<%BANNER%>

Finite Element Modeling of Behavior of Mass Concrete Placed on Soil

MISSING IMAGE

Material Information

Title:
Finite Element Modeling of Behavior of Mass Concrete Placed on Soil
Physical Description:
1 online resource (151 p.)
Language:
english
Creator:
Do, Tu Anh
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
Tia, Mang
Committee Members:
Najafi, Fazil T
Roque, Reynaldo
Muszynski, Larry C
Lawrence, Adrian M

Subjects

Subjects / Keywords:
concrete -- cracking -- differential -- early-age -- element -- finite -- footing -- instrumentation -- insulation -- isothermal -- mass -- monitoring -- r-value -- soil -- 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 finiteelement model for the prediction of temperatures and cracking potential of massconcrete footings placed on soil. To evaluate the effectiveness of thetemperature predictions from the model, three different bridge pier footings inFlorida weremonitored for temperature developments. The measured temperatures were comparedwith the predicted results obtained from the model. Isothermal calorimetrytesting was done on the cementitious materials of concrete mixtures todetermine the energy released during hydration, which was then converted totemperature rise as inputs for the finite element model. Analysis of influencesof thermal properties of soil on temperature development and cracking in massconcrete footings was conducted. A parametric study on the effects ofdimensions of three types of rectangular footings on the maximum allowabletemperature differential to prevent cracking in concrete was conducted. Auser-friendly computer program called “DIANA Input File Generator” wasdeveloped to provide the needed input files to the TNO DIANA software formodeling of typical mass concrete structures such as rectangular footings andcolumns. The developed finite element model in this study predictedtemperatures reasonably well in mass concrete footings based on the comparisonsof the computed and measured temperatures. The thermal properties of the soilupon which the footing is placed have great influence on the temperature developmentof the concrete and thus the soil needs to be properly modeled in the analysis.From the parametric study conducted, it was found that bottom insulation wouldnot be needed when a mass concrete footing is placed on dry soil, or on soilwith an R-value of 0.41 or greater. Smaller footings do not require a smallermaximum allowable temperature differential to prevent cracking by thermalcontraction. Recommendations on evaluating the thermal properties ofsoil in different in situ conditions, monitoring of footings directly placed onsoil, and development of a data base of rate of heat production of differentcement blends 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 Tu Anh Do.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Tia, Mang.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045352:00001

MISSING IMAGE

Material Information

Title:
Finite Element Modeling of Behavior of Mass Concrete Placed on Soil
Physical Description:
1 online resource (151 p.)
Language:
english
Creator:
Do, Tu Anh
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
Tia, Mang
Committee Members:
Najafi, Fazil T
Roque, Reynaldo
Muszynski, Larry C
Lawrence, Adrian M

Subjects

Subjects / Keywords:
concrete -- cracking -- differential -- early-age -- element -- finite -- footing -- instrumentation -- insulation -- isothermal -- mass -- monitoring -- r-value -- soil -- 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 finiteelement model for the prediction of temperatures and cracking potential of massconcrete footings placed on soil. To evaluate the effectiveness of thetemperature predictions from the model, three different bridge pier footings inFlorida weremonitored for temperature developments. The measured temperatures were comparedwith the predicted results obtained from the model. Isothermal calorimetrytesting was done on the cementitious materials of concrete mixtures todetermine the energy released during hydration, which was then converted totemperature rise as inputs for the finite element model. Analysis of influencesof thermal properties of soil on temperature development and cracking in massconcrete footings was conducted. A parametric study on the effects ofdimensions of three types of rectangular footings on the maximum allowabletemperature differential to prevent cracking in concrete was conducted. Auser-friendly computer program called “DIANA Input File Generator” wasdeveloped to provide the needed input files to the TNO DIANA software formodeling of typical mass concrete structures such as rectangular footings andcolumns. The developed finite element model in this study predictedtemperatures reasonably well in mass concrete footings based on the comparisonsof the computed and measured temperatures. The thermal properties of the soilupon which the footing is placed have great influence on the temperature developmentof the concrete and thus the soil needs to be properly modeled in the analysis.From the parametric study conducted, it was found that bottom insulation wouldnot be needed when a mass concrete footing is placed on dry soil, or on soilwith an R-value of 0.41 or greater. Smaller footings do not require a smallermaximum allowable temperature differential to prevent cracking by thermalcontraction. Recommendations on evaluating the thermal properties ofsoil in different in situ conditions, monitoring of footings directly placed onsoil, and development of a data base of rate of heat production of differentcement blends 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 Tu Anh Do.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Tia, Mang.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045352:00001


This item has the following downloads:


Full Text

PAGE 1

FINITE ELEMENT MODELING OF BEHAV IOR OF MASS CONCRET E PLACED ON SOIL By TU ANH DO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORID A IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013 1

PAGE 2

2013 Tu Anh Do 2

PAGE 3

To my fa mily 3

PAGE 4

ACK NOWLEDGMENTS First of all, I would like to express my sincere gratitude to Dr. Mang Tia for his valuable support, encouragement, and guidance during my doctoral research. I have benefited tremendously from his experienc e and research methodology. He has provided for me not only his knowledge but also his kind consideration. I would also like to thank the other members of my committee, Dr. Reynaldo Roque, Dr. Fazil Najafi, Dr. Larry Muszynski, and Dr. Adrian M. Lawrence for their valuable comments and suggestions. I would like to thank Dr. Yu Chen for her assistance in the testing of heat of hydration of cementitious materials and gui dance on using the DIANA software. I would like to thank Dr. Dale DeFord of the FDOT Materials Laboratory, Gai nesville, for his help on the isothermal calorimetry testing. I woul d also like to thank Ohhoon Kwon for his assistance in the field testing of mass concrete. I would like to thank my family for encouraging my studies. Finally, I extend thanks to my friends who have given me s upport and motivation throughout my years of study. 4

PAGE 5

TABL E OF CONTENTS page ACKNOWLEDGMENTS ..................................................................................................4 LIST OF TABLES ............................................................................................................8 LIST OF FIGURES ..........................................................................................................9 ABSTRACT ...................................................................................................................14 CHA PTER 1 INTRODUC TION ....................................................................................................16 Background .............................................................................................................16 Hypothesis ..............................................................................................................18 Research Needs .....................................................................................................18 Objectives of Research ...........................................................................................18 Research Approach ................................................................................................19 Outline of Dissertation .............................................................................................20 2 LITERATURE REVIEW ..........................................................................................22 Overview of Literature Review ................................................................................22 Two-Dimensional Finite Element and Finite Difference Analyses ...........................22 Three-Dimensional Finite Element Analysis ...........................................................26 Adiabatic Temperature Rise Model .........................................................................31 3 FINITE ELEMENT THERMAL MO DEL ...................................................................39 Overview of Finite Element Thermal Model ............................................................39 Element Selection ...................................................................................................40 Input Parameters ....................................................................................................41 Heat of Hydration .............................................................................................41 Conductivity and Heat Capacity .......................................................................44 Convection .......................................................................................................47 Model Geometry .....................................................................................................48 Boundary Conditions ..............................................................................................48 4 FINITE ELEMENT ST RUCTURAL MO DEL ............................................................55 Overview of Finite Element Structural Model ..........................................................55 Element Selection ...................................................................................................55 Material Model ........................................................................................................56 Input Parameters ....................................................................................................56 Modulus of Elasticity .........................................................................................56 5

PAGE 6

Poissons Ratio .................................................................................................57 Coefficient of Thermal Expansion .....................................................................57 Tensile Strength ...............................................................................................58 Symmetry and Boundary Conditions ......................................................................58 5 INSTRUMENTATION AND MONITO RING OF MASS CONCRETE ......................60 Overview .................................................................................................................60 Selected Mass Concrete Structures .......................................................................60 Instrumentation .......................................................................................................61 Proposed Locations for Temperature Sensors .................................................61 Footings .....................................................................................................61 Columns and Pier Cap ...............................................................................61 Data Acquisition Equipment .............................................................................61 Monitoring of Selected Mass Concrete Structures ..................................................62 Footing 1 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) ..........................62 Footing 2 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) ..........................63 Footing 3 (at I-4 US-192 Braided Ramp, Orlando, FL) .....................................64 6 COMPARISONS OF FINITE EL EMENT RESUL TS WITH FIELD MEASUREME NTS.................................................................................................76 Overview .................................................................................................................76 Footing 1 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) ................................76 Footing 2 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) ................................76 Footing 3 (at I-4 US-192 Braided Ramp, Orlando, FL) ...........................................77 7 EFFECTS OF THERMAL PROPERTI ES OF SOIL ON TEMPERATURE DEV ELOPMENT AND CRACKING IN FO OTINGS DIRECTLY PLACED ON SOIL........................................................................................................................87 Description of Analysis Method ...............................................................................87 Soil Temperature Distribution .................................................................................88 Temperature Development in Concrete ..................................................................89 Thermal Cracking Analysis .....................................................................................89 Summary of Findings ..............................................................................................91 8 EFFECTS OF FOOTINGS DIME NSIONS AND INSULATION ON TEMPERATURE DEVELOPMENT AND CRACKING IN CONCRETE ...................99 Description of the Parametric Study .......................................................................99 Effects of Footings Dimensions on Temperature Develo pment and Cracking .......99 Effects of Footings Shape on Tem perature Development and Cracking .............101 Determination of Required Insulation Thickness ...................................................102 Summary of Findings ............................................................................................103 9 DEVELOPMENT OF SOFTWARE FOR GENE RATING DIANA INPUT FILES ....117 6

PAGE 7

Overview ...............................................................................................................117 DIANA Input File Generator ..................................................................................117 Running DIANA ....................................................................................................118 Example ................................................................................................................119 Creating a Model Using DIFG ........................................................................119 Results and Post-Processing Commands in iDIANA ......................................120 Thermal Results .......................................................................................120 Stress Results ..........................................................................................121 10 CLOSUR E ............................................................................................................134 Summary of Findings ............................................................................................134 Conclusions and Recommendations ....................................................................135 APPENDIX A iDIANA INPUT COMMANDS OF A FULLY INSULATED CONCRETE MODEL...138 B CONTENTS OF CONCRETE PROPER TY FILE CONCRE TE.DAT ..................143 LIST OF REFERENCES .............................................................................................149 BIOGRAPHICAL SKETCH ..........................................................................................151 7

PAGE 8

LIST OF TABLES Table page 5-1 Selected mass concrete structures .....................................................................66 5-2 Temperature sensor elevation in Footing 2 ........................................................66 5-3 Thermal properties of concrete, sand, insulat ing blanket, plywood and polystyrene foam ................................................................................................66 7-1 Thermal Properties of Sand and Clay .................................................................93 7-2 Physical Properties of Concrete .........................................................................93 7-3 Footing Dimesions and Vo lume-to-Surface Area Ratio ......................................93 8-1 Temperatures and crack index in cubic footings insu lated with 0.5-in Styrofoam .........................................................................................................105 8-2 Temperatures and crack i ndex in cubic footings in sulated with 1-in Styrofoam 105 8-3 Temperatures and crack index in cubic footings insulated with 1.25-in Styrofoam .........................................................................................................105 8-4 Temperatures and crack index in 4:4:1 footings insulated with 0.5-in Styrofoam .........................................................................................................105 8-5 Temperatures and crack i ndex in 4:4:1 footings in sulated with 1-in Styrofoam 106 8-6 Temperatures and crack index in 4:4:1 footings insulated with 1.25-in Styrofoam .........................................................................................................106 8-7 Temperatures and crack index in 4:2:1 footings insulated with 0.5-in Styrofoam .........................................................................................................106 8-8 Temperatures and crack i ndex in 4:2:1 footings in sulated with 1-in Styrofoam 106 8-9 Temperatures and crack index in 4:2:1 footings insulated with 1.25-in Styrofoam .........................................................................................................107 8-10 Required insulation thickness and maximum temperature differential for different V/As ....................................................................................................107 8

PAGE 9

LIST OF FIGURES Figure page 1-1 Research approach diagram. .............................................................................21 2-1 Diagram of the vertical cross-sect i on assumed in modeling a 2-D footing (Riding 2007). .....................................................................................................33 2-2 Rectangular footi ng model (Riding 2007). ..........................................................33 2-3 Locations for temperature and stress measurements in a reinforced concrete wall (Machida and Uehara 1987). .......................................................................34 2-4 Finite element mesh (Machida and Uehara 1987). .............................................35 2-5 Thermocouple and strain gauge locations in the James Bay concrete monolith (Ayotte et al. 1997). ..............................................................................36 2-6 Finite element model of one fourth of the concrete block with insulation (Lawrence et al. 2012). .......................................................................................37 2-7 Typical location and distribution of cracking found in experimental blocks (Lawrence et al. 2012) (photo c ourtesy of Adrian M. Lawrence). .......................37 2-8 K and values of adiabatic tem perature rise (Radovanic 1998). .......................38 3-1 Elements used to model early age concrete behavior. .......................................50 3-2 Four-node isoparametric boundary element (BQ4HT). .......................................50 3-3 Hydration power of cementitious mi xture (used in Footing at I-4 US-192 Braided Ramp, Orlando, FL) obtained from isothermal calorimetry testing. .......50 3-4 Adiabatic temperature rise of a concrete mixture calculated from the hydration power obtained in the isothermal calorimetry testing. .........................51 3-5 One-dimensional c onduction heat transfer. ........................................................51 3-6 Differential volume for a rectangular solid. .........................................................52 3-7 Convection heat transfer (Thomas 1980). ..........................................................52 3-8 General finite element me sh of one-quarter of footing. .......................................53 3-9 External temperatures imposed on fi nite element model representing the ambient conditions. .............................................................................................54 9

PAGE 10

3-10 Ambient temperature duri ng the monitoring of a pier footing at S.R. 826 and S.R. 836 Interchange, Miami, FL. .......................................................................54 4-1 Twenty-node isoparametric solid brick element CHX60. ....................................59 4-2 Symmetry conditions and supports of model. .....................................................59 5-1 Data logger attached to reinforcing steel bar of footi ng (photo courtesy of Adrian M. Lawrence). .........................................................................................67 5-2 Data acquisition equipm ent used in Footing 2 and Footing 3 (photo courtesy of Adrian M. Lawrence). .....................................................................................67 5-3 Mass concrete block, plywoo d panels, bottom and top insulation. .....................68 5-4 Concrete being placed for Footing 1 (photo courtesy of Ad rian M. Lawrence). ..68 5-5 Data acquisition equip ment with thermocouple wiring (photo courtesy of Adrian M. Lawrence). .........................................................................................69 5-6 Temperatures measured at bo ttom, middle and top of Footing 1. ......................69 5-7 View of Footing 2 (photo c ourtesy of Adrian M. Lawrence). ...............................70 5-8 Locations of temperat ure sensors in Footing 2. ..................................................71 5-9 Ambient temperature during the monitoring of Footing 2. ...................................71 5-10 Profile of temperatures measured along vertic al centerline of Footing 2. ...........72 5-11 Profile of temperatures m easured at mid-side of Footing 2. ...............................72 5-12 Profile of temperatures meas ured at the corner of Footing 2. ............................73 5-13 Profile of temperatures measur ed by sensors 16 to 20 in Footing 2. ..................73 5-14 Footing at I-4 US-192 Braided Ramp, Orlando, FL (photo courtesy of Adrian M. Lawrence). .....................................................................................................74 5-15 Dimensions of Footing 3. ....................................................................................74 5-16 Measured temperatur es at top, mi ddle, and bottom of footing. ..........................75 6-1 Temperature contour at 7 day in Footing 1 model.th...........................................78 6-2 Comparison between measured temper atures and FE results of Footing 1. ......78 6-3 Predicted temperature dist ribution 7 days after concrete placement in Footing 2. ........................................................................................................................79 10

PAGE 11

6-4 Predicted and measured temperatures in Sensors 1 and 2 along vertical centerline of Footing 2. .......................................................................................79 6-5 Predicted and measured te mperatures in Sensor 3 along vertical centerline of Footing 2. ........................................................................................................80 6-6 Predicted and measured te mperatures in Sensor 4 along vertical centerline of Footing 2. ........................................................................................................80 6-7 Predicted and measured te mperatures in Sensor 5 along vertical centerline of Footing 2. ........................................................................................................81 6-8 Predicted and measured temperatures in Sensors 6 and 7 at mid-side of Footing 2. ...........................................................................................................81 6-9 Predicted and measured temperatures in Sensors 8 and 9 at mid-side of Footing 2. ...........................................................................................................82 6-10 Predicted and measured temperatures in Sensors 11 and 12 at the corner of Footing 2. ...........................................................................................................82 6-11 Predicted and measured tem peratures in Sensor 13 at the corner of Footing 2. ........................................................................................................................83 6-12 Predicted and measured tem peratures in Sensor 14 at the corner of Footing 2. ........................................................................................................................83 6-13 Predicted and measured tem peratures in Sensor 15 at the corner of Footing 2. ........................................................................................................................84 6-14 Predicted temperature dist ribution 7 days after concrete placement in Footing 3. ........................................................................................................................84 6-15 Predicted and measur ed temperatures at t he top of Footing 3. ..........................85 6-16 Predicted and measured temperatures at the center of Footing 3. .....................85 6-17 Predicted and measur ed temperatures at t he bottom of Footing 3. ....................86 7-1 Finite element mesh of concrete footing in direct contact with soil. ....................94 7-2 Temperature distribution in soil 7 days after concrete placement. ......................94 7-3 Temperature with respect to depth in dry sand 7 days after concrete placement. ..........................................................................................................95 7-4 Temperature with respect to depth in saturated sand 7 days after concrete placement. ..........................................................................................................95 11

