-14) and (3-15) must be equal to the rate of energy storage reflected in the time rate of change of the average temperature, t avg given by dzdydx x t t cavg p (3-16) If we set the equality and divi de by the volume of the element, dx dy dz while allowing dx dy and dz to go to zero, and t avg to go to t q z t k zy t k yx t k x t cp (3-17) This equation represents a volumetric heat balanc e which must be satisfied at each point in the body, and describes the dependence of the temperat ure in a solid on the sp atial coordinates and on time. With the results of the thermal diffusivity and specific heat capacity experiments described in Chapter 6, the conductivity of conc rete created based on the cementitious mixtures can be calculated by using the relationship pCk (3-18) Where, diffusivity m 2 /hr = density kg/m 3 = heat capacity J/gram-C pC The conductivity and heat capacity values of the polystyrene foam we re obtained from the manufacturers specifications, while for the plywood, the typical conductivity and specific heat capacities for plywood used in North America were used. 48

PAGE 49

Convection Convection refers to the energy transported as a result of macroscopic motion. In other words, the transfer of heat from the surface of a material to a fluid that is moving over it. Figure 3-8 presents an approach to the analysis of convection heat tran sfer from a surface from which equation 3-19 is derived. FsscTTAhq (3-19) where, q c = the rate of heat transfer W/m 2 -C T s = temperature at the Surface C T F = Fluid temperature C A s = the surface area m 2 h = the mean coefficient of heat transfer The heat lost and gained to the surrounding environment by the hydrating concretes exposed surface and also the interaction of the foam with ambient conditions is modeled by imposing boundary convection elements. This is conveniently done using the convection element found in DIANA to specify the convection and boundary conditions. The heat flow through the surface of the elements, q S due to convection is modele d by the following equation: q S = h c ( e S ) (3-20) where: h c = the convection coefficient, W/m 2 -C e = the external environment temperature, C S = the surface temperature of the concrete block, C The convection coefficient can be constant, temperature-dependent, or time dependent. The convection coefficient was calculated using the equation smv v smvv hc/5 ,6.7 /5,95.36.578.0 (3-21) 49

PAGE 50

where, v = the wind speed, m/s In this research, a constant conve ction coefficient value of 5.6 W/ m 2 -C or 20106 J/m 2 hr-C was used for all analyses since all experimentation was conducted in a controlled environment which was maintained at a constant temperature with negligible forced air flow. Model Geometry Figure 3-9 shows the model depicting the conc rete exposed to ambient conditions at the top surface and with the plywood and polystyrene in sulation at the bottom and sides. To improve the efficiency of the analysis, advantage was taken of the double symmetry of the block which allowed for the modeling of one-quarter of th e block. The polystyrene insulation, plywood and concrete were explicitly di scretized and modeled according to their corresponding thermal properties. Boundary Conditions The boundary conditions imposed for the thermal analysis consisted of an initial temperature of the model and the external temp erature. Both temperatures were set at the temperatures recorded inside the laboratory on the day each concrete mix was made. Figure 3-10 presents the temperature histor y of the laboratory during the monitoring of the experimental blocks. The description of the block e xperiment is presented in Chapter 5. The average temperature of the laboratory fo r Blocks 1, 2 and 3 which were cast during the summer months of July and August was a pproximately 23 C, while for Block 4 which was cast in October was 20 C. Figure 3-11 shows the ex ternal temperature load of 23 C that was imposed on the BQ4HT boundary convection el ements in the model for Mixture 1. 50

PAGE 51

Table 3-1. Example of direct input of concrete internal heat production Degree of Hydration 0.10 0.20 0.25 0.40 0.5 0.60 0.75 0.90 1.0 Heat Production Rate (J/m 3 -hr) 0.320 0.850 0.960 1.00 0.890 0.400 0.230 0.060 0.00 Total Heat Produced (J/m 3 ) 3.23e4 Maximum Value of Heat Production Rate (J/m 3 -hr) 7.5e9 ARRHEN 5000 Table 3-2. Example of adiaba tic temperature rise input ADIAB 0.0 23.0 0.1 25.5 0.2 31.8 0.3 34.3 0.4 38.7 0.5 44.1 1.0 50.9 2.0 54.6 3.0 57.4 4.0 61.6 5.0 66.7 6.0 69.5 8.0 73.3 10.0 75.3 70.0 75.3 ARRHEN 5000 Table 3-3. Cementitious content of each mixture Mixture # 1 2 3 4 Percentage of Mixture that is cementitious paste by weight 27.10% 27.10% 27.50% 27.50% 51

PAGE 52

A B Figure 3-1. Elements used to model early age concrete behavior. A) Twenty-node Isoparametric Solid Brick Element CHX60. B)Eight-node Isoparametric Brick Element HX8HT. Figure 3-2. Four-node Isoparame tric Boundary Element BQ4HT 52

PAGE 53

0 10 20 30 40 50 60 70 80 90 020406080100120140160180Time (hours)Temperature ( C) Mix 1 100% Portland Cement Mix 2 50% Portland Cement 50% Slag Mix 3 65% Portland Cement 35% Fly Ash Mix 4 65% Portland Cement 30% Slag 20% Fly Ash Figure 3-3. Adiabatic temperatur e rise of each concrete mixtur e obtained from semi-adiabatic calorimetry testing 0 5 10 15 20 25 01020304050607080901Time (hours)Power W/g 00 Mix 1 100% Portland Cement Mix 2 50% Portland Cement 50% Slag Mix 3 65% Portland Cement 35% Fly Ash Mix 4 50% Portland Cement 30% Slag 20% Fly Ash Figure 3-4. Hydration power of each cementitious mixture obtained from isothermal calorimetry testing 53

PAGE 54

0 20 40 60 80 100 120 020406080100120140160180Time (hours)Temperature ( C) Mix 1 100% Portland Cement Mix 2 50% Portland Cement 50% Slag Mix 3 65% Portland Cement 35% Fly Ash Mix 4 50% Portland Cement 30% Slag 20% Fly Ash Figure 3-5. Adiabatic temperatur e rise of each concrete mixtur e calculated from the hydration power obtained in the isothermal calorimet ry testing of cementitious mixtures Figure 3-6. One dimensiona l conduction heat transfer 54

PAGE 55

Figure 3-7. Differential volum e for a rectangular solid Figure 3-8. Convection heat transfer (Funda mentals of Heat Transfer, Lindon C Thomas) 55

PAGE 56

Figure 3-9. Finite element model of concrete block with insulation 0 5 10 15 20 25 30 020406080100120140160180200Time (hours)Temperature (C) Mix 1 Mix 2 Mix 3 Mix 4 Figure 3-10. Ambient temperatures dur ing experimental block monitoring 56

PAGE 57

Figure 3-11. External temperatures imposed on finite element model representing the ambient conditions of the laboratory 57

PAGE 58

CHAPTER 4 FINITE ELEMENT ST RUCTURAL MODEL Introduction Heat produced during the hydration of concrete cau ses an increase in its temperature. However, because there is the combined effect of the hydration process not being homogeneous and a loss of heat to the surrounding environment, temperature differences will occur throughout the concrete element. These temperature differences can induce thermal strains and stresses that could potentially initiate cracking if they exceed the early age tensile strength of the concrete. The temperature distribution solution obtained from the thermal analysis is imposed as a thermal load in the structural analysis of the concrete. The mechanical response to the stresses induced by the ther mal gradient is greatly dependent on the physical characteristics of the concrete. This chapter will describe the elements used in DIANA to model the concrete and the physical input parameters required to measure the mechanical behavior. Element Selection As stated in Chapter 3, the structural be havior of the concrete block was modeled using the three dimensional twenty-node CHX60 isoparametric solid brick element reproduced here in Figure 4-1. By default, a 3 x 3 x 3 integration scheme is applied, but a 2 x 2 x 2 integration scheme can be used in a patch of more than one element to obtain optimal stress points. The stress and strain distribution is approximated over the volume of the element. Stress xx and strain xx vary linearly in the x direction and quadratically in the y and z directions. Stress yy and strain yy vary linearly in the y direction and quadratically in the x and z directions. Stress zz and strain zz vary linearly in the z 58

PAGE 59

direction and quadr atically in the x and y directions. It utilizes linear interpolation and Gauss integration in its computational scheme. Material Model The modeling of the structural behavior presented a few challenges as early age concrete exhibits both an elastic component and a viscous component. To model the linear elasticity of the concrete, the Youngs modulus E Poissons ratio v and coefficient of thermal expansion a, were directly input into the model. The viscoelastic behavior was mode led based on a Maxwell chain which is also in the form of the direct input of the progression of the Youngs modulus with age. The potential for cracking is tracked by sp ecifying the tensile strength evolution by way of a discrete function that is dependent on time. Input Parameters Modulus of Elasticity Cracking in mass concrete occurs when the tensile stresses induced by the thermal gradients are greater than the tensile stre ngth. The modulus of elasticity (MOE) of concrete is the ratio between the stress and re versible strain and is important because it influences the rigidity of the concrete structure. This linear re lationship is known as Hookes Law and is expressed in Equation 4-1 E (4-1) Where, = stress (MPa) E = Youngs Modulus (MPa) = linear strain 59

PAGE 60

The elastic limit represents the maximum allo wable stress before the concrete will crack and undergo permanent deformation. In heterogeneous multiphase materials like concrete, the modulus of elasticity increases as it hydrates, which is detrimental to the concrete because the probability of cracking increases as the modulus increases. Poissons Ratio Poissons ratio is the ratio of the lateral st rain to the axial stra in within the elastic range of the concrete. Accord ing to Mehta and Monteiro (1976), Poissons ratio has no consistent relationship with the curing age of the concrete. Valu es obtained during the testing for compression modulus of elasticity was c onsistently 0.2, which is within the universally accepted range of 0.15 and 0.20 for concrete. Coefficient of Thermal Expansion The coefficient of thermal expansion is used to describe the sensitivity of concrete expansion or contraction to changes in temper ature. It is defined as the change in unit length per degree of temperature change (M ehta and Monteiro 1976). The value of the coefficient of thermal expansion is particul arly important in mass concrete because the strain induced during the c ooling period is dependent on both the magnitude of the change in temperature and the co efficient of thermal expansion. Tensile Strength In normal concrete applications, the low te nsile strength of concrete is usually of little concern because reinforcing steel bars, which have high tensile strength values, are used to increase the overa ll strength of the structure. However, in mass concrete applications, the use of steel is either impractical, such as in the case of dams, or due to 60

PAGE 61

the size of the structure, the spaces between the steel are large creating elements that are weak in tension. There are two tests commonly used to estimate the tensile strength of concrete. They are the ASTM C 78 third-point flexur al loading test, and the ASTM C 496 splitting tension test, both of which are described in Chapter 6. Symmetry and Boundary Conditions The boundary conditions imposed for the stru ctural analysis of the quarter block consisted of the restriction of displacements along the symmetry planes. The base of the block was modeled as being in a fixed s upport condition and so displacements along the Z direction were also rest ricted. Both conditions ar e presented in Figure 4-2. 61

PAGE 62

Figure 4-1. Twenty-node Isoparametric Solid Brick element CHX60 Figure 4-2. Symmetry conditi ons and supports of model 62

PAGE 63

CHAPTER 5 BLOCK EXPERIMENT Introduction To verify that the finite element model cr eated is effective in modeling the early age behavior of hydrating mass concre te, four different mixes of c oncrete, typical of use in mass concrete applications in Florid a, were produced. Each mixture was used to make large concrete blocks with dimensions that qualify them to be characterized as massive concrete elements. Measurements of the temperature and strain at predetermined loca tions within the blocks were recorded until the equilibrium temperature was achieved. These temperatures and strains will then be compared with the results obta ined from the finite element model. Concrete Mix Design All of the four concrete mixes used in th is study had a water to cementitious material ratio of 0.5 to allow for compatibility with isothe rmal calorimetry testing that will be used to determine the activation energies and h eat of hydration of each concrete mix. Mix 1 consisted of 100% Type I Portland cement concrete; Mix 2 had 50% of the Portland cement mass replaced by ground granulat ed blast-furnace slag; Mix 3 contained 65% Portland cement and 35% Class F fly ash; and Mix 4 was a blend of 50% Portland cement, 30% granulated blast furnace slag, 20% Class F fly ash. The mix designs for each block are shown in Table 5-1. The coarse and fine aggregates were adjusted according to the volumetric differences caused by the varying densities of each cementitious material. Block Geometry Two 42 x 42 x 42 (1.07m x 1.07m x 1.07m) forms were created for pouring of the experimental concrete blocks. The geometry of the blocks is presented in Figure 5-1. The side faces and base of both blocks consisted of a 0.75 inch thick plywood formwork surrounded by a 63

PAGE 64

three inch thick layer of polysty rene plates. However, one of th e blocks had a cover with the same make up as the sides placed on its top surface af ter pouring was completed in an effort to simulate a fully adiabatic process, while the top face of the other block was left open and exposed to environmental conditions. Figure 5-2 is a photograph of the two blocks after the concrete had been poured. Instrumentation for Data Collection The two concrete blocks were instrumented for the monitoring of early age temperatures and strain at predetermined locations. The da ta acquisition equipment consisted of Type K thermocouples with an accuracy of 2.2 C and embedded strain gages. The layout of the thermocouples and strain gages are presented in Figure 5-3 through Figure 5-5. The thermocouple data and the strain da ta were recorded in order to validate the finite element models ability to accurately pred ict the early age behavior of the concrete block specimens Temperature Profiles The location of the thermocouples in the bloc ks were chosen to capture the temperature difference between the center of the block and the exposed surface, as well as to monitor the near surface temperature gradient to determine if it would contribute to thermal cracking of the concrete. The thermocouples at the sides and bottom of the block were placed to validate the effectiveness of the insulation and by extensi on the thermal boundary conditions that would be used in the finite element model. The temperatures measured by the thermocouples placed along the center of the uncovered concrete block of mix 1 are presented in Figure 5-6. It can be seen that, as expected, the highest temperature, 67 C at 20 hours after pouring, was measured at the center of the block (21 inches below the top surface). The peak temper ature measured at the bottom of the block (42 64

