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2e514f1252e3e0ca456f317848d80ab99759e521 40937 F20101118_AAAFQT liu_y_Page_151.pro dbea3b84013e1559dfe060294cde27e9 9f497ac42e7210f946887d17e92ab468b17bc7db 80408 F20101118_AAAEOF liu_y_Page_058.jpg 9f12965bbfff3b3fbef2a7824ba9ac55 f44bce5d6a6855f650be2f55254456031309de69 54019 F20101118_AAAENR liu_y_Page_044.jpg fb9f34654f7ac212fdd05e5ff1267cbe f3ccbf8b3c0acd7816b81a4e511f63fe87ad77de STRENGTH, MODULUS OF ELASTICITY, SHRINKAGE AND CREEP OF CONCRETE By YANJUN LIU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 2007 Yanjun Liu To my Mom and Dad, Ren Shuzhen and Liu Yuchun, for everything they have done and are doing for their child, my daughter for her understanding and consideration for 6yearlong life without dad's company, and my brother and sisters for their great support and encouragement. ACKNOWLEDGMENTS It is my immense pleasure in thanking the persons and organizations that helped me over years to bring my PhD dissertation to the final form. Firstly, great appreciation goes to the chairman, Dr. Mang Tia, and cochairman, Dr. Reynaldo Roque for sincere encouragement and patient guidance. You are the beacons guiding me throughout my tough trek of pursuing PhD. Without your help, this dissertation can not be completed. Please let me regard you as loyal friends and great mentors. Secondly, great appreciation goes to the members of my supervisory committee, Dr. N.D. Cristescu and Dr. Larry.C.Muszynski, for your great enlightenment and keen research assistance. Thirdly, graceful acknowledgement extends to Florida Department of Transportation (FDOT) for providing the financial support, testing equipment, materials that made this research possible. The Florida Department of Transportation personnel Messrs. Michael Bergin, Richard Delorenzo, Joseph Fitzgerald, and Craig Roberts are appreciated for their help with the entire process of fabricating test samples. Fourthly, I like to thank all my colleagues in the materials section of Civil & Coastal Engineering Department. Danny Brown, Chuck Broward, Nard Hubert and George A. Lopp are acknowledged for their assistance in this study. In addition, special thanks are given to the Florida Rock Industries Company for donating slag, Boral Materials Company for donating fly ash, and W. R. Grace & Co for donating chemical admixtures, and Carolina Stalite Company for donating lightweight aggregate. Without your sincere help, this study could not be completed on time. At last, my sincere thanks go to my parents for their persistent encouragement and unconditional love, which motivated me to complete my study. I believe the fulfillment of my study will bring you joy, which is the only thing you need from your child. TABLE OF CONTENTS page A CK N O W LED G M EN TS ................................................................. ........... ............. 5 L IS T O F T A B L E S .........................................................................................10 LIST OF FIGURES .................................. .. .. .... .... .......... ....... 12 A B S T R A C T ............ ................... ............................................................ 17 CHAPTER 1 INTRODUCTION ............... ................. ........... .............................. 19 1.1 Background and Research Needs .................................. .....................................19 1.2 H y p oth esis ................................................................2 1 1.3 Objectives of Study.................. ...................................21 2 L ITE R A TU R E R E V IE W ........................................................................ ... ......................23 2 .1 Introdu action ............................................................................................2 3 2.2 Strength of C concrete ................. .... ................ .................... .... .. ........ ............ 23 2.2.1 Significance of Studying Strength of Concrete.....................................................23 2.2.2 Effect of Coarse Aggregate on Strength of Concrete...........................................24 2.2.3 Prediction of Strength of Concrete ................................ ................................. 26 2.3 Elastic M odulus of C concrete ...................................... .. ......................... ...............27 2.3.1 Definition and Determination of Elastic Modulus of Concrete..............................27 2.3.2 Significance of Studying Elastic Modulus of Concrete ......................................28 2.3.3 Effect of Coarse Aggregate on Elastic Modulus of Concrete .............................29 2.3.4 Models for Predicting Elastic Modulus of Concrete ...........................................32 2.4 Shrinkage Behavior of Concrete ...................................................................... 35 2.4.1 Origin of Shrinkage of Concrete ....................................... ......................... 35 2.4.2 Significance of Studying Shrinkage of Concrete ................................................36 2.4.3 Effect of Raw Materials on Shrinkage of Concrete...............................................37 2.4.3.1 Effect of aggregate content on shrinkage behavior of concrete .................37 2.4.3.2 Effects of coarse aggregate type on concrete shrinkage.............................39 2.4.3.3 Effects of size and shape of coarse aggregate on concrete shrinkage ..........40 2.4.3.4 Effect of other factors on shrinkage behaviors of concrete........................41 2.4.4 M odels to Predict Concrete Shrinkage...................................... ..................42 2.4.4.1 CEBFIP Model for shrinkage strain prediction ............................. 43 2.4.4.2 Prediction model recommended by ACI209 Report [1992] .....................45 2.5 Creep of Concrete ................. .. ...... ...... .......... ...... ............. ..........46 2.5.1 Rheology of Materials and Definition of Creep of Concrete .............................46 2.5.2 Significance of Studying Creep Behavior of Concrete .......................................48 2.5.3 Effect of Aggregate on Creep of Hardened Concrete ................. ... ............ 49 2.5.4 Prediction Models and Their Limitations of Concrete Creep .............................51 2.5.4.1 C .E .B F.I.P M odel C ode ........................................ ......................... 53 2.5.4.2 M odel of A CI 209 ...... ................................... ......... ...............55 3 MATERIALS AND EXPERIMENTAL PROGRAMS ............... ............................... 58 3 .1 In tro d u ctio n ................................................................................................................. 5 8 3.2 C concrete M fixtures E evaluated ........................................ .............................................58 3.2.1 M ix Proportion of Concrete...................................................... ................... 58 3.2.2 M ix Ingredients .......................................... ............. .... ....... 59 3.3 Fabrication of C concrete Specim ens...................................................................... .. .... 60 3.3.1 The Procedure to M ix Concrete ........................................ ........................ 60 3.3.2 The Procedure to Fabricate Specim ens ...................................... ............... 66 3.4 Curing Conditions for Concrete Specim ens ........................................ .....................66 3 .5 T ests on F resh C oncrete.......................................................................... ....................67 3.6 Tests on Hardened Concrete ....................................................................... 69 3.6.1 C om pressive Strength Test................. .. ....................... ............... ... 69 3.6.2 Splitting Tensile Strength Test (or Brazilian Test)......................................... 70 3.6.3 Elastic M odulus Test ........................... .................................... ............... 72 3.6.4 Shrinkage Test ......... ......... ...... .................. .. ..... ...... .. ............ 73 4 CREEP TEST APPARATUS DESIGN AND TESTING PROCEDURE .............................76 4 .1 In tro d u ctio n ................................................................................................................. 7 6 4.2 Creep Test Apparatus ....................................... ........ .......... .. ...... .... 76 4.2.1 Design Requirements of Creep Test Apparatus ............................................. 76 4.2.2 D esign of Creep A pparatus .................................................... .......................... 77 4.2.2.1 The determination of the maximum capacity of the creep Apparatus .........77 4.2.2.2 The design of springs ............................................................................77 4.2.2.3 Design of header plate ...... .......................... ..........79 4.2.2.4 Determination of the size of steel rod .............. ..................... ................81 4.2.2.5 Stress relaxation due to the deflection of header plate and creep of co n create .................. ...................................... ............................. 8 1 4.3 Design of GagePoint Positioning Guide ........................................ ...... ............... 82 4.4 D design of A lignm ent Fram e ........................................................... ............. ..82 4 .5 M echanical Strain G auge......................................................................... ...................85 4.6 O their D details on C reep A pparatus........................................................................ ...... 85 4 .7 C reep T testing P rocedure............................... ............................................ .................. 86 4.8 Summary on the Performance of the Creep Apparatus ..............................................93 5 ANALYSIS OF STRENGTH TEST RESULTS....................... ...... ...............95 5 .1 Introdu action ....................... ...... ............................................ ................. 9 5 5.2 Results and Analysis of Compressive Strength Tests.......................... ...............95 5.2.1 Effects of Water to Cement Ratio and Water Content on Compressive Strength ....................................... ........... ..... .. ..................... ............ 95 5.2.2 Effects of Aggregate Types on Compressive Strength .........................................98 5.2.3 Effects of Fly Ash and Slag on Compressive Strength of Concrete.....................102 5.2.4 Prediction of Compressive Strength Development ................... ............... 103 5.3 Analysis of Splitting Tensile Strength Test Results ........................................ ............105 5.3.1 Effects of Water to Cement Ratio on Splitting Tensile Strength .........................105 5.3.2 Effects of Coarse Aggregate Type on Splitting Tensile Strength ......................105 5.3.3 Effects of Fly Ash and Slag on Splitting Tensile Strength of Concrete.............13 5.4 Relationship between Compressive Strength and Splitting Tensile Strength ..............114 5.5 Analysis of Elastic M odulus Test Results ................................. ..... ............... 117 5.6 Relationship between Compressive Strength and Elastic Modulus .............................120 5.7 Sum m ary of F findings ........................................................................... ....................122 6 ANALYSIS OF SHRINKAGE TEST RESULTS .................................... ............... 127 6 .1 In tro d u ctio n ................................ ............................................................................... 12 7 6.2 Results and Analysis of Shrinkage Tests.............. ........ ... .. ...............127 6.2.1 Effects of Curing Conditions on Shrinkage Behavior of Concrete .......... ......127 6.2.2 Effects of Mineral Additives on Shrinkage Behavior ............... ...................129 6.2.3 Effects of Water Content on Shrinkage Behavior .................... ... .............130 6.2.4 Effects of Aggregate Types on Shrinkage Behavior................... ...................131 6.2.5 Relationship between Compressive Strength and Shrinkage Strain...................133 6.2.6 Relationship between Elastic Modulus and Shrinkage Strain.............................135 6.3 Evaluation on Shrinkage Prediction M models ...................................... ............... 137 6.3.1 ACI209 m odel ............. .. ........ ... ... ................. ..... ......... 137 6.3.2 CEB FIP M odel ......... .. .......................... ........ ..... .... .......... ............ 138 6.4 Prediction of Ultimate Shrinkage Strain................................... ...............140 6.4.1 Least Square Method of Curvefitting...... ................. ............141 6.4.2 Evaluation Methods on the Goodness of Fit ............. ...... ...............142 6.4.3 Predicted R results ........ ...... .............................. ...... .. ........ .... 145 6.5 Sum m ary of F findings ........................................................................... ....................146 7 ANALYSIS OF CREEP TEST RESULTS ........................................ ...................... 148 7.1 Introduction ........... ....................... ......... .......................148 7.2 Analysis of Creep Test Results.................................................................. ............... 148 7.2.1 Effects of Curing Conditions on Creep Behavior of Concrete..........................148 7.2.2 Effects of Loading Condition on Creep Behavior of Concrete............................ 151 7.2.3 Effects of Aggregate Types on Creep Behavior of Concrete .............................153 7.2.5 Effects of Water to Cement Ratio and Air Content on Creep Strain..................156 7.2.6 Relationship between Compressive Strength and Creep Strain .........................157 7.3 Creep Coefficient............................. ...... .......... ...... ...... .......... 163 7.3.1 Effects of Loading Conditions on Creep Coefficient ................ ................163 7.3.2 Effects of Curing Conditions on Creep Coefficient ............................................163 7.3.3 Effects of Water Content on Creep Coefficient .................................. ..............165 7.3.4 Effects of Compressive Strength at Loading Age on Creep Coefficient............166 7.3.5 Relationship between Elastic Modulus at Loading Age and Creep Coefficient..169 7.3.6 Effects of Coarse Aggregate Type on Creep Coefficient................................171 7.4 C reep M odulu s......................................................... ...................................... .... 172 7.5 Prediction of U ltim ate Creep Strain ........................................ .......................... 174 7.6 Evaluation on Creep Prediction M odels................................ ................................. 175 7.7 Sum m ary of F findings ........................................................................... ....................186 8 CONCLUSIONS AND RECOMMENDATIONS .................................... ............... 188 8.1 D design of C reep A pparatu s............................................................................................. 188 8.2 F findings from T his Study ............................................................... .......................188 8.2.1 Strength and Elastic M odulus............... .. ...................... ............... ....188 8.2.2 Shrinkage Characteristics of Concretes Investigated ........................................190 8.2.3 Creep Characteristics of Concretes Investigated...............................................191 8.3 R ecom m endations...... .......... .................................... .. ............ .. ........... 192 APPENDIX A MEASUREMENTS FROM STRENGTH TESTS................................... .....................193 B MEASURED AND CALCULATED RESULTS FROM CREEP TESTS .......................... 199 L IST O F R E F E R E N C E S .................................................................................. .....................2 12 B IO G R A PH IC A L SK E T C H ............................................................................. ....................2 18 LIST OF TABLES Table page 31 Mix proportions of the 14 concrete mixtures involved in this study .............................61 32 Physical properties of Type I cem ent....................................................... .............. 62 33 Chem ical ingredients of Type I cem ent...................................... .................. ......... 62 34 Physical and chemical properties of fly ash.......................... .............................. 62 35 Physical and chem ical properties of slag................................................ ........ ....... 62 36 Physical properties of fine aggregate........................................................... ............... 62 37 Physical properties of coarse aggregates ........................................ ....................... 62 38 The testing programs on fresh concrete.............................. ............................... 67 39 P properties of fresh concrete ...................................................................... ................ .....68 310 The testing program on hardened concrete.......................... ............................... 69 51 Compressive strength of the concrete mixtures evaluated.........................................95 52 Comparison of the accuracy between ACI equation and Modified ACI Equation.......... 106 53 Regression analysis on the prediction of compressive strength of concrete....................107 54 Values of the constants,a, 3 and c/l and the time ratio ....... ...................................108 55 Splitting tensile strengths of the concrete mixtures evaluated .............. ... ...............109 56 Regression analysis for relating compressive strength to splitting tensile strength......... 115 57 Elastic module of the concrete mixtures evaluated..................................... ................. 117 58 Regression analysis using the expression recommended by ACI 31889 .......................123 59 Regression analysis on ACI 31895 equation with forcing it through origin point.........123 510 Regression analysis using the expression recommended by ACI 31895 .....................125 61 Shrinkage strains of the concrete mixtures evaluated at various curing ages ................128 62 Regression analysis on relationship of compressive strength to shrinkage strain ..........135 63 Regression analysis on relationship of elastic modulus to shrinkage strain.................... 136 64 Correction factors for the ACI 209 model on shrinkage prediction .............................138 65 R egression analy sis results ...................................................................... ..................146 71 Regression analysis on relationship between compressive strength and creep strain .....160 72 Regression analysis on relationship of compressive strength to creep coefficient ..........167 73 Regression analysis on relationship of elastic modulus to creep coefficient...................171 74 Regression analysis on relation of creep coefficient to fE/E ................... ............... 171 75 The predicted ultimate creep strain and creep coefficient ........................................175 76 Regression analysis on relation of creep coefficient to fE/E ................... ............... 182 77 Correction factors for the ACI 209 model ............................................ ............... 185 A1 Results of compressive strength tests ....... ...............................................................194 A2 Normalized compressive strength development characteristics of the concrete m fixtures evaluated .......................................... ............................. ....195 A 3 Results of splitting tensile strength tests................................................... ......... ...... 196 A4 Normalized Splitting tensile strength development characteristics of the concrete m fixtures evaluated .......................................... ................... .. ...... .... 197 A5 Results of elastic m odulus tests ......................................................................... 198 Bl M measured and calculated results from creep tests ....................................... .................200 LIST OF FIGURES Figure page 21 Representation of the stressstrain relation for concrete...................... ..................27 22 Stressstrain relations for cement paste, aggregate and concrete.................. ............29 23 Effect of coarse aggregate content on the shrinkage of concrete.................. ............37 24 Creep diagram of concrete m material ....................................................... ............... 47 25 Straintime plot of concrete under a sustained load and after release of load ...................48 31 Gradation of fine aggregate (Godenhead sand) ................. ............................63 32 Gradation of coarse aggregate (Miami Oolite limestone)..........................................63 33 Gradation of coarse aggregate (Georgia granite)........................................64 34 Gradation of lightweight aggregate (Stalite)................................................................... 64 35 C om pulsive P an M ixer ............................................................................ ....................65 36 Typical failure model of concrete cylinder in compression test................... ..............70 37 Loading configuration for splitting tensile test...... ....................... ............71 38 MTS system for elastic modulus and compressive strength test .......................................73 39 Cylindrical specimen with gage point installed...... ....................... ...........74 41 Creep test apparatus ........... .. .................................... ....................... 78 42 Boundary conditions used for finite element analysis...................................................79 43 M esh plot of H leader plate analysis.......... ................. ........................ ............... 80 44 Contour plot of deflection of header plate............................... ...................80 45 Design of Gagepoint positioning guide.................................................. ............... 83 46 Gauge position guide ............................................ ........................ 84 47 Plastic cylindrical mold inside gauge position guide............................................. 84 48 Schematic of Alignment Frame Design............... ........... .......................87 49 M mechanical gauge ..................................... .. ... ... .. .................. 88 410 Positioning springs on the bottom plate....................................... .......................... 88 412 Concrete cylinder with both end surfaces ground.................................. ............... 89 413 How to center the specimens into creep frame ...................................... ............... 90 414 How to center the hydraulic jack cylinder............................ ...... .................91 415 Leveling the plate on the top of load cell.......................... ..................... ............ 91 51 Effect of water to cementitious materials ratio on compressive strength at 28 days.........96 52 Effect of water to cementitious materials on compressive strength at 91 days .................97 53 Effect of water content on compressive strength at 28 days ................ ......... ..........97 54 Effect of water content on compressive strength at 91 days..............................................98 55 Effect of coarse aggregate type on compressive strengths of Mix2F and Mix2GF......100 56 Effect of coarse aggregate type on compressive strength of Mix3F and Mix3GF .......100 57 Effect of coarse aggregate type on compressive strength of Mix5S and Mix5GS .......101 58 Effect of coarse aggregate type on compressive strength of Mix7S and Mix7GS .......101 59 Effect of fly ash and slag on compressive strength of concrete ............... ...............102 510 Effect of water to cement ratio on splitting tensile strength at 28 days........................... 109 511 Effect of water to cement ratio on splitting tensile strength at 91 days ...........................110 512 Effect of aggregate type on splitting tensile strength of Mix2F and Mix2GF ..............111 513 Effect of aggregate type on splitting tensile strength of Mix3F and Mix3GF ..............111 514 Effect of aggregate type on splitting tensile strength of Mix5S and Mix5GS ..............112 515 Effect of aggregate type on splitting tensile strength of Mix7S and Mix7GS ..............112 516 Effect of fly ash and slag on splitting tensile strength of concrete ..................................114 517 Relationship between compressive strength and splitting tensile strength ......................116 518 Effect of coarse aggregate type on modulus of elasticity of Mix2F and Mix2GF........ 118 519 Effect of coarse aggregate type on modulus of elasticity of Mix3F and Mix3GF........119 520 Effect of coarse aggregate type on modulus of elasticity of Mix5S and Mix5GS........ 119 521 Effect of coarse aggregate type on modulus of elasticity of Mix7S and Mix7GS........120 522 Relationship between compressive strength and elastic modulus based on ACI Code...124 523 Plot of elastic modulus against w 1f' for all curing conditions............... .................124 61 Effect of curing condition on shrinkage strain of concrete mixtures at 91 days............130 62 Effect of water content on shrinkage strain at 91 days............. ....................................131 63 Effect of water to cementitious materials ratio on shrinkage strain at 91 days .............132 64 Effect of coarse aggregate type on shrinkage behavior of concrete .............................133 65 Relationship between compressive strength and shrinkage strain at 91 days................135 66 Relationship between shrinkage strain at 91 days and modulus of elasticity ................36 67 Comparison between the shrinkage strain at 91 days and the shrinkage strain calculated by ACI 209 model and C.E.BF.I.P model...............................................140 68 Comparison among the ultimate shrinkage strains from curvefitting, CEBFIP m odel and A C I 209 m odel ......................................................................... ................ 14 5 71 Effect of curing condition on creep of concrete loaded at 40% of compressive strength ................... ......................................................................... 150 72 Effect of curing condition on creep of concrete loaded at 50% of compressive strength ................... ......................................................................... 150 73 Effect of stress level on creep of concrete moistcured for 7 days...............................152 74 Effect of stress level on creep of concrete moistcured for 14 days..............................153 75 Effect of aggregate type on creep behavior of Mix2F....... ......................................154 76 Effect of aggregate type on creep behavior of Mix3F ..............................................155 77 Effect of aggregate type on creep behavior of Mix5S ............. .... ...............155 78 Effect of aggregate type on creep behavior of Mix7S............. .... ...............156 79 Effect of water to cementitious materials ratio and air content on creep of concrete moistcured for 7 days and loaded at 40% of compressive strength..............................158 710 Effect of water to cementitious materials ratio and air content on creep of concrete moistcured for 7 days and loaded at 50% of compressive strength..............................159 711 Effect of water to cementitious materials ratio and air content on creep of concrete moistcured for 14 days and loaded at 40% of compressive strength..............................159 712 Effect of water to cementitious materials ratio and air content on creep of concrete moistcured for 14 days and loaded at 50% of compressive strength ..............................160 713 Relationship between compressive strength and creep strain of concrete moistcured fo r 7 d ay s ...................................................................................... 16 1 714 Relationship between compressive strength and creep strain of concrete moistcured fo r 14 d ay s .................................................................................... 16 1 715 Relationship between compressive strength and creep strain of concrete under all cu ring con edition s............................. ...................................................... ............... 162 716 Relationship of compressive strength to instantaneous strain measured in creep test.....162 717 Effect of stress level on creep coefficient of concrete moistcured for 7 days..............164 718 Effect of stress level on creep coefficient of concrete moistcured for 14 days............164 719 Effect of curing condition on creep coefficient of concrete .................................. 165 720 Effect of water content on creep coefficient at 91 days............................166 721 Relationship between compressive strength and creep coefficient for specimens loaded at 14 day s ........................................................................ 16 8 722 Relationship between compressive strength and creep coefficient for specimens loaded at 2 8 day s ........................................................................ 169 723 Relationship between compressive strength at loading age and corresponding creep coefficient at 91 days ................................ .... .......................... 169 724 Effect of Elastic modulus at loading age on creep coefficient at 91 days .................... 170 725 Relationship between creep coefficient at 91 days and fo/E ....................... ...............171 726 Effect of coarse aggregate type on creep coefficient at 91 days................................... 172 727 Typical decay curve of creep modulus with time .......................................................173 728 B ehaviors of a B urgers M odel ............................................................................ ... 176 729 Evaluation on creep prediction m odels....................................... ......................... 178 730 Comparison on the effectiveness of C.E.BF.I.P model and ACI model ......................180 731 Comparison between the creep strain at 91 days from experimental data and the predicted creep strain using CEBFIP model..................................... ......... ............... 181 732 Relationship between creep strain and mechanical properties at loading age...............82 733 Comparison between the ultimate creep strain calculated by C.E.BF.I.P model and that by curvefitting ....... .......................................................................... ...... ... .... 183 734 Evaluation on ACI209 model and C.E.BF.I.P model ......................................... 185 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STRENGTH, MODULUS OF ELASTICITY, SHRINKAGE AND CREEP OF CONCRETE By Yanjun Liu December 2007 Chair: Mang Tia Cochair: Renaldo Roque Major: Civil Engineering In the application of prestressed concrete, there are concerns on severe prestress loss caused mainly by elastic shortening, shrinkage and creep of concrete, which will result in the extreme reduction of the design capacity of prestressed concrete structure, or even the premature structure failure. Hence, the values of elastic modulus, ultimate shrinkage strain, and ultimate creep coefficient of concrete have to be estimated reasonably and accurately at the production stage in order to avoid loss of structural capacity, or even unexpected structural failure caused by prestress loss. At present, the modulus of elasticity, shrinkage and creep properties of concrete that are used in structural design are either based on the arbitrary available literature or based on the limited research of the locally available materials. Thus, there is a great need for a comprehensive testing and evaluation of locally available concrete mixes to determine their mechanical and physical properties so that correct values for these properties can be used in structural design. Also, there is a great need to design a simple, effective, practical and reliable creep apparatus to carry this massive investigation on creep behavior of concrete out. In this study, a creep test apparatus was designed, and twenty four creep apparatus were constructed for use in performing creep tests. The creep apparatus was evaluated to be working satisfactorily. An effective creep testing procedure was developed and documented. Also, a gauge point position guide was designed for installing gauge point on the cylindrical mold and it was proved to be an effective tool in preparation of specimens for creep tests. In addition, an alignment frame was designed and it was proved to be a very useful tool to ensure that the specimens can be set up in the creep apparatus vertically. In this study, 14 concrete mixtures were evaluated, and replicate batches for ten of these mixes were also produced and evaluated. Three types of coarse aggregate, fly ash and ground blastfurnace slag were incorporated in the mix designs in this study. Concrete specimens were fabricated and tested for their compressive strength, splitting tensile strength, elastic modulus, shrinkage and creep. This study has generated valuable data and determined general trends on the compressive strength, splitting tensile strength, elastic modulus, drying shrinkage strains and creep coefficient of structural concretes investigated in this study. Most importantly, the inter relationships among compressive strength, elastic modulus and shrinkage and creep properties of concrete were found through regression analysis. These relationships make the predictions of shrinkage and creep possible with the information from compressive strength and elastic modulus. CHAPTER 1 INTRODUCTION 1.1 Background and Research Needs Prestressed concrete structures, such as prestressed girder for longspan bridge, prestressed shell concrete structure for the storage of water or gas, nuclear reactor vessels and offshore oil drilling platforms so on, are widely used in the U.S as well as other countries in the world. This is attributed mainly to the advantages of prestressed concrete structure, which include) eliminating or considerably reducing the net tensile stresses caused by load, 2) increasing the capacity of the structure, and 3) decreasing the selfweight of concrete members. Also, prestressed concrete element is slimmer than reinforced concrete and more pleasing aesthetically. In the application of prestressed concrete, there are concerns on severe prestress loss caused mainly by elastic shortening, shrinkage and creep of concrete. Consequently, the design capacity of prestressed concrete structure will be extremely reduced, or even the structure will fail prematurely. Hence, the values of elastic modulus, ultimate shrinkage strain, and ultimate creep coefficient of concrete have to be estimated reasonably and accurately at the production stage in order to avoid loss of structural capacity, or even unexpected structural failure caused by prestress loss. For the sake of avoiding unexpected prestress loss, the strict requirements on shrinkage and creep properties of the concrete used for prestressed concrete structures have been specified by ACI Code as well as other Specifications. For example, the "AASHTO LRFD Bridge Construction Specifications2001 Interim Revisions" [AASHTO, 2001] specifies that, for the design of continuous prestressed concrete Igirder superstructures, the ultimate creep coefficient should be 2.0 and the ultimate shrinkage strain will take the value of 0.0004, in accordance with the recommendation of ACI 209. The Specification also states that, when specific data are not available, estimates of shrinkage and creep may be made using the provisions of CEBFIP model or ACI 209 model. The creep behavior of concrete has been the focus of engineer's attention and may still be the engineer's concentration for decades to come because of the volatility of the creep property of concrete. Over the years, many attempts have been tried to develop the general constitutive equation for the description of timedependent behavior of concrete. However, most of them are empirical in nature and are limited to the scopes of the experiments. There are great uncertainties in extrapolation to later times and to the conditions not covered in the laboratory. AASHTO LRFD Specifications state the following: "without results from tests on the specific concretes or prior experience with the materials, the use of the creep and shrinkage values referenced in these Specifications can not be expected to yield results with errors less than +50%." The values of the modulus of elasticity, ultimate shrinkage strain and ultimate creep coefficient of concrete, which are used in structural design in Florida, are either based on the arbitrary available literature or based on the limited research of the locally available material. Particularly, since very limited creep testing has been performed on Florida concretes, the knowledge of creep characteristics of Florida concrete is still a blind page. More importantly, the susceptibility of the elastic modulus, shrinkage and creep of concrete to the variation of concrete mix ingredients, such as particular aggregates in Florida, water content and mineral additives so on, puts more uncertainties in using these values. There is a great need for a comprehensive testing and evaluation of locally available concrete mixes to determine these mechanical and physical properties of Florida normalweight as well as lightweight concretes, especially for the concretes used in prestressed concrete structure, so that correct values for these properties can be used in structural design. In addition, there is also an immediate need to determine the most effective and practical laboratory test setups and procedures for obtaining the modulus of elasticity, creep and shrinkage properties of structural concretes used in Florida. This research study was carried out to meet these needs of the FDOT. 1.2 Hypothesis * Creep is related other mechanical properties of concrete, especially strength and elastic modulus. Thus, it is possible to estimate or predict its creep behavior based on the knowledge of its other mechanical properties. * Shrinkage of concrete is related to its water content and other mechanical properties, specially strength and elastic modulus. Thus, it is possible to estimate shrinkage behavior from its water content and other mechanical properties. * Ultimate creep coefficient of concrete may exceed a value of 2.0, which is usually assumed to be the maximum value in structure design. Thus, creep testing on the specific concrete is needed to obtain reliable value of its ultimate creep coefficient. 1.3 Objectives of Study This research has the following major objectives: * To design and recommend an effective and reliable laboratory testing setup and procedure for performing creep tests on concrete. * To evaluate the effects of aggregate, mineral additives and water to cementitious materials ratio on strength, elastic modulus, shrinkage and creep behavior of concrete. * To determine the strength, elastic modulus, shrinkage and creep behavior of the typical concretes used in Florida. * To determine the relationship among compressive strength, splitting tensile strength and modulus of elasticity of concretes made with typical Florida aggregate. * To develop prediction equations or models for estimation of shrinkage and creep characteristics of typical Florida concretes. 1.4 Scope of Study The scope of this research covered the following major tasks: * To review the literature about previous and current study on elastic modulus, shrinkage and creep of concrete. * To design, construct and evaluate the effectiveness of creep test setup and procedures. * To perform a comprehensive laboratory study on the physical and mechanical properties of typical Class II, IV, V and VI concrete mixtures made with normal weight aggregate and lightweight aggregate, including compressive strength, indirect tensile strength, modulus of elasticity, creep and shrinkage behavior. A total of 14 different concrete mixes was evaluated, and ten of them were replicated. * To analyze the experimental data, and to determine the relationships among different properties, and to develop prediction equations for estimation of shrinkage and creep behaviors of concrete. 1.5 Research Approach Objectives of this study are realized by the following research approaches: * Conduct laboratory testing programs to determine the various properties of concrete. ASTM standard test methods were used for compressive strength test, splitting tensile test, elastic modulus test and shrinkage test. A creep test setup was designed, evaluated and refined to be used for this purpose. * Perform statistical analysis to determine relationships and trends among the fundamental properties of the concretes evaluated in this study. * Evaluate existing prediction models for creep and shrinkage and develop improved models for estimation of shrinkage and creep behaviors of concrete. CHAPTER 2 LITERATURE REVIEW 2.1 Introduction The following content presents a literature review on the susceptibility of strength, elastic modulus, shrinkage and creep properties of concrete to various factors, and on the existing models for predicting the strength, elastic modulus, and shrinkage and creep properties of concrete. 2.2 Strength of Concrete 2.2.1 Significance of Studying Strength of Concrete Strength is commonly considered as the most valuable property of concrete, and it gives an overall picture of the quality of concrete because of its direct relation to the microstructure of the hydrated cement paste. Moreover, the strength of concrete is almost invariably a vital element of structural design and is specified for compliance purpose. Also, knowing strength development characteristic of concrete is very critical in decisionmaking about when to remove formworks, when to continue next construction step, or when to open structure to service. Apparently, the economic analyzer will be very pleased for knowing the aforementioned information to optimize project budget. Over the past decades, with the broad development and application of new concrete technique characterized by high strength concrete and high performance concrete, durable concrete structure and complex structural design become realizable. For example, highrise building enables humankind to make full use of limit living space on this planet plausible; and longspan bridge are more pleasing aesthetically, costeffective and resourcesaving. However, even though a large amount of information has been accumulated about concrete strength design, engineers are still fore from knowing well the strength properties of concrete. To design a concrete mixture with preassigned properties is still an engineer's dream. The causes are attributed to the volatility of concrete strength induced by the variation of raw materials and their proportions. Thus, the properties of concrete materials are still worthy of study. 2.2.2 Effect of Coarse Aggregate on Strength of Concrete The investigation on the effect of raw materials and their proportions on strength development has been the focus of many engineers' effort. For example, Aitcin and Mehta [Aitcin, PC and Mehta, P. K, 1990] studied the effect of coarse aggregate characteristics on mechanical properties of high strength concrete. The experiment was carried out using four coarse aggregate types available in Northern California and similar mix proportions. The results showed that using diabase and limestone aggregates produced concretes with significantly higher strength and elastic modulus than those using granite and river gravel. They concluded that the mineralogical differences in the aggregate types were responsible for this behavior. Sarkar and Aitcin [Sarkar, S. L and Aitcin, PC, 1990] carried out research on the importance of petrological, petrographical and mineralogical characteristics of aggregate in very high strength concrete. They pointed out that aggregate intrinsic strength, particularly that of coarse aggregates, receives scant attention from concrete technologists and researchers as long as the w/c ratio falls within the 0.50to0.70 range, primarily due to the fact that the cement aggregate bond or the hydrated cement paste fails long before aggregates do. This, however, does not hold true for very highstrength concretes, with very low w/c ratios of 0.20 to 0.30. Compressive strength testing of very highstrength concrete has indicated that aggregates can assume the weaker role, exhibited in the form of transgranular fractures on the surface of failure, as has already been observed in some lightweight concretes. The authors have carried out detailed petrological, petrographical and mineralogical characterization of twelve different coarse aggregates that have performed with variable success in very highstrength concrete in Canada and the United States. Suitability for such an application has been linked to a special set oflithological characteristics: the minerals must be strong, unaltered, and fine grained. Intra and intergranular fissures partially decomposed coarsegrained minerals, and the presence of cleavages and lamination planes tend to weaken the aggregate, and therefore the ultimate strength of the concrete. Ezeldin and Aitcin [Ezeldin, A. S. and Aitcin, PC, 1991] studied the effect of four coarse aggregates with different characteristics on the compressive strength, flexural strength, and flexural strength/compressive strength ratio of normal and highstrength concretes. The study investigated the possibility of obtaining a relatively high flexural strength/compressive strength ratio at high compressive strength by using different aggregate types. The study by Alexander and Addis [Alexander, M. G. and Addis, B. J., 1992] showed that aggregates play an important role in governing mechanical properties of high strength concrete. Generally, andesite and dolomite aggregates give superior results. Tests were also done on "artificial" interfaces between paste and these two rock types in order to characterize the interfacial bond properties. Results show that andesite achieves higher interfacial fracture energy values than dolomite, which helps to confirm the macroscopic engineering properties measured on concretes. Giaccio, Rocco, Violini, Zappitelli, and Zerbino [Giaccio, G. et al, 1992] pointed out that concrete is a heterogeneous material whose properties depend on the properties of its component phases and the interactions between them. They studied the effects of granitic, basaltic, and calcareous aggregates on the mechanical properties of high strength concrete, including compressive strength, flexural strength, modulus of elasticity and stressstrain behavior of concrete. The results indicated that the effect of coarse aggregate characteristics on the mechanical properties of highstrength concretes is substantial. The impact of aggregate strength on concrete compressive strength was evaluated by Lindgard, and Smeplass [Lindgard, J. and Smeplass, S, 1993] as well. The significance of the aggregate strength has been compared with the effect of the cement type and the use of silica fume. According to the obtained results, the impact of the aggregate strength on the strength of high strength concrete is limited, compared with the impact of the binder type, while the differences in elastic modulus between the different aggregate types is fully reflected in the concrete elastic modulus. This contradiction is explained by a hypothesis based on stress concentrations due to the difference in rigidity between the binder and the aggregates. 2.2.3 Prediction of Strength of Concrete If there is no specific testing data available, it is a good alternative to have an equation reliable to give an effective prediction on the strength of concrete at desired age. An accurate approximation to the strength of concrete at specific ages is of great importance to know in order to decide on when to remove formwork, when to continue next construction step, and when to open the structure into service. In analyzing the characteristics of development of compressive strength with time, an empirical equation has been provided by ACI 209R Code as follows: f() = f (21) c a+(t t c28 Where a in days and / are constants, f28 is compressive strength of concrete at 28 days, and t in days is the age of concrete. For the tests using 6"x 12" cylinder, type I cement and moist curing condition, two constants, a and /, are equal to 4.0 and 0.85 respectively. Because of substantial effect of coarse aggregate type on the properties of concrete, and because of no such mineral additives as fly ash and slag involved, which have substantial effects on the development of concrete strength, when the aforementioned formula was developed, caution should be taken when it is used. If possible, further investigation should be carried out to calibrate the above equation. 2.3 Elastic Modulus of Concrete 2.3.1 Definition and Determination of Elastic Modulus of Concrete The modulus of elasticity or "Young's Modulus", a very important mechanical property reflecting the capability of concrete to deform elastically, is defined as the slope of the stress strain curve within the proportional limit of a material. Initial tangent Tangent__ modulus 7 Loading V/ Loadi Unloading Secant modulus Strain Figure 21 Representation of the stressstrain relation for concrete For a concrete material, usually, the most commonly used value in structure design is the secant modulus, which is defined as the slope of the straight line drawn from the origin of axes to the stressstrain curve at some percentage of the ultimate strength. Since no portion of the stress strain curve is a straight line, the usual method of determining the modulus of elasticity is to measure the tangent modulus, which is defined as the slope of the tangent to the stressstrain curve at some percentage of the ultimate strength of the concrete as determined by compression tests on 6"x 12" cylinders. Figure 21 illustrates the stressstrain plot of a concrete as it is loaded and unloaded. From this figure, we can see that the secant modulus is almost identical to the tangent modulus obtained at some lower percentage of the ultimate strength. 2.3.2 Significance of Studying Elastic Modulus of Concrete Concrete, as a building material, is utilized in the elastic range. Thus, it is very important to know the relationship between stress and strain for a given concrete before it can be used for buildings, bridges, pavement and so forth. The relationship between stress and strain for a concrete material can be characterized by its elastic modulus, which is the property of concrete materials. For reinforced concrete structures, the knowledge of the elastic property of a specific concrete will not only make the deformation of the concrete members wellcontrolled, but also decrease the extra stress transfer to other concrete elements, which can cause the concrete to crack or fail prematurely. For prestressed concrete structures, elastic shortening is blamed for causing prestress loss. The prestress loss, on one hand, will decrease the capacity of a concrete structure, and even lead to unexpected collapse of the structure; and on the another hand, it will results in the increased volume of tendon for satisfying the design requirement because of overestimation on elastic shortening, which can result in possible waste of materials and increased cost. In addition, in order to make full use of the compressive strength potential, the structures using highstrength concrete tend to be slimmer and require a higher elastic modulus to maintain its stiffness. Therefore, the knowledge of the elastic modulus of high strength concrete is very important in avoiding excessive deformation, providing satisfactory serviceability, and achieving the most costeffective designs. At last, for concrete pavement, high elastic modulus concrete is not desirable because it increases the pavement cracking probability. Thus, high strength but low modulus concrete is preferable. As to how to obtain the concrete material with the properties desired, one way to approach this goal is to change the properties of individual concrete components and their proportions. And most importantly, the significant effects of different types of coarse aggregate on elastic modulus of concrete have to be investigated. 2.3.3 Effect of Coarse Aggregate on Elastic Modulus of Concrete 50 50 Aggregate 40 Concrete U 30 20 Cement paste 10 0 1000 2000 3000 Strain 106 Figure 22 Stressstrain relations for cement paste, aggregate and concrete Since concrete is a multiphase material, modulus of elasticity is very susceptible to the variation of coarse aggregate content and coarse aggregate type. In a study by Stock, Hannant and Williams [Stock et al, 1979], it was reported that for concretes with a fixed w/c of 0.5, as the volume of coarse aggregate varied from 20 to 60 %, the compressive strength of concrete remained almost same. This result is very consistent with the 'W/C law' established by Duff Abrams in 1919. That is to say, for a given mix proportion, the compressive strength of concrete will be determined by its water to cement ratio. This is especially true for normal concrete with compressive strength less than 60MPa. However, the elastic modulus of the concrete was substantially influenced by the changes in its coarse aggregate content. As shown in Figure 22 [A.M.Neville, 1996], we can see that the elastic modulus of concrete is remarkably different from that of hardened cement paste. Also, Neville [A.M.Neville, 1996] pointed out that, for a concrete of a given strength, because normal weight aggregate has a higher elastic modulus than hydrated cement paste, a higher aggregate content results in a higher modulus of elasticity of the concrete. In a study by Persson [Persson, 2001], it was reported that the elastic modulus of self compacting concrete was the same as that for normal concrete as long as their compressive strengths were the same. However, in the study by Schlumpf [Schlumpf, 2004], the elastic modulus of selfcompacting concrete was reported to be 20% lower than that of a normal concrete with similar strength. In addition, the findings from the study by Chi [Chi, 2003] also indicated that the aggregate fraction in concrete had a considerable effect on the elastic modulus of concrete. Coarse aggregate type is another very important factor affecting the elastic modulus of hardened concrete. Different types of aggregate can have quite distinct effects on elastic modulus. Even different coarse aggregates of the same type but from different locations can have substantially different properties. The reported findings by Zhou, Lydon and Barr [Zhou et al, 1995] show that the coarse aggregate type has a considerable influence on the elastic modulus of concrete. In their study, the effects of expanded clay, sintered fly ash, limestone, gravel, glass and steel aggregate on the elastic modulus of concrete were investigated. In addition, the study by Shideler [Shideler, 1957] on concrete mixtures using gravel and expanded clay as aggregate also indicate the same conclusion as reported by Zhou, Lydon and Barr [Zhou et al, 1995]. In 1990, Aitcin and Mehta [P. C. Aitcin and P. K. Mehta, 1990] also investigated the effect of coarse aggregate characteristics on mechanical properties of high strength concrete. In their study, the influence of four coarseaggregate types available in Northern California on the compressive strength and elastic behavior of a very high strength concrete mixture was studied using identical materials and similar mix proportions. The results indicated that the diabase and limestone aggregates were found to produce concretes with significantly higher strength and elastic modulus than did the granite and river gravel. The mineralogical differences in the aggregate types are considered to be responsible for this behavior. The study by Alexander [Mark G. Alexander, 1996] on the influence of 23 different aggregate types on the properties of hardened concrete showed that aggregates exert a profound and important influence on the elastic property of concrete. In 1998, Cetin and Carrasquillo [Aykut Cetin and Ramon L. Carrasquillo, 1998] carried out an investigation on the effects of four coarse aggregate types locally available in central Texas on the mechanical properties of highperformance concrete. Test results showed that the mineralogical characteristics of coarse aggregate as well as the aggregate shape, surface texture, and hardness appeared to be responsible for the differences in the performance of high performance concretes. Also, it was observed that it appeared that there was no one single equation for highperformance concrete mixtures with different coarse aggregates that coulc estimate the elastic modulus with sufficient accuracy as in the case of normal strength concretes. Wu, Chen amd Yao [Wu K.R, Chen B, Yao W, Zhang D, 2001] carried out a study on the effects of the coarse aggregate type, including crushed quartzite, crushed granite, limestone, and marble coarse aggregate, on the compressive strength, splitting tensile strength, fracture energy, characteristic length, and elastic modulus of concrete. The results indicated that the stiffness of concrete depends on the type of aggregate, especially for highstrength concrete. Beshr and Maslehuddin [Beshr H et al, 2003], Rashid, Mansur and Paramasivam [M. A. Rashid et al, 2002]; Huo, AlOmaishi and Tadros [Xiaoming Sharon Huo et al, 2001] reported that different types of coarse aggregate have pronounced effects on elastic modulus of concrete. 