PAGE 12

7-5 Temperature development in concrete footing placed on dry sand. ...................96 7-6 Temperature developm ent in concrete footi ng placed on saturated sand. .........96 7-7 Minimum calculated crack index in concrete on sand. ........................................97 7-8 Minimum calculated crack index in concrete on clay. .........................................97 7-9 Minimum calculated crack index in concrete on soil with varying R-value. .........98 7-10 Minimum calculated crack index in diffe rent concrete footings on soil with Rvalues of 0.29 and 0.41. .....................................................................................98 8-1 Maximum temperature in cubic footings. ..........................................................108 8-2 Maximum temperature difference in cubic footings. .........................................108 8-3 Crack Index in cubic footings. ...........................................................................109 8-4 Maximum temperature in 4:4:1 footings. ..........................................................109 8-5 Maximum temperature diffe rence in 4:4:1 footings. ..........................................110 8-6 Crack Index in 4:4:1 footings. ...........................................................................110 8-7 Maximum temperature in 4:2:1 footings. ..........................................................111 8-8 Maximum temperature diffe rence in 4:2:1 footings. ..........................................111 8-9 Crack Index in 4:2:1 footings. ...........................................................................112 8-10 Maximum temperature in footings insulated with 0.5-in Styrofoam. ..................112 8-11 Maximum temperature in footings insulated with 1-in Styrofoam. .....................113 8-12 Maximum temperature in footings insulated with 1.25-in Styrofoam. ................113 8-13 Maximum temperature difference in f ootings insulated with 0.5-in Styrofoam. .114 8-14 Maximum temperature difference in f ootings insulated with 1-in Styrofoam. ....114 8-15 Maximum temperature difference in footings insulated with 1.25-in Styrofoam. ........................................................................................................115 8-16 Crack Index in footings in sulated with 0.5in Styrofoam. ..................................115 8-17 Crack Index in footings insulated with 1in Styrofoam. .....................................116 8-18 Crack Index in footings in sulated with 1.25in Styrofoam. ................................116 12

PAGE 13

9-1 Software for generati ng DIANA input files. .......................................................123 9-2 Browsing a concrete property file. ....................................................................123 9-3 Generating process. .........................................................................................124 9-4 Message indicating the process is completed. .................................................124 9-5 DIANA analysis setup. ......................................................................................124 9-6 Selecting analysis type. ....................................................................................125 9-7 Open command file. .........................................................................................125 9-8 Input parameters for DIFG. ...............................................................................126 9-9 Detailed contents of CONCRET E.dat file. ......................................................126 9-10 Open FLOW.V72 for thermal results. ...............................................................127 9-11 Sketch of model. ...............................................................................................127 9-12 Transparent mesh view of concrete and soil. ...................................................128 9-13 Hidden-fill view of concrete and soil. ................................................................128 9-14 Another view using eye-rotation of 30, 45 and 45 degrees. ..............................129 9-15 Labeling node names of current mesh. ............................................................129 9-16 Temperature graph vs. ti me at Nodes 3850, 957, and 1245. ...........................130 9-17 Temperature contour in concrete and soil at 100th hour. .................................130 9-18 First principal stress graph vs. time of node of element . ..............131 9-19 Crack index contour of concrete at 167th hour. ................................................132 9-20 First principal stress contour of concrete at 24th hour. .....................................133 13

PAGE 14

Abstract of Dissertation Pr esented to the Graduate School of the University of Fl orida in Partial Fulf illment of the Requirements for t he Degree of Doctor of Philosophy FINITE ELEMENT MODELING OF BEHAV IOR OF MASS CONCRETE PLACED ON SOIL By Tu Anh Do August 2013 Chair: Mang Tia Major: Civil Engineering This dissertation presents the development of a finite element model for the prediction of temperatures and cracking potential of mass co ncrete footings placed on soil. To evaluate the effectiveness of the te mperature predictions from the model, three different bridge pier footings in Florida we re monitored for temperature developments. The measured temperatures were compared with the predicted resu lts obtained from the model. Isothermal calorimetry testing was done on the cementitious materials of concrete mixtures to determine the energy released during hydration, which was then converted to temperature rise as inputs fo r the finite element model. Analysis of influences of thermal properties of soil on temperature development and cracking in mass concrete footings was conducted. A param etric study on the effects of dimensions of three types of rectangular footings on the maximum allowable temperature differential to prevent cracking in concrete was conducted. A user-friendly com puter program called DIANA Input File Generator was developed to provide the needed input files to the TNO DIANA software for modeling of typica l mass concrete structures such as rectangular footings and columns. 14

PAGE 15

15 The developed finite element model in this study predicted temperatures reasonably well in mass concrete footings based on the comparisons of the computed and measured temperatures. The thermal proper ties of the soil upo n which the footing is placed have great influence on the temper ature development of the concrete and thus the soil needs to be properly modeled in the analysis. From the parametric study conducted, it was found that bottom insu lation would not be needed when a mass concrete footing is placed on dry soil, or on soil with an R-value of 0.41 or greater. Smaller footings do not require a smaller ma ximum allowable temper ature differential to prevent cracking by thermal contraction. Recommendations on evaluating the thermal properties of so il in different in situ conditions, monitoring of footings direct ly placed on soil, and development of a data base of rate of heat production of diffe rent cement blen ds are presented.

PAGE 16

CHA PTER 1 INTRODUCTION Background During hydration of cement, heat is gener ated causing a rise in internal temperature in mass concrete structures. Th e temperature at the exterior surface is dissipated to the surrounding environment while the interior portion of the concrete mass is still being heated, or cooling more slo wly, resulting in temperature differential. This temperature drop at the surface results in thermal contraction of the concrete. With the interior of the concrete being more mature than the surfac e, it acts as a restraint against the contraction, induci ng tensile stresses at the surface. Since the concrete is still in its early age, its full tensile strength is not develo ped, and if the tensile stresses exceed the early age tensile str ength of the concrete, therma l cracking will occur (ACI 207.1R 2005; ACI 207.2R 2007). For mass conc rete structures below grade such as footings, no amount of cracking is permissi ble due to the high threat of moisture infiltration (groundwater) and the deleterious e ffect that will have on reinforcing steel and the concrete itself. Mass concrete is defined by the Americ an Concrete Institute (ACI) as any volume of concrete with dimensions large en ough to require that measures be taken to cope with generation of heat from hydration of the ce ment and attendant volume change, to minimize cracking. The Flor ida Department of Tr ansportation (FDOT) Structures Manual defines mass concrete to be the following: 1) All Bridge components Except Drill ed Shafts: When the minimum dimension of the concrete exceeds 3 feet and the ratio of volume of concrete to the surface area is greater than 1 foot, provide for mass concrete. (The surface area for this ratio includes the summati on of all the surface areas of the concrete component being considered, including the full underside (bottom) 16

PAGE 17

surface of footings, caps, construction joints, etc.) Note volume and surface area calculations in units of feet. 2) Drilled Shafts: All drilled shafts with diameters greater t han 6 feet shall be designated as mass concrete and a Technical Special Provision shall be required (FDOT 2009; FDOT 2013). To minimize thermal cracking problem in mass concrete, the Florida Department of Transportation Standard Specifications for Road and Bridge Construction (FDOT 2007; FDOT 2010) requires that the maximum allowable temperature is 180F (82C) and temperature differential bet ween the concrete core and the exterior surface does not exceed 35F (20C). To reduce the temperature differentia ls, and thus prevent cracking in mass concrete, some of the common methods such as precooling of concrete, post cooling of concrete with cooling pipes, and insulation or insulated formwork should be used. The thermal stresses in large mass concrete elem ents were effectively reduced with the use of thick layers of insulating polystyrene foam This method is advantageous because the polystyrene foam, if removed carefully, c an be reused often making it relatively inexpensive when compared to other single use methods such as cooling pipes and liquid nitrogen. Adequate insulation shoul d be used in conjunction with the usual formwork material to reduce t he temperature differentials dur ing the early age hydration of massive concrete (Tia et al. 2010). In practice, mass concrete structures such as footings have usually been placed directly on top of a soil layer and an insulation layer is not used at the bottom of the concrete. The rationale for this practice is that the soil on which the concrete is placed is already an insulating material. 17

PAGE 18

Hypothesi s An insulating layer between concrete and soil may be needed to prevent earlyage thermal cracking if the soil is wet or if the soil has a low R-value. Smaller footings may require a sm aller maximum allowable temperature differential than larger footings to prevent cracking induced by thermal contraction. Larger footings may require thicker layers of insulation than smaller footings to prevent early-age cracking in the concrete. Research Needs Although the FDOT Standard Specifications for Road and Bridge Construction The requires that the maximu m temperature differential between the concrete core and the exterior surface does not exceed 35F (20 C), it is not clear whether or not this limiting value is dependent on a footings dimensions. This research investigates the effects of a rectangular footings dimensio ns on the maximum allowable temperature differential to prevent cracking in the concrete. This study also investigates the thermal performance and cracking risk of rectangular mass concrete footings placed directly and indirectly on soil, and determines the required insulation to prevent early-age cracking in the concrete. Objectives of Research The specific objectives of the research are: To develop a 3-D finite element model of mass concrete footings and compare the predicted temperatures from the model with measured temperatures. To evaluate the effects of thermal properties of soil on the temperature development and thermal cracking in mass concrete footings placed directly on soil. To investigate the effects of a foot ings dimensions and insulation on the maximum allowable temperature different ial to prevent cracking induced by thermal contraction. 18

PAGE 19

Research Approach The research is an analytical study s upplemented by laboratory testing and field testing. The overall research approach is pr esented in a flow chart in Figure 1-1. The main tasks performed are as follows: Literature review on the behavior of mass co ncrete at early age and review of finite element method for predicting temperat ures, thermal stresses, and cracking potential in mass concrete structures. Finite Element Modeling of Mass Conc rete Footings: Rectangular mass concrete footings were modeled. The analyses invo lved thermal analysis, stress analysis and cracking prediction. The temper ature predictions from the finite element model were compared with the temperatures measured in the field. Laboratory Testing Program: The material properties which were needed as input parameters for the finite elem ent modeling were obtained in this laboratory testing program. The input parameters needed for the envisioned finite element modeling included the following: 1. Cement Heat of Hydration: Obta ined via Isothermal Calorimetry Testing (University of Florida Method (Tia et al. 2010)) 2. Coefficient of Thermal Expansi on of Concrete (AASHTO TP 60) 3. Modulus of Elasticity for Concrete (ASTM C469) 4. Splitting Tensile Strength of Concrete (ASTM C496) 5. Poissons Ratio of Concrete (ASTM C469) Instrumentation and Monitoring of Select ed Mass Concrete Footings: Temperature sensors were installed on the selected mass concrete footings to record temperatures. Comparison of Predictions from Finite Element Modeling with Field Measurements: Comparisons were made between the predi cted temperatures from the finite element model and the measurements fr om the instrumented mass concrete footings. Necessary adjustments in the finite element modeling were made as needed. The results from the finite element modeling were used to identify areas where cracking was likely to occur. Development of Computer Software for Mass Concrete Structures in Florida: As a by-product, a user-friendly computer pr ogram was developed fo r generating inputs to the DIANA software for analysis of some common mass concrete structures such as rectangular footings, columns and pier caps. 19

PAGE 20

Outline of Dissertation Chapter 2 presents a literat ure review on the behavior of mass concrete at early ages and a review of fi nite element mode ling for predicting temperatures, thermal stresses, and cracking potential in mass concrete structures. Chapters 3 and 4 discuss the finite element modeling including input parameters, material model, structural model, element types, and boundary conditions used in the thermal and stress analyses. Chapter 5 describes instrumentation and monitoring of selected mass concrete footings and discusses the measured results. Chapter 6 presents the comparisons of the finite element results with the field measurements. Chapter 7 presents the analysis on the effe cts of thermal properties of soil on temperature development and thermal cr acking in mass concrete footings. Chapter 8 presents the investigation on the effects of a footings dimensions on temperature development and thermal cracki ng in the concrete, and the determination of the required insulation thickness for footings. Chapter 9 presents the devel opment of computer prog ram for generating inputs to the DIANA software for analysis of some common mass concrete structures such as rectangular footings, columns and pier caps in Florida. Chapter 10 presents the findings and conclusions from this study, and recommendations for future research. 20

PAGE 21

21 Figure 1-1. Research approach diagram. Adiabatic Temperature Rise of Cementitious Material Mechanical and Thermal Properties of Concrete Laboratory Tests FE Model Actual Mass Concrete Input Parameters Ambient Temperature Thermal Properties of Soil and Insulating Materials Stress Analysis Cracking Analysis Temperature Analysis Measured Temperature Compare Evaluation Conclusions and Recommendations Mix Design Info. Effects of Thermal Properties of Soil on Temperature Development and Cracking in Footings Directly Placed on Soil Effects of Footings Dimensions and Insulation on Temperature Development and Cracking in Rectangular Footings Literature Review

PAGE 22

CHA PTER 2 LITERATURE REVIEW Overview of Lite rature Review Mass concrete is defined by the Americ an Concrete Institute (ACI) as any volume of concrete with dimensions large en ough to require that measures be taken to cope with generation of heat from hydration from cem ent and attendant volume change to minimize cracking. Increas ingly, this definition refers to a larger spectrum of structures, but most impor tantly applies to concrete dams and large concrete foundations, the failure of which can have disastrous consequences to human life and property. For this reason, the study and understanding of mass concrete has been of interest to engineers fo r the last 70 years. Along with the observation of mass c oncrete experiments at early ages, numerical models have been devel oped in the past decades to investigate the early-age behavior of mass concrete and predict ther mal cracking potential in mass concrete structures. This chapter presents a lit erature review on the methods for analysis of mass concrete structures. Two-Dimensional Finite Element and Finite Difference Analyses In 1998, Radovanovic conducted a 2-D fini te element (FE) analysis with the aid of the commercial software ANSYS to predi ct the early stage behavior of concrete of a dam structure. The analysis consisted of tw o theoretical models, namely a transient thermal model and a transient stress model. The finite element analysis sought to investigate 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 22

PAGE 23

construction joints. The early thermal behavio r of a 0.6-m 0.6-m laboratory concrete specimen and a dam structur e model consisting of an upper and lower block cast 102 hours apart were modeled and observed. The the rmal characteristics of interest were the temperature field, thermal flux and thermal gradient. The Long Spruce Dam in northern Manitoba, Canada, t hat was found to have a crack that runs from the downstream side to the upstream side of the structure, was used as a case study. The thermal properties of the concrete in t he laboratory specimen model were assumed to be independent of time and temperature during hydration. T he thermal conduc tivity was assigned a constant value of 4.1 KJ/m-h r-C, and the specific heat was assigned a value of 1971 KJ/m3 -C, obtained from literature. The ambient temperature in the laboratory analysis was also kept const ant at 23C to represent a controlled environment. For the dam structure model, the thermal properties were slightly different to reflect the use of larger aggregate. The initial temperature of the concrete was set at 10C because of the use of ice water to pre-cool the large blocks. The boundary condition of convection is imposed on all si des except the bottom where a prescribed temperature is described. Fo r the stress analysis, the botto m surface is constrained in all directions, representing the contact fric tion of the block resting on the floor. The analysis for the laboratory specimen model wa s conducted in six-hour load steps. The beginning of thermal process in the dam stru cture model was analyz ed every six hours, and then increased to every 12 hours, then finally every 24 hours. The adiabatic temperature rise resulting from the heat of hydration was calculated using the expression developed and presen ted by Tanabe et al. (1986). The highest temperature was found to occur in the middle section of th e specimen and decreased as it got closer 23

PAGE 24

to the sides of the model. This confirms the theory that the outer section of the concrete loses heat more quickly than the middle bec ause of its greater exposure to the atmospheric conditions. Radovanov ic (1998) found that the 0.6-m 0.6-m laboratory specimen was too small to realistically predict the behavior of massive concrete structures. This led to the enlargement of the FE model by two, five and ten orders of magnitude. The size that came closest to a realistic characterizati on of the behavior of the Long Spruce Dam was the 6-m 6-m model. However the maximum temperature for this size model was much higher than the dam specimen. The reason given by Radov anovic (1998) was that the dam specimen was cast in September, when the outside temperature was much lower than the initial temperature used for the laboratory specimen. Radovanovic (1998) concluded that assumptions made in the calculation of the heat generation rates, material properties and boundary conditions were reasonable and that the finite element algorithm was accurate enough to predict the early age thermal behavior of the laboratory concrete specimen and dam. Afterw ards, a finite elemen t stress analysis of the laboratory specimen and the dam were c onducted. As a worse-case scenario, the maximum stress occurring in the models were considered as the residual stress. The process of hardening was impl emented by calculating the dev elopment of the modulus of elasticity of the concrete with time based on the ACI charts. Radovanovic (1998) concluded that the results of the analysis showed that the stresses produced by the thermal gradients were significant enough to cause cracking in the early age concrete. Riding (2007) developed a software pa ckage named ConcreteWorks based on a plane strain finite-difference scheme that involved calculations of the temperature 24