PAGE 65

inches below the top surface), also 67 C, but occurring 33 hours after the concrete is poured, shows that the assumption that the bottom is insulate d is valid. It is also shown, as expected, that the lowest temperatures were recorded in the thermocouples located nearest to the exposed top surface of the concrete block. The temperature data shown in Figure 5-7 pr ovide the temperature profiles measured by the thermocouples located 2 inches from the side surface of the uncovered block. The maximum temperature of 65 C is again recorded at th e thermocouple located 21 inches below the top surface. This temperature is 2.0 C less than the temperature recorded at the center of the block, which is within the thermal tolerance of 2.2 C of the thermocouples. This again serves to validate the assumption of the sides of the block being well insulated. The temperature profile for the uncovered concrete block with a cement replacement of 50% ground granulated blast-furnac e slag is presented in Figure 5-8. As expected in concrete containing slag, the section of the profile representing the incr easing temperatures has a slope that is less than that obtained in the concrete containing 100% Portland cement. This is due to ground granulated blast-furnace slag having a ve ry slow rate of hydration reaction. It is interesting to note that while the peak temperatur e for this concrete was approximately the same as the concrete containing 100% Portland cement in mix 1, it occurred 40 hours after being poured, approximately twice as long. Figure 5-9 shows the temperatures measured in the concrete of mix 3 in which 35% of the Portland cement was replaced by fly ash. The te mperature increase trend in this block shows a lower heat of hydration rate as compared with what was obt ained in mix 1 containing 100% Portland cement. The peak temperatures at each location we re lower in mix 3. 65

PAGE 66

The combined effects of the ground granulated blast-furnace slag and the fly ash on the hydration rate and peak temperatures of the concre te respectively, is seen in the temperature-time plots of mix 4 presented in Figure 5-10. The slope of the profile during th e temperature increase period is very similar to the trend observed in mix 2, showing a slower rate of temperature rise as compared with mix 1 and mix3. The peak temperat ure in mix 4 was much lower than those of mixes 1 and 2, similar to that of mix 3. 66

PAGE 67

Table 5-1. Mix designs of concrete used in the large-scale blocks Material Mix 1 100% Portland Cement (lb/yd 3 ) Mix 2 50% Portland50% Slag (lb/yd 3 ) Mix 3 65% Portland35% Fly Ash (lb/yd 3 ) Mix 4 50% Portland30% Slag-20% Fly Ash (lb/yd 3 ) Cement 681 341 443 341 GGBF Slag 0 341 0 204 Fly Ash 0 0 238 136 Water 341 341 341 341 Fine Agg. 1095 1088 1036 1050 Course Agg. 1650 1668 1660 1650 67

PAGE 68

Figure 5-1. Experiment al block geometry Figure 5-2. Uninsulated (left) and insula ted (right) mass concrete block specimens 68

PAGE 69

Figure 5-3. Thermocoup le location (Plan) Figure 5-4. Thermocoup le location (Section) 69

PAGE 70

Figure 5-5. Instrumentation la yout for experimental block 0 10 20 30 40 50 60 70 020406080100120140160180200220240260280300Time (hr)Temperature (C) Center 1" Below Top Surface Center 2" Below Top Surface Center 4" Below Top Surface Center 21" Below Top Surface Center 42" Below Top Surface Figure 5-6. Temperatures al ong the center line of the unc overed concrete block mix 1 70

PAGE 71

0 10 20 30 40 50 60 70 020406080100120140160180200220240260280300Time (hr)Temperature (C) 2" Side 1" Below Top Surface 2" Side 2" Below Top Surface 2" Side 4" Below Top Surface 2" Side 21" Below Top Surface Figure 5-7. Temperatures 2 from the side of the uncovered block in mix 1 0 10 20 30 40 50 60 70 80 020406080100120140160180200Time (hrs)Temeperature (C) 1" Center Below Top Surface 2" Center Below Top Surface 4" Center Below Top Surface 21" Center Below Top Surface 42" Center Below Top Surface Figure 5-8. Temperatures along the center line of the uncovered block in mix 2 71

PAGE 72

0 10 20 30 40 50 60 020406080100120140160180200220Time (hours)Temperature (C) Center 1" Below Top Surface Center 2" Below Top Surface Center 4" Below Top Surface Center 21" Below Top Surface Center 42" Below Top Surface Figure 5-9. Temperatures along the center line of the uncovered block in Mix 3 0 10 20 30 40 50 60 70 020406080100120140160180Time (hours)Temperature (C) Center 1" Below Top Surface Center 2" Below Top Surface Center 4" Below Top Surface Center 21" Below Top Surface Center 42" Below Top Surface Figure 5-10. Temperatures along the cente r line of the uncovered block in mix 4 72

PAGE 73

CHAPTER 6 MATERIAL TESTS AND PROPERTIES Introduction The laboratory testing of th e concrete mixtures used to create each of the experimental blocks focused on characterizi ng and relating the heat production, maturity, physical and strength properties of concrete at early ages. The results obtained were used as input parameters for the finite element model of the blocks. Heat of Hydration The determination of the heat generated during the hydration of the concrete is essential for the characterization of its th ermal behavior at early ages. Two of the experimental methods in use today, Semi -Adiabatic Calorimetry and Isothermal Calorimetry testing, were u tilized in this research. Semi-Adiabatic Calorimetry A Semi-Adiabatic Calorimeter is defined as a calorimeter where the maximum heat losses are less than 100J/(Kh) (RILEM 1997 p451). Semi-adiabatic calorimetry is used in this research instead of adiabati c testing because producing a true adiabatic testing system is extremely difficult and tech nically advanced as it requires a controlled supply of heat to the system over time. The Semi-adiabatic calorimetry system is a purely passive one which only requires the monitoring of time, temper ature and the heat flux for the acquisition of temperature data. The system consists of an insulated cylinder which contains two thermocouples and a heat-flu x sensor. One of the thermocouples is embedded into the concrete specimen in the center of the calorimeter while the other thermocouple is located on the exterior. The heat flux sensor is embedded within the 73

PAGE 74

insulation of the semi adiabatic calorimeter. Figure 6-1 presents the energy history recorded from the concrete produced from mix 1. Isothermal Conduction Calorimetry Isothermal conduction calorimetry is a very useful testing method for the determination of the heat energy that is evolved from the hydration of a cementitious material over time. It provides a direct meas urement of the heat generated by a specimen, avoiding the errors associated with methods th at utilize chemical analyses. The resulting data from the heat-flow sensor in the calorimeter is a voltage signal (in the order of millivolts) that is proportional to the thermal pow er from the sample. The integral of the thermal power over the time of the test is th e heat of hydration of the specimen. For this research, a relatively small sample (6 grams) of the cementitious material used in each mass concrete block was taken and tested in the isothermal calorimeter. The specimens were tested at temperatures of 15 C, 23 C, 38 C, and 49 C. The data curves produced by the test at each temperature were analyzed for the energy rise versus time, as presented in Figure 6-2. This plot show s a trend of the energy rise with respect to time being significantly larger as the test temperature is increased. However, Figure 6-3 indicates that regardless of the test temperature, the values for the energy rise with respect to equivalent age are virtually e qual. Therefore, from this observation we can obtain the relationship between energy rise and temperature rise which can then be used in the input for the finite element model. Figures 6-4 to Figure 6-6 show the energy ri se with respect to equivalent age for mixes 2, 3 and 4 respectively. All except the plot for mix 2 indicate that the values of the energy rise with respect to equivalent ag e are essentially same. The reason for the 74

PAGE 75

anomaly in mix 2 is not fully understood but is attributed to the high replacement of Portland cement (50%) with ground granulated blast-furnace slag. The full procedures and explanation of the Semi-Adiabatic Calorimetry and Isothermal conduction calorimetry tests are described by Ferraro (Dissertation, 2009). Specific Heat Capacity Specific heat is the amount of heat requi red per unit mass to cause a unit rise of temperature. The specific heat capacity testi ng in this research is being conducted with a calorimeter similar to the apparatus used by De Schutte r and Taerwe, 1995, shown in Figure 6-7. It contains an interi or bath of oil and an exterior bath of polypropylene glycol. These liquids were chosen because of their ability to rapidly transfer heat. A known flux of heat energy (E1) is supplie d to the interior bath containing oil and the resulting temperature increase (1) observed. The stir paddle is used to distribute the heat evenly throughout the interior bath. The cementitious material was then added to the oil bath and energy (E2) was again supplie d to the bath. The resulting change in temperature of the cementitious material (2) is the final temperature minus the initial temperature of the cementitious material at introduction to the bath. The specific heat capacity of cementitious material then calculated using the following formula. 1 1 2 21EE m Cc (6-1) Thermal Diffusivity Thermal diffusivity is a measure of th e ease or difficulty with which concrete undergoes temperature change (A CI 207.2). Diffusivity is direc tly related to the type of aggregate used and the density of the concrete The higher the diffusiv ity value, the easier it is for the concrete to gain or lose heat. 75

PAGE 76

Three cylindrical 6 x 12 c oncrete specimens instrumented with thermocouples at the center of their mass are removed from the moist cure room where they were maintained at a temperature of 73 F 2 F ( 0 ) and 100% relative humidity and placed in a water bath at temperature 0 + s the cylinders are heated by the hot water, the temperature (t) at the center axis of the specime ns are measured with respect to time until they reach a steady temperature of 176 F The results of the three cylinders are averaged, and inserted in the following equation: log[( 0 + (t))/ (6-2) Plotted as a function of time, the curve beco mes linear after some time, and the slope of this curve is directly related to the thermal diffusivity. The results of the test show that thermal diffusivity of the concrete used in th e first three blocks varies as concrete ages, presented in Figure 6-8. Flexural Strength The flexural strength of concrete is a measure of the tensile strength of the concrete. It is also often referred to as th e modulus of rupture (MOR). Beam specimens, shown in Figure 6-9, with dimensions of 6 x 6 x 22 in. are cast from the concrete used in the mass concrete blocks. The flexural strengt h of the concrete in this research was measured by applying two point loads to the unreinforced beam at 1/3 and 2/3 of the loaded span length of 18 inches, as shown in Figure 6-10. A load rate of 30 lbs/sec which is approximately 6% of the ultimate load as specified in ASTM C78, is applied to the beams so as to not induce significant creep, while restricti ng the occurrence of premature rupture. 76

PAGE 77

Figure 6-11 shows the stress and strain distribution, according to Bernoullis theorem. The modulus of rupture (MOR) of th e beam cross-section shown is taken as the maximum stresses in the extreme fibers. Figure 6-12 is a graphical representati on MOR versus time for the companion beam specimens cast from each mixture. The re sults are consistent with typical findings where the mixture containing 100% Portland cement gained flexural strength the fastest while the mixture in which 35% of the Po rtland cement is replaced by fly ash gains flexural strength the slowest. The mixt ure containing 50% slag and the mixture containing the ternary blend gained flexural st rength at a rate between the mixtures with 100% Portland cement and 35% fly ash. Splitting Tensile Strength The splitting tensile strength test was performed on 4 x 8 in. cylinders specimens, sampled from each concrete mixture, in accordance with ASTM C496, the set up of which is shown in Figure 6-13. The tests were carried out at ages of 1, 2, 3, 7, 14 and 28 days and are presented in Figure 6-14 were the strength development over time of the concrete of each mix is observed. As was the ca se in the flexural beam test, the concrete containing 100% Portland cement gained streng th the fastest, the c oncrete with 35% fly ash gained strength the slowest, while the concretes that contained 50% slag and the ternary blend gained strength at a rate between them. The results obtained from the splitting tensi on test were used as the inputs for the finite element model of the experimental c oncrete blocks. These results were chosen because they are the smaller than the results obtained from th e flexural test and therefore are more conservative. 77

PAGE 78

Modulus of Elasticity a nd Poissons Ratio Testing The compressive modulus of elasticity and Poissons ratio of concrete was determined using the ASTM C469 standard te st method. The rate of development of the modulus of elasticity wi th age, obtained from the compression testing of 4 inch by 8 inch cylinder samples taken from each concrete mi x used in the experimental blocks is presented in Figure 6-15. The stress-strain relationship obtained from the middle third section of the beams during the flexural tests descri bed previously was used to ca lculate the tensile modulus of elasticity of the resp ective concrete mixtures, show n in Figure 6-16. This was done because cracking in mass concrete is primar ily a phenomenon of tensile action, which is also the failure mode of the flexural test beams. The compressive modulus, which was highe r of the two type s of modulus of elasticity, was used in the finite element analysis as it is the more conservative description of the stress-strain relationship of the concrete. Coefficient of Thermal Expansion Testing The results of testing for the coefficien t of thermal expansion of the concrete mixtures used in this research are shown in Figure 6-17. There was very little change in the values for each mix over the first seven days which is the duration of the analysis of the finite element model. It was thus decided that a c onstant input value for the coefficient of thermal expansion of each model block was sufficient for the analysis. Summary of Material Properties The thermal properties of the concrete are listed in Table 6-1. The effect of the ground granulated blast-furnace slag on the therma l behavior of the concrete in mix 2 and mix 4 is evident. The slower adiabatic temperature increases observed in the 78

PAGE 79

experimental blocks with these mixes can be attributed to the high activation energies, which is the energy that must be overcome in order for the hydration reaction to occur. Table 6-2 presents the ther mal conductivities and heat cap acities of the plywood and polystyrene insulation used in the formwork of the block. The mechanical properties used to desc ribe the strength development of the concrete are listed in Table 6-3. The effect of the ground granulated blast-furnace slag and fly ash on the early age strength of the conc rete in mixtures 2, 3 and 4 is evident. The tensile strength at day one in each mix is extremely low, confirming the theory that the benefit of lower rates of temperature rise produced by the use of supplementary cementitious materials occurs at the expens e of lower ductility, in a higher elastic modulus to strength ratio, a nd a reduced strain capacity. The constant values of Poissons ratio and the coefficient of thermal expansion are presented in Table 6-4. 79