2.3.4 Models for Predicting Elastic Modulus of Concrete As mentioned in the literature about the factors affecting elastic modulus of concrete, for a given type of aggregate, although the modulus of elasticity of concrete will increase with the strength of concrete, the factors that affect the modulus of elasticity of concrete do not always have a corresponding effect on the strength of concrete. Thus, there is no universal equation that can be possibly applied to relate compressive strength to elastic modulus of concrete. Thus, the models, both ACI model and CEBFIP model, may need to be modified in order to be applied to a structure to achieve full function and serviceability in its entire life span. The above hypothesis can be easily confirmed by an extensive testing program to investigate the effects of coarse aggregate types on elastic modulus of concrete. The study by Shih, Lee, and Chang [Shih, T. S. et al, 1989] suggested that Young's modulus of highstrength concrete has a somewhat higher value than that of normalstrength concrete. Pauw's equation for modulus of elasticity of concrete, which is based on experimental normalstrength concrete, needs to be reexamined. Baalbaki, Benmokrane, Chaallal, and Aitcin, [Baalbaki, W., 1991] studied the influence of different types of crushed rocks on elastic properties of high performance concrete. Testing results pointed to the important role played by coarse aggregates through the elastic properties of the parent rock. They also recommended that the present formulas relating the prediction of elastic modulus of concrete recommended by some codes should be reviewed. Nilsen and Aitcin [Nilsen, A. U. and Aitcin, PC., 1992] investigated the properties of high strength concrete containing lightweight, normal weight and heavyweight aggregates. In this study, a comparison of the values of elastic modulus determined experimentally with those calculated according to the formula recommended by the ACI Building Code, the British Standard Code, and the Norwegian Standard Code, showed that all codes overestimated the elastic modulus of highstrength heavyweight concrete. In the following section, the formula used to predict the elastic modulus of concrete by Florida LRFD Guidelines, ACI model, and CEBFIP model are given. * Model recommended by Florida LRFD Guidelines [2002] According to this guideline, in the absence of more precise data, the modulus of elasticity for concretes with unit weights between 0.090 and 0.155 kcf, can be estimated from the following formula: E =a.w .f (22) C C C (2 Where E, Elastic modulus in ksi. wc Unit weight of concrete (kcf). fc Compressive strength of concrete (ksi). a Constant, a = 33000 is recommended by Florida LRFD Guidelines. p constant, / = 1.5 is recommended by Florida LRFD Guidelines. * Prediction equations recommended by ACI 209 The prediction equations recommended by ACI for estimating the elastic modulus of concrete are given as follows: Ec = A (23) Where Ec Elastic modulus (psi) f Compressive strength of concrete (psi) A constant, A = 57000 is recommended by ACI 318. The following equation recommended by ACI 31889 (revised 1992) for structural calculation is applicable to normal weight concrete: E = ac +/ (24) Where Ec Elastic modulus (GPa) f/ Compressive strength of concrete (MPa) a constant, a = 3.32 is recommended by ACI 318. p constant, / = 6.9 is recommended by ACI 318. The next equation given by ACI 363R92 is applicable for predicting elastic modulus of concretes with compressive strength up to 83 MPa (12000 psi) Ec = 3.65 (25) Where Ec Elastic modulus (GPa) f Compressive strength of concrete (MPa) CEBFIP Model (1990) CEBFIP Model (COMITE EUROINTERNATIONAL DU BETON) Code (1990) also offers the following model for prediction of timedependent modulus of elasticity. The equation is given as follows: 0.5 0.5 28 E (t)= exp s. 1 E (26) Where s A coefficient depending on the type of cement; s = 0.20 for rapid hardening high strength cements, 0.25 for normal and rapid hardening cements, and 0.38 for slow hardening cements. t Age of concrete (days). ti1 day Eci Modulus of elasticity of concrete at age of 28 days. 2.4 Shrinkage Behavior of Concrete 2.4.1 Origin of Shrinkage of Concrete According to the mechanisms of concrete shrinkage, shrinkage of concrete consists of plastic shrinkage, autogenous shrinkage (a process known as selfdesiccation), drying shrinkage, and carbonation shrinkage. Autogenous shrinkage is the consequence of withdrawal of water from the capillary pores by the anhydrous cement particles. Most of the autogenous shrinkage will take place at the early age of hydration of cement. However, for concrete mixtures with a very low W/C ratio, this procedure may last longer if moisture is available from ambient environment. Plastic shrinkage and drying shrinkage are caused by withdrawal of water from concrete under the condition of humidity gradient between the interior of concrete and air. Plastic shrinkage may lead to the interconnection among capillary pores, the main factor contributing to cracking of concrete at early age as well as increasing permeability of concrete. Carbonation shrinkage is caused by carbonation of calcium hydroxide in the concrete. Thus, carbonation shrinkage normally takes place on the surface of concrete elements. But, if there are penetrated cracks in concrete, carbonation shrinkage may take place in the interior of concrete. Carbonation of concrete will decrease the PHvalue inside concrete so that reinforcement can be easily corroded. 2.4.2 Significance of Studying Shrinkage of Concrete Shrinkage of concrete, one of the main factors in determination of the endurance of concrete structure, is a very important property of concrete to be evaluated. Excessive shrinkage is blamed for leading concrete to crack, even fail. At the early age of concrete, low early strength can not resist the stresses induced by drying shrinkage so that shrinkageinduced cracking can subsequently lead to premature failure of the concrete structure. Cracks in concrete increase the permeability of concrete and control the corrosion initiation time and corrosion rate of steel reinforcement in the concrete structure. Shrinkageinduced cracks become a severe problem for marine concrete structures or concrete structures close to the coastal region. The penetration of aggressive ions through cracks into the interior of concrete is a very critical factor in causing the corrosion of steel reinforcement. For prestressed concrete elements, not only does the shrinkage induced cracking speed up the corrosion of reinforcement, shrinkage deformation, which accounts for up to 15% of total prestress loss, is also one of the main factors contributing to prestress loss. The shrinkage behavior of concrete is great affected by coarse aggregate content, coarse aggregate type, cementitious material content and water content. For instance, an increase in volume of aggregate in concrete will usually lead to a decrease in cement content, which would lead to reduced shrinkage for the concrete. However, a reduction in cement content does not necessarily cause a reduction in the strength of the concrete. Thus, through optimizing mix proportion of concrete mixture, it is possible to design a concrete with low cement content and low shrinkage without sacrifice of strength. 2.4.3 Effect of Raw Materials on Shrinkage of Concrete 2.4.3.1 Effect of aggregate content on shrinkage behavior of concrete The contribution of coarse aggregate to decreased shrinkage of concrete is attributed to the decrease of cement paste volume in the concrete mix. In 1956, Pichett [G.Pichett, 1956] reported that the shrinkage ratio increases significantly as the aggregate content decreases. The possible reason to explain the effects of coarse aggregate content on shrinkage strain of concrete is shown in Figure 23. For the lean concrete mixture with a high coarse aggregate content, the coarse aggregate particles will have pointtopoint contacts or even facetoface contacts with each other. So a concrete with such a stiff aggregate skeleton will be very effective in resisting stresses caused by cement paste shrinkage because aggregate particles cannot be pushed more closely under the action of interior stress cause by shrinkage. Thus, shrinkage strain is dramatically reduced. But, for rich concrete, the situation is otherwise. CA .. . . ............... ........................:::::: a. Lean concrete b. Rich concrete Figure 23 Effect of coarse aggregate content on the shrinkage of concrete Similarly, in 1960, Hermite [R.L'Hermite, 1960] carried out a study of the effects of cement content on shrinkage behavior of concrete. The tests were performed at a curing temperature of 68F, 50% relative humidity and wind velocity of 2.25 mph. The results indicated that, at the early age of concrete, the shrinkage strain of the concrete with a cement content of 850 lb/yd3 (typical cement content for flowable concrete) is almost three times higher than that of concrete mixtures with a cement content of 340 lb/yd3. Leming [Leming, M. L, 1990] investigated the mechanical properties of high strength concrete with different raw materials. These materials represent those used in structures built under North Carolina Department of Transportation control. The data from shrinkage tests showed that shrinkage strain of concrete varies significantly depending on the specific raw materials used and the strength levels attained. Research was carried out by Alfes [Alfes, 1992] on how shrinkage was affected by the aggregate content, the aggregate modulus of elasticity, and the silica fume content. The experiment was conducted using W/C ratio in the range of 0.25 to 0.3 with 20% silica fume by weight of cement and varying amount and type of aggregates (basalt, LDslag, and iron granulate), and compressive strength of concretes at 28day age were in the range of 102 to 182 MPa (14,600 to 26,000 psi). The test results showed that there is a direct and linear relationship between the shrinkage value and the modulus of elasticity of the concrete. In 1993, Zia et al. [Zia et al, 1993c, 1993d, 1993e] evaluated the shrinkage behavior of VES, HES, VHS concretes with different aggregates (crushed granite, marine marl, rounded gravel, and dense limestone). Shrinkage measurements were made for three to nine months in different cases. The observed behavior followed the general trend of conventional concrete except for the two cases of VES concrete using special blended cement (Pyrament) with marine marl and rounded gravel as aggregates. In these two cases, the specimens exhibited an expansion of approximately 140 microstrains, rather than shrinkage for the entire period of 90 days. The expansion was attributed to the lack of evaporable water in the concrete because of its very low W/C (0.17 for marine marl, and 0.22 for rounded gravel). 2.4.3.2 Effects of coarse aggregate type on concrete shrinkage The skeleton of coarse aggregate in a concrete can restrain the shrinkage of the cement matrix. The extend that the coarse aggregate skeleton can resist the stress caused by shrinkage induced stress from cement matrix depends on how stiff the coarse aggregate is. That is to say, the elastic modulus of the aggregate determines the extent of restraining action to the shrinkage of concrete. For example, the shrinkage of a concrete made with a steel aggregate will be lower than the one made with a normal aggregate. Similarly, the shrinkage of a concrete made with expanded shale aggregate will be higher than the one made with a normal aggregate. The above hypothesis was verified by the many studies performed in the past decades. In 1958, Troxell, Raphael and Davis [Troxell et al, 1958] performed tests to study the effects of coarse aggregate of different types on shrinkage behavior of concrete. The tests were carried out on the concrete mixtures with a fixed mix proportion. The results showed that there is a considerable variation in the shrinkage strain of the resulting concrete batched with coarse aggregate of different types. They made a conclusion that this phenomenon is due very likely to the difference in modulus of elasticity among aggregates of different types. Generally speaking, the elastic property of aggregate determines the degree of restraint to the cement matrix. Reichard [Reichard, 1964] agreed that the coarse aggregate has significant effect on shrinkage behavior of concrete. A normal natural aggregate is usually not subject to shrinkage. However, there exist rocks that can shrink up to the same magnitude as the shrinkage of concrete made with nonshrinking aggregate. 2.4.3.3 Effects of size and shape of coarse aggregate on concrete shrinkage Aggregate size and shape also affect the shrinkage of hardened concrete. The experimental study conducted by Collins [Collins, 1989] on shrinkage of five highstrength concrete mixtures with varied paste content, aggregate size showed that shrinkage deformations were somewhat less for concrete mixtures with lower paste contents and larger aggregate size. A study by Bisschop, Pel, and Van Mier [Bisschop et al, 2000] indicated that the total length and the depth of microcracking caused by shrinkage of concrete will increase with larger aggregate size. McQueen, Rapol, Flynn [Roy D. McQueen et al, 2002] performed laboratory shrinkage tests in accordance with ASTM C 157 on a matrix of 16 concrete mixes to evaluate the effects coarse aggregate size on shrinkage of concrete. The tests were conducted on mixes with ASTM C 33, No.57 (38mm maximum aggregate size) and No. 467 (64mm maximum aggregate size) coarse aggregates. The results of the laboratory shrinkage tests revealed that the maximum size of the coarse aggregate (No.57 or 467) did not influence the shrinkage. A study on evaluation of high performance concrete pavement carried out by Ozyildirim [Ozyildirim, C, 2000] showed that concrete using smaller coarse aggregate commonly exhibits greater shrinkage and increases potential for slab cracking because of increased paste requirements. Larger maximum coarse aggregate sizes, on the other hand, require less paste, less cementitious material, and less water, thereby resulting in reduced shrinkage; they also provide increased mechanical interlock at joints and cracks. Thus, there is still some controversy about how coarse aggregate size will affect the shrinkage behavior of concrete. Test data from the specific concrete are necessary to control concrete quality. 2.4.3.4 Effect of other factors on shrinkage behaviors of concrete Shrinkage behavior of concrete is affected not only by coarse aggregate, but also by other factors, such as water content, specimen size, ambient conditions, admixtures as well as mineral additives. Water content is the most important factor influencing shrinkage behavior of concrete. Normally, the higher the W/C ratio is, the higher the shrinkage. This occurs due to two interrelated effects. As W/C increases, paste strength and stiffness decrease; and as water content increases, shrinkage potential increases. The specimen size affects the diffusion rate of free water from the interior to exterior of concrete. Thus, both the rate and the total magnitude of shrinkage decrease with an increase in the volume of the concrete member because, for larger members, more time is needed for shrinkage effects to reach the interior regions. For instance, the study by Hindy et al. [Hindy et al, 1994] showed that dry shrinkage of small specimens measured by the conventional laboratory test was found to overestimate shrinkage of the concrete in the real structure. Ambient conditions, such as relative humidity and temperature, greatly affect the magnitude of shrinkage. They are blamed for affecting shrinkage behavior because they create the relative humidity gradient and relative temperature gradient between the interior and exterior of concrete, which is driving force to concrete shrinkage. The higher the relative humidity, the lower the rate of shrinkage is. The lower the temperature gradient, the lower the shrinkage rate is. Thus, the investigation conducted on shrinkage behavior of concrete has to simulate the real environmental conditions in order not to overestimate shrinkage strain. For example, Aitcin et al. [Aitcin et al, 1990] reported that the surface shrinkage strains under the field condition were considerably lower than those measured under the laboratory conditions. Mineral additive effect on shrinkage behavior varies according to the type of mineral additive. Any material which substantially changes the pore structure of the paste will affect the shrinkage characteristics of the concrete. In general, as pore refinement is enhanced, shrinkage is increased. Pozzolans typically increase the drying shrinkage, due to several factors. With adequate curing, pozzolans generally increase pore refinement. Use of a pozzolan results in an increase in the relative paste volume due to the following two mechanisms: 1) In practice, slowly reacting pozzolans (such as Class F fly ash) are frequently added to replace cement by weight rather than by volume according to conventional concrete mix design method. This will increase paste volume since pozzolans have a lower specific gravity than Portland cement. 2) Additionally, since pozzolans such as fly ash and slag do not contribute significantly to early strength, concrete containing pozzolans generally has a lower stiffness at earlier ages as well, making them more susceptible to increased shrinkage under standard testing conditions. 2.4.4 Models to Predict Concrete Shrinkage Misprediction of shrinkage usually does not cause structural collapse, but puts the structure out of service, i.e. the structure does not live as long as the projected life span. The widespread occurrence of such lack of longterm serviceability inflicts a tremendous economic damage on many nations. The direct signs of damage that put a structure out of service are typically cracks, which may cause major fractures. Even though the mechanisms of shrinkage, such as micromechanics mechanism and diffusion mechanism, have been studied extensively, their correlations with macroscopic behaviors have been intuitive and nonquantitative. As pointed out by Bazant and Carol [Bazant et al, 1993], such studies generally have not borne much fruit. Since the uncertainty in the prediction of shrinkage behavior with the variations of concrete compositions and random environmental conditions is enormous, the models established at present relies on purely empirical relations without micromechanics models involved. In addition, substantial effort has been paid in stochastic phenomena and probabilistic models, but similar to the preceding topic, nothing is being introduced into practice. At present, the empirical formula given by the ACI Committee 209 [1993] is widely used to predict shrinkage strain. But, it should be noted that ACI 209 equation could well be in error unless broad corrections are applied, for instance, to correct for curing and size effect, and to account for humidity and composition effects. As pointed out by Hindy et al. [Hindy et al, 1994], the ACI 209 predictive equation was found to be valid for the high performance concretes only if new values for the parameters were introduced. Thus, owing to many uncertainties in current models, it is very necessary to perform tests on the specific concrete mixtures designed using local available materials to guarantee the safety of structures. Then, based on the accumulated data, constitutive parameters characterizing the shrinkage behaviors of concretes designed based on local available materials can be obtained. In the following sections, the shrinkage prediction models offered by CEBFIP model code (1990) and ACI209 (1992) are reviewed briefly. 2.4.4.1 CEBFIP Model for shrinkage strain prediction In this model, the effects of cement type, ambient relative humidity, compressive strength of concrete, and size effect of specimen on shrinkage strain of concrete are taken into consideration. The total shrinkage strain may be estimated by the following equation: E [t, t =_ E t t t (27) cs s csO s s) Where E, (t, t,) Time dependent total shrinkage strain E ,o Notational shrinkage coefficient /8, (t ts)Coefficient to describe the development of shrinkage with time Eco can be estimated by the following equation: E == 160+10sc 9 cm x106 .RH (28) csO sc f RH Where sc, A coefficient which depends on the type of cement: sL, = 4 for slowly hardening cements; 5 for normal or rapid hardening cements; 8 for rapid hardening high strength cements. fc, The mean compressive strength of concrete at the age of 28 days. fcmo=1 MPa /RH = 1.55,sRH for 40% < RH < 99% ; /RH = 0.25 for RH > 99% Where Ps = 1r (29) sRH RH RH The relative humidity of the ambient environment (%). RH0 100% s, (t ts) can be estimated by the following equation: 0.5 (t ts) s t ts )= tl2 (210) 350. + hWh te Where 2A h = 2A The notational size of member (in mm), where A, is the crosssectional area u (mm2) and u is the perimeter (mm) of the member in contact with the atmosphere. ho100 mm ti 1 day 2.4.4.2 Prediction model recommended by ACI209 Report [1992] The concrete shrinkage prediction model recommended by ACI209 (1992) is shown by the following equation: S) t (211) ( sh )t 35 +t ( sh )u (211) Where (Esh ) Time dependent shrinkage strain (sh )u Ultimate shrinkage strain t Time in days If there is no available shrinkage data from the concrete to be evaluated, the ultimate shrinkage strain, (Esh ) can be assumed to be the following: sh) = 780 x106 xh (212) where Ysh a product of all the applicable correction factors for the testing conditions other than the standard condition; Ysh = 1 under standard testing condition. Ysh is obtained by multiplying the ultimate shrinkage strain under the standard condition by the appropriate correction factors as described in the following: Correction factors for the effect of initial moist curing. The correction factor is equal to 1.0 for concrete cylinders moistcured for 7 days, and 0.93 for that moistcured for 14 days. * Correction factor for the effect of ambient relative humidity. The following formulas are given for use in obtaining the correction factor for shrinkage test performed under the condition of ambient relative humidity greater than 40%. =1.40 0.0102A, for 40 < A < 80 (213) y, =3.00 0.030A, for 80 < A < 100 (214) where y, Correction factor for the effect of relative humidity k Relative humidity * Correction factor for the effects of specimen size. The correction factor in consideration of the specimen size effect (y,) is given by the following equation: yV =1.2exp(0.12 ) (215) s where ys Correction factor for the effects of specimen size v  Volumesurface area ratio of the specimen in inches s * Correction factor for concrete composition. Various equations for calculating the correction factors for the effects of the slump of the fresh concrete, aggregate content, cement content and air content of the concrete have also been given in this model. 2.5 Creep of Concrete 2.5.1 Rheology of Materials and Definition of Creep of Concrete The philosophical origin of rheology is owed to Heraclitus. As exemplified in his famous aphorism "Panta Rhei" ("Panta Rei"): Everything flows and nothing stands still. Inspired by this expression, rheology, the term was coined by Eugene Bingham, a professor at Lehigh University, in 1920, and was defined as the study of the deformation and flow of matter under the influence of an applied stress. One of the tasks of rheology is to empirically establish the relationships between deformations and stresses by adequate measurements. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics. The theological phenomenon of concrete materials, also termed as creep, is one of very important theological properties of concrete. Since creep behavior of concrete is characterized by timedependence, it generates substantial effects on the structural stability during its service life. Thus, it is of great importance to know the creep behavior of specific concrete before it can be used for structure design. Ct Ct I I Tertiary creep Steadystate creep Transient creep Time Figure 24 Creep diagram of concrete material Creep of concrete can be defined as the timedependent deformation of concrete materials under a sustained stress. As shown in Figure 24, loadinduced creep consists of three stages, namely primary or transient creep stage, steadystate creep or secondary creep stage and tertiary creep stage. The primary or transient creep is characterized by a monotonic decrease in the rate of creep. The feature of secondary or steadystate creep is that material will show constant creep rate. At last, in tertiary creep stage, creep rate will increase till material fails. Figure 25 shows a plot of strain versus time for a concrete that was loaded for some time and then unloaded. The permanent strain that remains after the load has been released is called the creep strain. For concrete materials, creep strain consists of two main components. The first component is the true or basic creep, which occurs under the conditions of no moisture movement to or from the ambient medium. This is the case for concrete element functioning as underground foundation, or inside water. The second component is the drying creep, which takes place while concrete is subjected in ambient conditions. Normally, the creep strain that is considered in structural design is the sum of basic creep strain and drying creep strain. Due to the difficulty to differentiate delayed elastic strain from creep strain and the convenience to build a numerical model to simulate timecreep strain curve with the delayed elastic deformation included, the total creep strain would usually include both the delayed elastic deformation and permanent creep deformation. Also, the above mentioned approach is usually taken since the delayed elastic strain is usually very small compared with the total creep strain. The creep behavior of concrete materials plays a great role in the stability of concrete structures. Also, the creep behavior of concrete is subjected to the severe volatility caused by the variation of raw materials for concrete mixtures and their proportions. Therefore, over the past decades, the study on creep of concrete has been one of engineers' focuses. Instantaneous recovery Delayed elas ic recovery Elastic strain Perman t creep Time since application of load Figure 25 Straintime plot of concrete under a sustained load and after release of load 2.5.2 Significance of Studying Creep Behavior of Concrete Creep in concrete can have both positive as well as negative effects on the performance of concrete structures. On the positive side, creep can relieve stress concentrations induced by shrinkage, temperature changes, or the movement of supports. For example, in indeterminate beam with two fixed ends, creep deformation will be very helpful in reducing tensile stress caused by shrinkage and temperature variation. On the other hand, in some concrete structures, creep can do harm to the safety of the structures. For instance, creep deformation can lead to an excessive deflection of structural members, creep buckling or other serviceability problems especially in highrise building, eccentrically loaded columns and long bridges. In mass concrete, creep may be a cause of cracking when a restrained concrete mass undergoes a cycle of temperature change due to the development of heat of hydration and subsequent cooling. For prestressed concrete structures, such as composite bridges, prestressed shells, or continuous girders, the desirable creep of concrete would be as low as possible. Heavily prestressed members and long members are particularly susceptible to large volume changes. If a prestressed member is restrained in position prior to the majority of the volume change has taken place, the prestressed members will exert excessive forces on its connections and supporting structures that could cause a structural failure. Also, another very important issue caused by creep deformation is prestress loss, accounting for more than 25% of total prestress loss. 2.5.3 Effect of Aggregate on Creep of Hardened Concrete Aggregates play an important role in creep of concrete. Coarse aggregate reduces creep deformation by reducing the cement paste content and restraining the cement paste against contraction. Generally, concretes made with an aggregate that is hard and dense and have low absorption and high modulus of elasticity are desirable when low creep strain is needed. The study by Troxell, Raphael, and Davis [Troxell et al, 1958] indicated that the creep strains of the concrete mixtures with different types of aggregate will behave differently. The highest creep value is obtained from the concrete made with sandstone aggregate, and the lowest creep value is obtained from the concrete made with limestone. Rusch et al [Rusch, 1963] found an even greater difference between the creep strains of concretes made with different aggregates. After 18 months under the load at a relative humidity of 65%, the maximum creep strain of the concrete made with sandstone was five times higher than the minimum creep strain of the concrete made with basalt. Alexander, Bruere and Ivanusec studied the influence of 23 aggregate types on creep deformation of concrete [Alexander et al, 1980]. Creep tests were conducted in a controlled environment at 23 C and 60 % relative humidity. Creep tests were conducted for six months after a 28day water cured period in limesaturated water to allow for minimal effects of hydration. Strains were measured using longitudinal gages on two opposite faces of the prism with a gage length of 100 mm (4 in). The conclusion shows that aggregates with a lower absorption will produce concrete with a lower creep deformation. It was further determined that the aggregate with a high elastic modulus will produce low creep values. Collins [Collins, 1989] examined the creep property of high strength concrete. Creep tests were conducted according to ASTM C 512. The results demonstrated that a concrete with a larger aggregate size and lower paste content would provide a lower creep strain. Creep tests done by Hua [Hua, 1995] on pure hardened cement pastes and on a reference concrete (made with the same paste) also show that creep is reduced by the presence of aggregate. In addition, the conclusion on the effect of coarse aggregate content on creep of concrete is also confirmed by the tests on lightweight aggregate concrete. The study by Gesoglu, Ozturan and Guneyisi [GesoAlu et al, 2004] showed that concretes containing higher lightweight coarse aggregate content had a lower creep strain at all W/C. 2.5.4 Prediction Models and Their Limitations of Concrete Creep With the exception of creep buckling, overestimation or underestimation of creep usually does not lead to structural collapse, but merely shortens the structural service life. But, misprediction of creep could put tremendous economic loss. Thus, accurate prediction of the ultimate creep strain of concrete is of great importance. In order to obtain an accurate prediction, the following mechanisms possibly resulting in creep of concrete have been studied, including micromechanics mechanism, diffusion phenomenon, thermodynamics mechanism, and other mechanism coupled with damage and fracture. Micromechanics mechanism in creep behavior has been studied extensively through the study of the microstructure of cement and concrete for decades. However, the macroscopic constitutive relations based on the intuitively and nonquantitatively observed phenomenon or postulated on the microstructure or even molecular level generally are not promising. The uncertainty in the prediction of longterm creep associated with the variations of concrete composition is enormous, actually much larger than any uncertainty except that due to the randomness of environment. Thus, even though the attempts at the mathematical micromechanical modeling of some phenomena have already begun, there is sill quite a distance to make them practical. Diffusion phenomenon can be considered another very important mechanism for creep behavior of concrete because creep of concrete is always associated with the moisture and heat transport between the interior concrete and outside environment. Therefore, in concrete structures exposed to the environment or subjected to variable temperatures, there is no hope of obtaining realistic stresses without actually solving the associated problems of moisture and heat transport, at least in an approximate manner. It has been shown that creep and shrinkage analysis based on diffusion analysis of a box girder bridge segment yields enormous stresses which are routinely neglected in practice. The models based on statistics have been studied extensively. Although the statistical variability of concrete creep under controlled laboratory conditions is quite small, very large statistical fluctuations are caused by the environment as well as the uncertainties in the effect of concrete composition. In most practical situations, sophisticated deterministic mathematical analysis makes in fact little sense, because the uncertainties of stochastic origin are much larger than the errors of simple effective modulus solutions compared with sophisticated deterministic analytical solutions of differential or integral equations. Due to complex influences coming from raw materials and ambient environment, the common problem with the current models is that they are only feasible to be used for the creep prediction of similar concretes, which means concretes from the same geographical region. The concretes used in the Florida region are generally quite similar and, instead of repeating measurements for each new major structure, one can greatly improve predictions on the basis of previously obtained data for a similar concrete from the same region. Equally important will be application of the existing fundamental research results in practice. Since each of these models is applicable under specific conditions for a certain class of materials, the proper utilization of these models depends essentially on the practical experience of the researcher. The accumulation of this experience is the purpose of most experimental works on creep. This is due mainly to the fact that 1) more than one microscope mechanism are involved in inducing creep of concrete, and 2) some empirical models only can be used for certain types of concretes without the variation of concrete components, proportions and applied environmental conditions. If the empirical model obtained from the concretes used in a given region is applied to predict creep strain of the concretes in another region, the results could be very scary. Over the years, many equations have been developed for the description of steadystate and transient creep. But, most of them are either too complicated theoretically to bring them into practical use, or have an empirical character and were determined on the basis of a fit to the experiments, which cause great uncertainties in the extrapolation to long time intervals and to conditions not covered in the laboratory. In the following sections, two creep prediction models, namely CEBFIP model and ACI 209 model will be reviewed. 2.5.4.1 C.E.BF.I.P Model Code In this model, the creep strain can be predicted by the following equation: c (to) Ecr (t, t) = 0 28(t t0) (216) cl Where cr (t, t,) Creep strain at time t ca (to) Applied stress 2, (t, to) Creep coefficient Ec Modulus of elasticity at the age of 28 days The modulus of elasticity can be estimated by the following equation: 4 f k+Af E =ca *10 c4.( C3 cW E rfe cmo Where (217) fck Characteristic strength of concrete (in MPa); Af = 8MPa; fm = 10MPa; aE = 2.15x 104MPa The creep coefficient 28(t, t) can be calculated as follows: 28 (t, tO) = O 8c (t tO) Where 0 Notational creep coefficient. p Coefficient to describe the development of creep with time after loading t Age of concrete in days to Age of concrete when loaded in days The notational creep coefficient can be estimated as follows: 0 = RH "(fcm) f(to) 1RH/RH0 ORH= + 10/ 0.46. (hI/h)ll3 5.3 fl(fc) !=~fcm fcmo O.l+(to0 /tl02 Where fc, = fck+ Af , h Notational size of the member (in mm)= 2A /u . Ac Crosssectional area (in mm2) u Perimeter of the member in contact with the atmosphere (in mm) ho 100 mm. RH Relative humidity of the ambient environment (in %). (218) (219) RHO 100% t, 1 day. (tt t)/t1 p8(t to) = +( tt (t to)06 (220) 28(tt ) (to). 0.6 (221) 10 + (t t0 Where 28 (t, to) Creep coefficient at time t & (to) Ultimate creep coefficient to Time of loading The ultimate creep coefficient can be expressed as: oo (t0) = c"o (222) The constant & = 2.35 is recommended. The correction factors yT consist of the following terms: Yc = la YRH Yat *s *Yp Ya (223) Where y)a Correction factor for loading age. For loading ages later than 7 days and moist cured concrete, yo = 1.25 (to) 0118 For loading ages later than 13 days and steam cured concrete, yo = 1.13 (t 0)Y 094 YRH Correction factor ambient relative humidity. For ambient relative humidity greater than 40%, y, = 1.27 0.0067 RH (RH is the ambient relative humidity in %) y, Correction factor for slump of fresh concrete. y, = 0.82 + 0.00264 S, (S, in mm) Yp Correction factor for fine to total aggregate ratio. y/ = 0.88 + 0.0024 pa (P is fine to total aggregate ratio) ya Correction factor for air content. yT = 0.46 + 0.09 aa (aa is air content) Yt, Correction factor for thickness of member. When the average thickness or volume to surface ratio of a structural member differs from 150 mm or 38 mm, respectively, two methods are offered for estimating the factor of member size y,: S Averagethickness method For an average thickness of a member smaller than 150 mm, the factors are given by ACI 209 Report. For an average thickness of a member larger than 150 mm and up to about 300 to 380 mm, the correction factor for thickness is given as: Ya, = 1.14 0.00092 ha During the first year after loading ya, = 1.10 0.00067 h For ultimate values Where ha = Average thickness of a member in mm. S Volumesurface ratio method 2 013 213 (224) 2T I +1.13 e (224) 3 Where v s = Volume to surface ratio in mm. CHAPTER 3 MATERIALS AND EXPERIMENTAL PROGRAMS 3.1 Introduction This chapter describes the mix proportions and ingredients of typical concrete mixtures used in this research, the method of preparation of the concrete mixtures, fabrication procedure of the test specimens and routine ASTM testing methods and procedures used in this study. 3.2 Concrete Mixtures Evaluated 3.2.1 Mix Proportion of Concrete The concrete mixtures were randomly selected from typical Class II, IV, V and VI concretes made with normalweight and lightweight aggregates. They are representative concrete mixes broadly used in Florida. The range of designed compressive strength of concretes varied from 4,000 to 11,000 psi at the age of 28 days. Class F fly ash and ground blastfurnace slag were used as additives in these mixes. Water reducing and air entraining admixtures were used throughout all the mixtures. Water to cementitious materials ratio for all the mixtures was determined according to the design strength of specified concrete. Workability of fresh concrete in terms of slump value, was controlled by the dosage of water reducer, super plasticizer and air entraining agents. Since strength of concrete is very sensitive to the variation of air content and water content, to meet target slump value, the dosage of water reducer and superplasticizer were adjusted rather than the dosage of air entraining agent and water. In addition, another reason to add air entraining agent to concrete is to improve durability of concrete. A total of 14 different concrete mixtures were evaluated. The detailed mix proportions for the fourteen mixtures are presented in Table 31. Miami Oolite limestone was used as a coarse aggregate for MixiF, 2F, 3F, 4F, 5S, 6S, 7S, and 8S. Stalite lightweight aggregate was used for Mix9LF and MixO1LS. Mix2GF, Mix3GF, Mix5GS and Mix7GS had identical mix proportion to the Mix2F, Mix3F, Mix5S and Mix7S with the exception that the coarse aggregate was replaced by a granite aggregate by volume. Fly ash was used in Mixes 1F, 2F, 3F, 4F, 9LF, 2GF and 3GF, and slag was used in Mixes 5S, 6S, 7S, 8S, 10LS, 5GS and 7GS. Mixes 1F, 2F, 3F, 4F, 5S, 6S, 7S, 8S, 9LF and 10LS were replicated. 3.2.2 Mix Ingredients The mix ingredients used in producing the concrete mixtures are described as follows: * Water Potable water was used as mixing water for production of the concrete mixtures. The water temperature was around 64F. * Cement TypeI Portland cement from CEMEX Company was used. The physical and chemical properties of the cement as provided by Florida State Materials Office are shown in Table 32 and Table 33. * Fly ash The fly ash used in this study was provided by Boral Company. Its physical and chemical properties as provided by Florida State Materials Office are presented in Table 34. * Slag The slag used in this study was provided by Lafarge Company. Its physical and chemical properties as provided by Florida State Materials Office are shown in Table 35. * Fine aggregate The fine aggregate used was silica sand from Goldhead of Florida. The physical properties of the fine aggregate as determined by Florida State Materials Office are shown in Table 3 6. The gradation of the fine aggregate is shown in Figure 31. The fine aggregate was ovendried before it was mixed with the other mix ingredients in the production of the concrete mixtures. * Airentraining admixture The airentraining admixture used was Darex AEA from W.R. Grace & Co. Darex AEA is a liquid admixture for use as an airentraining agent, providing freeze thaw durability. It contains a catalyst for more rapid and complete hydration of Portland cement. As it imparts workability into the mix, Darex AEA is particularly effective with slag, lightweight, or manufactured aggregates which tend to produce harsh concrete. * Coarse aggregates Three different types of coarse aggregates were used in this study. The first one is a normal weight Miami Oolite limestone. The second one is Georgia granite aggregate. The third one is called 'Stalite', a lightweight aggregate from South Carolina. The physical properties of these three coarse aggregates are displayed in Table 37. The gradation of the Miami Oolite is shown in Figure 32; the gradation of the Georgia granite aggregate is plotted in Figure 33; and the gradation of Stalite aggregate is presented in Figure 34. In order to have a good control on the moisture content of coarse aggregates, the coarse aggregates were soaked in water for at least 48 hours and then drained off the free water on the surface of aggregate before they were mixed with the other mix ingredients in the production of the concrete mixtures. * Waterreducing admixture The waterreducing admixture used included WRDA60, WRDA64, and ADVA120 from W.R.Grace & Co. WRDA 60 is a polymer based aqueous solution of complex organic compounds producing a concrete with lower water content (typically 810% reduction), improved workability and higher strengths. It can be used in ready mix, job site and concrete paver plants for normal and lightweight concrete. It also can be used in block, precast and prestress work. In addition, it offers significant advantages over single component water reducers and performs especially well in warm and hot weather climates to maintain slump and workability in high ambient temperatures. WRDA 64 is a polymer based aqueous solution of complex organic compounds producing a concrete with lower water content (typically 810% reduction), greater plasticity and higher strength. Except significant advantages like WRDA 60, WRDA 64 performs especially well in concrete containing fly ash and other pozzolans. ADVA 120, a superplasticizer, is a polymer based liquid organic compounds increasing plasticity of concrete. 3.3 Fabrication of Concrete Specimens 3.3.1 The Procedure to Mix Concrete The concrete mixtures investigated in this study were produced in the laboratory using a compulsive pan mixer with capacity of 17 cubic feet, as shown in Figure 35. For each mixture, thirteen (13) cubic feet of fresh concrete was produced to fabricate sixty (60) 6"x 12" cylindrical specimens. Table 31 Mix proportions of the 14 concrete mixtures used in this study Coarse Agg. No. of Mix W/C Cement (lbs/yd3) Fly ash (lbs/yd3) Slag (lbs/yd3) Mix1F* 0.24 800 Mix2F* Mix3F* Mix4F* 0.33 656 0.41 494 0.37 600    400 380 461 306  423   400 461 Mix5S* 0.33 400 Mix6S* 0.36 Mix7S* 0.41 Mix8S* 0.44 Mix9LF* 0.31 Stalite lightweight M 9L* Mix10LS* 0.39 Mix2GF 0.33 Mix3GF 0.41 Georgia Granite 41 Mix5GS 0.33 Mix7GS 0.41 Note: AEair entraining admixture; 197  306  602 150 282  656 144 494 123 400  197  * Mixtures were replicated. Water FA CA 3? 3. 3 ? ? Admixture I Miami Oolite (OIs/yed) (lbs/yr) (lbs/ydr) AE WRDA/ADVA (WRDA60)300Z 236.0 931 1679 7.5 OZ (WRDA60)300Z (ADVA120)600Z 265.6 905 1740 12.0 OZ (WRDA6 30OZ 254.0 1175 1747 0.5 OZ (WRDA60)33.40Z 278.0 1000 1774 2.0 OZ (WRDA60) 560Z (WRDA60)240Z 262.0 1062 1750 6.0 OZ (WDA60)240Z (ADVA120)480Z 270.0 1049 1736 1.9 OZ (ADVA120) 380Z 267.0 1121 1750 4.6 OZ (WRDA60)32.90Z 269.0 1206 1710 3.1 OZ (WRDA60)30.60Z 235.3 952 1239 9.6 OZ (WRDA64) 300Z 275.0 853 1300 8.8 OZ (WRDA64)31.70Z 265.6 909 1981 12.0 OZ (WRDA60) 300Z 254.0 1176 2027 0.5 OZ (WRDA60)33.40Z 262.0 1066 2045 6.0 OZ (WRDA60)240Z 267.0 1125 2045 4.6 OZ (WRDA60)482.90Z 267.0 1125 2045 4.6 OZ (WRDA60)32.90Z I Table 32 Physical properties of Type I cement Loss on Ignition Insoluble Setting Time Fineness Compressive Strength Compressive Strength (%) Residue (%) (min) (m2/kg) at 3 days (psi) at days (psi) 1.5% 0.48% 125/205 402.00 2400 psi 2930 psi Table 33 Chemical ingredients of Type I cement Ingredients Si02 A1203 CaO SO3 Na20K20 MgO Fe203 C3A C3S C2S C4AF+C2F (%) 20.3% 4.8% 63.9% 3.1% 0.51% 2.0% 3.3% 7% 59% 13.8% 15.8% Table 34 Physical and chemical properties of fly ash SO3 Oxide of Si, Fe, Fineness (%) Strength(7d) Strength (28d) Loss on Ignition % of Water (%) Al (%) (ASTM C430) (ASTM C109) (ASTM C109) (%) (%) (ASTM C311) (ASTM C618) 0.3 84 32 N/A 78 4.3 102 Table 35 Physical and chemical properties of slag SO3 Oxide of Si, Fineness (%) Strength (7d) (%) Strength (28d) Loss on Ignition % of water (%) Fe, Al (ASTM C430) (ASTM C109) (ASTM C109) (%) (%) (ASTM C311) (ASTM C618) 1.7% N/A 4 92% 129 N/A N/A Table 36 Physical properties of fine aggregate Fineness Modulus SSD Specific Gravity Apparent Specific Gravity Bulk Specific Gravity Absorption 2.30 2.644 2.664 2.631 0.5% Table 37 Physical properties of coarse aggregates Aggregate SSD Specific Gravity Apparent Specific Gravity Bulk Specific Gravity Absorption Miami Oolite Stalite Georgia Granite 2.431 1.55 2.82 2.541 2.360 2.85 2.80 3.03% 6.60% 0.58% 100  90 9 80 70o w \ 60 40  20 10  0 #4 #8 #16 #30 #50 #100 #200 Size of Sieve Figure 31 Gradation of fine aggregate (Godenhead sand) 100 90  8 0 _ 80 S 70 60 .I1 50^ 0 c50 a 5 40 c 30  I.. 20  20 10 0 1.5" 1" 0.5" 4# 8# 200# Size of Sieve Figure 32 Gradation of coarse aggregate (Miami Oolite limestone) 1.5" 1" 0.5" 4# 8# 200# Size of Sieve Figure 33 Gradation of coarse aggregate (Georgia granite) 1.5" 1" 0.5" 4# 8# 200# Size of Sieve Figure 34 Gradation of lightweight aggregate (Stalite) Figure 35 Compulsive Pan Mixer The procedures to fabricate cylindrical specimens were given as follows: * According to mix proportion design, measure out the coarse aggregate, fine aggregate, cement, mineral admixtures, water, high range water reducer, air entraining agent. * Place coarse aggregate and fine aggregate into the pan mixer to mix for about 30 seconds. * Place two thirds of the water together with the airentraining admixture into the mixer and mix for 1 minute. * Place cement, mineral additives, such as slag or fly ash, as well as certain amount of high range water reducer into the pan mixer and mix for 3 minutes, followed by a 2minute rest, then, followed by a 3 minute mixing. * Perform a slump test (according to ASTM C143) to determine whether or not the target slump has been reached. * If the target slump is not satisfied, add some more waterreducing admixture instead of water to adjust slump of fresh concrete. In doing so, we can assure the design strength of concrete will not be affected by adding extra water into concrete, which will change the water to cementitious material ratio. * Remix the fresh concrete for two more minutes. Then, perform another slump test to check if the target slump has been reached. Repeat this procedure until the target slump is achieved. 3.3.2 The Procedure to Fabricate Specimens After the mixing procedure is completed, place the fresh concrete into 6"x 12" plastic cylinder molds. Then two different procedures will be taken to consolidate the fresh concrete inside plastic cylinder molds. The first one is that, if the slump of the fresh concrete is less than 7 inches, fill each cylinder mold to one third of its height, and place the mold on a vibrating table for 45 seconds. Then fill the mold to another one third of its height, and place the mold on the vibrating table for 45 seconds. Then fill the mold fully, and place the mold on the vibrating table for 45 seconds. In addition, for the mixtures without any slump value, the vibrating time to consolidate concrete should be increased, or the vibrating intensity should be adjusted. The second one is that, if the slump is more than 7 inches, fill each cylinder mold in three layers, and rod each layers manually 25 times, as specified in ASTM C31. In doing so, we can assure that the mixtures with low slump value can be wellcompacted, while the mixtures with very high slump value will not be segregated due to overconsolidation. After consolidation, finish the surface of each concrete specimen with a trowel, and cover the top of the cylinder with a plastic lid to keep moisture from evaporating. Then, allow the concrete to be cured in the cylinder molds for 24 hours before demolding. But, for concretes with very low compressive strength after 24 hours, allow another 24 hours of curing in the mold before demolding. At last, set the demolded concrete specimens in the standard moist curing room for the specified curing time until testing. 3.4 Curing Conditions for Concrete Specimens The concrete specimens for compressive strength test, split tensile strength test, and elastic modulus test were cured in standard moist room until the age to be tested. Two different curing 66 conditions were applied to the concrete specimens of MixIF to MixO1LS for shrinkage and creep tests. The first condition is to cure the concrete specimens for 7 days in the moist room and followed by room condition for another 7 days. The second one is to cure the concrete specimens for 14 days in the moist room and followed by room condition for another 14 days. But, only one curing condition was applied to Mix2GF, Mix3GF, Mix5GS and Mix7GS, i.e.14 days in moisture room, and then in room condition for another 14 days. 3.5 Tests on Fresh Concrete In order to obtain concrete mixtures with uniform quality, ASTM standard tests, as shown in Table 38, on fresh concrete were performed and described in detail as follows: Table 38 The testing programs on fresh concrete Test Slump Air Content Unit Weight Setting Time Temperature ASTM ASTM ASTM ASTM ASTM Test Standard C143 C 173 C138 C403/C 403M C 1064 * Slump test Slump test was performed in accordance with ASTM C143 standard. The slump value was used to evaluate the consistency of fresh concrete. * Air content test Air content test was carried out in accordance with ASTM C 173 standard. The volumetric method was employed for this test. * Unit weight test The procedures of ASTM C138 standard was followed in running the unit weight test. This test was carried out to verify the density of concrete mixtures for quality control. * Setting time test ASTM C403/C 403M standard was followed to perform the setting time test. The mortar specimen for the setting time test was obtained by wetsieving the selected portion of fresh concrete through a 4.75mm sieve. The proctor penetration probe was employed for running this test. In this test, the initial setting time is determined when the penetration resistance equals 500 psi, and the final setting time is determined when the penetration resistance reaches 4000 psi. * Temperature test Temperature of the fresh concrete was determined in accordance with ASTM C 1064 standard. This test was used to ensure that the temperature of the fresh concrete was within the normal range, and that there was no unexpected condition in the fresh concrete. A digital thermometer was used to monitor the temperature of concrete. The properties of the fresh concrete for each of the ten mixtures are presented in Table 39. As can be seen from Table 39, the slump values of all the concrete mixtures fell in the range of target slump value other than Mix2F. The replicated Mix2F had a slump value higher than the target value. Also, the air contents of all the concretes were in the range of designed target value other than Mix2F and Mix5S, which had air content slightly higher than the maximum target value. Table 39 Properties of fresh concrete Mix7GS 2.25 Target slump 1.54.5 Air Target Air Air Content C ent Content (o) (%) 1.50 5 1.05.0 /1.25" 7.30 2.45.6 /4.50* 1.60 1.06.0 /2.50* 1.30 0.04.0 /2.00* 6.80 80 1.05.0 /3.75* 3.40 1.05.0 /2.25* 5.50 5.30 1.06.0 /3.75* 5.20 3.06.0 /3.00* 5.50 55 1.06.0 /5.25* 7.40 2.45.6 1.50 1.06.0 5.50 1.05.0 3.80 1.06.0 Unit Weight (lbs/yd3) 143.1 /145.5* 133.4 /137.7* 145.7 /143.9* 142.6 /143.8* 136.9 /141.6* 143.4 /141.4* 138.8 /138.0* 138.9 /140.4* 116.9 /117.78 111.6 /109.3* 144.9 150.1 145.8 147.3 Setting Time Initial 7h0min 2h 50min 4h 55min 3h 10min 5h 35min 7h 45min Final 8h 50min 4h 35min 7h 15min 4h 55min 7h 20min 10h Omin Mixture Temperature (F) 80/81* 79/73* 79/76* 74/74* 81/78* 79/81* 77/79* 80/76* 79/80* 77/78* 78 79 76 74 * From first phase study Mix Number MixIF Mix2F Mix3F Mix4F Mix5S Mix6S Mix7S Mix8S Mix9LF MixO1LS Mix2GF Mix3 GF Mix5GS Slump (in) 7.75 /9.75* 7.50 /4.25* 1.50 /2.00* 3.00 /3.00* 7.25 /9.00* 3.50 /5.50* 4.00 /5.75* 2.75 /3.00* 3.75 /2.50* 3.50 /2.75* 4.50 2.50 6.50 3.6 Tests on Hardened Concrete Routine ASTM standard tests on the hardened concrete specimens are given in Table 310. Table 310 The testing program on hardened concrete Compressive Splitting Tensile Elastic Test Shnnkage Creep Strength Strength Modulus Shrinkage Creep Test ASTM ASTM ASTM Described in Described in Standard C 39 C 496 C 469 this chapter this chapter 3.6.1 Compressive Strength Test Compressive strength test were performed on all the concrete mixtures investigated in this study. Through the compressive strength test, the strength development characteristics of the concretes typically used in Florida can be obtained. Furthermore, the results from compressive strength tests can be used to calibrate the prediction equation given by ACI 209R Code so that a reliable prediction equation can be obtained. The test procedure of ASTM C 39 standard was followed for compressive strength test. For each concrete mixture, three replicate 6"x 12" cylindrical specimens were tested for their compressive strength at the age of 3, 7, 14, 28, 56, and 91 days, with a total of 18 specimens tested. Before testing, both ends of concrete cylinders were ground in order to support the load uniformly. The loading rate was controlled at 1000 lbf per second. Two typical failure modes in the compression test are (1) column failure, and (2) shear failure. These two failure modes are shown in Figure 36. The compressive strength of the test specimen is calculated by dividing the maximum load attained from the test by the crosssectional area of the specimen, as shown by the following equation: p. 4p (31) i rr eD2 Where f is ultimate compressive strength of cylinder in psi; p, is ultimate compressive axial load applied to cylinder in lbs; D is diameter of cylinder specimen in inch. The average value of compressive strength from three cylinders will be taken as the compressive strength of the concrete. Figure 36 Typical failure modes of concrete cylinders in compression test 3.6.2 Splitting Tensile Strength Test (or Brazilian Test) Splitting tensile strength test is simple to perform than other tensile tests, such as flexural strength test and direct tensile test. The strength determined from splitting tensile test is believed to be close to the direct tensile strength of concrete. In this study, the testing procedure of ASTM C 496 standard was followed in running the splitting tensile strength test. A 6"x 12" cylindrical specimen, which is identical to that used for compressive strength test, with four lines drawn on the sides of specimen to mark the edges of the loaded plane to help align the test specimen before the load was applied, is placed with its axial horizontally between the platens of a testing machine. Figure 37 shows the loading configuration for this test. As shown in Figure 37, two strips of plywood as packing material, 3mm thick and 25mm wide, are interposed between the cylinder and the platens so that the force applied to the cylinder can be uniformly distributed. Then, the load will be applied and increased until failure by indirect tension in the form of splitting along vertical diameter takes place. 61__u Plywood 12" ttttttttttttttt t Figure 37 Loading configuration for splitting tensile test The splitting tensile strength of a cylinder specimen can be calculated by the following equation: 2p. T. = (32) 1 /. D Where T splitting tensile strength of cylinder in psi; p, maximum applied load to break cylinder in lbf. / length of cylinder in inch; D diameter of cylinder in inch. The splitting tensile strength of concrete will take the average value of splitting tensile strengths of three cylinders. Due to the sensitivity and susceptibility of the splitting tensile strength to the effects of internal flaws, such as voids, the results of some splitting tensile strength tests may be unusually low and may need to be discarded. For this reason, five extra concrete cylinders were prepared for use in repeating this test if needed. At last, the same curing conditions as those for the compressive strength test were used for the splitting tensile strength test. Three replicate specimens were tested at each of the curing times, which were 3, 7, 14, 28, 56, and 91 days. A total of 18 specimens per concrete mixture were tested for splitting tensile strength. 3.6.3 Elastic Modulus Test The testing procedure of ASTM C 469 standard was followed to determine the elastic modulus of the concrete specimens. In this method, the chord modulus of elasticity of concrete cylinders is determined when a compressive load is applied on a concrete cylinder in the longitudinal direction. A strain gage will be attached on the concrete cylinder to measure the deformation of the concrete cylinder during a compression test. The load and deformation data were recorded by means of a computer data acquisition system. A MTS machine, as shown in Figure 38, controls the loading rate by controlling displacement automatically. Prior to the test for modulus of elasticity, one of the three concrete cylinders was broken first to determine the compressive strength of concrete in accordance with ASTM C39 standard. Then, 40% of ultimate compressive strength of concrete specimen was applied on the other two concrete cylinders to perform the elastic modulus test. The cylinders for the modulus of elasticity test were loaded and unloaded three times. Then, the data from the first load cycle were disregarded. The average value from the last two load cycles was recorded as the elastic modulus of the concrete. Since the elastic modulus of concrete will vary with the age of concrete, the elastic modules of concrete at the ages of 3, 7, 14, 28, 56, and 91 days were evaluated. Throughout the test, the ambient temperature and relative humidity were maintained at 73 F and 100%, respectively. Figure 38 MTS system for elastic modulus and compressive strength test 3.6.4 Shrinkage Test For the concrete mixtures with either Miami Oolite limestone aggregate or Stalite lightweight aggregate, six 6"x 12" concrete cylinders were made to evaluate their shrinkage behavior under two distinct curing conditions. Three cylinders were cured for 7 days in a moist room, and then followed by a room condition curing for another 7 days. Another three cylinders were cured for 14 days in a moist room, and then cured for another 14 days in room condition. For concrete mixtures with Georgia granite aggregate, their shrinkage behaviors were investigated under just one curing condition, i.e. moist curing for 14 days, followed by curing in room condition for 14 days. Three pairs of gauge points, which were spaced 10 inches apart, were placed on each of concrete cylinder. A gaugepoint guide was used to position the gauge points on the plastic cylinder mold before the concrete was cast. Figure 39 shows a picture of the concrete with the gauge points attached on them after the molds have been removed. Figure 39 Cylindrical specimen with gage points installed A digital mechanical gauge was used to measure the change in the distance between the gage points as the concrete cylinder shrinks. The digital mechanical gauge has a resolution of 0.0001 in. Three sets of measurements were taken from each specimen. A total of nine sets of measurements were taken from the three replicate specimens for each concrete mixture. Measurements were taken every day in the first two weeks, and then once a week up to three months. The initial distance between the gauge points was measured immediately after required curing time was fulfilled. Then, the shrinkage test was run under the condition of the temperature of 73 F and 50% relative humidity. The shrinkage strain was taken as the average of the nine readings from the three replicate cylinders, and can be expressed as follows: 1 9 (1. 1 E = 1 (33) sh 9 1/ =1 0 Where 1, Measured distance between ith pair of gage points I i IC~ur rl It; ~L~  10 Original distance between ith pair of gage points measured immediately after demoded. CHAPTER 4 CREEP TEST APPARATUS DESIGN AND TESTING PROCEDURE 4.1 Introduction This chapter describes the design of the creep test apparatus, and its auxiliary tools, which include a gagepoint positioning guide for positioning gage points on a creep test specimen, and an alignment frame for aligning the specimens in a vertical direction. The creep testing procedures are also described in detail in this chapter. 