PAGE 25

development for several types of concre te members and the thermal stress cracking probability for several mass concrete member s. A temperature prediction model was developed to predict the concrete temperat ure development, including the interaction between the concrete edges and the environment. Over 12 ma ss concrete members, a bridge dec k, and several precast concrete beam s were instrumented for temperature to calibrate the temperature prediction module in ConcreteWorks. According to Riding (2007), rectangular footings had some unique features that required special considerations for modeling. When footi ngs were modeled in 2-D, ConcreteWorks assumed a vertical cross-section of the footing as shown in Figure 2-1 with no heat transfer perpendicular to the cross section. The heat exchange between the footing and the environment was dependent on: the formwork, cure blank ets and plastic used, soil conditions, weather, orientation of t he footing, shading from scaffolding and embankments, and heat conduction from the concrete interior. Solar radiation, atmospheric radiation, irradi ation from the footing, and t he radiation exchange between the vertical surface and form horizontal cro ss bracing models were used in the side and top boundary condition calculations. Radiation emitted by the ground surface was assumed to be incident on the side surface onl y. If the user chose to shade the sides of the footing because of scaffolding or the em bankment, then the solar radiation was set to zero. Conduction to or from the soil underneath the footing was modeled by assuming a constant depth of soil. The initial temperature of the soil was set to the userdefined average soil temperature. The temperature at the bo ttom of the modeled soil was set to the user-defined average soil temperature. Figure 2-2 shows how the 25

PAGE 26

rectangular footing was modeled. Symmetry was assumed in the model in the width and length (when calculated in three dimensions) direction. Riding (2007) concluded that from the concrete member temperature data measured, the concrete te mperature prediction perform ed well. The average absolute error for the measured temperatures to the predicted member temperatures ranged from 0.5 to 4.6C (1.0 8. 4F). However, the footing model might deviate from the actual member stresses because the stress in the third dimension might not be small relative to the other two dimensions. Three-Dimensional Finite Element Analysis A very early 3-D FE model was introduced by Machida and Uehara (1987) for forecasting thermal cracking in massive concrete using the ADINAT and ADINA programs. A wall stru cture consisting of reinforced concrete measuring 1.0 m thick, varying height of 3.9 m to 4.73 m, and 15.0 m long cast on a 1.5-m thick basemat concrete slab, was instrum ented with thermocouples, effect ive stress meters, mold type strain gauges, and non-stress strain gauges, to capture the temperatures, strain and stress responses at different locations within t he wall, as shown in Figure 2-3. The finite element thermal model consisted of half of the concrete wa ll, basemat slab, and the soil beneath as shown in Figure 2-4. The heat transfer analysis of the exothermic phenomenon cements heat of hydration, and the phenomena of heat conduction and convection was performed, then followed by a thermal stress analysis for the mechanical characteristics. The heat generation rate for the concrete used in the wall was calculated by differentiating with re spect to time the equation for adiabatic temperature rise developed by Tanabe et al (1986). A comparis on of the thermal analysis results with the experimental re sults revealed that the maximum measured 26

PAGE 27

temperature occurred along t he mid-length of the wall and was 2.1C higher than the maximum analytical temperature which also occurred along the mid-length of the wall model. After the peak temperature was obtained, the analytical temperature decrease was larger than the experimental but after 12 days, the te mperature of the structure equaled the ambient temperatur e. The difference in the estimation of temperature decrease was attributed to the difference in the assumed heat convectivity in the model and the actual convect ion and to the varianc e 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 direction perpendicular to the structural symmetry plane and perpendicular to the subsoils out side surface plane. The compressive and tensile strengths and elastic modulus of t he wall were calculated using empirical formulas that related their development to the temperature of the hydrating concrete. Constant values for the Poissons ratio and c oefficient of thermal expansion were also assumed. The results showed that the ma ximum compressive stress occurred in the mid-length one day after concrete placement in both the experimen t and finite element analysis. The compressive stress became a t ension stress in the middle and bottom of the wall as the concrete aged. The upper mi d-length of the stru cture experienced a small compression peak at 18 hours, which then became a tensile stress, peaking after about 2 days and 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 which it began to 27

PAGE 28

decrease but remained in the tensile stre ss region. Aga in, the difference in the measured and analytical results for the midlength point close to the surface was attributed to the real atmospheric conditions of the structure bei ng different than the assumed constant values assigned in the finite element model. Ayotte et al. (1997) focused on developing a methodology, based on finite elements, that could be used to predict the heat generated and resulting thermal stresses in mass concrete. The study incl uded both an experimental component and a modeling component. Three concrete monoliths were built directly on bedrock in the St. James Bay Territory in Northern Quebec, Canada, on the site of a major hydroelectric project. The dimensions of the monoliths were 2 m wide, 10 m long, and 2 to 3 m high, with the height depending on the bedrock profile. Each mono lith was instrumented with 26 T-type (Copper-Constantan alloy) thermocoupl es to monitor tem perature distribution with time, and 8 pairs of mechanical strain targets on the skin reinforcement to measure the induced strain (see Figure 2-5). To obs erve the performance of the concrete when subjected to severe freeze thaw cycles, the m onoliths were cast in February inside large individual heated shelters in which the temper ature was maintained at 30 to 32C during the construction phase. The 2-D and 3-D FE modeling conducted by Ayotte et al. (1997) consisted of the concrete thermal behavior using the fi nite element software ADINA-T and the mechanical response (stresses and stra ins) using ADINA. To accommodate simultaneous changes of temperature and mechanical proper ty, a modeling technique which employed a step-by-step incremental approach of ca lculating the thermally induced strains was developed to bypa ss the link between ADINA-T and ADINA. The 28

PAGE 29

cement type used was Portland cement Type 20M which was specially made for HydroQuebec, so a generic function for the heat of hydration as a function of time was obtained by interpolating between the known functions of Type 20 and Type 50 cements, which was then calibrated by com paring the calculated te mperatures 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 literat ure sources. Radiati on was not considered because the monoliths were built inside shel ters which blocked the heat radiation. Convection boundary conditions were used to m odel the heat loss to the ambient air, while rock elements were added below the conc rete elements for the heat dissipation through the rock foundation. The structural model for the m onolith 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 elastic modulus, compressive and tensile strength, were modeled as varying with time, while the coefficient of thermal expansion was given a constant value of 10 /C. To include creep and relaxation, an effective reduced elastic modulus that a ccounts for the reduction in stresses was adopted. Ayotte et al. (1997) found t hat the calculated temperatur e at the center of the monolith model followed almost perfectly the temperatures measured experimentally. However there was a gap between the temperat ures calculated at a point near the top of the monolith and those experi mentally measured. In the structural analysis, it was found that the largest strains were located at the top of the m onolith where there was 29

PAGE 30

the least restraint, while the st rains at the base were very small due to the restraint of the foundation. It was also obser v ed 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 t he formwork which limited the temperature difference between this surface and the core. Lawrence et al. (2012) used a 3-D finite element analysis to study the effects of the variation in hydration rates on the di stribution of temper atures, the thermal gradients, and resulting stresses. His finite element model was successfully verified by performing analyses on eight 1.07-m 1.07-m 1.07-m (3.5 ft 3.5 ft 3.5 ft) concrete blocks containing four different concrete mixtures. The finite element model of onefourth of the concrete block wit h insulation is illustrated in Figure 2-6. All of the concrete mixes used in this study had water to cementit ious material ratio of 0.5. Mix 1 consisted of 100% Type I Portland cement concrete; Mi x 2 had 50% of the Po rtland cement mass replaced by ground granulated blast-furnace sl ag; Mix 3 contained 35% Class F fly ash; and Mix 4 was a blend of 50% Portland ce ment, 30% granulated blast furnace slag, 20% Class F fly ash. The concrete blocks were cast in a controlled laboratory environment in which the ambient temperature remained constant and the flow of air kept at a minimum for the dur ation of the monitoring peri od. The model of the blocks was constructed using the adiabatic temperatur e rise data for each concrete mixture. These adiabatic temperatures were obtai ned by measuring t he hydration energy produced when the various combinations of the cementitious components are mixed with water in an adiabatic calorimetric cham ber. The other properties used to model the thermal behavior of the concrete blocks were the activation energy, the specific heat, 30

PAGE 31

and the thermal conductivity (which was deriv ed from diffusivity testing on cylinders made from sampling the concrete used in eac h block mixture), which were also measured experimentally. The models also utilized the thermal material properties of the formwork and insulation, as well as the mechanical properties of each concrete block measured from cylindrical and pr ismatic test specimens. The predicted temperature profiles in his model closel y agreed with those from the experiment, and thermal cracking which occurred in the concrete blocks, as shown in Figure 2-7, were very similar in location to those predicted in the finite element models. The results of his study also show that cracking in mass c oncrete is more dependent on the attained early age strength of concrete than the magnitude of the maximum temperature differential. Adiabatic Temperature Rise Model Past research leading to the creation of numerical models for the prediction of temperature distribution in mass concrete primarily focused on using generic heat generation functions for the calculation of adiabatic temperature rise (Machida and Uehara 1987; Radovanovic 1998; Ayotte et al. 1997). The adiabatic temperature rise resulting from the heat of hydration was ca lculated using the expression developed and presented by Tanabe et al. (1986): )eK(1T(t)t (2-1) where T = temperature (C) t = time (days) K = constant based on cast ing temperature (C) = constant based on casting temperature The values for K and are obtained from the pl ots in Figure 2-8. 31

PAGE 32

The total amount of heat generated wa s then calculated by the following equation: )e (1KC (t)CQ(t)t P P (2-2) where Cp = specific heat capacity of the concrete (J/g-C) = density of the concrete (g/m3) t = time (days) K = constant based on cast ing temperature (C) = constant based on casting temperature And the rate of heat generation calculated as: t PeKCR(t) (2-3) Recently, consideration of supplementary cementitious materials has been taken, and calculated adiabatic energy rise obtained from laboratory or field tests has been used as inputs for finite element models to account for better prediction of behavior of concrete at early ages (Riding 2007; Ferra ro 2009; Tia et al. 2010; Lawrence et al. 2012). Tia et al. (2010) investigated three ca lorimetry methods for the measurement of heat generation in concrete materials: is othermal conduction calorimetry (Evju 2003), semi-adiabatic calorimetry, and Sure-Cure/adiabatic calorimetry. Tia et al. (2010) found that of the three methods investigated, the isothe rmal calorimetry method was determined to be the most appropriate meth od for the quantificat ion and modeling of heat generation of cementitious materials at early ages. 32

PAGE 33

Figure 2-1. Diagram of the vertical cro ss-section assumed in modeling a 2-D footing (Riding 2007). Figure 2-2. Rectangular f ooting model (Riding 2007). 33

PAGE 34

Figure 2-3. Locations for temperatur e and stress measurements in a reinforced concrete wall (Machida and Uehara 1987). 34

PAGE 35

Figure 2-4. Finite element mesh (Machida and Uehara 1987). 35

PAGE 36

Figure 2-5. Thermocouple and strain gauge locations in the James Bay concrete monolith (Ayotte et al. 1997). 36

PAGE 37

Figure 2-6. Finite element model of one f ourth of the concrete block with insulation (Lawrence et al. 2012). Figure 2-7. Typical location and distributi on of cracking found in experimental blocks (Lawrence et al. 2012) (photo courtesy of Adrian M. Lawrence). 37

PAGE 38

38 Figure 2-8. K and values of adiabatic temperature rise (Radovanic 1998).

PAGE 39

CHA PTER 3 FINITE ELEMENT THERMAL MODEL Overview of Finite Element Thermal Model The modeling of the early age thermal beha vior of concrete was conducted with the aid of the commercially available TNO DIANA 9.4.4 (2012a) software package. This software package was chosen because it offers a wide range of material models for the analysis of nonlinear concrete material behavior, including the behavior of young hardening concrete. It can make the assessm ent of the temperat ure development due to the cement hydration and the computat ion of the associated stress development within the concrete mass (Lawrence 2009; Lawrence et al. 2012). Main modeling features utilized are: Equivalent age calculation; Temperature and time dependent material properties; and Crack index calculation to assess risk of cracking. The finite element analysis utilized DIANAs Heatflow-Stress Staggered 3D feature, in which the thermal analysis is combined with a subsequent structural analysis. The model comprises two domains: one for t he 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 calle d the flow-stress domain. Formwork used in the construction of ma ssive concrete structures, including plywood and polystyrene foam, was explicitly modeled. Since researchers were interested only in their effects on the transfe r of the thermal ener gy generated by the concrete, 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 39

PAGE 40

concrete is modeled with a quadratically in ter polated structural element that is converted during the thermal analysis to a linearly interpolated flow element. Although the reinforcing steel in the conc rete conducts heat rapidly, it was not modeled in the thermal model due to its complexity of geometry. Element Selection As stated above, the concrete in this analys is is active in the flow-stress domain and therefore is modeled with a st ructural 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 isoparam etric 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 disregarded in the thermal analysis. The basic theory and required material properties needed for the structural analysis with elemen t CHX60 will be discussed in further detail in Chapter 4. Element HX8HT is effective in si mulating the phenomenon of convectiondiffusion, and is especially useful for the analysis of heat transfer problems. It utilizes linear interpolation and Gau ss integration with a 2 x 2 x 2 integration scheme. Heat transfer is modeled by assigning the ther mal conductivity and heat capacity of the concrete, where the conductivity can be modeled as isotropic, orthotropic or anisotropic, 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 research, both the conductivity and heat capacity were modeled as constant. 40

PAGE 41

Additional properties used to model the internal heat generation of the concrete are the Arrhenius constant (activation energy divided by the universal gas constant), and the heat generation function, which can eit her be a table that provides a direct description of the heat production rate with respect to the degree of hydration, or a table that describes the adiabatic temperature rise, in degrees Celsius (C), with respect to time. The plywood and polys tyrene were directly modeled with element HX8HT, using each of its conductivity and heat capacity to describe the way the heat would be transferred between the concre te, plywood and polystyrene. The boundary convection was modeled us ing the BQ4HT element, shown in Figure 3-2, which is a four-node isoparametric quadrilateral element specially used to describe boundaries in three-dimensional the rmal analyses. It uses linear interpolation and Gauss integration in its co mputational scheme. The four nodes in this element 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 hydr ating concrete, knowledge of the heat produced during the hydration reaction, as well as both the material properties of the concrete itself and the environmental conditi ons in which it is placed are needed. As previously stated, t he heat produced during hydratio n is a function of the temperature history of the concrete. The mo mentary heat production rate is defined as (DIANA 2012b): 41

PAGE 42

(T)(r)q q=T)(r,qTr v (3-1) where roduction rate (J/m3-s) (scaled to one) qT = temperature dependent heat production, and qv = momentary heat p r = degree of reaction T = temperature (C) = maximum value of the heat production rate (J/m3-s) qr = degree of reaction dependent heat production 273T T)(r, R E exp(T)qa T (3-2) where nditions is used as the input in this case. DIANA deriv es the heat production q(t) from Ea = the activation energy of the concrete (J/mol) R = the universal gas constant (8.3144 J/mol-C) The heat production rate, qr, which is dependent on degree of reaction can also be determined by DIANA using preprocessing. The temperature history produced under adiabatic hydration co t r)c(T,q(t) (3 T -3) where n approximates the degree of reaction and the temperature dependent heat productioc(T,r) = the capacitance dependent on tem perature and degree of reaction. DIANA the n n m mQ Q r (3-4) (3-5) i 1i ii mT) r,c(T Q m ** 42

PAGE 43

where n = specified time points m = 1 ,,n and 1i (3-6) iiTT T 2 rr ri1i i (3-7) 2 Ti (3Finally, DIANA approximates T/ t numerically at m = 1,,n points and uses equations (3-1) and (3-2) TTi1i *8) to calculate the corresponding degree of reaction dependent heat production rate qr,m 1m1m 1m1m mmtt TT c t T cq (3-9) mT, mr,qThe preprocessing method was utiliz ed in this research. This method w chosen because the adiabatic te mperatmq q (3-10) as ure rise with re spect to time could be conven ustrated in Figur e 3-3, can be integrated with re spect to time to obtain the energy rise, (3-11) hen approximated to t he energy rise of the hydrating concrete made from the mixture iently input into DIANA directly. Power data obtained from isothermal calo rimetry testing on a cementitious mixture, as illtPdtQ 0twhich is t 43

PAGE 44

Finally, the adiabatic temperature rise, presented in Figure 3-4, is calculated from the energy using the relations hip described by the first law of thermodynamics and expressed in Equati of input used to describe the concrete hydration. or on 3-12. Th is method was used to maintain consistency in the type TmC Q pmC Q T p (3-12) where J/g-C) ental heat transfer through a finite area conduction, expressed by Equation 313, and illustrated in Figure 3-5, Q = energy rise (J) m = mass of concrete (g) Cp = specific heat capacity ( T = the change in tem perature 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. Experim observations have shown that in the one dim ensional plane, the ra te of can be expressed by w hat is known as Fouriers law of heat xx x T kAQ (3-13) where tivity (J/m-s-C) ea (m2) xQ = heat flow (J/s) k = the thermal conduc Ax = The surface ar T = Temperature (C) x = coordinate (m) 44