PAGE 80

Table 6-1. Thermal properties of concrete CONDUCTIVITY (J/m-hr-C) HEAT CAPACITY (J/m 3 -C) ACTIVATION ENERGY (J/mol) Mixture 1 7920 2675596 34235 Mixture 2 4418 2017434 50400 Mixture 3 5883 2603101 32982 Mixture 4 4838 2024985 37330 Table 6-2. Thermal properties of plywood and polystyrene CONDUCTIVITY (J/m-hr-C) HEAT CAPACITY (J/m 3 -C) Plywood 540 85440 Polystyrene 224.85 20824 Table 6-3. Mechanical properties of concrete Time (Days) Modulus of Elasticity (MPa) Tensile Strength (MPa) 1 13445 1.25 2 16892 1.66 3 18064 1.93 7 20236 2.206 Block 1 (100% Portland Cement) 14 22248 2.972 28 25213 3.303 1 8618 0.255 2 13170 0.807 3 14893 1.23 7 19443 2.31 14 21481 2.45 Block 2 (50% Portland 50% Slag) 28 24921 2.99 1 9791 0.669 2 13996 0.931 3 14479 1.28 7 16547 1.63 14 18985 1.91 Block 3 (65% Portland 35% Fly ash) 28 25235 3.30 1 7722 0.393 2 10963 0.765 3 1.01 7 16905 1.82 14 20053 2.20 Block 4 (50% Portland 30% Slag 20% Fly Ash) 28 23352 2.85 80

PAGE 81

Table 6-4. Mechanical properties of concrete Poissons Ratio Coefficient of Thermal Expansion (in/in -C) Block 1 0.19 9.16E-06 Block 2 0.20 1.11E-05 Block 3 0.20 1.11E-05 Block 4 0.20 1.004E-05 81

PAGE 82

0 50 100 150 200 250 300 350 400 0 50 100150200250300350400Time (hours)Energy (J/g) Concrete Semi-Adiabatic Figure 6-1. Resultant semi-adiabatic calorimetric energy curve for mix 1 0 50 100 150 200 250 300 350 400 0 50100150200250300350400Time (hours)Energy (J/g) Cement Isothermal (15 C) Cement Isothermal (23 C) Cement Isothermal (38 C) Cement Isothermal (49 C) Figure 6-2. Resultant isothermal calorimetric curves with regard to energy versus time for mix 1 82

PAGE 83

0 50 100 150 200 250 300 350 400 0 50100150200250300350400Equivalent A g e (Hours) Energy (J/g) Cement Isothermal (15 C) Cement Isothermal (23 C) Cement Isothermal (38 C) Cement Isothermal (49 C) Figure 6-3. Resultant isothermal calorimetri c curves with regard to energy versus equivalent Age for mix 1 0 50 100 150 200 250 300 350 400 0 50100150200250300350400Equivalent Age (hours)Energy (J/g) Cement Isothermal (15 C) Cement Isothermal (23 C) Cement Isothermal (38 C) Cement Isothermal (49 C) Figure 6-4. Resultant isothermal calorimetri c curves with regard to energy versus equivalent Age for mix 2 83

PAGE 84

0 50 100 150 200 250 300 350 400 0 50 100150200250300350400Equivalent Age (hours)Energy (J/g) Cement Isothermal (15 C) Cement Isothermal (23 C) Cement Isothermal (38 C) Cement Isothermal (49 C) Figure 6-5. Resultant isothermal calorimetri c curves with regard to energy versus equivalent Age for mix 3 0 50 100 150 200 250 300 350 400 0 50 100150200250300350400Equivalent Age (hours)Energy (J/g) Cement Isothermal (15 C) Cement Isothermal (23 C) Cement Isothermal (38 C) Cement Isothermal (49 C) Figure 6-6. Resultant isothermal calorimetri c curves with regard to energy versus equivalent Age for mix 4 84

PAGE 85

Figure 6-7. Schematic of the speci fic heat capacity calorimeter 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 1271 42 8Age (Days)Diffusivity (ft2/in) Block 1 Block 2 Block 3 Block 4 Figure 6-8. Thermal diffusivity vs. age of the experimental blocks 85

PAGE 86

Figure 6-9. Beam specimens fo r flexural strength testing Figure 6-10. Beam specimen unde rgoing flexural strength testing 86

PAGE 87

Bernoulli's Beam TheoryStrain Stress Tension Compression Beam Cross-Section c fc Neutral Axis Figure 6-11. Theoretical stress and strain distribution through beam cross section 0 100 200 300 400 500 600 700 0 5 10 15 20 25 30Age (days)MOR (psi) 100% PCC 50% Slag 35% Fly Ash 30% Slag 20% Fly Ash Figure 6-12. The modulus of rupture of the beam specimens taken from mixtures 1, 2, 3 and 4 87

PAGE 88

Figure 6-13. Diagrammatic arrangement of splitting tension test ASTM C496 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 30Age (Days)Splitting Stregth (MPa) Mix 1 100% Portland Cement Mix 2 50% Portland Cement 50% Slag Mix 3 65% Portland Cement 35% Fly Ash Mix 4 50% Portland Cement 30% Slag 20% Fly ash Figure 6-14. Splitting tensile strength of concrete used in mixtures 1, 2, 3 and 4 88

PAGE 89

0 5000 10000 15000 20000 25000 30000 0 5 10 15 20 25 30Age (Days)MOE (MPa) Mix 1 100% Portland Cement Mix 2 50% Slag Mix 3 35% Fly Ash Mix 4 30% Slag 20% Fly Ash Figure 6-15. Compressive modulus of elasticity versus time 0 5000 10000 15000 20000 25000 0 5 10 15 20 25 30Time (days)MOE (MPa) Mix 1: 100% Portland Cement Mix 2: 50% Portland Cement 50% Slag Mix 3: 65% Portland Cement 35% Fly Ash Mix 4: 50% Portland Cement 30% Slag 20% Fly Ash Figure 6-16. Tensile modulus of elasticity versus time 89

PAGE 90

0.00E+00 2.00E-06 4.00E-06 6.00E-06 8.00E-06 1.00E-05 1.20E-05 1.40E-05 0 5 10 15 20 25 30Age (Days)CTE (in/in/C) Mix 1 100% Portland Cement Mix 2 50% Portland Cement 50% Slag Mix 3 65% Portland Cement 35% Fly Ash Mix 4 50% Portland Cement 30%Slag 20% Fly Ash Figure 6-17. Coefficient of thermal e xpansion versus time for each mixture 90

PAGE 91

CHAPTER 7 THERMAL ANALYSIS RESULTS Introduction In this chapter, the temperatures calculat ed in the model block using the energy input from Semi-Adiabatic and Isothermal calorimetry testing are presented and discussed. The results are compared with temperatures in the experimental block measured by embedded thermocouples. The locations of the thermocouples in the block were presented in Chapter 5. They are duplicated in Figure 7-1 and Figure 7-2 for convenience. The degree of hydration and the equivalent ag e with respect to actual time at the top (Element 5069) and central (Element 4069) regions of the model block were conducted and are presented in Figures 7-3 and 7-4 respectively. The equivalent age of each point in the concrete is calculated according to the Arrhenius-type equation t dt eet0 T(t) 1 T 1 R Earef (7-1) Where: t e = equivalent age at the re ference temperature, hours T(t) = average temperature of concrete at time t, C T = reference temperature, C E a = activation energy of concrete, J/mol R = universal gas constant, 8.3144 J/mol-C It can be seen from these two plots that th e rate of hydration and hence the maturity of concrete varies within the block due to the different time-tempe rature histories of the hydrating cement. Figure 7-5 shows the quarter block of hydrati ng concrete with insulation on the bottom and sides at time step 1. 91

PAGE 92

Semi-Adiabatic Calorimetry Finite Element Results Points 2 inches, 4 inches, and 21 inches belo w the top surface along the centerline of the block were chosen for the analysis. These locations were chosen because various DOT specifications for mass concrete generally limit th e temperature differential, measured between temperature sensors, between the midpoint and a point 2 inches inside the exposed face. Figures 7-6 through to 7-17 show the comparis on of the temperatures measured in the experimental blocks of each mixture, with the temperature profiles with respect to time produced by the analysis with DIANA. The trends for the increase and decrease temperature produced by the finite element model for the block containing Mixture 1 were similar to the trend recorded experimentally at all three locations. The time lag in the finite elem ent model with respect to the experimental temperatures can be attributed to the delivery of the concrete over an hour after the commencement of mixing whereas the beginning of the hydration reaction was captured by the semi-adiabatic calorimetry test. Usually the semi -adiabatic test is conducted on a sample of concrete obtained directly from the batch used in the block, however at the time of delivery for mixture 1 the FDOT computer server experi enced a communication failure delaying the initiation of the semi-adiabatic test per the IQ drum by approximately 7 hours. To correct this discrepancy, the mixture was recreated in the lab at a starting temperature of 23 C, and new specimens were created and used in the semi-adiabatic test. Figure 7-6 presents the temperatures 2 inches below the exposed top surface of the block. The peak temperature of 49.5 C calculated by the m odel is identical to the peak temperature of 49.3 C measured in the experimental block. On the face of it, this is an impressively accurate simulation, however the fact that the concrete in the experimental block spent over an hour in the delivery truck means that some energy which cannot be measured was lost to the environment. 92

PAGE 93

Another factor that should be ta ken into consideration is that a companion test that monitored cracking with the aid of acoustic emissions apparatus was being conducted. The dips in experimental blocks temperatur e represents each time the plasti c cover was lifted off to place the sensors. Figure 7-7 presents the temperatures 4 inches below the top surface. The peak temperatures of 52 C in the model and the peak temperature of 53.34 C measured in the experimental block lie within the .2 C accura cy of the thermocouples used. Again, the peak temperature in the experimental block is affected by the energy lost while the concrete was in the delivery truck and the lifting off of the cove r when placing the acoustic emission sensors. The block temperatures 21 inches below the top surface of the block are presented in Figure 7-8. At this distance from the surface, there seems to be little effect from the cover being lifted off to place the acoustic em ission sensors. The peak temper ature of 67.2 C measured in the experimental block is 6 C higher than the te mperature calculated by finite element model. It is important to reiterate that the trends in temperature gain and loss are similar. The results for mixture 2 show that the fin ite element model again produced an increasing temperature trend similar to that measured in the experimental block. The calculated temperatures in the model, shown in Figure 7-9, peaked at 39.6 C, thirty -eight hours after the start of the analysis. This is a significant 6 C lower than the peak temperature of 45.7 C occurring at 35 hours, measured in the experimental block. Figure 7-10 presents the temperatures 4 in ches below the top surface where a similar difference between the model and experimental te mperatures is observed. The temperature in the model peaked at 39 hours with a value of 42.4 C while the experimental block peaked at 49.6C in 33.6 hours. An even more significant difference between the analytical and experimental peak 93

PAGE 94

temperatures is observed 21 inches below the top surface of the block, 55 C and 67 C respectively, as pres ented in Figure 7-11. The results for mixture 3 show better corre spondence between the finite element model and the experimentally measured temperatures. Both the increase and decrease in temperature trends are similar. At a depth of 2 inches below the top surface the calculated peak temperature in the model, shown in Figure 7-12, was 40.2 C, while the peak temperature measured in the experimental block at the same depth was 41.8 C Figure 7-13 shows that at 4 inches below the top surface the peak temperatures were 42.5 C and 44.3 C in the model experimental block respectively. The temperatures at 21 inches are presented in Figure 7-14. Although the temperature trends are similar, the peak te mperature in the model is 51.6 C while the experimentally measured temperature was 56.4C, a difference of 4.5 C which is greater than the accuracy range of the thermocouples. The results for mixture 4 presented in Figur e 7-15 through to Figure 7-17 show the same trends as was reported previously for Mixtures 1 and 3 where at depths of 2 inches and 4 inches below the top surface, the difference between the calculated peak temperatures in the model and the measured peak temperatures in the experiment al blocks were within the accuracy of .2 C of the thermocouples. However at 21 inches, th e difference increases to approximately 4 C. Isothermal Calorimetry Finite Element Results Figures 7-18 through to 7-29 show a comparison of the temperature profiles with respect to time measured in the experimental block, w ith those obtained from the analytical finite element model using the energy input from the isot hermal calorimetry tests. Again, the locations within the block chosen for analysis are 2 inch es, 4 inches, and 21 inches below the top surface along the centerline of the block. 94

PAGE 95

The temperature-time histories of mixture 1 at 2 inches below the top surface produced by the finite element model and measured in the experimental block are pr esented in Figure 7-18. The increases in temperature for both are identica l however the predicted peak temperature in the model is 54.6 C while the experimentally meas ured peak temperature was 49.3 C. As reported earlier, the dips in the experime ntal blocks temperature represent each time the plastic cover placed over the block (to prevent evaporation of the surface water) was lifted off to place the sensors used by the crac k monitoring acoustic emissions appa ratus. This no doubt affected the peak temperature of points close to the top surface of the block. Figure 7-19 shows the comparison of the te mperature profiles 4 inches below the top surface. Again the peak temperature measured expe rimentally is affected by the removal of the plastic cover. The increase and subsequent decr ease in temperatures however are identical At 21 inches below the top surface, the effect of the removal of the plastic cover is negligible, and it can be seen in Figure 7-20 that the peak temper ature of 69 C calculated in the finite element model is only 2 C greater than the 67.2 C measured experimentally. Figure 7-21 shows the comparison between temp eratures calculated in finite element model and those measured experimentally in th e block containing mixture 2. Figure 7-22 is the comparison at 4 inches and Figure 7-23 at 21 inches. The maximum temperatures obtained in the m odel at the three locations are all within 2C of the temperatures recorded experiment ally. Considering that the accuracy of the thermocouples used measure the temperatures in the experimental bl ock .2 C, it can be concluded that the model has exactly modeled the behavior of the experimental block. The results for mixture 3 show good corres pondence between the fi nite element model and the experimentally measured temperatures. Both the increase and decrease in temperature 95