4.2 Creep Test Apparatus 4.2.1 Design Requirements of Creep Test Apparatus In order to carry out the creep test program, a simple creep test apparatus was designed to satisfy the following design requirements: * Creep test apparatus should be capable of applying and maintaining the required load on specimen, despite of any change in the dimension of the specimen. * The bearing surfaces of the header plates shall not depart from a plane by more than 0.001 inch to insure even pressure distribution on the concrete test specimens. * Several specimens can be stacked for simultaneous loading so that more measurements can be made, and the reliability of test results will be increased by taking average of all the measurements. * The height between two header plates shall not exceed 70 inches. If the height between two header plates is over 70 inches, the apparatus will not be easily operated manually. Also, if the total height of the stacked test specimens is very high, the specimens may buckle easily under load. * The applied load should be controlled so that it will vary by less than 2% of the target applied load. * Means shall be provided to make sure that concrete specimens are centered properly and vertical. The designed creep test apparatus, which is spring supported system, is shown in Figure 4 1. The detailed design of creep apparatus used in this study is presented as follows. 4.2.2 Design of Creep Apparatus 4.2.2.1 The determination of the maximum capacity of the creep Apparatus In this study, the maximum design capacity of creep apparatus was determined according to the maximum compressive strength (10 ksi) of concrete mixtures commonly used in Florida. Creep test was run under the loading condition of 50% of compressive strength of concrete on 6"x 12" cylindrical concrete specimens. Thus, the maximum load applied to the creep frame can be computed as: Pmax = 0.5 x 10000 x tr x 32 = 1413001bf If a 4"x 8" cylindrical concrete specimen is used, the creep test can be run on the concrete with compressive strength as high as 22 ksi. 4.2.2.2 The design of springs The spring constant of the larger spring (k,) was selected as 9822 lbf/in, while the spring constant of the smaller spring (k2) was selected as 3314 lbf/in. The maximum travel distance (A) for both springs is 1.625 in. If nine sets of springs are used, the maximum load (Pspnng ) that the springs can hold can be calculated to be: Psrng =9x(k +k)xA = 1.92x105lbf>Pmax OK Thus, the spring capacity is ok. It is of importance to mention that the design maximum travel distance of spring can not be more than the maximum travel capacity of the springs in order to maintain the load on specimen constant, and keep the frame stable. Load Cell Hydraulic Jack Circular Steel Plate 01.125in' Gauge Concrete 1 Cylinder Circular Steel Springs 01.25in Figure 41 Creep test apparatus t'l  " tc 4o 00 * S 18in N 4.2.2.3 Design of header plate I II ' ..' .   I :    ,II :I! .. . . : ' _Z o e ...... ... .. 6i 6in I II, I 1 .25in Figure 42 Boundary conditions used for finite element analysis In order to apply load uniformly to the test specimens, the deflection of header plate should not deviate too much for a plane surface when the specimens are loaded. The required thickness of the header plates was determined using a finite element analysis. The steel plate was modeled as an isotropic elastic material with an elastic modulus of 29,000 ksi and Poisson's ratio of 0.30, which are typical properties of steel. The plate was modeled as fixed from rotation about the x, y and z axis along the four boundary lines along the four holes on the steel plate as shown in Figure 42. The loading zone was modeled as a circular area identical to the cross sectional area of a 6 inch diameter concrete cylinder. The maximum load used in the analysis had a pressure of 5000 psi, which is 50% of the maximum compressive strength of concrete investigated in this study. Figure 43 Finite element mesh used in the header plate analysis A TIME 1.0DO DISP HAG 4619. Z A DISPLACEMEN7 D TIME 1.000 I 0 o.oo O.CO39M NI . A 0.002P9 0.0003 MAXIMUM MNIMUM Figure 44 Contour plot of deflection of header plate The finite element mesh used in the analysis consisted of triangle elements and rectangular elements as shown in Figure 43. The header plate with a thickness of 1.5 inches was analyzed. The deflection contour plot is shown in Figure 44. As we can see from Figure 44, the deflection from center of header plate to the position 3 inches away from center changes from 0.00408 to 0.0033 inch. In other words, if the test specimens are loaded to a maximum pressure of 5,000 psi, the deflection of steel plate will differ by less than 0.00078 inch, which is less than 0.001 inch. Thus, a header steel plate with a thickness of 1.5 inches was determined to be adequate and selected for use. A 1IME 1.0~ DISP HAG 4698. Z D I NI A 4.2.2.4 Determination of the size of steel rod When the concrete specimens are loaded in the creep frame, each of the four steel rods will carry one quarter of total load. The steel rods are 1.125 in. in diameter and are made of high strength alloy steel with yield strength of 105,000 psi. If the concrete specimens are loaded up to the maximum capacity of the creep apparatus of 141,300 lbf, the maximum stress in the steel rods would be equal to: 141300 = 35556psi 4.0.56252 2 This maximum possible stress in the steel rods is less than half of the yield strength of the steel rod, which is 105,000 psi. Thus, the selected steel rod meets the design requirements. 4.2.2.5 Stress relaxation due to the deflection of header plate and creep of concrete When the full capacity of creep frame is used, the total stress released due to the plate deflection can be approximated as follows: Prelaxed = Adeflecton x kol = 0.0041 x 13136 x9 = 485pounds Where Adeflecton is the maximum deflection of header plate, and kpng is the elastic constant of spring. While according to the design requirement, the allowable load relaxation is 141300 x 0.02 = 2826pounds In addition, since partial load will be relaxed due to the creep of concrete, the applied load to the concrete specimen should be adjusted in order to keep the load the same as the initially applied one. To have an error of less than 2,826 lbf in the applied load, the following inequality has to be satisfied: 36 cr. ktota + 4851bf < 28261bf Solving the above inequality, we obtain that s,, < 0.0006 This means that the applied load should be adjusted at every 0.0006 increment of creep strain. Otherwise, the load relaxed would be more than 2826 lbf, the allowable maximum load relaxation. 4.3 Design of GagePoint Positioning Guide Three pairs of gage points with a gage distance of 10 inches are to be placed in each test concrete specimen. A gagepoint positioning guide, as shown in Figure 45, was designed for use in positioning the gaugepoints on the plastic cylinder mold. By inserting a 6"x 12" cylinder mold into gagepoint position guide and tightening the six screws on the guide, the precise locations for the three pairs of gage points, with a gage distance of 10 inches, can be marked conveniently on the mold. Three lines of gage points are uniformly distributed with 120 angle along the periphery of specimen. The use of the gage positioning guide is of great importance because the maximum travel distance of mechanical strain gage is 0.4 in. The mechanical strain gage can not be used to measure a distance of more than 10.4 inches. Thus it is very important that the two gage points be place at an exact distance of 10 inches from one another. Figure 46 shows a picture of the gaugeposition guide. Figure 47 shows a picture with a plastic cylinder inside the gaugeposition guide. 4.4 Design of Alignment Frame An alignment frame was designed and constructed to be used to align the concrete specimens in a vertical direction when they are placed in the test frame. Figure 48 shows the design of the alignment frame. The alignment frame consists of one piece of angle steel and one piece of channel steel with three pieces of 0.5"x2"x 10" steel plates welded on them respectively. They are connected together by using 6 steel rods. The use of the alignment frame is described in creep testing procedure. D 6.05" o Figure 45 Design of Gagepoint positioning guide Figure 46 Gauge position guide Figure 47 Plastic cylindrical mold inside gauge position guide I 4.5 Mechanical Strain Gauge A mechanical strain gauge, as shown in Figure 49, was used to measure the distance change between two gauge points. The instrument frame is made of aluminum alloy and has five master settings of 2", 4", 6", 8", and 10" that are easily set for gauging. The digital indicator has a minimum graduation of 0.0001". In this study, the master setting of 10" was selected so that the mechanical strain gage is suitable for the measurement of longitudinal strain to the nearest 10 millionths. In addition, the effective range of displacement measurement is 0.3". 4.6 Other Details on Creep Apparatus For each test frame, three 6"x 12" cylindrical specimens are placed on top of one another and tested under the same load. The load is applied by means of an electronic hydraulic jack (with a maximum capacity of 200,000 lbs) and monitored by a load cell with a digital readout indicating the load applied. The load cell has a capacity of 200 kips, and the minimum readable digit of 10 pounds. When the desired load is reached, the nuts on the threaded rods is tightened so that they are snugly pressing against the plate underneath the hydraulic jack so as to hold the plate in that position, and thus holding the applied load. After the nuts are positioned properly to hold the applied load, the jack and the load cell can be removed from the test frame and used to load another test frame. The springs at the bottom of the creep frame help to maintain the balance of creep frame as well as a constant load on the specimens despite any change in its length, as the concrete specimens creep under load. Up to 9 sets of springs can be used in this test frame. Figure 410 shows the positions of the springs in the test frame. Each set of springs consists of a smaller spring sitting inside a larger spring. In addition, the springs should be manufactured so that both ends of spring should be flatted, and nine sets of springs should have the same height, and positioned symmetrically to keep load distribution evenly. In doing so, there is no spherical bearing device needed to guarantee the load to be evenly transferred to the specimens. As the concrete specimens are loaded in the creep frame, the rectangular steel plates, which are at the top and bottom of the test specimens, are deflected slightly. To keep the loading surfaces flat and the test specimens vertical when the load is applied, two 1inch thick circular steel plates with a diameter of 6 inches are placed on the top and bottom of the stack of concrete test specimens, as shown in Figure 41. Both surfaces of the circular plate should be polished to avoid of any uneven pressure on the concrete cylinder. 4.7 Creep Testing Procedure 1. Install gauge points on plastic cylindrical molds using the Gauge Position Guide. Each creep test specimen contains three pairs of gage points installed on concrete cylinder using Gauge position guide, which are placed 10 inches apart from each other. 2. Place the fresh concrete in the plastic cylinder molds. Place the fresh concrete into plastic cylinder in three layers. Consolidate each layer with 45 seconds of vibration on a vibrating table. After consolidation, the top surface of concrete should be finished gently. This is a very important detail in making specimen to avoid cracking around gauge insert as shown in Figure 411. If too much pressure is applied to finish the surface, gauge inserts may be pushed downward because the plastic cylinder is not very stiff and can not keep the gauge inserts from being pushed downward. Once pressure is released, the gauge insert will return to its original position, while concrete can not because plastic deformation can not be recovered. Thus, some space between gauge insert and concrete will be created and it will affect the measurement. 3. Demold the concrete specimens after 24 hours of curing. Place the specimens in a moist room to cure for the required time. 4. Grind both end surfaces of each concrete cylinder. Both end surfaces of specimen should be ground in order to make them even, as shown in Figure 412. 5. Cap both ends of each cylinder using sulfur mortar to make end surfaces smooth and even. 6. Using the alignment frame designed for this study to stack the three replicate specimens vertically on top of one another. 7. Put two circular plates on top of concrete cylinder as well as at the bottom of concrete cylinders. 0.5in         . C) F ~  I r  3  . . ! II I i II :4 10.OOin i I r 4 0.5in  '0.5in I I I I I I I I I I I I I I 1.5M Figure 48 Schematic of alignment frame design 87 0 O o* 0T 0T :1 75jn II I __iljlllllllg~jg~jg~gj~ _ DO.5in ?   lllllllllllllllII I rTT TT TT TI II re, r Me hac gag Figure 49 Mechanical gauge Inside Outside Large 02.94i 05.50in Small  spring 6in 12in Figure 410 Positioning springs on the bottom plate    Pressure applied while finishing Gauge Insert Space Created Figure 411 Cracking around gauge insert Figure 412 Concrete cylinder with both end surfaces ground 8. Adjust the creep frame and concrete specimens to make sure the specimens are centered and vertical. The creep frame can be adjusted through moving the header plate back and forth with the nuts on the top of the plate. As shown in Figure 413, the centers of header plate and the plate on the top of springs are marked. On each plate is also marked a 3 inch diameter with 8 mark points along the boundary of the circle. If the concrete column consisting of three cylinders is placed so that it lines up with the circles on the header and the bottom plates, then the concrete cylinders are centered and vertical. 9. After the concrete specimens are centered, turn the nuts supporting the header plate downward at least 1.65 in. away from the bottom of header plate to avoid the header plate contacting with the nuts once load is applied. Then, tighten the four nuts on the top of header plate slightly to hold the centered concrete specimens. Header Plate Mark . Point 1.65in Circular Plate (D6in Figure 413 How to center the specimens into creep frame 10. Set up a hydraulic jack and load cell in the creep frame, and check the position of hydraulic jack to make sure that it is coaxial with concrete specimens in order to avoid loading the concrete specimens eccentrically. As shown in Figure 414, in order to make the hydraulic jack coaxial with concrete specimens, the center of the header plate has also been marked on the top side. A circle with diameter identical to the diameter of jack cylinder has also been drawn on top of the header plate, with 4 marks hammered along the boundary of the circle 11. As shown in Figure 415, check the plate on the top of load cell to make sure that the plate is level. Then, tighten slightly the four steel nuts holding the top plate. 12. Preload the frame up to 500 lbf to properly seat the concrete test specimens in the creep frame. 13. Take the initial measurements, which are the initial distance between two gauge points. 14. Apply the load through the electronic hydraulic jack up to the target load. It is strongly recommended to use electronic hydraulic jack because of several advantages in using electronic hydraulic jack. Firstly, by using electronic hydraulic jack, the load can be applied to the loading frame continuously. Secondly, since the electronic hydraulic jack can apply load on the cylinder within 1 minute, the instantaneous measurements can be taken within seconds immediately after the loading procedure was completed. Thus, the instantaneous measurement taken in this way is very close to the true elastic deformation. Thirdly, in using the electronic hydraulic jack, the dynamic effect, which can cause the cylinders to break easily, can be avoided. In addition, less effort is needed to load frame in comparison with using manual hydraulic jack, which takes hundreds of pushes to reach the desired load level. Jack Cylinder Mark Point Figure 414 How to center the hydraulic jack cylinder Jack Cylinder Load cell Figure 415 Leveling the plate on the top of load cell 15. Immediately after the target load is reached, tighten the four nuts on the top of the header plate to hold the load on the specimens. r\ff 1 0 16. Take instantaneous measurements using the digital mechanical gage immediately after loading. Then take the measurements in 1 hour, 3 hours and 6 hours. Then every day in the first two weeks, and then once a week until 91 days, and then once a month if tests were kept going. 17. Adjust load at every 0.0008 increment of creep strain to keep the load loss due to creep relaxation less than 2% of total load applied at the beginning. It deserves to emphasize again that it is important to take the first set of readings as quickly as possible in order to obtain a more accurate instantaneous deformation of the concrete. Otherwise, substantial early creep deformation may have taken place before the initial readings can be taken. The first set of readings can be taken within 3 minutes. The creep strain was calculated by subtracting the shrinkage strain from the total strain as follows: 9 1 / 1 1I ET T S 0(i) 0(i) Where Ec Creep strain of concrete cE The sum of creep strain and shrinkage strain Es Shrinkage strain of concrete I The measurement taken from the ith pair of gage points for creep test IT The initial length of the ith pair of gage points for creep test Is The measurement taken from the ith pair of gage points for shrinkage test Is The initial length of the ith pair of gage points for shrinkage test i No. of pair of gage points from 1 to 9 The creep coefficient, which is used in concrete structure design, is calculated by taking the ratio of creep strain of the concrete at the testing age to elastic strain of concrete at the same curing age. It can be expressed as follows: sC C C (42) cr Where C, Creep coefficient Ec Creep strain of concrete EE Elastic strain of concrete Creep modulus, Ec, is computed dividing the applied stress by the total strain without including shrinkage strain, as shown by Equation 43. E (43) c E + 4.8 Summary on the Performance of the Creep Apparatus The creep apparatus designed in this study is capable of applying and maintaining the required load on the test specimens. Three specimens can be stacked for simultaneous loading. The unevenness of the deflection of bearing surface of the header plates is less than 0.001 in. and the pressure distribution on the concrete specimens varies by less than 0.026%, or 1.5 psi. Load can be applied to a precision of 10 lbs, as a load cell with resolution of 10 lbs is used control the applied load. The mechanical gauge used is able to measure longitudinal strain to a precision of 0.00001. Strains are measured on three gage lines spaced uniformly around the periphery of the specimen. An electronic hydraulic pump system is used to apply load to the creep frame. This enables the loading process to be done in seconds, and instantaneous strains can measured from creep test within a short time after loading. The gauge point position guide, which has been designed to position gauge points on a plastic cylindrical mold, is a very effective and important auxiliary tool in preparation of test specimens. It enables the placement of gauge points at accurate locations on the test specimen so that the maximum travel distance of mechanical gauge will not be exceeded and measurement error can be reduced. The alignment frame, which has been designed to align concrete specimens vertically in the creep frame, makes the job of stacking three concrete specimens together for testing possible. Experimental results indicate that creep apparatus designed in this study is effective, reliable and practical. It can be used to run creep test on concrete with a maximum compressive strength up to 10,000 psi if 6"x 12" cylinder specimens are used. If 4"x8" cylinder specimens are used, the maximum compressive strength of the concrete can be as high as 22,000 psi. CHAPTER 5 ANALYSIS OF STRENGTH TEST RESULTS 5.1 Introduction This chapter presents the results from compressive strength, splitting tensile strength and elastic modulus tests on the 14 concretes mixes evaluated in this study. The effects of various factors on strength are discussed. The prediction equations establishing interrelationship between compressive strength and splitting tensile strength are given. The prediction equations relating compressive strength to elastic modulus are also presented. 5.2 Results and Analysis of Compressive Strength Tests The average compressive strengths at various curing times of the fourteen concrete mixes evaluated are presented in Table 51. The individual compressive strength values are shown in Table Ai in Appendix A. Table 51 Compressive strength of the concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag Age of T g 3 7 14 28 56 91 MixIF 0.24 20% 8077 8572 8993 9536 10771 11267 Mix2F 0.33 20% 4077 4658 6028 6506 6838 7607 Mix3F 0.41 20% 5289 6470 7567 8241 8449 9426 Mix4F 0.37 20% 5712 6919 7114 7236 8996 9271 Mix5S 0.33 50% 5554 7235 8248 8832 9139 9456 Mix6S 0.36 50% 6375 7699 8587 9111 9529 9661 Mix7S 0.41 70% 4324 5374 5927 6392 6794 6917 Mix8S 0.44 50% 4795 6114 6939 7525 8119 8208 Mix9LF 0.31 20% 3039 3941 5136 5929 6690 6961 MixO1LS 0.39 60% 1467 2191 2937 3744 4312 4727 Mix2GF 0.33 20% 3885 4952 5807 6469 6952 7201 Mix3GF 0.41 20% 3818 5151 6137 7262 7782 8041 Mix5GS 0.33 50% 2961 4692 5692 7008 7854 8105 Mix7GS 0.41 70% 2267 4303 5222 6612 6741 7233 5.2.1 Effects of Water to Cement Ratio and Water Content on Compressive Strength In engineering practice, the strength of concrete at a given age and cured in water at a prescribed temperature is assumed to depend on primarily on water to cementitious materials ratio and the degree of compaction. In this study, for the eight selected concrete mixtures using Miami Oolite limestone aggregate, the effects of water to cementitious materials ratio on compressive strength at ages of 28 days and 91 days are shown in Figure 51 and Figure 52 respectively. The graph of compressive strength versus water to cementitious materials ratio is approximately in the shape of a hyperbola. Compressive strength tends to decrease as water to cementitious materials ratio increases. Water content is another important factor influencing the strength of concrete because the higher the water content, the more porous the hardened concrete tends to be. As shown in Figure 53 and Figure 54, compressive strength of concrete decreases dramatically as water content increases. 16000 14000 12000 10000 8000 6000 4000 2000 0 0.1 0.2 0.3 0.4 Water to Cementitious Materials Ratio 0.5 0.6 Figure 51 Effects of water to cementitious materials ratio on compressive strength at 28 days 16000 14000 12000 10000 8000 6000 4000 2000 0 0 0.1 0.2 0.3 0.4 Water to Cementitious Materials Ratio 0.5 0.6 Figure 52 Effects of water to cementitious materials on compressive strength at 91 days 16000 14000 12000 10000 8000 6000 4000 2000 0 220 230 240 250 260 270 Water Content (Ibs/yard3) Figure 53 Effects of water content on compressive strength at 28 days O O 0 o O ^^o 0 8 ^ 280 290 o 0 0 0 0 a 00 i i i i i i 16000 14000 12000 0 10000 S8000 . 6000 E 4000 2000 0 220 230 240 250 260 270 280 290 Water Content (Ibs/yard3) Figure 54 Effects of water content on compressive strength at 91 days 5.2.2 Effects of Aggregate Types on Compressive Strength The influence of coarse aggregate type on compressive strengths of four concrete mixtures is shown in Figures 55 through 58. Figure 55 shows the compressive strength development with time for Mix2F and Mix2GF containing 20 % fly ash. Both concrete mixtures have identical mix proportions other than the different types of aggregate. Miami Oolite limestone aggregate was used for Mix2F, and Georgia granite aggregate was used for Mix2GF. It can be seen that the compressive strength of Mix2F is comparable to that of Mix2GF at various curing ages. For Mix5S and Mix5GS, the different aggregate types gave considerable impact to the compressive strength. As can be seen from Figure 56, Mix5GS using Georgia granite aggregate had very much lower compressive strength than Mix5S using Miami Oolite limestone aggregate at various ages. The same phenomenon can also be observed from Mix3F and Mix3GF, as shown in Figure 57, and Mix7S and Mix7GS, as depicted in Figure 58. O O O O O o o o According to the concrete mixtures investigated in this study, the concrete mixtures using Miami Oolite limestone as coarse aggregate developed higher compressive strength than those using Georgia granite as coarse aggregate. The cause can be attributed probably to the shape of aggregate, surface characteristic and other physical properties such as water absorption. Most of aggregate particles of Georgia granite have elongated and flaky shape, which is not desirable to be used for high strength concrete because flaky particles tend to be oriented in one plane, with bleeding water and air voids forming underneath. Thus, the interfacial transition zone between aggregate and hardened mortar may be weaker causing the compressive strength of concrete to be lower. Most of the aggregate particles of Miami Oolite limestone have spherical shape, which is preferred for durable concrete mix because the spherical aggregate particles have lower surface to volume ratio, and they will pack better in a mortar matrix. The surface texture of Georgia granite aggregate is very dense and smooth, which may have a disadvantage in developing tight interlock between aggregate and mortar matrix. Miami Oolite limestone has a very rough texture and appreciable voids on the surface, and thus strong interlock can be formed since the cement slurry can penetrate into those voids. The water inside limestone aggregate can migrate outward as cement hydration proceeds since the relative humidity gradient will be generated between internal aggregate and mortar. This water may possibly provide the water needed for hydration of the cement as moisture is lost through evaporation to the environment. Figure 55 Effects of coarse aggregate type on compressive strengths of Mix2F and Mix2GF Figure 56 Effects of coarse aggregate type on compressive strength of Mix3F and Mix3GF Figure 57 Effects of coarse aggregate type on compressive strength of Mix5S and Mix5GS Figure 58 Effects of coarse aggregate type on compressive strength of Mix7S and Mix7GS 5.2.3 Effects of Fly Ash and Slag on Compressive Strength of Concrete Fly ash and slag are used mandatorily in Florida mainly for concrete durability purpose. The investigation on their effects on the development of compressive strength of concrete mixture is of great importance because of significance of their use in concrete. In this study, fly ash was as a cement substitute in an amount of 20% of total cementitious materials by mass, and slag was in an amount of 50%70% of total cementitious materials by mass. The strength development characteristics of fly ash concrete and slag concrete with time were normalized as the ratio of compressive strength at various curing ages to the compressive strength at 91 days and the normalized values are presented in Table A2 in Appendix A. The strength development characteristics of two typical fly ash concretes and two slag concretes are illustrated in Figure 59. As can be seen from Figure 59, the fly ash concretes had significant strength gain from 28 days to 91 days, while the slag concretes had already achieved more than 90% of their 91day strength at 28 days. c 0.95 " o_ 0.85 ' // SMx1FFly ashW/C=0 24 7 0.80 _ Mx6SSlagW/C=0 36 o X Mlx5SSlagW/C=0 33 0) S0.75 0.70 0 20 40 60 80 100 Ages (days) Figure 59 Effects of fly ash and slag on compressive strength of concrete 5.2.4 Prediction of Compressive Strength Development Knowledge of the strengthtime relation is of great importance when a structure is put into service, i.e. subjected to full loading condition and for long time duration. The gain in strength after 28 days can be taken into consideration in design. In some other cases, for instance, in precast or prestressed concrete, or when early removal of formwork is required, the strength at early ages needs to be known. According to ACI 209R5, a general equation for predicting compressive strength at a given age has the following form: fco= a+j t c28 (51) Where a in days and / are constants, f28 is compressive strength of concrete at 28 days, and t in days is the age of concrete. Equation 51 can be transformed into fc(t) = fu (52) Sa/3+t cu Where ac/l is the age of concrete in days at which one half of the ultimate compressive strength of concrete, fc is reached. For the tests using 6xl2in cylinders, type I cement and moist curing condition, two constants, the average values of a and f, are equal to 4.0 and 0.85 respectively. The ranges of a and / in Equation 51 and 52 for the normal weight, sand lightweight, and all lightweight concretes (using both moist curing and steam curing, and type I and III cement) given by Branson, D.E.; Meyers, B.L.; and Kripanarayanan, K.M[Branson, D.E et al. 1973] are: a=0.05 to 9.25, and / =0.67 to 0.98. They were obtained from the tests on 88 6xl2in concrete cylinders and cited by ACI 209 COMMITTEE REPORT in 1996. As mentioned in ACI 209R4, the values of a and / are not applicable to the concretes containing pozzolanic materials, such as fly ash and slag. Furthermore, ACI 209R4 indicates that the use of normal weight, sand lightweight, or all lightweight aggregate does not appear to affect a and / significantly. In this study, regression analysis using the form of ACI 209R5 equation (as shown in Equation 51) was performed on the results of compressive strength tests on the 432 concrete cylinders from this study to determine the a and / values for each mix. Table 52 shows the a and /values for all the mixes from this analysis. The detailed results of this analysis are presented in Table 53. Table 54 presents the average a and / values of the different concrete f'(t) f'(t) mixes as grouped by aggregate type. Table 54 also shows the time ratios ( and f at f"28 f different during times for these different groups of concrete mix in comparison with the corresponding values as predicted by the ACI209R equation. As can be seen from Table 52, there is substantial difference between a and / values among the different mixes. For the concrete mixtures using Miami Oolite limestone coarse aggregate, the value of a varies from 1.1 to 2.6, and its average value of 1.89 is significantly lower than 4.0 recommended by the ACI209 code; and the value of 3 is in the range of 0.82 to 0.93, and its average value of 0.90 is slightly higher than 0.85 given by the ACI code. This means that the concrete mixes using Miami Oolite limestone aggregate and fly ash and slag tend to develop strength faster than the concrete mixtures as predicted by the ACI209R equation. For the concrete mixtures using Georgia granite aggregate, the value of a varies from 2.6 to 5.3, and its average value of 4.12 is close to 4.0 recommended by the ACI code; and the value of P is in the range of 0.82 to 0.89, and its average value of 0.86 is agreeable with 0.85 given by the ACI code. Thus, this indicates that the concrete mixtures using Georgia granite aggregate had similar strength development as predicted by the ACI equation. For the concrete mixtures using the Stalite lightweight aggregate, the average value of ac is 5.5 and the average value of 3 is equal to 0.78. This indicates that coarse aggregate type can have significant effects on the strength development process. 5.3 Analysis of Splitting Tensile Strength Test Results The average splitting tensile strengths at various curing times of the fourteen concrete mixes evaluated are displayed in Table 55. The individual splitting tensile strength values are shown in Table A3 in Appendix A. 5.3.1 Effects of Water to Cement Ratio on Splitting Tensile Strength Water to cementitious materials ratio has a significant effect not only on compressive strength, but also on splitting tensile strength. Figure 510 and Figure 511 show the effect of water to cementitious materials ratio on splitting tensile strength of concrete at 28 days and at 91 days respectively. They indicate that splitting tensile strength decreases as water to cementitious materials ratio increases. 5.3.2 Effects of Coarse Aggregate Type on Splitting Tensile Strength The effect of coarse aggregate types on splitting tensile strength of concrete was evaluated on four concrete mixtures. Mix2F, Mix3F, Mix5S, and Mix7S have Miami Oolite limestone as coarse aggregate, and Mix2GF, Mix3GF, Mix5GS, and Mix7GS have Georgia granite as coarse aggregate. Mix2F and Mix2GF, Mix3F and Mix3GF, Mix5S and Mix5GS, and Mix 7S and Mix7GS have identical mix proportions with the exception that a different coarse aggregate of the same volume was used. As shown in Figures 512 through 515, the effects of coarse aggregate types on splitting tensile strength of concrete are quite significant. In comparison with Mix2F, Mix3F, Mix5S and Mix7S, the four mixtures using Georgia granite Table 52 Results of regression analysis for prediction of compressive strength development using ACI 209 equation a by ACI 1.10 2.67 2.25 1.57 2.04 1.57 1.79 2.15 4 4.20 6.74 2.64 3.51 4.99 5.35 Square root of Absolute S p sum of squares by by ACI b A Modified ACI Equation 0.90 673 0.89 371 0.90 343 0.83 676 0.92 67 0.94 125 0.92 275 0.91 0.85 150 0.82 230 0.74 131 0.89 180 0.88 197 0.82 160 0.86 269 Square root of Absolute sum of squares by ACI Equation 1904 541 792 1571 886 1214 1698 726 261 385 445 257 311 547 Mix M1F M2F M3F M4F M5S M6S M7S M8S M9LF M10LS M2GF M3GF M5GS M7GS Table 53 Results of regression analysis on the prediction of compressive strength development using ACI 209 equation Results i M1F M2F M3F M4F M5S M6S M7S a 1.098 2.673 2.252 1.573 2.039 1.574 1.792 P 0.9017 0.8886 0.9043 0.8261 0.9231 0.9363 0.9213 a(SE) 0.3482 0.4901 0.3071 0.4732 0.05387 0.08311 0.1261 P3(SE) 0.03574 0.0344 0.02365 0.04108 0.004384 0.007592 0.01085 0.2026 to 1.413 to 1.463 to 0.3568 to 1.901 to 1.361 to 1.468 to a (95%CI) 1.993 3.933 3.042 2.790 2.178 1.788 2.116 0.8098 to 0.8002 to 0.8435 to 0.7205 to 0.9118 to 0.9168 to 0.8934 to p (95%CI) 0.9935 0.9770 0.9651 0.9317 0.9344 0.9558 0.9492 DOF 5 5 5 5 5 5 5 R2 0.9736 0.9801 0.9902 0.9625 0.9997 0.9989 0.9978 ASS 2266000 769806 589302 2168000 22420 73904 75810 Sy.x 673.3 392.4 343.3 658.4 66.96 121.6 123.1 Points Analyzed 7 7 7 7 7 7 7 Table 53 Continued Six Mix2GF Mix3GF Mix5GS Mix7GS M esuts M8S M9LF M10LS Mix2GF Mix3GF Mix5GS Mix7GS Results ca 2.152 P 0.9054 a(SE) 0.1427 P (SE) 0.01122 1.786 to a (95%CI) 2.519 0.8765 to p (95%CI) 0.9343 01.9343 DOF 5 R2 0.9978 ASS 112202 Sy.x 149.8 Points Analyzed 7 4.203 0.8239 0.4144 0.02191 3.138 to 5.268 0.7675 to 0.8802 5 0.9927 263786 229.7 7 6.744 0.74 0.5222 0.01987 5.402 to 8.087 0.6889 to 0.7911 5 0.9949 85405 130.7 7 2.635 0.8916 0.2175 0.0154 2.076 to 3.194 0.8520 to 0.9312 5 0.996 151718 174.2 7 3.512 0.8777 0.2677 0.01618 2.824 to 4.200 0.8361 to 0.9193 5 0.996 193402 196.7 7 4.993 0.815 0.2823 0.01346 4.267 to 5.718 0.7804 to 0.8496 5 0.9975 128354 160.2 7 5.345 0.8554 0.4698 0.02215 4.137 to 6.552 0.7984 to 0.9123 5 0.9941 251535 224.3 7 Table 54 Values of the constants,a, Time Type of Cement Ratio Curing Type P and c/1 and the time ratios from Equation 51 and 52 Aggregate a, 3 and Concrete ages (days) type ca/ 3 7 14 Ultimate 28 56 91 in time ACI 209R4 Miami Oolite Limestone Granite Stalite ACI 209R4 Miami Oolite Granite Stalite a=4.00 3=0.85 a=1.89 P=0.90 a=4.12 P=0.86 a=5.50 3=0.78 c/P=4.71 c/P=2.10 c/P=4.79 c/p=7.05 0.46 0.70 0.88 1.00 1.08 1.12 1.18 0.65 0.85 0.97 1.00 1.07 1.09 1.11 0.45 0.69 0.87 1.00 1.07 1.10 1.16 0.38 0.64 0.85 1.00 1.14 1.19 1.28 0.39 0.59 0.39 0.29 0.60 0.77 0.59 0.50 0.75 0.87 0.75 0.67 0.86 0.93 0.85 0.80 0.92 0.96 0.95 0.89 0.95 0.98 0.95 0.93 1.00 1.00 1.00 1.00 Moist cured f (t) fc28 f(t) Moist cured Table 55 Splitting tensile strengths of the concrete mixtures evaluated (psi) W/C Fly ash 0.24 20% 0.33 20% 0.41 20% 0.37 20% Mix Number MixIF Mix2F Mix3F Mix4F Mix5S Mix6S Mix7S Mix8S Mix9LF Mix10LS Mix2GF Mix3 GF Mix5GS Mix7GS 20% 20% 20% Slag Age of Testing (days) 3 592 408 513 457 50% 442 50% 570 70% 426 50% 372 350 60% 212 352 382 50% 282 70% 245 1200 1000 U) 600 D U) C 2 400 ) 200 Cl) 200 0 ! 0.1 0.2 0.3 0.4 0.5 0.6 Water to cementitious Materials Ratio Figure 510 Effects of water to cement ratio on splitting tensile strength at 28 days 0.33 0.36 0.41 0.44 0.31 0.39 0.33 0.41 0.33 0.41 0 0 1200 1000 800 600 400 200 0 0.1 0.2 0.3 0.4 0.5 0.6 Water to Cementitious Materials Ratio Figure 511 Effects of water to cement ratio on splitting tensile strength at 91 days O 0 0o 0 0 6 Figure 512 Effects of aggregate type on splitting tensile strength of Mix2F and Mix2GF Figure 513 Effects of aggregate type on splitting tensile strength of Mix3F and Mix3GF Figure 514 Effects of aggregate type on splitting tensile strength of Mix5S and Mix5GS Figure 515 Effects of aggregate type on splitting tensile strength of Mix7S and Mix7GS aggregate have significant lower splitting tensile strength. For example, Mix3F has an average splitting tensile strength of 731 psi at 91 days, while the splitting tensile strength of the corresponding Mix3GF is 624 psi. At 91 days, the splitting tensile strength of Mix5S is 738 psi, which is 16.8% higher than that of the corresponding Mix5GS. 5.3.3 Effects of Fly Ash and Slag on Splitting Tensile Strength of Concrete Fly ash and slag have significant effect on splitting tensile strength. In order to see the effects of fly ash and slag on splitting tensile strength, the strength development characteristics of splitting tensile strength was normalized as the ratio of splitting tensile strength at various curing ages to the splitting tensile strength at 91 days and the normalized values are listed in Table A4 in Appendix A. As can be seen from Table A4, the splitting tensile strengths of fly ash concrete mixtures increase slowly in 28 days after demolding, and the 28day splitting tensile strength is around 85% of splitting tensile strength at 91 days, while the splitting tensile strength of slag concrete increased very rapidly in 28 days after demolding, up to 94% of splitting tensile strength at 91 days. For example, the splitting tensile strength of Mix2F at 91 days is 659 psi, increasing 21.6 percent in comparison with that at 28 days. Mix3F has a splitting tensile strength of 73 psi at 91 days, increasing 17.1 percent in comparison with that at 28 days. But, for the concrete mixtures with slag and limestone coarse aggregate, there is no appreciable increase in splitting tensile strength after 28 days curing. For example, Mix5S, Mix6S, Mix7S, and Mix8S increase in splitting tensile strength by less than 10% at 91 days as compared with that at 28 days. For the concrete mixtures with Georgia granite aggregate, substantial increase in splitting tensile strength after 28 days also happened to the mixtures with fly ash, while no significant increase was found in concrete mixtures with slag. For two lightweight aggregate concrete mixtures, similar situation can be observed as well. The development characteristics of two typical fly ash concretes and two slag concretes with time are shown in Figure 516. 1.00 S0.95 0o  0.90 cn S0.85 0.80 Q. c o 0.75 0.70 Time (days) Figure 516 Effects of fly ash and slag on splitting tensile strength of concrete 5.4 Relationship between Compressive Strength and Splitting Tensile Strength The compressive strengths of the concretes (as tabulated in Table A1) were plotted against the corresponding splitting tensile strengths (as tabulated in Table A2) for all curing conditions in Figure 517. Regression analyses to establish empirical relationship between compressive strength and splitting tensile strengths were performed using the following equations: fct = A (53) S=( (54) where f = splitting tensile strength (psi) f = compressive strength (psi) Mix5SSSlagW/C=O 33 Mix6SSlagW/C=O 36 x Mix2FFly ashW/C=0 33 I I m Mix4FFly ashW/C= 37t A, B = coefficients The ACI Code 318 uses Equation 53 for estimation of splitting tensile strength of lightweight concrete, where the coefficient A is equal to 6.7 [ACI, 1983]. The investigation by Carino and Lew [Carino et al, 1982] determined that the coefficient A was approximately 6.49. They suggested that Equation 54 was better than Equation 53 in the estimation of splitting tensile strength from compressive strength. The coefficient B was determined to be 0.73 in their investigation. The results of the regression analyses are summarized in Table 54. The coefficient A (6.91) is slightly higher than both the values suggested by ACI (6.7) and the value by Carino and Lew (6.49). The coefficient B (0.7185) is slightly lower than that suggested by Carino and Lew (0.73). These two regression equations are also plotted on Figure 517. As can be seen from Figure 517, Carino and Lew model gives a better fit to the experimental data than the ACI model, while ACI Building Code 31892 tends to overestimate splitting tensile strength at low compressive strength and underestimate splitting tensile strength at high compressive strength because the power exponent of the equation is too low. Table 56 Regression analysis for relating compressive strength to splitting tensile strength Square root of Square root of absolute sum absolute sum Equation Curing Coefficient Standard s o Equation A or B Error of squares by of squares by condition A or B Error modified original equation equation ACI = A.Moist f =Aoit 6.91 0.76 60 62.3 st curing A = 6.7 Carino and Lew Moist SMoist 0.72 0.015 45 75.7 st curing B = 0.73 1000 Measurement 900 C arino and Lew model ACI code 800 400    ^ ^  700 0) 600 0 500 400 S300 200 _ 100 0 0 2000 4000 6000 8000 10000 12000 14000 Compressive Strength (psi) Figure 517 Relationship between compressive strength and splitting tensile strength 5.5 Analysis of Elastic Modulus Test Results The average elastic modulus values at various curing ages of the fourteen concrete mixes evaluated are displayed in Table 57. The individual elastic modulus values are shown in Table A3 in Appendix A. Table 57 Elastic module of the concrete mixtures evaluated (x 106 psi) Mix W/C Fly ash Slag Age of Testing (days) Number 3 7 14 28 56 91 Mix1F 0.24 20% 4.74 4.93 5.23 5.40 5.54 5.58 Mix2F 0.33 20% 3.43 3.77 4.08 4.31 4.43 4.67 Mix3F 0.41 20% 4.40 4.85 5.05 5.14 5.28 5.70 Mix4F 0.37 20% 4.49 4.61 4.88 5.01 5.15 5.29 Mix5S 0.33 50% 4.11 4.66 4.88 5.09 5.23 5.23 Mix6S 0.36 50% 4.27 4.92 5.18 5.45 5.62 5.66 Mix7S 0.41 70% 3.90 4.30 4.52 4.60 4.73 4.76 Mix8S 0.44 50% 3.96 4.39 4.84 5.00 5.13 5.16 Mix9LF 0.31 20% 2.76 2.92 3.13 3.27 3.40 3.50 MixO1LS 0.39 60% 1.75 1.88 2.36 2.69 3.01 3.04 Mix2GF 0.33 20% 3.80 4.22 4.61 4.96 5.06 5.19 Mix3GF 0.41 20% 4.15 4.62 5.52 5.61 5.93 5.96 Mix5GS 0.33 50% 3.15 3.82 4.65 5.17 5.37 5.56 Mix7GS 0.41 70% 2.69 3.38 4.10 5.25 5.60 5.73 As can be seen from Table 57, for the normal weight aggregate concretes investigated in this study, the elastic modulus of concrete varies from 4.50x106 to 6.00x106 psi. For the lightweight aggregate concrete, the modulus of elasticity varies from 3.00x106psi to 3.70x106 psi. As shown in Figures 518 through 521, two different normal weight coarse aggregates give considerable influence on the elastic modulus of concrete. With other mixture components constant in volume, the concrete mixtures with Georgia granite aggregate have higher elastic modulus than those with Miami Oolite limestone aggregate. For example, Mix7GS has an elastic modulus of 5.73x106 psi at 91 days, 20.4% higher than 4.76x106 psi, which is the value of elastic modulus of Mix7S at 91 days. Mix7S has a compressive strength at 91 days slightly higher than that of Mix7GS. Also, we can see from the comparison between Mix2F and Mix 2GF, Mix3F and Mix3GF, and Mix5S and Mix5GS that Mix2F, Mix3F and Mix5S have a lower elastic modulus than the corresponding Mix2GF, Mix3GF and Mix5GS, respectively. The compressive strengths of Mix2F, Mix3F and Mix5S are higher than those of the corresponding Mix2GF, Mix3GF and Mix5GS, respectively, at various curing ages. It is interesting to note that high strength but low elastic modulus concrete can be obtained through using lightweight aggregate. For example, Mix9LF, lightweight aggregate concrete, has similar compressive strength and splitting tensile strength to Mix7S, with Miami Oolite limestone aggregate, while the elastic modulus of Mix9LF at 91 days is only about 3.50x106 psi, which is about 36% lower than that of Mix7S. Thus, to achieve high strength but low elastic modulus concrete mixture, which is desirable for concrete pavement, a lightweight aggregate may be used. O 4 00E +06 2.00E+06 1.00E+06 .,,, 0.00E+00 0 3 7 14 28 ULimestone 0 3.43E+06 3.77E+06 4.08E+06 4.31E+ OGranite 0 3.80E+06 4.22E+06 4.61E+06 4E+ Curing Age o Figure 518 Effects of coarse aggregate type on modulus of elasticity of Mix2F and Mix2GF I I,'E ,' 0 ,1:'E t Ln.: i .:.r, `Gr n,.i :4 :" 1 56 i:, 4 4i:,E :,i 4 ,:,'E ,:,i ". L'E. E ii M14E U06 S a 1"SE,: ,1 4 62E S S+ S 2E ',O 5. 61E+06 Cuir.rg Age dljaS 5 28E+ Figure 519 Effects of coarse aggregate type on modulus of elasticity of Mix3F and Mix3GF Figure 520 Effects of coarse aggregate type on modulus of elasticity of Mix5S and Mix5GS 4.00E +06 0 3 7 14 28 56 Limestone 0 3.90E+06 4.30E+06 4.52E+06 460E+06 473E+ OGranite 0 2.69E+06 3.38E+06 4.10E+06 525E+065 Curing Age Figure 521 Effects of coarse aggregate type on modulus of elasticity of Mix7S and Mix7GS 5.6 Relationship between Compressive Strength and Elastic Modulus The elastic modulus of concrete is affected by the modulus of elasticity of the aggregate and by the volumetric proportion of aggregate in the concrete. Thus, there is no surprise that there is no agreement on the precise form of the relationship between compressive strength and elastic modulus. In this study, modification was made on the expression recommended by ACI 31889, given as follows: E = a (55) In the equation ac is a parameter to be determined through curvefitting regression analysis. Its value recommended by ACI is 57000. The regression analysis was carried out on the expression recommended by ACI 31895, given as follows, to fit the experimental data. In this formula, the unit weight of concrete was also used. E =A w15 (56) Where E is elastic modulus in psi; f/ is compressive strength in psi; w is unit weight of concrete in pcf; and A is coefficient to be determined through regression analysis. The recommended value by ACI 31895 is 33.0. The compressive strengths of fourteen concrete mixtures were plotted against elastic modules at corresponding curing ages, as shown in Figure 522. It indicates that coarse aggregate type has significant effects on the elastic modulus of concrete. The results from regression analysis were presented in Table 58. And the modified ACI 209 equation was plotted in Figure 522 together with the experimental measurements. It can be seen that the determined values of coefficient ac for the concrete mixtures with three different types of aggregate are fairly far away from the ACI suggested value of 57000. Regression analysis was performed using ACI 31895 equation, which was required to go through the origin. The analyzed results are presented in Table 59. It can be seen from Table 5 9 that the coefficient A (33.64) obtained from regression analysis is nearly identical to the coefficient (33.0) given by ACI code. However, the errors from the regression equation which is required to go though the origin are higher than those from that regression equation that is not required to go through the origin, as seen from Table 59. In addition, the results of regression analysis for different curing conditions using ACI 31895 formulas are presented in Table 510. The elastic modulus of concrete at all curing conditions is plotted against w15" in Figure 523. As can be seen from Table 510, curing time appears to have a significant effect on the coefficient of the regression equations. The regression coefficients obtained from the samples moistcured for 28 days are higher than those obtained from other curing times. Thus, the prediction will be conservative if the regression coefficients are obtained from the samples moistcured for 28 days. For the concretes investigated in this study, the following modified ACI 31895 equation can be used for prediction of elastic modulus: E=30.16wl.5 f +484200 (57) Where E is elastic modulus in psi; c is compressive strength in psi; w is unit weight of concrete in pcf 5.7 Summary of Findings This chapter presents the testing results from the strength tests in this study. The major findings are given as follows: (1) Splitting tensile strengths of the concrete mixtures using granite aggregate were significantly lower than those using Miami Oolite limestone aggregate. This is due probably to the poor bonding condition between hardened cement paste and granite aggregate. (2) Compressive strengths of concretes with granite aggregate were comparable to or lower than those of concretes with Miami Oolite limestone aggregate. (3) The concrete with granite aggregate had higher elastic modulus than that with Miami Oolite limestone aggregate, while the lightweight aggregate concretes had lower elastic modulus than the normal weight concretes. (4) Fly ash concretes develop compressive strength and splitting tensile strength at a slower rate than the slag concretes. Fly ash concrete shows significant strength gain after 28 days, while this was not seen from the slag concrete mixtures. (5) The ACI 209 Equation for prediction on compressive strength ( f (t)) at various curing age from compressive strength at 28 days (f2 (t)), which is given as follows, was modified to give better strength prediction for the various mixtures. Table 58 Results of regression analysis for prediction of elastic modulus using the equation recommended by ACI 31889 Results A t granite lightweight Limestone a (Bestfit values) 62721 43777 55949 Standard Error of ca 870.6 692.3 309.1 95% confidence intervals for a 60920 to 64523 42253 to 45301 55327 to 56572 Degrees of Freedom 23 11 47 R2 0.8712 0.922 0.8758 Absolute Sum of Squares 2.478E+12 2.693E+11 1.619E+12 Sy.x 328220 156461 185594 Number of points Analyzed 24 12 48 Table 59 Results of regression analysis for prediction of elastic modulus using ACI 31895 equation With equation going through the Without forcing the equation to go Bestfit values origin through the origin Slope 33.64 0.2671 30.18 1.169 Yintercept when X=0.0 0.0000 484200 + 159900 Xintercept when Y=0.0 0.0000 16040 I/slope 0.02973 0.03313 95% Confidence Intervals Slope 33.10 to 34.17 27.85 to 32.51 Sy.x 335100 319700 8.00E+06 _ o Georgia granite 7.00E+06 Stalite lightweight A Miami Oolite limestone 6.00E+06 j A" 5.00E+06 A :0 A A A& S4.00E+06 / , 5 3.00E+06  0 2.00E+06 ' 1.00E+06 / 0.00E+00 0 2000 4000 6000 8000 10000 12000 14000 Compressive Strength (psi) Figure 522 Relationship between compressive strength and elastic modulus based on ACI Code 7.00E+06 6.00E+06  5.00E+06 4.00E+06 0 * S* 3.00E+06  0 2.00E+06 1.00E+06 0.OOE+00  0 40000 80000 120000 160000 200000 W15f 05 Figure 523 Plot of elastic modulus against w15"* for all curing conditions 124 Table 510 Results of regression analysis for prediction of elastic modulus using the ACI 31895 equation for different curing conditions Overall 3day 7day 14day 28day 56day 91day Slope 30.18 + 1.169 26.24 + 3.857 27.76 + 3.763 29.17 + 3.123 30.00 + 2.217 28.78 2.965 29.38 + 2.771 484200+ 800000+ 644500+ 614000+ 581900+ 779700+ 704200+ Yintercept when X=0.0 159900 437100 478400 424400 315800 438000 418700 Xintercept when Y=0.0 16040 30490 23220 21050 19400 27090 23970 I/slope 0.03313 0.03811 0.03602 0.03428 0.03334 0.03475 0.03404 95% Confidence Intervals 27.85 to 17.84 to 19.56 to 22.37 to 25.16 to 22.32 to 23.34 to Slope 32.51 34.64 35.96 35.98 34.83 35.24 35.41 165500 to 152400 to 397900 to 310800 to 106200 to 174800 to 208100 to Yintercept when X=0.0 802900 1752000 1687000 1539000 1270000 1734000 1616000 28780 to 97520 to 85720 to 68530 to 50350 to 77450 to 69070 to Xintercept when Y=0.0 5098 4433 11130 8673 3056 4974 5892 Goodness of Fit r2 0.8906 0.7941 0.8194 0.8791 0.9385 0.887 0.9035 Sy.x 319700 394800 386700 310500 216700 292900 275100 Is slope significantly nonzero? F 667.2 46.29 54.43 87.25 183.1 94.22 112.4 DFn, DFd 1.000, 82.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 P value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 Deviation from zero? Significant Significant Significant Significant Significant Significant Significant Data Number of X values 84 14 14 14 14 14 14 Maximum number of Y replicates 1 1 1 1 1 1 1 Total number of values 84 14 14 14 14 14 14 I t fc (t) = fc28 fc() 4.0+0.85,t c28 The modified equation has the following form for the concrete with different coarse aggregates: fc(= a .t c28 The value of a was found to vary from 1.1 to 2.6 for the concretes with Miami Oolite limestone aggregate, from 2.6 to 5.3 for the concretes with Georgia granite aggregate, and from 4.2 to 6.7 for lightweight aggregate concretes; the value of 3 was found to vary from 0.82 to 0.93 for the concretes with Miami Oolite limestone aggregate, from 0.82 to 0.89 for the concrete with Georgia granite aggregate, and from 0.74 to 0.82 for lightweight aggregate concrete in this study. (6) The relationship between compressive strength ( f) and splitting tensile strength ( f,) is established for the concrete mixtures investigated in this study. The Carino and Lew model, given as follows, S)0.73 was modified to the following equation: t = 0.7185 fct c Where f, and fc, are in units of psi. (7) The relationship between compressive strength and modulus of elasticity was refined in this study using Least Square of Curvefitting Technique. The ACI 31889 Equation, which is Ec = 57000Ff was modified to the following equation: Where a is equal to 55,949 for Miami Oolite limestone aggregate; 62,721 for Georgia granite aggregate; and 43,777 for Stalite lightweight aggregate. f, and Ec are in units of psi. (8) For all three aggregate types investigated in this study, a modified ACI 31895 prediction equation was developed: E = 30.16 w1 f + 484200 Where w is the density of concrete in pound per cubit foot. fc and Ec are in units of psi. CHAPTER 6 ANALYSIS OF SHRINKAGE TEST RESULTS 6.1 Introduction This chapter presents the results from shrinkage tests on the concrete mixes evaluated in this study. The effects of various factors on shrinkage behavior of concrete were discussed. Regression analysis was performed to establish the relationship between compressive strength at the age when shrinkage test was started and shrinkage strain at 91 days, and the relationship between elastic modulus and shrinkage of concrete. Empirical equations relating compressive strength and elastic modulus to shrinkage of concrete are given. Also, the evaluation was made on ACI 209 model and C.E.BF.I.P model for their effectiveness in shrinkage prediction. At last, ultimate shrinkage strain of the concretes investigated in this study was approximated using an asymptotic equation with three unknown parameters to fit experimental data. 6.2 Results and Analysis of Shrinkage Tests Table 61 presents the measured shrinkage strains at the ages up to 91 days for the fourteen concrete mixes evaluated in this study. For MixIF through MixO1LS, one group of concrete specimens was moistcured for 7 days and then airdried in the laboratory for the rest of the time; another group of specimens were moistcured for 14 days and then airdried for the rest of the time, while, for Mix2FG through Mix7SG, only one curing condition, i.e. 14day moist curing and then airdried for the rest of time, was evaluated. 6.2.1 Effects of Curing Conditions on Shrinkage Behavior of Concrete As can be seen from Table 61 as well as Figure 61, curing condition has substantial effects on shrinkage behavior of concrete mixtures. For the concrete mixtures with fly ash, the specimens moistcured for 14 days have appreciable lower shrinkage strains than those moist cured for 7 days. For example, the shrinkage strain of MixIF moistcured for 14 days is Table 61 Shrinkage strains of the concrete mixtures evaluated at various curing ages Age of testing (days) No. of Mix Curing condition Predicted ultimate 3 7 1 2 5 shrinkage strain MixIF 7day moist cure Mix 1F 14day moist cure Mix2F 7day moist cure Mix2F   14day moist cure Mix3F 7day moist cure 14day moist cure 7day moist cure 14day moist cure 7day moist cure 14day moist cure 7day moist cure 14day moist cure Mix7S 7day moist cure Mix7S 14day moist cure Mix8S 7day moist cure 14day moist cure ,. 7day moist cure 1vh1xLJLr MixlOLS T%.Aivu9 (TF 14day moist cure 7day moist cure 14day moist cure 7day moist cure 14day moist cure Mix3GF 7day moist cure Mix3GF 14day moist cure Mix5GF 7day moist cure Mix5GF 14day moist cure 7day moist cure VI1X / Tr 0.20E04 0.14E04 0.51E04 0.31E04 0.40E04 0.24E04 0.37E04 0.31E04 0.44E04 0.43E04 0.42E04 0.33E04 0.39E04 0.38E04 0.73E04 0.50E04 0.49E04 0.46E04 0.67E04 0.38E04 0.32E04 0.29E04 0.39E04 0.43E04 0.44E04 0.35E04 0.97E04 0.69E04 0.73E04 0.50E04 0.71E04 0.53E04 0.88E04 0.74E04 0.84E04 0.71E04 0.81E04 0.73E04 1.23E04 0.98E04 0.96E04 0.83E04 1.30E04 0.90E04 0.61E04 0.75E04 0.61E04 1.54E04 1.12E04 1.24E04 0.87E04 1.18E04 0.92E04 1.30E04 1.10E04 1.23E04 1.12E04 1.26E04 1.11E04 1.61E04 1.36E04 1.34E04 1.34E04 1.98E04 1.52E04 1.09E04 0.54E04 0.84E04 0.64E04 1.04E04 1.18E04 1.00E04 2.10E04 1.73E04 1.77E04 1.37E04 1.76E04 1.42E04 1.70E04 1.49E04 1.56E04 1.41E04 1.70E04 1.48E04 1.94E04 1.69E04 2.25E04 1.84E04 2.60E04 2.09E04 1.61E04 1.23E04 1.40E04 1.63E04 1.36E04 2.61E04 2.33E04 2.21E04 1.84E04 2.33E04 1.97E04 2.01E04 1.78E04 1.83E04 1.64E04 2.02E04 1.84E04 2.28E04 2.02E04 2.87E04 2.41E04 3.20E04 2.80E04 2.04E04 1.57E04 1.68E04 2.02E04 1.67E04 2.86E04 2.58E04 2.48E04 2.16E04 2.67E04 2.31E04 2.16E04 1.93E04 1.95E04 1.76E04 2.23E04 2.04E04 2.50E04 2.30E04 3.22E04 2.76E04 3.58E04 3.17E04 2.31E04 1.82E04 1.84E04 2.66E04 2.27E04 3.39E04 3.20E04 3.03E04 2.85E04 3.64E04 3.44E04 2.46E04 2.29E04 2.16E04 1.93E04 2.55E04 2.40E04 2.43E04 2.20E04 3.95E04 3.49E04 4.22E04 3.96E04 2.83E04 2.62E04 2.18E04 0.74E04 1.00E04 1.31E04 1.63E04 IVllx4r Mix5S UlYiv;S 14day moist cure 1.81E04 2.19E04 0.000167 at 91 days, which is 23.2% less than that of the same mix moistcured for 7 days. The shrinkage strain at 91 days is 0.000258 for Mix2F moistcured for 14 days, which is 10.9% less than that of the same mix moistcured for 7 days. Also, the shrinkage strain of Mix3F moist cured for 14 days is 0.000216, which is 14.8% less than that of the same mix moistcured for 7 days. Substantial decrease in shrinkage strain also can be seen from Mix4F. Shrinkage strain of 7day moistcured specimens is 13.5% higher than that of 14day moistcured specimens for Mix4F. For the concrete mixtures with slag, the effects of curing condition on shrinkage strain are significant as well. For instance, the shrinkage strain ofMix5S moistcured for 14 days is 11.9% less than that of the same mix moistcured for 7 days. Also, for Mix6S, Mix7S and Mix8S, the shrinkage strains of the specimens moistcured for 14 days are at least 10% less than those of the same mixtures moistcured for 7 days. In addition, curing condition has similar effects on shrinkage strain of lightweight aggregate concretes as that on normal weight aggregate concrete. The shrinkage strains of Mix 9FL and Mix1OSL moistcured for 14 days are 16.5% and 11.6%, respectively, less than those of the same mixtures moistcured for 7 days. 6.2.2 Effects of Mineral Additives on Shrinkage Behavior As can be seen from Table 61 as well as Figure 61, the results from 14 mixtures indicate that the concrete mixtures with fly ash have higher shrinkage strains than those with slag. For example, Mix3F has the same water to cementitious materials ratio as Mix7S, while the shrinkage strain of Mix3F moistcured for 7 days is 0.000248, which is more than 10% higher than that of Mix7S moistcured for 7 days even though the water content of Mix3F (254 lbs per cubit yard) is less than that of Mix7S (267 lbs per cubit yard). For another example, Mix2F and 129 4.00E04 07 day moist curing S14day moist curing 3.50E04 3.00E04 5 2.50E04 2 2.00E04 1F 2F 3F 4F 5S 6S 7S 8S 9LF 10LS Mixture Figure 61 Effects of curing condition on shrinkage strain of concrete mixtures at 91 days Mix5S have identical water to cementitious ratio, while the shrinkage strain of Mix2F moist cured for 7 days is 0.000286 at 91 days, or 24.5% higher than that of Mix5S moistcured for 7 days. As also can be seen from the concrete mixtures with Georgia granite aggregate, Mix2FG and Mix3FG have higher shrinkage strains as compared with the corresponding Mix5SG and Mix7SG, respectively, even though Mix2GF has identical water to cementitious materials ratio as Mix5SG, and Mix3GF has the same water to cementitious material ratio as Mix7GS. 6.2.3 Effects of Water Content on Shrinkage Behavior Water content per unit volumetric concrete is an important factor influencing the magnitude of shrinkage strain since drying shrinkage is caused by the moisture movement from the concrete. Generally, the higher the water content, the more the free water inside concrete is available because water can not be consumed rapidly and completely. Thus, shrinkage strain of concrete is increased with an increase of free water content. As can be seen from Figure 62, the 130 shrinkage strains at 91 days increase with the increase of water content for the normalweight concrete mixtures evaluated in this study. 