PAGE 45

The th nsmits heat. The minus sign denotes a negative temperature gr adient reflecting the fact that the heat flows in the direction of decreasing temperature. e Equat ion (3-13) by the area to give: ermal conductivity of a solid is its ability or the ease with which it tra It is often convenient to divid x T A Qx x k qx (3-14) where qx is the heat flux (J/s-m2). Expanded to the three-dimensional case, as shown in Figure 3-6, the Fourier omes (Mills 1995): equation for heat transfer bec zyx where x, y, z = coordinates i, j, k = the unit vector s in the x, y, and z direc kjikTkqn (3-15) tions, respectively has an ote the rate at which heat is bein ermal energy in} {rate of therma l energy out} + {rate of total heat generated} = {rate of accumulation The rate of heat inflow ac ross the face at x is qxdydz, and the outflow across the TTT Consider the case of a heat-conducting solid such as mass concrete which als o internal source of heat generation. If q* is used to den g internally generat ed per unit volume, then rate of total heat generated = q* (dxdydz) (3-16) The principle of conservati on of energy requires that {rate of th of thermal energy} (3-17) face at x +dx is dydzdx x q qdydzqx x dxx 3-18) ( 45

PAGE 46

The net inflow in the x direction is then dxdydz q dydzqdydzqx xdxx x Similar terms arise from conduction in the y and z directions. Thus, the net heat transfer into the volume by conduction is dxdydz z q y q x qz y x Substituting in Equation (3-17) and dividing by dxdydz gives t T cq z q y q x qp z y x (3-19) Introducing Fouriers law, Equation (3-14), for qx, qy, and qz, pq T k T k T k T c (3-2 zzyyxxt 0) This equation represents a volumetric heat ba point in the body, and describes the dependence of the temperature in a solid on the Assuming thermal conductivity, specific heat and density of concrete being relatively constant values (Faria et al. 2006), the conductivity of concrete created based on the cementitious mixtures can be calculated using the relationship: (3-21) usivity (m2/s) lance which must be satisfied at each spatial coor dinates and on time. ckpwhere = diff = density (kg/m3) cp = heat capacity (J/kg-C) 46

PAGE 47

Convection Convection refers to the energy transported as a result of macroscopi c motion. In other words, the transfe he analysis of convection heat transfer from a surface from which equation 3-22 is derived. r of heat from the surface of a material to a fluid that is moving over it. Figure 3-8 presents an approach to t )T(TAhqFssc (3-22) where r (W/m2-C) T qc = rate of heat transfes = temperature at the surface (C) TF = Fluid temperature (C) As = surface area (m2) h = mean coefficient of heat transfer The heat lost and gained to the surr ounding environment by the hydrating concretes exposed surface and also the interaction of the foam with ambient conditions is modeled by imposing boundary c onvection elements. This is conveniently done using the convection elemen of the elements, qS, due to convection is modele (3-23) where perature of the concrete block (C) t found in DIANA to specify the convection and boundary conditions. The heat flow through the surface d by the following equation: ) ( hqS ec S qS = heat flow through surface (W/m2) hc= convection coefficient (W/m2-C) e = external environment temperature (C) S = surface tem 47

PAGE 48

The convection coefficient can be cons tant, temperature-dependent, or time depen (3-24) ed in this study consists of a rectan f the rectangular footing, only on and concre te were explicitly discretized and modeled according to their corresponding thermal properties. Boundary Conditions set dent. The convection coefficient was calculated using the equation (similar to Ali and Urgess a (2012)): 5m/sv,7.6v0.78 cwhere v = wind speed, m/s. The assumed convection coefficient values for the thermal model in this research range from 9.0 W/m 5m/sv3.95v, 5.6 h2-C to 50.0 W/m2-C. Model Geometry The general finite element model develop gular mass concrete footing lying on a soil layer. The concrete is insulated at the top, bottom, and all the sides. Based on the double symmetry o e-quarter of the whole structure wa s to be modeled to reduce the computation time and the output file size from the DIANA software. The finite element mesh of onequarter of the footing is illustrated in Figure 3-8. The polystyrene insulation, plywood The modeled concrete had the full depth but half length and half width of the actual concrete of the footing. The model soil layer beneath the footing extended 5 m deeper and 3 m wider on each side of the footing in order to ensure adequate medium for heat transfer from the footing concrete. The boundary conditions imposed for the t hermal analysis consist of an initial temperature of the model and the external te mperature. The initia l temperature was 48

PAGE 49

at the placement temperature of the concrete whereas the external temperature wa at mean environmental temperat ure recorded in the field dur ing the monitoring period the footing. Figure 3-9 illustrates the boundary temperat ures imposed on the finite element model. The external temperature is applied to the surfaces of the structure that are exposed to the environment including the ou ter surfaces of the conc s set of rete-insulation structu e de these two loads is that there is air convection at the surface where the external temperature is applied while there is no convection at the surface where t he fixed temperature is imposed. Figure 3-10 presents the temperature histor y of the environment during the monitoring of a pier footing at S.R. 826 and S.R. 836 Interchange, Miami, FL. The description of the field testing is presented in Chapter 5. re and the top su rface of the soil layer. The fixe d temperature is applied to th bottom and the sides of the soil layer. The fi xed temperature is the same in magnitu as the external temperature, the only differ ence between 49

PAGE 50

A B Figure 3-1. Elements used to model early age concrete behavior. A) Twenty-node isoparametric solid brick element CHX 60. B) Eight-node is oparametric brick element HX8HT. Figure 3-2. Four-node isoparamet ric boundary element (BQ4HT). 0 5 10 15 20 024487296120144168 Hydration Time (hr)Power (mW/g) Figure 3-3. Hydration power of cementitious mixture (us ed in Footing at I-4 US-192 Braided Ramp, Orlando, FL) obtained from isothermal calorimetry testing. 50

PAGE 51

0 20 40 60 80 100 024487296120144168 Hydration Time (hr)Temperature (C) Figure 3-4. Adiabatic temperature rise of a concrete mixture calculated from the hydration power obtained in the is othermal calorimetry testing. Figure 3-5. One-dimensiona l conduction heat transfer. 51

PAGE 52

Figure 3-6. Differential volume for a rectangular solid. Figure 3-7. Convection heat transfer (Thomas 1980). 52

PAGE 53

Top Insulation Side Insulation Mass Concrete Figure 3-8. General finite elemen t mesh of one-quarter of footing. Bottom Insulation Soil 3m 3 m 5 m 53

PAGE 54

54 External Temperature Figure 3-9. External tem peratures imposed on finite el ement model representing the ambient conditions. 15 20 25 30 35 40 020406080100120140160180 Time after concrete placement (hour)Temp. (C) Figure 3-10. Ambient temperature during the monitoring of a pier footing at S.R. 826 and S.R. 836 Interchange, Miami, FL.Mass Concrete Soil Fixed Temperature

PAGE 55

CHA PTER 4 FINITE ELEMENT STRUCTURAL MODEL Overview of Finite El ement Structural Model Heat produced during the hy dration of concrete causes an increase in its temperature. However, because of the i nhomogeneous hydration within the concrete element and the inhomogeneous 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 a ge tensile strength of the concrete. The temperature distribution solution obt ained 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 thermal gradient is greatly dependent on the physical characteristics of the concrete. This chapter describes the elements used in DIANA to model the concrete and the physical input paramet ers required to measure the mechanical behavior. Element Selection As stated in Chapter 3, t he structural behavior of a concrete footing was modeled using the three dimensional twenty-node CHX60 isoparametric solid brick element reproduced here in Figure 4-1. The stress and strain distri bution 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 direction and quadratically in the x and y directions. It utilizes linear interpolation and Gauss integrati on in its computational scheme. 55

PAGE 56

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. Although the actual reinforcing steel in the concrete can hold potential cracks caused by thermal contraction, it was not modeled in the structural model due to its complexity of geometry. Shrinkage of concrete was also not considered in this study. To model the elasticity of t he concrete, the Youngs modulus E, Poissons ratio v, and coefficient of thermal expansion were directly input into the model. The viscoelastic behavior was modeled based on a Ma xwell 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 specifying 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 th an the tensile str ength. The modulus of elasticity (MOE) of concrete is the ratio between the stre ss and reversible strain and is important because it influences the rigidity of the conc rete structure. This linear relationship is known as Hookes Law and is expressed in Equation 4-1, = E (4-1) where = stress (MPa) E = Youngs Modulus (MPa) = linear strain. 56

PAGE 57

The elastic limit represents the maximu m allowable stress before the concrete will crack and undergo permanent deformation. In heterogeneous multiphase materials lik e concrete, the modulus of elasticity increases as it hydrates, which is detriment al to the concrete because the probability of cracking increases as the modulus increases. To correctly model the thermal stresses in young concrete, it is essential to include the variation of the mechanical properties with time of the concrete (De Schutter 2002; Lawrence et al. 2012), most importantly the elastic modulu s. Therefore, testing for the tensile modulus of elasticity of concrete at early ages is needed for input parameters of modeling. Poissons Ratio Poissons ratio is the ratio of the lateral st rain to the axial strain within the elastic range of the concrete. According to Mehta a nd Monteiro (2006), Poissons ratio has no consistent relationship with the curing age of the concrete. Values obtained during the testing for compression modulus of elasticity were consistent ly 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 de scribe the sensitivity of concrete expansion or contraction to changes in temperature. It is defined as the change in unit length per degree of temperat ure change (Mehta an d Monteiro 2006). The value of the coefficient of thermal expansion is par ticularly important in mass concrete because the strain induced during t he cooling period is dependent on both the magnitude of the change in tem perature and the coefficient of thermal expansion. 57

PAGE 58

Tensile Strength In normal concrete applications, the low tens ile strength of concrete is usually of little concern because reinforcing steel bars, which have high tens ile strength values, are used to increase the overall 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 the size of the structure, the spaces between the steel are large creating elements that are weak in tension. Symmetry and Boundary Conditions The boundary conditions imposed for the stru ctural analysis of the quarter footing consisted of the restriction of displace ments against the symmetry planes. Since the depth of footing was relatively thick, it wa s assumed that there was no curling in the footing. Therefore, the base of the footing was modeled as being constrained against displacements along the z direction, but was free in the x and y directions as friction between the base of footing and soil was neglected. Both c onditions are presented in Figure 4-2. 58

PAGE 59

Figure 4-1. Twenty-node isoparamet ric solid brick element CHX60. X Y Concrete Z Figure 4-2. Symmetry conditions and supports of model. 59

PAGE 60

CHA PTER 5 INSTRUMENTATION AND MONI TORING OF MASS CONCRETE Overview An FDOT-funded study (Tia et al. 2010) has successfully verified the developed finite element model by performing and monito ring concrete specimens in the laboratory conditions. It is needed to extend monitoring of actual concrete structures such as footings, columns, and pier caps that are large enough to be classified as mass concrete. To achieve this task, some of foot ings that were constructed in the field in Florida were selected for temperature monitoring after concrete placement. The temperature measurements were then com pared with the results obtained from the finite element modeling developed in Chapter 3. Selected Mass Concrete Structures During November 2011 and July 2012, three di fferent bridge pier footings were monitored for temperature developments in Florida, as listed in Table 5-1. Measurements of the temperature in these structures were recorded 7 days from placement of concrete. The concrete mix design used in Foot ing 1 and Footing 2 was a Class IV concrete mix with a total cementitious content of 666 lbs/yd3, 48% of which is Type F fly ash as a replacement of Portland cement, an d water-to-cementitious content ratio of 0.36. The concrete mix design used in Footing 3 was a Class IV concrete mix with a total cementitious content of 700 lbs/yd3, of which 64.3% was Portland cement, 32.1% Type F fly ash, and 3.6% Boral Micron 3 Ultr a-Fine Fly Ash. The wa ter-to-cementitious content ratio of this concrete mixture was 0.38. 60

PAGE 61

Instrumentation Proposed Locations for Temperature Sensors Temperature sensors were installed on the selected ma ss concrete structures. The proposed locations for the temperature sensors are de scribed in the following sections. Footings The FDOT specifications require that t he temperature sensors be placed at the center, top, and bottom of the fo oting placements, in the shortest direction. The top and bottom temperature sensors should be located two inches, inside the concrete, from the outer surfaces. For this research, it wa s proposed that in addition to the locations required by the specifications, temperat ure sensors should be placed at six inch intervals between the center and top and bottom of the footing. It was further proposed that temperature sensors be placed at one corner, and along the si de furthest from the center of the footing, spaced six inches apart and two inches within the top, bottom and side surface. Columns and Pier Cap The FDOT specifications require that t he temperature sensors be placed at the center and sides of the column and cap plac ements, in the shortest direction. The temperature sensors placed at the sides should be located two inches, inside the concrete, from the outer surfaces. Data Acquisition Equipment There were 2 types of temperature sensor used in this research: thermocouples and data loggers. Thermocouples were used to measure temperatures for Footing 1, 61

PAGE 62

whereas d ata loggers, as illustrated in Figure 5-1, were used to reco rd temperatures for Footing 2 and Footing 3. For Footing 2 and Footing 3, an advanced data acquisition system was used to measure and record the temperatures. This data acquisition system, called the Command Center, consists of temperature data l oggers that allow for pre-programming to start recording temperatures at a spec ific time (usually set at the scheduled placement time) before being placed at the m onitoring locations, as shown in Figure 52. The system also does not require an exter nal power source, ther efore eliminates the need for intermittent changing of batteries Once the sensors are installed and programmed, they can be left in place unattended, and the data would be downloaded at the end of the monitoring period. Monitoring of Selected Mass Concrete Structures Footing 1 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) Concrete for the bridge pier footing lo cated at the S.R. 826 (or Palmetto Expressway) and S.R. 836 (or Dolphin Ex pressway) interchange was placed in November 2011. The dimensions of the footing are 14.02 m (46 ft.) long, 8.53 m (28 ft.) wide and 2.13 m (7 ft.) deep. The pier footing was insulated on top with insulating blankets, while the bottom was insulated wi th polystyrene foam boards. The footing was formed on the sides by plywood panels as illustrated in Figure 5-3. The thermocouples were inst alled at the top, middle and bottom elevations of the centroidal axis of the horiz ontal plan view. Figure 5-4 show s the concrete being placed into the bridge pier footing, while Figure 5-5 shows the data acquisition equipment that was used to record the temperatures in t he pier footing during the hydration of the 62

PAGE 63

concrete. The temperatures recorded by the thermocouples plac ed at the top, middle and bottom of the footing ar e shown in Figure 5-6. Footing 2 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) Concrete of this footing was intended to be placed on top of a seal concrete slab. However, due to the contract ors inability to completely stop the flow of ground water into the footing area, a 3-inch layer of gravel was placed on top of the seal concrete prior to pouring the concrete for the footi ng to prevent the water from contacting the bottom of the footing. Figure 5-7 shows view of the footing with reinforcement before concrete was placed. Temperatures in the footing were measured and stored using the Command Center data acquisition system. The locations of the temperature s ensors installed in the pier footing are shown in Figure 5-8. Sensors 1 through 5 were placed along the vertical centerline; Sensors 6 through 10 and Sensors 16 through 20 were placed 50 mm (2 in.) from mid-sides of the footing; and Sensor s 11 through 15 were placed 50 mm from the corner of the f ooting. Details of sensor elev ation are given in Table 5-2. The pier footing was insulated at the t op with a 25-mm (1-in. ) thick insulating blanket. The concrete was directly placed on top of the sand without any insulation in between. The thermal properties of the insulating blanket, concrete and sand are given in Table 5-3. The ambient temperature at the time of placement was 23C (73F) and the concrete had a placement temperature of 25.5 C (78F). During the monitoring of the temperature development of the footing, the ambient te mperature was recorded as shown in Figure 5-9. 63

PAGE 64

The temperatures measured in the s ensors are presented in Figur es 5-10 through 5-13. Interestingly, the temperatures measured 407 mm (16 in.) above the centroid (Sensor 4) were always higher than the temperatures measured at the centroid of the footing (Sensor 3) duri ng cement hydration. An expl anation for this is that the footing was insulated at the top while there was no insulation at the bottom. The peak temperature in the pier footing was measured as 66C (151F) in Sensor 4, at 55 hours after placement of concrete. Sensors 1, 6, 11, and 16, which were located 100 mm (4 in.) above the bottom surface of the pier footing at the cent er, western side, corner, and southern side, respectively, each recorded a peak temperature of approximately 35C (95F) as a result of the gr ound water infiltrating the footing area, rising to a level that resulted in these sensors being submerged. The maximum temperature difference recorded was 34C between Sensor 4 and Sensor 12. The erratic behavior observed in sensor s 15 and 20, which were located beneath the top surface of the footing, could be attributed to the fact that the elevations of the rebar to which the sensors at these locations were attached were raised to compensate for the change in the bottom elevation of the footing caused by the placement of gravel over the seal concrete. This change in elev ation caused the sensors to be so close to the top surface of the footer that whenever the insulation blanket was lifted to inspect the concrete, sharp reductions in t he temperature measurement occurred. Footing 3 (at I-4 US-192 Braided Ramp, Orlando, FL) A mass concrete structure at the I-4 US-192 Braided Ramp was monitored for temperature development in July 2012. The mass concrete structure was a 6.71-m (22) long, by 3.05-m (10) wide, by 1.75-m (5-9) deep pier footing as shown in Figure 5-14 and Figure 5-15. 64

PAGE 65

The temperature sensors were placed 2 inches below the top surface, at the center, and 2 inches above the bottom surface of the footing (on the vertical axis of symmetry). The concrete was placed at 7:30 AM and had a placement temperature of 32.2C (90F), while the average ambient temperat ure during monitoring period was 30.8C (87.4F). The temperatures recorded in the sensors are presented in Figures 5-16. The peak temperature in the pier footing was meas ured as 74C (165F) at the center of the footing 42 hours after concrete placemen t. The maximum temperature difference recorded was 15C (27F) between the middle sensor and the top sensor. 65