PAGE 96

trends are similar. At a depth of 2 inches belo w the top surface, the calculated peak temperature in the model, shown in Figure 7-24, was 43.6 C, while the peak temperature measured in the experimental block at the same depth was 41.8 C Figure 7-25 shows that at 4 inches below the top surface the peak temperatures were 46.4 C and 44.3 C in the model and experimental block, respectively. The temperatures at 21 inch es are presented in Figure 7-26. Although the temperature trends are similar, the peak te mperature in the model is 56.7 C while the experimentally measured temperature was 56.4 C, an insignificant difference of 0.3 C. The trend of the temperature increases obtaine d from the model of the block with mixture 4 differed from what obtained in the experime ntal block, as shown in Figures 7-27 through Figure 7-29. The reason for this difference is unk nown but the fact that the peak temperatures obtained at 2 inches, 4 inches and 21 inches we re all within 2.2 C of the peak temperatures measured in the experimental block and the decreasing trend is also similar provided enough comfort that the temperature gradient within the block was properly modeled. Summary of Findings The semi-adiabatic calorimeter was designed to obtain the temperature rise of the concrete in the field, therefore was never intended to serve as a high precision instrument. The temperature results for each of the mixtures mo deled were less than the temperatures measured experimentally. This suggests an underestimati on of the adiabatic temperature rise of the concrete mixtures and by extension confirms that not all the energy evol ved from the concrete was measured. The adiabatic temperature input from th e isothermal calorimetry tests produced temperature profiles that were very similar to the temperatures measured experimentally. In some cases the temperatures in the model were higher than what obtaine d in the experimental 96

PAGE 97

block. Accordingly, the temperatures obtained from isothermal calorimetry can be considered conservative, and thus the preferred input for modeling concrete. 97

PAGE 98

Figure 7-1. Thermocoup le location (Plan) Figure 7-2. Thermocoup le location (Section) 98

PAGE 99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 020406080100120140160180Time (hours)Degree of Hydration Element 4069 Center Element 5069 Top Center Figure 7-3. Degree of hydrati on at the center and top of the block in mixture 1 0 100 200 300 400 500 600 700 800 900 020406080100120140160180Time (hours)Equivalent Age (hours) Element 4069 Center Element 5069 Top Center Figure 7-4. Equivalent age at the cente r and top of the block in mixture 1 99

PAGE 100

Figure 7-5. Concrete quarter block with insulation at time step 1 0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-6. Semi-adiabatic and e xperimentally measured temperatur e-time histories at the center of the block, 2 below the exposed top surface of mixture 1 100

PAGE 101

0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-7. Semi-adiabatic and e xperimentally measured temperature-time histories at the center of the block, 4 below the exposed top surface of mixture 1 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-8. Semi-adiabatic and e xperimentally measured temperatur e-time histories at the center of the block, 21 below the exposed top surface of mixture 1 101

PAGE 102

0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-9. Semi-adiabatic and e xperimentally measured temperatur e-time histories at the center of the block, 2 below the exposed top surface of mixture 2 0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-10. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 4 below the exposed top surface of mixture 2 102

PAGE 103

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hrs)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-11. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 2 0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-12. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 2 below the exposed top surface of mixture 3 103

PAGE 104

0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-13. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 4 below the exposed top surface of mixture 3 0 10 20 30 40 50 60 020406080100120140160180Time (hrs)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-14. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 3 104

PAGE 105

0 10 20 30 40 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-15. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 2 below the exposed top surface of mixture 4 0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-16. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 4 below the exposed top surface of mixture 4 105

PAGE 106

0 10 20 30 40 50 60 020406080100120140160180Time (hrs)Temperature (C) Analytical Semi-Adiabatic Experimental Figure 7-17. Semi-adiabatic and experimentally measured temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 4 0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-18. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 1 106

PAGE 107

0 10 20 30 40 50 60 70 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-19. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 1 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hrs)Temperature (C) Analytical Isothermal Experimental Figure 7-20. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 1 107

PAGE 108

0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-21. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 2 0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-22. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 2 108

PAGE 109

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hrs)Temperature (C) Analytical Isothermal Experimental Figure 7-23. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 2 0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-24. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 3 109

PAGE 110

0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-25. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 3 0 10 20 30 40 50 60 020406080100120140160180Time (hrs)Temperature (C) Analytical Isothermal Experimental Figure 7-26. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 3 110

PAGE 111

0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-27. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 2 below the expos ed top surface of mixture 4 0 10 20 30 40 50 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 7-28. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 4 below the expos ed top surface of mixture 4 111

PAGE 112

0 10 20 30 40 50 60 020406080100120140160180Time (hrs)Temperature (C) Analytical Isothermal Experimental Figure 7-29. Isothermal and experimentally measur ed temperature-time histories at the center of the block, 21 below the exposed top surface of mixture 4 112

PAGE 113

CHAPTER 8 STRUCTURAL ANALYSIS RESULTS Stress Results In this chapter, the stresses and strains i nduced by the differences in temperature within the hydrating concrete using the isothermal calorimetry data ar e presented and discussed. As stated earlier, these temperatur e gradients are produced when th e heat being generated in the concrete is dissipated to the su rrounding environment causing the te mperature at regions close to the surface of the concrete to be lower than the temperat ure at the interior of the concrete. At the same time the heat generated is a function of the temperature and time history of the concrete, therefore individual locations in the concrete will experience different leve ls of heat. Figure 8-1 shows the location of the elements that will be an alyzed for their stress and strain states during the hydration process. These locations were chos en because the largest tensile and compressive actions will be experienced at the top and central region of the concrete respectively. Figure 8-2 presents the calculated stress in the X-X plane, occurring in the block with Mixture 1, with respect to tim e of Element 4069 (node 638) and Element 5069 (node 508) which are located at the center and top center of the finite element model respectively. The plot shows that the model accurately predicts Element 5069 undergoes tensile (positive) stresses as the concrete hydrates and expands, while Element 4069 experiences compressive stresses. This is consistent with the theory that a faster hydrati ng central region of a ma ssive concrete structure will be in compression as it tries to expand but is restricted by the less ma ture concrete around it. Figure 8-3 presents the calculated stress in th e X-X plane with respect to time of Element 4259 (node 1208) and Element 5159(node 618) which are located at the ce nter edge and top edge of the finite element model respectively. Element 5159 undergoes tensile (positive) stresses as the concrete hydrates and expands. Element 4259 also ac ts in tension as it is being pushed against by 113

PAGE 114

the expanding inner concrete. As expected, the maximum tensile stress of 1.34 MPa occurs at the top edge of the block in Element 5159. The effect on the induced stresses in the conc rete of Mixture 2 whic h contains slag is shown in Figure 8-4 and Figure 8-5. The peak tensile stresses in Element 5069 (0.97 MPa) and Element 5159 (1.18 MPa), at the top of block, were slightly less than the tensile stresses experienced in Mixture 1 cont aining 100% Portland cement, but occurred approximately 10 hours later. The similarities in peak tensile stress values is a resu lt of the closeness of the peak temperatures in each mixture, while the time diffe rence can be attributed to the slow rate of hydration, and hence slow rate of temperature increase, in the concrete. Inte restingly the stresses across the top of the block transition to comp ressive stresses 150 hours after placement. The stress at the center edge of th e block (Element 4259) acts in tens ion, as was the case in Mixture 1. The stress in Element 4069 begins in compre ssion but becomes tensile after 164 hours of hydration. The stresses produced in Mixture 3 were similar in trend to those obtained in Mixture 1. This is to be expected given th at the rate of temperature rise in Mixture 3 was steep as was the case of the temperature rise in Mixture 1. Fi gure 8-6 shows that the highest tensile stress experienced at the top center of the bloc k (Element 5069) was 0.878 MPa occurring 26 hours after concrete placement, while the maximum co mpressive stress of, 0.358 MPa, at the center of the block (Element 4069) occurred 40 hours afte r placement. The maximum tensile stress value of 1.10 MPa again occurred at th e top edge of the block (Eleme nt 5159) as shown in Figure 8-7. Figure 8-8 shows the stresses calculated in the top center and center of the block containing Mixture 4, while Figure 8-9 presents the stresses at th e edge. The tensile stresses induced in this block were si gnificantly less than the stresse s in Mixture 1and Mixture 3, but 114

PAGE 115

slightly larger than the stress es in Mixture 2. The rate of te mperature rise of Mixture 4 like Mixture 2, both of which were presented in Ch apter 7, was slow. Therefore this reduction in tensile stresses can likely be attributed to th e presence of the ground gr anulated blast-furnace slag. Cracking Potential Cracking in concrete will occur when the tensile stresses, induced by the temperature gradients, exceed the low tensile strength that exis ts at early ages. The probability of cracking is measured by the function presented in Equation 8-1 called the cracking index. )( )( )(t tf tII t cr (8-1) Where, I cr = the crack index f t = the tensile strength I = the maximum principal stress I cr is given a value of 100 if I 0.01f t If I cr falls below 1.0 this is an indication that cracking has been initiated. A plot of the progression of the crack index along the center line of the block in Mixture 1 is presented in Figure 8-10. It shows that almo st immediately after the concrete hardens, the crack index for Element 5069 is less than 1.0, indicating that the te nsile stress at the top surface edge exceeded the tensile strength of the conc rete, and hence cracking has occurred. Element 4069, which is at the center of the block is always in a compressive state, therefore has a constant crack index of 100. Figure 8-11 sh ows the crack indices for the center edge (Element 4259) and top edge (Element 5159) respectively. Elemen t 4259 only just remains above 1.0, while Element 5159 shows a high probability that cracking occurs during the first 25 hours. This was confirmed 115

PAGE 116

by a close examination of the experimental bloc k that contained mixture 1, shown in Figure 822, where cracking can be observed at all the top surface edges. In Mixture 2, cracking occurs at the top cen ter of the block appr oximately 10 hours after pouring, as shown in Figure 8-12. The same figure al so shows that while the center of block goes into tension after 80 hours, the concrete is in a mature state and the tensile strength is well developed. Figure 8-13 shows the crack indices at the edge of the block. As was expected, cracking occurs at the top edge of the block, ho wever the center edge of the block just barely stays above the crack threshold. Mixtures 3 and 4 act in a similar manner to Mixture 1, where their centers are constantly in compression and hence have negligible risks of cracking. In Mixture 3, the crack indices in Element 5069 and Element 5159 suggest that cracking will occur, shown in Figures 8-14 an 8-15 respectively. While Figure 8-16 and 8-17 show th at for Mixture 4 the tensile stresses that develop in these elements will not exceed thei r tensile strength and hence will not crack. It appears that the ratio of substitution of cementitious materials used in the concrete of Mixture 4 is effective in mitigating the cr acking risk in massive concrete elements. Temperature Difference and Cracking As previously stated, the requirements for the control of heat generation and in particular the maximum allowable temperature difference in mass concrete vary on a state by state basis. Currently, there is no agreement on what s hould be the maximum allowable temperature differential between the center of a mass concrete element and its surface so as to reduce the occurrence of thermal cracking. The critical temperat ure differences for the mixtures used in this project are determined from the results of the finite element analyses on each block. 116

PAGE 117

Figure 8-18 shows the plot of the temperatur e difference between the center and surface of the block with Mixture 1. The calculated tensile stresses at th e surface exceeded the early age tensile strength value of 1.25 MPa at a temperature differential of 17.3 C. Cracking in Mixture 2, whic h contained ground granulated blast-furnace slag, occurred when the temperature differential reached a bout 3.2 C, as shown in Figure 8-19. This is significantly less than th e differential in Mixture 1, which s hows that although the addition of slag to Portland cement slowed the rate of temper ature rise, it also caused the concrete to have a lower early age tensile strength of 0.255 MPa. This was to the detr iment of the integrity of the structure. The temperature differential of 8.4 C at wh ich cracking initiated in Mixture 3, shown in Figure 8-20, was larger than the differential in Mixture 2. In this case, although the fly ash lowered the peak temperature of the concrete, as shown in Figur e 7-12 through to Figure 7-14, it did not have any effect on rate of initial temperature rise, and ther efore a low value of the tensile strength caused the concrete to crack at a lowe r temperature differential than the block with mixture 1. Although the crack index for Mixture 4, pres ented in Figure 8-17, shows that thermal cracking does not occur, it was only just avoided. It was theref ore decided to still investigate the relationship between the temperature difference a nd induced stress at the surface of the block. Figure 8-21 shows the plot of this relationship, an d it can be seen that the induced stress reaches the 24 hour (Day 1) tensile stre ngth of 0.393 MPa when the temp erature differential is 20.6 C, 26 hours after being poured. Summary of Findings The investigation of the structural response of the concrete used in each Mixture to the internal heat generation and resulting temperatur e distribution found that: 117

PAGE 118

The concrete mixture containing 100% Port land cement had the highest induced stress but also cracked at the highe st temperature difference. Although the ground granulated blast furnace slag had a slower rate of temperature increase, it cracked at a very low temperat ure differential. This was due to the lower tensile strength typical of slag concrete. The percent fly ash substituted for Portla nd cement did not have much effect on the induced stresses. Cracking occurred at a temp erature differential of 8.4 C which also low and which is also due to the c oncretes low tensile strength. The mixture proportion of 50% Portland cement, 30% slag and 20% fly ash effectively reduces the probability of thermal cracking du e to hydration reaction. Never the less, the temperature differential at which cracking could occur is derived as 20.6 C. 118

PAGE 119

Figure 8-1. Location of elements analyzed for stress 119

PAGE 120

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 4069 Center ELEMENT 5069 Top Center Figure 8-2. Stress state at the t op center and center of the finite element concrete block with mixture 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 4259 Center Edge ELEMENT 5159 Top Edge Figure 8-3. Stress state at the top edge and center edge of the finite element concrete block with mixture 1 120

PAGE 121

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 4069 Center ELEMENT 5069 Top Center Figure 8-4. Stress state at the t op center and center of the finite element concrete block with mixture 2 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 4259 Center Edge ELEMENT 5159 Top Edge Figure 8-5. Stress state at the top edge and center edge of the finite element concrete block with mixture 2 121

PAGE 122

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 4069 Center ELEMENT 5069 Top Center Figure 8-6. Stress state at the t op center and center of the finite element concrete block with mixture 3 0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 4259 Center Edge ELEMENT 5159 Top Edge Figure 8-7. Stress state at the top edge and center edge of the finite element concrete block with mixture 3 122

PAGE 123

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 4069 Center ELEMENT 5069 Top Center Figure 8-8. Stress state at the t op center and center of the finite element concrete block with mixture 4 0 0.1 0.2 0.3 0.4 0.5 0.6 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 4259 Center Edge ELEMENT 5159 Top Edge Figure 8-9. Stress state at the top edge and center edge of the finite element concrete block with mixture 4 123