3.50E04 1 0 Miami Oolite limestone 3.OOE04 Georgia granite 3.00E04  S2.50E04 " 2.00E04 a 1.50E04 u 1.00E04 5.00E05 0.00E+00 I I 220 230 240 250 260 270 280 290 Water Content (Ibs/yard3) Figure 62 Effects of water content on shrinkage strain at 91 days Figure 63 shows a plot of water to cementitious materials ratio versus shrinkage strain of concrete at 91 days. No clear trend can be observed to relate water to cementitious materials ratio to the magnitude of shrinkage strain of concrete. The significant role played by water content also extends to the lightweight aggregate concretes, Mix9FL and Mix1OSL. As can be seen from Table 61, the water content of Mix 10SL is 275 lbs per cubit yard, higher than 235 lbs for Mix9FL. The shrinkage strain at 91 days for Mix10SL is much higher than that of Mix9FL. 6.2.4 Effects of Aggregate Types on Shrinkage Behavior In this study, two types of normal weight coarse aggregate, Miami Oolite limestone aggregate and Georgia granite aggregate were investigated for their effects on shrinkage 0 0 o 0 0 behavior of four concrete mixtures. The experimental data from the specimens moistcured for 14 days indicate that the concrete mixtures using Georgia granite aggregate developed significantly less shrinkage strain at 91 days than those with Miami Oolite limestone aggregate. For example, as can be seen from Figure 64, Mix2FG, which has the same mix proportion as Mix2F other than the coarse aggregate replaced by Georgia granite aggregate, has a shrinkage strain of 0.000231, which is 23.8% lower than that of Mix2F using Miami Oolite limestone as coarse aggregate. 2.80E04 2.60E04 2.40E04 2.20E04 2.00E04 1.80E04 1.60E04 1.40E04 1.20E04 1.00E04 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Water to Cementitious Materials Ratio Figure 63 Plot of water to cementitious materials ratio versus shrinkage strain at 91 days The same situation can be seen from the comparison between Mix3F and Mix3FG, Mix 5S and Mix5SG, and Mix7S and Mix7SG. The shrinkage strain of Mix3FG is 0.000182 at 91 days, which is 18.7% less than that of Mix3F, which has shrinkage strain of 0.000216. Shrinkage strains of Mix5S and Mix7S at 91 days are also 10% higher than those of Mix5SG and Mix7SG. o Miami Oolite limestone o 0.33 Georgia Granite S0.33 o 0.41 o 0.37 00.33 o 00.37 W  o C.44 o 0.33 o 0.41 0.33 ___ 41 o C.44 o 0.36 o C.24 o0.33o 0.36 0C.24 For lightweight aggregate concretes, such as Mix9LF and Mix1OLS, their shrinkage strains are significantly higher than the concrete mixtures using normal weight aggregate. 3.00E04 SMiami Oolite limestone BGeorgla granite 2.50E04  2.00E04 e 1.50E04... . S1.00E04...... ... 5.00E05 0.00E+00 Mix2 Mix3 Mix5 Mix7 Mixture Figure 64 Effects of coarse aggregate type on shrinkage behavior of concrete 6.2.5 Relationship between Compressive Strength and Shrinkage Strain Over the past decades, the study on shrinkage behavior of concrete has been carried out extensively. The effects of various factors, such as water to cement ratio, aggregate type, aggregate content, mineral additives, and cement content so on, on shrinkage behavior have been studied. However, since concrete is a complicated composite material, the effects of various components and their proportions on shrinkage behavior are intertwisted together. Also, because of massive introduction of chemical admixtures to concrete, such as air entraining agent and water reducer, shrinkage behavior of concrete becomes more complex. Thus, shrinkage behavior of concrete can not be reasonably estimated based on the simple addition of every individual factor's function. Therefore, it is desirable to relate the shrinkage behavior of concrete to one or more fundamental properties of concrete, for example, compressive strength, tensile strength or elastic modulus at a particular age. In doing so, it assumes that the fundamental properties of concrete are closely related to one another, i.e. one fundamental property can be predicted from another. In doing so, a complicated fundamental property can be estimated by a simple fundamental property without complicated and timeconsuming experimental test involved. In trying to find out the relationship between compressive strength and shrinkage behavior of concrete, compressive strength at the age when shrinkage test was started was plotted against shrinkage strain at 91 days in Figure 65. As shown in Figure 65, it appears that there exists a very interesting relationship between the shrinkage strains at 91 days and compressive strength regardless of which type of coarse aggregate was used for concrete. Then, regression analysis was carried out using an exponential function with two unknown parameters, given as Equation 61. The regression analysis results are presented in Table 62. esh = e (61) In this formula, f, is compressive strength of concrete at the age of initial shrinkage test. As can be seen from Table 62, best fit value ofc is 5.113x104; best fit value of 3 is 1.127x104; and correlation coefficient, R2, is 0.8226. The above equation with parameters obtained from regression analysis was plotted in Figure 65 as solid line. It indicated that shrinkage strain at 91 days can be well estimated by the compressive strength of concrete at the age of when shrinkage test was started. Furthermore, this relationship is not affected by such factors as aggregate type and curing age. Therefore, even though exponential equation from regression analysis may not be a fundamental relationship between compressive strength and shrinkage of concrete, it may be very convenient way practically to have an accurate enough estimation on shrinkage strain just based on the compressive strength without timeconsuming shrinkage test involved. 134 Table 62 Results of regression analysis on relationship of compressive strength to shrinkage strain Absolute Sum of Regression Bestfit Standard Error 95% Confidence 2 Sque Rot du Results Value (SE) Interval to Error (ootS to Error (SSE) 4.706E04 a 5.113E04 2.042E05 5.521E04 5.521E00.8226 2.131E05 1.014E04 3 1.127E04 5.654E06 1.01 1.239E04 5.00E04  o Miami Oolite limestone 4.50E04 0 Lightweight aggregate A Georgia granite 4.00E04 ( 3.50E04 Q 0 3.00E04  r u o 2 2.50E04 o 0 2.00E04  o__o 1.50E04 0 1.00E04 5.00E05 0.00E+00 0 2000 4000 6000 8000 10000 12000 14000 Compressive Strength at the Age of Initial Shrinkage Test (psi) Figure 65 Relationship between compressive strength and shrinkage strain at 91 days 6.2.6 Relationship between Elastic Modulus and Shrinkage Strain Since close relationship has been found between compressive strength and shrinkage of concrete, and since there is direct relationship between compressive strength and elastic modulus, elastic modulus and shrinkage should be related to each other as well. As shown in Figure 66, shrinkage strains at 91 days for all the concretes investigated in this study, including normal weight aggregate concrete and lightweight aggregate concrete, were plotted against elastic modulus at the age of shrinkage test starts. There is no surprise that similar relationship to compressive strength and shrinkage can be found between elastic modulus and shrinkage. Regression analysis was performed using an exponential function with two unknown parameters, as given in Equation 62, and the analyzed results are presented in Table 63. P.E, Esh = Ec (62) In this equation, Ec is elastic modulus of concrete at the age when shrinkage test was started. Table 63 Results of regression analysis on relationship of elastic modulus to shrinkage strain Regression Bestfit Standard Error 95% Confidence 2 (S Results Value (SE) Interval ) 5.911E04 U 6.595E04 3.429E05E04 7.279E04 0.8152 2.175E05 2.045E04 3 2.270E07 1.129E08 2 E4 2.495E04 5.00E04 o Miami Oolite limestone Lightweight aggregate 4.00E04 A Georgia granite a) 0 3.00E04 S* o 1.00E04 2.00E04 1.00 E 04  0.OOE+00 0.00E+00 2.00E+06 4.00E+06 6.00E+06 8.00E+06 Modulus of Elasticity (psi) Figure 66 Relationship between shrinkage strain at 91 days and modulus of elasticity 6.3 Evaluation on Shrinkage Prediction Models In this study, the ACI 209 model and C.E.BF.I.P model were evaluated on their effectiveness and accuracy in prediction of shrinkage behavior of typical concretes used in Florida. 6.3.1 ACI209 model The concrete shrinkage prediction model recommended by ACI209 (1992) is given as follows: ( ) (63) v sh t 35 +t ( sh u Where (esh ) time dependent shrinkage strain; (esh ) ultimate shrinkage strain; and t  time variable in days If there is no available shrinkage data from the specific concrete mixture, the ultimate shrinkage strain, (sh ) can be assumed to be the following: (Esh ) = 780 x 106 x h (64) Where Ysh a product of all the applicable correction factors for the testing conditions other than the standard condition; Ysh = 1 under standard testing condition. Ysh is obtained by multiplying the ultimate shrinkage strain under the standard condition by the appropriate correction factors, such as correction factors for the effect of initial moist curing, correction factor for the effect of ambient relative humidity, correction factor for the effects of specimen size, correction factor for concrete composition and so on. In this study, Ysh is calculated as follows: 7sh = 71a 7rh 7s 7a *at *p (65) The correction factors applicable to the concrete mixes evaluated in this study are shown in Table 64. Table 64 Correction factors for the ACI 209 model on shrinkage prediction No. of Mix MixIF Mix2F Mix3F Mix4F Mix5S Mix6S Mix7S Mix8S Mix9LF Mix10LS Mix2GF Mix3GF Mix5GS Mix7GS Yla 7day moist 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 14day moist 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 Ysh Yrh Ys Ya Yat Yp 7day moist 0.77 0.85 0.57 1.00 0.88 0.30 0.77 0.83 0.87 1.00 0.88 0.45 0.77 0.83 0.69 1.00 0.88 0.36 0.77 0.83 0.64 1.00 0.88 0.33 0.77 0.84 0.80 1.00 0.88 0.42 0.77 0.83 0.66 1.00 0.88 0.34 0.77 0.84 0.96 1.00 0.88 0.50 0.77 0.83 0.80 1.00 0.88 0.41 0.77 0.83 0.73 1.00 0.88 0.38 0.77 0.83 0.93 1.00 0.88 0.48 0.77 0.83 1.13 1.00 0.88 0.58 0.77 0.83 0.60 1.00 0.88 0.31 0.77 0.84 0.96 1.00 0.88 0.50 0.77 0.83 0.80 1.00 0.88 0.41 6.3.2 CEBFIP Model In this model, the effects of cement type, ambient relative humidity, compressive strength of concrete, and size effect of specimen on shrinkage strain of concrete are taken into consideration. The total shrinkage strain may be estimated by the following equation: E t,' t )= E t t) (66) cs \ s / cs0 s J s ) Where Es(t, t ) = time dependent total shrinkage strain; Ec, = notational shrinkage coefficient; and f, (t ts) = coefficient to describe the development of shrinkage with time. E S can be estimated by the following equation: (67) Ecs = 160 +10,8s 9 ] x 106 X/JRH where /l, a coefficient depending on the type of cement is equal to 5 for normal or rapid hardening cements; fm = the mean compressive strength of concrete at the age of initial shrinkage tests. f,,o is a constant, equal to 10MPa. /RH can be computed as follows: 14day moist 0.27 0.40 0.32 0.29 0.37 0.30 0.44 0.37 0.33 0.43 0.52 0.27 0.44 0.37 f ^3 RH = 1.55 1 RH for 40% < RH < 99% (68) R RH0 With RH equal to 75% in this study and RHO equal to 100%, then, csO = 160+10Pf,, 9 x106 x 0.8959 (69) p, (t t) can be estimated by the following equation: S (tts) 0.5 8s t ) t) tl2 (610) h tt WA t \ \ 0} Il Where h = 2Ac = the notational size of member (in mm), where A, is the crosssectional u area (mm2) and u is the perimeter (mm) of the member circular cross section (27r) in contact with the atmosphere. H is equal to 1.5 for 6xl2in cylinder. h0 is equal to 100 mm. t1 is equal to 1 day. Therefore, the above equation can be simplified as follows: P (t) = t (611) s() 203.23 + t The shrinkage strains at 91 days for all the concrete mixtures investigated in this study were compared with the calculated results using ACI 209 model and C.E.BF.I.P model in Figure 67. The hollow circle indicates the prediction by C.E.BF.I.P model, and solid black dot represents the prediction by ACI 209 model. As shown in Figure 67, C.E.BF.I.P model gives encouraging prediction in comparison with the experimental data, while ACI209 model provides extreme overestimation. 139 5.00E04  4.00E04 __ E 'y= x S3.00E04 0 2.00E04 o  1.00E04 * 0.OOE+00 0.00E+00 1.00E04 2.00E04 3.00E04 4.00E04 5.00E04 Predicted Shrinkage Strain Figure 67 Comparison between the shrinkage strain at 91 days and the shrinkage strain calculated by ACI 209 model and C.E.BF.I.P model 6.4 Prediction of Ultimate Shrinkage Strain Shrinkage of concrete lasts for a long time with decreasing shrinkage rate. Generally, it is assumed that concrete will shrink with time to a limiting value, called ultimate shrinkage strain, which is a very important parameter in concrete structural design. In this study, an asymptotic equation, given as follows, was used to fit the experimental data. sh )= a ./ (612) As can be seen from the above equation, shrinkage strain will approach its limiting value 3 as time goes to infinite value. Thus, 3 is the ultimate shrinkage strain. Curvefitting regression analysis was performed using Least Square Method, which is detailed as follows: 140 6.4.1 Least Square Method of Curvefitting The method of least squares was used when fitting data. The model selected to relate the response data to the predictor data with two coefficients is given as follows: ,= .,6 (613) x+ Where a P and y are two constitutive parameters to be determined from curve fitting process; x is time variable, and y is response variable, and it is the creep strain in this study. The goal of the fitting process is to estimate the "true" but unknown coefficients of the model. To obtain the coefficient estimates, the residual for the ith data point, r. defined as the difference between the observed response value y. and the fitted response value jK and identified as the error associated with the data is computed by r=yy (614) Then, the summed square of residuals is given by Sn 2 n \ (615) Where nl is the number of data points included in the fit, and S is the sum of squares error estimate. The least squares method minimizes the summed square of residuals, and then the optimized coefficients will be achieved. Since the model used to fit the data is the ratio of two polynomials, it is a nonlinear equation. Therefore Nonlinear Least Squares Method was used to do curvefitting analysis in this study. In matrix form, nonlinear models are given by the formula y = f(X,p)+ E (616) Where y is an nby1 vector of responses, f is a function of 3 and X, p is a mby1 vector of coefficients, x is the nbym design matrix for the model, and E is an nby1 vector of errors. Unlike linear models, the coefficients are estimated using simple matrix techniques; an iterative approach is used to estimate coefficients of nonlinear model. The fitted response value is given by y = f(X,b) (617) and involves the calculation of the Jacobian of f(X,b), which is defined as a matrix of partial derivatives taken with respect to the coefficients. Then, the coefficients are adjusted and determination was made as to whether the fit improves. The direction and magnitude of the adjustment depend on the fitting algorithm. In this study, Trustregion algorithm was used because it can solve difficult nonlinear problems more efficiently than the other algorithms, and it represents an improvement over the popular LevenbergMarquardt algorithm. Because nonlinear models can be particularly sensitive to the starting points, the initial values of the estimates should be carefully defined to guarantee the convergence of regression analysis. 6.4.2 Evaluation Methods on the Goodness of Fit In this study, after fitting data with the model, the goodness of fit was evaluated by graphical illustration, such as a visual examination of the fitted curve and residual plot, and numerical measures, such as goodness of fit statistics confidence, standard error, and regression correlation coefficient (R2). In doing so, graphical illustration allows us to view the entire data set at once, and they can easily display a wide range of relationships between the model and the data. The numerical measures are more narrowly focused on a particular aspect of the data and often try to compress that information into a single number. In the following content, the methods used to evaluate the goodness of fit in this study are described briefly. * The sum of squares due to error (SSE) This statistic, also called the summed square of residuals, measures the total deviation of the response values from the fit to the response values. It is usually labeled as SSE. S nS ( i (618) SSE = Z w i y y i i= 1 A value closer to 0 indicates a better fit. * Rsquare Rsquare, also called the square of the multiple correlation coefficient and the coefficient of multiple determination, is the square of the correlation between the response values and the predicted response values. It measures how successful the fit is in explaining the variation of the data. Rsquare is defined as the ratio of the sum of squares of the regression (labeled as SSR) and the total sum of squares (labeled as SST), also called the sum of squares about the mean. SSR is defined as SSR = w ( y)2 (619) And SST is defined as And SST is defined as SST = SSR + SSE = w w (y, y)2 (620) 1i1 Then, according to the definition, Rsquare is expressed as 2SSR SST SSE SSE R = = = 1 (621) SST SST SST Rsquare can take on any value between 0 and 1, with a value closer to 1 indicating a better fit. * Root mean squared error (RMSE) RMSE is also known as the fit standard error and the standard error of the regression RMSE = s = MSE (622) Where MSE is the mean square error or the residual mean square SSE MSE = SSE (623) v A RMSE value closer to 0 indicates a better fit. * Confidence and Prediction Bounds Confidence and prediction bounds define the lower and upper values of the associated interval, and define the width of the interval, which indicates how uncertain we are about the fitted coefficients, the predicted observation, or the predicted fit. Confidence bounds were obtained through regression analysis for the fitted coefficients, and prediction bounds for the fitted function. In this study, the confidence bounds are given numerically, while the prediction bounds are displayed graphically. In this study, the bounds are defined with a certainty of 95%. In this study, the regression analysis was carried out using statistic analysis software, GraphPad Prism, programmed by GraphPad Prism software Inc. 144 6.4.3 Predicted Results The results of regression analysis using Equation 612 are presented in Table 65. The ultimate shrinkage strains predicted for 14 concrete mixtures, which are represented the values for p, are summarized in Table 65. Graphically, predicted ultimate shrinkage strain based on experimental data was compared with the predictions made by original ACI209 model and C.E.BF.I.P model in Figure 68. As can be seen from the graphical plots as well as Table65, the predicted ultimate shrinkage strains,3, for fourteen concrete mixtures vary from 0.0002 to 0.00041, which is considerable less than the predicted values by ACI 209 model and C.E.BF.I.P model. 6.00E04 0 S5.00E04 i 0 4.00E04 6 3.00E04 ' 2.00E04 U) E S1.00E04 E+00 O.OOE+00 0.OOE+0( ) 2.00E04 4.00E04 Calculated by C.E.BF.I.P model and ACI model 3.00E04 Figure 68 Comparison among the ultimate shrinkage strains from curvefitting, CEBFIP model and ACI 209 model As shown in Table 65, a has a value close to 1 for all concrete mixtures, while yvalue is significantly different between fly ash concrete and slag concrete. a has an average value of * ACI 209 model OC.E.BF.I.P model O * /o o 0 03 o/ oo o o 7   1.04, and y has an average value of 30.0. As can be seen from Table 65, yvalue for the specimens moistcured for 7 days is higher than that for the specimens moistcured for 14 days. This is due probably to the fact that the evaporation rate of free water concrete becomes slower at a longer curing age when the concrete is denser. At last, based on the 14 concrete mixtures investigated in this study, the ultimate shrinkage strain predicted through curvefitting the threeparameter model to experimental data is less than 3.5x104 for normalweight aggregate concrete, and 4.5x104 for lightweight aggregate concrete. Table 65 Results of regression analysis for prediction of shrinkage strain using Equation 612 Mix a SE p SE Y SE R2 SSE 1F 0.983 0.024 2.66E04 2.70E06 31.18 1.804 0.9997 1.20x106 1.122 0.049 2.27E04 4.31E06 31.10 3.117 0.9992 1.67x106 2F 1.027 0.021 3.39E04 1.51E06 16.48 0.649 0.9998 1.27x106 1.137 0.042 3.21E04 3.35E06 19.13 1.515 0.9994 1.23x106 3F 1.011 0.022 3.03E04 1.69E06 20.05 0.869 0.9998 1.19x106 0.920 0.031 2.85E04 3.89E06 31.74 2.545 0.9994 1.81x106 4F 0.867 0.013 3.44E04 2.74E06 27.84 1.530 0.9999 1.10x106 0.855 0.032 3.24E04 8.93E06 32.44 3.910 0.9990 2.45x106 5S 0.996 0.045 2.46E04 1.83E06 12.52 1.005 0.9992 2.02x106 0.812 0.026 2.29E04 1.86E06 20.88 1.427 0.9994 1.50x106 6S 1.227 0.041 2.16E04 0.86E06 8.172 0.432 0.9997 1.16x106 1.332 0.125 1.93E04 1.54E06 6.511 0.761 0.9985 2.20x106 7S 1.196 0.028 2.55E04 0.93E06 11.37 0.449 0.9998 0.98x106 0.910 0.034 2.40E04 2.13E06 18.89 1.429 0.9993 1.74x106 8S 1.325 0.087 2.43E04 1.82E06 7.822 0.789 0.9989 2.42x106 1.232 0.089 2.20E04 2.52E06 11.61 1.406 0.9984 2.56x106 9LF 0.836 0.030 3.95E04 3.09E06 20.53 1.220 0.9996 2.11x106 1.018 0.030 3.49E04 4.89E06 31.49 2.756 0.9992 2.51x106 10LS 1.055 0.026 4.22E04 3.30E06 21.74 1.349 0.9983 4.42x106 0.851 0.066 3.96E04 7.12E06 21.04 2.796 0.9995 2.05x106 2GF 1.105 0.053 2.83E04 3.39E06 18.09 1.632 0.9994 2.16x106 3GF 0.832 0.052 2.62E04 3.16E06 48.32 2.263 0.9999 5.93x106 5GS 0.897 0.010 2.18E04 1.96E06 18.44 1.661 0.9988 2.35x106 7GS 0.668 0.045 2.19E04 5.61E06 31.11 5.619 0.9976 3.17x106 6.5 Summary of Findings This chapter presents the results of shrinkage tests on the concrete mixtures investigated in this study. The summary of this chapter and major findings are provided as follows: (1) Fly ash concrete mixtures had slightly higher shrinkage strain at 91 days than slag concretes. This is due probably to the slow hydration rate of fly ash in comparison with that of slag. As a result of slower rate of hydration, there is more free water evaporating from the interior concrete out, which can cause concrete to shrink more. Thus, it is recommended that using a longer wet curing time would be helpful to reduce shrinkage of fly ash concrete. (2) Water content has a significant effect on drying shrinkage strain of concrete. The higher the water content, the more the concrete tends to shrink. However, no clear trend can be seen on the effects of water to cementitious materials ratio on shrinkage of concrete. (3) For the four concrete mixtures with Georgia granite aggregate, shrinkage strain is slightly lower than the four corresponding concrete mixtures with Miami Oolite limestone aggregate. Lightweight aggregate concrete shrinks more than normal weight aggregate concrete. This might be explained by their difference in elastic modulus. The concrete with higher elastic modulus would have a stronger resistance to the movement caused by shrinkage of cement paste. (4) For the concretes tested, there appeared to be a relationship between the compressive strength ( f) at the age when shrinkage test was started and the shrinkage strain (,h ) at 91 days as follows: 0.0001 ' sh = 0.0005 1 e sh Where fi is in unit of psi. (5) For the concretes tested, there appeared to have a relationship between elastic modulus (Ec) at the age when shrinkage test was started and the shrinkage strain (,h ) at 91 days as follows: 2x107. .E E h = 0.0007 e2x10 .E, Where E, is in unit of psi. (6) According to the shrinkage test results from this study, the C.E.BF.I.P model (as shown in Equation 66) appeared to give better predictions than the ACI 209 model (as shown in Equation 63). Using ACI 209 model may result in overestimation of the ultimate shrinkage strain. (7) For the concrete investigated in this study, the ultimate shrinkage strain ranged from 1.93 x 104 to 3.64x 104 for the concretes with Miami Oolite limestone aggregate; from 2.18x104 to 2.83x104 for the concretes with Georgia granite aggregate; and from 3.49x 104 to 4.22x 104 for the concretes with Stalite lightweight aggregate concrete. CHAPTER 7 ANALYSIS OF CREEP TEST RESULTS 7.1 Introduction This chapter presents the results from creep tests on the fourteen concrete mixes evaluated in this study. The effects of various factors on creep behavior of concrete were analyzed. Empirical equations relating creep to other fundamental properties, such as compressive strength and elastic modulus, were established through regression analysis. Evaluation was made on C.E.BF.I.P model and ACI 209 model for their effectiveness and accuracy in creep prediction. Ultimate creep strain was approximated using a threeparameter asymptotic equation to fit experimental data, and ultimate creep coefficient was computed using ultimate creep strain divided by instantaneous strain. 7.2 Analysis of Creep Test Results The measured and calculated results from the creep tests on the fourteen concrete mixes evaluated in this study were presented in Table B1 in Appendix B. The results presented include the total strain, shrinkage strain, creep strain, elastic strain, creep coefficient and creep modulus at various loading ages. 7.2.1 Effects of Curing Conditions on Creep Behavior of Concrete As shown in Figure 71 and Figure 72, the curing condition has a significant effect on the creep behavior of such concrete mixtures as MixiF, Mix2F, Mix3F, and Mix4F. Generally, the concrete specimens moistcured for 14 days had creeping strains which were less than those moistcured for 7 days by more than 13 percent. This observation applies to the specimens loaded at both 40% of compressive strength and 50% of compressive strength at the two given loading ages. Also, it is of significance to mention that, for ultrahigh strength concrete, the effect of curing condition on creep strain is extremely important. For example, the specimens from Mix1F moistcured for 14 days have creep strain at 91 days over 25 percent less than those moistcured for 7 days. This is due probably to its high cementitious materials content, 1000 lbs per cubit yard, and low water to cementitious ratio of 0.24. Thus, longterm moist curing condition is needed to make cement hydration as complete as possible. The tremendous effects of curing conditions on creep behavior also extend to the concrete mixtures with lightweight aggregate, such as Mix9LF and Mix1OLS. For example, the creep strain of Mix9LF moistcured for 14 days and loaded at 50% of compressive strength is 0.000749, which is 29.8% lower than that of Mix9LF moistcured for 7 days and loaded at the same loading level. The creep strain of MixO1LS moistcured for 14 days and loaded at 50% of compressive strength is 0.000776, which is 47.3% lower than that of MixO1LS moistcured for 7 days and loaded at 50% of its compressive strength. However, no substantial effect of curing condition on creep strain was seen from the concrete mixtures containing ground granulated blastfurnace slag as mineral additives. For example, the creep strain of Mix5S moistcured for 14 days is nearly identical to that of Mix5S moistcured for 7 days. This similar situation can also be seen from Mix6S, Mix7S and Mix 8S. The cause can be attributed probably to the fact that the slag concretes nearly develop their compressive strength fully in 14 days. That is to say, in comparison with the compressive strength at 14 days, slag concrete mixtures have no significant increase in compressive strength at age of 28 days. That means the specimens moistcured for 14 days has no significant change in microstructure in comparison with those moistcured for 7 days. Thus, creep strains of slag concretes obtained under two different curing conditions show no significant difference. 1.40E03 E 7day moist curing 0 14day moist curing 1.20E03 1.00E03 D 8.00E04 / 6.00E04 o 4.00E04    2.00E04 0.00E+00 1F 2F 3F 4F 5S 6S 7S 8S 9LF 10LS Mixture Figure 71 Effects of curing condition on creep of concrete loaded at 40% of compressive strength 1.60E03i O 7day moist curing S14day moist curing 1.40E03 1.20E03 1.00E03    8.00E04 6.00E04 :: 4.00E04   2.00E04 ' 0.00E+00 1F 2F 3F 4F 5S 6S 7S 8S 9LF 10LS Mixture Figure 72 Effects of curing condition on creep of concrete loaded at 50% of compressive strength 7.2.2 Effects of Loading Condition on Creep Behavior of Concrete The effects of stress level on creep of the concretes investigated in this study are presented in Figure 73 and Figure 74. As shown in Figure 73 and Figure 74, the concrete specimens loaded at 50% of compressive strength develop considerably higher creep strain than those loaded at 40% of compressive strength at loading age, and the significant effects of stress level on creep strain can be seen from both the normal weight aggregate concretes and lightweight aggregate concretes. As shown in Table 71, for the concrete mixtures with fly ash, after 7 days moist curing the specimens of Mix1F loaded at 50% of compressive strength have creep strain of 0.00093, nearly 20% higher than those loaded at 40% of compressive strength. The 7day moistcured specimens from Mix2F loaded at 40% of compressive strength have creep strain at 91 days 18.5 percent less than those loaded at 50% of compressive strength. For Mix3F and Mix4F, creep strain of specimens moistcured for 7 days and loaded at 40% of compressive strength is 31.6% and 22.7% lower than those of the same concretes moistcured under the same condition but loaded at 50% of compressive strength. For the concrete mixtures with slag, creep strains of Mix5S, Mix6S, Mix7S and Mix8S moistcured for 7 days and loaded at 50% of compressive strength are 22.8%, 11.9%, 17.2%, and 16.3% higher than those of the same corresponding concretes cured under the same condition but loaded at 40% of compressive strength. Significant effects of loading conditions on creep behavior can also be observed from the specimens moistcured for 14 days. For the fly ash concretes, the specimens of MixiF, Mix2F, Mix3F and Mix4F moistcured for 14 days and loaded at 50% of compressive strength creep 12.7%, 22.1%, 18.5% and 18.5% higher than those of the same corresponding concretes loaded at 40% of compressive strength correspondingly. For slag concretes, the creep strains of Mix5S, Mix6S, Mix7S and Mix8S moistcured for 14 days and loaded at 50% of compressive strength are 18.3%, 16.1%, 16.4% and 18.6% higher than those of the same corresponding concretes loaded at 40% of compressive strength. In addition, significant effect of loading condition on creep behavior can be seen from the concrete mixtures with granite aggregate. For example, in comparison with the specimens loaded at 40 percent of compressive strength, the creep strain of the specimens loaded at 50 percent of compressive strength is over 23% higher. Similar observation can also be seen from the concrete mixtures with lightweight aggregate. 1.60E03 1.40E03 1.20E03 C) o S1.00E03 O, .s 8.00E04 C 6.00E04 0 4.00E04 2.00E04 O.OOE+00 :  . ..  .. . 1F 2F 3F ... ...i...tu..r... ::i~~iU : :R~iU :: i~~ C ... ... ... ... :: ~~iCU ::Rii ~ : : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1F 2F 3F 4F 5S 6S 7S 8S 9LF 1OLS Mixture Figure 73 Effects of stress level on creep of concrete moistcured for 7 days E 40% of compressive strength 050% of compressive strength 1.40E03 5 40% of compressive strength E 50% of compressive strength 1.20E03 1.00E03 8.00E04 6.00E04 6 4.00E04 2.00E04 0.00E+00 Mixture Figure 74 Effects of stress level on creep of concrete moistcured for 14 days 7.2.3 Effects of Aggregate Types on Creep Behavior of Concrete The effect of two different normal coarse aggregates on creep behavior was investigated on four typical concrete mixtures, i.e. Mix2F, Mix3F, Mix5S and Mix7S. These mixes used a Miami Oolite limestone as coarse aggregate. The four concrete mixtures with Georgia granite aggregate were labeled as Mix2GF, Mix3GF, Mix5GS, and Mix7GS. The creep behavior of these concrete mixtures was compared under the same curing conditions and loading conditions. As shown in Figures 75 through 78, the comparison between Mix2F and Mix2GF, Mix3F and Mix3GF, Mix5S and Mix5GS, and Mix7S and Mix7GS indicate that Mix2GF, Mix 3GF, Mix5GS, and Mix7GS creep slightly more than the corresponding Mix2F, Mix3F, Mix 5S and Mix7S for all loading conditions. This agrees with the findings from the study by G.E. Troxell et al [G.E. Troxell et al, 1958]. He carried out the study on the effect of six different types of aggregate on creep behavior of concrete. The results indicate that the concrete with 153 limestone aggregate has the lowest creep strain in comparison with the concretes with other types of coarse aggregates, including quartz, granite, gravel, basalt and sandstone. In addition, the concrete mixtures with lightweight aggregate, such as Mix9LF and Mix 10LS, do not creep as much as the concrete mixtures with normal weight aggregate. As can be seen from Table 71, Mix9LF and Mix1OLF develop much less creep strain than the concrete mixtures, such as Mix2F, 3F, 4F, 5S, 6S, 7S, and 8S, even though the compressive strengths of Mix9LF and MixLS are considerable lower than those of concrete mixtures with normal weight aggregate. These results agree with the conclusion made by A.M. Neville [A.M. Neville, 1996], which stated that, as a general rule, the creep of structural quality lightweight aggregate concrete is about the same as that of concrete made with ordinary aggregate. 1.50E03 1.20E03 c 9.00E04 (U, o 6.00E04 3.00E04 0.00E+00 10 20 30 40 50 Time (days) 60 70 80 90 Figure 75 Effects of aggregate type on creep behavior of Mix2F S*Georgia granite40%28day curing Georgia granite50%28day curing AMiami Oolite limestone40%28day curing x Miami Oolite limestone50%28day curing 1.20E03 1.00E03 8.00E04 S6.00E04 4.00E04 2.00E04 0.00E+00 0 10 20 30 40 50 60 70 80 90 100 Time (days) Figure 76 Effects of aggregate type on creep behavior of Mix3F 1.50E03 I I 1.20E03 9.OOE04 6.OOE04 3.OOE04 0.OOE+00 0 10 20 30 40 50 60 70 80 90 100 Time (days) Figure 77 Effects of aggregate type on creep behavior of Mix5S *Georgia granite40%28day curing  Georgia granite50%28day curing SMiami Oolite Limestone40%28day curing SMiami Oolite limestone50%28day curing  Georgia granite40%28day curing eGeorgia granite50%28day moist curing SMiami Oolite limestone40%28day curing SMiami Oolite limestone50%28day curing 1.50E03 1.20E03  9.00E04 o 6.00E04 3.00E04 0.00E+00 0 10 20 30 40 50 60 70 80 90 100 Time (days) Figure 78 Effects of aggregate type on creep behavior of Mix7S 7.2.5 Effects of Water to Cement Ratio and Air Content on Creep Strain The main component of creep in concrete is from creep of the hydrated cement paste. Creep is related to internal movement of absorbed or intracrystalline water, i.e. to internal seepage [A.M.Neville, 1996]. Glucklich's study has shown that concrete from which all evaporable water has been removed exhibits practically no creep [J. Glucklich, 1962]. Thus, water to cementitious materials ratio gives a significant effect on the magnitude of creep strain. Also, voids in the concrete play a critical role in influencing creep behavior of concrete because internal seepage of water from the absorbed layers to voids such as capillary voids is quite possible. A.M.Neville [A.M.Neville, 1996] stated that creep appears to be a function of the relative amount of the unfilled space, and that the voids in the gel govern creep in concrete. The effects of water to cementitious materials ratio and air content on creep of concrete are illustrated in Figures 79 through 712. From these figures, it can be seen that creep of concrete 156   *Georgia granite40% loading level SGeorgia granite50% loading level Miami Oolite limestone40% loading level xMiami Oolite limestone50% loading level increases as water to cementitious materials ratio increases. It can also been seen from these figures that the creep strain increases with increase of air content of fresh concrete, even though air content of fresh concrete may not be directly related to the void content of hardened concrete. 7.2.6 Relationship between Compressive Strength and Creep Strain It is always desirable in practice to find the relationship between compressive strength and creep strain. If a simple relationship can be found between compressive strength and creep, it is not necessary to consider the effect of type of cement, aggregate content and aggregate type, water to cement ratio, air content and age on creep behavior separately. In addition, possible accurate estimation on creep strain based on characteristic strength of concrete will make us free from timeconsuming creep test. In Figure 713, compressive strength of concrete at 14 days is plotted against creep strain at 91 days for the concretes moistcured for 7 days and loaded at 40% and 50% of compressive strength. In Figure 714, the compressive strength of concrete at 28 days is plotted against creep strain at 91 days for the concretes moistcured for 14 days and loaded at 40% and 50% of compressive strength. As seen from Figure 713 and Figure 714, the creep strain decreases with increase of compressive strength of concrete. Regression analysis was performed to determine the relationship between compressive strength and creep strain at 91 days using following simple linear function Ec91 =a fc (71) The results of the regression analysis are presented in Table 72. As shown in Table 72, loading condition has a significant influence on the slope and interception of the above linear equation, while curing age has nearly no effect on the slope and interception. That is to say, the relationship between compressive strength and creep strain obtained under the load at 40% of compressive strength can be expressed as one single linear equation regardless of what curing condition was applied to the specimens. The same conclusion also applies to concrete specimens loaded at 50% of compressive strength. The above hypothesis is confirmed by the results of regression analysis given in Table 71, and also shown in Figure 7 15. In addition, instantaneous strains of normalweight aggregate concrete are plotted against compressive strength of concrete at corresponding curing ages in Figure 716. It indicates that instantaneous strain measured in creep test increases with increase of compressive strength of concrete. 1.40E03 1.20E03 1.00E03 8.00E04 6.00E04 A tAAM" t A 't.UUr_U't 2.OOE04 0.OOE+00 0.20 0.25 0.30 0.35 0.40 0.45 Water to Cementitious Materials Ratio Figure 79 Effects of water to cementitious materials ratio and air content on creep of concrete moistcured for 7 days and loaded at 40% of compressive strength A high air content * low air content A e TTa A ^ ^^ ^ a 0.50 1.50E03 1.20E03 9.00E04 6.00E04 3.00E04 0.OOE+00  0.20 0.25 0.30 0.35 0.40 0.45 Water to Cementitious Materials Ratio Figure 710 Effects of water to cementitious materials ratio and air content on creep of concrete moistcured for 7 days and loaded at 50% of compressive strength 1.20E03 1.00E03 8.00E04 6.00E04 4.00E04 2.00E04 0.OOE+00 0.20 0.25 0.30 0.35 0.40 0.45 Water to Cementitious Materials Ratio Figure 711 Effects of water to cementitious materials ratio and air content on creep of concrete moistcured for 14 days and loaded at 40% of compressive strength 0.50 A high air content N low air content a a 0.50 i i i i i 2.00E03 1.60E03 1.20E03 8.00E04 4.00E04 0.00E+00 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Water to Cementitious Materials Ratio Figure 712 Effects of water to cementitious materials ratio and air content on creep of concrete moistcured for 14 days and loaded at 50% of compressive strength Table 71 Regression analysis on relationship between compressive strength and creep strain using Ecuation 71 Curing Loading condition condition 14day 40% 95% Confidence c Interval 1.19E07~ 8.57E08 .2E 5.29E08 1.62E07 1.20E07 E0 7.75E08 1.23E07 9.27E08 .2 0 6.29E08 1.46E07 1.11E07 7.62E08 1.10E07 8.99E08 .94E 6.94E08 1.39E07 1.13E07 E0 8.80E08 95% Confidence j3 Interval 1.54 3 1.28E03 ~ 1.54E03 1.81E03 1.65E03 ~ 1.98E03 2.32E03 1.35E03 ~ 1.59E03 35E03 1.84E03 1.67E03 ~ 1.95E03 2.24E03 57E03 1.41E03 1.57E03 1.74E03 1.75E03 ~ 1.95E03 2.16E03 2.16E03 R Syx 0.69 8.38E05 0.72 1.08E04 0.70 8.70E05 0.71 1.01E04 0.70 8.33E05 0.71 1.03E04 A high air content Slow air content Aa 7day moist curing 40% 50% moist curing All curing conditions 50% 40% 50% 1.80E03 1.50E03 1.50E03  7day50% 1.20E03 9.00E04   c^^, 0 n ^   3 9.00E04 (C 6.00E04 3.00E04 0.00E+00 4000 5000 6000 7000 8000 9000 10000 11000 12000 Compressive Strength at loading age Figure 713 Relationship between compressive strength and creep strain of concrete moistcured for 7 days 1.80E03 1.50E03 1.20E03 . 9.00E04 0) S6.00E04 3.00E04 0.00E+00 ! 5000 6000 7000 8000 9000 10000 11000 12000 Compressive Strength at loading age Figure 714 Relationship between compressive strength and creep strain of concrete moistcured for 14 days 1.80E03 I o 40% loading level S50% loading level 1.50E03 6 1.20E03  >  . 9.00E04 0 o o S6.00E04 o " 3.00E04 0.00E+00 4000 5000 6000 7000 8000 9000 10000 11000 12000 Compressive Strength (psi) Figure 715 Relationship between compressive strength and creep strain of concrete under all curing conditions 1.20E03 S40% of compressive strength o 50% of compressive strength 1.00E03 F o S8.00E04  E 0 0 0 * 6.00E04 . IP 0 c 4.00E04 cu 2.00E04 0.00E+00 5000 6000 7000 8000 9000 10000 11000 12000 Compressive Strength (psi) Figure 716 Relationship of compressive strength to instantaneous strain measured in creep test 162 7.3 Creep Coefficient Creep coefficient, which is calculated by dividing creep strain by elastic strain, is a very important parameter in prestressed concrete design. Creep coefficient is significantly affected not only by those factors influencing creep strain, but also by the elastic property of concrete. 7.3.1 Effects of Loading Conditions on Creep Coefficient For the specimens moistcured for 7 days, the creep coefficients obtained from two different stress levels are plotted in Figure 717 for ten concrete mixtures. It shows that two different stress levels have nearly no effect on the creep coefficient of all the concrete mixtures. The same observation can be seen from the specimens moistcured for 14 days as well, as shown in Figure 718. In this study, two stress levels include 40% of compressive strength and 50% of compressive strength. Thus, the conclusion can be arrived that the ratio of creep strain to instantaneous strain of concretes investigated in this study is proportional to the stress applied up to 50% of compressive strength at loading age. 7.3.2 Effects of Curing Conditions on Creep Coefficient Curing conditions have some effects on creep coefficient. As shown in Figure 719, the effects of curing conditions on creep coefficients of MixiF, Mix2F, and Mix3F are substantial. For example, the creep coefficient of Mix1F moistcured for 14 days is 0.81 at 91 days, which is 35.8% lower than that of Mix1 moistcured for 7 days. Also, the creep coefficients of Mix2F and Mix3F moistcured for 14 days are 23.9% and 17.7% lower than those of the same corresponding concretes moistcured for 7 days. However, for some concrete mixtures, such as Mix6S, Mix7S, Mix8S, and Mix4F, the effects of curing conditions on creep coefficient are not very appreciable. For instance, the creep coefficients of Mix6S, Mix7S, Mix8S and Mix 4F moistcured for 14 days are just about 10% lower than those of them moistcured for 7 days. 163 The cause can be attributed to the fact that there was not too much additional strength development from the age of 14 days to the age of 28 days for the slag concretes. 2.00 0 40% of compressive strength 1 50% of compressive strength I Difference 1.50 1.00 340% of compressive strength 1F 2F 3F 4F 5S 6S 7S 8S 9LF 1erence LS 0.50       . ::: 0.50 Mixture Figure 718 Effects of stress level on creep coefficient of concrete moistcured for 14 days 0.00 0.50 0 0.50 Mixture Figure 717 Effects of stress level on creep coefficient of concrete moistcured for 7 days 2.00 1.50 Mixture Figure 718 Effects of stress level on creep coefficient of concrete moistcured for 14 days The effects of curing condition on creep coefficient of lightweight aggregate concrete are very significant. For instance, the creep coefficient of Mix9LF moistcured for 14 days is about 1.14, nearly 18% lower than that of Mix9LF moistcured for 7 days. Also, the specimens of MixO1LS moistcured for 14 days has creep coefficient of 1.13, which is over 42% lower than 1.61, creep coefficient of Mix6 moistcured for 7 days. Thus, apparently, longer curing time can decrease creep coefficient tremendously for lightweight aggregate concrete. 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 1F 2F 3F 4F 5S 6S 7S 8S 9LF 10LS Mixture Figure 719 Effects of curing condition on creep coefficient of concrete 7.3.3 Effects of Water Content on Creep Coefficient Since water content of fresh concrete affect significantly drying creep of concrete, they should have considerable effects on creep coefficient as well. As can be seen from Figure 720, water content of fresh concrete have significant effects on creep coefficient of concrete at 91 days. Creep coefficient at 91 days increases as water content of fresh concrete increases. 2.50 2.00 cj o S1.50 C 1.00 O O 0.50 0.00 100 150 200 250 300 350 400 Water Content (Ibs/yard3) Figure 720 Effects of water content on creep coefficient at 91 days 7.3.4 Effects of Compressive Strength at Loading Age on Creep Coefficient As shown in Table 71, the higher the compressive strength of concrete is at the loading age, the lower the creep coefficient is. For example, for the concrete mixtures with Miami Oolite limestone aggregate, Mix1 has the highest compressive strength, and it has the lowest creep coefficient. Also, it is of great importance to see that the creep coefficient is not affected by the loading conditions, i.e. the creep coefficient obtained under the loading condition of 40% of compressive strength is identical to that obtained under the loading condition of 50% of compressive strength. To find out how the compressive strength of concrete at loading age is related to the creep coefficient at 91 days, compressive strength at loading age was plotted against corresponding creep coefficient at 91 days in Figure 721 and Figure 722, for specimens loaded at 14 days and o Miami Oolite limestone * Georgia granite A Stalite lightweight aggregate Go8 A i i i i i  28 days, respectively. Then linear regression analysis using Equation 72 was performed, and the analyzed results are displayed in Table 72. (P, =a f, + P (72) Where ypc = creep coefficient at 91 days; f, = compressive strength; ac and 3 = the slope and interception of linear equation. Table 72 Regression analysis on relationship of compressive strength to creep coefficient using Equation 72 95% 95% Curing condition a Confidence p Confidence R2 Syx Interval Interval 2.39E04 ~ 14day curing 2.02E04 1.E04 3.016 2.717 3.316 0.9041 0.0951 1.64E04 2.43E04 ~ 28day curing 2.06E04 .E04 3.077 2.774 3.379 0.8855 0.1071 1.69E04 All curing conditions 2.03E04 1.79E04 3.042 2.842 3.242 0.8919 0.0999 1.79E04 As can be seen from Table 72 as well as Figure 721 and Figure 722, compressive strength of concrete at loading age is nearly linearly related to the creep coefficient at 91 days. This situation is true for the specimens under two different curing conditions. Also, it is to be noted that the slope and interception of the linear regression equations are nearly identical to one another for the specimens under two different curing conditions. That is to say, once compressive strengths of specific concrete mixtures are given, the creep coefficient can be computed using the linear relationship between compressive strength and creep coefficient at 91 days regardless of what curing condition was applied to the specimens. Therefore, linear regression analysis was carried out on the experimental data obtained from both curing conditions, and the analyzed results are plotted in Figure 723 and presented in Table 72 as well. As can be seen from Table 72, the slope and interception of linear regression equation from combined analysis are approximately equal to the average of slopes and interceptions from separate analyses. 2.50 2.00 0. 1o50 1.00 0.50 0.00 2000 4000 6000 8000 10000 12000 14000 Compressive strength at 14 days (psi) Figure 721 Relationship between compressive strength and creep coefficient for specimens loaded at 14 days 2.50 2.00 S1.50 (Ds 0 D 1.00 0.50 0.00 400 10 6000 8000 10000 12000 Compressive Strength at 28 Days (psi) 14000 Second phase o First phase S 0 Figure 722 Relationship between compressive strength and creep coefficient for specimens loaded at 28 days 2.50 O Limestone S Granite 2.00 S1.50 0.50 0.00 4000 6000 8000 10000 12000 14000 Compressive Strength (psi) Figure 723 Relationship between compressive strength at loading age and corresponding creep coefficient at 91 days 7.3.5 Relationship between Elastic Modulus at Loading Age and Creep Coefficient After realizing the close relationship between compressive strength and creep coefficient, it is not difficult to note that because, for a given concrete, compressive strength and elastic modulus is related, creep coefficient and elastic modulus should be related as well. As shown in Figure 724, elastic modulus was plotted against creep coefficient at 91 days for the concrete with normalweight aggregate. A linear regression analysis was performed using Equation 73. p, = a E +p/ (73) The results of the regression analysis are shown in Table 73. As can be seen from Figure 724, for the normalweight aggregate concrete, creep coefficient at 91 days is linearly related to the elastic modulus at the loading age, while for lightweight aggregate concrete creep coefficient can not be related to elastic modulus using the linear equation from normalweight aggregate concrete. More data from creep test on lightweight aggregate concrete are needed to establish reliable relationship between elastic modulus and creep coefficient for lightweight concrete. In addition, creep coefficient at 91 days was plotted against the ratio of compressive strength and elastic modulus in Figure 725. It indicates that creep coefficient at 91 days is linearly related to the ratio of compressive strength to elastic modulus of concrete at loading age. A linear regression analysis was performed to relate creep coefficient to the ratio of compressive strength to elastic modulus by the following equation: C = fa + (74) E The results of the regression analysis are presented in Table 74. 2.40 o Normal weight aggregate 20* Lightweight aggregate 2.00 N_ 0 oc cP 1.60 0 o 0 1.20 # oo S** 00 0.80 0 0\ 0.40 0.00 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06 7.00E+06 8.00E+06 Elastic Modulus at Loading Ages (psi) Figure 724 Effects of Elastic modulus at loading age on creep coefficient at 91 days 2.50 2.00 U, o ) 1.50 Ea, o 1.00 0 a, 0.50 0.00 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 Figure 725 Relationship between creep coefficient at 91 days and f,/E Table 73 Regression analysis on relationship of elastic modulus to creep coefficient using Equation 73 95% 95% 2 S 0 R SSE confidence interval confidence interval 5.67E07 3.151 4.55E07 3 7 3.725 0.6671 0.1742 3.43E07 4.299 Table 74 Regression analysis on relation of creep coefficient to fo/E using Equation 74 95% 95% R2 SSE confidence interval confidence interval 1609 3.010 1132 3.485 0.7026 0.1647 1014 3.959 7.3.6 Effects of Coarse Aggregate Type on Creep Coefficient As can be seen from Figure 726, the creep coefficients of concretes made with Georgia granite is higher than those of concretes with Miami Oolite limestone aggregate. This is due probably to the lower elastic deformation of concretes with Georgia granite aggregate in comparison with those with Miami Oolite limestone aggregate. Therefore, the ratio of creep strain to elastic strain is larger for Georgia granite aggregate concrete. However, lightweight aggregate concrete behaves in a different way in comparison with Georgia granite aggregate concrete. Since the elastic deformation of lightweight aggregate concrete is significantly higher than that of Georgia granite aggregate concrete and Miami Oolite limestone aggregate concrete, the ratio of creep strain to elastic strain is lower for lightweight aggregate concrete. This observation is in agreement with the conclusion given by Neville [A.M. Neville, 1996]. 2.00 E Miami Oolite limestone 1.80 1 Georgia granite_ 1.60 1.40 m 1.20 1.00 0.00 o 0.80 0.60 a 0.40 0.20 0.00 Mix2 Mix3 Mix5 Mix7 Mixture Figure 726 Effects of coarse aggregate type on creep coefficient at 91 days 7.4 Creep Modulus Creep modulus, defined as the ratio of stress applied to concrete specimen to the total strain excluding shrinkage strain, reflects the decay of stiffness with time. Apparently, this parameter is of great important in inelastic structural material analysis to obtain timedependent elastic modulus so that accurate deformation of material can be computed correctly using the reduced elastic modulus. Figure 727 presents a typical decay curve of concrete mixture investigated in this study. As can be seen from Table 71, for the fly ash concrete mixtures, curing condition has significant effects on the creep modulus as a function of time. That is to say, the decay of creep modulus of specimen moistcured for 14 days is considerably less than that of the same concrete moistcured for 7 days. The same observation can also be made on the lightweight aggregate concrete as well. This indicates that curing condition plays a very significant role in decreasing creep strain of fly ash concrete and lightweight aggregate concrete. However, for the slag concrete mixtures, no appreciable effects of curing condition on creep modulus can be observed. This means that a longer curing time beyond 14 days has no significant influence on the creep behavior of slag concrete. 6.00E+06  7day moist curing40% of compressive strength 7day moist curing50% of compressive strength 5.00E+06  14day moist curing40% of compressive strength 14day moist curing50% of compressive strength 4.00E+06 3.00E+06  2.00E+06  1.00E+06 0.00E+00 0 10 20 30 40 50 Time (days) 60 70 80 90 100 Figure 727 Typical decay curves of creep modulus with time 7.5 Prediction of Ultimate Creep Strain It is often assumed that creep rate for a concrete material decreases with time, and the creep strain will approach a limiting value after an infinite time under load. The study by G.E. Troxell et al [G.E.Troxell et al, 1958] indicates that the average value of creep strain after 30 years is 1.36 times the oneyear creep strain. In engineering practical point of view, it is often assumed that the 30year creep strain represents the ultimate creep stain. The ultimate creep strain of concrete investigated in this study was determined using asymptotic equation, given as follows, to fit the experimental data. c =_a (75) This equation is the ratio of two polynomials. As the time variable approaches infinity, the ratio of two polynomials will be equal to 1. Therefore, ultimate creep strain is equal to a. In this equation, a and 3 are two parameters to be determined from curvefitting, and y, which is the factor borrowed from CEBFIP Equation, reflects the effect of geometrical characteristics of specimen and relative humidity on creep behavior of concrete. The relative humidity was controlled at 75% in this study. 6"x 2" cylindrical specimens were used for creep tests. The geometric characteristic of the test specimen, h, can be computed as follows: 2Ac 2x"xx32 h = 2 2= 3in = 76.2mm (76) u "x6 Then, y can be obtained as follows: ( 175% 8 h =150 1+1.2. +250=381.5<1500 (77) y 0100% 100 Thus, the equation used to fit the experimental data becomes t >8 sc =a. (78) Sa t +381.5 ( Least Squares Method of curve fitting as described in Chapter 6 was used to determine two unknown parameters, ac and p. Ultimate creep strains and ultimate creep coefficient after regression analysis for 14 concrete mixtures are presented in Table 75. Table 75 The predicted ultimate creep strain and creep coefficient Predicted items Ultimate creep strain ultimate creep coefficient Curing conditions curing condition 1 Curing condition 2 curing condition 1 Curing condition 2 Loading conditions 40% 50% 40% 50% 40% 50% 40% 50% MixIF 1.06E03 1.30E03 0.88E03 1.03E03 1.48 1.55 1.14 1.16 Mix2F 1.93E03 2.08E03 1.66E03 2.11E03 2.91 2.59 2.37 2.44 Mix3F 1.45E03 1.86E03 1.39E03 1.56E03 2.30 2.40 2.11 1.90 Mix4F 1.37E03 1.59E03 1.24E03 1.63E03 2.28 2.14 2.14 2.32 Mix5S 1.40E03 1.84E03 1.25E03 1.64E03 2.10 2.17 1.74 1.84 Mix6S 1.68E03 1.87E03 1.55E03 1.75E03 2.51 2.23 2.23 2.05 Mix7S 1.41E03 1.69E03 1.46E03 1.60E03 2.71 2.71 2.61 2.46 Mix8S 1.58E03 1.97E03 1.45E03 1.95E03 2.57 2.72 2.21 2.34 Mix9LF 1.11E03 1.40E03 0.99E03 1.16E03 1.78 1.83 1.46 1.49 MixO1LS 0.94E03 1.19E03 0.76E03 0.97E03 1.61 1.45 1.32 1.26 Mix2GF   1.80E03 2.10E03   2.99 2.70 Mix3GF   1.57E03 1.81E03   2.96 2.72 Mix5GS   1.42E03 1.77E03   2.51 2.55 Mix7GS   1.49E03 1.76E03   2.89 2.69 As shown in Table 76, it is to be pointed out that most of the concretes investigated in this study have an ultimate creep coefficient higher than 2.0. 7.6 Evaluation on Creep Prediction Models The effectiveness of other creep prediction models, such as Burgers model, C.E.BF.I.P model and ACI 209 model, were evaluated in this study. S Burgers model Burgers Model or fourelement model, as shown in Figure 728, was also used to fit the experimental data to evaluate the feasibility of the Burgers model to predict creep strain of concrete at a later time, based on the experimental data obtained in three months. 00 R1 81  ti t  ^~ .  