PAGE 66

Table 5-1. Selected mass concrete structures Name of Structure Dimensions (m) Location Placement Date Footing 1 14.028.532.13 S.R. 826 and S.R. 836 Interchange, Miami, FL 11/2011 Footing 2 10.3610.362.03 S.R. 826 and S.R. 836 Interchange, Miami, FL 03/2012 Footing 3 6.713.051.75 I-4 US-192 Braided Ramp, Orlando, FL 07/2012 Table 5-2. Temperature sens or elevation in Footing 2 Sensor Distance from Bottom (mm) Distance from Top (mm) 1, 6, 11, and 16 100 1,930 2, 7, 12, and 17 406 1,624 3, 8, 13, 18, and 21 965 1,065 4, 9, 14, and 19 1,422 608 5, 10, 15, and 20 1,930 100 Table 5-3. Thermal properties of conc rete, sand, insulating blanket, plywood and polystyrene foam Material Conductivity (J/sec-m-C) Heat Capacity (J/m3-C) Insulating Blanket 0.058 1.45105 Polystyrene Foam 0.029 2.84104 Plywood 0.15 8.54105 Concrete 2.2 2.676106 Sand 0.27 1.212106 66

PAGE 67

Figure 5-1. Data logger attached to reinforc ing steel bar of footi ng (photo courtesy of Adrian M. Lawrence). Figure 5-2. Data acquisiti on equipment used in Footing 2 and Footing 3 (photo courtesy of Adrian M. Lawrence). 67

PAGE 68

Bottom Insulation, 3/4 polystyrene 46X28X7 concrete Ambient Temperature 23C Top Insulation, 1 polystyrene 1 Plywood Side Figure 5-3. Mass concrete block, plyw ood panels, bottom and top i nsulation. Figure 5-4. Concrete being placed for Footing 1 (photo courtesy of Adrian M. Lawrence). 68

PAGE 69

Figure 5-5. Data acquisition equipment with thermocouple wiring (photo courtesy of Adrian M. Lawrence). Figure 5-6. Temperatures measured at bottom, middle and top of Footing 1. 69

PAGE 70

Figure 5-7. View of Footing 2 (phot o courtesy of Adrian M. Lawrence). 70

PAGE 71

Sensor 10 Sensor 9 Sensor 8 Sensor 7 Sensor 6 Sensor 5 Sensor 4 Sensor 3 Sensor 2 Sensor 1 Sensor 15 Sensor 14 Sensor 13 Sensor 12 Sensor 11 Sensor 20 Sensor 19 Sensor 18 Sensor 17 Sensor 16 Figure 5-8. Locations of tem perature sensors in Footing 2. 15 20 25 30 35 40 020406080100120140160180 Time after concrete placement (hour)Temp. (C) Figure 5-9. Ambient te mperature during the moni toring of Footing 2. 71

PAGE 72

20 30 40 50 60 70 024487296120144168 Time (hours)Temp. (C) Sensor 1: 0.1m from Bottom Sensor 2: 0.406m from Bottom Sensor 3: 0.965m from Bottom Sensor 4: 1.422m from Bottom Sensor 5: 1.930m from Bottom Figure 5-10. Profile of tem peratures measured along vertical centerline of Footing 2. 20 30 40 50 60 024487296120144168 Time (hours)Temp. (C) Sensor 6: 0.1m from Bottom Sensor 7: 0.406m from Bottom Sensor 8: 0.965m from Bottom Sensor 9: 1.422m from Bottom Figure 5-11. Profile of temperatures measured at mid-side of Footing 2. 72

PAGE 73

20 30 40 50 60 024487296120144168 Time (hours)Temp. (C) Sensor 11: 0.1m from Bottom Sensor 12: 0.406m from Bottom Sensor 13: 0.965m from Bottom Sensor 14: 1.422m from Bottom Sensor 15: 1.930m from Bottom Figure 5-12. Profile of te mperatures measured at t he corner of Footing 2. 0 10 20 30 40 50 60 050100150200250Time (hours)Temperature ( C) Sensor 16 Sensor 17 Sensor 18 Sensor 19 Sensor 20 Figure 5-13. Profile of tem peratures measured by sensor s 16 to 20 in Footing 2. 73

PAGE 74

Figure 5-14. Footing at I4 US-192 Braided Ramp, Orlando, FL (photo courtesy of Adrian M. Lawrence). 22 ( 6.71 m ) 10 (3.05 m) 5-9 (1.75 m) Figure 5-15. Dimensions of Footing 3. 74

PAGE 75

75 25 35 45 55 65 75 020406080100120140160180 Time (hours)Temperature (C) Bottom Sensor Middle Sensor Top Sensor Figure 5-16. Measured tem peratures at top, middle, and bottom of footing.

PAGE 76

CHA PTER 6 COMPARISONS OF FINITE ELEMENT RESULTS WITH FIELD MEASUREMENTS Overview The finite element model described in C hapter 3 was used to predict temperature developments in each monitored mass concrete structure presented in Chapter 5. The computed temperatures from the finite element model we re then compared with the recorded temperatures in the field. Each finite element model corresponding to each structure to be analyzed had different boundary conditions from one another. Footing 1 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) The finite element model predicted the te mperature profiles at the top, middle, and bottom elevations along the central line as indicated in Figure 6-1. The results at Nodes 1849 (top surface), 2719 (middle), and 862 (bottom surface) were compared with field test results as shown in Figure 6-2. The experimental and predicted temperatures were relatively close, especially in the latter half of the field results. Footing 2 (at S.R. 826 and S.R. 836 Interchange, Miami, FL) The finite element model of the pier footing with the pr edicted temperature distribution contours is pres ented in Figure 6-3. The high est temperature was found to occur in the middle section of the model and dec reased as it got closer to the surfaces of the model. Figures 6-4 through 6-13 present the com parisons of the predicted temperature time histories of the pier footing model with the measur ed temperatures obtained in the field at the respective locations. The trend of the temperature incr eases obtained from the model is relatively close to the trend of those recorded in the sensors. Most of the temperatures predicted in the finite element model closely match with the temperatures 76

PAGE 77

measured in the field. Howev e r, the computed temperatures near the top surface were lower than the measured ones (in Sensors 5 and 15). This is probably due to factors that impact the surface temper ature of the concrete in the field such as ambient temperature change with time, solar radiat ion and radiation from the atmosphere. Footing 3 (at I-4 US-192 Braided Ramp, Orlando, FL) The finite element model of the pier footing with the pr edicted temperature distribution contours is pres ented in Figure 6-14. The model included full insulation at the top, side, and bottom surfaces using Styrofoam. Figures 6-15 through 6-17 show the comparisons of the temperature profiles at the top, center and bottom of the pier footing calculated by the finite element model with the measured temperatures obtained in the field. The computed temperatures at the top of the pi er footing were fairly close to those recorded in the top sensor. T he temperatures calculated at the center and bottom of the footing were close to those recorded in the field for the first 40 hours of monitoring. However, the temperatures in the field dropped more rapidly after 40 hours. This difference can be explained by t he fact that there were variables affecting the actual temperature development in the concrete in the field, which were not accounted for in the model. First, the time of placement of the top insulati on was delayed after concrete placement due to strike-off of the concrete surf ace, resulting in heat loss in the concrete which was not considered in the finite element model. The second reason is that the formwork used for this footing was a steel form work and it was in direct contact with the concrete surface (Styrofoam was placed outside of the steel formwork), causing more rapid heat transfer from the concrete to t he steel formwork and thus more rapid heat dissipation, while the steel formwork was not modeled for temperature predictions. 77

PAGE 78

Figure 6-1. Temper ature contour at 7th day in Footing 1 model. Figure 6-2. Comparison between measured te mperatures and FE results of Footing 1. 78

PAGE 79

Figure 6-3. Predicted temper ature distribution 7 days after concrete placement in Footing 2. 10 15 20 25 30 35 40 45 50 55 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 1 Sensor 2 Predicted temp. at Sensor 1 Predicted temp. at Sensor 2 Figure 6-4. Predicted and measured temperat ures in Sensors 1 and 2 along vertical centerline of Footing 2. 79

PAGE 80

15 20 25 30 35 40 45 50 55 60 65 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 3 Predicted temp. at Sensor 3 Ambient temperature Figure 6-5. Predicted and measur ed temperatures in Sensor 3 along vertical centerline of Footing 2. 25 30 35 40 45 50 55 60 65 70 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 4 Predicted temp. at Sensor 4 Figure 6-6. Predicted and measur ed temperatures in Sensor 4 along vertical centerline of Footing 2. 80

PAGE 81

20 25 30 35 40 45 50 55 60 65 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 5 Predicted temp. at Sensor 5 Figure 6-7. Predicted and measur ed temperatures in Sensor 5 along vertical centerline of Footing 2. 15 20 25 30 35 40 45 50 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 6 Sensor 7 Predicted temp. at Sensor 6 Predicted temp. at Sensor 7 Figure 6-8. Predicted and measured temperat ures in Sensors 6 and 7 at mid-side of Footing 2. 81

PAGE 82

25 30 35 40 45 50 55 60 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 8 Sensor 9 Predicted temp. at Sensor 8 Predicted temp. at Sensor 9 Figure 6-9. Predicted and measured temperat ures in Sensors 8 and 9 at mid-side of Footing 2. 25 30 35 40 45 50 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 11 Sensor 12 Predicted temp. at Sensor 11 Predicted temp. at Sensor 12 Figure 6-10. Predicted and meas ured temperatures in Sens ors 11 and 12 at the corner of Footing 2. 82

PAGE 83

25 30 35 40 45 50 55 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 13 Predicted temp. at Sensor 13 Figure 6-11. Predicted and meas ured temperatures in Sens or 13 at the corner of Footing 2. 20 25 30 35 40 45 50 55 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 14 Predicted temp. at Sensor 14 Figure 6-12. Predicted and meas ured temperatures in Sens or 14 at the corner of Footing 2. 83

PAGE 84

20 25 30 35 40 45 50 020406080100120140160180 Time after concrete placement (hour)Temp. (oC) Sensor 15 Predicted temp. at Sensor 15 Figure 6-13. Predicted and meas ured temperatures in Sens or 15 at the corner of Footing 2. Figure 6-14. Predicted temperature distribution 7 days after concrete placement in Footing 3. 84

PAGE 85

30 40 50 60 70 024487296120144168 Time (hours)Temperature (C) Measured temp. at Top Predicted temp. at Top Figure 6-15. Predicted and measured temper atures at the top of Footing 3. 25 35 45 55 65 75 85 024487296120144168 Time (hours)Temperature (C) Measured temp. at Middle Predicted temp. at Middle Figure 6-16. Predicted and measured temperatures at the center of Footing 3. 85

PAGE 86

25 35 45 55 65 75 85 024487296120144168 Time (hours)Temperature (C) Measured temp. at Bottom Predicted temp. at Bottom Figure 6-17. Predicted and measured temper atures at the bottom of Footing 3. 86

PAGE 87

CHA PTER 7 EFFECTS OF THERMAL PROPERTIES OF SOIL ON TEMPERATURE DEVELOPMENT AND CRACKING IN FOOTIN GS DIRECTLY PLACED ON SOIL Description of Analysis Method Many times, when mass concrete is placed directly on top of a soil layer, an insulation layer is not used at the bottom of the concrete. The rationale for this practice is that the soil on which the concrete is pl aced is already an insulating material. This chapter presents the investi gation on the question of whether or not the absence of an insulating layer between the mass concrete and the soil may c ause a problem with cracking of the concrete at early ages. A finite element analysis was conducted to investigate the thermal behavior of a mass concrete footing placed directly on a soil layer. The modeled concrete was insulated at the top and sides while there was no insulation at the bottom, which was in direct contact with the soil. The model footing had the dimensions of 10.36 m 10.36 m 2.03 m (the same as Footing 2 (Table 5-1)). The concrete properties used were the same as those of Concrete Mix 1 that had wa ter to cementitious ma terial ratio of 0.5 and consisted of 100% Type I Portland cem ent concrete (Lawrence et al. 2012). The model soil layer beneath the footi ng extended 5 m deeper (close to Kim (2001)), and 3 m wider on each side of the f ooting in order to ensure adequate medium for heat transfer from the f ooting. The initial temperatur e and the ambient temperature were set at 25.5C and 26C, respectively. Several soils were modeled in this study, including sand and clay, each in three states of hydration, dry, moist, and saturated, and four other soils. Thermal conductivities, R-values, and heat capacities of these soils are given in Table 7-1. Note 87

PAGE 88

that the model moist sand and moist clay here were assumed based upon their thermal conductivities but not on their moisture cont ents. The thermal conductivity of soil was determined from the R *-value of the soil layer by the following equation: *R t k (7-1) where k = thermal c onductivity (W/m-C) t = thickness of the layer (m) R* = thermal resistance (m2-C/W) The R*-value can be converted to the commonl y used R-value which has the units of ft2-F-h/(BTU-in). The R-values per inch of soil are given in Table 7-1. Soil Temperature Distribution To investigate the temperature in so il caused by heat of hydration generated from a mass concrete footing placed directly on it, two cases of soil, including dry sand and saturated sand, were analyzed. The ther mal conductivity and R-value of each type of sand are listed in Table 7-1. The temperature contours in dry and saturated sand are illustrated in Figure 7-2. Figures 7-3 and 7-4 show plots of temperature with respect to depth in dry and saturated sand at 3 locations: center, mid-si de and corner of the f ooting. It can be seen that among the 3 locations, the temperature in soil at the c enter of footing was highest while the temperature in soil at the corner was lowest. This was due to the large contact area between the concrete and the soil at the bottom middle allowing more heat to transfer to the soil, and the small contact area at mid-sides and corner allowing less heat to transfer. The top layer of dry s and had a higher temperature than that of saturated sand. The surface of the dry soil at the center, midside, and corner of footing 88

PAGE 89

had temperatures of 77.4C, 68.4C, and 59.8 C, respectively, whereas that of the saturated soil had lower temperatures of 64.3C, 44.9C, and 35.1C, respectively. Howev er, due to the lower R-value, the satu rated sand allowed heat from the concrete to transfer to a lower depth of around 5 m as compared with a depth of 1 m in the dry sand. It was also noted from the figures that heat from the concrete transferred downwards better than sidewards in soil. Temperature Development in Concrete Figures 7-5 and 7-6 show the temperatur e developments in the concrete placed directly on dry sand and saturated sand, respecti vely. The center of concrete in the two cases had similar temperature profiles as it peaked 81C in the case of dry sand and 77.5C in the case of saturated sand at 7th day. However, the obvious difference between the 2 cases occurred in the concrete at the bottom corner. For the dry sand, the concrete temperature at this location gradually increased after 30 hours before it reached a high point of 59.8C at 167th hour, while for the saturated sand, it remained constant at 35C throughout this time period. The temperature different ial, therefore, in the concrete on the dry sand was 21.2C while it was doubled (42.5C) in the concrete on the saturated sand. This sign revealed t hat the concrete on the saturated sand was likely to crack while the cracking probability in the concrete on the dry sand needed to be investigated. Thermal Cracking Analysis The probability of cracking is measured by the function called the crack index: (t) (t)f (t)II t cr (7-2) where Icr = crack index (if Icr falls below 1.0, cra cking has been initiated) 89

PAGE 90

ft = tensile strength I = maximum principal stress t = time from concrete placement (hour) The physical properties of the concrete were obtained from la boratory testing as shown in Table 7-2 (Lawrence et al. 2012) The concrete had density of 2,248 kg/m3, Poissons ratio of 0.2, and coeffici ent of thermal ex pansion of 9.1610-6 mm/mm-C. Figure 7-7 illustrates the performance of t he concrete with respect to the crack index for dry, moist, and saturated sand. As stated earlier, a crack index value less than 1.0 occurs when the induced tens ile stress exceeds the earlyage tensile strength of the concrete and indicates the initiation of cracking. The results in this figure show that for the saturated and moist sands, the crack index dropped to a value less than 1.0 within the first 24 hours while for the dry sand, the crack index rema ined above 1.4. Therefore, this suggested that the dr y sand provided good protecti on against heat loss at the concrete bottom leading to low thermal gradients and thus low tensile stresses. Thermal cracking analysis was also conduc ted for dry, moist, and saturated clays in this chapter and the minimum calculated cra ck indices are plotted in Figure 7-8. This figure shows a similar trend observed in Figure 7-7 as the crack index for the dry clay stayed above 1.9 while it fell below 1. 0 for the saturated and moist clays. It was needed to extend analysis to moist sand and moist clay with different Rvalues in order to investigate the threshol d of R-value of soil that provides adequate insulation for the concrete to prevent early -age thermal cracking. Figure 7-9 shows the minimum calculated crack indices of the concre te on the soil with R-values ranging from 0.53 to 0.072. It is clearly seen that the crack index decreased wi th the decrease of Rvalue. At an R-value of 0.29, the crack index remained sli ghtly above 1.0 throughout 7 90