PAGE 124

0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80100120140160180Time (hours)Crack Index Element 4069 Center Element 5069 Top Center Figure 8-10. Crack index for elements al ong the center line of bl ock with mixture 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 020406080100120140160180Time (hours)Crack Index Element 4259 Center Edge Element 5159 Top Edge Figure 8-11. Crack index for elements along the edge of block with mixture 1 124

PAGE 125

0 10 20 30 40 50 60 70 80 90 100 020406080100120140160180Time (hours)Crack Index Element 4069 Center Element 5069 Top Center Figure 8-12. Crack index for elements al ong the center line of bl ock with mixture 2 0 10 20 30 40 50 60 70 80 90 100 020406080100120140160180Time (hours)Crack Index Element 4259 Center Edge Element 5159 Top Edge Figure 8-13. Crack index for elements along the edge of block with mixture 2 125

PAGE 126

0 10 20 30 40 50 60 70 80 90 100 020406080100120140160180Time (hours)Crack Index Element 4069 Center Element 5069 Top Center Figure 8-14. Crack index for elements al ong the center line of bl ock with mixture 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 020406080100120140160180Time (hours)Crack Index Element 4259 Center Edge Element 5159 Top Edge Figure 8-15. Crack index for elements along the edge of block with mixture 3 126

PAGE 127

0 10 20 30 40 50 60 70 80 90 100 020406080100120140160180Time (hours)Crack Index Element 4069 Center Element 5069 Top Center Figure 8-16. Crack index for elements al ong the center line of bl ock with mixture 4 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 020406080100120140160180Time (hours)Crack Index Element 4259 Center Edge Element 5159 Top Edge Figure 8-17. Crack index for elements along the edge of block with mixture 4 127

PAGE 128

Figure 8-18. Induced stress with respect to temperature differential for mixture 1 Figure 8-19. Induced stress with respect to temperature differential for mixture 2 128

PAGE 129

Figure 8-20. Induced stress with Respect to temperature differential for mixture 3 Figure 8-21. Induced stress with respect to temperature differential for mixture 4 129

PAGE 130

Figure 8-22. Top surface of experimental block containing mixture 1 showing numerous cracks along the edges 130

PAGE 131

CHAPTER 9 PARAMETRIC STUDY Introduction This chapter discusses the results of a pa rametric study conducted with the aid of the DIANA finite element program. The parameters inve stigated are effects of the heat generation rate, size of the structure and the amount of insulation, on the peak temperature, temperature distribution and induced stresses in mass concrete structures. Effect of Specimen Size The standard specimen size used in this study was a block si ze of 1.07m x 1.07m x 1.07m. To study the effect of size on the behavior of concrete, three addi tional block sizes were modeled. The sizes chosen were a half sized bloc k (0.5m x 0.5m x 0.5m), a block twice the size (2m x 2m x 2m), and a block four times the size (4m x 4m x 4m). A comparison of the temperature profiles at the cente r of blocks containing concrete using mix 1 is presented in Figure 9-1. Figure 9-2 shows the progression of the peak temperatures calculated in the block, as the size is increased. As expected, the peak te mperature increased as the size of the block increased. A closer analysis of the effect of block size on the maximum te mperature difference is presented in Figure 9-3, where it is shown that the maximum temperature differential between the center and top surface edge increases from 12.8 C in the 0.5m block to 56.5 C in the 4m block. Figures 9-4 and 9-5 are plots of the induced stress at the center of the top surface and the top surface edge respectively. In the 1m x 1m x 1m and 2m x 2m x2m blocks, the induced stress increases as we move from the center towards the edge of the blocks. However, in the 4m x 4m x 4m block we see that the stresses are the same at the top surface center and top surface edge suggesting that the stress is constant across the entire surface. The re lationship between the maximum induced stress and the increasing maximum temperature differential caused by 131

PAGE 132

increasing block size is presented in Figure 9-6, which shows that for a given concrete mixture, the maximum induced stress will increase with increasing maximum temperature differential. Figure 9-7 presents the maximum stress induced in each of the four types of concrete mixtures that were discussed in the prev ious chapters with respect to the maximum temperature difference for each size block. The maximum temperature di fference and resulting stress in concrete elements larger than 1.07m x 1.07m x 1.07m is hi ghly dependent on the type of concrete used. Figure 9-8 shows the maximum induced stre ss with respect to maximum temperature gradient in each of the four types of concre te mixtures for each size block. The temperature gradients in the larger blocks tend to be lower for each type of concrete used in this study. A comparison of the results presented in Figure 9-7 with those presented in Figure 9-8 show that while maximum stress appears to be a function of temperature difference regardless of block size, it is not a function of temperature gradient alone. It appears that temperature difference, rather than temperature gradient is a better indicator of maximum stress in mass concrete. Effect of Insulation Thickness Two model blocks, one insulated 1.5 inch thic k layer of polystyrene foam, and the other with a 6 inch thick layer polystyrene foam were created, analyzed and their results compared with the model analyzed in the previous chapte rs, to quantify the effect that the amount of insulation would have on the temperature distribu tion in a hydrating conc rete element containing 100% Portland cement. Figure 9.9 and Figure 9.10 pres ent the temperature pr ofiles with respect to time of the concrete block insulated with 1.5 in ch thick and 6 inch thick layers of polystyrene foam respectively. The block with the 1.5 inch thick layer of insulation had a maximum temperature difference between the center of th e block and a point 2 inches below the exposed top surface of 14.9 C, occurring 32 hours after casting, and was maintained for 7 hours before steadily decreasing to 3.6 C. The maximum temperature differe nce between the center and a 132

PAGE 133

point 2 inches below the exposed top surface calcul ated in the block with the 6 inch layer of insulation was 20 C. This maximum difference wa s attained after 70 hours of hydration, slowly decreasing to 15.8 C at the end of the analysis at 167 hours. Figure 9-11 shows the comparison of the temperatures with respect to time 2 inches below the exposed top surface of the concrete bloc ks with varying insulation thickness. The peak temperature at this location was found to be the same and occurred at the same time in all three blocks. However the rate of temperature decreas e was slowest in the model with the 6 inch insulation, and fastest in the mode l with the 1.5 inch insulation. Th e temperatures 4 inches below the top surface presented in Figure 9-12 were similar to those observed at 2 inches in terms of the three blocks attaining the same peak temperat ure at approximately th e same time but having different rates of decline. The comparison of the temperatures 21 inches below the top surface are shown in Figure 9-13. At this depth, the peak temperature and the time it is attained increa se in accordance with the thickness of the polystyrene foam. Although the top surface of the blocks modeled in this project were exposed to ambient conditions, the effectiveness of the insulation in reducing temperature di fferences within the concrete varied with respect to its thickness. This was determined by ev aluating the temperature difference between the center of the block and a point at the same depth but on the side of the block. Figure 9-14 shows the temperature in the c oncrete block modeled with the 1.5 inch thick polystyrene insulation where a maximum temperature difference of 8.3 C between the center and the side is observed. The te mperatures in the block with the 3 inch thick polystyrene insulation are presented in Figure 9-15. Here, we see that the maximum temperature difference 133

PAGE 134

between the two points decreases to 3.4 C. Figure 9-16, shows that for the block insulated with a 6 inch thick layer of polystyrene the temperatur e difference was only 1.9 C. Having assessed the effects of the insulation thickness on the temperature distribution in the uncovered block, an investigation on the eff ect of the insulation thickness on the maximum temperature differential and maximum induced stre ss in a concrete block insulated on all faces was conducted. Figure 9-17 and Figure 9-18 show co mparisons of the experimentally measured and numerically calculated temperature profiles 2 inches and 4 inches below the top surface of the fully insulated concrete block wi th mixture 1 for validation purposes. Figure 9-18 presents the variation in maxi mum temperature differential within the concrete with respect to insulation thickness. Figure 9-19 also shows how the block size determines the effect increasing the insulation thickness will have on th e maximum temperature differential within the concrete. As shown in Figure 9-19, increasing the insulation thickness from 1.5 inches up to 9 inches will reduce the te mperature difference between the center and top surface of the block. In the 0.5m block, the maximum temperature difference moved from 5.6 C with 1.5 inches of insulation, to 4.2 C with 3 in ches of insulation, to 3.2 C with 6 inches of insulation, to 2.8 C with 9 inches of insula tion. The 1.07m block had values of 12.4 C, 8.9 C, 6.5 C, and 5.4 C with insulati on thicknesses of 1.5 inches, 3 in ches, 6 inches, and 9 inches respectively. The 2m block had a temperature di fference of 22.8 C at 1.5 inches, 16.7 C at 3 inches, 11.6 C at 6 inches, and 9.3C at 9 inches Finally, the 4m block saw the largest reduction in the magnitude of the maximum temperature difference with increasing insulation thickness. The maximum temperature difference in the block w ith 1.5 inches of insulation was calculated at 37.7 C, with 3 inches of insulation, 27.2 C, 6 in ches of insulation, 18.1 C and finally with 9 inches of insulation, 14 C. 134

PAGE 135

Figure 9-20 and Figure 9-21 show the effect of increasing the insulation thickness had the maximum induced stress in the concrete with respect to temperature difference. Figure 9-20 shows that the reduced magnitude of temperatur e difference caused by an increase in insulation thickness will result in lower induced stress with in the concrete block. Figure 9-21 shows that by increasing the insulation thickness, significant reductions in stress es can be achieved in large concrete elements. Time of Formwork Removal Effect The effect model was modified so that th e effect that the time of removal of the formwork had on the induced concrete stresses could be assessed. Knowledge of the optimal time to remove of the formwork and insulation around mass concrete is im portant in that the scheduling of construction time sequence is an essential aspect of project management. The times chosen for analysis were 12 hours, 1 day, 2 days, 3 days, 4 days and 6 days after pouring of the concrete. Figure 9-22 through to Figure 9-27 show the induced stress with respect to time in a 1.07m x 1.07m x 1.07m concrete block concrete when the formwork and insulation is removed at times of 12 hours, 1 day, 2 days, 3 days, 4 days and 6 days. A sharp sudden increase in tensile stre ss occurred along the surf ace immediately after formwork removal. The peak stress calculated fo r the removal times of 12 hours, 1 day, 2 days and 3 days were 0.964 MPa, 1.08 MPa, 1.31 MPa, 1.30 MPa respectively. These were 77% 86.4%, 79% and 67.4% of the attain ed concrete tensile strength respectively. While not exceeding the tensile strength of the concrete, these stress levels are high enough to cause microcracking. These micro-cracks do not pose an immediat e threat to the structural integrity of the concrete however they will provide an entry poin t for invasive deleterious substances that can compromise the long term durabili ty of the concrete. Figure 926 shows the state of stress in 135

PAGE 136

concrete when the formwork is removed after 4 days of hydration. The stress also undergoes a sharp increase in magnitude the instant the form work is removed, but is only slightly above 50% of the tensile strength at 4 days, therefore the risk of micro-cracking is small. Figure 9-27 shows the stresses for the concrete that had the form work and insulation removed after 6 days of hydration. Here the peak stress of 1.08 MPa is 49% of the tensile strength of the concrete. The results of the parametric study on the e ffect time of formwork and insulation removal suggests that the risk of micro-cracking is s ubstantially reduced if the removal is done a minimum of 4 days after the concrete is poured. Heat Generation Rate Effect The effect the rate of intern al heat generation has on the dist ribution of temperatures in a concrete element can be seen from the analysis of the block model with varying mixture designs described in Chapter 7. It was obs erved that concrete with 100% Portland cement generated heat at the fastest rate, followed by the concrete with the 35% replacement of fly ash, then by the substitution of 50% ground granulated blast-furnace slag, and the sl owest rate of heat generation occurred in the mixture with 50% Portland cemen t, 30% Slag and 20% Fly Ash (ternary blend). Figure 9-28 shows the temperature profile with respect to time at the center of the concrete blocks containing each mix. It is seen that the concrete contai ning the highest rate of heat generation (100% Portland cement) had the sharpest rise in temperature and the highest peak temperature. The ternary blend concrete with the slowest rate of heat generation had the lowest temperature rise slope and also the lowest peak temperature. Summary of Findings The parametric study of the factors affecting the behavior of concrete resulted in the following: 136

PAGE 137

The peak temperature, internal temperat ure gradients and induced thermal stresses increase as the amount of concrete used in any one pour is increased. The thickness of the insulating layer around the block formwork has an indirect effect on the magnitude of the maximum temperature difference in the hydrating concrete. For a given Resistance value (R-Value) of an insula ting material the temperature difference in concrete will decrease with increasing insulation thickness. Concrete with a fast rate of heat generation will have higher peak temperatures increasing the likelihood that thermal cracking will occur. The effectiveness of insulation thickness in the reduction of the maximum temperature differential in concrete is dependent on th e size of the concrete block. An increase in insulation thickness from 1.5 in ches to 9 inches reduced the maximum temperature differential by 50% in a 0.5m x 0.5m x 0.5m block while the reduction in a 4m x 4m x 4m block was 62.9%. Increasing the insulation thickness can achieve significant reductions in thermal stresses in large concrete elements. Although the tensile stresses that resulted from the removal of formwork and insulation 12 hours, 1 day, 2 days and 3 days after the pouring concrete were less than the tensile strength of the concrete as measured in th e laboratory, the stresses were large enough to initiate micro-cracking. These micro-cracks can serve as an entry point for deleterious materials that can undermine th e durability of the concrete. 137

PAGE 138

0 10 20 30 40 50 60 70 80 90 100 020406080100120140160180Time (hours)Temperature (C) 0.5m x 0.5m x 0.5m Block 1m x 1m x 1m Block 2m x 2m x 2m Block 4m x 4m x 4m Block Figure 9-1. Comparison of temp erature profiles calculated at the center of each block 0 10 20 30 40 50 60 70 80 90 100 0 5124Block Size (Length in m)Peak temperature (C) Figure 9-2. Calculated peak temperatur e values with respect to block size 138

PAGE 139

0 10 20 30 40 50 60 0.5 1.0 2.0 4.0Block Size (Length in m)Maximum Tempertaure Difference (C) Figure 9-3. Effect of concre te block size on the maximum in ternal temperature difference -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 020406080100120140160180Time (hours)Stress (MPa) 0.5m x 0.5m x 0.5m Block 1m x 1m x 1m Block 2m x 2m x 2m Block 4m x 4m x 4m Block Figure 9-4. Comparison of st resses at the center of th e top surface of each block 139