SA' 83 R2 2 ..83. CA3 O ,1 D Figure 728 Burgers Model The total strain predicted by the Burgers model can be considered as the sum of the strain responses of each element under the applied load, and can be expressed by the following equation: E = 8, + E2 + E3 (79) Where ;1 is the elastic strain of spring in a Maxwell model, and it can be given as 1, (710) Ri 82 is viscous flow of dashpot in a Maxwell model, and its rate type formula can be expressed as E, = (711) 83 is the strain of a Kelvin unit, and it can be related to the applied stress as E'3+ E3 (712) 172 72 Eliminating 8, 82, and 83 from the above four equations, the constitutive relationship between 8 and a in the Burgers model can be expressed as a + 1 + +2 ,+ 1a12 o 12 e" (713) R1 R2 R2) RR2 R2 Solving the above second order differential equation with initial conditions of R1 t = 0 > = E3 =0 (714) s'= + O /71 /72 The creep behavior of Burgers model under the constant stress can be derived as: E(t)= + t + 1 exp 2 t (715) R, ,1 R2 /2 )) In this study, only creep strain was considered. Thus, we can eliminate the first term in Equation 79. Therefore, the strain in the Burgers model becomes: E(t)= ao t + O 1 exp R2 t (716) l7, R2 172 ) Three material constants, R2, rf and "2, can be easily determined by curvefitting Equation 716 to the experimental data. As can be seen from Equation 716, after a certain time, the second term on right side of equation will decay and approaches , and the creep rate will become a constant value, i.e. R2 0 So, after a long time, the expression for the strain from the Burgers model can be simplified 771 as follows: E(t) = o t + (717) 7, R, Burgers model with constitutive parameters determined from regression analysis was plotted in Figure 729. As can be seen from Figure 729, Burger's model is very capable to simulate the development trend of creep of concrete. However, it indicates that the extrapolation made by Burgers model results in overestimation of the ultimate creep strain. This is due the lack of longterm creep data from this study. It is not possible to determine the constitutive parameters accurately without longterm creep data. 1.50E03 1.20E03  .S 9.00E04  S6.00E04 / 14day40% o 14day50% 3.00E04  Regression analysis H' Burger's Model 0.00E+00 0 20 40 60 80 100 Time (days) Figure 729 Prediction of strain using the Burger's model * C.E.BF.I.P Model (1990) C.E.BF.I.P Model is an empirical model recommended by Europe Union in 1990. In this model, the creep strain can be predicted based on the information from ultimate compressive strength and modulus of elasticity at loading age, and a time function determined according to the mechanical properties of specific concrete mixture, the geometry of specimen, and the curing conditions applied to the specimen, and so on. The general equation is given as follows: 178 Sc (t, to) = (t, to) (718) Ec, For the detail description about C.E.BF.I.P model, please refer to the literature review in Chapter 2. Finally, combining all the equations together and simplifying them, we have the following equation used to predict the development of creep strain with time. o (to) 1RH/RHo 5.3 1 (tto)/t ccr (t, to) E0.46. (h/h3) fJ f.1/ fcmo O.l+ (to t)0 2 H (t _t 1 E, 0. o46. (h Iyo fi r _)It,_1 (719) In this study, the relative humidity is controlled at 75%. For 6"x 12" cylinder, the geometrical characteristic of the test specimen, h, can be computed as follows: 2A 2xrx32 h = rx 3in = 76.2mm (720) u ix6 Then, /,h can be obtained as follows: 18 75%o 76.2 /H =15.0 1+ 1.2 75 ] 7. +250=381.5<1500 (721) H 5 100%) 100 Then, the prediction formula can be simplified as follows: For concrete cured for 14 days: to) c(to) 18.55 (t 14) 0 (722) 8cr (t,t0) = K(722) Ecl4 \fc. L 381.5 + (t 14) The above equation is an asymptotic function. As time approaches infinity, creep strain .. c(to) 18.55 will reach ultimate creep strain t ,j . Similarly, for the concrete specimen cured for 28 days, the prediction equation becomes 179 scr(t, to) = UC(t0) 18.55 1. (t 28) .1o3 (723) s )= (t, to) = (723) Ec28 381.5 + (t 28) As can be seen from the above equation, this asymptotic equation approaches a limiting value as time approaches infinity. Therefore, ultimate creep strain can be computed by the following formula: u(to) 18.55 (724) Ec28 m To evaluate the effectiveness of the C.E.BF.I.P model, the C.E.BF.I.P Equation was plotted in Figure 730. It indicates that C.E.BF.I.P model gives very good prediction. To verify this conclusion, the creep strain at 91 days from experimental measurements is plotted against the creep strain computed according to C.E.BF.I.P model in Figure 731. It clearly shows that the measurements match very well with the predictions made by the C.E.BF.I.P model. 1.50E03 14day40% o 14day50%  Regression analysis 1.20E03  CEBFIP model o ACI 209 model . c 9.00E04 .. 0 6.00E04 3.00E04  0.00E+00 0 10 20 30 40 50 60 70 80 90 100 Time (days) Figure 730 Comparison on the effectiveness of C.E.BF.I.P model and ACI model 1.80E03 A First phase o Second Phase 1.50E03 o0 y=x 1.20E03 o AO 9.00E04 o 2 00 2A S6.00E04 0 0 0 3.00E04  0.00E+00 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 Predicted Creep Strain at 91 days Figure 731 Comparison between the creep strain at 91 days from experimental data and the predicted creep strain using CEBFIP model Also, in order to verify if there is simple linear relationship between creep strain and, the creep strain at 91 days was plotted against in Figure 731, where oy is E E E stress applied to the specimen; E is elastic modulus of concrete at loading age; and fcm is characteristic strength of concrete at loading age. Then, a linear regression analysis was performed to determine the relationship between creep strain at 91 days and and the analyzed results are shown in Table 76. As can be seen from Figure 731, creep strain at 91 days is linearly related to The regression equation is given as follows: c91 =13.40 U 1.758x104 (725) E7 If Table 76 Regression analysis on relation of creep coefficient to 95% 95% 2 confidence interval confidence interval 11.21 ~ 3.649E04 ~ 13.40 1 1.758E04 6E 0.6848 1.193E04 15.58 1.333E04 In addition, the ultimate creep strains predicted by curvefitting to experimental data were plotted against the creep strains calculated using the original C.E.BF.I.P model in Figure 732. It indicates that original C.E.BF.I.P model gives very good creep strain prediction for the normal weight concrete mixtures investigated in this study. 1.80E03 1.50E03 > 1.20E03 0 o ~ o /o 0 a 6.00E04 P 3.00E04 0.00E+00 0.00E+00 3.00E05 6.00E05 9.00E05 1.20E04 1.50E04 c/(Exfe,, 0.5) Figure 732 Relationship between creep strain and mechanical properties at loading age 3.00E03 2.50E03  S/ y=x 0) 0 0 a S2.00E03  00 I 1.50E03 .000 8 D 0 given as follows: 28 (726) S1.00E03 C p COefficient 0 E 5.OOE04________ 0.00E+00 _ 0.OOE+00 5.00E04 1.00E03 1.50E03 2.00E03 2.50E03 3.00E03 Predicted Ultimate Creep Strain by CEBFIP model Figure 733 Comparison between the ultimate creep strain calculated by C.E.BF.I.P model and that by curvefitting SACI209R model The evaluation on ACI 209 model was performed in this study. ACI 209 (1992) model is given as follows: (t t)06 028 Q(, to)=0 ^(tot (726) 10 + (t to)06 Where 028 (t, to ) Creep coefficient at time t; & (to) Ultimate creep coefficient; to Time of loading. In this study, to = 14 days for concrete cured for 14 days before loading; and to = 28 days for concrete cured for 28 days before loading. The ultimate creep coefficient can be expressed as: q.(to)= '. (727) The constant & = 2.35 is recommended. The correction factors y, consist of the following terms: Yc = Ya YRH Yat Y. Yp Ya (728) Where Y1, Correction factor for loading age, which is equal to 0.916 for specimen cured for 14 days, and 0.814 for specimen cured for 28 days. yRH Correction factor for ambient relative humidity. In this study, the ambient relative humidity is 75%, thenyRH = 0.77. y, Correction factor for slump of fresh concrete. y, = 0.82 + 0.00264 S, (S, is slump in mm). Yp Correction factor for fine to total aggregate ratio. /y = 0.88 + 0.0024 pa (Pa is fine to total aggregate ratio) /a Correction factor for air content. yT = 0.46 + 0.09 a, (a, is air content) Yt, Correction factor for thickness of member. In this study, the volumesurface ratio method is used to obtain y2, 2, = 3 1+1.13 .e s (729) Where Volume to surface ratio in mm. s The correction factors based on the concrete mixtures, geometry of specimen and ambient conditions employed in this study for the ACI 209 model are provided in Table 77. Table 77 Correction factors for the ACI 209 model 14day moist 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 0.814 Yc Yrh Ys Ya Yat Yp 7day moist 0.77 1.34 0.57 1.00 0.88 0.30 0.77 1.32 0.87 1.00 0.88 0.45 0.77 0.92 0.69 1.00 0.88 0.36 0.77 1.02 0.64 1.00 0.88 0.33 0.77 1.31 0.80 1.00 0.88 0.42 0.77 1.05 0.66 1.00 0.88 0.34 0.77 1.09 0.96 1.00 0.88 0.50 0.77 1.00 0.80 1.00 0.88 0.41 0.77 0.82 0.73 1.00 0.88 0.38 0.77 0.82 0.93 1.00 0.88 0.48 0.77 1.12 1.13 1.00 0.88 0.58 0.77 0.99 0.60 1.00 0.88 0.31 0.77 1.26 0.96 1.00 0.88 0.50 0.77 0.97 0.80 1.00 0.88 0.41 14day moist 0.27 0.40 0.32 0.29 0.37 0.30 0.44 0.37 0.33 0.43 0.52 0.27 0.44 0.37 As can be seen from Figure 734, ACI 209 model greatly underestimates the creep strain of the concretes investigated in this study. 1.80E03 1.50E03 0) E a0 I 1.20E03 E o (, 9.00E04 tO e 6.00E04 U) o 3.00E04 0.OOE+00 K 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 Calculated Creep strain at 91 days Figure 734 Evaluation on ACI209 model and C.E.BF.I.P model Mix Mix1F Mix2F Mix3F Mix4F Mix5S Mix6S Mix7S Mix8S Mix9LF Mix10LS Mix2GF Mix3 GF Mix5GS Mix7GS Yla 7day moist 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 1.80E03 7.7 Summary of Findings This chapter presents the results from the creep tests in this study. The following is a summary of major findings from the creep tests: (1) Curing condition has some effect on creep of fly ash concrete and lightweight aggregate concrete, while its effect is very slight on slag concrete. (2) For the stress levels used (40 and 50% of compressive strength), the measured creep strain and instantaneous strain were linearly proportional to the stress applied. Thus, the computed creep coefficients were not affected by the stress level in this study. (3) Water to cementitious materials ratio has some effects on creep behavior of concrete. The higher the water to cementitious materials ratio, the more the concrete creeps. (4) For the concrete with identical water to cementitious materials ratio, the higher the air content of fresh concrete, the more the concrete creeps. (5) The concretes with granite aggregate creeps slightly more than the concretes with Miami Oolite limestone aggregate and lightweight aggregate under the same stress level. However, due to the much lower elastic modulus of lightweight aggregate concrete, the creep coefficient of lightweight aggregate concrete is much lower than that of normal weight aggregate concrete. Due to the higher elastic modulus of granite aggregate concrete, creep coefficient of granite concrete was much higher than that of the concretes with Miami Oolite limestone aggregate. (6) A simple linear relationship was established between compressive strength at loading age and creep strain at 91 days. (7) A linear relationship was also found between creep coefficient at 91 days and compressive strength (f,), elastic modulus (Ec), and the ratio of compressive strength and elastic modulus. The regression equation related compressive strength at loading age to creep coefficient at 91 days ((o91) is given as follows: c91 = a* fc +/P (72) Where a is equal to 2.03x104 and 3 equal to 3.042; f is in unit of psi. The regression equation relating elastic modulus to creep coefficient at 91 days is given as follows: (pc91 = a E + p (73) Where a is equal to 4.55x10.7 and 3 equal to 3.725; Ec is in unit of psi. The equation related creep coefficient at 91 days to the ratio of compressive strength to elastic modulus is given as follows: (Pc91 _= c  + (74) Ec With ac equal to 1132 and 3 equal to 3.485. Among these regression equations, Equation 72 gave the best prediction. (8) Ultimate creep coefficient of some of the concretes appeared to exceed 2.0. These concrete mixtures included Mix2F, Mix3F, Mix4F, Mix5S, Mix6S, Mix7S, Mix8S, Mix2GF, Mix3GF, Mix5GS and Mix7GS. (9) CEBFIP model (as shown in Equation 717) appeared to give better prediction on the creep behaviors of concretes investigated in this study than ACI 209 model (as shown in Equation725). CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Design of Creep Apparatus Performance and characteristics of creep apparatus designed for this study are presented as follows: 1) The creep apparatus designed in this study is capable of applying and maintaining a load up to 145,0001bs on the test specimens with an error of less than 2%. 2) Three specimens can be stacked for simultaneous loading. 3) When a maximum load of 145,0001bs is applied, the deflection of bearing surfaces of the header plates is less than 0.001in, and the pressure distribution on the test specimen varies by less than 0.026%, or 1.5psi. 4) The creep testing procedures developed in this study was found to work very well. They are given in detail in Section 4.3. 8.2 Findings from This Study 8.2.1 Strength and Elastic Modulus 1) Splitting tensile strengths of the concrete mixtures using granite aggregate were significantly lower than those using Miami Oolite limestone aggregate. This is due probably to the poor bonding condition between hardened cement paste and granite aggregate. 2) Compressive strengths of concretes with granite aggregate were comparable to or lower than those of concretes with Miami Oolite limestone aggregate. 3) The concrete with granite aggregate had higher elastic modulus than that with Miami Oolite limestone aggregate, while the lightweight aggregate concretes had lower elastic modulus than the normal weight concretes. 4) Fly ash concretes develop compressive strength and splitting tensile strength at a slower rate than the slag concretes. Fly ash concrete shows significant strength gain after 28 days, while this was not seen from the slag concrete mixtures. 5) The ACI 209 Equation for prediction of compressive strength (f (t)) at various curing age from compressive strength at 28 days (f,, (t)), which is given as follows, was modified to give better strength prediction for the various mixtures. t ' fc(t)= 4.0 +0.85t fc28 The modified equation has the following form for the concrete with different coarse aggregates: t c(t) a+t c2 The value of a was found to vary from 1.1 to 2.6 for the concretes with Miami Oolite limestone aggregate, from 2.6 to 5.3 for the concretes with Georgia granite aggregate, and from 4.2 to 6.7 for lightweight aggregate concretes; the value of 3 was found to vary from 0.82 to 0.93 for the concretes with Miami Oolite limestone aggregate, from 0.82 to 0.89 for the concrete with Georgia granite aggregate, and from 0.74 to 0.82 for lightweight aggregate concrete in this study. 6) The relationship between compressive strength ( f ) and splitting tensile strength (f, ) is established for the concrete mixtures investigated in this study. The Carino and Lew model, given as follows, S)0.73 was modified to the following equation: t )0.7185 Where f, and fc, are in units of psi. 7) The relationship between compressive strength and modulus of elasticity was refined in this study using Least Square of Curvefitting Technique. The ACI 31889 Equation, which is Ec = 57000Ff was modified to the following equation: Where a is equal to 55,949 for Miami Oolite limestone aggregate; 62,721 for Georgia granite aggregate; and 43,777 for Stalite lightweight aggregate. f, and Ec are in units of psi. 8) For all three aggregate types investigated in this study, a modified ACI 31895 prediction equation was developed: E = 30.16 w1 f + 484200 Where w is the density of concrete in pound per cubit foot. f" and E, are in units of psi. 8.2.2 Shrinkage Characteristics of Concretes Investigated 1) Fly ash concrete mixtures had slightly higher shrinkage strain at 91 days than slag concretes. This is due probably to the slow hydration rate of fly ash in comparison with that of slag. As a result of slower rate of hydration, there is more free water evaporating from the interior of the concrete, which can cause the concrete to shrink more. Thus, it is recommended that using a longer wet curing time would be helpful to reduce shrinkage of fly ash concrete. 2) Water content has a significant effect on drying shrinkage strain of concrete. The higher the water content, the more the concrete tends to shrink. However, no clear trend can be seen on the effects of water to cementitious materials ratio on shrinkage of concrete. 3) For the four concrete mixtures with Georgia granite aggregate, shrinkage strain is slightly lower than the four corresponding concrete mixtures with Miami Oolite limestone aggregate. Lightweight aggregate concrete shrinks more than normal weight aggregate concrete. This might be explained by their difference in elastic modulus. The concrete with a higher elastic modulus would have a stronger resistance to the movement caused by shrinkage of cement paste. 4) For the concretes tested, there appeared to be a relationship between the compressive strength ( f,) at the age when shrinkage test was started and the shrinkage strain (sh ) at 91 days as follows: 0.0001 ' sh = 0.0005 . e00 sh Where f is in unit of psi. 5) For the concretes tested, there appeared to be a relationship between elastic modulus (Ec) at the age when shrinkage test was started and the shrinkage strain (sh) at 91 days as follows: 2x107. .E Eh = 0.0007 e 2 10 E Where E, is in unit ofpsi. 6) According to the shrinkage test results from this study, the C.E.BF.I.P model (as shown in Equation 66) appeared to give better prediction than the ACI 209 model (as shown in Equation 63). Using ACI 209 model may result in overestimation of the ultimate shrinkage strain. 7) For the concrete investigated in this study, the ultimate shrinkage strain ranged from 1.93 x 104 to 3.64x 104 for the concretes with Miami Oolite limestone aggregate; from 2.18x104 to 2.83x104 for the concretes with Georgia granite aggregate; and from 3.49x104 to 4.22x104 for the concretes with Stalite lightweight aggregate concrete. 8.2.3 Creep Characteristics of Concretes Investigated 1) Curing condition has some effects on creep of fly ash concrete and lightweight aggregate concrete, while its effect on slag concrete is very small. 2) For the stress levels used (40 and 50% of compressive strength), the measured creep strain and instantaneous strain were linearly proportional to the stress applied. Thus, the computed creep coefficients were not affected by the stress level in this study. 3) Water to cementitious materials ratio has some effects on creep behavior of concrete. The higher the water to cementitious materials ratio, the more the concrete creeps. 4) For the concrete with identical water to cementitious materials ratio, the higher the air content of fresh concrete, the more the concrete creeps. 5) The concretes with granite aggregate creeps slightly higher than the concretes with Miami Oolite limestone aggregate and lightweight aggregate under the same stress level. However, due to the much lower elastic modulus of lightweight aggregate concrete, the creep coefficient of lightweight aggregate concrete is much lower than that of normal weight aggregate concrete. Due to the higher elastic modulus of granite aggregate concrete, creep coefficient of granite concrete was much higher than that of the concretes with Miami Oolite limestone aggregate. 6) A simple linear relationship was established between compressive strength at loading age and creep strain at 91 days. 7) A linear relationship was also found between creep coefficient at 91 days and compressive strength (f,), elastic modulus (Ec), and the ratio of compressive strength and elastic modulus. The regression equation, which relates compressive strength at loading age to creep coefficient at 91 days ((o91) is given as follows: c91 = a fc'+ 8 (72) Where a is equal to 2.03x104 and 3 equal to 3.042. Andf is in unit of psi. The regression equation, which relates elastic modulus to creep coefficient at 91 days is given as follows: (pc91 = a Ec + (73) Where a is equal to 4.55x10.7 and 3 equal to 3.725. And E, is in unit ofpsi. The equation related creep coefficient at 91 days to the ratio of compressive strength to elastic modulus is given as follows: (Pc91 = a c + P (74) EC With ac equal to 1132 and 3 equal to 3.485. Among these regression equations, Equation 72 gave the best prediction. 8) Ultimate creep coefficient of some of the concretes appeared to exceed 2.0. These concrete mixtures included Mix2F, Mix3F, Mix4F, Mix5S, Mix6S, Mix7S, Mix8S, Mix2GF, Mix3GF, Mix5GS and Mix7GS. 9) CEBFIP model (as shown in Equation 717) appeared to give better prediction on the creep behaviors of concretes investigated in this study than ACI 209 model (as shown in Equation725). 8.3 Recommendations Based on this study, the following recommendations are given for the further study: 1) Study on effects of aggregate gradation on shrinkage and creep of concrete. Since the gradation of aggregate has a great effect on the compressive strength of concrete [A.M.Neville, 1996] [Larry C. Muszynski et al, 1997] and compressive strength was found to be related to shrinkage and creep in this study, the effects of aggregate gradation on shrinkage and creep behavior of concrete should be studied in order to have a better understanding of this factor on shrinkage and creep of concrete. 2) Study on the optimization of mix proportion. The optimization of mix proportion should be studied to reduce shrinkage and creep of concrete. 3) Study on the interfacial characteristics between coarse aggregate and mortar paste in order to have a better interpretation on the effects of different aggregate types on strength of concrete. 4) Study on theological properties of concrete under sustained load in order to have a better understanding about the creep behavior of concrete. APPENDIX A MEASUREMENTS FROM STRENGTH TESTS Table A1 Results of compressive strength tests (psi) No. of Age of Testing (days) No. of7 14 mix 3 7 14 1 2 3 8018 8091 8123 4110 4195 3927 5325 5424 5118 5669 5783 5684 5351 5772 5539 6300 6402 6423 4323 4482 4166 4415 5017 4954 3019 3007 3092 1486 1411 1504 3982 3867 3807 2960 2865 3099 3746 3861 3847 2249 2205 2346 2 3 8554 8607 4680 4635 6449 6512 6762 6922 7739 6908 7316 8004 5435 5375 6202 6308 3939 3974 2310 2088 5046 4888 4612 4655 5211 5145 4178 4298 2 3 8869 9182 6032 5999 7649 7578 7208 6910 8208 8541 8481 8169 5902 5886 6967 6971 5174 5194 2860 3201 5812 5735 5778 5829 6087 6127 5182 5175 56 1 10665 6661 8479 8668 9071 9604 6773 7856 6655 4496 6887 7818 7895 7072 2 10799 6604 8400 8994 9255 9540 6812 8253 6953 4204 7001 7801 7683 6629 91 3 1 10847 11123 6648 7631 8468 9415 9325 9273 9092 9348 9593 9779 6798 6990 8249 8262 6462 7043 4236 4863 6969 7387 7943 7862 7769 8047 7176 7226 2 11302 7582 9496 9072 9615 9734 6837 8148 7092 4725 6909 7915 8090 7200 3 11376 7609 9366 9467 9406 9770 6923 8214 6750 4595 7308 8105 7986 7273 Table A2 Normalized compressive strength development characteristics of the concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag Age of T g 3 7 14 28 56 91 MixIF 0.24 20% 0.72 0.76 0.80 0.85/0.93* 0.96 1 Mix2F 0.33 20% 0.54 0.61 0.79 0.86/0.87* 0.90 1 Mix3F 0.41 20% 0.56 0.69 0.80 0.87/0.85* 0.90 1 Mix4F 0.37 20% 0.62 0.75 0.77 0.78/0.87* 0.97 1 Mix5S 0.33 50% 0.59 0.77 0.87 0.93/0.99* 0.97 1 Mix6S 0.36 50% 0.66 0.80 0.89 0.94/0.95* 0.99 1 Mix7S 0.41 70% 0.63 0.78 0.86 0.92/0.93* 0.98 1 Mix8S 0.44 50% 0.58 0.74 0.85 0.92/0.92* 0.99 1 Mix9LF 0.31 20% 0.44 0.57 0.74 0.85/0.84* 0.96 1 MixO1LS 0.39 60% 0.31 0.46 0.62 0.79/0.85* 0.91 1 Mix2GF 0.33 20% 0.54 0.69 0.81 0.90 0.97 1 Mix3GF 0.41 20% 0.47 0.64 0.76 0.90 0.97 1 Mix5GS 0.33 50% 0.37 0.58 0.70 0.86 0.97 1 Mix7GS 0.41 70% 0.31 0.59 0.72 0.91 0.93 1 o Note: Data from the replication tests. Table A3 Results of splitting tensile strength tests (psi) No. of Age of Testing (days) Mix 3 7 14 28 2 3 1 2 3 1 2 3 1 573 582 657 613 614 673 768 706 823 428 401 501 484 468 551 521 515 545 527 510 550 502 568 579 541 567 644 434 459 604 440 517 581 455 663 678 429 405 567 557 599 724 507 677 757 523 580 633 586 589 616 755 575 696 415 434 467 476 475 553 509 493 567 383 409 428 512 557 555 530 564 617 369 399 425 350 438 470 460 416 472 203 222 316 295 253 366 351 376 413 340 366 425 429 408 518 446 502 541 288 276 433 411 417 442 522 422 521 410 372 381 391 456 507 509 494 563 258 245 363 353 371 411 418 460 540 56 91 2 3 1 2 3 1 2 3 794 770 833 826 844 863 834 851 542 539 650 596 617 675 645 658 620 608 678 673 671 740 722 731 684 647 776 737 764 796 748 766 615 697 716 704 713 748 772 695 658 663 711 654 707 728 708 719 604 473 489 657 625 572 602 616 603 681 702 691 686 696 709 704 486 512 563 549 542 579 601 552 404 400 433 401 420 444 433 414 557 535 557 550 539 585 606 595 508 547 516 646 611 617 646 684 564 553 621 600 578 652 642 659 582 515 566 623 607 555 584 593 1F 2F 3F 4F 5S 6S 7S 8S 9LF 10LS 2GF 3GF 5GS 7GS Table A4 Normalized Splitting tensile strength development characteristics of the concrete mixtures evaluated (psi) Mix Age of Testing (days) W/C Fly ash Slag Number 3 7 14 28 56 91 Mix1F 0.24 20% 0.70 0.74 0.84 0.94/0.86* 0.98 1.00 Mix2F 0.33 20% 0.62 0.73 0.80 0.82/0.87* 0.94 1.00 Mix3F 0.41 20% 0.70 0.74 0.77 0.850.83* 0.92 1.00 Mix4F 0.37 20% 0.59 0.68 0.74 0.87/0.80* 0.99 1.00 Mix5S 0.33 50% 0.60 0.78 0.86 0.93/0.92* 0.96 1.00 Mix6S 0.36 50% 0.79 0.84 0.90 0.94/0.87* 0.96 1.00 Mix7S 0.41 70% 0.71 0.79 0.87 0.92/0.87* 0.99 1.00 Mix8S 0.44 50% 0.53 0.71 0.78 0.90/0.93* 0.99 1.00 Mix9LF 0.31 20% 0.61 0.70 0.78 0.85/0.88* 0.95 1.00 MixO1LS 0.39 60% 0.49 0.67 0.85 0.94/0.82* 0.97 1.00 Mix2GF 0.33 20% 0.59 0.71 0.82 0.89 0.92 1.00 Mix3GF 0.41 20% 0.59 0.63 0.77 0.86 0.92 1.00 Mix5GS 0.33 50% 0.43 0.65 0.71 0.81 0.91 1.00 Mix7GS 0.41 70% 0.42 0.63 0.75 0.87 0.96 1.00 Note: Data from the replication tests Table A5 Results of elastic modulus tests (xl06psi) No. of Age of Testing (days) Mix 3 7 14 28 56 91 1 2 1 2 1 2 1 2 1 2 1 2 1F 4.71 4.77 4.92 4.94 5.20 5.25 5.37 5.43 5.56 5.52 5.57 5.59 2F 3.47 3.38 3.72 3.82 4.11 4.04 4.28 4.34 4.46 4.40 4.77 4.50 3F 4.37 4.42 4.87 4.83 5.02 5.07 5.08 5.19 5.38 5.18 5.66 5.73 4F 4.50 4.47 4.63 4.59 4.85 4.90 4.98 5.03 5.16 5.14 5.33 5.25 5S 4.11 4.11 4.53 4.78 4.86 4.89 5.06 5.12 5.19 5.26 5.23 5.22 6S 4.42 4.11 4.97 4.86 5.08 5.28 5.23 5.67 5.48 5.75 5.54 5.78 7S 3.99 3.80 4.30 4.30 4.53 4.51 4.59 4.61 4.75 4.71 4.78 4.74 8S 3.87 4.04 4.43 4.35 4.90 4.78 5.02 4.98 5.14 5.12 5.16 5.15 9LF 2.71 2.81 2.94 2.90 3.16 3.10 3.29 3.25 3.34 3.36 3.69 3.31 10LS 1.77 1.73 2.01 1.74 2.40 2.32 2.73 2.65 3.07 2.94 2.98 3.09 3GF 3.61 3.99 4.10 4.33 4.59 4.63 4.85 5.07 5.17 5.06 5.25 5.12 S 4GF 4.08 4.21 4.28 4.95 5.56 5.48 5.62 5.59 5.83 6.03 5.95 5.97 5GS 3.24 3.06 3.66 3.97 4.54 4.76 5.42 4.92 5.48 5.26 5.47 5.64 7GS 2.63 2.74 3.28 3.48 4.05 4.14 5.17 5.33 5.64 5.56 5.77 5.68 APPENDIX B MEASURED AND CALCULATED RESULTS FROM CREEP TESTS Table Bl Measured and calculated results from creep tests Load level Age of testing (days) Strain Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Creep 50% Elastic Creep coefficient Creep modulus 3.71E+06 3.51E+06 3.35E+06 3.16E+06 2.98E+06 2.92E+06 No. of Mix Curing condition 7day moist cure 14day moist cure 3 0.001160 0.000021 0.000716 0.000430 0.60 3.44E+06 0.001310 0.000021 0.000804 0.000450 0.54 3.32E+06 0.001070 0.000014 0.000760 0.000290 0.38 3.78E+06 0.001250 0.000014 0.000350 0.000880 0.40 7 0.001240 0.000043 0.000716 0.000480 0.68 3.16E+06 0.001420 0.000043 0.000804 0.000530 0.64 3.24E+06 0.001150 0.000033 0.000760 0.000350 0.46 3.58E+06 0.001340 0.000033 0.000420 0.000880 0.48 14 0.001330 0.000076 0.000716 0.000540 0.76 3.07E+06 0.001520 0.000076 0.000804 0.000610 0.72 3.02E+06 0.001230 0.000063 0.000760 0.000400 0.53 3.44E+06 0.001420 0.000063 0.000480 0.000880 0.54 28 0.001460 0.000120 0.000716 0.000620 0.87 2.88E+06 0.001660 0.000120 0.000804 0.000700 0.84 2.84E+06 0.001340 0.000100 0.000760 0.000470 0.62 3.26E+06 0.001530 0.000100 0.000550 0.000880 0.62 56 0.001600 0.000160 0.000716 0.000720 1.00 2.65E+06 0.001840 0.000160 0.000804 0.000840 1.00 2.65E+06 0.001450 0.000140 0.000760 0.000550 0.72 3.06E+06 0.001660 0.000140 0.000640 0.000880 0.73 91 0.001700 0.000200 0.000716 0.000780 1.10 2.52E+06 0.001970 0.000200 0.000804 0.000930 1.13 2.52E+06 0.001550 0.000170 0.000760 0.000620 0.81 2.84E+06 0.001760 0.000170 0.000710 0.000880 0.81 Table B1. Continued Total Shrinkage Elastic 40% Creep 7day moist cure 14day moist cure Creep coefficient Creep Modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep Modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep Modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep Modulus 0.001141 0.000051 0.000663 0.000427 0.64 2.21E+06 0.001471 0.000051 0.000803 0.000617 0.77 2.10E+06 0.001114 0.000031 0.000669 0.000414 0.62 2.45E+06 0.001385 0.000031 0.000842 0.000512 0.61 0.001313 0.000097 0.000663 0.000553 0.83 1.98E+06 0.001614 0.000097 0.000803 0.000714 0.89 1.97E+06 0.001244 0.000069 0.000669 0.000506 0.76 2.28E+06 0.001557 0.000069 0.000842 0.000646 0.77 0.0015 0.000154 0.000663 0.000683 1.16 1.80E+06 0.001811 0.000154 0.000803 0.000854 1.07 1.80E+06 0.00139 0.000112 0.000669 0.000609 0.91 2.09E+06 0.00176 0.000112 0.000842 0.000806 0.96 0.001724 0.000210 0.000663 0.000851 1.28 1.61E+06 0.002057 0.000210 0.000803 0.001044 1.30 1.59E+06 0.001601 0.000173 0.000669 0.000759 1.13 1.85E+06 0.001972 0.000173 0.000842 0.000957 1.14 0.001961 0.000261 0.000663 0.001037 1.56 1.46E+06 0.002306 0.000261 0.000803 0.001242 1.55 1.42E+06 0.001834 0.000233 0.000669 0.000932 1.39 1.66E+06 0.002232 0.000233 0.000842 0.001157 1.37 0.002115 0.000286 0.000663 0.001166 1.76 1.37E+06 0.002471 0.000286 0.000803 0.001382 1.72 1.32E+06 0.001955 0.000258 0.000669 0.001028 1.54 1.55E+06 0.002398 0.000258 0.000842 0.001298 1.54 2.45E+06 2.23E+06 2.02E+06 1.85E+06 1.66E+06 1.55E+06 Table B1. Continued Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus 0.001032 0.000040 0.000609 0.000383 0.61 3.05E+06 0.001221 0.000040 0.000751 0.000430 0.57 3.20E+06 0.000957 0.000021 0.000633 0.000303 0.48 3.52E+06 0.001254 0.000021 0.000776 0.000457 0.59 0.001165 0.000073 0.000609 0.000483 0.77 2.77E+06 0.00139 0.000073 0.000751 0.000566 0.75 2.87E+06 0.001093 0.000047 0.000633 0.000413 0.65 3.15E+06 0.001389 0.000047 0.000776 0.000566 0.73 0.001318 0.000124 0.000609 0.000585 0.93 2.53E+06 0.001575 0.000124 0.000751 0.000700 0.93 2.61E+06 0.001217 0.000087 0.000633 0.000497 0.79 2.92E+06 0.001537 0.000087 0.000776 0.000674 0.87 0.001477 0.000177 0.000609 0.000691 1.10 2.33E+06 0.001764 0.000177 0.000751 0.000836 1.11 2.38E+06 0.001381 0.000137 0.000633 0.000611 0.97 2.76E+06 0.001700 0.000137 0.000776 0.000787 1.01 0.001669 0.000221 0.000609 0.000839 1.33 2.09E+06 0.00199 0.000221 0.000751 0.001018 1.36 2.14E+06 0.001557 0.000182 0.000633 0.000742 1.17 2.41E+06 0.001890 0.000182 0.000776 0.000932 1.20 0.001796 0.000248 0.000609 0.000939 1.49 1.96E+06 0.002132 0.000248 0.000751 0.001133 1.51 2.01E+06 0.001686 0.000217 0.000633 0.000836 1.32 2.27E+06 0.002023 0.000217 0.000776 0.001030 1.33 3.34E+06 3.07E+06 2.84E+06 2.72E+06 2.41E+06 2.27E+06 7day moist cure 14day moist cure Table B1. Continued Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus 3.90E+06 2.68E+06 2.47E+06 2.30E+06 2.09E+06 1.98E+06 7day moist cure 14day moist cure 0.001060 0.000037 0.000600 0.000420 0.71 2.95E+06 0.001400 0.000037 0.000703 0.00066 0.94 2.79E+06 0.001078 0.000021 0.000571 0.000486 0.85 3.90E+06 0.001208 0.000021 0.000702 0.000485 0.69 0.001200 0.000073 0.000600 0.000530 0.89 2.68E+06 0.001523 0.000073 0.000703 0.000747 1.06 2.52E+06 0.001166 0.000042 0.000571 0.000553 0.97 2.68E+06 0.001361 0.000042 0.000702 0.000617 0.88 0.001340 0.000120 0.000600 0.000630 1.05 2.47E+06 0.001642 0.000120 0.000703 0.000819 1.17 2.32E+06 0.001259 0.000080 0.000571 0.000608 1.06 2.47E+06 0.001518 0.000080 0.000702 0.000736 1.05 0.001510 0.000170 0.000600 0.000740 1.24 2.28E+06 0.001804 0.000170 0.000703 0.000931 1.32 2.13E+06 0.001386 0.000132 0.000571 0.000683 1.20 2.31E+06 0.001699 0.000132 0.000702 0.000865 1.23 0.001680 0.000230 0.000600 0.000850 1.42 2.09E+06 0.001984 0.000230 0.000703 0.001051 1.50 1.96E+06 0.001543 0.000186 0.000571 0.000786 1.38 2.09E+06 0.001886 0.000186 0.000702 0.000998 1.42 0.001810 0.000270 0.000600 0.000940 1.57 1.98E+06 0.002120 0.000270 0.000703 0.001147 1.63 1.85E+06 0.001654 0.000223 0.000571 0.000860 1.51 1.98E+06 0.002020 0.000223 0.000702 0.001095 1.56 Table B1. Continued Total Shrinkage Elastic 40% Creep 7day moist cure 14day moist cure Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 0.001168 0.000044 0.000669 0.000455 0.409 2.99E+06 0.001455 0.000044 0.000846 0.000565 0.67 2.99E+06 0.001222 0.000043 0.000718 0.000461 0.64 3.00E+06 0.001464 0.000043 0.000889 0.000532 0.62 2.79E+06 2.60E+06 2.38E+06 2.19E+06 2.11E+06 0.001299 0.000088 0.000669 0.000542 0.580 2.69E+06 0.00162 0.000088 0.000846 0.000686 0.81 2.69E+06 0.001323 0.000074 0.000718 0.000531 0.74 2.79E+06 0.001596 0.000074 0.000889 0.000633 0.74 0.001423 0.000130 0.000669 0.000624 0.683 2.49E+06 0.001783 0.000130 0.000846 0.000807 0.95 2.49E+06 0.001439 0.000110 0.000718 0.000611 0.85 2.60E+06 0.001747 0.000110 0.000889 0.000748 0.87 0.001587 0.000170 0.000669 0.000748 1.101 2.28E+06 0.001977 0.000170 0.000846 0.000961 1.14 2.28E+06 0.001594 0.000149 0.000718 0.000727 1.01 2.38E+06 0.001937 0.000149 0.000889 0.000899 1.04 0.001744 0.000201 0.000669 0.000874 1.320 2.09E+06 0.002175 0.000201 0.000846 0.001128 1.33 2.09E+06 0.001747 0.000178 0.000718 0.000851 1.19 2.19E+06 0.002118 0.000178 0.000889 0.001051 1.22 0.00184 0.000216 0.000669 0.000955 1.476 1.98E+06 0.002299 0.000216 0.000846 0.001237 1.46 1.98E+06 0.001834 0.000193 0.000718 0.000923 1.29 2.11E+06 0.002212 0.000193 0.000889 0.001130 1.31 Creep modulus 2.99E+06 Table B1. Continued Total Shrinkage Elastic 40% Creep 7day moist cure 14day moist cure Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 0.000975 0.000042 0.000670 0.000263 0.39 3.58E+06 0.001194 0.000042 0.000837 0.000325 0.41 3.54E+06 0.001037 0.000038 0.000692 0.000307 0.43 3.70E+06 0.001263 0.000038 0.000854 0.000371 0.44 3.35E+06 3.12E+06 2.85E+06 2.51E+06 2.10E+06 0.001105 0.000082 0.000670 0.000353 0.54 3.22E+06 0.001391 0.000082 0.000837 0.000472 0.54 3.15E+06 0.001164 0.000076 0.000692 0.000396 0.57 3.40E+06 0.001467 0.000076 0.000854 0.000537 0.57 0.001255 0.000123 0.000670 0.000462 0.70 2.91E+06 0.001550 0.000123 0.000837 0.000570 0.69 2.89E+06 0.001291 0.000114 0.000692 0.000485 0.71 3.15E+06 0.001567 0.000114 0.000854 0.000599 0.70 0.001405 0.000157 0.000670 0.000588 0.90 2.65E+06 0.001707 0.000157 0.000837 0.000713 0.87 2.62E+06 0.001448 0.000141 0.000692 0.000615 0.89 2.87E+06 0.001727 0.000141 0.000854 0.000732 0.87 0.001600 0.000183 0.000670 0.000747 1.15 2.38E+06 0.001901 0.000183 0.000837 0.000891 1.08 2.31E+06 0.001648 0.000163 0.000692 0.000793 1.11 2.56E+06 0.001941 0.000163 0.000854 0.000924 1.06 0.001758 0.000196 0.000670 0.000892 1.34 2.36E+06 0.002048 0.000196 0.000837 0.001015 1.25 2.30E+06 0.001796 0.000177 0.000692 0.000927 1.27 2.21E+06 0.002104 0.000177 0.000854 0.001073 1.21 Creep modulus 3.69E+06 Table B1. Continued Total Shrinkage Elastic 40% Creep 7day moist cure 14day moist cure Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 0.000907 0.000039 0.000519 0.000349 0.67 2.66E+06 0.001101 0.000039 0.000616 0.000446 0.72 2.78E+06 0.000948 0.000038 0.000546 0.000364 0.67 2.84E+06 0.001160 0.000038 0.000643 0.000479 0.74 2.52E+06 2.30E+06 2.08E+06 1.90E+06 1.82E+06 0.001094 0.000080 0.000519 0.000495 0.95 2.33E+06 0.001285 0.000080 0.000616 0.000589 0.96 2.45E+06 0.001081 0.000073 0.000546 0.000462 0.85 2.57E+06 0.001308 0.000073 0.000643 0.000592 0.92 0.001264 0.000126 0.000519 0.000619 1.19 2.11E+06 0.001486 0.000126 0.000616 0.000744 1.21 2.17E+06 0.001209 0.000111 0.000546 0.000552 1.01 2.36E+06 0.001466 0.000111 0.000643 0.000712 0.001399 0.000170 0.000519 0.00071 1.37 1.92E+06 0.001664 0.000170 0.000616 0.000878 1.43 1.98E+06 0.001384 0.000148 0.000546 0.00069 1.26 2.09E+06 0.001646 0.000148 0.000643 0.000855 1.33 0.001561 0.000202 0.000519 0.00084 1.62 1.74E+06 0.001836 0.000202 0.000616 0.001018 1.65 1.81E+06 0.001556 0.000183 0.000546 0.000827 1.51 1.89E+06 0.001821 0.000183 0.000643 0.000995 1.55 0.001656 0.000223 0.000519 0.000914 1.76 1.65E+06 0.001941 0.000223 0.000616 0.001102 1.79 1.72E+06 0.001651 0.000204 0.000546 0.000901 1.65 1.79E+06 0.001921 0.000204 0.000643 0.001074 1.67 Creep modulus 2.78E+06 Table B1. Continued Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 2.53E+06 2.34E+06 2.14E+06 1.93E+06 1.78E+06 7day moist cure 14day moist cure 0.001131 0.000073 0.000614 0.000443 0.72 2.71E+06 0.001296 0.000073 0.000722 0.000500 0.69 2.56E+06 0.001140 0.000050 0.000654 0.000436 0.67 2.92E+06 0.001374 0.000050 0.000831 0.000493 0.59 0.001263 0.000123 0.000614 0.000526 0.86 2.53E+06 0.001438 0.000123 0.000722 0.000592 0.82 2.38E+06 0.001262 0.000098 0.000654 0.000510 0.78 2.68E+06 0.001524 0.000098 0.000831 0.000596 0.72 0.001409 0.000161 0.000614 0.000633 1.03 2.34E+06 0.001606 0.000161 0.000722 0.000722 1.00 2.17E+06 0.001394 0.000136 0.000654 0.000604 0.92 2.51E+06 0.001677 0.000136 0.000831 0.000710 0.85 0.000157 0.000194 0.000614 0.000761 1.24 2.04E+06 0.001821 0.000194 0.000722 0.000904 1.25 1.97E+04 0.001549 0.000169 0.000654 0.000726 1.11 2.26E+06 0.001881 0.000169 0.000831 0.000881 1.06 0.001762 0.000228 0.000614 0.000920 1.50 1.82E+06 0.002048 0.000228 0.000722 0.001098 1.52 1.77E+06 0.001733 0.000202 0.000654 0.000877 1.34 2.02E+06 0.002118 0.000202 0.000831 0.001084 1.30 0.001914 0.000250 0.000614 0.001050 1.71 1.68E+06 0.002227 0.000250 0.000722 0.001254 1.74 1.63E+06 0.001889 0.000230 0.000654 0.001004 1.53 1.87E+06 0.002294 0.000230 0.000831 0.001233 1.48 Creep modulus 2.71E+06 Table B1. Continued 7day moist cure 9LF 14day moist cure Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 2.08E+06 1.98E+06 1.88E+06 1.79E+06 1.72E+06 0.001118 0.000049 0.000626 0.000443 0.71 1.99E+06 0.001337 0.000049 0.000767 0.000521 0.68 1.92E+06 0.001169 0.000046 0.000677 0.000447 0.66 2.29E+06 0.001297 0.000046 0.000777 0.000474 0.61 0.001231 0.000096 0.000626 0.000510 0.82 1.85E+06 0.001487 0.000096 0.000767 0.000624 0.81 1.81E+06 0.001272 0.000081 0.000677 0.000514 0.76 2.12E+06 0.001433 0.000081 0.000777 0.000576 0.74 0.001380 0.000162 0.000626 0.000592 0.95 1.74E+06 0.001642 0.000162 0.000767 0.000713 0.93 1.69E+06 0.001392 0.000137 0.000677 0.000579 0.86 2.00E+06 0.001564 0.000137 0.000777 0.000651 0.84 0.001528 0.000226 0.000626 0.000677 1.08 1.62E+06 0.001811 0.000226 0.000767 0.000819 1.07 1.58E+06 0.001507 0.000189 0.000677 0.000641 0.95 1.91E+06 0.001691 0.000189 0.000777 0.000726 0.93 0.001684 0.000288 0.000626 0.000771 1.23 1.51E+06 0.001987 0.000288 0.000767 0.000932 1.22 1.47E+06 0.001633 0.000239 0.000677 0.000718 1.06 1.79E+06 0.001836 0.000239 0.000777 0.000820 1.06 0.001792 0.000322 0.000626 0.000844 1.35 1.43E+06 0.002112 0.000322 0.000767 0.001023 1.33 1.40E+06 0.001714 0.000276 0.000677 0.000762 1.13 1.72E+06 0.001940 0.000276 0.000777 0.000888 1.14 Creep modulus 2.21E+06 Table B1. Continued 7day moist cure 10LS 14day moist cure Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient Creep modulus 1.67E+06 1.58E+06 1.51E+06 1.42E+06 1.33E+06 1.26E+06 0.001206 0.000070 0.000546 0.000590 1.08 1.16E+06 0.001517 0.000070 0.000721 0.000726 1.01 1.03E+06 0.000874 0.000038 0.000781 0.000276 0.62 1.67E+06 0.001169 0.000038 0.000713 0.000418 0.59 0.001314 0.000130 0.000546 0.000639 1.17 1.10E+06 0.001648 0.000130 0.000721 0.000797 1.10 0.99E+06 0.000898 0.000090 0.000898 0.000337 0.74 1.58E+06 0.001286 0.000090 0.000713 0.000482 0.68 0.001433 0.000198 0.000546 0.000690 1.26 1.04E+06 0.001780 0.000198 0.000721 0.000861 1.19 0.95E+06 0.000941 0.000152 0.001083 0.000380 0.82 1.51E+06 0.001406 0.000152 0.000713 0.000540 0.76 0.001559 0.000260 0.000546 0.000753 1.38 0.97E+06 0.001939 0.000260 0.000721 0.000958 1.33 0.90E+06 0.000997 0.000209 0.001123 0.000486 0.93 1.42E+06 0.001539 0.000209 0.000713 0.000617 0.87 0.001694 0.000319 0.000546 0.000830 1.52 0.92E+06 0.002098 0.000319 0.000721 0.001058 1.47 0.85E+06 0.001062 0.000279 0.001274 0.000501 1.05 1.33E+06 0.001694 0.000279 0.000713 0.000702 0.99 0.001789 0.000360 0.000546 0.000883 1.62 0.88E+06 0.002224 0.000360 0.000721 0.001143 1.59 0.82E+06 0.001116 0.000320 0.001377 0.000554 1.16 1.26E+06 0.001809 0.000320 0.000713 0.000776 1.09 Table B1. Continued 2GF 14day moist cure Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep 3GF 14day moist cure Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 3.19E+06 2.82E+06 2.53E+06 2.28E+06 2.14E+06 0.001023 0.000032 0.000601 0.000390 0.65 2.61E+06 0.001334 0.000032 0.000777 0.000526 0.001173 0.000061 0.000601 0.000511 0.85 2.33E+06 0.001494 0.000061 0.000777 0.000657 0.001333 0.000109 0.000601 0.000623 1.04 2.11E+06 0.001690 0.000109 0.000777 0.000804 0.001532 0.000161 0.000601 0.000769 1.28 1.89E+06 0.001992 0.000161 0.000777 0.000984 0.001750 0.000204 0.000601 0.000944 1.57 1.67E+06 0.002171 0.000204 0.000777 0.001190 0.001873 0.000229 0.000601 0.001043 1.74 1.57E+06 0.002323 0.000229 0.000777 0.001318 0.68 2.48E+06 0.000811 0.000024 0.000530 0.000257 0.48 3.69E+06 0.001043 0.000024 0.000666 0.000353 0.85 2.26E+06 0.000931 0.000047 0.000530 0.000354 0.67 3.28E+06 0.001187 0.000047 0.000666 0.000474 1.04 2.05E+06 0.001084 0.000076 0.000530 0.000479 0.90 2.88E+06 0.001362 0.000076 0.000666 0.000621 0.93 1.27 1.84E+06 0.001243 0.000113 0.000530 0.000600 1.33 2.57E+06 0.001549 0.000113 0.000666 0.000770 1.16 1.53 1.64E+06 0.001428 0.000157 0.000530 0.000741 1.40 2.29E+06 0.001747 0.000157 0.000666 0.000924 1.39 1.70 1.54E+06 0.001541 0.000183 0.000530 0.000828 1.56 2.14E+06 0.001879 0.000183 0.000666 0.001030 1.55 0.53 0.71 Creep modulus 3.56E+06 Table B1. Continued 5GS 14day moist cure Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep 7GS 14day moist cure Creep coefficient Creep modulus Total Shrinkage Elastic 40% Creep Creep coefficient Creep modulus Total Shrinkage Elastic 50% Creep Creep coefficient 2.57E+06 2.33E+06 2.10E+06 1.90E+06 1.84E+06 0.001024 0.000039 0.000556 0.000429 0.77 2.87E+06 0.001261 0.000039 0.000703 0.000519 0.001163 0.000064 0.000556 0.000543 0.98 2.57E+06 0.001427 0.000064 0.000703 0.000660 0.001296 0.000104 0.000556 0.000636 1.14 2.35E+06 0.001594 0.000104 0.000703 0.000787 0.001454 0.000140 0.000556 0.000758 1.36 2.13E+06 0.001783 0.000140 0.000703 0.000940 0.001615 0.000168 0.000556 0.000891 1.60 1.94E+06 0.001977 0.000168 0.000703 0.001106 0.001690 0.000184 0.000556 0.000950 1.71 1.86E+06 0.002084 0.000184 0.000703 0.001197 0.74 2.85E+06 0.000953 0.000043 0.000517 0.000393 0.76 2.91E+06 0.001208 0.000043 0.000652 0.000512 0.94 2.55E+06 0.001078 0.000074 0.000517 0.000487 0.94 2.64E+06 0.001361 0.000074 0.000652 0.000634 1.12 2.35E+06 0.001213 0.000100 0.000517 0.000597 1.15 2.38E+06 0.001517 0.000100 0.000652 0.000764 1.17 1.34 2.13E+06 0.001383 0.000131 0.000517 0.000736 1.42 2.11E+06 0.001708 0.000131 0.000652 0.000924 1.42 1.57 1.94E+06 0.001551 0.000162 0.000517 0.000872 1.69 1.90E+06 0.001899 0.000162 0.000652 0.001084 1.66 1.70 1.84E+06 0.001627 0.000181 0.000517 0.000929 1.80 1.83E+06 0.001977 0.000181 0.000652 0.001143 1.75 0.79 0.97 Creep modulus 2.84E+06 LIST OF REFERENCES AASHTO, 2001. 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The effect of aggregate concentration upon the strength and modulus of elasticity of concrete. Mag. Concr. Res., 31, No. 109, pp.225234. Thomas, Jeffrey J. and Jennings, Hamlin M., 2001. Chemical Aging and the Colloidal Structure of the CSH Gel: Implication for Creep and Shrinkage. Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasibrittle Materials edited by F,J. Ulm, Z.P. Ba2ant and F.H. Wittmann. (2001), pp.3338. Troxell, G.E., Raphael, J.M. and Davis, R.E., 1958. Longtime creep and shrinkage tests of plain and reinforced concrete. Proc. ASTM., 58, pp. 11011120. Wu K.R., Chen B., Yao W., Zhang D, 2001. Effect of coarse aggregate type on mechanical properties of highperformance concrete. Cement and Concrete Research, Volume 31, Number 10, October 2001, pp. 14211425(5). Zhou, F.P., Lydon, F.D. and Barr, B.I.G., 1995. Effect of coarse aggregate on elastic modulus and compressive strength of high performance concrete. Cement and Concrete Research, Vol. 25, No. 1, pp.177186. Zia, P., Leming, M.L., Ahmad, S.H. 1991. HighPerformance Concrete: A StateoftheArt Report. Strategic Highway Research Program, National Research Council, Washington, D. C., (SHRPC/FR91103; PB92130087), pp.251. Zia, P., Ahmad, S.H., Leming, M.L., Schemmel, J.J., Elliott, R.P. 1993. Mechanical Behavior of High Performance Concretes. Volume 5: Very High Strength Concrete. Strategic Highway Research Program, National Research Council, Washington, D. C., xi, (SHRPC365), pp.101. BIOGRAPHICAL SKETCH Liu Yanjun, born in 1973 in China, is a civil engineer. He went to Shenyang Architectural and Civil Engineering Institute in 1993. Four years later, he earned his bachelor's degree in civil engineering in 1997. Then, he got scholarship from China Building Materials Academy and worked on his Master's study in Material Science and Engineering. After three years, in 2000, he earned his Master's degree at China Building Materials Academy in Material Science and Engineering with minor focus on cement and concrete materials. After that, he worked for China Building Materials Academy for 2 years. Then, he obtained full scholarship from Civil and Coastal Engineering Department of University of Florida and involved PhD program on the research on cement and concrete materials. At last, he achieved his PhD at the University of Florida in 2007. 218 PAGE 1 1 STRENGTH, MODULUS OF ELASTICITY, SHRINKAGE AND CREEP OF CONCRETE By YANJUN LIU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 2007 Yanjun Liu PAGE 3 3 To my Mom and Dad, Ren Shuzhen and Liu Yu chun, for everything they have done and are doing for their child, my daughter for her understanding and cons ideration for 6yearlong life without dads company, and my brother and sisters for their great support and encouragement. PAGE 4 5 ACKNOWLEDGMENTS It is m y immense pleasure in thanking the pe rsons and organizations that helped me over years to bring my PhD dissertation to the final form. Firstly, great appreciation goes to the ch airman, Dr. Mang Tia, and cochairman, Dr. Reynaldo Roque for sincere encouragement and patient guidance. You are the beacons guiding me throughout my tough trek of pursuing PhD. Wi thout your help, this di ssertation can not be completed. Please let me regard you as loyal friends and great mentors. Secondly, great appreciation goes to the member s of my supervisory committee, Dr. N.D. Cristescu and Dr. Larry.C.Muszynski, for your great enlightenment and keen research assistance. Thirdly, graceful acknowledgement extends to Florida Department of Transportation (FDOT) for providing the financial s upport, testing equipment, materials that made this research possible. The Florida Department of Transpor tation personnel Messrs. Mi chael Bergin, Richard Delorenzo, Joseph Fitzgerald, and Craig Roberts ar e appreciated for their help with the entire process of fabricating test samples. Fourthly, I like to thank all my colleagues in the materials section of Civil & Coastal Engineering Department. Danny Br own, Chuck Broward, Nard Hube rt and George A. Lopp are acknowledged for their assistance in this study. In addition, special thanks are given to th e Florida Rock Industries Company for donating slag, Boral Materials Company for donating fly ash, and W. R. Grace & Co for donating chemical admixtures, and Carolina Stalite Comp any for donating lightweight aggregate. Without your sincere help, this study could not be completed on time. At last, my sincere thanks go to my pare nts for their persiste nt encouragement and unconditional love, which motivated me to comp lete my study. I believe the fulfillment of my study will bring you joy, which is the only thing you need from your child. PAGE 5 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................5 LIST OF TABLES................................................................................................................. ........10 LIST OF FIGURES.......................................................................................................................12 ABSTRACT...................................................................................................................................17 CHAP TER 1 INTRODUCTION..................................................................................................................19 1.1 Background and Research Needs..................................................................................... 19 1.2 Hypothesis........................................................................................................................21 1.3 Objectives of Study........................................................................................................ ...21 2 LITERATURE REVIEW.......................................................................................................23 2.1 Introduction............................................................................................................... ........23 2.2 Strength of Concrete.........................................................................................................23 2.2.1 Significance of Studying Strength of Concrete......................................................23 2.2.2 Effect of Coarse Aggreg ate on Strength of Concrete ............................................. 24 2.2.3 Prediction of Strength of Concrete.........................................................................26 2.3 Elastic Modulus of Concrete............................................................................................ 27 2.3.1 Definition and Determination of Elastic Modulus of Concrete.............................. 27 2.3.2 Significance of Studying Elastic Modulus of Concrete ......................................... 28 2.3.3 Effect of Coarse Aggregate on Elastic Modulus of Concrete ................................ 29 2.3.4 Models for Predicting Elas tic Modulus of Concrete .............................................. 32 2.4 Shrinkage Behavior of Concrete.......................................................................................35 2.4.1 Origin of Shrinkage of Concrete............................................................................ 35 2.4.2 Significance of Studying Shrinkage of Concrete...................................................36 2.4.3 Effect of Raw Materials on Shrinkage of Concrete................................................ 37 2.4.3.1 Effect of aggregate content on shrinkage behavior of concrete ................... 37 2.4.3.2 Effects of coarse aggregate type on concrete shrinkage ............................... 39 2.4.3.3 Effects of size and shape of coarse aggregate on concrete shrinkage .......... 40 2.4.3.4 Effect of other factors on shrinkage behaviors of concrete .......................... 41 2.4.4 Models to Predict Concrete Shrinkage................................................................... 42 2.4.4.1 CEBFIP Model for shrinkage strain prediction.......................................... 43 2.4.4.2 Prediction model recommended by ACI209 Report [1992].......................45 2.5 Creep of Concrete.............................................................................................................46 2.5.1 Rheology of Materials and Definition of Creep of Concrete.................................46 2.5.2 Significance of Studying Creep Behavior of Concrete .......................................... 48 2.5.3 Effect of Aggregate on Creep of Hardened Concrete............................................ 49 2.5.4 Prediction Models and Their Li m itations of Concrete Creep................................ 51 PAGE 6 7 2.5.4.1 C.E.BF.I.P Model Code..............................................................................53 2.5.4.2 Model of ACI 209........................................................................................55 3 MATERIALS AND EXPERIMENTAL PROGRAMS......................................................... 58 3.1 Introduction............................................................................................................... ........58 3.2 Concrete Mixtures Evaluated........................................................................................... 58 3.2.1 Mix Proportion of Concrete.................................................................................... 58 3.2.2 Mix Ingredients......................................................................................................59 3.3 Fabrication of Concrete Specimens..................................................................................60 3.3.1 The Procedure to Mix Concrete............................................................................. 60 3.3.2 The Procedure to Fabricate Specimens.................................................................. 66 3.4 Curing Conditions for Concrete Specimens..................................................................... 66 3.5 Tests on Fresh Concrete.................................................................................................... 67 3.6 Tests on Hardened Concrete............................................................................................. 69 3.6.1 Compressive Strength Test..................................................................................... 69 3.6.2 Splitting Tensile Strength Test (or Brazilian Test) ................................................. 70 3.6.3 Elastic Modulus Test..............................................................................................72 3.6.4 Shrinkage Test........................................................................................................73 4 CREEP TEST APPARATUS DESI GN AND TESTING PROCEDURE ............................. 76 4.1 Introduction............................................................................................................... ........76 4.2 Creep Test Apparatus.......................................................................................................76 4.2.1 Design Requirements of Creep Test Apparatus.....................................................76 4.2.2 Design of Creep Apparatus.................................................................................... 77 4.2.2.1 The determination of the maximum capacity of the creep Apparatus ......... 77 4.2.2.2 The design of springs................................................................................... 77 4.2.2.3 Design of header plate..................................................................................79 4.2.2.4 Determination of the size of steel rod.......................................................... 81 4.2.2.5 Stress relaxation due to the deflec tion of header plate and creep of concrete.................................................................................................................81 4.3 Design of GagePoint Positioning Guide.........................................................................82 4.4 Design of Alignment Frame............................................................................................. 82 4.5 Mechanical Strain Gauge.................................................................................................. 85 4.6 Other Details on Creep Apparatus....................................................................................85 4.7 Creep Testing Procedure...................................................................................................86 4.8 Summary on the Performance of the Creep Apparatus.................................................... 93 5 ANALYSIS OF STRENGTH TEST RESULTS.................................................................... 95 5.1 Introduction............................................................................................................... ........95 5.2 Results and Analysis of Co m pressive Strength Tests....................................................... 95 5.2.1 Effects of Water to Cement Rati o and W ater Content on Compressive Strength....................................................................................................................... .95 5.2.2 Effects of Aggregate Types on Compressive Strength........................................... 98 5.2.3 Effects of Fly Ash and Slag on Co m pressive Strength of Concrete..................... 102 PAGE 7 8 5.2.4 Prediction of Compressive Strength Development.............................................. 103 5.3 Analysis of Splitting Tensile Strength Test Results....................................................... 105 5.3.1 Effects of Water to Cement Ra tio on Splitting Tensile S trength......................... 105 5.3.2 Effects of Coarse Aggregate T ype on Splitting Tensile S trength........................ 105 5.3.3 Effects of Fly Ash and Slag on Split ting Tensile Strength of Concrete ...............113 5.4 Relationship between Compressive Stre ngth and Splitting Tensile S trength................ 114 5.5 Analysis of Elastic Modulus Test Results...................................................................... 117 5.6 Relationship between Compressive Strength and Elastic Modulus ............................... 120 5.7 Summary of Findings.....................................................................................................122 6 ANALYSIS OF SHRINKAGE TEST RESULTS ...............................................................127 6.1 Introduction............................................................................................................... ......127 6.2 Results and Analysis of Shrinkage Tests........................................................................ 127 6.2.1 Effects of Curing Conditions on Shrinkage Behavior of Concrete ...................... 127 6.2.2 Effects of Mineral Additiv es o n Shrinkage Behavior.......................................... 129 6.2.3 Effects of Water Content on Shrinkage Behavior................................................ 130 6.2.4 Effects of Aggregate Types on Shrinkage Behavior............................................ 131 6.2.5 Relationship between Compressive Strength and Shrinkage Strain..................... 133 6.2.6 Relationship between Elastic Modulus and Shrinkage Strain ..............................135 6.3 Evaluation on Shrinkage Prediction Models.................................................................. 137 6.3.1 ACI209 model..................................................................................................... 137 6.3.2 CEBFIP Model....................................................................................................138 6.4 Prediction of Ultimat e Shrinkage Strain ......................................................................... 140 6.4.1 Least Square Method of Curvefitting..................................................................141 6.4.2 Evaluation Methods on the Goodness of Fit........................................................142 6.4.3 Predicted Results..................................................................................................145 6.5 Summary of Findings.....................................................................................................146 7 ANALYSIS OF CREEP TEST RESULTS ..........................................................................148 7.1 Introduction............................................................................................................... ......148 7.2 Analysis of Creep Test Results.......................................................................................148 7.2.1 Effects of Curing Conditions on Creep Behavior of Concrete ............................. 148 7.2.2 Effects of Loading Condition on Creep Behavior of Concrete............................151 7.2.3 Effects of Aggregate Types on Creep Behavior of Concrete............................... 153 7.2.5 Effects of Water to Cement Rati o and Air Content on Creep Strain .................... 156 7.2.6 Relationship between Compressive Strength and Creep Strain........................... 157 7.3 Creep Coefficient............................................................................................................163 7.3.1 Effects of Loading Conditions on Creep Coefficient........................................... 163 7.3.2 Effects of Curing Conditions on Creep Coefficient............................................. 163 7.3.3 Effects of Water Content on Creep Coefficient................................................... 165 7.3.4 Effects of Compressive Strength at Loading Age on Creep Coefficient .............. 166 7.3.5 Relationship between Elastic Modulus at Loading Age and Creep Coefficient .. 169 7.3.6 Effects of Coarse Aggregat e Type on Creep Coefficient ..................................... 171 7.4 Creep Modulus................................................................................................................172 7.5 Prediction of Ultimate Creep Strain............................................................................... 174 PAGE 8 9 7.6 Evaluation on Creep Prediction Models......................................................................... 175 7.7 Summary of Findings.....................................................................................................186 8 CONCLUSIONS AND RECOMMENDATIONS ...............................................................188 8.1 Design of Creep Apparatus............................................................................................. 188 8.2 Findings from This Study............................................................................................... 