PAGE 91

days of cement hydration, t herefore indicating that cracki ng did not initiate in the concrete of the 10.36-m 10.36-m 2.03-m footing. Analyses on 4-m 4-m 1-m, 20-m 20-m 5-m, 32-m 32-m 8-m, and 48-m 48-m 12-m footings, as listed in Table 7-3, were also conducted. Soil with R-values of 0.29 and 0.41 were analyzed for each analysis. The minimum calculated crack index in these footings with respect to footi ngs volume-to-surface area ratio (V/A) are presented in Figure 7-10. It was found that so il with an R-value of 0.29 did not provide adequate insulation for a footing with a V/ A of greater than 2. 4, as the minimum calculated crack index dropped below 1.0. Howe ver, with an R-valu e of 0.41, the soil provided adequate insulation for a f ooting with a V/A up to 13.0. Therefore, it could be concluded that soil (sand/clay) wi th an R-value of 0.41 or greater would provide adequate insulation at the bottom of mass concrete footing in terms of preventing thermal cracking. Summary of Findings The main findings from the parametric st udy in this chapter can be summarized as follows: At the contact surface between the mass concrete footing and soil, dry soil had higher temperatures than wet or saturat ed soil. This was because wet soil allowed the heat of hydration generated from the concrete to tr ansfer to a greater depth than dry soil did. The concrete footing on soil had the highes t temperatures at its bottom center and had the lowest temperatures at its bottom corner. Mass concrete footing developed similar te mperatures at its c enter regardless of whether it was placed on dry or saturated soil. However, the temperatures at its corner were quite different for the case of dry soil as compared with the case of saturated soil. 91

PAGE 92

Dry sand and dry clay provided good insu lation at the bottom of mass concrete footing, as indicated from the crack indices obtained from the thermal cracking analysis performed. Soil with an R-value of 0.41 or greater (o r thermal conductivity of 0.35 J/sec-m-C or lower) would provide adequate insulation at t he bottom of concrete footing using Mix 1 to prevent cracking. For footings with a V/A of less than 2.4 ft, soil with an R-value of 0.29 would be adequate to prevent cra cking. Thus, an insulating layer between the mass concrete and the soil would not be needed in such situations. 92

PAGE 93

Table 7-1. Thermal Properties of Sand and Clay Material Conductiv ity (J/sec-m-C) R-value (ft2-F-h/BTU-in) Heat Capacity (J/m3-C) Dry Sand 0.27 R-0.53 1.212106 Moist Sand 2.0 R-0.072 1.56106 Saturated Sand 4.0 R-0.036 1.92106 Dry Clay 0.15 R-0.96 1.285106 Moist Clay 0.9 R-0.16 1.285106 Saturated Clay 2.5 R-0.058 1.285106 Soil 1 0.35 R-0.41 1.212106 Soil 2 0.4 R-0.36 1.212106 Soil 3 0.5 R-0.29 1.285106 Soil 4 0.6 R-0.24 1.212106 Table 7-2. Physical Properties of Concrete Time (day) 1 2 3 7 Tensile Strength (MPa ) 1.25 1.66 1.93 2.206 Youngs Modulus (MPa ) 13,445 16,892 18,064 20,202 Table 7-3. Footing Dimesions and Volume-to-Surface Area Ratio Length (m) 4 10.36 20 32 48 Width (m) 4 10.36 20 32 48 Depth (m) 1 2.03 5 8 12 Volume:Surface Area Ratio (ft) 1.09 2.39 5.47 8.75 13.12 93

PAGE 94

Top Insulation Side Insulation Mass Concrete Soil 3m 3 m 5 m Figure 7-1. Finite element mesh of concre te footing in direct contact with soil. A B Figure 7-2. Temperature distribution in soil 7 days after concrete placement. A) Dry sand. B) Saturated sand. 94

PAGE 95

0 0.25 0.5 0.75 1 1.25 1.5 26364656667686 Temperature (C)Depth (m) Center Side Corner Figure 7-3. Temperature with respect to depth in dry sand 7 days after concrete placement. 0 1 2 3 4 5 6 263646566676 Temperature (C)Depth (m) Center Side Corner Figure 7-4. Temperature with respect to dept h in saturated sand 7 days after concrete placement. 95

PAGE 96

25 35 45 55 65 75 85 024487296120144168 Time (hours)Temperature (C) Center Bottom Center Bottom Mid side Bottom Corner Figure 7-5. Temperature development in concrete footing placed on dry sand. 20 30 40 50 60 70 80 024487296120144168 Time (hours)Temperature (C) Center Bottom Center Bottom Mid side Bottom Corner Figure 7-6. Temperature dev elopment in concrete foot ing placed on saturated sand. 96

PAGE 97

0 0.5 1 1.5 2 2.5 3 024487296120144168 Time (hour)Crack Index Dry Sand, R 0.53 Moist Sand, R 0.072 Saturated Sand, R 0.036 Figure 7-7. Minimum calculated cr ack index in concrete on sand. 0 0.5 1 1.5 2 2.5 3 024487296120144168 Time (hour)Crack Index Dry Clay, R 0.96 Moist Clay, R 0.16 Saturated Clay, R 0.058 Figure 7-8. Minimum calculated cr ack index in concrete on clay. 97

PAGE 98

0.5 1 1.5 2 024487296120144168 Time (hour)Crack Index R 0.53 R 0.36 R 0.29 R 0.24 R 0.16 R 0.072 Figure 7-9. Minimum calculat ed crack index in concrete on soil with varying R-value. 0 0.5 1 1.5 2 135791113 Volume:Surface Area Ratio (ft)Crack Index R 0.29 R 0.41 Figure 7-10. Minimum calculated crack index in different concrete footings on soil with R-values of 0.29 and 0.41. 98

PAGE 99

CHA PTER 8 EFFECTS OF FOOTINGS DIMENSIONS AND INSULATION ON TEMPERATURE DEVELOPMENT AND CRACKING IN CONCRETE Description of the Parametric Study Although the FDOT Standard Specifications for Road and Bridge Construction require that the maximum temperature diffe rential between the concrete core and the exterior surface does not exceed 35F (20C), it is not clear whether or not this limiting value is dependent on a footings dimensions. This research in vestigates the effects of a footings dimensions on the maximum allowable temperature differential to prevent cracking in concrete. The study also determi nes the required insula tion to prevent earlyage cracking in concrete footings. For this task, a parametric study consis ting of 63 finite element analyses (63 cases) was conducted. Three different shapes of rectangular footings were considered: cubic shape; length:wi dth:depth ratio = 4:4:1; and length: width:depth ratio = 4:2:1. The dimensions of footing for a ll the cases studied are given in Tables 8-1 through 8-9. The modeled concrete footing was fully insulated at its top, sides, and bottom with Styrofoam that had an Rvalue of 5.0 per inch. The insulation thicknesses modeled were 0.5 in., 1 in., and 1.25 in. The concrete properties used were the same as those of Concrete Mix 1 that had water to cementitious material ratio of 0.5 and the cementitious material consisted of 100% Type I Portland cement (Lawrence et al. 2012). Effects of Footings Dime nsions on Temperature Development and Cracking Figure 8-1 presents the maximu m temperatures in cubic footings for 3 cases of insulation thickness: 0.5, 1.0, and 1.25 in For a cubic footing that had a volume-tosurface area ratio (V/A) between 1.0 ft and 4.0 ft, the maximum temperature developed in concrete increased with the increase in in sulation thickness. For instance, a 2-m 299

PAGE 100

m 2-m footing had a maximum temperatur e of 71.4C, 74. 9C, and 76.3C when insulated with 0.5 in., 1.0 in., and 1.25 in. of Styrofoam, respectively. However, the maximum temperature developed in a cubic foot ing that had a V/A greater than 4.0 ft was not dependent on thickness of insulation. It was also observed that the maximum temperature in a footing with V/A greater than 4.0 ft nearly re mained unchanged at 84C. Figure 8-2 clearly shows the influence of insulation thic kness on the temperature difference in cubic footings. The temperature difference in the concrete decreased with the increase in insulation thickness. With a V/A of less than 4.5 ft, and under the same insulation condition, a larger cubic f ooting had a higher maximum temperature difference. Interestingly, with a V/A of 4. 5 ft or greater, a larger cubic footing had a similar or slightly smaller temperature di fference under the same insulation condition. Crack indices in cubic footings with diffe rent V/As and insulati on thickness levels are shown in Figure 8-3. With a V/A of le ss than 4.5 ft, and under the same insulation condition, a larger cubic footing had a lower cr ack index. However, with a V/A of 4.5 ft or greater, a cubic footing had an almost constant crack index under the same insulation condition. This means that cracking potentia l no longer increased with increasing size after V/A exceeded 4.5 ft. Figures 8-4 through 8-6 show the maximum temperatures, maximum temperature differences, and crack indices in 4:4:1 footings while those for 4:2:1 footings are shown in Figures 8-7 thr ough 8-9. There was a similar trend in the maximum temperatures developed in these footings as in cubic footings: the maximum temperature rapidly increased as the V/A increased from 1.0 ft to 4.5 ft, then it grew only 100

PAGE 101

slightly as the V/A became la rger than 4.5 ft. The temperat ure difference increased as the V/A rose from 1.0 ft to 4.5 ft, then it slight ly decreas ed as V/A became larger than 4.5 ft. The crack index dropped as the V/A grew from 1.0 ft to 4.5 ft, however, it leveled off as the V/A became larger than 4.5 ft. As shown in Figures 8-5 and 8-6, the 4: 4:1 footing insulat ed with 0.5 in. of Styrofoam, with a V/A of 1. 09 ft, had a maximum temperature difference of 25.2C and a crack index of 1.05 indicating no occurrenc e of cracking. The footing insulated with 1.0 in. of Styrofoam, with a V/A of 4.37 ft, had a maximu m temperature difference of 22.9C and a crack index of 1.01. Of these two footings, the smaller one had a higher maximum temperature difference but lower likelihood of cracking than the larger one, thus the smaller footing did not require a smaller maximum allowable temperature to prevent cracking. With a V/A of 4.5 ft or gr eater and with the same insulation thickness, a larger footing had a similar or slightly smaller maximum temperature difference but similar cracking potential (a similar crack index ). The same results were drawn from the observations of cubic footings and 4:2:1 footings. Therefore, sma ller footings do not require a smaller maximum allowable temper ature than larger footings to prevent cracking. Effects of Footings Shape on Temp erature Development and Cracking The maximum temperatures, maximum temperature differences, and crack indices in all the modeled footings were then compared together for each insulation thickness level. Figures 8-10 through 8-12 show the maximum temperatures in footings fully insulated with 0.5 in., 1.0 in., and 1.25 in. of Styrofoam, respectively. For each insulation thickness level, the maximum temper atures that occurred in footings with the same V/A were very similar regardless of the footings shapes. The difference in the 101

PAGE 102

maximum temperatures in the different foot ings having the same V/A did not exceed 2.3C. Figures 8-13 through 8-15 present the maximum temperature differences in the different footings fully insulated with 0.5 in., 1.0 in., and 1. 25 in. of Styrofoam, respectively. For each insulation thickness level, the maximum temperature differences in footings that had the same V/A were ve ry close to each other regardless of their shapes. Figures 8-16 through 8-18 show the crack indi ces in the different footings for the cases of insulation with 0.5 in., 1.0 in., and 1. 25 in. of Styrofoam, res pectively. Again, for each insulation thickness level, the crack indice s in footings that had the same V/A were very similar regardless of their shapes. Determination of Required Insulation Thickness In the analyses presented above, the insulation thickness was increased from 0.5 in. until it was adequate to prevent cracking in the concrete. Figure 8-16 shows the crack indices in all the footings insulated wi th 0.5 inch of Styrof oam. Beginning from a value slightly above 1.0 at a V/ A of 1.09 ft, the crack index dropped sharply to below 1.0 as the V/A increased. Theref ore, 0.5 inch of Styrofoam did not provide adequate insulation for footings with a V/A of greater than 1.09 ft to prevent cracking. As shown in Figure 8-17, the crack index in a footing insulated with 1.0 in. of Styrofoam was greater than 1.0 at a V/A in the r ange of 1.0 ft and 4.0 ft, and was slightly below 1.0 as the V/A became la rger. Hence, one inch of Styrofoam was adequate for footings with a V/A of 4.0 ft or smaller to insu re no occurrence of cracking in the concrete. 102

PAGE 103

Figure 8-18 shows the crack index in foot ings insulated with 1.25 inches of insulation. There was a sharp drop in the cra ck index as the V/A incr eased from 1.0 ft to 2.5 ft. The crack index then remai ned almost constant at a value of 1.1 when the V/A became larger than 4.0 ft. Therefore, an insulation thickness of 1.25 inches was adequate for footings with a V/A up to 13.0 ft to prevent cracking in the concrete induced by thermal contraction. Table 8-10 shows the required insulation thickness to prevent cracking and the maximum temperature differentials for the footings (using conc rete of Mix 1) with V/As ranging from 1.1 to 13.1. It was found that the maximum tem perature differentials varied according to the size of the mass concrete footings especial ly for V/As less than 4.5 ft. Summary of Findings The main findings from the parametric st udy in this chapter can be summarized as follows: The maximum temperature developed in a rectangular footing wi th a V/A of less than 4.5 ft was higher if insulated with thicker insulation. In a footing with a V/A of 4.5 ft or greater, however, it was not dependent on insulation thickness. The temperature differential in a concre te footing decreased with the increase in insulation thickness. With a V/A of less than 4.5 ft, under the same insulati on condition and using the same concrete mix, a larger footing had a higher maximum temperature difference, and lower crack index. However, with a V/A of 4.5 ft or greater, a larger footing had a similar or slightly smaller maximum tem perature difference, and an almost constant crack index. Thus, cracking potential wa s not dependent on how large a footing was when its V/A was 4.5 ft or greater. Rectangular footings that had the same V/A but different s hapes (dimensional proportions) would develop a similar maxi mum temperature, a similar maximum temperature difference, and a similar cr ack index under the same insulation condition. Smaller footings allow slightly higher maximum temperature differential to prevent cracking by thermal contraction. 103

PAGE 104

When Styrofoam with an R-va lue of 5.0 per inch was used, 0.5 inch would provide adequate insulation for a footing with a V/A of around 1.0 ft; 1.0 inch would provide adequate insulation for a footing with a V/A less than 4.0 ft; 1.25 inches would provide adequate insulation for a footing with a V/A up to 13.0 ft. If another type of insulating material is used, an equivalent insulation thickness can be determined from the materials R-value. 104

PAGE 105

Table 8-1. Temperatures and crack index in cubic footin gs insulated with 0.5-in Styrofoam Length (m) 2 3 4 8 12 16 24 Width (m) 2 3 4 8 12 16 24 Depth (m) 2 3 4 8 12 16 24 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 71.4 78.8 82.6 83.9 83.9 84.1 84.6 Max. Temp. Difference (C) 21.5 30.2 32.9 35.2 35.1 35 34.8 Crack Index 1.22 0.864 0. 727 0.628 0.605 0.588 0.576 Table 8-2. Temperatures and crack index in cubic foot ings insulated with 1-in Styrofoam Length (m) 2 3 4 8 12 16 24 Width (m) 2 3 4 8 12 16 24 Depth (m) 2 3 4 8 12 16 24 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 74. 9 80.9 83.1 83.9 83.9 84 84.3 Max. Temp. Difference (C) 15 20.4 22.5 23.2 23 22.9 22.4 Crack Index 1.77 1.24 1. 07 0.973 0.953 0.933 0.929 Table 8-3. Temperatures and crack index in cubic footin gs insulated with 1.25-in Styrofoam Length (m) 2 3 4 8 12 16 24 Width (m) 2 3 4 8 12 16 24 Depth (m) 2 3 4 8 12 16 24 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 76. 3 81.5 83.3 83.9 83.9 84 84.3 Max. Temp. Difference (C) 13 17.6 19.3 19.5 19.6 19.4 19 Crack Index 2.04 1.43 1.25 1.15 1.13 1.11 1.11 Table 8-4. Temperatures and crack index in 4:4:1 footi ngs insulated with 0.5-in Styrofoam Length (m) 4 6 8 16 24 32 48 Width (m) 4 6 8 16 24 32 48 Depth (m) 1 1.5 2 4 6 8 12 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 72. 3 77.9 80.3 83.6 84 84.3 84.9 Max. Temp. Difference (C) 25.2 29.9 31.9 34.9 35 34.7 33.9 Crack Index 1.05 0.838 0. 753 0.634 0.599 0.583 0.581 105

PAGE 106

Table 8-5. Temperatures and crack index in 4:4:1 foot ings insulated with 1-in Styrofoam Length (m) 4 6 8 16 24 32 48 Width (m) 4 6 8 16 24 32 48 Depth (m) 1 1.5 2 4 6 8 12 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 76. 3 80 81.5 83.7 83.9 84.1 84.6 Max. Temp. Difference (C) 17. 6 20.1 21.1 22.9 22.9 22.6 21.8 Crack Index 1.53 1.29 1. 19 1.01 0.958 0.937 0.953 Table 8-6. Temperatures and crack index in 4:4:1 footi ngs insulated with 1.25-in Styrofoam Length (m) 4 6 8 16 24 32 48 Width (m) 4 6 8 16 24 32 48 Depth (m) 1 1.5 2 4 6 8 12 Volume:Surface Area Ratio (ft) 1.09 1.64 2.19 4.37 6.56 8.75 13.12 Max. Temperature (C) 77. 4 80.5 81.8 83.8 83.9 84 84.5 Max. Temp. Difference (C) 15. 2 17.1 17.9 19.6 19.4 19.1 18.4 Crack Index 1.79 1.54 1.41 1.2 1.14 1.12 1.14 Table 8-7. Temperatures and crack index in 4:2:1 footi ngs insulated with 0.5-in Styrofoam Length (m) 4.6 7 9.4 20 28 36 56 Width (m) 2.3 3.5 4.7 10 14 18 28 Depth (m) 1.15 1.75 2.35 5 7 9 14 Volume:Surface Area Ratio (ft) 1.08 1.64 2.20 4.69 6.56 8.44 13.12 Max. Temperature (C) 71. 5 78.2 81.2 83.9 84 84.2 84.6 Max. Temp. Difference (C) 23.4 30 32.6 35.1 35.1 35 34.2 Crack Index 1.2 0.868 0. 73 0.619 0.595 0.582 0.576 Table 8-8. Temperatures and crack index in 4:2:1 foot ings insulated with 1-in Styrofoam Length (m) 4.6 7 9.4 20 28 36 56 Width (m) 2.3 3.5 4.7 10 14 18 28 Depth (m) 1.15 1.75 2.35 5 7 9 14 Volume:Surface Area Ratio (ft) 1.08 1.64 2.20 4.69 6.56 8.44 13.12 Max. Temperature (C) 75. 5 80.2 82.1 83.9 83.9 84 84.3 Max. Temp. Difference (C) 16.4 20 21.6 23.1 22.9 22.7 21.9 Crack Index 1.79 1.27 1. 11 0.972 0.94 0.925 0.936 106