PAGE 140

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 020406080100120140160180Time (hours)Stress (MPa) 0.5m x 0.5m 0.5m Block 1m x 1m x 1m Block 2m x 2m x 2m Block 4m x 4m x 4m Block Figure 9-5. Comparison of stresses at the top surface edge of each block Figure 9-6. Maximum induced stress with respect to maximum temperature differential as a result of increasing block size 140

PAGE 141

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 01 02 03 04 05 06 07 0Maximum Temperature Difference (C)Maximum Stress (MPa) 8 0 0.5m x 0.5m x 0.5m 1m x 1m x1m 2m x 2m x 2m 4m x 4m x 4m Linear (0.5m x 0.5m x 0.5m) Linear (1m x 1m x1m) Linear (4m x 4m x 4m) Linear (2m x 2m x 2m) Figure 9-7. Plot of maximum st ress versus maximum temperature difference with respect to block size and type of concrete used. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 01 02 03 04 05 06 0Maximum Temperature Gradient (C/m)Maximum Stress (MPa) 7 0 0.5m x 0.5m x 0.5m 1.0m x 1.0m x 1.0m 2.0m x 2.0m x 2.0m 4.0m x 4.0m x 4.0m Linear (2.0m x 2.0m x 2.0m) Linear (1.0m x 1.0m x 1.0m) Linear (0.5m x 0.5m x 0.5m) Linear (4.0m x 4.0m x 4.0m) Figure 9-8. Plot of maximum stress versus maximum temperature gr adient with respect to block size and type of concrete used. 141

PAGE 142

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) 2" Below Top Surface 4" Below Top Surface 21" Below Top Surface Figure 9-9. Temperature profiles with respect to time 2 inches, 4 inches and 21 inches below the top surface of the block insu lated with a 1.5 inch thick layer of polystyrene foam 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) 2" Below Top Surface 4" Below Top Surface 21" Below Top Surface Figure 9-10. Temperature profiles with respect to time 2 inches, 4 inches and 21 inches below the top surface of the block insulated with a 6.0 inch thick layer of polystyrene foam 142

PAGE 143

0 10 20 30 40 50 60 020406080100120140160180Time (hours)Temperature (C) 1.5 Inch Thick Insulation 3.0 Inch Thick Insulation 6.0 Inch Thick Insulation Figure 9-11. Comparison of temperature profiles with respect to time 2 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation 0 10 20 30 40 50 60 70 020406080100120140160180Time (hours)Temperature (C) 1.5 Inch Thick Insulation 3.0 Inch Thick Insulation 6.0 Inch Thick Insulation Figure 9-12. Comparison of temperature profiles with respect to time 4 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation 143

PAGE 144

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) 1.5 Inch Thick Insulation 3.0 Inch Thick Insulation 6.0 Inch Thick Insulation Figure 9-13. Comparison of temperature profiles with respect to time 21 inches below the top surface of the blocks with varying thic knesses of polystyrene foam insulation 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Side Center Figure 9-14. Temperatures calcul ated at the side and center of a concrete block with 1.5 inch thick insulation 144

PAGE 145

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Side Center Figure 9-15. Temperatures calcul ated at the side and center of a concrete block with 3.0 inch thick insulation 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Side Center Figure 9-16. Temperatures calcul ated at the side and center of a concrete block with 6.0 inch thick insulation 145

PAGE 146

0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 9-17. Comparison of experimentally m easured and calculated temperature profiles 2 inches below the top surface at the centerline of concrete block with 3.0 inch thick insulation 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) Analytical Isothermal Experimental Figure 9-18. Comparison of experimentally m easured and calculated temperature profiles 4 inches below the top surface at the centerline of concrete block with 3.0 inch thick insulation 146

PAGE 147

0 5 10 15 20 25 30 35 40 0123456789Insulation Thickness (inch)Maximum Temperature Difference (C) 10 0.5m x 0.5m x 0.5m Block 1m x 1m x 1m Block 2m x 2m x 2m Block 4m x 4m x 4m Block Figure 9-19. Variation in maximu m temperature differential within the concrete with respect to insulation thickness fo r each block size 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 5 10 15 20 25 30 35 40Maximum Temperature Difference (C)Maximum Stress (MPa) 1.5 Inch Thick Insulation 3 Inch Thick Insulation 6 Inch Thick Insulation 9 Inch Thick Insulation Figure 9-20. Effect of reduction of temperat ure differential caused by increasing insulation thickness on the maximum induced stress 147

PAGE 148

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 00.511.522.533.544Block Size (Length in m)Maximum Stress (MPa) .5 1.5 Inch Insulation 3.0 Inch Insulation 6.0 Inch Insulation 9.0 Inch Insulation Figure 9-21. Effect of insulation thickness on the maximum induced stress in each block size -0.2 0 0.2 0.4 0.6 0.8 1 1.2020406080100120140160180Time (hours)Stress (MPa) ELEMENT 5213 Removed 12 hours ELEMENT 5213 No Removal Figure 9-22. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 12 hours after casting 148

PAGE 149

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 5213 Removed 24 hours ELEMENT 5213 No Removal Figure 9-23. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 1 day after casting -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 5213 Removed 48 hours ELEMENT 5213 No Removal Figure 9-24. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 2 days after casting 149

PAGE 150

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 5213 Removed 72 hours ELEMENT 5213 No Removal Figure 9-25. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 3 days after casting -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 020406080100120140160180Time (hours)Stress (MPa) ELEMENT 5213 Removed 96 hours ELEMENT 5213 No Removal Figure 9-26. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 4 days after casting 150

PAGE 151

0 0.2 0.4 0.6 0.8 1 1.2 020406080100120140160180 Time (hours)Stress (MPa) ELEMENT 5213 Removed 144 hours ELEMENT 5213 No Removal Figure 9-27. Plot of stress versus time at a point on the center of the surface of the concrete block when formwork is removed 6 days after casting 0 10 20 30 40 50 60 70 80 020406080100120140160180Time (hours)Temperature (C) 100% Portland Cement 50% Portlan Cement 50% Slag 65% Portland Cement 35% Fly Ash 50% Portland 30% Slag 20% Fly ash Figure 9-28. Temperature profiles with respect to time at the center of a concrete block with varying heat generation rates. 151

PAGE 152

CHAPTER 10 CONCLUSIONS AND RECOMMENDATIONS Findings Results from analysis from a finite element model built to predict th e early age behavior a hydrating concrete element in an effort to quantify the maximum allowable temperature difference to prevent cracking ha ve been presented and discusse d. To validate the accuracy of the model and hence verify the results obtained from the model, four different concrete mixtures were used in experimental blocks with di mensions 3.5ft x 3.5ft x 3.5ft and monitored for temperature distributions. The ma terial and physical properties of the concretes used were obtained from laboratory testing and used in the finite element model. The two types of tests done on the concrete mixtures to determine th e energy released during hydration were semiadiabatic calorimetry and isothermal calorimetr y. The calculated adiabati c energy rise obtained from each test was used in the model to determine which procedure would give the best results when compared with the temperatures measured in the experimental block. Based on the results of the thermal analysis of the concrete bloc k model the following findings were made: The semi-adiabatic calorimetry test consiste ntly gave lower heat of hydration and lower predicted temperature of concrete as compar ed with the isothermal calorimetry test. The input of adiabatic ener gy captured in the isothermal calorimetry test provided temperature distributions that were very similar to those m easured in the experimental blocks. At some locations the predicted te mperatures were higher than the measured temperatures and so the isothermal test can be said to provide cons ervative predictions of the temperature distribution. The induced stresses caused by the varying temp eratures within the concrete element of each mixture were analyzed using the results fr om the model that utilized the energy from isothermal calorimetry test. The magnitude and type of the stresses were of particular interest so 152

PAGE 153

as to determine the likelihood of thermal cracking. The results of th is structural analysis for the concrete block study led to the following observations: The highest tensile stresses were located at the top edge of the surface exposed to ambient conditions. Concrete containing 100% Portland cement e xperienced tensile stresses high enough to cause cracking on all surfaces, even those insu lated, when the temperature difference was 17.3 C. In the case where 50% of the Portland cemen t was replaced with ground granulated blastfurnace slag the rate of hydration reaction a nd hence rate of temperature increase was significantly slower. The associat ed reduction in early age tens ile strength resulted in the cracking risk not being reduced. In the case where 35% of the Portland cemen t was substituted with Fly Ash there was little effect on the early age rate of hydration and thus the time in which the maximum temperature was achieved was not affected significantly. However, the maximum temperature achieved was itself significantly less. Again the early age tensile strength was less than the 100% Portland cement case resulting in similar cracking on all surfaces as before even though the tensile stresses experienced were less. Concrete that had a blend of 50% Port land Cement, 30% Sla g, and 20% Fly Ash performed the best in terms of reducing the induced thermal stresses relative to the tensile strength, and hence th e cracking potential. The temperature differential that induced cracking in the concretes used in this project varied from mixture to mixture. This was due to the corresponding ch anges in the tensile strength. The parametric study on factors affecting th e temperature distribution in concrete produced very interesting results The thermal stresses in large mass concrete elements were effectively reduced with the use of thick layers of insulating polystyrene foam. This method is advantageous because the polystyrene foam if removed carefully can be reused often making it relatively inexpensive when compared to other single us e methods such as cooling pipes and liquid nitrogen. Although the tensile stresses that resulted from the removal of formwork and insulation 12 hours, 1 day, 2 days and 3 days after the pouring concrete were less than the tensile strength of the concrete as measured in th e laboratory, the stresses could be large enough to initiate micro-cracking. These micro-cracks can serve as an entry point for deleterious materials that can undermine the durability of the concrete. For insulation removed after 153

PAGE 154

4 days, the tensile stresses were significantly less than the tensile strength, reducing the risk of microcracking. Conclusions Based on the results obtained in this study, the following conclusions are made: The heat of hydration energy data obtained from the isothermal calorimetry test should be used for the input for the heat generation function in the finite element modeling of concrete hydration. Reliance on a limiting maximum temperature diffe rential to control cracking in massive concrete applications should be supplemented with a requirement for the presentation of a finite element analysis showing the cal culated stress respons e to the predicted temperature distribution within the concrete, to ensure that the induced tensile stresses will not exceed the tensile strength of the concrete. Adequate insulation should be used in conjunc tion with the usual formwork material to reduce the temperature differentials during th e early age hydration of massive concrete. However caution should be take n as the occurrence of delaye d ettringite formation (DEF) and drying shrinkage due to high conc rete temperatures was not studied. A safety factor should be applied to the tens ile strength values for concrete obtained from the splitting tension and third-point flexural strength tests to guard against the initiation of micro-cracks which although by themselves w ill not cause structural failure, can act as an entry point for deleterious materials which can undermine the durability of the concrete. The current restrictions on maximum temp erature imposed by state regulating bodies should take into consideration the type of cem entitious materials that will be used in the concrete mix. Recommendations for Future Research The testing and analysis of additional blends of cementitious materials and on additional and larger blocks of mass concre te in order to assess the universal applicab ility of the hypotheses deduced and concluded from this study. 154

PAGE 155

APPENDIX A GRAPHICAL USER INTER FACE INPUT COMMANDS Define Geometry Points for Base of Model GEOMETRY POINT COORDINATE 0 0 0 GEOMETRY POINT C OORDINATE 0.5334 0 0 GEOMETRY POINT C OORDINATE 0.552445 0 0 GEOMETRY POINT C OORDINATE 0.62865 0 0 GEOMETRY POINT C OORDINATE 0 0.5334 0 GEOMETRY POINT C OORDINATE 0.5334 0.5334 0 GEOMETRY POINT C OORDINATE 0.552445 0.5334 0 GEOMETRY POINT C OORDINATE 0.62865 0.5334 0 GEOMETRY POINT C OORDINATE 0 0.55245 0 GEOMETRY POINT C OORDINATE 0.5334 0.55245 0 GEOMETRY POINT C OORDINATE 0.552445 0.55245 0 GEOMETRY POINT C OORDINATE 0.62865 0.55245 0 GEOMETRY POINT C OORDINATE 0 0.62865 0 GEOMETRY POINT C OORDINATE 0.5334 0.62865 0 GEOMETRY POINT C OORDINATE 0.552445 0.62865 0 GEOMETRY POINT C OORDINATE 0.62865 0.62865 0 Connectivity GEOMETRY SURFACE 4POINTS P1 P2 P6 P5 GEOMETRY SURFACE 4POINTS P2 P3 P7 P6 GEOMETRY SURFACE 4POINTS P3 P4 P8 P7 GEOMETRY SURFACE 4POINTS P5 P6 P10 P9 GEOMETRY SURFACE 4POINTS P6 P7 P11 P10 GEOMETRY SURFACE 4POINTS P7 P8 P12 P11 GEOMETRY SURFACE 4POINTS P9 P10 P14 P13 GEOMETRY SURFACE 4POINTS P10 P11 P15 P14 GEOMETRY SURFACE 4POINTS P11 P12 P16 P15 Merge Geometries CONSTRUCT SET BOTFOAM APPEND ALL VIEW GEOMETRY ALL BLUE LABEL GEOMETRY LINES ALL RED LABEL GEOMETRY SURFACE ALL BLUE Group Lines with Equal Di visions into Sets CONSTRUCT SET SELIN1 APPEND LINES L1 L2 L3 L4 L6 L9 L12 L19 CONSTRUCT SET SELIN2 APPE ND LINES L5 L7 L8 L10 L11 L13 L14 L15 L16 L17 CONSTRUCT SET SELIN2 APPEND LI NES L18 L20 L21 L22 L23 L24 155