188 8.2.1 Strength and Elastic Modulus............................................................................... 188 8.2.2 Shrinkage Characteristics of Concretes Investigated ........................................... 190 8.2.3 Creep Characteristics of Concretes Investigated.................................................. 191 8.3 Recommendations...........................................................................................................192 APPENDIX A MEASUREMENTS FROM STRENGTH TESTS ............................................................... 193 B MEASURED AND CALCULATED RESULTS FROM CREEP TESTS ..........................199 LIST OF REFERENCES.............................................................................................................212 BIOGRAPHICAL SKETCH.......................................................................................................218 PAGE 9 10 LIST OF TABLES Table page 31 Mix proportions of the 14 concrete m ixtures involved in this study................................. 61 32 Physical properties of Type I cement................................................................................. 62 33 Chemical ingredients of Type I cement............................................................................. 62 34 Physical and chemical properties of fly ash .......................................................................62 35 Physical and chemical properties of slag........................................................................... 62 36 Physical properties of fine aggregate .................................................................................62 37 Physical properties of coarse aggregates ...........................................................................62 38 The testing programs on fresh concrete............................................................................. 67 39 Properties of fresh concrete............................................................................................... 68 310 The testing program on hardened concrete........................................................................69 51 Compressive strength of the concrete m ixtures evaluated................................................. 95 52 Comparison of the accuracy between ACI equation and Modified ACI Equation.......... 106 53 Regression analysis on the prediction of com pressive strength of concrete....................107 54 Values of the constants, and / and the time ratio .................................................. 108 55 Splitting tensile strengths of th e concrete m ixtures evaluated......................................... 109 56 Regression analysis for relating compre ssive strength to splitting tensile strength......... 115 57 Elastic module of the concrete mixtures evaluated.......................................................... 117 58 Regression analysis using the expression recomm ended by ACI 31889....................... 123 59 Regression analysis on ACI 31895 equati on with forcing it through origin point ......... 123 510 Regression analysis using the expression recomm ended by ACI 31895....................... 125 61 Shrinkage strains of the concrete mi xtures evaluated at various curing ages .................. 128 62 Regression analysis on re lationship of com pressive st rength to shrinkage strain...........135 63 Regression analysis on relationship of elastic modulus to shrinkage strain ....................136 PAGE 10 11 64 Correction factors for the ACI 209 model on shrinkage prediction ................................ 138 65 Regression analysis results.............................................................................................. 146 71 Regression analysis on relationship betw een compressive strength and creep strain ..... 160 72 Regression analysis on rela tionship of com pressive strength to creep coefficient.......... 167 73 Regression analysis on re lationship of elastic modulus to creep coefficient ................... 171 74 Regression analysis on relati on of creep coefficient to fc/E............................................ 171 75 The predicted ultimate creep strain and creep coefficient............................................... 175 76 Regression analysis on relati on of creep coefficient to fc/E............................................ 182 77 Correction factors for the ACI 209 model ....................................................................... 185 A1 Results of compressive strength tests.............................................................................. 194 A2 Normalized compressive strength deve lopm ent characteristics of the concrete mixtures evaluated........................................................................................................... 195 A3 Results of splitting tensile strength tests .......................................................................... 196 A4 Normalized Splitting tens ile strength developm ent char acteristics of the concrete mixtures evaluated........................................................................................................... 197 A5 Results of elastic modulus tests....................................................................................... 198 B1 Measured and calculated results from creep tests ............................................................200 PAGE 11 12 LIST OF FIGURES Figure page 21 Representation of the stressstrain relation for concrete.................................................... 27 22 Stressstrain relations for cemen t paste, aggregate and concrete ....................................... 29 23 Effect of coarse aggregate cont ent on the shrinkage of concrete ....................................... 37 24 Creep diagram of concrete material...................................................................................47 25 Straintime plot of concrete under a su stained load and after release of load ...................48 31 Gradation of fine aggregate (Godenhead sand).................................................................63 32 Gradation of coarse aggreg ate (Miam i Oolite limestone).................................................. 63 33 Gradation of coarse a ggregate (Georgia granite) ............................................................... 64 34 Gradation of lightwei ght aggregate (S talite)...................................................................... 64 35 Compulsive Pan Mixer...................................................................................................... 65 36 Typical failure model of conc rete cylinder in compression test ........................................ 70 37 Loading configuration fo r splitting tensile test .................................................................. 71 38 MTS system for elastic modulus and com pressive strength test....................................... 73 39 Cylindrical specimen with gage point installed .................................................................74 41 Creep test apparatus....................................................................................................... ....78 42 Boundary conditions used for finite element analysis....................................................... 79 43 Mesh plot of Header plate analysis.................................................................................... 80 44 Contour plot of defl ection of header plate ......................................................................... 80 45 Design of Gagepoint positioning guide............................................................................ 83 46 Gauge position guide.........................................................................................................84 47 Plastic cylindrical mold inside gauge position guide ......................................................... 84 48 Schematic of Alig nm ent Frame Design............................................................................. 87 49 Mechanical gauge........................................................................................................... ...88 PAGE 12 13 410 Positioning springs on the bottom plate............................................................................. 88 412 Concrete cylinder with both end surfaces ground.............................................................. 89 413 How to center the specimens into creep frame.................................................................. 90 414 How to center the hydraulic jack cylinder......................................................................... 91 415 Leveling the plate on the top of load cell ........................................................................... 91 51 Effect of water to cementitious material s ratio on com pressive strength at 28 days......... 96 52 Effect of water to cementitious mate rials on com pressive strength at 91 days................. 97 53 Effect of water content on compressive strength at 28 days.............................................. 97 54 Effect of water content on compressive strength at 91 days.............................................. 98 55 Effect of coarse aggreg ate type on com pressive strengths of Mix2F and Mix2GF......100 56 Effect of coarse aggreg ate type on com pressive strength of Mix3F and Mix3GF....... 100 57 Effect of coarse aggreg ate type on com pressive strength of Mix5S and Mix5GS....... 101 58 Effect of coarse aggreg ate type on com pressive strength of Mix7S and Mix7GS....... 101 59 Effect of fly ash and slag on com pressive strength of concrete.......................................102 510 Effect of water to cement ratio on splitting tensile st rength at 28 days ........................... 109 511 Effect of water to cement ratio on splitting tensile st rength at 91 days ........................... 110 512 Effect of aggregate type on splitting tensile strength of Mix2F and Mix2GF .............. 111 513 Effect of aggregate type on splitting tensile strength of Mix3F and Mix3GF .............. 111 514 Effect of aggregate type on splitting tensile strength of Mix5S and Mix5GS .............. 112 515 Effect of aggregate type on splitting tensile strength of Mix7S and Mix7GS .............. 112 516 Effect of fly ash and slag on sp litting tensile strength of concrete .................................. 114 517 Relationship between compressive st rength and splitting tensile strength ...................... 116 518 Effect of coarse aggregate type on modul us of elasticity of Mix2F and Mix2GF ........118 519 Effect of coarse aggregate type on modul us of elasticity of Mix3F and Mix3GF ........119 520 Effect of coarse aggregate type on modul us of elasticity of Mix5S and Mix5GS ........119 PAGE 13 14 521 Effect of coarse aggregate type on modul us of elasticity of Mix7S and Mix7GS ........120 522 Relationship between compressive strengt h and elastic m odulus based on ACI Code... 124 523 Plot of elastic modulus against w1.5fc for all curing conditions......................................124 61 Effect of curing condition on shrinkage st rain of concrete m ixtures at 91 days.............. 130 62 Effect of water content on shrinkage strain at 91 days .................................................... 131 63 Effect of water to cementitious materi als ratio on shrinkage strain at 91 days ...............132 64 Effect of coarse aggregate type on shrinkage behavior of concrete ................................ 133 65 Relationship between compressive strength and shrinkage strain at 91 days ..................135 66 Relationship between shrinkage strain at 91 days and m odulus of elasticity.................. 136 67 Comparison between the shrinkage strain at 91 days and the shrinkage strain calculated by ACI 209 model and C.E.BF.I.P model ..................................................... 140 68 Comparison among the ultimate shrinkage strain s from curvefitting, CEBFIP model and ACI 209 model...............................................................................................145 71 Effect of curing condition on creep of concrete loaded at 40% of com pressive strength.............................................................................................................................150 72 Effect of curing condition on creep of concrete loaded at 50% of com pressive strength.............................................................................................................................150 73 Effect of stress level on creep of concrete m oistcured for 7 days.................................. 152 74 Effect of stress level on creep of concrete m oistcured for 14 days................................ 153 75 Effect of aggregate type on creep behavior of Mix2F .................................................... 154 76 Effect of aggregate type on creep behavior of Mix3F .................................................... 155 77 Effect of aggregate type on creep behavior of Mix5S .................................................... 155 78 Effect of aggregate type on creep behavior of Mix7S .................................................... 156 79 Effect of water to cementitious material s ratio an d air content on creep of concrete moistcured for 7 days and loaded at 40% of compressive strength................................158 710 Effect of water to cementitious material s ratio an d air content on creep of concrete moistcured for 7 days and loaded at 50% of compressive strength................................159 PAGE 14 15 711 Effect of water to cementitious material s ratio an d air content on creep of concrete moistcured for 14 days and loaded at 40% of compressive strength..............................159 712 Effect of water to cementitious material s ratio an d air content on creep of concrete moistcured for 14 days and loaded at 50% of compressive strength..............................160 713 Relationship between compressive strength and creep strain of concrete m oistcured for 7 days..........................................................................................................................161 714 Relationship between compressive strength and creep strain of concrete m oistcured for 14 days........................................................................................................................161 715 Relationship between compressive strength and creep strain of concrete under all curing conditions ..............................................................................................................162 716 Relationship of compressive strength to in stantaneous strain measured in creep test ..... 162 717 Effect of stress level on creep coefficient of concrete m oistcured for 7 days................ 164 718 Effect of stress level on creep coefficient of concrete m oistcured for 14 days.............. 164 719 Effect of curing condition on creep coefficient of concrete ............................................ 165 720 Effect of water content on creep coefficient at 91 days ................................................... 166 721 Relationship between compressive stre ngth and creep coefficient for specim ens loaded at 14 days..............................................................................................................168 722 Relationship between compressive stre ngth and creep coefficient for specim ens loaded at 28 days..............................................................................................................169 723 Relationship between compressive strength at loading age and corresponding creep coefficient at 91 days ....................................................................................................... 169 724 Effect of Elastic modulus at load ing age on creep coefficient at 91 days ....................... 170 725 Relationship between creep coefficient at 91 days and fc/E............................................ 171 726 Effect of coarse aggregate t ype on creep coefficient at 91 days ...................................... 172 727 Typical decay curve of creep modulus with time............................................................ 173 728 Behaviors of a Burgers Model......................................................................................... 176 729 Evaluation on creep prediction models............................................................................ 178 730 Comparison on the effectiveness of C.E.BF.I.P model and ACI m odel........................ 180 PAGE 15 16 731 Comparison between the creep strain at 91 days from experimental data and the predicted creep strain using CEBFIP model................................................................... 181 732 Relationship between creep strain and m echanical properties at loading age................. 182 733 Comparison between the ultimate creep stra in calculated by C.E.BF.I.P model and that by curvefitting..........................................................................................................183 734 Evaluation on ACI209 model and C.E.BF.I.P model................................................... 185 PAGE 16 17 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STRENGTH, MODULUS OF ELASTICITY, SHRINKAGE AND CREEP OF CONCRETE By Yanjun Liu December 2007 Chair: Mang Tia Cochair: Renaldo Roque Major: Civil Engineering In the application of prestres sed concrete, there are concerns on severe prestress loss caused mainly by elastic shortening, shrinkage and creep of concrete, which will result in the extreme reduction of the design capacity of prestre ssed concrete structure, or even the premature structure failure. Hence, the values of elastic modulus, ultimate shrinkage strain, and ultimate creep coefficient of concrete have to be es timated reasonably and accurately at the production stage in order to avoid loss of structural capaci ty, or even unexpected structural failure caused by prestress loss. At present, the modulus of elasticity, shrinkage and creep properties of concrete that are used in structural design are either based on the arbitrary available literature or based on the limited research of the locally available mate rials. Thus, there is a great need for a comprehensive testing and evaluation of locally available concrete mixes to determine their mechanical and physical properties so that correct values for these properties can be used in structural design. Also, there is a great need to design a simple, e ffective, practical and reliable creep apparatus to carry this massive investigation on creep behavior of concrete out. In this study, a creep test a pparatus was designed, and twenty four creep apparatus were constructed for use in performing creep tests. Th e creep apparatus was evaluated to be working PAGE 17 18 satisfactorily. An effective creep testing pr ocedure was developed and documented. Also, a gauge point position guide was designed for insta lling gauge point on the cy lindrical mold and it was proved to be an effective t ool in preparation of specimens for creep tests. In addition, an alignment frame was designed and it was proved to be a very useful tool to ensure that the specimens can be set up in the creep apparatus vertically. In this study, 14 concrete mixtures were ev aluated, and replicate batches for ten of these mixes were also produced and evaluated. Three types of coarse aggregate, fly ash and ground blastfurnace slag were incorporated in the mi x designs in this study. Concrete specimens were fabricated and tested for their compressive stre ngth, splitting tensile st rength, elastic modulus, shrinkage and creep. This study ha s generated valuable data and determined general trends on the compressive strength, splitti ng tensile strength, elastic modulus drying shrinkage strains and creep coefficient of structural concretes investigated in this study. Most importantly, the interrelationships among compressive strength, elastic modulus and shrinkage and creep properties of concrete were found through regression analysis. These relationships make the predictions of shrinkage and creep possible with the informa tion from compressive strength and elastic modulus. PAGE 18 19 CHAPTER 1 INTRODUCTION 1.1 Background and Research Needs Prestressed concrete structures, such as prestressed girder fo r longspan bridge, prestressed shell concrete structure for the storage of water or gas, nuclear reactor vessels and offshore oil drilling platf orms so on, are widely used in the U. S as well as other countr ies in the world. This is attributed mainly to the advantages of pr estressed concrete structure, which include1) eliminating or considerably reducing the net te nsile stresses caused by load, 2) increasing the capacity of the structure, and 3) decreasing the selfweight of concrete members. Also, prestressed concrete element is slimmer than rein forced concrete and more pleasing aesthetically. In the application of prestres sed concrete, there are concerns on severe prestress loss caused mainly by elastic shortening, shrinkage an d creep of concrete. Consequently, the design capacity of prestressed concrete structure will be extremely reduc ed, or even the structure will fail prematurely. Hence, the values of elastic modulus, ultimate shrinkage strain, and ultimate creep coefficient of concrete have to be es timated reasonably and accurately at the production stage in order to avoid loss of structural capaci ty, or even unexpected structural failure caused by prestress loss. For the sake of avoiding unexpected prestre ss loss, the strict requirements on shrinkage and creep properties of the concrete used for pres tressed concrete structures have been specified by ACI Code as well as other Specifications. For example, the AASHTO LRFD Bridge Construction Specifications2001 Interim Revisi ons [AASHTO, 2001] specifies that, for the design of continuous prestressed concrete Igirder superstructures, the ultimate creep coefficient should be 2.0 and the ultimate shrinkage strain will take the value of 0.0004, in accordance with the recommendation of ACI 209. The Specification also states that, when specific data are not PAGE 19 20 available, estimates of shrinkage and creep may be made using the provisions of CEBFIP model or ACI 209 model. The creep behavior of concrete has been the focus of engineers attention and may still be the engineers concentration for decades to come because of the volatility of the creep property of concrete. Over the years, many attempts have been tried to develop the general constitutive equation for the description of tim edependent behavior of concrete. However, most of them are empirical in nature and are limited to the scopes of the experiments. There are great uncertainties in extrapolation to later times and to the c onditions not covered in the laboratory. AASHTO LRFD Specifications state the following: without re sults from tests on the specific concretes or prior experience with the materials, the use of the creep and shrinka ge values referenced in these Specifications can not be expected to yield results with errors less than 50%. The values of the modulus of elasticity, ultimate shrinkage strain and ultimate creep coefficient of concrete, which are used in structural design in Florida, are either based on the arbitrary available literature or based on the lim ited research of the locally available material. Particularly, since very limited creep testing has been performed on Fl orida concretes, the knowledge of creep characteristics of Florida conc rete is still a blind page. More importantly, the susceptibility of th e elastic modulus, shrinkage and creep of concrete to the variation of concrete mix ingredients, such as particular a ggregates in Florida, water content and mineral additives so on, puts more uncerta inties in using these values. There is a great need for a comprehensive testing and evaluation of locally available concrete mixes to determine these mechanical and physical properties of Florida normalweight as well as lightweight concretes, especially fo r the concretes used in prestressed concrete structure, so that correct values for these properties can be used in structural design. In addition, PAGE 20 21 there is also an immediate need to determine the most effective and practical laboratory test setups and procedures for obtaining the modulus of elasticity, creep and sh rinkage properties of structural concretes used in Flor ida. This research study was carri ed out to meet these needs of the FDOT. 1.2 Hypothesis Creep is related other m echanical properties of concrete, especially strength and elastic modulus. Thus, it is possible to estimate or predict its creep be havior based on the knowledge of its other mechanical properties. Shrinkage of concrete is rela ted to its water content and other mechanical properties, specially strength and elastic modulus. Thus, it is possible to estimate shrinkage behavior from its water content and other mechanical properties. Ultimate creep coefficient of concrete may ex ceed a value of 2.0, which is usually assumed to be the maximum value in structure design. Th us, creep testing on the specific concrete is needed to obtain reliable value of its ultimate creep coefficient. 1.3 Objectives of Study This research has the following m ajor objectives: To design and recommend an effective and relia ble laboratory testi ng setup and procedure for performing creep tests on concrete. To evaluate the effects of aggregate, minera l additives and water to cementitious materials ratio on strength, elastic modulus, shrinka ge and creep behavior of concrete. To determine the strength, elastic modulus, sh rinkage and creep behavior of the typical concretes used in Florida. To determine the relationship among compressi ve strength, splitting tensile strength and modulus of elasticity of concretes made with ty pical Florida aggregate. To develop prediction equati ons or models for estimation of shrinkage and creep characteristics of typical Florida concretes. 1.4 Scope of Study The scope of this research c overed the following major tasks: To review the literature a bout previous and current study on elastic modulus, shrinkage and creep of concrete. PAGE 21 22 To design, construct and evaluate the effectiveness of creep test setup and procedures. To perform a comprehensive laboratory study on the physical and mechanical properties of typical Class II, IV, V and VI concrete mixtures made with normal weight aggregate and lightweight aggregate, in cluding compressive strength, indirect tensile strength, modulus of elasticity, cr eep and shrinkage behavior. A tota l of 14 different concrete mixes was evaluated, and ten of them were replicated. To analyze the experimental data, and to determine the relationships among different properties, and to develop pr ediction equations for estimation of shrinkage and creep behaviors of concrete. 1.5 Research Approach Objectives of this study are realized by the following research approaches: Conduct laboratory testing programs to dete rmine the various properties of concrete. ASTM standard test methods were used for co mpressive strength test, splitting tensile test, elastic modulus test and shrinkage test. A creep test setup was designed, evaluated and refined to be used for this purpose. Perform statistical analysis to determine relationships and trends among the fundamental properties of the concretes evaluated in this study. Evaluate existing prediction models for cree p and shrinkage and develop improved models for estimation of shrinkage and creep behaviors of concrete. PAGE 22 23 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction The f ollowing content presents a literature review on the susceptibility of strength, elastic modulus, shrinkage and creep prope rties of concrete to variou s factors, and on the existing models for predicting the stre ngth, elastic modulus, and shri nkage and creep properties of concrete. 2.2 Strength of Concrete 2.2.1 Significance of Studying Strength of Concrete Strength is comm only considered as the most valuable property of concrete, and it gives an overall picture of the quality of concrete because of its direct relation to the microstructure of the hydrated cement paste. Moreover, the strength of concrete is almost invariably a vital element of structural design and is specified for compliance purpose. Also, knowing strength development characteristic of concrete is very critical in decisionmaking about when to remove formworks, when to continue next construction step, or when to open structure to service. Apparently, the economic analyzer will be very pleased for knowing the aforementioned information to optimize project budget. Over the past decades, with the broad development and application of new concrete technique characterized by high strength concrete and high performance concrete, durable concrete structure and complex structural design become rea lizable. For example, highrise building enables humankind to make full use of limit living space on this planet plausible; and longspan bridge are more pleasing estheti cally, costeffective and resourcesaving. However, even though a large amount of inform ation has been accumulated about concrete strength design, engineers are still fore from knowi ng well the strength proper ties of concrete. To PAGE 23 24 design a concrete mixture with preassigned proper ties is still an engineers dream. The causes are attributed to the volatilit y of concrete strength induced by the variation of raw materials and their proportions. Thus, the properties of concre te materials are still worthy of study. 2.2.2 Effect of Coarse Aggregate on Strength of Concrete The investigation on the eff ect of raw m aterials and th eir proportions on strength development has been the focus of many engineers effort. For example, Aitcin and Mehta [Aitcin, PC a nd Mehta, P. K, 1990] studied the effect of coarse aggregate characteristics on mechanic al properties of high strength concrete. The experiment was carried out using four coarse aggregate types av ailable in Northern California and similar mix proportions. The results showed that using diabase and limestone aggregates produced concretes with signifi cantly higher strength and elastic modulus than those using granite and river gravel. They concluded that the mineralogical differences in the aggregate types were responsible for this behavior. Sarkar and Aitcin [Sarkar, S. L and Aitcin, PC, 1990] carried out research on the importance of petrological, petrogr aphical and mineralogical charact eristics of aggregate in very high strength concrete. They pointed out that aggregate intrinsic strength, particularly that of coarse aggregates, receives scan t attention from concrete technol ogists and researchers as long as the w/c ratio falls within the 0.50to0.70 range, primarily due to the fact that the cementaggregate bond or the hydrated cement paste fails long before aggregates do. This, however, does not hold true for very highstrength concre tes, with very low w/c ratios of 0.20 to 0.30. Compressive strength testing of very highstrength concrete has indicated that aggregates can assume the weaker role, exhibited in the form of transgranular fractures on the surface of failure, as has already been observed in some lightwei ght concretes. The aut hors have carried out detailed petrological, petrogra phical and mineralogical characte rization of twelve different PAGE 24 25 coarse aggregates that have perf ormed with variable success in very highstrength concrete in Canada and the United States. Suitability for such an application has been linked to a special set of lithological characteristics: th e minerals must be strong, unalte red, and fine grained. Intraand intergranular fissures partially decomposed co arsegrained minerals, and the presence of cleavages and lamination planes tend to weaken the aggregate, and therefore the ultimate strength of the concrete. Ezeldin and Aitcin [Ezeldin, A. S. and Aitcin, PC, 1991] studied the e ffect of four coarse aggregates with different characteristics on the compressive strength, flexural strength, and flexural strength/compressive st rength ratio of normaland hi ghstrength concretes. The study investigated the possibility of obt aining a relatively high flexural strength/compressive strength ratio at high compressive strength by using different aggregate types. The study by Alexander and Addis [Alexander, M. G. and Addis, B. J., 1992] showed that aggregates play an important role in governing mechanical proper ties of high strength concrete. Generally, andesite and dolomite aggregates give superior resu lts. Tests were also done on "artificial" interfaces between paste and these two rock types in order to characterize the interfacial bond properties. Results show that andesite achieves hi gher interfacial fracture energy values than dolomite, which help s to confirm the macroscopic e ngineering properties measured on concretes. Giaccio, Rocco, Violini, Zappitelli, and Zerbino [Giaccio, G. et al, 1992] pointed out that concrete is a heterogeneous material whose prope rties depend on the properties of its component phases and the interactions between them. They studied the effects of granitic, basaltic, and calcareous aggregates on the mechanical prop erties of high strengt h concrete, including compressive strength, flexural st rength, modulus of elasticity and stressstrain behavior of PAGE 25 26 concrete. The results indicated that the effect of coarse aggregate characteristics on the mechanical properties of highstre ngth concretes is substantial. The impact of aggregate strength on concrete compressive strength was evaluated by Lindgard, and Smeplass [Lindgard, J. and Smeplass S, 1993] as well. The significance of the aggregate strength has been compared with the effect of the cement type and the use of silica fume. According to the obtained results, the imp act of the aggregate strength on the strength of high strength concrete is limite d, compared with the impact of the binder type, while the differences in elastic modulus between the differe nt aggregate types is fully reflected in the concrete elastic modulus. This contradicti on is explained by a hypot hesis based on stress concentrations due to the difference in rigi dity between the binder and the aggregates. 2.2.3 Prediction of Strength of Concrete If there is no specific testi ng data available, it is a good a lternative to have an equation reliable to give an effective prediction on the st rength of concrete at desired age. An accurate approximation to the strength of concrete at specific ages is of great impor tance to know in order to decide on when to remove formwork, when to continue next construc tion step, and when to open the structure into service. In analyzing the characteristics of developm ent of compressive strength with time, an empirical equation has been provi ded by ACI 209R Code as follows: 28 )( c f t t t c f (21) Where in days and are constants, 28 cf is compressive strength of concrete at 28 days, and t in days is the age of concrete. For the tests using "12"6 cylinder, type I cement and moist curing condition, two constants, and are equal to 4.0 and 0.85 respectively. PAGE 26 27 Because of substantial effect of coarse aggregate type on th e properties of concrete, and because of no such mineral additives as fly ash and slag involved, which have substantial effects on the development of concrete strength, when the aforementioned formula was developed, caution should be taken when it is used. If possible, further inves tigation should be carried out to calibrate the above equation. 2.3 Elastic Modulus of Concrete 2.3.1 Definition and Determination of Elastic Modulus of Concrete The m odulus of elasticity or Youngs Modulus a very important mechanical property reflecting the capability of concrete to deform elastically, is defi ned as the slope of the stressstrain curve within the proportional limit of a material. Figure 21 Representation of the st ressstrain relation for concrete For a concrete material, usually, the most co mmonly used value in structure design is the secant modulus, which is defined as the slope of the straight line drawn from the origin of axes to the stressstrain curve at some percentage of th e ultimate strength. Since no portion of the stressstrain curve is a st raight line, the usual method of determin ing the modulus of elasticity is to measure the tangent modulus, which is defined as the slope of the tangen t to the stressstrain Strain Stress Unloading Loading Initial tangent modulus Tangent modulus Secant modulus PAGE 27 28 curve at some percentage of the ultimate strength of the concrete as determined by compression tests on "12"6 cylinders. Figure 21 illustrate s the stressstrain plot of a concrete as it is loaded and unloaded. From this figure, we can see that the secant modulus is almost identical to the tangent modulus obtained at some lower percentage of the ultimate strength. 2.3.2 Significance of Studying Elastic Modulus of Concrete Concrete, a s a building material, is utilized in the elastic range. Thus, it is very important to know the relationship between st ress and strain for a given concre te before it can be used for buildings, bridges, pavement and so forth. The relationship between stress and strain for a concrete material can be characterized by its el astic modulus, which is th e property of concrete materials. For reinforced concrete structures, the knowledge of the elastic property of a specific concrete will not only make the deformation of the concrete members wellcontrolled, but also decrease the extra stress transfer to other conc rete elements, which can cause the concrete to crack or fail prematurely. For prestressed concrete struct ures, elastic shortening is blam ed for causing prestress loss. The prestress loss, on one hand, will decrease the cap acity of a concrete stru cture, and even lead to unexpected collapse of the structure; and on th e another hand, it will re sults in the increased volume of tendon for satisfying the design requir ement because of overestimation on elastic shortening, which can result in possible wa ste of materials and increased cost. In addition, in order to make full use of the compressive strength potential, th e structures using highstrength concrete tend to be slimmer and require a highe r elastic modulus to maintain its stiffness. Therefore, the knowledge of the elastic modulus of high strength concrete is very important in avoiding excessive deformation, pr oviding satisfactory serviceability, and achieving the most costeffective designs. PAGE 28 29 At last, for concrete pavement, high elastic modulus concrete is not desirable because it increases the pavement cracking probability. Th us, high strength but low modulus concrete is preferable. As to how to obtain the concrete material with th e properties desired, one way to approach this goal is to change the propertie s of individual concrete components and their proportions. And most importantly, th e significant effects of differe nt types of coarse aggregate on elastic modulus of concrete have to be investigated. 2.3.3 Effect of Coarse Aggregate on Elastic Mo dulus of Concrete Figure 22 Stressstrain relations for cement paste, aggregate and concrete Since concrete is a multiphase material, modulus of elasticity is very susceptib le to the variation of coarse aggregate content and coar se aggregate type. In a study by Stock, Hannant and Williams [Stock et al, 1979], it was reported that for concretes with a fixed w/c of 0.5, as the volume of coarse aggregate varied from 20 to 60 %, the compressive strength of concrete remained almost same. This result is very cons istent with the W/C law established by Duff Abrams in 1919. That is to say, for a given mix proportion, the compressive strength of concrete 50 40 30 20 10 0 1000 2000 3000Stress MPa Strain 106 Aggregate Concrete Cement paste PAGE 29 30 will be determined by its water to cement ratio. Th is is especially true for normal concrete with compressive strength less than 60MPa. Howeve r, the elastic modulus of the concrete was substantially influenced by the changes in its co arse aggregate content. As shown in Figure 22 [A.M.Neville, 1996], we can see that the elastic modulus of concre te is remarkably different from that of hardened cement paste. Also, Neville [A.M.Neville, 1996] pointed out that, for a concrete of a given strength, because normal weight aggregate has a higher elastic modulus than hydrated cement paste, a higher aggregate content results in a highe r modulus of elasticity of the concrete. In a study by Persson [Persson, 2001], it was re ported that the elas tic modulus of selfcompacting concrete was the same as that for normal concrete as long as their compressive strengths were the same. However, in the study by Schlumpf [Schlu mpf, 2004], the elastic modulus of selfcompacting conc rete was reported to be 20% lower than that of a normal concrete with similar strength. In addition, th e findings from the study by Chi [Chi, 2003] also indicated that the aggregate frac tion in concrete had a considerab le effect on the elastic modulus of concrete. Coarse aggregate type is another very importa nt factor affecting th e elastic modulus of hardened concrete. Different types of aggregate can have quite distinct effects on elastic modulus. Even different coarse aggregates of the same type but from different locations can have substantially different properties. Th e reported findings by Zhou, Lydon and Barr [Zhou et al, 1995] show that the coarse aggregate type ha s a considerable influence on the elastic modulus of concrete. In their study, the effects of expanded clay, sintered fly ash, limestone, gravel, glass and steel aggregate on the elastic modulus of concrete were i nvestigated. In addition, the study PAGE 30 31 by Shideler [Shideler, 1957] on c oncrete mixtures using gravel and expanded clay as aggregate also indicate the same conclusion as reporte d by Zhou, Lydon and Barr [Zhou et al, 1995]. In 1990, Aitcin and Mehta [P. C. Aitcin and P. K. Mehta, 1990] also investigated the effect of coarse aggregate characteristics on mechanical properties of high strength concrete. In their study, the influence of four coar seaggregate types available in Northern California on the compressive strength and elastic behavior of a very high strength concre te mixture was studied using identical materials and similar mix proporti ons. The results indicated that the diabase and limestone aggregates were found to produce conc retes with significantly higher strength and elastic modulus than did the granite and river gravel. The mine ralogical differences in the aggregate types are considered to be responsible for this behavior. The study by Alexander [Mark G. Alexander, 1996] on the influence of 23 different aggregate types on the properties of hardened co ncrete showed that a ggregates exert a profound and important influence on the elastic property of concrete. In 1998, Cetin and Carrasquillo [Aykut Cetin and Ramon L. Carrasquillo, 1998] carried out an investigation on the effect s of four coarse aggregate type s locally available in central Texas on the mechanical properties of highperfor mance concrete. Test results showed that the mineralogical characteristics of coarse aggregate as well as the aggregate shape, surface texture, and hardness appeared to be responsible fo r the differences in the performance of high performance concretes. Also, it was observed th at it appeared that there was no one single equation for highperformance concrete mixtures with different coarse aggregates that coulc estimate the elastic modulus with sufficient accuracy as in the case of nor mal strength concretes. Wu, Chen amd Yao [Wu K.R, Chen B, Yao W, Zhang D, 2001] carried out a study on the effects of the coarse aggregate type, including crushed quartzite, crushed granite, limestone, and PAGE 31 32 marble coarse aggregate, on the compressive strength, splitting tensile strength, fracture energy, characteristic length, and elastic modulus of concrete. The results indicated that the stiffness of concrete depends on the type of aggregate, especially for highstrength concrete. Beshr and Maslehuddin [Beshr H et al, 2003] Rashid, Mansur and Paramasivam [M. A. Rashid et al, 2002]; Huo, AlOmaishi and Tadr os [Xiaoming Sharon Huo et al, 2001] reported that different types of coarse aggregate have pronounced effects on elastic modulus of concrete. 2.3.4 Models for Predicting El astic Modulus of Concrete As m entioned in the literature about the factors affecting elastic modulus of concrete, for a given type of aggregate, although the modulus of elastic ity of concrete will increase with the strength of concrete, the factors that affect the modulus of elasti city of concrete do not always have a corresponding effect on the strength of conc rete. Thus, there is no universal equation that can be possibly applied to relate compressive st rength to elastic modulus of concrete. Thus, the models, both ACI model and CEBFIP model, may need to be modified in order to be applied to a structure to achieve full func tion and serviceability in its entire life span The above hypothesis can be easily confirmed by an ex tensive testing program to inve stigate the effects of coarse aggregate types on elastic modulus of concrete. The study by Shih, Lee, and Chang [Shih, T. S. et al, 1989] suggested that Young's modulus of highstrength concre te has a somewhat higher value than that of normalstrength concrete. Pauw's equation for modulus of elastici ty of concrete, which is based on experimental normalstrength concrete, needs to be reexamined. Baalbaki, Benmokrane, Chaallal, and Aitcin, [Baalbaki, W., 1991] studied the influence of different types of crushed rocks on elastic pr operties of high performa nce concrete. Testing results pointed to the important role played by co arse aggregates through the elastic properties of PAGE 32 33 the parent rock. They also recommended that the present formulas relating the prediction of elastic modulus of concrete recommended by some codes should be reviewed. Nilsen and Aitcin [Nilsen, A. U. and Aitcin, PC., 1992] investigated the properties of high strength concrete containing lightweight, normal weight and heavyweight aggregates. In this study, a comparison of the values of elastic m odulus determined experimentally with those calculated according to the formula recomm ended by the ACI Building Code, the British Standard Code, and the Norwegian Standard Co de, showed that all codes overestimated the elastic modulus of highstreng th heavyweight concrete. In the following section, the formula used to predict the elastic modulus of concrete by Florida LRFD Guidelines, ACI model, and CEBFIP model are given. Model recommended by Florida LRFD Guidelines [2002] According to this guideline, in the absence of more precise data, the modulus of elasticity for concretes with unit weights between 0.090 and 0.155 kcf, can be estimated from the following formula: c f c w c E (22) Where EcElastic modulus in ksi. cw Unit weight of concrete (kcf). 'cf Compressive strength of concrete (ksi). Constant, 33000 is recommended by Florida LRFD Guidelines. constant, 5.1 is recommended by Florida LRFD Guidelines. Prediction equations recommended by ACI 209 PAGE 33 34 The prediction equations recommended by AC I for estimating the elastic modulus of concrete are given as follows: c fA c E (23) Where cE Elastic modulus (psi) cfCompressive strength of concrete (psi) A constant, 57000 Ais recommended by ACI 318. The following equation recommended by ACI 31889 (revised 1992) for structural calculation is applicable to normal weight concrete: c f c E (24) Where cEElastic modulus (GPa) cfCompressive strength of concrete (MPa) constant, 32.3 is recommended by ACI 318. constant, 9.6 is recommended by ACI 318. The next equation given by ACI 363R92 is appl icable for predicting elastic modulus of concretes with compressive strength up to 83 MPa (12000 psi) 65.3 c f c E (25) Where cEElastic modulus (GPa) cfCompressive strength of concrete (MPa) CEBFIP Model (1990) PAGE 34 35 CEBFIP Model (COMITE EUROINTERNATI ONAL DU BETON) Co de (1990) also offers the following model for prediction of timedependent modulus of el asticity. The equation is given as follows: ci E tt st ci E 5.0 5.0 1 / 28 1exp) ( (26) Where sA coefficient depending on the type of cement; s = 0.20 for rapid hardening high strength cements, 0.25 for normal and rapid ha rdening cements, and 0.38 for slow hardening cements. t Age of concrete (days). t11 day Eci Modulus of elasticity of concrete at age of 28 days. 2.4 Shrinkage Behavior of Concrete 2.4.1 Origin of Shrinkage of Concrete According to the mechanisms of concrete shri nkage, shrinkage of c oncrete consists of plastic shrinkage, autogenous shrinkage (a pro cess known as selfdesiccation), drying shrinkage, and carbonation shrinkage. Autogenous shrinkage is the consequence of w ithdrawal of water from the capillary pores by the anhydrous cement particles. Most of the autogenous shrinkage will take place at the early age of hydration of cement. However, for concre te mixtures with a very low W/C ratio, this procedure may last longer if moisture is available from ambient environment. Plastic shrinkage and drying shrinkage are caused by withdrawal of water from concrete under the condition of humidity gr adient between the interior of concrete and air. Plastic PAGE 35 36 shrinkage may lead to the interc onnection among capillary pores, th e main factor contributing to cracking of concrete at early age as well as increasing permeability of concrete. Carbonation shrinkage is cause d by carbonation of calcium hy droxide in the concrete. Thus, carbonation shrinkage normally takes place on the surface of concrete elements. But, if there are penetrated cracks in concrete, carbonation shrinkage may take place in the interior of concrete. Carbonation of concrete will decreas e the PHvalue inside concrete so that reinforcement can be easily corroded. 2.4.2 Significance of Studying Shrinkage of Concrete Shrinkage of concrete, one of the main f actors in determinatio n of the endurance of concrete structure, is a very im portant property of concrete to be evaluated. Excessive shrinkage is blamed for leading concrete to crack, even fail At the early age of conc rete, low early strength can not resist the stresses indu ced by drying shrinkage so that shrinkageinduced cracking can subsequently lead to premature failure of the conc rete structure. Cracks in concrete increase the permeability of concrete and control the corrosion initiation time and corrosion rate of steel reinforcement in the concrete structure. Shri nkageinduced cracks become a severe problem for marine concrete structures or concrete structures close to the coastal re gion. The penetration of aggressive ions through cracks into th e interior of concrete is a very critical factor in causing the corrosion of steel reinforcement. For prestresse d concrete elements, not only does the shrinkageinduced cracking speed up the corrosion of reinforcement, shrinkage deformation, which accounts for up to 15% of total prestress loss, is also one of the main factors contributing to prestress loss. The shrinkage behavior of conc rete is greaty affected by coar se aggregate content, coarse aggregate type, cementitious material content and water content. For instance, an increase in volume of aggregate in concrete will usually lead to a decrease in cement content, which would PAGE 36 37 lead to reduced shrinkage for the concrete. However, a reduction in cement content does not necessarily cause a reduction in the strength of the concrete. Thus, through optimizing mix proportion of concrete mixture, it is possible to design a concrete with low cement content and low shrinkage without s acrifice of strength. 2.4.3 Effect of Raw Materials on Shrinkage of Concrete 2.4.3.1 Effect of aggregate co ntent on shrinkage behavior of concrete The contribution of coarse aggregate to decreased shrinkage of concrete is attributed to the decrease of cement paste volume in the concre te mix. In 1956, Pichett [G.Pichett, 1956] reported that the shrinkage ratio increases signifi cantly as the aggregate content decreases. The possible reason to explain the effects of coarse ag gregate content on shrinkage strain of concrete is shown in Figure 23. For the l ean concrete mixture with a high coarse aggregate content, the coarse aggregate particles will have pointtopoi nt contacts or even facetoface contacts with each other. So a concrete with such a stiff aggreg ate skeleton will be very effective in resisting stresses caused by cement paste shrinkage because aggregate particles cannot be pushed more closely under the action of inte rior stress cause by shrinkage Thus, shrinkage strain is dramatically reduced. But, for rich co ncrete, the situation is otherwise. Figure 23 Effect of coarse aggregate content on the shrinkage of concrete a. Lean concrete b. Rich concrete CA Mortar PAGE 37 38 Similarly, in 1960, Hermite [R.LHermite, 1960] carried out a study of the effects of cement content on shrinkage behavior of conc rete. The tests were performed at a curing temperature of 68oF, 50% relative humidity and wind velo city of 2.25 mph. The results indicated that, at the early age of concrete the shrinkage strain of the c oncrete with a cement content of 850 lb/yd3 (typical cement content for fl owable concrete) is almost three times higher than that of concrete mixtures with a cement content of 340 lb/yd3. Leming [Leming, M. L, 1990] investigated th e mechanical properties of high strength concrete with different raw mate rials. These materials represent those used in structures built under North Carolina Department of Transportatio n control. The data from shrinkage tests showed that shrinkage strain of concrete va ries significantly dependi ng on the specific raw materials used and the strength levels attained. Research was carried out by Alfes [Alfes, 1992] on how shrinkage was affected by the aggregate content, the aggregate modulus of elasticity, and the silica fume content. The experiment was conducted using W/C ratio in the range of 0.25 to 0.3 with 20% silica fume by weight of cement and varying amount and type of aggregates (basalt, LDslag, and iron granulate), and compressive strengt h of concretes at 28day age we re in the range of 102 to 182 MPa (14,600 to 26,000 psi). The test results showed that there is a direct and linear relationship between the shrinkage value and the modu lus of elasticity of the concrete. In 1993, Zia et al. [Zia et al, 1993c, 1993d, 1993e] evaluated the shrinkage behavior of VES, HES, VHS concretes with different aggregates (crushed granite, marine marl, rounded gravel, and dense limestone). Shrinkage measuremen ts were made for three to nine months in different cases. The observed behavior followed the general trend of conventional concrete except for the two cases of VES concrete using special blended cement (Pyrament) with marine PAGE 38 39 marl and rounded gravel as aggregates. In these two cases, the specimens exhibited an expansion of approximately 140 microstrains, rather than shrinkage for th e entire period of 90 days. The expansion was attributed to the lack of evaporable water in the concrete because of its very low W/C (0.17 for marine marl, and 0.22 for rounded gravel). 2.4.3.2 Effects of coarse aggregate type on concrete shrinkage The skeleton of coarse aggregate in a concre te can restrain the shrinkage of the cement matrix. The extend that the coarse aggregate sk eleton can resist the stress caused by shrinkageinduced stress from cement matrix depends on how stiff the coarse aggregate is. That is to say, the elastic modulus of the aggregate determines th e extent of restraining action to the shrinkage of concrete. For example, the shrinkage of a c oncrete made with a steel aggregate will be lower than the one made with a normal aggregate. Sim ilarly, the shrinkage of a concrete made with expanded shale aggregate will be higher than the one made with a normal aggregate. The above hypothesis was verified by the many studies performed in the past decades. In 1958, Troxell, Raphael and Davis [Troxell et al, 1 958] performed tests to study the effects of coarse aggregate of differe nt types on shrinkage be havior of concrete. Th e tests were carried out on the concrete mixtures with a fixed mix pr oportion. The results showed that there is a considerable variation in the sh rinkage strain of the resulting concrete batched with coarse aggregate of different types. They made a conclu sion that this phenomenon is due very likely to the difference in modulus of elasticity among aggr egates of different types. Generally speaking, the elastic property of aggregate determines the degree of restraint to the cement matrix. Reichard [Reichard, 1964] agreed that the coarse aggregate has significant effect on shrinkage behavior of concrete. A normal natural aggregate is usually not subject to shrinkage. However, there exist rocks that can shrink up to the same magnitude as the shrinkage of concrete made with nonshrinking aggregate. PAGE 39 40 2.4.3.3 Effects of size and shape of coarse aggregate on concrete shrinkage Aggregate size and shape also affect the shrinkage of hardened concrete. The experimental study conducted by Collins [Collins, 1989] on shrinka ge of five highstrength concrete mixtures with varied paste content, aggregate size showed that shrinkage deformations were somewhat less for concrete mixtures with lower past e contents and larger aggregate size. A study by Bisschop, Pel, and Van Mier [Bisschop et al, 2000] indicated that the total length and the depth of microcracking caused by sh rinkage of concrete will increase with larger aggregate size. McQueen, Rapol, Flynn [Roy D. McQueen et al, 2002] performed laboratory shrinkage tests in accord ance with ASTM C 157 on a matrix of 16 concrete mixes to evaluate the effects coarse aggregate size on shrinkage of c oncrete. The tests were conducted on mixes with ASTM C 33, No.57 (38mm maximum aggreg ate size) and No. 467 (64mm maximum aggregate size) coarse aggregates. The results of the laboratory shrinkage tests revealed that the maximum size of the coarse aggregate (No.57 or 467) did not influence the shrinkage. A study on evaluation of high performance concrete pavement carried out by Ozyildirim [Ozyildirim, C, 2000] showed that concrete usi ng smaller coarse aggregate commonly exhibits greater shrinkage and increases potential fo r slab cracking because of increased paste requirements. Larger maximum coarse aggregate si zes, on the other hand, re quire less paste, less cementitious material, and less water, thereby resu lting in reduced shrinkage; they also provide increased mechanical interl ock at joints and cracks. Thus, there is still some controversy about how coarse aggregate size will affect the shrinkage behavior of concrete. Test data from the specific concrete are necessary to control concrete quality. PAGE 40 41 2.4.3.4 Effect of other factors on shrinkage behaviors of concrete Shrinkage behavior of concrete is affected not only by coarse aggreg ate, but also by other factors, such as water content, specimen size, ambient conditions, admixtures as well as mineral additives. Water content is the most important factor influencing shrinkage behavior of concrete. Normally, the higher the W/C ratio is, the hi gher the shrinkage. This occurs due to two interrelated effects. As W/C increases, paste strength and stiffness decrease; and as water content increases, shrinkage potential increases. The specimen size affects the diffusion rate of fr ee water from the interior to exterior of concrete. Thus, both the rate and the total magnitude of shrinkage decrease with an increase in the volume of the concrete member because, for larger members, more time is needed for shrinkage effects to reach the in terior regions. For instance, the study by Hindy et al. [Hindy et al, 1994] showed that dry shrinkage of small sp ecimens measured by the conventional laboratory test was found to overestimate shrinkage of the concrete in the real structure. Ambient conditions, such as relative humid ity and temperature, greatly affect the magnitude of shrinkage. They are blamed for affe cting shrinkage behavior because they create the relative humidity gradient a nd relative temperature gradient be tween the interior and exterior of concrete, which is driving fo rce to concrete shrinkage. The higher the relative humidity, the lower the rate of shrinkage is. The lower the te mperature gradient, the lo wer the shrinkage rate is. Thus, the investigation conducted on shrinkage be havior of concrete has to simulate the real environmental conditions in order not to overestimat e shrinkage strain. For example, Aitcin et al. [Aitcin et al, 1990] reported that the surface sh rinkage strains under the field condition were considerably lower than those measured under the laboratory conditions. PAGE 41 42 Mineral additive effect on shrinkage behavior varies according to the type of mineral additive. Any material which substantially changes the pore structure of the paste will affect the shrinkage characteristics of the c oncrete. In general, as pore refine ment is enhanced, shrinkage is increased. Pozzolans typically increase the drying shrinkage, due to several factors. With adequate curing, pozzolans generally increase por e refinement. Use of a pozzolan results in an increase in the relative paste volume due to the following two mechanisms: 1) In practice, slowly reacting pozzolans (such as Class F fly ash) ar e frequently added to replace cement by weight rather than by volume according to conventional concrete mix design method. This will increase paste volume since pozzolans have a lower sp ecific gravity than Portland cement. 