PAGE 107

Table 8-9. Temperatures and crack index in 4:2:1 footi ngs insulated with 1.25-in Styrofoam Length (m) 4.6 7 9.4 20 28 36 56 Width (m) 2.3 3.5 4.7 10 14 18 28 Depth (m) 1.15 1.75 2.35 5 7 9 14 Volume:Surface Area Ratio (ft) 1.08 1.64 2.20 4.69 6.56 8.44 13.12 Max. Temperature (C) 76. 8 80.7 82.4 83.9 83.9 84 84.2 Max. Temp. Difference (C) 14.2 17 18.5 19.7 19.5 19.3 18.4 Crack Index 2.09 1.49 1.31 1.15 1.12 1.1 1.12 Table 8-10. Required insulation thickne ss and maximum temperature differential for different V/As V/A (ft) R-value per in. Required Insulation Thickness (in.) Maximum Temperature Differential (C) 1.1 5.0 0.5 25.2 1.6 5.0 0.7 25.4 2.2 5.0 1.0 22.5 4.4 5.0 1.1 21.6 6.6 5.0 1.2 20.8 8.8 5.0 1.2 20.3 13.1 5.0 1.2 20.1 107

PAGE 108

70 72 74 76 78 80 82 84 86 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-1. Maximum temperature in cubic footings. 12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-2. Maximum temperatur e difference in cubic footings. 108

PAGE 109

0 0.5 1 1.5 2 2.5 135791113 Volume:Surface Area Ratio (ft)Crack Index 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-3. Crack Index in cubic footings. 70 72 74 76 78 80 82 84 86 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-4. Maximum temper ature in 4:4:1 footings. 109

PAGE 110

12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-5. Maximum temperatur e difference in 4:4:1 footings. 0 0.5 1 1.5 2 135791113 Volume:Surface Area Ratio (ft)Crack Index 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-6. Crack Index in 4:4:1 footings. 110

PAGE 111

70 72 74 76 78 80 82 84 86 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-7. Maximum temper ature in 4:2:1 footings. 12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-8. Maximum temperatur e difference in 4:2:1 footings. 111

PAGE 112

0 0.5 1 1.5 2 2.5 135791113 Volume:Surface Area Ratio (ft)Crack Index 0.5 in. thick 1 in. thick 1.25 in. thick Figure 8-9. Crack Index in 4:2:1 footings. 68 72 76 80 84 88 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) Cubic 4:4:1 4:2:1 Figure 8-10. Maximum temper ature in footings insulat ed with 0.5-in Styrofoam. 112

PAGE 113

72 76 80 84 88 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) Cubic 4:4:1 4:2:1 Figure 8-11. Maximum temper ature in footings insula ted with 1-in Styrofoam. 72 76 80 84 88 135791113 Volume:Surface Area Ratio (ft)Max. Temperature (C) Cubic 4:4:1 4:2:1 Figure 8-12. Maximum temper ature in footings insulat ed with 1.25-in Styrofoam. 113

PAGE 114

12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) Cubic 4:4:1 4:2:1 Figure 8-13. Maximum temper ature difference in footings insulated with 0.5-in Styrofoam. 12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) Cubic 4:4:1 4:2:1 Figure 8-14. Maximum te mperature difference in footings insulated with 1-in Styrofoam. 114

PAGE 115

12 16 20 24 28 32 36 135791113 Volume:Surface Area Ratio (ft)Max. Temp. Difference (C) Cubic 4:4:1 4:2:1 Figure 8-15. Maximum temper ature difference in footings insulated with 1.25-in Styrofoam. 0 0.5 1 1.5 135791113 Volume:Surface Area Ratio (ft)Crack Index Cubic 4:4:1 4:2:1 Figure 8-16. Crack Index in footings insulated with 0.5-in Styrofoam. 115

PAGE 116

0 0.5 1 1.5 2 135791113 Volume:Surface Area Ratio (ft)Crack Index Cubic 4:4:1 4:2:1 Figure 8-17. Crack Index in footings insulate d with 1-in Styrofoam. 0 0.5 1 1.5 2 2.5 135791113 Volume:Surface Area Ratio (ft)Crack Index Cubic 4:4:1 4:2:1 Figure 8-18. Crack Index in footings insulated with 1.25-in Styrofoam. 116

PAGE 117

CHA PTER 9 DEVELOPMENT OF SOFTWARE FOR GE NERATING DIANA INPUT FILES Overview DIANA (DIsplacement ANAlyzer) is an ex tensive multi-purpose finite element software package that is dedicated, but not exclusive, to a wide range of problems arising in civil engineering. However, it does not have available templates for prompt analysis of mass concrete structures such as footings, columns, and pier caps. It is therefore needed to develop a user-friendly computer program so as to aid users to easily create a mass concrete model, and to mi nimize time for constructing geometry of mass concrete structures with typical shapes and various options of insulation. DIANA Input File Generator User-friendly software named DIANA I nput File Generator (DIFG) was developed using the Delphi programming la nguage to provide prompt input files for DIANA before performing an analysis of mass concrete. The software interface is shown in Figure 9-1. The software can produce DIANA input files for rectangular footings as shown in the figure under Concrete Structure on its inte rface. In this group box, the user must enter dimensions of a footing in x, y and z-di rections as well as a division (number of elements) in each direction. The program will create a model of one-quarter of the whole structure, that means the x and y dimensions of the actual structure will be reduced to a half in the finite element model. In the group box Temperatures, the user must enter the placement temperature of concrete (initial temperature) and external temperature. The Insulating Materials and Soil group box provides options of insulation at the top, si des and bottom of the footing. 117

PAGE 118

A soil layer beneath the footing will be automatically included to the model as a default. The user must enter the thi ckness, thermal conductivity and heat capacity for each of insulating layers and the soil layer. In the Air Convection group box, boundary air convection coefficients at the top and sides of the footing must be entered. Finally, the user must spec ify the input file name of concrete properties being modeled and the input file name for DIANA in the File Names group box. These file names are in the extension of .dat. The pre-created concre te property input file must include the thermal and mechanical properties of the concrete. The user can browse the concrete property input file using the Bro wse button as illustr ated in Figure 9-2. After all the parameters are determined and entered, the user may click the Generate button to start the generating process of DIANA in put file. DIANA Input File Generator will set up the Dian a 9.4.4 Environment and automatic ally create a .dat file by running iDIANA (preand post-processing of DI ANA) (iDIANA Release 9.4.4., 2012) in silent mode as shown in Figure 9-3. If the generating proce ss is successfully completed, a message will be shown by the softwar e as illustrated in Figure 9-4. Running DIANA Once the DIANA input file is generated, it is ready to be used in DIANA. The user should run the DIANA softwar e using the following steps: Choose Working direct ory (see Figure 9-5) Select Initialize new Click Add and select the DIANA input f ile that has been generated, then click OK After reading input is completed, click OK. ADINA will then show a window asking for anal ysis type as illustrated in Figure 9-6. Click Cancel, DIANA will appear as shown in Figure 9-7. 118

PAGE 119

Open command file (i.e., Command.dcf) and run. There are two types of output files creat ed during running of DIANA that have the following names: FLOW.* (.V72 and .G72): stores thermal resu lts of the finite el ement thermal model STRUC.* (.V72 and .G72): stores stress results of the finite element structural model Note: These files should be renamed pr ior to running another model, otherwise they will be overwritten. Example Creating a Model Using DIFG A mass concrete footing is to be model ed and analyzed to illustrate the use of DIFG and DIANA. The footing has the dimensions of 10. 36 m 10.36 m 1.98 m. The steps to create the finite element model using DIFG are as follows: Step 1: Enter a length of 10.36 m (in x-dire ction), a width of 10. 36 m (in y-direction), and a depth of 1.98 m (in z-direction) in Box A (see Figure 9-8). Note: these numbers are the full dimensions of the f ooting. DIFG will gener ate a model of onequarter of the whole foot ing, thus the finite element mo del of the concrete will have dimensions of 5.18 m 5.18 m 1.98 m. Step 2: Enter 16, 16, and 8 for divisions in x, y, and z-directions in Box B. This will create 16 16 8 = 2048 elements for the concrete. Step 3: In Box C, enter 25.5 (C) for the placement temperature, 26 (C) for the ambient temperature. Step 4: Enter or browse a file name of concrete properties in Box D. A concrete property file named CONCRETE.dat was created for the concrete used in the footing. Detailed content s of this file are shown in Figure 9-9. Step 5: Enter a name for the file to be generated in Box E. For instance, enter footing.dat with a full path. Step 6: Select Top and Side for t op and side insulation in Box F. Enter 0.0762 m (3 inch) of thickness for each of them. En ter Conductivity and Heat Capacity values for each of insulating materials. 119

PAGE 120

Step 7: A soil layer is selected by default. Enter thickness (i.e., 5 m), Conductivity and Heat Capacity values for the soil layer in Box G. Step 8: Enter air convection coefficients for the top and side boundary surfaces. For instance, enter 30 for top and 20 for sides. Step 9: Click the Generate button. DIFG will call and run iDIANA to create the footing.dat file. Contents of this file type are given in Appendix B of Development of design parameters for mass concrete usi ng finite element analysis Final Report (Tia et al. 2010). Run DIANA and follo w the steps described in Section 8.3. Results and Post-Processing Commands in iDIANA Thermal Results To view thermal results fr om the thermal analysis, t he user should run iDIANA (iDIANA Release 9.4.4. 2012) and open the F LOW.V72 file (see Figure 9-10). The sketch of the model will appear as shown in Figure 9-11. The user then should interact with iDIANA by entering command lines. T he following are standard commands to postprocess the results (DIANA 2012c). View model: VIEW MESH ALL (to view all the meshes of model) VIEW MESH BLOCK (to view the concrete mesh) VIEW MESH SOIL (to view the soil mesh) VIEW MESH TOPINS (or BOTINS, SIDEINS: to view top, bottom, or side insulation mesh) VIEW MESH +BLOCK (to add (+) the co ncrete mesh to the current mesh) LABEL MESH NODES (iDIANA will label all the node names of current mesh) LABEL MESH ELEMENTS (iDIANA will label all the element names of current mesh) VIEW HIDDEN FILL (to provide a hidden su rface representation of the model) For instance, the following comm ands will generate Figure 9-12: VIEW MESH SOIL VIEW MESH +BLOCK 120

PAGE 121

To turn off the transparent view as shown in F igure 9-13, use: VIEW HIDDEN FILL To rotate the model to a position as illustrated in Figure 9-14, use: EYE ROTATE TO 30 45 45 (30, 45, and 45 are the rotation angles about the screen X Y Z axes, respectively) To see all the node names as shown in Figure 9-15, use: LABEL MESH NODES Display temperature graph: To plot a graph of temperatures vs. ti me of 3 nodes: 3850 (concrete center), 957 (concrete bottom center), and 1245 (concrete bottom corner) as shown in Figure 9-16, enter: RESULTS LOADCASE ALL (to choose all the time steps to be plotted (1-167)) RESULTS NODAL PTE....S PTE (to choose temperature to be plotted) PRESENT GRAPH NODE 3850 957 1245 (to plot the graph of 3 specific nodes) Display temperature contour (as shown in Figure 9-17): RESULTS NODAL PTE....S PTE (to choose temperature to be plotted) RESULTS LOADCASE TR1 100 (to set time step at 100 hour) PRESENT CONTOUR LEVELS (to plot temp erature contour of model (at 100 hour)) Stress Results To view stress results from the structural analysis, the user should open the STRUC.V72 file. Display First Principal Stress graph (as shown in Figure 9-18): VIEW MESH BLOCK VIEW HIDDEN FILL RESULTS LOADCASE ALL (to choose all the time steps to be plotted (1-167)) 121

PAGE 122

RESULTS ELEMENT EL.S1 S1 (to calc ulate First Principal Stresses) PRESENT GRAPH ELEMENT 4961 NODE 957 (to pl ot graph of node 57 of element ) Display First Principal Stress contour (as shown in Figure 9-19): RESULTS LOADCASE LC5 24 (to set time step = 24 hour, LC5 = gravity load) RESULTS ELEMENT EL.S1 S1 PRESENT CONTOUR LEVELS (to plot Firs t Principal Stress contour of model) Calculate crack index and display cont our levels (as shown in Figure 9-20): RESULTS LOADCASE LC5 167 (to set time step = 167 hour) RESULTS ELEMENT EL.ICR.S ICR PRESENT CONTOUR FROM .9 TO 1 LEVELS 8 (to display crack index contour of model with 8 levels from .9 to 1) 122

PAGE 123

Figure 9-1. Software for gener ating DIANA input files. Figure 9-2. Browsing a concrete property file. 123

PAGE 124

Figure 9-3. Generating process. Figure 9-4. Message indicating the process is completed. Figure 9-5. DIANA analysis setup. 124

PAGE 125

Figure 9-6. Selecting analysis type. Figure 9-7. Open command file. 125

PAGE 126

Figure 9-8. Input parameters for DIFG. Figure 9-9. Detailed contents of CONCRETE.dat file. 126

PAGE 127

Figure 9-10. Open FLOW.V 72 for thermal results. Figure 9-11. Sketch of model. 127

PAGE 128

Figure 9-12. Transparent mesh view of concrete and soil. Figure 9-13. Hidden-fill view of concrete and soil. 128

PAGE 129

Figure 9-14. Another view using eye-rotation of 30, 45 and 45 degrees. Figure 9-15. Labeling node names of current mesh. 129

PAGE 130

Figure 9-16. Temperature graph vs. time at Nodes 3850, 957, and 1245. Figure 9-17. Temperature contour in concrete and soil at 100th hour. 130

PAGE 131

Figure 9-18. First principal stress graph vs. time of node of element . 131

PAGE 132

Figure 9-19. Crack index contour of concrete at 167th hour. 132

PAGE 133

Figure 9-20. First principal stress contour of concrete at 24th hour. 133

PAGE 134

CHA PTER 10 CLOSURE Summary of Findings A finite element model using the commercially available TNO DIANA 9.4.4 software package was developed for the predi ction of temperatures and cracking potential of mass concrete footings placed on soil. To evaluate the effectiveness of the temperature predictions from the model, three different bridge pier footings in Florida were monitored for temperature developm ents. The measured temperatures were compared with the results obtained from the model. Isothermal calorimetry testing was done on the cementitious materials of the concrete mixtures to determine the energy released during hydration, which was then conv erted to temperature rise as inputs for the finite element model. Analysis of influences of thermal properties of soil on temperature development and cracking in mass concrete footings was conducted. A parametric study on the effect s of dimensions of rectangul ar footings on the maximum allowable temperature different ial to prevent cracking in concrete was conducted. A user-friendly computer program called DIANA Input File Generat or was developed to provide the needed input files to the TNO DI ANA software for modeling of typical mass concrete structures such as re ctangular footings and columns. The in situ condition of the soil upon whic h a concrete footing is directly placed affects the temperature development of the f ooting and determines whether or not an insulation layer would be needed to reduce t he temperature differential in the mass concrete and the likelihood for cracking. At the contact surface between the mass concrete footing and soil, dry soil had higher temperatures than we t or saturated soil. This was because wet soil allowed the heat of hydration generated from the concrete to 134

PAGE 135

transfer to a greater depth than dry soil did. In addition, dry sand and dry clay provided good insulation at the bottom of mass concrete footing as indicated from the crack indic es obtained from the ther mal cracking analysis performed. Soil with an R-value of 0.41 or greater (or thermal conductivity of 0.35 J/sec-m-C or lower) would provide adequate insulation at the bottom of concrete f ooting using Mix 1 with a V/A of 13 ft or less to prevent thermal cracking. Thus, an insulating layer between the mass concrete and the soil would not be needed in such situation. Rectangular footings that had the same V/A but different shapes (dimensional proportions) would develop a similar maxi mum temperature, a similar maximum temperature difference, and a similar crack index under the same insulation condition. With a V/A of less than 4.5 ft under the same insulation condition and using the same concrete mix, a larger footing had a higher maximum temperature difference, and lower crack index. However, with a V/A of 4.5 ft or gr eater, a larger footing had a similar or slightly smaller maximum temperature differ ence, and an almost constant crack index. Thus, cracking potential was not dependent on a footings dimensions when its V/A was 4.5 ft or greater. When Styr ofoam with an R-value of 5.0 per inch was used, 0.5 inch would provide adequate insulation for a footing with a V/A of around 1.0 ft; 1.0 inch would provide adequate insulation for a footing with a V/A less than 4.0 ft; 1.25 inches would provide adequate insulation for a footing with a V/A up to 13.0 ft. If another type of insulating material is used, an equivalent insulation thickness can be determined from the materials R-value. Conclusions and Recommendations Based on the findings from this study, the following conclusions are made: 135