PAGE 156

Divide Lines MESHING DIVISION LINE SELIN1 10 MESHING DIVISION LINE SELIN2 1 Create Volumes for 3D Model GEOMETRY SWEEP BOTFOAM BO TPLY 1 TRANSLATE 0 0 0.762 GEOMETRY SWEEP BOTPLY BOTB LOCK 1 TRANSLATE 0 0 0.0381 GEOMETRY SWEEP BOTBLOC TO PBLOC 20 TRANSLATE 0 0 1.0668 CONSTRUCT SET MODEL APPEND ALL LABEL GEOMETRY BODIES ALL BLUE Group Geometries into Materials CONSTRUCT SET CONCRE TE APPEND BODIES B19 CONSTRUCT SET OPEN POLSTYRENE CONSTRUCT SET APPEND BODIES B1 B2 B3 B4 B5 B6 B7 B8 B9 B12 CONSTRUCT SET APPEND BODIES B15 B16 B17 B18 B21 B24 B25 B26 B27 CONSTRUCT SET CLOSE CONSTRUCT SET PLYWOOD APPEND BODIES B10 B11 B13 B14 B20 B22 B23 Generate Mesh for Entire Model MESHING TYPES MODEL HE8 HX8HT MESHING GENERATE Turn of DIANAs Element Space Conflict Check CONSTRUCT SPACE TOLERANCE OFF GEOMETRY COPY CONCRETE CONC TRANSLATE 0 0 0 Specifiy Element Type For Concrete used in Flow-Stress Analysis CONSTRUCT SET SELIN3 APPEND LINE S L145 L146 L147 L148 L149 L150 L151 L152 CONSTRUCT SET SELIN4 APPE ND LINES L153 L154 L155 L156 MESHING DIVISION LINE SELIN3 20 MESHING DIVISION LINE SELIN4 40 MESHING TYPES CONC HE20 CHX60 MESHING GENERATE MESHING MERGE ALL 0.001 Merges all nodes within a distance of 0.001 156

PAGE 157

Identify Surfaces that Experience Boundary Convection CONSTRUCT SET OPEN BOUNDA CONSTRUCT SET APPEND SURFACES S1 S2 S3 S4 S5 S6 S7 S8 S9 S27 CONSTRUCT SET APPEND SURFACES S34 S 37 S40 S41 S42 S60 S67 S70 S73 S74 CONSTRUCT SET APPEND SURFACES S75 S 77 S78 S79 S81 S82 S83 S84 S93 S100 CONSTRUCT SET APPEND SURFAC ES S103 S106 S107 S108 S110 CONSTRUCT SET CLOSE CONSTRUCT SPACE TOLERANCE OFF GEOMETRY COPY BOUNDA OUTER TRANSLATE 0 0 0 MESHING TYPES OUTER QU4 BQ4HT MESHING GENERATE MESHING MERGE ALL 0.001 Define Material Properties Properties are Defined Using the Property Manager Dialog Box View Property Manager Materials Material Name: CONC External External Data from File: concrete.dat Material Name: MAPLY (Plywood) Conductivity=540 J/m-hr-C, Heat Capacity=8.54E5 J/m 3 -C Material Name: MAINSUL (Polystyrene Insulation) Conductivity=126 J/m-hr-C, Heat Capacity=2.84E4 J/m 3 -C Material Name: MAOUT (Boundary Elements) Convection Coefficient=2.016E4 J/m 3 -hr-C Assign Properties to Geometries and Elements PROPERTY ATTACH CONC MACONC PROPERTY ATTACH PLY MAPLY PROPERTY ATTACH POLYSTRENE MAINSUL PROPERTY ATTACH OUTER MAOUT Boundary Conditions PROPERTY LOADS EXTTEMP 1 OUTER 23 PROPERTY LOADS GRAVITY 2 CONC -0.981E-5 3 Weight acting downwards Assign Variations of Loads and Boundary Conditions to Time CONSTRUCT TCURVE TCDUM LIST 0 1. 168.1. PROPERTY ATTACH LOADCASE 1 TCDUM 157

PAGE 158

PROPERTY ATTACH LOADCASE 2 TCDUM Boundary Constraints ie. Support Conditions and Symmetry Conditions PROPERTY BOUNDARY CONSTRAINT S109 Z PROPERTY BOUNDARY CONSTRAINT S111 Y PROPERTY BOUNDARY CONSTRAINT S114 X Set Initial Temperatures PROPERTY INITIAL INITEMP ALL 23 UTILITY WRITE DIANA QUARTERBLOCKMODEL 158

PAGE 159

APPENDIX B BATCH FILE INPUT COMMANDS FEMGEN MODEL : QUARTERBLOCK1 ANALYSIS TYPE : Heatflow-Stress Staggered 3D 'UNITS' LENGTH M TIME HOUR TEMPER CELSIU FORCE N 'COORDINATES' 1 0.000000E+00 0.000000E+00 0.000000E+00 2 5.334000E-02 0.000000E+00 0.000000E+00 3 1.066800E-01 0.000000E+00 0.000000E+00 4 1.600200E-01 0.000000E+00 0.000000E+00 5 2.133600E-01 0.000000E+00 0.000000E+00 6 2.667000E-01 0.000000E+00 0.000000E+00 7 3.200400E-01 0.000000E+00 0.000000E+00 8 3.733800E-01 0.000000E+00 0.000000E+00 9 4.267200E-01 0.000000E+00 0.000000E+00 10 4.800600E-01 0.000000E+00 0.000000E+00 Lines Skipped 12460 1.600200E-01 4.800600E-01 1.154430E+00 12461 2.133600E-01 4.800601E-01 1.154430E+00 12462 2.667000E-01 4.800601E-01 1.154430E+00 12463 3.200400E-01 4.800601E-01 1.154430E+00 12464 3.733800E-01 4.800601E-01 1.154430E+00 12465 4.267200E-01 4.800601E-01 1.154430E+00 12466 4.800600E-01 4.800601E-01 1.154430E+00 'ELEMENTS' CONNECTIVITY 1 HX8HT 1 2 13 12 122 123 134 133 2 HX8HT 2 3 14 13 123 124 135 134 3 HX8HT 3 4 15 14 124 125 136 135 4 HX8HT 4 5 16 15 125 126 137 136 5 HX8HT 5 6 17 16 126 127 138 137 6 HX8HT 6 7 18 17 127 128 139 138 7 HX8HT 7 8 19 18 128 129 140 139 8 HX8HT 8 9 20 19 129 130 141 140 9 HX8HT 9 10 21 20 130 131 142 141 10 HX8HT 10 11 22 21 131 132 143 142 Lines Skipped 3168 HX8HT 3589 3609 3869 3849 3588 3608 3868 3848 3169 CHX60 339 3888 340 3899 351 3909 350 3898 4347 4386 5888 5868 647 4366 666 6050 5969 6059 1388 5887 159

PAGE 160

3170 CHX60 340 3889 341 3900 352 3910 351 3899 4386 4425 5889 5888 666 4405 685 6051 5970 6060 5969 6050 3171 CHX60 341 3890 342 3901 353 3911 352 3900 4425 4464 5890 5889 685 4444 704 6052 5971 6061 5970 6051 3172 CHX60 342 3891 343 3902 354 3912 353 3901 4464 4503 5891 5890 704 4483 723 6053 5972 6062 5971 6052 3173 CHX60 343 3892 344 3903 355 3913 354 3902 4503 4542 5892 5891 723 4522 742 6054 5973 6063 5972 6053 3174 CHX60 344 3893 345 3904 356 3914 355 3903 4542 4581 5893 5892 742 4561 761 6055 5974 6064 5973 6054 3175 CHX60 345 3894 346 3905 357 3915 356 3904 4581 4620 5894 5893 761 4600 780 6056 5975 6065 5974 6055 3176 CHX60 346 3895 347 3906 358 3916 357 3905 4620 4659 5895 5894 780 4639 799 6057 5976 6066 5975 6056 3177 CHX60 347 3896 348 3907 359 3917 358 3906 4659 4698 5896 5895 799 4678 818 6058 5977 6067 5976 6057 3178 CHX60 348 3897 349 3908 360 3918 359 3907 4698 4737 4776 5896 818 4717 837 4756 856 6068 5977 6058 Lines Skipped 5168 CHX60 12205 12376 990 5089 1009 5128 1028 12385 12466 5069 5108 5147 616 4306 617 4317 628 4327 627 4316 5169 BQ4HT 1 2 13 12 5170 BQ4HT 2 3 14 13 5171 BQ4HT 3 4 15 14 5172 BQ4HT 4 5 16 15 5173 BQ4HT 5 6 17 16 5174 BQ4HT 6 7 18 17 5175 BQ4HT 7 8 19 18 5176 BQ4HT 8 9 20 19 5177 BQ4HT 9 10 21 20 5178 BQ4HT 10 11 22 21 5179 BQ4HT 12 13 24 23 Lines Skipped 5982 BQ4HT 626 627 3377 3376 5983 BQ4HT 627 628 3378 3377 :Nodes Grouped to Materials MATERIALS / 145-254 265-275 2289-2488 2689-2908 / 1 / 5169-5983 / 2 / 3169-5168 / 3 / 1-144 255-264 276-288 2489-2688 2909-3168 / 4 160

PAGE 161

'MATERIALS' :Plywood Properties 1 CONDUC 5.400000E+02 CAPACI 8.543999E+05 :Boundary Properties 2 CONVEC 2.016000E+04 :Concrete Properties 3 CONDUC 7.920E+03 CAPACI 2.675596E+06 ADIAB 0.0 23 1.0 23.73796428 2.0 25.42189049 3.0 28.73104768 4.0 33.31326448 5.0 38.24138423 6.0 42.95409819 7.0 47.74431264 8.0 52.63938071 9.0 56.42322844 10.0 59.06166443 11.0 61.06186104 12.0 62.68025374 13.0 64.07070381 14.0 65.2901969 15.0 66.38432155 16.0 67.38157057 17.0 68.30473824 18.0 69.14242742 19.0 69.94022664 20.0 70.68673876 21.0 71.37626523 22.0 72.03160031 23.0 72.65274398 24.0 73.23969627 25.0 73.78675859 26.0 74.30532808 27.0 74.79540474 28.0 75.26838571 29.0 75.71287385 30.0 76.13456772 31.0 76.5391659 32.0 76.91527124 33.0 77.28567802 161

PAGE 162

34.0 77.63329054 35.0 77.96950592 36.0 78.29432418 37.0 78.60204673 38.0 78.90407072 39.0 79.18899902 40.0 79.46822874 41.0 79.73606134 42.0 80.00389393 43.0 80.2603294 44.0 80.50536773 45.0 80.75040606 46.0 80.98404726 47.0 81.22338703 48.0 81.43993253 49.0 81.6621766 50.0 81.87302353 51.0 82.08956904 52.0 82.29471741 53.0 82.49986578 54.0 82.70501415 55.0 82.90446395 56.0 83.09251663 57.0 83.28626786 58.0 83.4800191 59.0 83.66237321 60.0 83.84472732 61.0 84.02708142 62.0 84.20373697 63.0 84.37469394 64.0 84.55704805 65.0 84.72230646 66.0 84.89326343 67.0 85.05852184 68.0 85.22947882 69.0 85.3833401 70.0 85.54859851 71.0 85.70815835 72.0 85.86201963 73.0 86.01588091 74.0 86.16974219 75.0 86.32930203 76.0 86.47746474 77.0 86.61992889 78.0 86.77379017 79.0 86.91625431 162

PAGE 163

80.0 87.05871846 81.0 87.20688117 82.0 87.34364675 83.0 87.48041233 84.0 87.62287648 85.0 87.75964206 86.0 87.88501051 87.0 88.02177609 88.0 88.15854167 89.0 88.28960868 90.0 88.41497713 91.0 88.54604415 92.0 88.67711116 93.0 88.80817817 94.0 88.92784806 95.0 89.05321651 96.0 89.17288639 97.0 89.29825484 98.0 89.41792472 99.0 89.5375946 100.0 89.65156592 101.0 89.7712358 102.0 89.89090569 103.0 90.004877 104.0 90.11314976 105.0 90.22712107 106.0 90.34109239 107.0 90.44936514 108.0 90.55193933 109.0 90.66591064 110.0 90.77418339 111.0 90.87675758 112.0 90.9907289 113.0 91.08760452 114.0 91.1901787 115.0 91.29845145 116.0 91.39532707 117.0 91.49220269 118.0 91.60047544 119.0 91.6916525 120.0 91.79422668 121.0 91.87970517 122.0 91.98227935 123.0 92.07915497 124.0 92.17033203 125.0 92.26150908 163

PAGE 164

126.0 92.35268613 127.0 92.44956175 128.0 92.53504024 129.0 92.63191586 130.0 92.71739435 131.0 92.8085714 132.0 92.89404989 133.0 92.97952838 134.0 93.06500687 135.0 93.15048535 136.0 93.24166241 137.0 93.3271409 138.0 93.40122225 139.0 93.49239931 140.0 93.57217923 141.0 93.65765772 142.0 93.7431362 143.0 93.82291612 144.0 93.90839461 145.0 93.98247597 146.0 94.06225589 147.0 94.14203581 148.0 94.23321287 149.0 94.30159566 150.0 94.38707414 151.0 94.45545693 152.0 94.53523686 153.0 94.61501678 154.0 94.68909813 155.0 94.76317949 156.0 94.84295941 157.0 94.92273933 158.0 94.99682069 159.0 95.07090205 160.0 95.1449834 161.0 95.21906476 162.0 95.28744755 163.0 95.3615289 164.0 95.4299117 165.0 95.50399305 166.0 95.57237584 167.0 95.6464572 ARRHEN 4117.75 EQUAGE ARRTYP TEMREF 23.0 YOUNG 2.523500E+04 164

PAGE 165

POISON 2.000000E-01 DENSIT 2.2480000E+03 THERMX 9.160000E-06 FTTIME 0. 24. 48. 72. 167. FTVALU 0. 1.25 1.66 1.93 2.206 MAXWEL 1 ,1 TIME 0. 24. 48. 72. 167. YOUNG 13445. 13445. 16892. 18064. 20202. :Polystyrene Properties 4 CONDUC 2.248500E+02 CAPACI 2.082400E+04 :Geometry and Element Groupings 'GROUPS' NODES 1 BOTFOAM / 1-121 243-253 265-275 287-297 309 311 313-323 335 337 / 2 SELIN1 / 1-12 22 23 33 34 44 45 55 56 66 67 77 78 88 89 99 100 110-121 243-253 265-275 287-297 313-323 / 3 SELIN2 / 11 111 121 243 253 265 275 287 297 309 311 313 323 335 337 / 4 BOTPLY / 122-242 254-264 276-286 298-308 310 312 324-334 336 338 / 5 BOTBLOC / 339-507 / 6 TOPBLOC / 508-628 2928-2938 3148-3158 3368-3378 3588 3608 3628-3638 3848 3868 / ELEMEN 7 MODEL / 1-3168 / NODES 8 MODEL_N / 1-3887 / ELEMEN 9 CONCRE / 289-2288 / NODES 10 CONCRE_N / 339-459 508-2927 / ELEMEN 11 POLYSTY / 1-144 255-264 276-288 2489-2688 2909-3168 / NODES 12 POLYSTY_N / 1-338 460-507 2928-3887 / ELEMEN 13 PLY / 145-254 265-275 2289-2488 2689-2908 / NODES 14 PLY_N / 122-242 254-264 298-308 310 339-470 482-493 518 529 540 551 562 573 584 595 606 617-628 819-1217 2928-3147 3368-3607 / 165