2) Additionally, since pozzolans such as fly ash an d slag do not contribute significantly to early strength, concrete containing pozzo lans generally has a lower stiffn ess at earlier ages as well, making them more susceptible to increased shrinkage under standard testing conditions. 2.4.4 Models to Predict Concrete Shrinkage Misprediction of shrinkage usually does not cau se structural collapse, but puts the structure out of service, i.e. the structure does not live as long as the proj ected life span. The widespread occurrence of such lack of l ongterm serviceability inflicts a tremendous economic damage on many nations. The direct signs of damage that put a structure out of service are typically cracks, which may cause major fractures. Even though the mechanisms of shrinkage, such as micromechanics mechanism and diffusion mechanism, have been studied extens ively, their correlations with macroscopic behaviors have been intuitive and nonquantitative. As pointed out by Bazant and Carol [Bazant et al, 1993], such studies genera lly have not borne much fruit. Since the uncertainty in the prediction of shrinkage behavior with the variations of concrete compositions and random environmental conditions is enormous, the m odels established at present relies on purely PAGE 42 43 empirical relations without micromechanics models involved. In addition, substantial effort has been paid in stochastic phenomena and probabilis tic models, but similar to the preceding topic, nothing is being introduced into practice. At present, the empirical formula given by the ACI Committee 209 [1993] is widely used to predict shrinkage strain. But, it should be not ed that ACI 209 equation could well be in error unless broad corrections are applied, for instance to correct for curing and size effect, and to account for humidity and composition effects. As pointed out by Hindy et al. [Hindy et al, 1994], the ACI 209 predictive equation was found to be valid for the high performance concretes only if new values for the parameters were introduced. Thus, owing to many uncertainties in current models, it is very necessary to perform tests on the specific concrete mixtures designed using lo cal available materials to guarantee the safety of structures. Then, based on the accumulated data, constitutive parameters characterizing the shrinkage behaviors of concretes designed based on local available materials can be obtained. In the following sections, the shrinkage pred iction models offered by CEBFIP model code (1990) and ACI209 (1992) ar e reviewed briefly. 2.4.4.1 CEBFIP Model for shrinkage strain prediction In this model, the effects of cement type, ambient relative humidity, compressive strength of concrete, and size effect of specimen on sh rinkage strain of concrete are taken into consideration. The total shrinkage strain ma y be estimated by the following equation: s tt scss tt cs 0 (27) Where scstt Time dependent total shrinkage strain 0 cs Notational shrinkage coefficient PAGE 43 44 s (t ts)Coefficient to describe the deve lopment of shrinkage with time 0 cs can be estimated by the following equation: RH cmo f cm f sc cs 6 10 910160 0 (28) Where sc A coefficient which depends on the type of cement: 4 sc for slowly hardening cements; 5 for normal or rapid ha rdening cements; 8 for rapid hardening high strength cements. cmf The mean compressive strength of concrete at the age of 28 days. cmof =1 MPa sRH RH 55.1 for %99 %40 RH; 25.0 RH for %99 RH Where 3 0 1 RH RH sRH (29) RH The relative humidity of the ambient environment (%). 0RH 100% sstt can be estimated by the following equation: 5.0 1 2 0 350 1 t s tt h h t s tt s tt s (210) Where PAGE 44 45 u A hc2 The notational size of member (in mm), where Ac is the crosssectional area (mm2) and u is the perimeter (mm) of the me mber in contact with the atmosphere. 0h 100 mm 1t1 day 2.4.4.2 Prediction model recommended by ACI209 Report [1992] The concrete shrinkage prediction model recommended by ACI209 (1992) is shown by the following equation: u sh t t t sh 35 (211) Where t sh Time dependent shrinkage strain u sh Ultimate shrinkage strain t Time in days If there is no available shrinkage data from the concrete to be evaluated, the ultimate shrinkage strain,u sh can be assumed to be the following: shu sh 610780 (212) where sh a product of all the applicable correction factors for the testing conditions other than the standard condition; sh = 1 under standard testing condition. sh is obtained by multiplying the ultimate shrinkage strain under the standard condition by the appropriate correction factors as described in the following: Correction factors for the effect of initial moist curing. The corre ction factor is equal to 1.0 for concrete cylinders moistcured for 7 days, and 0.93 for that moistcured for 14 days. PAGE 45 46 Correction factor for the effect of ambient relative humid ity. The following formulas are given for use in obtaining the correction f actor for shrinkage test performed under the condition of ambient relative humidity greater than 40%. 0102.040.1 for 8040 (213) 030.000.3 for 100 80 (214) where Correction factor for the e ffect of relative humidity Relative humidity Correction factor for the effects of specimen si ze. The correction factor in consideration of the specimen size effect (vs ) is given by the following equation: )12.0exp(2.1 s vvs (215) where vs Correction factor for the effects of specimen size s v Volumesurface area ratio of the specimen in inches Correction factor for concrete compositi on. Various equations for calculating the correction factors for the effect s of the slump of the fresh concrete, aggregate content, cement content and air content of the concrete have also been given in this model. 2.5 Creep of Concrete 2.5.1 Rheology of Materials and Defi nition of Creep of Concrete The philosophical origin of rheo logy is owed to Heraclitus. As exemplified in his famous aphorism "Panta Rhei" ("Panta Rei"): Ever ything flows and nothing stands still. Inspired by this expression, rheology, the term was coined by Eugene Bingham, a professor at Lehigh University, in 1920, and wa s defined as the study of the deformation and flow of matter under the influen ce of an applied stress. One of the tasks of rheology is to empirically establish the relationships betw een deformations and stresses by adequate measurements. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics. PAGE 46 47 The rheological phenomenon of concrete materials, also termed as creep, is one of very important rheological properties of concrete. Since creep behavior of concrete is characterized by timedependence, it generates subs tantial effects on the st ructural stability dur ing its service life. Thus, it is of great importance to know the creep behavior of speci fic concrete before it can be used for structure design. Figure 24 Creep diagram of concrete material Creep of concrete can be defined as the time dependent deformation of concrete materials under a sustained stress. As shown in Figure 24, loadinduced creep consists of three stages, namely primary or transient creep stage, steadyst ate creep or secondary cr eep stage and tertiary creep stage. The primary or transient creep is characterized by a monotonic decrease in the rate of creep. The feature of secondary or steadystate creep is that mate rial will show constant creep rate. At last, in tertiary creep stage, creep rate will increase t ill material fails. Figure 25 shows a plot of strain versus time for a concrete that was loaded for some time and then unloaded. The permanent strain that rema ins after the load has b een released is called the creep strain. For concrete materials, creep stra in consists of two main components. The first component is the true or basic creep, whic h occurs under the conditions of no moisture movement to or from the ambient medium. This is the case for concrete element functioning as Time Cree p strain Transient creep Stead y state cree p Tertiary creep PAGE 47 48 underground foundation, or inside water. The second component is the drying creep, which takes place while concrete is subjected in ambient conditions. Normally, the creep strain that is considered in structural design is the sum of basic creep strain and drying creep strain. Due to the difficulty to differentiate delaye d elastic strain from creep strain and the convenience to build a numerical model to simula te timecreep strain curve with the delayed elastic deformation included, the total creep stra in would usually include both the delayed elastic deformation and permanent creep deformation. Also, the above mentioned approach is usually taken since the delayed elastic stra in is usually very small compared with the total creep strain. The creep behavior of concrete materials play s a great role in the stability of concrete structures. Also, the creep behavior of concrete is subj ected to the severe volatility caused by the variation of raw materials for c oncrete mixtures and their propor tions. Therefore, over the past decades, the study on creep of concrete has been one of engineers focuses. Figure 25 Straintime plot of concrete under a sustained load and af ter release of load 2.5.2 Significance of Studying Creep Behavior of Concrete Creep in concrete can have both positive as we ll as negative effect s on the performance of concrete structures. On the positive side, cr eep can relieve stress concentrations induced by Time since application of load Strain Instantaneous recovery Delayed elastic recovery Permanent creep Elastic strain PAGE 48 49 shrinkage, temperature changes, or the movement of supports. For example, in indeterminate beam with two fixed ends, creep deformation will be very helpful in reducing tensile stress caused by shrinkage and temp erature variation. On the other hand, in some concrete structur es, creep can do harm to the safety of the structures. For instance, creep deformation can lead to an excessive deflection of structural members, creep buckling or other serviceability problems especi ally in highrise building, eccentrically loaded columns and long bridges. In mass concrete, creep may be a cause of cracking when a restrained concrete mass undergoes a cycle of temperature change due to the development of heat of hydration and subsequent cooling. For prestresse d concrete structures, such as composite bridges, prestressed shells or continuous girders, the desirable creep of concrete would be as low as possible. Heavily prestressed members and long members are particularly susceptible to larg e volume changes. If a prestressed member is restrained in position prior to the majority of the volume ch ange has taken place, the prestressed members will exert excessive forces on its connections and supporting structures that could cause a structural failure. Also, another very important issue caused by creep deformation is prestress loss, accounting for more than 25% of total prestress loss. 2.5.3 Effect of Aggregate on Creep of Hardened Concrete Aggregates play an important role in creep of concrete. Coarse aggregate reduces creep deformation by reducing the cement paste content and restraining the cement paste against contraction. Generally, concrete s made with an aggregate that is hard and dense and have low absorption and high modulus of elasticity are de sirable when low creep strain is needed. The study by Troxell, Raphael, and Davis [Troxe ll et al, 1958] indicat ed that the creep strains of the concrete mixtures with different types of aggregate will behave differently. The PAGE 49 50 highest creep value is obtained from the concrete made with sandstone aggregate, and the lowest creep value is obtained from the concrete made with limestone. Rsch et al [Rsch, 1963] found an even grea ter difference between the creep strains of concretes made with different a ggregates. After 18 months under th e load at a relative humidity of 65%, the maximum creep strain of the concre te made with sandstone was five times higher than the minimum creep strain of the concrete made with basalt. Alexander, Bruere and Ivanusec studied th e influence of 23 aggregate types on creep deformation of concrete [Alexa nder et al, 1980]. Creep tests were conducted in a controlled environment at 23 C and 60 % relative humidity. Creep tests were conducted for six months after a 28day water cured period in limesaturated water to allow for minimal effects of hydration. Strains were measured using longitu dinal gages on two opposite faces of the prism with a gage length of 100 mm (4 in). The c onclusion shows that aggregates with a lower absorption will produce concrete wi th a lower creep deformation. It was further determined that the aggregate with a high elastic m odulus will produce low creep values. Collins [Collins, 1989] examined the creep prope rty of high strength concrete. Creep tests were conducted according to ASTM C 512. The results demonstrated that a concrete with a larger aggregate size and lower paste cont ent would provide a lower creep strain. Creep tests done by Hua [Hua, 1995] on pure hardened cement pastes and on a reference concrete (made with the same paste) also s how that creep is reduced by the presence of aggregate. In addition, the conclusion on the effect of coarse aggregate content on creep of concrete is also confirmed by the tests on lightweight aggregate concrete. The study by Geso lu, zturan PAGE 50 51 and Gneyisi [Geso lu et al, 2004] showed that concrete s containing higher lightweight coarse aggregate content had a lower creep strain at all W/C. 2.5.4 Prediction Models and Their Limita tions of Concrete Creep With the exception of creep buckling, overest imation or underestimation of creep usually does not lead to structural collapse, but merely shortens the structur al service life. But, misprediction of creep could put tremendous economic loss. Thus, accurate prediction of the ultimate creep st rain of concrete is of great importance. In order to obtain an accurate prediction, the foll owing mechanisms possibly resulting in creep of concrete have been studied, including micromechanics m echanism, diffusion phenomenon, thermodynamics mechanism, and other mechanism coupled with damage and fracture. Micromechanics mechanism in creep behavior has been studied extensively through the study of the microstructure of cement and conc rete for decades. However, the macroscopic constitutive relations based on the intuitively and nonquantitatively observed phenomenon or postulated on the microstructure or even molecu lar level generally are not promising. The uncertainty in the prediction of longterm creep associated with the variations of concrete composition is enormous, actually much larger than any uncertainty except that due to the randomness of environment. Thus, even though the attempts at the mathematical micromechanical modeling of some phenomena have already begun, there is sill quite a distance to make them practical. Diffusion phenomenon can be considered anot her very important mechanism for creep behavior of concrete because creep of concrete is always associated with the moisture and heat transport between the interior concrete and out side environment. Therefore, in concrete structures exposed to the envir onment or subjected to variable temperatures, there is no hope of obtaining realistic stresses without actually solving the associated problems of moisture and heat PAGE 51 52 transport, at least in an approximate manner. It has been shown that creep and shrinkage analysis based on diffusion analysis of a box girder bridge segment yields enormous stresses which are routinely neglected in practice. The models based on statistics have been studied extensively. Although the statistical variability of concrete creep under controlled la boratory conditions is qui te small, very large statistical fluctuations are caused by the environmen t as well as the uncerta inties in the effect of concrete composition. In most practical situations, sophisticated deterministic mathematical analysis makes in fact little sense, because the un certainties of stochastic origin are much larger than the errors of simple effective modulus solutions compared with sophisticated deterministic analytical solutions of differe ntial or integral equations. Due to complex influences coming from raw materials and ambient environment, the common problem with the current models is that th ey are only feasible to be used for the creep prediction of similar concretes, which means c oncretes from the same geographical region. The concretes used in the Florida region are genera lly quite similar and, instead of repeating measurements for each new major structure, one can greatly improve predictions on the basis of previously obtained data for a similar concrete from the same region. Equally important will be application of the existing fundament al research results in practice. Since each of these models is applicable under specific conditions for a certain class of material s, the proper utilization of these models depends essentially on the practical e xperience of the researcher. The accumulation of this experience is the purpose of most experimental works on creep. This is due mainly to the fact that 1) more than one microscope mech anism are involved in induc ing creep of concrete, and 2) some empirical models only can be used for certain types of concretes without the variation of concrete compone nts, proportions and applied e nvironmental conditions. If the PAGE 52 53 empirical model obtained from the concretes used in a given region is ap plied to predict creep strain of the concretes in another region, the result s could be very scary. Over the years, many equations have been deve loped for the description of steadystate and transient creep. But, most of them are either too complicated theoretically to bring them into practical use, or have an empirical character a nd were determined on the basis of a fit to the experiments, which cause great uncertainties in the extrapolation to long time intervals and to conditions not covered in the laboratory. In the following sections, two creep predic tion models, namely CEBFIP model and ACI 209 model will be reviewed. 2.5.4.1 C.E.BF.I.P Model Code In this model, the creep strain can be predicted by the following equation: ) 0 ,( 28 ) 0 ( ) 0 ,( tt ci E t c tt cr (216) Where ),(0ttcr Creep strain at time t )(0tc Applied stress ),(028tt Creep coefficient ciE Modulus of elasticity at the age of 28 days The modulus of elasticity can be estimated by the following equation: 3 1 )( 4 10 cmo f f ck f Eci E (217) Where PAGE 53 54 ckf Characteristic strength of concrete (in MPa);MPaf8 ;MPa fcmo10 ; MPaE41015.2 The creep coefficient ) ,(028tt can be calculated as follows: ) 0 ( 0 ) 0 ,( 28 tt c tt (218) Where 0 Notational creep coefficient. c Coefficient to describe the developm ent of creep with time after loading t Age of concrete in days 0t Age of concrete when loaded in days The notational creep coefficient can be estimated as follows: 2.0 ) 1 / 0 (1.0 1 ) 0 ( / 3.5 )( 3/1 ) 0 /(46.0 0 /1 1 ) 0 ()( 0 tt t cmo f cm f cm f hh RHRH RH t cm f RH (219) Where fffck cm h Notational size of the member (in mm) uAc/2 cA Crosssectional area (in mm2) u Perimeter of the member in contact with the atmosphere (in mm) 0h 100 mm. RH Relative humidity of the ambient environment (in %). PAGE 54 55 0RH 100% 1t 1 day. 1500250 0 18 0 2.11150 3.0 1 /) 0 ( 1 /) 0 ( ) 0 ( h h RH RH H ttt H ttt tt (220) 2.5.4.2 Model of ACI 209 In the ACI 209 (1992) model, the creep coefficient is estimated as follows: 6.0 ) 0 (10 6.0 ) 0 ( ) 0 () 0 ,( 28 tt tt ttt (221) Where ),(028tt Creep coefficient at time t )(0t Ultimate creep coefficient to Time of loading The ultimate creep coefficient can be expressed as: c t ) 0 ( (222) The constant 35.2 is recommended. The correction factors c consist of the following terms: asatRHlac (223) Where PAGE 55 56 la Correction factor for loading age. For lo ading ages later than 7 days and moist cured concrete, 118.0 0)(25.1tla. For loading ages later th an 13 days and steam cured concrete, 094.0 0)(13.1tla RH Correction factor ambient relative humidity. For ambient relative humidity greater than 40%, RHRH 0067.027.1 (RH is the ambient relative humidity in %) s Correction factor for slump of fresh concrete. l sS 00264.082.0 (lS in mm) Correction factor for fine to total aggregate ratio. a 0024.088. 0 (a is fine to total aggregate ratio) a Correction factor for air content. a aa 09.046.0 (aais air content) at Correction factor for thickness of member. When the average thickness or volume to surface ratio of a structural member differs from 150 mm or 38 mm, respectively, two methods are offered for estimating the factor of member sizeat : Averagethickness method For an average thickness of a member sma ller than 150 mm, the factors are given by ACI209 Report. For an average thickness of a me mber larger than 150 mm and up to about 300 to 380 mm, the correction factor for thickness is given as: a ath 00092.014.1 During the first year after loading a ath 00067.010.1 For ultimate values Where ah= Average thickness of a member in mm. Volumesurface ratio method s v ate0213.013.11 3 2 (224) PAGE 56 57 Where s v = Volume to surface ratio in mm. PAGE 57 58 CHAPTER 3 MATERIALS AND EXPERIMENTAL PROGRAMS 3.1 Introduction This chapter describes the mix proportions and ingredients of typical concrete mixtures used in this research, the met hod of preparation of the concrete mixtures, fabrication procedure of the test specimens and routin e ASTM testing methods and proce dures used in this study. 3.2 Concrete Mixtures Evaluated 3.2.1 Mix Proportion of Concrete The concrete mixtures were randomly select ed from typical Class II, IV, V and VI concretes made with normalweight and lightweight aggregates. They are re presentative concrete mixes broadly used in Florida. The range of de signed compressive strength of concretes varied from 4,000 to 11,000 psi at the age of 28 days. Class F fly ash and gr ound blastfurnace slag were used as additives in these mixes. Water reducing and air entraining admixtures were used throughout all the mixtures. Water to cementitious materials ratio for all the mixtures was determined according to the design strength of specified concre te. Workability of fresh concrete in terms of slump value, was controlled by the dosage of water reducer, supe r plasticizer and air en training agents. Since strength of concrete is very se nsitive to the variation of air co ntent and water content, to meet target slump value, the dosage of water reducer a nd superplasticizer were adjusted rather than the dosage of air entraining agent and water. In addition, another r eason to add air entraining agent to concrete is to improve durability of concrete. A total of 14 different concrete mixtures were evaluated. The deta iled mix proportions for the fourteen mixtures are presente d in Table 31. Miami Oolite limestone was used as a coarse aggregate for Mix1F, 2F, 3F, 4F, 5S, 6S, 7S, and 8S. Stalite lightweight aggregate was used for PAGE 58 59 Mix9LF and Mix10LS. Mix2G F, Mix3GF, Mix5GS and Mix7GS had identical mix proportion to the Mix2F, Mix3F Mix5S and Mix7S with th e exception that the coarse aggregate was replaced by a granite aggregate by volume. Fly ash was used in Mixes 1F, 2F, 3F, 4F, 9LF, 2GF and 3GF, and slag was used in Mixes 5S, 6S, 7S, 8S, 10LS, 5GS and 7GS. Mixes 1F, 2F, 3F, 4F, 5S, 6S, 7S, 8S, 9LF and 10LS were replicated. 3.2.2 Mix Ingredients The mix ingredients used in producing the c oncrete mixtures are described as follows: Water Potable water was used as mixing water for pr oduction of the concrete mixtures. The water temperature was around 64oF. Cement TypeI Portland cement from CEMEX Company was used. The physical and chemical properties of the cement as provided by Florid a State Materials Office are shown in Table 32 and Table 33. Fly ash The fly ash used in this study was provided by Boral Company. Its physical and chemical properties as provided by Flor ida State Materials Office ar e presented in Table 34. Slag The slag used in this study was provided by Lafarge Company. Its physical and chemical properties as provided by Florida State Ma terials Office are s hown in Table 35. Fine aggregate The fine aggregate used was silica sand from Go ldhead of Florida. The physical properties of the fine aggregate as determined by Florid a State Materials Office are shown in Table 36. The gradation of the fine aggregate is shown in Figure 31. The fine aggregate was ovendried before it was mixed with the othe r mix ingredients in the production of the concrete mixtures. Airentraining admixture The airentraining admixture used was Darex AEA from W.R. Grace & Co. Darex AEA is a liquid admixture for use as an airentraini ng agent, providing freeze thaw durability. It contains a catalyst for more rapid and comple te hydration of Portland cement. As it imparts PAGE 59 60 workability into the mix, Darex AEA is partic ularly effective with slag, lightweight, or manufactured aggregates which te nd to produce harsh concrete. Coarse aggregates Three different types of coarse aggregates were used in this study. The first one is a normal weight Miami Oolite limestone. The second on e is Georgia granite aggregate. The third one is called Stalite, a lightweight aggr egate from South Carolina. The physical properties of these three coarse aggregates are displayed in Table 37. The gradation of the Miami Oolite is shown in Figure 32; the grad ation of the Georgia granite aggregate is plotted in Figure 33; and the gr adation of Stalite aggregate is presented in Figure 34. In order to have a good control on the moisture content of coarse a ggregates, the coarse aggregates were soaked in water for at leas t 48 hours and then drained off the free water on the surface of aggregate before they were mi xed with the other mix ingredients in the production of the concrete mixtures. Waterreducing admixture The waterreducing admixture used incl uded WRDA60, WRDA64, and ADVA120 from W.R.Grace & Co. WRDA 60 is a polymer base d aqueous solution of complex organic compounds producing a concrete with lower water content (typically 810% reduction), improved workability and higher strengths. It can be used in ready mix, job site and concrete paver plants for normal and lightweight concrete. It also can be used in block, precast and prestress work. In addition, it o ffers significant advantages over single component water reducers and performs especia lly well in warm and hot weather climates to maintain slump and workability in high ambient temperatures. WRDA 64 is a polymer based aqueous solution of complex organic compounds producing a concrete with lower water content (typically 810% reduction), gr eater plasticity and hi gher strength. Except significant advantages like WR DA 60, WRDA 64 performs especially well in concrete containing fly ash and other pozzolans. ADVA 1 20, a superplasticizer, is a polymer based liquid organic compounds increasing plasticity of concrete. 3.3 Fabrication of Concrete Specimens 3.3.1 The Procedure to Mix Concrete The concrete mixtures investigated in this study were produced in the laboratory using a compulsive pan mixer with capacity of 17 cubic f eet, as shown in Figure 35. For each mixture, thirteen (13) cubic feet of fresh concre te was produced to fabricate sixty (60) "12"6 cylindrical specimens. PAGE 60 61Table 31 Mix proportions of the 14 conc rete mixtures used in this study Admixture Coarse Agg. No. of Mix W/C Cement (lbs/yd3) Fly ash (lbs/yd3) Slag (lbs/yd3) Water (lbs/yd3) FA (lbs/yd3) CA (lbs/yd3) AE WRDA/ADVA Mix1F* 0.24 800 200 236.0 931 1679 7.5 OZ (WRDA60)30OZ (ADVA120)60OZ Mix2F* 0.33 656 144 265.6 905 1740 12.0 OZ (WRDA60) 30OZ Mix3F* 0.41 494 123 254.0 1175 1747 0.5 OZ (WRDA60)33.4OZ Mix4F* 0.37 600 152 278.0 1000 1774 2.0 OZ (WRDA60) 56OZ Mix5S* 0.33 400 400 262.0 1062 1750 6.0 OZ (WRDA60)24OZ (ADVA120)48OZ Mix6S* 0.36 380 380 270.0 1049 1736 1.9 OZ (ADVA120) 38OZ Mix7S* 0.41 197 461 267.0 1121 1750 4.6 OZ (WRDA60)32.9OZ Miami Oolite Mix8S* 0.44 306 306 269.0 1206 1710 3.1 OZ (WRDA60)30.6OZ Mix9LF* 0.31 602 150 235.3 952 1239 9.6 OZ (WRDA64) 30OZ Stalite lightweight Mix10LS* 0.39 282 423 275.0 853 1300 8.8 OZ (WRDA64)31.7OZ Mix2GF 0.33 656 144 265.6 909 1981 12.0 OZ (WRDA60) 30OZ Mix3GF 0.41 494 123 254.0 1176 2027 0.5 OZ (WRDA60)33.4OZ Mix5GS 0.33 400 400 262.0 1066 2045 6.0 OZ (WRDA60)24OZ (ADVA120)48OZ Georgia Granite Mix7GS 0.41 197 461 267.0 1125 2045 4.6 OZ (WRDA60)32.9OZ Note: AEair entraining admixture; Mixtures were replicated. PAGE 61 62Table 32 Physical properties of Type I cement Loss on Ignition (%) Insoluble Residue (%) Setting Time (min) Fineness (m2/kg) Compressive Strength at 3 days (psi) Compressive Strength at 7days (psi) 1.5% 0.48% 125/205 402.00 2400 psi 2930 psi Table 33 Chemical ingredients of Type I cement Ingredients SiO2 Al2O3 CaO SO3 Na2OK2OMgO Fe2O3 C3A C3S C2S C4AF+C2F (%) 20.3% 4.8% 63.9% 3.1% 0.51% 2.0% 3.3% 7% 59% 13.8% 15.8% Table 34 Physical and chem ical properties of fly ash SO3 (%) Oxide of Si, Fe, Al (%) Fineness (%) (ASTM C430) Strength(7d) (ASTM C109) Strength (28d) (ASTM C109) (%) Loss on Ignition (%) (ASTM C311) % of Water (ASTM C618) 0.3 84 32 N/A 78 4.3 102 Table 35 Physical and chemical properties of slag SO3 (%) Oxide of Si, Fe, Al Fineness (%) (ASTM C430) Strength (7d) (%) (ASTM C109) Strength (28d) (ASTM C109) (%) Loss on Ignition (%) (ASTM C311) % of water (ASTM C618) 1.7% N/A 4 92% 129 N/A N/A Table 36 Physical properties of fine aggregate Fineness Modulus SSD Specific Gravity Apparent Sp ecific Gravity Bulk Specific Gravity Absorption 2.30 2.644 2.664 2.631 0.5% Table 37 Physical properti es of coarse aggregates Aggregate SSD Specific Gravity Apparent Specific Gravity Bulk Specific Gravity Absorption Miami Oolite 2.431 2.541 2.360 3.03% Stalite 1.55 6.60% Georgia Granite 2.82 2.85 2.80 0.58% PAGE 62 63 0 10 20 30 40 50 60 70 80 90 100 #4#8#16#30#50#100#200 Size of SieveCumullative passing Percentage (%) Figure 31 Gradation of fine aggregate (Godenhead sand) 0 10 20 30 40 50 60 70 80 90 100 1.5"1"0.5"4#8#200# Size of SieveCumullative Passing Percentage (%) Figure 32 Gradation of coarse a ggregate (Miami Oolite limestone) PAGE 63 64 0 10 20 30 40 50 60 70 80 90 100 1.5"1"0.5"4#8#200# Size of SieveCumullative Passing Percentage (%) Figure 33 Gradation of coarse aggregate (Georgia granite) 0 10 20 30 40 50 60 70 80 90 100 1.5"1"0.5"4#8#200# Size of SieveCumulative Passing Percentage (%) Figure 34 Gradation of light weight aggregate (Stalite) PAGE 64 65 Figure 35 Compulsive Pan Mixer The procedures to fabricate cylindric al specimens were given as follows: According to mix proportion desi gn, measure out the coarse a ggregate, fine aggregate, cement, mineral admixtures, water, high ra nge water reducer, air entraining agent. Place coarse aggregate and fine aggregate into the pan mixer to mix for about 30 seconds. Place two thirds of the water t ogether with the airentraining admixture into the mixer and mix for 1 minute. Place cement, mineral additives, such as slag or fly ash, as well as certain amount of highrange water reducer into the pan mixer and mix for 3 minutes, followed by a 2minute rest, then, followed by a 3minute mixing. Perform a slump test (according to ASTM C143) to determine whether or not the target slump has been reached. If the target slump is not satisfied, add so me more waterreducing admixture instead of water to adjust slump of fresh concrete. In doing so, we can assure the design strength of concrete will not be affected by adding extra water into concrete, which will change the water to cementitious material ratio. Remix the fresh concrete for two more minut es. Then, perform another slump test to check if the target slump has been reached. Re peat this procedure until the target slump is achieved. PAGE 65 663.3.2 The Procedure to Fabricate Specimens After the mixing procedure is completed, place the fresh concrete into "12"6 plastic cylinder molds. Then two different procedures will be taken to consolidate the fresh concrete inside plastic cylinder molds. The first one is that, if the slump of the fr esh concrete is less than 7 inches, fill each cylinder mold to one third of its height, and place the mold on a vibrating table for 45 seconds. Then fill the mold to another one third of its he ight, and place the mold on the vibrating table for 45 seconds. Then fill the mold fully, and place the mold on the vibrating table for 45 seconds. In addition, for the mixtures without any slump valu e, the vibrating time to consolidate concrete should be increased, or the vibrati ng intensity should be adjusted. The second one is that, if the slump is more than 7 inches, fill each cylinder mold in three layers, and rod each layers manually 25 times, as specified in ASTM C31. In doing so, we can assure that the mixtures with low slump value can be wellcompacted, while the mixtures with very high slump value will not be segregated due to overconsolidation. After consolidation, finish th e surface of each concrete spec imen with a trowel, and cover the top of the cylinder with a plastic lid to k eep moisture from evaporating. Then, allow the concrete to be cured in the cy linder molds for 24 hours before demolding. But, for concretes with very low compressive stre ngth after 24 hours, allow another 24 hours of curing in the mold before demolding. At last, set the demolded concrete specimens in the standard moist curing room for the specified curing time until testing. 3.4 Curing Conditions for Concrete Specimens The concrete specimens for compressive strength test, split tensile strength test, and elastic modulus test were cured in standard moist room until the age to be tested. Two different curing PAGE 66 67 conditions were applied to the concrete specim ens of Mix1F to Mix10LS for shrinkage and creep tests. The first condition is to cure the concrete specimens fo r 7 days in the moist room and followed by room condition for another 7 days. The second one is to cure the concrete specimens for 14 days in the moist room and followed by room condition for another 14 days. But, only one curing condition wa s applied to Mix2GF, Mix3GF, Mix5GS and Mix7GS, i.e.14 days in moisture room, and then in room condition for another 14 days. 3.5 Tests on Fresh Concrete In order to obtain concrete mixtures with uniform quality, ASTM standard tests, as shown in Table 38, on fresh concrete were perf ormed and described in detail as follows: Table 38 The testing programs on fresh concrete Test Slump Air Content Unit We ight Setting Time Temperature Test Standard ASTM C143 ASTM C 173 ASTM C138 ASTM C403/C 403M ASTM C 1064 Slump test Slump test was performed in accordance with ASTM C143 standard. The slump value was used to evaluate the consistency of fresh concrete. Air content test Air content test was carried out in accordan ce with ASTM C 173 standard. The volumetric method was employed for this test. Unit weight test The procedures of ASTM C138 standard was followed in running the unit weight test. This test was carried out to verify the density of concrete mixtures for quality control. Setting time test ASTM C403/C 403M standard was followed to perform the setting time test. The mortar specimen for the setting time test was obtained by wetsieving the sel ected portion of fresh concrete through a 4.75mm sieve. The pr octor penetration probe was employed for running this test. In this test, the initial se tting time is determined when the penetration resistance equals 500 psi, and the final setting time is determined when the penetration resistance reaches 4000 psi. PAGE 67 68 Temperature test Temperature of the fresh concrete was determined in accordance with ASTM C 1064 standard. This test was used to ensure th at the temperature of the fresh concrete was within the normal range, and that there was no unexpected condition in the fresh concrete. A digital thermometer was used to monitor the temperature of concrete. The properties of the fresh concrete for each of the ten mixtures are presented in Table 39. As can be seen from Table 39, the slump values of all the concrete mixtur es fell in the range of target slump value other than Mix2F. The replic ated Mix2F had a slump value higher than the target value. Also, the air contents of all the c oncretes were in the range of designed target value other than Mix2F and Mix5S, which had air content slightly higher than the maximum target value. Table 39 Properties of fresh concrete Setting Time Mix Number Slump (in) Target slump (in) Air Content (%) Target Air Content (%) Unit Weight (lbs/yd3) Initial Final Mixture Temperature (F) Mix1F 7.75 /9.75* 7.5~10.5 1.50 /1.25* 1.0~5.0 143.1 /145.5* 7h 0min 8h 50min 80/81* Mix2F 7.50 /4.25* 1.5~4.5 7.30 /4.50* 2.4~5.6 133.4 /137.7* 2h 50min 4h 35min 79/73* Mix3F 1.50 /2.00* 1.5~4.5 1.60 /2.50* 1.0~6.0 145.7 /143.9* 4h 55min 7h 15min 79/76* Mix4F 3.00 /3.00* 1.5~4.5 1.30 /2.00* 0.0~4.0 142.6 /143.8* 74/74* Mix5S 7.25 /9.00* 7.5~10.5 6.80 /3.75* 1.0~5.0 136.9 /141.6* 81/78* Mix6S 3.50 /5.50* 4.5~7.5 3.40 /2.25* 1.0~5.0 143.4 /141.4* 3h 10min 4h 55min 79/81* Mix7S 4.00 /5.75* 1.5~4.5 5.50 /5.50* 1.0~6.0 138.8 /138.0* 77/79* Mix8S 2.75 /3.00* 1.5~4.5 5.30 /3.75* 1.0~6.0 138.9 /140.4* 80/76* Mix9LF 3.75 /2.50* 1.5~4.5 5.20 /3.00* 3.0~6.0 116.9 /117.78 5h 35min 7h 20min 79/80* Mix10LS 3.50 /2.75* 1.5~4.5 5.50 /5.25* 1.0~6.0 111.6 /109.3* 7h 45min 10h 0min 77/78* Mix2GF 4.50 1.5~4.5 7.40 2.4~5.6 144.9 78 Mix3GF 2.50 1.5~4.5 1.50 1.0~6.0 150.1 79 Mix5GS 6.50 7.5~10.5 5.50 1.0~5.0 145.8 76 Mix7GS 2.25 1.5~4.5 3.80 1.0~6.0 147.3 74 From first phase study. PAGE 68 693.6 Tests on Hardened Concrete Routine ASTM standard tests on the hardened concrete specimen s are given in Table 310. Table 310 The testing progr am on hardened concrete Test Compressive Strength Splitting Tensile Strength Elastic Modulus Shrinkage Creep Test Standard ASTM C 39 ASTM C 496 ASTM C 469 Described in this chapter Described in this chapter 3.6.1 Compressive Strength Test Compressive strength test were performed on all the concrete mixtures investigated in this study. Through the compressive strength test, the strength development ch aracteristics of the concretes typically used in Flor ida can be obtained. Furthermore, the results from compressive strength tests can be used to calibrate the prediction equation given by ACI 209R Code so that a reliable prediction equation can be obtained. The test procedure of ASTM C 39 standard was followed for compressive strength test. For each concrete mixture, three replicate "12"6 cylindrical specimens were tested for their compressive strength at the age of 3, 7, 14, 28, 56, and 91 days, with a total of 18 specimens tested. Before testing, both ends of concrete cylinders were ground in order to support the load uniformly. The loading rate was controlled at 100 0 lbf per second. Two t ypical failure modes in the compression test are (1) column failure, and (2 ) shear failure. These two failure modes are shown in Figure 36. The compressive strength of the test specime n is calculated by dividing the maximum load attained from the test by the crosssectional area of the specimen, as shown by the following equation: 2 4 2 D i p r i p i f (31) Where PAGE 69 70 if is ultimate compressive strength of cylinderiin psi; ip is ultimate compressive axial load applied to cylinderiin lbs; D is diameter of cylinder specimen in inch. The average value of compressive strength fr om three cylinders will be taken as the compressive strength of the concrete. Figure 36 Typical failure modes of conc rete cylinders in compression test 3.6.2 Splitting Tensile Strength Test (or Brazilian Test) Splitting tensile strength test is simple to perfor m than other tensile tests, such as flexural strength test and direct tensile test. The strength determined from splitting tensile test is believed to be close to the direct tensile strength of concrete. In this study, the testing procedure of ASTM C 496 standard was followed in running the splitting tensile strength test. A "12"6 cylindrical specimen, which is identical to that used for co mpressive strength test, wi th four lines drawn on the sides of specimen to mark the edges of the load ed plane to help align the test specimen before the load was applied, is placed with its axia l horizontally between the platens of a testing machine. Figure 37 shows the loading configurati on for this test. As shown in Figure 37, two PAGE 70 71 strips of plywood as packing material, 3mm th ick and 25mm wide, are interposed between the cylinder and the platens so that the force applie d to the cylinder can be uniformly distributed. Then, the load will be applied and increased unt il failure by indirect tension in the form of splitting along vertical diameter takes place. Figure 37 Loading configurati on for splitting tensile test The splitting tensile strength of a cylinder specimen can be calculated by the following equation: Dl i p i T 2 (32) Where T splitting tensile strength of cylinder in psi; ip maximum applied load to break cylinder in lbf. llength of cylinder in inch; D diameter of cylinder in inch. The splitting tensile strength of concrete will take the average value of splitting tensile strengths of three cylinders. Due to the sensitivity and susceptibility of th e splitting tensile strength to the effects of internal flaws, such as voids, the results of some splitting tens ile strength tests may be unusually low and may need to be discarded. For this reason, five extra c oncrete cylinders were prepared for use in repeating this test if needed. "6 "12 Plywood PAGE 71 72 At last, the same curing conditions as those for the compressive strength test were used for the splitting tensile strength test. Three replic ate specimens were tested at each of the curing times, which were 3, 7, 14, 28, 56, and 91 days. A total of 18 specimens per concrete mixture were tested for splitting tensile strength. 3.6.3 Elastic Modulus Test The testing procedure of ASTM C 469 standa rd was followed to determine the elastic modulus of the concrete specimens. In this meth od, the chord modulus of elasticity of concrete cylinders is determined when a compressive lo ad is applied on a concrete cylinder in the longitudinal direction. A strain gage will be attached on the concrete cylinder to measure the deformation of the concrete cylinder during a compression test. Th e load and deformation data were recorded by means of a computer data acquisition system. A MTS machine, as shown in Figure 38, controls the loading rate by controlling displacement automatically. Prior to the test for modulus of elasticity, one of the three concrete cylinders was broken first to determine the compressive strength of co ncrete in accordance with ASTM C39 standard. Then, 40% of ultimate compressive strength of concrete specimen was applied on the other two concrete cylinders to perform the elastic modul us test. The cylinders for the modulus of elasticity test were loaded and unloaded three times. Then, the data from the first load cycle were disregarded. The average value from the la st two load cycles was recorded as the elastic modulus of the concrete. Since the elastic modulus of concrete will vary with the age of concrete, the elastic modules of concrete at the ages of 3, 7, 14, 28, 56, and 91 days were evaluated. Throughout the test, the ambient te mperature and relative humidity were maintained at 73 F and 100%, respectively. PAGE 72 73 Figure 38 MTS system for elastic modul us and compressive strength test 3.6.4 Shrinkage Test For the concrete mixtures with either Miami Oolite limestone aggregate or Stalite lightweight aggregate, six "12"6 concrete cylinders were made to evaluate their shrinkage behavior under two distinct curing conditions. Thr ee cylinders were cured for 7 days in a moist room, and then followed by a room condition curing for another 7 days. Another three cylinders were cured for 14 days in a moist room, and then cured for another 14 days in room condition. For concrete mixtures with Georgia granite aggregate, their shri nkage behaviors were investigated under just one curing condition, i.e. moist curing for 14 days, followed by curing in room condition for 14 days. Three pairs of gauge points, which were spaced 10 inches apart, were placed on each of concrete cylinder. A gaugepoint guide was used to position the gauge points on the plastic cylinder mold before the concrete was cast. Figu re 39 shows a picture of the concrete with the gauge points attached on them after the molds have been removed. PAGE 73 74 Figure 39 Cylindrical specimen with gage points installed A digital mechanical gauge was used to meas ure the change in the distance between the gage points as the concrete cyli nder shrinks. The digital mechan ical gauge has a resolution of 0.0001 in. Three sets of measurements were taken from each specimen. A total of nine sets of measurements were taken from the three replicate specimens for each concrete mixture. Measurements were taken every day in the first two weeks, and then once a week up to three months. The initial distance between the gauge points was measured immediately after required curing time was fulfilled. Then, the shrinkage test was run under the condition of the temperature of 73 F and 50% relative humidity. The shrinkage strain was taken as the average of the nine readings from the three replicat e cylinders, and can be expressed as follows: 9 1 0 ) 0 ( 9 1 i l l i l sh (33) Where il Measured distance between ith pair of gage points PAGE 74 75 0l Original distance between ith pair of gage points measured immediately after demoded. PAGE 75 76 CHAPTER 4 CREEP TEST APPARATUS DESIGN AND TESTING PROCEDURE 4.1 Introduction This chapter describes the design of the creep te st apparatus, and its auxiliary tools, which include a gagepoint positioning guide for positi oning gage points on a creep test specimen, and an alignment frame for aligning the specimens in a vertical direction. The creep testing procedures are also described in detail in this chapter. 4.2 Creep Test Apparatus 4.2.1 Design Requirements of Creep Test Apparatus In order to carry out the creep test program, a simple creep test apparatus was designed to satisfy the following design requirements: Creep test apparatus should be capable of applying and maintaining the required load on specimen, despite of any change in the dimension of the specimen. The bearing surfaces of the header plates sha ll not depart from a plane by more than 0.001 inch to insure even pressure distri bution on the concrete test specimens. Several specimens can be stacked for simultaneous loading so that more measurements can be made, and the reliability of test results will be increased by taking average of all the measurements. The height between two header plates shall not exceed 70 inches. If the height between two header plates is over 70 inches, the a pparatus will not be easily operated manually. Also, if the total height of the stacked test specimens is very high, the specimens may buckle easily under load. The applied load should be controlled so that it will vary by less than 2% of the target applied load. Means shall be provided to make sure that concrete specimens are centered properly and vertical. The designed creep test apparatus, which is spring supported system, is shown in Figure 41. The detailed design of creep apparatus used in this study is presented as follows. PAGE 76 77 4.2.2 Design of Creep Apparatus 4.2.2.1 The determination of the maximum capacity of the creep Apparatus In this study, the maximum design capacity of creep apparatus was determined according to the maximum compressive streng th (10 ksi) of concrete mixtur es commonly used in Florida. Creep test was run under the loading condition of 50% of compressive strength of concrete on "12"6 cylindrical concrete specimens. Thus, the ma ximum load applied to the creep frame can be computed as: lbf P 1413003 100005.02 max If a "8"4 cylindrical concrete specimen is used, th e creep test can be run on the concrete with compressive strength as high as 22 ksi. 4.2.2.2 The design of springs The spring constant of the larger spring (1k) was selected as 9822 lbf/in, while the spring constant of the smaller spring (2k) was selected as 3314 lbf/in. The maximum travel distance ( ) for both springs is 1.625 in. If nine sets of springs are used, the maximum load (springP ) that the springs can hold can be calculated to be: OK Plbf kk Pspringmax 5 211092.1 9 Thus, the spring capacity is ok. It is of importance to mention that the desi gn maximum travel distance of spring can not be more than the maximum travel capacity of the springs in order to maintain the load on specimen constant, and keep the frame stable. PAGE 77 78 Figure 41 Creep test apparatus 1 1 1.25in 1.125in 1.5in 1in 36in 1in 8.25in 1in 10in 18in 12in 12in 18in 1.5in 1in Hydraulic Jack Load Cell Springs Concrete Cylinder Gauge Circular Steel Plate Circular Steel PAGE 78 79 4.2.2.3 Design of header plate Figure 42 Boundary conditions used for finite element analysis In order to apply load uniformly to the test specimens, the deflection of header plate should not deviate too much for a plane surface when th e specimens are loaded. The required thickness of the header plates was determined using a fin ite element analysis. The steel plate was modeled as an isotropic elastic material with an elastic modulus of 29,000 ksi and Poissons ratio of 0.30, which are typical properties of st eel. The plate was modeled as fi xed from rotation about the x, y and z axis along the four boundary lines along the four holes on the steel plate as shown in Figure 42. The loading zone was modeled as a circular area identical to the cross sectional area of a 6inch diameter concrete cylinder. The maximum lo ad used in the analysis had a pressure of 5000 psi, which is 50% of the maximum compressive stre ngth of concrete investigated in this study. 12in 6in 6in 1.25in 6 in Loading Zone PAGE 79 80 Figure 43 Finite element mesh used in the header plate analysis Figure 44 Contour plot of deflection of header plate The finite element mesh used in the analysis consisted of triangle elements and rectangular elements as shown in Figure 43. The header pl ate with a thickness of 1.5 inches was analyzed. The deflection contour plot is s hown in Figure 44. As we can s ee from Figure 44, the deflection from center of header plate to the position 3 inches away fr om center changes from 0.00408 to 0.0033 inch. In other words, if the test specimens ar e loaded to a maximum pressure of 5,000 psi, the deflection of steel plat e will differ by less than 0.00078 inch, which is less than 0.001 inch. Thus, a header steel plate with a thickne ss of 1.5 inches was determined to be adequate and selected for use. PAGE 80 81 4.2.2.4 Determination of the size of steel rod When the concrete specimens are loaded in the creep frame, each of the four steel rods will carry one quarter of tota l load. The steel rods are 1.125 in. in diameter and are made of highstrength alloy steel with yield strength of 105,000 psi. If th e concrete specimens are loaded up to the maximum capacity of the creep apparatus of 141,300 lbf, the maximum stress in the steel rods would be equal to: psi 35556 5625.04 1413002 This maximum possible stress in the steel rods is less than half of the yield strength of the steel rod, which is 105,000 psi. Thus, the select ed steel rod meets the design requirements. 4.2.2.5 Stress relaxation due to the deflection of header plate and creep of concrete When the full capacity of creep frame is used, the total stress released due to the plate deflection can be approximated as follows: pounds k Ptotal deflection relaxed485913136 0041.0 Where deflection is the maximum deflection of header plate, and springk is the elastic constant of spring. While according to the design requirement, the allowable load relaxation is pounds 282602.0141300 In addition, since partial load will be relaxed due to the creep of concrete, the applied load to the concrete specimen should be adjusted in or der to keep the load th e same as the initially applied one. To have an error of less than 2,826 lbf in the app lied load, the following inequality has to be satisfied: lbf lbf ktotalcr2826 485 36 Solving the above inequality, we obtain that PAGE 81 82 0006.0 cr This means that the applied load should be adjusted at every 0.0006 increment of creep strain. Otherwise, the load relaxed would be more than 2826 lbf, the allowable maximum load relaxation. 4.3 Design of GagePoint Positioning Guide Three pairs of gage points with a gage distan ce of 10 inches are to be placed in each test concrete specimen. A gagepoint positioning gui de, as shown in Figure 45, was designed for use in positioning the gaugepoints on the plastic cylinder mold. By inserting a "12"6 cylinder mold into gagepoint position gu ide and tightening the six screws on the guide, the precise locations for the three pairs of gage points, wi th a gage distance of 10 inches, can be marked conveniently on the mold. Three lines of gage points are uniformly distributed with 120 angle along the periphery of specimen. The use of the gage positioning guide is of great importance because the maximum travel distance of mechanical strain gage is 0.4 in. The mechanical strain gage can not be used to measure a distance of mo re than 10.4 inches. Thus it is very important that the two gage points be place at an exact distance of 10 inches from one another. Figure 46 shows a picture of the gaugeposition guide. Figure 47 shows a picture with a plastic cylinder inside the gaugeposition guide. 4.4 Design of Alignment Frame An alignment frame was designed and construc ted to be used to align the concrete specimens in a vertical direction when they are placed in the test frame. Figure 48 shows the design of the alignment frame. The alignment fram e consists of one piece of angle steel and one piece of channel steel with three pieces of "10"2"5.0 steel plates welded on them respectively. They are connected together by using 6 steel rods The use of the alignment frame is described in creep testing procedure. PAGE 82 83 Figure 45 Design of Gagepoint positioning guide 10 6.05 120o 120 o 120 o PAGE 83 84 Figure 46 Gauge position guide Figure 47 Plastic cylindrical mold inside gauge position guide PAGE 84 85 4.5 Mechanical Strain Gauge A mechanical strain gauge, as shown in Fi gure 49, was used to measure the distance change between two gauge points. The instrument frame is made of aluminum alloy and has five master settings of 2", 4", 6", 8", and 10" that ar e easily set for gauging. The digital indicator has a minimum graduation of 0.0001". In this study, the master setting of 10" was selected so that the mechanical strain gage is suitable for the measur ement of longitudinal strain to the nearest 10 millionths. In addition, the effective range of displacement measurement is 0.3". 4.6 Other Details on Creep Apparatus For each test frame, three "12"6 cylindrical specimens are pla ced on top of one another and tested under the same load. The load is applied by means of an electronic hydraulic jack (with a maximum capacity of 200,000 lbs) and monitored by a load cell with a digital readout indicating the load applied. Th e load cell has a capacity of 200 kips, and the minimum readable digit of 10 pounds. When the desired load is reac hed, the nuts on the threaded rods is tightened so that they are snugly pressing against the plate underneath the hydr aulic jack so as to hold the plate in that position, and thus holding the applied load. After th e nuts are positioned properly to hold the applied load, the jack and the load cell ca n be removed from the test frame and used to load another test frame. The springs at the bottom of the creep frame help to maintain the balance of creep frame as well as a constant load on the sp ecimens despite any change in its length, as the concrete specimens creep under load. Up to 9 sets of springs can be used in this test frame. Figure 410 shows the positions of the springs in the test frame. Each set of springs consists of a smaller spring sitting inside a larger spring. In addition, the springs s hould be manufactured so that both ends of spring should be flatted, and nine sets of spri ngs should have the same height, and positioned symmetrically to keep load distribution evenly. In doing so there is no spherical bearing device needed to guarantee the load to be evenly transferred to the specimens. PAGE 85 86 As the concrete specimens are loaded in the creep frame, the rectangular steel plates, which are at the top and bottom of the test specimens, are deflected slightly. To keep the loading surfaces flat and the test specimens vertical when the load is applied, tw o 1inch thick circular steel plates with a diameter of 6 inches are plac ed on the top and bottom of the stack of concrete test specimens, as shown in Figure 41. Both surf aces of the circular plate should be polished to avoid of any uneven pressure on the concrete cylinder. 4.7 Creep Testing Procedure 1. Install gauge points on plastic cylindrical molds using the Gauge Position Guide. Each creep test specimen contains three pairs of gage points installed on concrete cylinder using Gauge position guide, which are placed 10 inches apart from each other. 2. Place the fresh concrete in the plastic cylinder molds. Place the fresh concrete into plastic cylinder in three layers. Consolidate each layer with 45 seconds of vibration on a vibrating table. After consolidation, the top su rface of concrete should be finished gently. This is a very important detail in making sp ecimen to avoid cracki ng around gauge insert as shown in Figure 411. If too much pressu re is applied to finish the surface, gauge inserts may be pushed downward because the plastic cylinder is not very stiff and can not keep the gauge inserts from being pushed dow nward. Once pressure is released, the gauge insert will return to its original pos ition, while concrete can not because plastic deformation can not be recovered. Thus, so me space between gauge insert and concrete will be created and it will affect the measurement. 3. Demold the concrete specimens after 24 hours of curing. Place the specimens in a moist room to cure for the required time. 4. Grind both end surfaces of each concrete cylinder. Both end surfaces of specimen should be ground in order to make them even, as shown in Figure 412. 5. Cap both ends of each cylinder using sulfur mortar to make end surfaces smooth and even. 6. Using the alignment frame designed for this study to stack the three replicate specimens vertically on top of one another. 