PAGE 136

The developed finite element model predi cted temperatures reasonably well in mass concrete footings. Bottom insulation would not be needed when a mass concrete footing is placed on dry soil, or on soil with an R-value of 0.41 or greater. Mass concrete footing loses more heat when placed directly on saturated soil than on dry soil as heat generated from concrete transfers to a depth of 5.0 m in saturated soil compared to 1.0 m in dry soil. With a V/A of less than 4.0 ft, larger footings require a greater thickness of insulation, however, with a V/A of 4.0 ft or greater, larger footings only require a similar thickness of insulation to prevent cracking. Smaller footings do not require a sm aller maximum allowable temperature differential to prevent cracki ng by thermal contraction. When the concrete of Mix 1 is used, footings with a V/A fr om 1.1 ft to 1.6 ft require a maximum allowable temperature differential of 25.2C, footings with a V/A from 1.7 ft to 4.4 ft require a maximum allowable te mperature differential of 21.6C, and footings with a V/A from 4. 5 ft to 13.1 ft require a ma ximum allowable temperature differential of 20.1C. In order to facilitate the implementati on of the developed method for analysis of mass concrete footings in Florida, it is recommended that the results from the study should be applied and additional work should be performed. First, bottom insulation should be used in the following ca ses: there is water at the bottom of footing, footings with a V/A of 2.0 ft or less are placed on so il that has an R-value of less than 0.29 per in., and footings with a V/A of greater than 2.0 ft are placed on soil that has an R-value of less than 0.41 per in. Second, less insula tion should be used for smaller footings and should be determined using the required insulation thickness method presented in this study. Third, thermal properties of soil in different in situ conditions should be evaluated and monitoring of footings directly placed on soil is needed to evaluate the predicted results. Since the properties of the soil upon which a mass concrete footing is placed greatly influence the thermal behavior of the concrete foot ing, further investigation 136

PAGE 137

needs to be conducted to determine the R-val ues for different types of soil and under different in situ conditions. Finally a data ba se of rate of heat pr oduction of different cement blends should be developed. Isot hermal calorimetry testing should be performed on the cementitious materials us ed in typical FDOT mass concrete mix designs to build a data base of adiabatic temper ature rise tables that can be used in the DIANA software for the modelin g of mass concrete stru ctures. The concrete mix designs that are to be analyzed consist of Type I/II Portland cement, ground-granulated blast furnace slag, Class F fly Ash, ultrafine fly ash, and silica fume, in various combinations and proportions. 137

PAGE 138

APPENDIX A iDIANA INPUT COMMANDS OF A FU LLY INSULATED CONCRETE MODEL femgen Footing property fe-prog diana htstag_3d yes utility setup units length meter utility setup units mass kilogram utility setup units force newton utility setup units time second utility setup units temperature celsius geometry point coord P1 0 0 0 geometry point coord P2 4.000E+0000 0.000E+0000 0.000E+0000 geometry point coord P3 0.000E+0000 4.000E+0000 0.000E+0000 geometry point coord P4 4.000E+0000 4.000E+0000 0.000E+0000 geometry surface 4points p1 p2 p4 p3 construct set botInBot append all construct set xline append lines l1 l3 construct set yline append lines l2 l4 meshing division line xline 16 meshing division line yline 16 construct space tolerance off geometry sweep botInBot SoilB ot 408 translate 0 0 -5.000E+0000 construct set Soil append bodies b1 construct set SoilY1 append surfaces s5 construct set SoilX1 append surfaces s4 geometry sweep botInBot BlockBot 1 translate 0 0 3.175E-0002 construct set botIns append bodies b2 meshing types botIns he8 hx8ht 138

PAGE 139

geometry sweep BlockBot BlockTop 8 translate 0 0 2.000E+0000 construct set fBlock append bodies b3 meshing types all he8 hx8ht geometry copy fBlock Block translate 0 0 0 construct set xline2 append lines l29 l31 l33 l35 construct set yline2 append lines l30 l32 l34 l36 construct set zline2 appe nd lines l37 l38 l39 l40 meshing division line xline2 32 meshing division line yline2 32 meshing division line zline2 16 meshing types Block he20 chx60 construct set InsY1 append surfaces s10 construct set InsX1 append surfaces s9 construct set InsY1 append surfaces s15 construct set InsX1 append surfaces s14 geometry sweep SoilY1 SoilY2 1 translate 0 3.175E-0002 0 geometry sweep InsY1 InsY2 1 translate 0 3.175E-0002 0 construct set SoilX1 append surfaces s24 construct set InsX1 append surfaces s30 construct set InsX1 append surfaces s34 construct set Soil append bodies b5 construct set SideIns append bodies b6 construct set SideIns append bodies b7 geometry sweep SoilX1 SoilX2 1 translate 3.175E-0002 0 0 geometry sweep InsX1 InsX 2 1 translate 3.175E-0002 0 0 construct set Soil append bodies b8 b9 139

PAGE 140

construct set sideIns append bodies b10 b12 construct set sideIns append bodies b11 b13 construct set SoilY2 append surfaces s45 construct set InsY2 append surfaces s59 construct set InsY2 append surfaces s61 meshing types sideIns he8 hx8ht geometry sweep SoilY2 SoilY 408 translate 0 3.000E+0000 0 construct set SoilX2 append surfaces s70 geometry sweep SoilX2 SoilX 408 translate 3.000E+0000 0 0 construct set SoilY append surfaces s83 construct set Soil append bodies b14 b15 b16 b17 b18 construct set soilBot append surfaces s27 s42 s44 s67 s69 s77 s79 s82 meshing types Soil he8 hx8ht construct set soilTop append surfaces s65 s68 s75 s78 s81 geometry sweep BlockTop Top 1 translate 0 0 3.175E-0002 construct set topIns append bodies b19 meshing types topIns he8 hx8ht construct set sideSur append surfaces InsX2 InsY2 construct set topSur append surfaces Top geometry copy topSur topExt translate 0 0 0 meshing types topExt qu4 bq4ht geometry copy sideSur sideExt translate 0 0 0 meshing types sideExt qu4 bq4ht geometry copy soilTop soilExt translate 0 0 0 meshing types soilExt qu4 bq4ht construct set soilFix append surfaces SoilX SoilY SoilBot 140

PAGE 141

meshing generate meshing merge all 0.001 property material concrete exte rnal external "CONCRETE.dat" property material topBo flow boundary convecti 5.000E+0001 0 property material sideBo flow boundary convecti 2.000E+0001 0 property material soilBo flow boundary convecti 2.000E+0001 0 property material topMat fl ow isotrop 2.900E-0002 2.840E+0004 property material sideMat flow isotrop 2.900E-0002 2.840E+0004 property material botMat flow isotrop 2.900E-0002 2.840E+0004 property material SoilMat flow isotrop 2.700E-0001 1.212E+0006 property attach fBlock concrete property attach Block concrete property attach topExt topBo property attach sideExt sideBo property attach soilExt soilBo property attach topIns topMat property attach sideIns sideMat property attach botIns botMat property attach Soil SoilMat property loads exttemp 1 sideExt 2.600E+0001 property loads exttemp 2 topExt 2.600E+0001 property loads exttemp 3 soilExt 2.600E+0001 property loads fixtemp 4 soilFix 2.600E+0001 property loads grav ity 5 Block -9.81 3 construct tcurve tcdum list 0 1 601200 1 property attach loadcase 1 tcdum property attach loadcase 2 tcdum 141

PAGE 142

142 property attach loadcase 3 tcdum property attach loadcase 4 tcdum property attach loadcase 5 tcdum property boundary constraint s17 z property boundary constraint s22 x property boundary constraint s19 y property initial initemp all 2.550E+0001 eye frame utility write diana Footing yes

PAGE 143

APPENDIX B CONTENT S OF CONCRETE PROPERTY FILE CONCRETE.DAT CONDUC 2.2 CAPACI 2.675596E+06 ADIAB 0 23 3600 25.42679371 7200 25.71257944 10800 26.04072774 14400 26.51625577 18000 27.23067965 21600 28.23307206 25200 29.52351384 28800 31.07516457 32400 32.82326773 36000 34.68964656 39600 36.59175871 43200 38.46492849 46800 40.26881443 50400 41.99678727 54000 43.66679452 57600 45.25854419 61200 46.75441214 64800 48.18317906 68400 49.50046125 72000 50.7506424 75600 51.93388422 79200 53.00556046 82800 54.01021652 86400 54.94785239 90000 55.77392269 93600 56.53297279 143

PAGE 144

97200 57.20277045 100800 57.82786103 104400 58.38601226 108000 58.89945643 111600 59.39066832 115200 59.83717314 118800 60.26136484 122400 60.66316259 126000 61.04272807 129600 61.42229354 133200 61.75715195 136800 62.09201035 140400 62.4269496 144000 62.73949489 147600 63.02972707 151200 63.31995924 154800 63.61019142 158400 63.87811048 162000 64.14594869 165600 64.41386775 169200 64.6594737 172800 64.90507965 176400 65.15060475 180000 65.37389758 183600 65.61950353 187200 65.84271552 190800 66.06600835 194400 66.26690722 198000 66.49020005 201600 66.69109893 205200 66.8919978 144

PAGE 145

208800 67.09297752 212400 67.29387639 216000 67.47246215 219600 67.67344187 223200 67.85202763 226800 68.03061339 230400 68.20919915 234000 68.38786575 237600 68.56645151 241200 68.72272415 244800 68.90130991 248400 69.05758256 252000 69.23616832 255600 69.39252181 259200 69.54879445 262800 69.7050671 266400 69.86133974 270000 70.01761239 273600 70.17388503 277200 70.33015767 280800 70.46411721 284400 70.62038985 288000 70.77666249 291600 70.91062203 295200 71.04458156 298800 71.2008542 302400 71.33481373 306000 71.46877326 309600 71.60273279 313200 71.73669232 316800 71.87065185 145

PAGE 146

320400 72.00461138 324000 72.13849007 327600 72.2724496 331200 72.40640913 334800 72.51805555 338400 72.65201508 342000 72.78597461 345600 72.89762102 349200 73.00918659 352800 73.14314612 356400 73.25479254 360000 73.38875207 363600 73.50039849 367200 73.6120449 370800 73.72361048 374400 73.83525689 378000 73.94690331 381600 74.05854972 385200 74.1701153 388800 74.28176171 392400 74.39340813 396000 74.50505454 399600 74.61670096 403200 74.72826653 406800 74.83991295 410400 74.92924625 414000 75.04081182 417600 75.15245824 421200 75.24179154 424800 75.35343796 428400 75.44269041 146

PAGE 147

432000 75.55433683 435600 75.64367013 439200 75.7552357 442800 75.844569 446400 75.93390231 450000 76.02315476 453600 76.13480118 457200 76.22413448 460800 76.31338694 464400 76.40272024 468000 76.4919727 471600 76.581306 475200 76.6706393 478800 76.78220487 482400 76.87153817 486000 76.96087148 489600 77.05012393 493200 77.13945724 496800 77.22879054 500400 77.31804299 504000 77.38506318 507600 77.47431564 511200 77.56364894 514800 77.6529014 518400 77.7422347 522000 77.80925489 525600 77.89850734 529200 77.98784065 532800 78.05477999 536400 78.14411329 540000 78.23336575 147

PAGE 148

148 543600 78.30038594 547200 78.38971924 550800 78.45665858 554400 78.54599188 558000 78.63524434 561600 78.70226453 565200 78.79151698 568800 78.85853717 572400 78.94778963 576000 79.01480982 579600 79.08174916 583200 79.17108246 586800 79.2380218 590400 79.32735511 594000 79.39429445 597600 79.46131464 601200 79.55064794 ARRHEN 4117.75 EQUAGE ARRTYP TEMREF 23.0 YOUNG 2.523500E+10 POISON 2.000000E-01 DENSIT 2.2480000E+03 THERMX 9.160000E-06 FTTIME 0. 86400 172800 259200. 601200. FTVALU 0. 1.25E+6 1.66E+6 1.93E+6 2.206E+6 MAXWEL 1 ,1 TIME 0. 86400. 172800. 259200. 601200. YOUNG 13445.E+6 13445.E+6 16892.E+6 18064.E+6 20202.E+6

PAGE 149

LIST OF REFERENCES Ali, W. and Urgessa, G. (2012). N umerical prediction model for temperature distributions in concrete at early ages. American Journal of Engineering and Applied Sciences, 5(4), 282-290. American Concrete Institute (ACI) Committee 207, 207.1R-05. (2005). Guide to mass concrete, Farmington Hills, MI. American Concrete Institute (ACI) Committee 207, 207.2R-07. (2007). Report on thermal and volume change effects on cracking of mass concrete, Farmington Hills, MI. Ayotte, E., Massicotte, B., Houde, J., and Go cevski, V. (1997). Modeling of thermal stresses at early ages in a concrete monolith. ACI Mater. J., 94(6), 577. De Schutter, G. (2002). Finite element si mulation of thermal cracking in massive hardening concrete elements using degree of hydration based material laws. Comput. Struct., 80(27), 2035. DIANA: Displacement Analyzer Versi on 9.4.4. (2012a). [Computer software]. TNO DIANA BV, Delft, Netherlands. DIANA. (2012b). Finite Element Analysis User's Manual Material Library Release 9.4.4. TNO DIANA BV, Delft, Netherlands. DIANA. (2012c). Finite Element Analysis User's Manual Preand Postprocessing Release 9.4.4. TNO DIANA BV, Delft, Netherlands. Evju, C. (2003). Initial hydration of cem entitious systems using a simple isothermal calorimeter and dynamic correction. J. Therm. Anal. Calorim., 71(3), 829. Faria, R., Azenha, M., and Figueiras, J. ( 2006). Modeling of concrete at early ages: Application to an externally restrained slab. Cem. Concr. Compos., 28(6), 572 585. Ferraro, C. C. (2009). Determi nation of test methods for the prediction of the behavior of mass concrete. Ph.D. dissertati on, Univ. of FL, Gainesville, FL. Florida Department of Transportation. (2007). Standard specificat ions for road and bridge construction. Florida Department of Trans portation (FDOT), Tallahassee, FL. Florida Department of Transportation. (2009). FDOT Structures Manual, Florida Department of Transportation, Tallahassee, FL. Florida Department of Transportation. (2010). Standard specificat ions for road and bridge construction. Florida Department of Transportation, Tallahassee, FL. 149

PAGE 150

150 Florida Department of Transportation. (2013). Structures Design Guidelines: FDOT Structures Manual Volume 1, Florida Department of Transportation, Tallahassee, FL. iDIANA Release 9.4.4. ( 2012). [Computer software]. TNO DIANA BV, Delft, Netherlands. Kim, J. K., Kim, K. H., Y ang, J. K. (2001). Thermal ana lysis of hydration heat in concrete structures with pipe-cooling system. Computers & Structures, 79(2), 163-171. Lawrence, A. M. (2009). A Finite Element Model for the Prediction of Thermal Stresses in Mass Concrete. Ph.D. dissertati on, Univ. of FL, Gainesville, FL. Lawrence, A. M., Tia, M., Ferraro, C., and Bergin, M. (2 012). Effect of Early Age Strength on Cracking in Mass Concrete Containing Different Supplementary Cementitious Materials: Experimental and Finite-Element Investigation. Journal of Materials in Civil Engineering, 24(4), 362. Machida, N., and Uehara, K. (1987). Nonlinear Thermal Stre ss Analysis of a Massive Concrete Structure. Comput. Struct., 26, 287-296. Mehta, P.K., and Montei ro, P. J. M. (2006). Concrete Microstructure, Properties and Materials. 3rd Edition. McGraw-Hill. Mills, A.F. (1995). Heat and Mass Transfer. Richard D. Irwin, Concord, MA. Radovanovic, S. (1998). Thermal and structural finite element analysis of early age mass concrete structures. Masters thesis, Univ. of Manitoba, Winnipeg, Manitoba, Canada. Tanabe, T., Kawasumi, M., and Yamashita, Y. (1986). Thermal Stress Analysis of Massive Concrete, Seminar Proceeding s For Finite Element Analysis of Reinforced Concrete Structures, Tokyo Japan, May 21-24, 1985, ASCE, New York, NY. Thomas, L.C. (1980). Fundamentals of Heat Transfer. Prentice-Hall. NJ. Tia, M., Lawrence, A., Ferraro, C., Smith, S., Ochiai, E. (2010). Development of design parameters for mass concrete using fini te element analysis. Final Report, Dept. of Civil and Coastal Engineering, Univ. of FL, Gainesville, FL.

PAGE 151

BIOGRAPHICAL SKETCH The author began his undergradu ate education in 1997 at the University of Transport and Communications (UCT) in Hanoi, Vietnam. He recei ved a Bachelor of Science degree and a Master of Science deg ree in civil engineering in May 2002 and May 2006, respectively. He worked at the D epartment of Civil Engineering, UCT from 2002 to 2008, before he enrolled at the University of Flori da to pursue a Doctor of Philosophy degree in civil engineering in Au gust 2008. He received his Ph.D. from the University of Florida in the summer of 2013. 151