PAGE 166

ELEMEN 15 CONC / 3169-5168 / NODES 16 CONC_N / 339-459 508-1388 3888-12466 / 17 SELIN3 / 339-350 360 361 371 372 382 383 393 394 404 405 415 416 426 427 437 438 448-459 508-519 529 530 540 541 551 552 562 563 573 574 584 585 595 596 606 607 617-628 3888-3898 3908 3919 3929 3940 3950 3961 3971 3982 3992 4003 4013 4024 4034 4045 4055 4066 4076 4087 4097-4118 4128 4139 4149 4160 4170 4181 4191 4202 4212 4223 4233 4244 4254 4265 4275 4286 4296 4307 4317-4327 / 18 SELIN4 / 339 349 449 459 508 518 618 628-647 819-837 1009-1027 1199-1217 4328-4347 4718-4737 5108-5127 5498-5517 / 19 BOUNDA / 1-121 243-253 265-297 309 311-338 471-481 494-628 2928-2938 3148-3378 3588 3608-3887 4108-4327 / ELEMEN 20 OUTER / 5169-6283 / NODES 21 OUTER_N / 1-121 243-253 265-297 309 311-338 471-481 494-628 2928-2938 3148-3378 3588 3608-3887 4108-4327 / 'SUPPORTS' (Boundary Constraints) / 339 350 361 372 383 394 405 416 427 438 449 508 519 530 541 552 563 574 585 596 607 618 629-647 1199-1388 3898 3919 3940 3961 3982 4003 4024 4045 4066 4087 4118 4139 4160 4181 4202 4223 4244 4265 4286 4307 4328-4347 5498-5887 / TR 1 / 339-349 508-518 629-837 3888-3897 4108-4117 4328-4737 / TR 2 / 339-459 3888-4107 / TR 3 :Ambient Temperature 'BOUNDA' CASE 1 ELEMEN 5169 EXTEMP 0.230000E+02 5170 EXTEMP 0.230000E+02 Lines Skipped 5982 EXTEMP 0.230000E+02 5983 EXTEMP 0.230000E+02 :Ambient Temperature Variation with Time 'TIMEBO' BOUNDA 1 TIMES 0.000000E+00 0.167000E+03 / FACTOR 0.100000E+01 0.100000E+01 / 166

PAGE 167

:Selfweight/Gravity Load 'LOADS' CASE 2 WEIGHT 3 -0.981000E-05 :Variation of Load with Time 'TIMELO' LOAD 2 TIMES 0.000000E+00 0.167000E+03 / FACTOR 0.100000E+01 0.100000E+01 / :Initial Temperatures 'INIVAR' TEMPER 1 1 0.230000E+02 2 0.230000E+02 Lines Skipped 12466 0.230000E+02 'DIRECTIONS' 1 1.000000E+00 0.000000E+00 0.000000E+00 2 0.000000E+00 1.000000E+00 0.000000E+00 3 0.000000E+00 0.000000E+00 1.000000E+00 'END' 167

PAGE 168

APPENDIX C STAGGERED ANALYSIS COMMANDS In this appendix, the analysis commands fo r the standard staggered analysis are presented. The standard staggered analysis is one in which the thermal flow analysis is coupled with the structural analysis. The temperatures calc ulated in the thermal analysis are automatically converted to input for th e structural analysis. 168

PAGE 169

*FILOS INITIA Initiate Analysis *INPUT *HEATTR Analysis Type Thermal BEGIN INITIA BEGIN NONLIN EQUAGE Calculate Equivalent Age HYDRAT DGRINI=0.01 END NONLIN TEMPER INPUT FIELD=1 END INITIA BEGIN EXECUT BEGIN NONLIN HYDRAT ITERAT BEGIN ITERAT CONVER TEMPER TOLCON=0.01 MAXITE=30 Maximum No. of Iterations END ITERAT END NONLIN SIZES 1.0(167) Magnitude & No. Time Steps END EXECUT BEGIN OUTPUT FEMVIE FILE="FLOW" File to print to output EQUAGE TOTAL INTPNT TEMPER REACTI TOTAL INTPNT END OUTPUT *NONLIN BEGIN TYPE BEGIN PHYSIC Analysis Type Structural TEMPER Read Temperatures as Input VISCOE Viscoelastic Behaviour END PHYSIC END TYPE BEGIN EXECUTE TIME STEPS EXPLIC SIZES 1.0(167) BEGIN ITERAT BEGIN CONVER SIMULT FORCE TOLCON=1.0E-2 DISPLA TOLCON=1.0E-2 END CONVER END ITERAT END EXECUT BEGIN OUTPUT FEMVIE FILE="STRUC" DISPLA STATUS 169

PAGE 170

STATUS CRACK STRAIN TEMPER STRAIN STRAIN CRACK GREEN STRESS STRESS TOTAL CAUCHY PRINCI STRESS TOTAL CAUCHY CRKIND TEMPER END OUTPUT *END 170

PAGE 171

APPENDIX D PHASED ANALYSIS COMMANDS In this appendix, the analysis commands for th e phased analysis in which the formwork is removed sometime during the hydration process is presented. The example presented here is for the removal of the formwork 96 hours (4 da ys) after the hydrati on reaction commences. 171

PAGE 172

*FILOS INITIA *INPUT *PHASE Start Phase 1 ACTIVE ELEMEN CONC PLY POLYSTY OUTER Elements active in Phase 1 *HEATTR BEGIN INITIA BEGIN NONLIN EQUAGE HYDRAT DGRINI=0.01 END NONLIN TEMPER INPUT END INITIA EXECUT SIZES 1.0(96) BEGIN OUTPUT FEMVIE FILE="FLOW_1m4Days" EQUAGE TEMPER REACTI END OUTPUT *NONLIN BEGIN TYPE BEGIN PHYSIC TEMPER VISCOE END PHYSIC END TYPE BEGIN EXECUTE TIME STEPS EXPLIC SIZES 1.0(96) BEGIN ITERAT BEGIN CONVER SIMULT FORCE TOLCON=1.0E-2 DISPLA TOLCON=1.0E-2 END CONVER END ITERAT END EXECUT BEGIN OUTPUT FEMVIE FILE="STRUC_1m4Days" DISPLA STRAIN TEMPER STRAIN STRESS STRESS TOTAL CAUCHY PRINCI STRESS TOTAL CAUCHY CRKIND TEMPER 172

PAGE 173

END OUTPUT *END *PHASE Start Phase 2 BEGIN ACTIVE ELEMEN CONC OUTER2 Elements active in Phase 2 END ACTIVE *HEATTR Analysis Type Thermal BEGIN INITIA BEGIN NONLIN EQUAGE HYDRAT DGRINI=0.01 END NONLIN TIME=96. Phase 2 Start time TEMPER INPUT END INITIA EXECUT SIZES 1.0(71) BEGIN OUTPUT FEMVIE FILE="FLOW_1m4Days2" EQUAGE TOTAL INTPNT TEMPER REACTI TOTAL INTPNT END OUTPUT *NONLIN BEGIN TYPE BEGIN PHYSIC Analysis Type Structural TEMPER VISCOE END PHYSIC END TYPE BEGIN EXECUTE BEGIN START TIME=96.0 Phase 2 Start time INITIA STRESS PHASE LOAD LOADNR=3 Activate Load No. 3 STEPS END START BEGIN ITERAT BEGIN CONVER SIMULT FORCE TOLCON=1.0E-2 DISPLA TOLCON=1.0E-2 END CONVER END ITERAT END EXECUT BEGIN EXECUTE 173

PAGE 174

TIME STEPS EXPLIC SIZES 1.0(71) BEGIN ITERAT BEGIN CONVER SIMULT FORCE TOLCON=1.0E-2 DISPLA TOLCON=1.0E-2 END CONVER END ITERAT END EXECUTE BEGIN OUTPUT FEMVIE FILE="STRUC_1m4Days2" DISPLA STRAIN TEMPER STRAIN STRESS STRESS TOTAL CAUCHY PRINCI STRESS TOTAL CAUCHY CRKIND TEMPER END OUTPUT *END 174

PAGE 175

LIST OF REFERENCES ACI Committee 207 (2005), 207.1R-05: Guide to Mass Concrete, Farmington Hill, MI USA. ACI Committee 207 (2005), 207.2R07: Report on Thermal and Volume Change Effects on Cracking of Mass Concrete, Farmington Hills, MI USA. Ayotte, E., Massicotte, B. Houde, J., Gocevski, V. (1997) Modeling of Thermal Stresses at Early Ages in a Concrete Monolith, ACI Ma terials Journal, 94,.6, Figure 1, 577-587 Bamforth, P.B., (1984). Mass Concrete. Concre te Society Digest. Concrete and Cement Association. Ballim, Y.A. (2003). A Numerical Model and Associated Calorimeter for Predicting Temperature Profiles in Mass Concrete. Cem. Concr. Compos., 26(6), 695-703 Branco, F., Mendes, P.E., Mirambell, E. (1992). Heat of Hydration E ffects in Concrete Structures. ACI Materials Journal, 89, 2, 139-145. Bentz, d. (1997). Three-Dimensional Computer Simulation of Portland Cement Hydration and Microstructure Development. J. Am Ceram. Soc., 80, 1. Burg, R.G., and Fiorato, A.E. (1999). High-Strength Concrete in Massive Foundation Elements. Research and Development Bulletin RD117, Portland Cement Association, Skokie, Illinois, U.S.A. De Schutter, G. (2002). Finite Element Simula tion of Thermal Cracking in Massive Hardening Concrete Elements Using Degree of Hydrati on Based Material Laws. Comput. Struct., 80, 2035-2042. De Schutter, G., and Taerwe, L. (1995). General Hydration Model for Portland Cement and Blast Furnace Slag Cement. Cem. Concr. Res., 25(3), 593-604. De Schutter, G., and Taerwe, L. (1995). Specifi c Heat and Thermal Diffusivity of Hardening Concrete. Mag. Concr. Res., 47(172), 203-208. Escalante-Garcia, J.I., and Sharp, J.H. (2001). The Microstructure and Mechanical Properties of Blended Cements Hydrated at Various Temp eratures. Cem. Concr. Res, 31(5) 675-702. Evju, C., (2003). Initial Hydration of Cementitious Systems Using a Simple Isothermal Calorimeter and Dynamic Correction. Journal of Thermal Analysis and Calorimetry 71, 829-840. Faria, R., Azenha, M., and Figueir as, J. (2006). Modeling of concre te at early ages: Application to an externally restrained sl ab. Cem. Concr. Compos., 28, 572-585. Florida Department of Transportation, Sta ndard Specifications for Road and Bridge Construction, Florida Department of Transportation, Tallahassee 2007. 175

PAGE 176

Gajda, J., (2007). Mass Concrete for Buildings and Bridges, Portland Cement Association Skokie, Illinois. Khan, A., Cook, W., and Mitchell, D. (1998). Ther mal Properties and Transient Analysis of Structural Members During Hydration. ACI Materials Journal. 95(28) 293-300. Klein, A., Pirtz, D., and Adams, R.F., (1963). Thermal Propertie s of Mass Concrete During Adiabatic Curing. Symposium on Mass Concrete, ACI SP-6, 199-218. Machida, N., and Uehara, K., (1987). Nonlinear Th ermal Stress Analysis of a Massive Concrete Structure. Comput. Struct., 26, 287-296. Majorana, C.E., Zavarise, G., Borsetto, M., and Giuseppetti (1990). Nonlinear Analysis of Thermal Stresses in Mass Concrete Castings. Cem. Concr. Res., 20, 559-578. Morabito, P., (1998). Methods to Determine Heat of Hydration of Concrete, Prevention of Thermal Cracking in Concrete at Earl y Ages., RILEM Report 15, Edited by R. Springenschmid, E&FN Spon, London. Nasser, K.W., Lothia, R.P. (1971). Mass Concre te Properties at High Temperatures. J. Am. Concr. Inst., 68(3), 180-186. Neville, A., (1995). Properties of Concrete 4th Edition., Essex, England Pearson Education Limited. Radovanovic, S., (1998). Thermal and Structural Finite Element Analysis of Early Age Mass Concrete Structures. University of Manitoba, Winnipeg, Manitoba, Canada. Ulm, F., and Coussy, O. (2001). What is a Mass ive Concrete Structure at Early Ages? Some Dimensional Arguments. J. Eng. Mech., 127(5), 512-522. U.S. Army Corps of Engineers. (1997). A ppendix A: Techniques for Performing Concrete Thermal Studies. Manual ETL 1110-2-542, Washington, D.C. U.S. Army Corps of Engineers. (1997). A ppendix A: Techniques for Performing Concrete Thermal Studies. Manual ETL 1110-2-542, Washington, D.C. 176

PAGE 177

BIOGRAPHICAL SKETCH The author began his undergraduate edu cation in 1996 at Howard University in Washington, D.C. On graduating with a Bachel or of Science degree in civil engineering in May 1999, he returned to his home country Jamaica to work at the civil engineering consulting firm Jentech Consultants Limited. In August 2000, the author returned to the United States to study at the University of Miami, Coral Gables, Florida obtaining a Master of Science degree in civil engineering, with emphasis in struct ural engineering, in December 2002. Once again the author returned to Jamaica to work at Jentech until August 2005 when he enrolled at the Univer sity of Florida to pursue a Doctor of Philosophy degree in civil engin eering, with a concentration in materials engineering. The author anticipates obtaining this degree in December 2009. 177