7. Put two circular plates on top of concrete cy linder as well as at the bottom of concrete cylinders. PAGE 86 87 Figure 48 Schematic of alignment frame design 0.5in 0.5in 12.00in 1.5in 1.75in 2.00in 2.00in 12.00in 12.00in 5.00in 0.19in 0.19in 0.5in 0.5in 3.00in 8.00in 4.00in 4.00in 0.5in 10.00in PAGE 87 88 Figure 49 Mechanical gauge Figure 410 Positioning springs on the bottom plate 6in 12in Large spring Small spring 12in 6in Outside 5.50in Inside 2.94i PAGE 88 89 Figure 411 Cracking around gauge insert Figure 412 Concrete cylinder with both end surfaces ground 8. Adjust the creep frame and concrete specimens to make sure the specimens are centered and vertical. The creep frame can be adjust ed through moving the h eader plate back and forth with the nuts on the top of the plate. As shown in Figure 413, the centers of header plate and the plate on the top of springs are marked. On each plate is also marked a 3inch diameter with 8 mark points along the boun dary of the circle. If the concrete column consisting of three cylinders is placed so that it lines up with the circ les on the header and the bottom plates, then the concrete cylinders are centered and vertical. 9. After the concrete specimens are center ed, turn the nuts supporting the header plate downward at least 1.65 in. away from the bottom of header plate to avoid the header plate contacting with the nuts once load is applie d. Then, tighten the four nuts on the top of header plate slightly to hold the centered concrete specimens. Pressure applied while finishing Space Created Gauge Insert PAGE 89 90 Figure 413 How to center the specimens into creep frame 10. Set up a hydraulic jack and load cell in the creep frame, and check the position of hydraulic jack to make sure that it is coaxial with concrete specimens in order to avoid loading the concrete specimen s eccentrically. As shown in Figure 414, in order to make the hydraulic jack coaxial w ith concrete specimens, the cen ter of the header plate has also been marked on the top side. A circle with diameter identical to the diameter of jack cylinder has also been drawn on top of the header plate, with 4 marks hammered along the boundary of the circle 11. As shown in Figure 415, check the plate on th e top of load cell to make sure that the plate is level. Then, tighten slightly th e four steel nuts holding the top plate. 12. Preload the frame up to 500 lbf to properly se at the concrete test specimens in the creep frame. 13. Take the initial measurements, which are th e initial distance between two gauge points. 14. Apply the load through the electr onic hydraulic jack up to the ta rget load. It is strongly recommended to use electronic hydraulic jack because of several advantages in using electronic hydraulic jack. Firstly, by usi ng electronic hydraulic ja ck, the load can be applied to the loading frame continuously. S econdly, since the elec tronic hydraulic jack can apply load on the cylinder within 1 minute, the instantaneous measurements can be taken within seconds immediat ely after the loading procedur e was completed. Thus, the instantaneous measurement taken in this way is very close to the true elastic deformation. Thirdly, in using the electr onic hydraulic jack, the dynamic effect, which can cause the =6in Mark Point Circular Plate Header Plate 1.65in PAGE 90 91 cylinders to break easily, can be avoided. In a ddition, less effort is needed to load frame in comparison with using manual hydraulic ja ck, which takes hundreds of pushes to reach the desired load level. Figure 414 How to center th e hydraulic jack cylinder Figure 415 Leveling the plat e on the top of load cell 15. Immediately after the target load is reached, tighten the four nuts on the top of the header plate to hold the load on the specimens. Jack Cylinder Load cell Mark Point Jack Cylinder PAGE 91 92 16. Take instantaneous measurements using the digital mechanical gage immediately after loading. Then take the measurements in 1 hour, 3 hours and 6 hours. Then every day in the first two weeks, and then once a week un til 91 days, and then once a month if tests were kept going. 17. Adjust load at every 0.0008 increment of creep strain to keep the lo ad loss due to creep relaxation less than 2% of total load applied at the beginning. It deserves to emphasize again that it is important to take the first set of readings as quickly as possible in order to obtain a more accurate instantaneous deformation of the concrete. Otherwise, substantial early creep deformation may have taken place before the initial readings can be taken. The first set of readings can be taken within 3 minutes. The creep strain was calculated by subtracting th e shrinkage strain from the total strain as follows: ) 9 1 )(0 )(0 9 1 )(0 )(0 ( 9 1 i S i l S i l S i l i T i l T i l T i l STC (41) Where C Creep strain of concrete T The sum of creep strain and shrinkage strain S Shrinkage strain of concrete TilThe measurement taken from the thi pair of gage points for creep test Til)(0The initial length of the thi pair of gage points for creep test SilThe measurement taken from the thi pair of gage points for shrinkage test Sil)(0The initial length of the thipair of gage points for shrinkage test iNo. of pair of gage points from 1 to 9 PAGE 92 93 The creep coefficient, which is used in conc rete structure design, is calculated by taking the ratio of creep strain of the concrete at the testing age to elastic strain of concrete at the same curing age. It can be expressed as follows: E C cr C (42) Where crC Creep coefficient C Creep strain of concrete E Elastic strain of concrete Creep modulus, EC, is computed dividing the applied stress by the total strain without including shrinkage strain, as shown by Equation 43. cE c E (43) 4.8 Summary on the Performance of the Creep Apparatus The creep apparatus designed in this study is capable of applying and maintaining the required load on the test specimens. Three specim ens can be stacked for simultaneous loading. The unevenness of the deflection of bearing surface of the header plates is less than 0.001 in. and the pressure distribution on the concrete specimens varies by less than 0.026%, or 1.5 psi. Load can be applied to a precision of 10 lbs, as a load cell with resolution of 10 lbs is used control the applied load. The mechanical gauge used is able to measure longitudinal strain to a precision of 0.00001. Strains are measured on three gage lines spaced uniformly around the periphery of the specimen. An electronic hydraulic pump system is us ed to apply load to the creep frame. This PAGE 93 94 enables the loading process to be done in second s, and instantaneous strains can measured from creep test within a short time after loading. The gauge point position guide, which has b een designed to position gauge points on a plastic cylindrical mold, is a very effective and important auxiliary tool in preparation of test specimens. It enables the placement of gauge points at accurate locations on the test specimen so that the maximum travel distance of mechanical gauge will not be exceeded and measurement error can be reduced. The alignment frame, which has been designed to align concrete specimens vertically in the creep frame, makes the job of stacking three concrete specimens together for testing possible. Experimental results indicate that creep apparatus designed in this study is effective, reliable and practical. It can be used to run creep test on conc rete with a maximum compressive strength up to 10,000 psi if "12"6 cylinder specimens are used. If "8"4 cylinder specimens are used, the maximum compressive strength of th e concrete can be as high as 22,000 psi. PAGE 94 95 CHAPTER 5 ANALYSIS OF STRENGTH TEST RESULTS 5.1 Introduction This chapter presents the results from comp ressive strength, splitti ng tensile strength and elastic modulus tests on the 14 concretes mixes ev aluated in this study. The effects of various factors on strength are discussed. The predic tion equations establis hing interrelationship between compressive strength and splitting tensil e strength are given. The prediction equations relating compressive strength to elastic modulus are also presented. 5.2 Results and Analysis of Compressive Strength Tests The average compressive strengths at various curing times of the fourteen concrete mixes evaluated are presented in Table 51. The individual compressive strength values are shown in Table A1 in Appendix A. Table 51 Compressive strength of th e concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag 3 7 14 28 56 91 Mix1F 0.24 20% 8077 8572 8993 9536 10771 11267 Mix2F 0.33 20% 4077 4658 6028 6506 6838 7607 Mix3F 0.41 20% 5289 6470 7567 8241 8449 9426 Mix4F 0.37 20% 5712 6919 7114 7236 8996 9271 Mix5S 0.33 50% 5554 7235 8248 8832 9139 9456 Mix6S 0.36 50% 6375 7699 8587 9111 9529 9661 Mix7S 0.41 70% 4324 5374 5927 6392 6794 6917 Mix8S 0.44 50% 4795 6114 6939 7525 8119 8208 Mix9LF 0.31 20% 3039 3941 5136 5929 6690 6961 Mix10LS 0.39 60% 1467 2191 2937 3744 4312 4727 Mix2GF 0.33 20% 3885 4952 5807 6469 6952 7201 Mix3GF 0.41 20% 3818 5151 6137 7262 7782 8041 Mix5GS 0.33 50% 2961 4692 5692 7008 7854 8105 Mix7GS 0.41 70% 2267 4303 5222 6612 6741 7233 5.2.1 Effects of Water to Cement Ratio and Water Conten t on Compressive Strength In engineering practice, the st rength of concrete at a given age and cured in water at a prescribed temperature is assumed to depend on primarily on water to cementitious materials ratio and the degree of compaction. In this study, for the eight selected concrete mixtures using PAGE 95 96 Miami Oolite limestone aggregate, the effects of water to cementitious materials ratio on compressive strength at ages of 28 days and 91 days are shown in Figure 51 and Figure 52 respectively. The graph of compressive strength versus water to cementitious materials ratio is approximately in the shape of a hyperbola. Compre ssive strength tends to decrease as water to cementitious materials ratio increases. Water content is another important factor infl uencing the strength of concrete because the higher the water content, the more porous the hardened concrete tends to be. As shown in Figure 53 and Figure 54, compressive strength of concrete decreases dramatically as water content increases. 0 2000 4000 6000 8000 10000 12000 14000 16000 00.10.20.30.40.50.6 Water to Cementitious Materials RatioCompressive Strength at 28 days Figure 51 Effects of water to cementitious materials ratio on compressive strength at 28 days PAGE 96 97 0 2000 4000 6000 8000 10000 12000 14000 16000 00.10.20.30.40.50.6 Water to Cementitious Materials RatioCompressive Strength at 91 days Figure 52 Effects of water to cementitious materials on compressive strength at 91 days 0 2000 4000 6000 8000 10000 12000 14000 16000 220230240250260270280290 Water Content (lbs/yard3)Compressive Strength at 28 days (psi) Figure 53 Effects of water content on compressive strength at 28 days PAGE 97 98 0 2000 4000 6000 8000 10000 12000 14000 16000 220230240250260270280290 Water Content (lbs/yard3)Compressive strength at 91 days (psi) Figure 54 Effects of water content on compressive strength at 91 days 5.2.2 Effects of Aggregate Types on Compressive Strength The influence of coarse aggregate type on compressive strengths of four concrete mixtures is shown in Figures 55 thr ough 58. Figure 55 shows the co mpressive strength development with time for Mix2F and Mix2GF containing 20 % fly ash. Both concrete mixtures have identical mix proportions other than the different types of aggregate. Miami Oolite limestone aggregate was used for Mix2F, and Georgia granite aggregate was used for Mix2GF. It can be seen that the compressive strength of Mix2F is comparable to that of Mix2GF at various curing ages. For Mix5S and Mix5GS, the different aggr egate types gave considerable impact to the compressive strength. As can be seen from Figur e 56, Mix5GS using Ge orgia granite aggregate had very much lower compressive strength than Mix5S using Miami Oolite limestone aggregate at various ages. The same phenomenon can also be observed from Mix3F and Mix3GF, as shown in Figure 57, and Mix7S and Mix7GS, as depicted in Figure 58. PAGE 98 99 According to the concrete mixtures investigated in this study, the concrete mixtures using Miami Oolite limestone as coarse aggregate deve loped higher compressive strength than those using Georgia granite as coarse aggregate. The cause can be attributed probably to the sh ape of aggregate, surface characteristic and other physical properties such as water absorption. Most of aggregate particles of Georgia granite have elongated and flaky shape, which is not desirable to be used for high strength concrete because flaky particles tend to be oriented in one plane, w ith bleeding water and air voids forming underneath. Thus, the interf acial transition zone between aggregate and hardened mortar may be weaker causing the compressive strength of concrete to be lower. Most of the aggregate particles of Miami Oolite limestone have spherical shape, which is preferred for durable concrete mix because the spherical aggregate particles have lower surface to volume ratio, and they will pack better in a mortar matrix. The surface texture of Georgia granite aggreg ate is very dense and smooth, which may have a disadvantage in devel oping tight interlock between aggr egate and mortar matrix. Miami Oolite limestone has a very rough texture and ap preciable voids on the surface, and thus strong interlock can be formed since the cement slurry can penetrate into those voids. The water inside limestone aggregate can mi grate outward as cement hydration proceeds since the relative humidity gradient will be gene rated between internal aggregate and mortar. This water may possibly provide th e water needed for hydration of th e cement as moisture is lost through evaporation to the environment. PAGE 99 100 0 1000 2000 3000 4000 5000 6000 7000 8000Compressive Strength (psi) Curing Age (days) Limestone 0407746586028650668387607 Granite 0388549525807646969527201 0 3 7 14285691 Figure 55 Effects of coarse aggregate type on compressive strengths of Mix2F and Mix2GF 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Compressive Strength (psi) Curing Age (days) Limestone 0528964707567824184499426 Granite 0381851516137726277828041 03714285691 Figure 56 Effects of coarse aggregate type on compressive strength of Mix3F and Mix3GF PAGE 100 101 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Compressive Strength (psi) Curing Age (days) Limestone 0555472358248883291399456 Granite 0296146925692700878548105 03714285691 Figure 57 Effects of coarse aggregate type on compressive strength of Mix5S and Mix5GS 0 1000 2000 3000 4000 5000 6000 7000 8000Compressive Strength (psi) Curing Age (days) Limestone 0432453745927639267946917 Granite 0226743035222661267417233 03714285691 Figure 58 Effects of coarse aggregate type on compressive strength of Mix7S and Mix7GS PAGE 101 102 5.2.3 Effects of Fly Ash and Slag on Compressive Strength of Concrete Fly ash and slag are used mandatorily in Fl orida mainly for concrete durability purpose. The investigation on their eff ects on the development of compressive strength of concrete mixture is of great importance becau se of significance of their use in concrete. In this study, fly ash was as a cement substitute in an amount of 20% of total cementitious materials by mass, and slag was in an amount of 50%~70% of tota l cementitious materials by mass. The strength development characteristics of fly ash concrete and slag concrete with time were normalized as the ratio of compressive strength at various curi ng ages to the compressive strength at 91 days and the normalized values are presented in Table A2 in Appendix A. The strength development characteristics of two typical fly ash concretes and two slag concretes are illustrated in Figure 59. As can be seen from Figur e 59, the fly ash concretes had significant strength gain from 28 days to 91 days, while the slag concretes had already achieved more than 90% of their 91day strength at 28 days. 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0 20 40 60 80 100 Ages (days)% of 91day Compressive Strength Mix1FFly ashW/C=0.24 Mix3FFly ashW/C=0.33 Mix6SSlagW/C=0.36 Mix5SSlagW/C=0.33 Figure 59 Effects of fly ash and slag on compressive streng th of concrete PAGE 102 103 5.2.4 Prediction of Compressive Strength Development Knowledge of the strengthtime relation is of great importance when a structure is put into service, i.e. subjected to full loading condition an d for long time duration. The gain in strength after 28 days can be taken into consideration in design. In some other cases, for instance, in precast or prestressed concrete, or when early rem oval of formwork is required, the strength at early ages needs to be known. According to ACI 209R5, a general equation for predicting compressi ve strength at a given age has the following form: 28 )( c f t t t c f (51) Where in days and are constants, 28cf is compressive strength of concrete at 28 days, and t in days is the age of concrete. Equation 51 can be transformed into / )( cu f t t t c f (52) Where / is the age of concrete in days at wh ich one half of the ultimate compressive strength of concrete, 'cuf is reached. For the tests using 6 12in cylinders, type I cement and moist curing condition, two constants, the average values of and are equal to 4.0 and 0.85 respectively. The ranges of and in Equation 51 and 52 for the normal weight, sand lightweight, and all lightweight concretes (using both moist curing and steam curing, and type I and III cement) given by Branson, D.E.; Meyers, B.L.; and Kripanarayanan, K.M[Branson, D.E et al. 1973] are: =0.05 to 9.25, and =0.67 to 0.98. They were obtained from the tests on 88 6 12in concrete cylinders and cited by ACI 209 COMMITTEE REPORT in 1996. As mentioned in ACI 209R4, the values of and are not applicable to the concretes containing pozzolanic PAGE 103 104 materials, such as fly ash and slag. Furthermor e, ACI 209R4 indicates that the use of normal weight, sand lightweight, or all lightwei ght aggregate does not appear to affect and significantly. In this study, regression anal ysis using the form of ACI 209R5 equation (as shown in Equation 51) was performed on the results of compressive strength tests on the 432 concrete cylinders from this study to determine the and values for each mix. Table 52 shows the and values for all the mixes from this analysis. The detailed results of this analysis are presented in Table 53. Table 54 presents the average and values of the different concrete mixes as grouped by aggregate type. Table 54 also shows the time ratios 28 ')(c cf tf and ')(cu cf tf at different during times for these different groups of concrete mix in comparison with the corresponding values as predic ted by the ACI209R equation. As can be seen from Table 52, th ere is substantial difference between and values among the different mixes. For the concrete mixtures using Miami Oolite limestone coarse aggregate, the value of varies from 1.1 to 2.6, and its av erage value of 1.89 is significantly lower than 4.0 recommended by th e ACI209 code; and the value of is in the range of 0.82 to 0.93, and its average value of 0.90 is slightly higher than 0.85 given by the ACI code. This means that the concrete mixes using Miami Oolit e limestone aggregate and fly ash and slag tend to develop strength faster than the concrete mixtures as predicted by the ACI209R equation. For the concrete mixtures using Geor gia granite aggregate, the value of varies from 2.6 to 5.3, and its average value of 4.12 is close to 4.0 recommended by the ACI code; and the value of is in the range of 0.82 to 0.89, and its aver age value of 0.86 is agreeable with 0.85 given by PAGE 104 105 the ACI code. Thus, this indicates that the concre te mixtures using Georgi a granite aggregate had similar strength development as predicted by the ACI equation. For the concrete mixtures using the Stalite lightweight aggregate, the average value of is 5.5 and the average value of is equal to 0.78. This indicates that coarse aggregate type can have significant effects on the strength development process. 5.3 Analysis of Splitting Tens ile Strength Test Results The average splitting tensile strengths at vari ous curing times of the fourteen concrete mixes evaluated are displayed in Table 55. Th e individual splitting tens ile strength values are shown in Table A3 in Appendix A. 5.3.1 Effects of Water to Cement Ratio on Splitting Tensile Strength Water to cementitious materials ratio has a significant effect not only on compressive strength, but also on splitting tensile strength. Figure 510 and Figure 511 show the effect of water to cementitious materials ratio on splitting tensile strength of concre te at 28 days and at 91 days re spectively. They indicate that splitting tensile strength decreases as water to cementitious materials ratio increases. 5.3.2 Effects of Coarse Aggregate Ty pe on Splitting Tensile Strength The effect of coarse aggregate types on splitti ng tensile strength of concrete was evaluated on four concrete mixtures. Mix2F, Mix3F, Mi x5S, and Mix7S have Miami Oolite limestone as coarse aggregate, and Mix2GF, Mix3GF, Mix5GS, and Mix7GS ha ve Georgia granite as coarse aggregate. Mix2F and Mix2GF, Mix3F and Mix3GF, Mix5S and Mix5GS, and Mix7S and Mix7GS have identical mix proportions with the exception that a different coarse aggregate of the same volume was used. As show n in Figures 512 through 515, the effects of coarse aggregate types on splitting tensile strength of concrete are quite significant. In comparison with Mix2F, Mix3F, Mix5S and Mix7S, the four mixtures using Georgia granite PAGE 105 106 Table 52 Results of regression analysis for prediction of compressive strength development using ACI 209 equation Mix by ACI by ACI Square root of Absolute sum of squares by Modified ACI Equation Square root of Absolute sum of squares by ACI Equation M1F 1.10 0.90 673 1904 M2F 2.67 0.89 371 541 M3F 2.25 0.90 343 792 M4F 1.57 0.83 676 1571 M5S 2.04 0.92 67 886 M6S 1.57 0.94 125 1214 M7S 1.79 0.92 275 1698 M8S 2.15 0.91 150 726 M9LF 4.20 0.82 230 261 M10LS 6.74 0.74 131 385 M2GF 2.64 0.89 180 445 M3GF 3.51 0.88 197 257 M5GS 4.99 0.82 160 311 M7GS 5.35 4 0.86 0.85 269 547 PAGE 106 107Table 53 Results of regression analysis on the prediction of compressive strength deve lopment using ACI 209 equation Mix Results M1F M2F M3F M4F M5S M6S M7S 1.098 2.673 2.252 1.573 2.039 1.574 1.792 0.9017 0.8886 0.9043 0.8261 0.9231 0.9363 0.9213 (SE) 0.3482 0.4901 0.3071 0.4732 0.05387 0.08311 0.1261 (SE) 0.03574 0.0344 0.02365 0.04108 0.004384 0.007592 0.01085 (95%CI) 0.2026 to 1.993 1.413 to 3.933 1.463 to 3.042 0.3568 to 2.790 1.901 to 2.178 1.361 to 1.788 1.468 to 2.116 (95%CI) 0.8098 to 0.9935 0.8002 to 0.9770 0.8435 to 0.9651 0.7205 to 0.9317 0.9118 to 0.9344 0.9168 to 0.9558 0.8934 to 0.9492 DOF 5 5 5 5 5 5 5 R 0.9736 0.9801 0.9902 0.9625 0.9997 0.9989 0.9978 ASS 2266000 769806 589302 2168000 22420 73904 75810 Sy.x 673.3 392.4 343.3 658.4 66.96 121.6 123.1 Points Analyzed 7 7 7 7 7 7 7 Table 53 Continued Mix Results M8S M9LF M10LS Mix2GF Mix3GF Mix5GS Mix7GS 2.152 4.203 6.744 2.635 3.512 4.993 5.345 0.9054 0.8239 0.74 0.8916 0.8777 0.815 0.8554 (SE) 0.1427 0.4144 0.5222 0.2175 0.2677 0.2823 0.4698 (SE) 0.01122 0.02191 0.01987 0.0154 0.01618 0.01346 0.02215 (95%CI) 1.786 to 2.519 3.138 to 5.268 5.402 to 8.087 2.076 to 3.194 2.824 to 4.200 4.267 to 5.718 4.137 to 6.552 (95%CI) 0.8765 to 0.9343 0.7675 to 0.8802 0.6889 to 0.7911 0.8520 to 0.9312 0.8361 to 0.9193 0.7804 to 0.8496 0.7984 to 0.9123 DOF 5 5 5 5 5 5 5 R 0.9978 0.9927 0.9949 0.996 0.996 0.9975 0.9941 ASS 112202 263786 85405 151718 193402 128354 251535 Sy.x 149.8 229.7 130.7 174.2 196.7 160.2 224.3 Points Analyzed 7 7 7 7 7 7 7 PAGE 107 108Table 54 Values of the constants, and / and the time ratios from Equation 51 and 52 Concrete ages (days) Time Ratio Type of Curing Cement Type Aggregate type and / 3 7 14 28 56 91 Ultimate in time ACI 209R4 =4.00 =0.85 0.46 0.70 0.88 1.00 1.08 1.12 1.18 Miami Oolite Limestone =1.89 =0.90 0.65 0.85 0.97 1.00 1.07 1.09 1.11 Granite =4.12 =0.86 0.45 0.69 0.87 1.00 1.07 1.10 1.16 28 ')(c cf tf Moist cured I Stalite =5.50 =0.78 0.38 0.64 0.85 1.00 1.14 1.19 1.28 ACI 209R4 / =4.71 0.39 0.60 0.75 0.86 0.92 0.95 1.00 Miami Oolite / =2.10 0.59 0.77 0.87 0.93 0.96 0.98 1.00 Granite / =4.79 0.39 0.59 0.75 0.85 0.95 0.95 1.00 ')(cu cf tf Moist cured I Stalite / =7.05 0.29 0.50 0.67 0.80 0.89 0.93 1.00 PAGE 108 109 Table 55 Splitting tensile strengths of the concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag 3 7 14 28 56 91 Mix1F 0.24 20% 592 628 715 795 834 849 Mix2F 0.33 20% 408 484 528 542 621 659 Mix3F 0.41 20% 513 539 562 624 674 731 Mix4F 0.37 20% 457 520 566 670 759 770 Mix5S 0.33 50% 442 574 634 689 711 738 Mix6S 0.36 50% 570 602 648 672 690 718 Mix7S 0.41 70% 426 473 518 548 590 596 Mix8S 0.44 50% 372 499 550 633 693 703 Mix9LF 0.31 20% 350 404 448 490 551 577 Mix10LS 0.39 60% 212 288 364 405 418 430 Mix2GF 0.33 20% 352 421 488 529 548 595 Mix3GF 0.41 20% 382 409 503 561 599 651 Mix5GS 0.33 50% 282 420 462 525 591 649 Mix7GS 0.41 70% 245 362 430 504 554 577 0 200 400 600 800 1000 1200 0.10.20.30.40.50.6 Water to cementitious Materials RatioSplitting Tensile Strength at 28 days (psi) Figure 510 Effects of water to cement ratio on splitting te nsile strength at 28 days PAGE 109 110 0 200 400 600 800 1000 1200 0.10.20.30.40.50.6 Water to Cementitious Materials RatioSplitting Tensile Strength at 91 days (psi) Figure 511 Effects of water to cement ratio on splitting te nsile strength at 91 days PAGE 110 111 0 100 200 300 400 500 600 700Splitting Tensile Strength (psi) Curing Age (days) Limestone 0408484528542621659 Granite 0352421488529548595 03714285691 Figure 512 Effects of aggregat e type on splitting tensile stre ngth of Mix2F and Mix2GF 0 100 200 300 400 500 600 700 800Splitting Tensile Strength (psi) Curing Age (days) Limestone 0513539562624674731 Granite 0382409503561599651 03714285691 Figure 513 Effects of aggregat e type on splitting tensile stre ngth of Mix3F and Mix3GF PAGE 111 112 0 100 200 300 400 500 600 700 800Splitting Tensile Strength (psi) Curing Age (days) Limestone 0442574634689711738 Granite 0282420462525591649 03714285691 Figure 514 Effects of aggregat e type on splitting tensile stre ngth of Mix5S and Mix5GS 0 100 200 300 400 500 600Splitting Tensile Strength (psi) Curing Age (days) Limestone 0426473518548590596 Granite 0245362430504554577 03714285691 Figure 515 Effects of aggregat e type on splitting tensile stre ngth of Mix7S and Mix7GS PAGE 112 113 aggregate have significant lower splitting tensile strength. For example, Mix3F has an average splitting tensile strength of 731 psi at 91 days, while the splitting tensile strength of the corresponding Mix3GF is 624 psi. At 91 days, the sp litting tensile strength of Mix5S is 738 psi, which is 16.8% higher than that of the corresponding Mix5GS. 5.3.3 Effects of Fly Ash and Slag on Spli tting Tensile Strength of Concrete Fly ash and slag have significant effect on sp litting tensile strength. In order to see the effects of fly ash and slag on splitting tensile strength, the strength development characteristics of splitting tensile strength was normalized as th e ratio of splitting tensile strength at various curing ages to the splitting tensile strength at 91 days and the normalized values are listed in Table A4 in Appendix A. As can be seen from Ta ble A4, the splitting tensile strengths of fly ash concrete mixtures increase sl owly in 28 days after demolding, and the 28day splitting tensile strength is around 85% of splitting tensile strength at 91 days, wh ile the splitting tensile strength of slag concrete increased very rapidly in 28 da ys after demolding, up to 94% of splitting tensile strength at 91 days. For example, the splitting tensile strength of Mix2F at 91 days is 659 psi, increasing 21.6 percent in comparison with that at 28 days. Mix3F has a splitting tensile strength of 731psi at 91 days, increasing 17.1 percent in co mparison with that at 28 days. Bu t, for the concrete mixtures with slag and limestone coarse aggregate, there is no appreciable increase in splitting tensile strength after 28 days curing. For example, Mix5S, Mix6S, Mix7S, and Mix8S increase in splitting tensile strength by less than 10% at 91 days as compared with that at 28 days. For the concrete mixtures with Georgia granite aggregate, substantial increase in splitting tensile strength after 28 days also happened to the mixtures with fly ash, while no signi ficant increase was found in concrete mixtures with slag. For two lightweight aggregate conc rete mixtures, similar situation can be observed as well. PAGE 113 114 The development characteristics of two typical fly ash concretes and two slag concretes with time are shown in Figure 516. 0.70 0.75 0.80 0.85 0.90 0.95 1.00 02 04 06 08 01 0 0 Time (days)Ratio to Splitting tensile Strength at 91 days Mix5SSlagW/C=0.33 Mix6SSlagW/C=0.36 Mix2FFly ashW/C=0.33 Mix4FFly ashW/C=0.37 Figure 516 Effects of fly ash and slag on splitting tensile strength of concrete 5.4 Relationship between Compressive St rength and Splitting Tensile Strength The compressive strengths of the concretes (as tabulated in Table A1) were plotted against the corresponding splitting tensile strengths (as ta bulated in Table A2) for all curing conditions in Figure 517. Regression analyses to establ ish empirical relationship between compressive strength and splitting tensile strengths were performed using the following equations: 'c fA ct f (53) Bc f ct f (54) where ctf= splitting tensile strength (psi) 'cf= compressive strength (psi) PAGE 114 115BA,= coefficients The ACI Code 318 uses Equation 53 for estimation of splitting tensile strength of lightweight concrete, where the coefficient A is equal to 6.7 [ACI, 1983]. The investigation by Carino and Lew [Carino et al, 1982] determined that the coeffici ent A was approximately 6.49. They suggested that Equation 54 was better than Equation 53 in the estimation of splitting tensile strength from compressive strength. The coefficient B was determined to be 0.73 in their investigation. The results of the regression analyses are su mmarized in Table 54. The coefficient A (6.91) is slightly higher than both the values suggested by ACI (6.7) and the value by Carino and Lew (6.49). The coefficient B (0.7185) is slig htly lower than that s uggested by Carino and Lew (0.73). These two regression equations are also plotted on Figure 517. As can be seen from Figure 517, Carino and Lew model gives a better fit to the experimental data than the ACI model, while ACI Building Code 31892 tends to overestimate splitting tens ile strength at low compressive strength and underestimate splitting tensile strength at high compressive strength because the power exponent of the equation is too low. Table 56 Regression analysis for relating compre ssive strength to spli tting tensile strength Equation Curing condition Coefficient A or B Standard Error Square root of absolute sum of squares by modified equation Square root of absolute sum of squares by original equation 7.6' A fAf ACIc st Moist curing 6.91 0.76 60 62.3 73.0' B ff Lewand CarinoB cst Moist curing 0.72 0.015 45 75.7 PAGE 115 116 0 100 200 300 400 500 600 700 800 900 1000 02000400060008000100001200014000 Compressive Strength (psi)Splitting Tensile Strength (psi) Measurement Carino and Lew model ACI code Figure 517 Relationship between compressive strength and splitting tensile strength PAGE 116 1175.5 Analysis of Elastic Modulus Test Results The average elastic modulus values at various curing ages of the four teen concrete mixes evaluated are displayed in Table 57. The indivi dual elastic modulus values are shown in Table A3 in Appendix A. Table 57 Elastic module of the concrete mixtures evaluated ( 106 psi) Age of Testing (days) Mix Number W/C Fly ash Slag 3 7 14 28 56 91 Mix1F 0.24 20% 4.74 4.93 5.23 5.40 5.54 5.58 Mix2F 0.33 20% 3.43 3.77 4.08 4.31 4.43 4.67 Mix3F 0.41 20% 4.40 4.85 5.05 5.14 5.28 5.70 Mix4F 0.37 20% 4.49 4.61 4.88 5.01 5.15 5.29 Mix5S 0.33 50% 4.11 4.66 4.88 5.09 5.23 5.23 Mix6S 0.36 50% 4.27 4.92 5.18 5.45 5.62 5.66 Mix7S 0.41 70% 3.90 4.30 4.52 4.60 4.73 4.76 Mix8S 0.44 50% 3.96 4.39 4.84 5.00 5.13 5.16 Mix9LF 0.31 20% 2.76 2.92 3.13 3.27 3.40 3.50 Mix10LS 0.39 60% 1.75 1.88 2.36 2.69 3.01 3.04 Mix2GF 0.33 20% 3.80 4.22 4.61 4.96 5.06 5.19 Mix3GF 0.41 20% 4.15 4.62 5.52 5.61 5.93 5.96 Mix5GS 0.33 50% 3.15 3.82 4.65 5.17 5.37 5.56 Mix7GS 0.41 70% 2.69 3.38 4.10 5.25 5.60 5.73 As can be seen from Table 57, for the norma l weight aggregate conc retes investigated in this study, the elastic modulus of concrete varies from 4.50 106 to 6.00 106 psi. For the lightweight aggregate conc rete, the modulus of elas ticity varies from 3.00 106psi to 3.70 106 psi. As shown in Figures 518 through 521, two di fferent normal weight coarse aggregates give considerable influence on the elastic modul us of concrete. With other mixture components constant in volume, the concrete mixtures with Georgia granite aggreg ate have higher elastic modulus than those with Miami Oolite limestone aggregate. For example, Mix7GS has an elastic modulus of 5.73 106 psi at 91 days, 20.4% higher than 4.76 106 psi, which is the value of elastic modulus of Mix7S at 91 days. Mix7S has a compressive strength at 91 days slightly higher than that of Mix7GS. Also, we can s ee from the comparison between Mix2F and Mix PAGE 117 118 2GF, Mix3F and Mix3GF, and Mix5S and Mix5GS that Mix2F, Mix3F and Mix5S have a lower elastic modulus than th e corresponding Mix2GF, Mix3GF and Mix5GS, respectively. The compressive strengths of Mix2F, Mix3F and Mix5S are higher than those of the corresponding Mix2GF, Mix3GF and Mix5GS, respectively, at various curing ages. It is interesting to note that high strength but low elastic m odulus concrete can be obtained through using lightweight aggregat e. For example, Mix9LF, light weight aggregate concrete, has similar compressive strength and splitting tens ile strength to Mix7S, with Miami Oolite limestone aggregate, while the elastic modulus of Mix9LF at 91 days is only about 3.50 106 psi, which is about 36% lower than that of Mix7S Thus, to achieve high strength but low elastic modulus concrete mixture, which is desirable for concrete pavement, a lightweight aggregate may be used. 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06Modulus of Elasticity (psi) Curing Age (days) Limestone 03.43E+063.77E+064.08E+064.31E+064.43E+064.67E+06 Granite 03.80E+064.22E+064.61E+064.96E+065.06E+065.19E+06 0371 42 85 69 1 Figure 518 Effects of coarse ag gregate type on modulus of elas ticity of Mix2F and Mix2GF PAGE 118 119 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06Modulus of Elasticity (psi) Curing Age (days) Limestone 04.40E+064.85E+065.05E+065.14E+065.28E+065.70E+06 Granite 04.15E+064.62E+065.52E+065.61E+065.93E+065.96E+06 0371 42 85 69 1 Figure 519 Effects of coarse ag gregate type on modulus of elas ticity of Mix3F and Mix3GF 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06Modulus of Elasticity (psi) Curing Age (days) Limestone 04.11E+064.66E+064.88E+065.09E+065.23E+065.23E+06 Granite 03.15E+063.82E+064.65E+065.17E+065.37E+065.56E+06 0371 42 85 69 1 Figure 520 Effects of coarse ag gregate type on modulus of elas ticity of Mix5S and Mix5GS PAGE 119 120 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06Modulus of Elasticity (psi) Curing Age (days) Limestone 03.90E+064.30E+064.52E+064.60E+064.73E+064.76E+06 Granite 02.69E+063.38E+064.10E+065.25E+065.60E+065.73E+06 0371 42 85 69 1 Figure 521 Effects of coarse ag gregate type on modulus of elas ticity of Mix7S and Mix7GS 5.6 Relationship between Compressive Strength and Elastic Modulus The elastic modulus of concrete is affected by the modulus of elasticity of the aggregate and by the volumetric proportion of aggregate in the concrete. Thus, there is no surprise that there is no agreement on the precise form of th e relationship between compressive strength and elastic modulus. In this study, modification was made on the expression recommended by ACI 31889, given as follows: c cfE (55) In the equation is a parameter to be determined thr ough curvefitting regression analysis. Its value recommended by ACI is 57000. PAGE 120 121 The regression analysis was carried out on the expression recommended by ACI 31895, given as follows, to fit the expe rimental data. In this formula, the unit weight of concrete was also used. '5.1 cfwAE (56) Where E is elastic modulus in psi; 'cf is compressive strength in psi; wis unit weight of concrete in pcf; and A is coefficient to be determined through regression analysis. The recommended value by ACI 31895 is 33.0. The compressive strengths of fourteen concre te mixtures were pl otted against elastic modules at corresponding curing ages, as shown in Figure 522. It indicates that coarse aggregate type has significant effects on the elastic modulus of concrete. The results from regression analysis were presented in Table 58. And th e modified ACI 209 equati on was plotted in Figure 522 together with the ex perimental measurements. It can be seen that the determined values of coefficient for the concrete mixtures with three different types of aggregate are fairly fa r away from the ACI suggested value of 57000. Regression analysis was performed using ACI 31895 equation, which was required to go through the origin. The analyzed re sults are presented in Table 59. It can be seen from Table 59 that the coefficient A (33.64) obtained from re gression analysis is ne arly identical to the coefficient (33.0) given by ACI code. However, th e errors from the regr ession equation which is required to go though the origin are higher than th ose from that regression equation that is not required to go through the origin, as seen from Table 59. In addition, the results of regression analysis for differe nt curing conditions using ACI 31895 formulas are presented in Table 510. Th e elastic modulus of concrete at all curing conditions is plotted against '5.1 cfw in Figure 523. As can be seen from Table 510, curing PAGE 121 122 time appears to have a significant effect on the coefficient of the regression equations. The regression coefficients obtained from the sample s moistcured for 28 days are higher than those obtained from other curing times. Thus, the pred iction will be conserva tive if the regression coefficients are obtained from the samples moistcured for 28 days. For the concretes investigated in this st udy, the following modified ACI 31895 equation can be used for prediction of elastic modulus: 484200 '5.1 16.30 c fw E (57) Where E is elastic modulus in psi; 'cf is compressive strength in psi; wis unit weight of concrete in pcf. 5.7 Summary of Findings This chapter presents the testing results from the strength tests in this study. The major findings are given as follows: (1) Splitting tensile strengths of the concrete mixtures using granite aggregate were significantly lower than thos e using Miami Oolite limestone aggregate. This is due probably to the poor bonding condition betw een hardened cement paste and granite aggregate. (2) Compressive strengths of concretes with gran ite aggregate were comparable to or lower than those of concretes with Miami Oolite limestone aggregate. (3) The concrete with granite aggregate had hi gher elastic modulus than that with Miami Oolite limestone aggregate, while the lightweight aggregate concretes had lower elastic modulus than the normal weight concretes. (4) Fly ash concretes develop compressive strength and splitting tensile st rength at a slower rate than the slag concretes. Fly ash conc rete shows significant strength gain after 28 days, while this was not seen fr om the slag concrete mixtures. (5) The ACI 209 Equation for prediction on compressive strength () ('tfc) at various curing age from compressive strength at 28 days () (' 28tfc), which is given as follows, was modified to give better strength prediction for the various mixtures. PAGE 122 123 Table 58 Results of regression analysis for prediction of elastic modulus using the equation recommended by ACI 31889 Aggregate type Results granite lightweight Limestone (Bestfit values) 62721 43777 55949 Standard Error of 870.6 692.3 309.1 95% confidence intervals for 60920 to 64523 42253 to 45301 55327 to 56572 Degrees of Freedom 23 11 47 R 0.8712 0.922 0.8758 Absolute Sum of Squares 2.478E+12 2.693E+11 1.619E+12 Sy.x 328220 156461 185594 Number of points Analyzed 24 12 48 Table 59 Results of regression analysis for prediction of elastic modulus using ACI 31895 equation Bestfit values With equation going through the origin Without forcing the equation to go through the origin Slope 33.64 0.2671 30.18 1.169 Yintercept when X=0.0 0.0000 484200 159900 Xintercept when Y=0.0 0.0000 16040 1/slope 0.02973 0.03313 95% Confidence Intervals Slope 33.10 to 34.17 27.85 to 32.51 Sy.x 335100 319700 PAGE 123 124 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06 7.00E+06 8.00E+06 02000400060008000100001200014000 Compressive Strength (psi)Modulus of Elasticity (psi) Georgia granite Stalite lightweight Miami Oolite limestone Figure 522 Relationship between compressive strength and elasti c modulus based on ACI Code 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06 7.00E+06 04000080000120000160000200000 w1.5fc 0.5Modulus of Elasticity Figure 523 Plot of elastic modulus against '5.1 cfw for all curing conditions PAGE 124 125Table 510 Results of regression analysis for prediction of elastic modulus using the ACI 31895 equation for different curing conditions Age Results overall 3day 7day 14day 28day 56day 91day Slope 30.18 1.169 26.24 3.857 27.76 3.763 29.17 3.123 30.00 2.217 28.78 2.965 29.38 2.771 Yintercept when X=0.0 484200 159900 800000 437100 644500 478400 614000 424400 581900 315800 779700 438000 704200 418700 Xintercept when Y=0.0 16040 30490 23220 21050 19400 27090 23970 1/slope 0.03313 0.03811 0.03602 0.03428 0.03334 0.03475 0.03404 95% Confidence Intervals Slope 27.85 to 32.51 17.84 to 34.64 19.56 to 35.96 22.37 to 35.98 25.16 to 34.83 22.32 to 35.24 23.34 to 35.41 Yintercept when X=0.0 165500 to 802900 152400 to 1752000 397900 to 1687000 310800 to 1539000 106200 to 1270000 174800 to 1734000 208100 to 1616000 Xintercept when Y=0.0 28780 to 5098 97520 to 4433 85720 to 11130 68530 to 8673 50350 to 3056 77450 to 4974 69070 to 5892 Goodness of Fit r 0.8906 0.7941 0.8194 0.8791 0.9385 0.887 0.9035 Sy.x 319700 394800 386700 310500 216700 292900 275100 Is slope significantly nonzero? F 667.2 46.29 54.43 87.25 183.1 94.22 112.4 DFn, DFd 1.000, 82.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 1.000, 12.00 P value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 Deviation from zero? Significant Significant Significant Significant Significant Significant Significant Data Number of X values 84 14 14 14 14 14 14 Maximum number of Y replicates 1 1 1 1 1 1 1 Total number of values 84 14 14 14 14 14 14 PAGE 125 126 28 85.00.4 )( c f t t t c f The modified equation has the following form for the concrete with different coarse aggregates: 28 )( c f t t t c f The value of was found to vary from 1.1 to 2.6 for the concretes with Miami Oolite limestone aggregate, from 2.6 to 5.3 for th e concretes with Georgia granite aggregate, and from 4.2 to 6.7 for lightweight aggregate concretes; the value of was found to vary from 0.82 to 0.93 for the concretes with Miam i Oolite limestone aggregate, from 0.82 to 0.89 for the concrete with Georgia granite aggregate, and from 0.74 to 0.82 for lightweight aggregate co ncrete in this study. (6) The relationship between compressive strength ('cf ) and splitting tensile strength (ctf ) is established for the concrete mixtures investigated in this study. The Carino and Lew model, given as follows, 73.0 c f ct f was modified to the following equation: 7185.0 c f ct f Where cf and ctf are in units of psi. (7) The relationship between compressive strength and modulus of elasticity was refined in this study using Least Square of Curvefitting Technique. The ACI 31889 Equation, which is '57000cf c E was modified to the following equation: cf c E Where is equal to 55,949 for Miami Oolite lim estone aggregate; 62,721 for Georgia granite aggregate; and 43,777 for Stalite lightweight aggregate. cf and cE are in units of psi. (8) For all three aggregate type s investigated in this study, a modified ACI 31895 prediction equation was developed: 484200 16.30'5.1cfw E Where w is the density of c oncrete in pound per cubit foot. 'cf and cE are in units of psi. PAGE 126 127 CHAPTER 6 ANALYSIS OF SHRINKAGE TEST RESULTS 6.1 Introduction This chapter presents the results from shrinka ge tests on the concrete mixes evaluated in this study. The effects of various factors on shrinkage behavior of concrete were discussed. Regression analysis was performed to establish the relationship between compressive strength at the age when shrinkage test was started and sh rinkage strain at 91 days, and the relationship between elastic modulus and shrinkage of conc rete. Empirical equations relating compressive strength and elastic modulus to shrinkage of c oncrete are given. Also, the evaluation was made on ACI 209 model and C.E.BF.I.P model for their e ffectiveness in shrinkage prediction. At last, ultimate shrinkage strain of the concretes invest igated in this study was approximated using an asymptotic equation with three unknown pa rameters to fit experimental data. 6.2 Results and Analysis of Shrinkage Tests Table 61 presents the measured shrinkage strain s at the ages up to 91 days for the fourteen concrete mixes evaluated in this study. Fo r Mix1F through Mix10LS, one group of concrete specimens was moistcured for 7 days and then airdried in the laboratory for the rest of the time; another group of specimens were moistcured for 14 days and then airdried for the rest of the time, while, for Mix2FG through Mix7SG, only one curing condition, i.e. 14day moist curing and then airdried for the rest of time, was evaluated. 6.2.1 Effects of Curing Conditions on Shrinkage Behavior of Concrete As can be seen from Table 61 as well as Figure 61, curing co ndition has substantial effects on shrinkage behavior of concrete mixtures For the concrete mixtures with fly ash, the specimens moistcured for 14 days have apprecia ble lower shrinkage strains than those moist cured for 7 days. For example, the shrinkage strain of Mix1F moistcured for 14 days is PAGE 127 128 Table 61 Shrinkage strains of the concrete mixtures evaluated at various curing ages Age of testing (days) No. of Mix Curing condition 3 7 14 28 56 91 Predicted ultimate shrinkage strain 7day moist cure 0.20E04 0.44E04 0.75E04 1.18E04 1.63E04 2.02E04 2.66E04 Mix1F 14day moist cure 0.14E04 0.35E04 0.61E04 1.00E04 1.36E04 1.67E04 2.27E04 7day moist cure 0.51E04 0.97E04 1.54E04 2.10E04 2.61E04 2.86E04 3.39E04 Mix2F 14day moist cure 0.31E04 0.69E04 1.12E04 1.73E04 2.33E04 2.58E04 3.20E04 7day moist cure 0.40E04 0.73E04 1.24E04 1.77E04 2.21E04 2.48E04 3.03E04 Mix3F 14day moist cure 0.24E04 0.50E04 0.87E04 1.37E04 1.84E04 2.16E04 2.85E04 7day moist cure 0.37E04 0.71E04 1.18E04 1.76E04 2.33E04 2.67E04 3.64E04 Mix4F 14day moist cure 0.31E04 0.53E04 0.92E04 1.42E04 1.97E04 2.31E04 3.44E04 7day moist cure 0.44E04 0.88E04 1.30E04 1.70E04 2.01E04 2.16E04 2.46E04 Mix5S 14day moist cure 0.43E04 0.74E04 1.10E04 1.49E04 1.78E04 1.93E04 2.29E04 7day moist cure 0.42E04 0.84E04 1.23E04 1.56E04 1.83E04 1.95E04 2.16E04 Mix6S 14day moist cure 0.33E04 0.71E04 1.12E04 1.41E04 1.64E04 1.76E04 1.93E04 7day moist cure 0.39E04 0.81E04 1.26E04 1.70E04 2.02E04 2.23E04 2.55E04 Mix7S 14day moist cure 0.38E04 0.73E04 1.11E04 1.48E04 1.84E04 2.04E04 2.40E04 7day moist cure 0.73E04 1.23E04 1.61E04 1.94E04 2.28E04 2.50E04 2.43E04 Mix8S 14day moist cure 0.50E04 0.98E04 1.36E04 1.69E04 2.02E04 2.30E04 2.20E04 7day moist cure 0.49E04 0.96E04 1.34E04 2.25E04 2.87E04 3.22E04 3.95E04 Mix9LF 14day moist cure 0.46E04 0.83E04 1.34E04 1.84E04 2.41E04 2.76E04 3.49E04 7day moist cure 0.67E04 1.30E04 1.98E04 2.60E04 3.20E04 3.58E04 4.22E04 Mix10LS 14day moist cure 0.38E04 0.90E04 1.52E04 2.09E04 2.80E04 3.17E04 3.96E04 7day moist cure Mix2GF 14day moist cure 0.32E04 0.61E04 1.09E04 1.61E04 2.04E04 2.31E04 2.83E04 7day moist cure Mix3GF 14day moist cure 0.29E04 0.54E04 0.84E04 1.23E04 1.57E04 1.82E04 2.62E04 7day moist cure Mix5GF 14day moist cure 0.39E04 0.64E04 1.04E04 1.40E04 1.68E04 1.84E04 2.18E04 7day moist cure Mix7GF 14day moist cure 0.43E04 0.74E04 1.00E04 1.31E04 1.63E04 1.81E04 2.19E04 PAGE 128 129 0.000167 at 91 days, which is 23.2% less than that of the same mix moistcured for 7 days. The shrinkage strain at 91 days is 0.000258 for Mix2F moistcured for 14 days, which is 10.9% less than that of the same mix moistcured for 7 da ys. Also, the shrinkage strain of Mix3F moistcured for 14 days is 0.000216, which is 14.8% less than that of the same mix moistcured for 7 days. Substantial decrease in shrinka ge strain also can be seen from Mix4F. Shrinkage strain of 7day moistcured specimens is 13.5% higher th an that of 14day moistcured specimens for Mix4F. For the concrete mixtures with slag, the eff ects of curing condition on shrinkage strain are significant as well. For instance, the shrinkage stra in of Mix5S moistcure d for 14 days is 11.9% less than that of the same mix moistcured for 7 days. Also, for Mix6S, Mix7S and Mix8S, the shrinkage strains of the specimens moistcured for 14 days are at least 10% less than those of the same mixtures moistcured for 7 days. In addition, curing condition has similar e ffects on shrinkage st rain of lightweight aggregate concretes as that on normal weight aggregate concrete. The shrinkage strains of Mix9FL and Mix10SL moistcured for 14 days are 16. 5% and 11.6%, respectively, less than those of the same mixtures moistcured for 7 days. 6.2.2 Effects of Mineral Additi ves on Shrinkage Behavior As can be seen from Table 61 as well as Fi gure 61, the results from 14 mixtures indicate that the concrete mixtures with fly ash have hi gher shrinkage strains than those with slag. For example, Mix3F has the same water to ceme ntitious materials ratio as Mix7S, while the shrinkage strain of Mix3F mois tcured for 7 days is 0.000248, which is more than 10% higher than that of Mix7S moistcured for 7 days ev en though the water content of Mix3F (254 lbs per cubit yard) is less than that of Mix7S (267 lbs per cubit yard). For another example, Mix2F and PAGE 129 130 0.00E+00 5.00E05 1.00E04 1.50E04 2.00E04 2.50E04 3.00E04 3.50E04 4.00E04 1F2F3F4F5S6S7S8S9LF10LS MixtureShrinkage Strain at 91 days 7day moist curing 14day moist curing Figure 61 Effects of curing condition on shrinkage strain of concrete mixtures at 91 days Mix5S have identical water to cementitious ratio, while the shrinkage strain of Mix2F moistcured for 7 days is 0.000286 at 91 days, or 24.5% higher than that of Mix5S moistcured for 7 days. As also can be seen from the concrete mixt ures with Georgia granite aggregate, Mix2FG and Mix3FG have higher shrinkage strains as compared with the corresponding Mix5SG and Mix7SG, respectively, even though Mix2GF has identical water to cementitious materials ratio as Mix5SG, and Mix3GF has the same water to cementitious material ratio as Mix7GS. 6.2.3 Effects of Water Content on Shrinkage Behavior Water content per unit volumetric concrete is an important fact or influencing the magnitude of shrinkage strain since drying shrink age is caused by the moisture movement from the concrete. Generally, the higher the water conten t, the more the free water inside concrete is available because water can not be consumed rapi dly and completely. Thus, shrinkage strain of concrete is increased with an increase of free wate r content. As can be seen from Figure 62, the PAGE 130 131 shrinkage strains at 91 days increase with the increase of water content for the normalweight concrete mixtures eval uated in this study. 0.00E+00 5.00E05 1.00E04 1.50E04 2.00E04 2.50E04 3.00E04 3.50E04 220230240250260270280290 Water Content (lbs/yard3)Shrinkage Strain at 91 days Miami Oolite limestone Georgia granite Figure 62 Effects of water content on shrinkage strain at 91 days Figure 63 shows a plot of water to cementitious materials ratio versus shrinkage strain of concrete at 91 days. No clear tr end can be observed to relate wate r to cementitious materials ratio to the magnitude of shrinkage strain of concrete. The significant role played by water content also extends to the lightweight aggregate concretes, Mix9FL and Mix10SL. As can be s een from Table 61, the water content of Mix10SL is 275 lbs per cubit yard, higher than 235 lbs fo r Mix9FL. The shrinkage strain at 91 days for Mix10SL is much higher than that of Mix9FL. 6.2.4 Effects of Aggregate Types on Shrinkage Behavior In this study, two types of normal weight coarse aggregate, Miami Oolite limestone aggregate and Georgia granite aggregate were investigated for their effects on shrinkage PAGE 131 132 behavior of four concrete mixtures. The experi mental data from the specimens moistcured for 14 days indicate that the concrete mixtures using Georgia granit e aggregate developed significantly less shrinkage strain at 91 days than those with Mi ami Oolite limestone aggregate. For example, as can be seen from Figure 64, Mix2FG, which has the same mix proportion as Mix2F other than the coarse aggregate replaced by Georgia granite aggregate, has a shrinkage strain of 0.000231, which is 23.8% lower than th at of Mix2F using Miami Oolite limestone as coarse aggregate. 0.24 0.33 0.41 0.37 0.33 0.36 0.41 0.44 0.33 0.41 0.33 0.41 0.24 0.33 0.33 0.41 0.36 0.41 0.44 0.37 1.00E04 1.20E04 1.40E04 1.60E04 1.80E04 2.00E04 2.20E04 2.40E04 2.60E04 2.80E04 0.200.250.300.350.400.450.50 Water to Cementitious Materials RatioShrinkage Strain at 91 days Miami Oolite limestone Georgia Granite Figure 63 Plot of water to cementitious material s ratio versus shrinkage strain at 91 days The same situation can be seen from the comparison between Mix3F and Mix3FG, Mix5S and Mix5SG, and Mix7S and Mix7SG. The shrinkage strain of Mix3FG is 0.000182 at 91 days, which is 18.7% less than that of Mi x3F, which has shrinkage strain of 0.000216. Shrinkage strains of Mix5S and Mix7S at 91 da ys are also 10% higher than those of Mix5SG and Mix7SG. PAGE 132 133 For lightweight aggregate conc retes, such as Mix9LF a nd Mix10LS, their shrinkage strains are significantly higher th an the concrete mixtures using normal weight aggregate. 0.00E+00 5.00E05 1.00E04 1.50E04 2.00E04 2.50E04 3.00E04 Mix2 Mix3 Mix5 Mix7 MixtureShrinkage Strain at 91 days Miami Oolite limestone Georgia granite Figure 64 Effects of coarse aggregate t ype on shrinkage behavior of concrete 6.2.5 Relationship between Compressive Strength and Shrinkage Strain Over the past decades, the study on shrinkage be havior of concrete has been carried out extensively. The effects of various factors, su ch as water to cement ratio, aggregate type, aggregate content, mineral additives, and cement content so on, on shrinkage behavior have been studied. However, since concrete is a complicat ed composite material, the effects of various components and their proportions on shrinkage beha vior are intertwisted together. Also, because of massive introduction of chemi cal admixtures to concrete, su ch as air entraining agent and water reducer, shrinkage behavior of concrete becomes more complex. Thus, shrinkage behavior of concrete can not be reasona bly estimated based on the simple addition of every individual factors function. Therefore, it is desirable to relate the shrinkage behavior of conc rete to one or more fundamental properties of concrete, for exam ple, compressive strength, tensile strength or elastic modulus at a particular age. In doing so, it assumes that the fundamental properties of PAGE 133 134 concrete are closely related to one another, i.e. one fundamental property can be predicted from another. In doing so, a complicated fundame ntal property can be estimated by a simple fundamental property without complicated and timeconsuming experimental test involved. In trying to find out the relationship between compressive strength and shrinkage behavior of concrete, compressive strength at the age when shrinkage test was star ted was plotted against shrinkage strain at 91 days in Figure 65. As shown in Figure 65, it appe ars that there exists a very interesting relationship between the shrinkage strains at 91 days and compressive strength regardless of which type of coarse aggregate was used for concrete. Then, regression analysis was carried out using an exponential function with two unknown parameters, given as E quation 61. The regression analysis results are presented in Table 62. cf she (61) In this formula, fc is compressive strength of concrete at the age of initial shrinkage test. As can be seen from Table 62, best fit value of is 5.113104; best fit value of is 1.127104; and correlation coefficient, R2, is 0.8226. The above equation with parameters obtained from regression analysis was plotted in Figure 65 as solid line. It indicated that shrinkage strain at 91 days can be well estimate d by the compressive strength of concrete at the age of when shrinkage test was started. Furtherm ore, this relationship is not affected by such factors as aggregate t ype and curing age. Therefore, even though exponential equation from regression analysis may not be a fundamental relationship between compressive st rength and shrinkage of concrete, it may be very convenient way practically to have an accu rate enough estimation on shrinkage strain just based on the compressive strength without timeconsuming shrinkage test involved. PAGE 134 135 Table 62 Results of regression analysis on rela tionship of compressive strength to shrinkage strain Regression Results Bestfit Value Standard Error (SE) 95% Confidence Interval R2 Absolute Sum of Square Root due to Error (SSE) 5.113E04 2.042E05 4.706E04~ 5.521E04 1.127E04 5.654E06 1.014E04~ 1.239E04 0.8226 2.131E05 0.00E+00 5.00E05 1.00E04 1.50E04 2.00E04 2.50E04 3.00E04 3.50E04 4.00E04 4.50E04 5.00E04 02000400060008000100001200014000 Compressive Strength at the Age of Initial Shrinkage Test (psi)Shrinkage Strain at 91 Days Miami Oolite limestone Lightweight aggregate Georgia granite Figure 65 Relationship between compressive strength and shrinkage strain at 91 days 6.2.6 Relationship between Elastic Modulus and Shrinkage Strain Since close relationship has been found between compressive strength and shrinkage of concrete, and since there is direct relations hip between compressive strength and elastic modulus, elastic modulus and shrinkage shoul d be related to each other as well. As shown in Figure 66, shrinka ge strains at 91 days for all the concretes investigated in this study, including normal weight aggregate concrete and lightweight aggregate concrete, were plotted against elastic modulus at the age of shrinkage test starts. There is no surprise that similar PAGE 135 136 relationship to compressive strength and shrinkage can be f ound between elastic modulus and shrinkage. Regression analysis was performed using an exponential function with two unknown parameters, as given in Equation 62, and the analyzed results are presented in Table 63. cE she (62) In this equation, Ec is elastic modulus of concrete at the age when shrinkage test was started. Table 63 Results of regression analysis on relati onship of elastic modulus to shrinkage strain Regression Results Bestfit Value Standard Error (SE) 95% Confidence Interval R2 (SSE) 6.595E04 3.429E05 5.911E04~ 7.279E04 2.270E07 1.129E08 2.045E04~ 2.495E04 0.8152 2.175E05 0.00E+00 1.00E04 2.00E04 3.00E04 4.00E04 5.00E04 0.00E+002.00E+064.00E+066.00E+068.00E+06 Modulus of Elasticity (psi)Shrinkage Strain at 91 Days Miami Oolite limestone Lightweight aggregate Georgia granite Figure 66 Relationship between shrinkage stra in at 91 days and modulus of elasticity PAGE 136 1376.3 Evaluation on Shrinkage Prediction Models In this study, the ACI 209 model and C.E. BF.I.P model were evaluated on their effectiveness and accuracy in prediction of shri nkage behavior of typical concretes used in Florida. 6.3.1 ACI209 model The concrete shrinkage prediction model recommended by ACI209 (1992) is given as follows: u sh t t t sh 35 (63) Where t sh time dependent shrinkage strain; u sh ultimate shrinkage strain; and t time variable in days If there is no available shrinkage data from the specific concrete mixture, the ultimate shrinkage strain,u sh can be assumed to be the following: sh u sh 610780 (64) Where sh a product of all the applic able correction factors for the testing conditions other than the standard condition; sh = 1 under standard testing condition. sh is obtained by multiplying the ultimate shri nkage strain under the standard condition by the appropriate correction factors, such as correction factors for the effect of initial moist curing, correction factor for the effect of ambient relative humidity, corre ction factor for the effects of specimen size, correction factor for concre te composition and so on. In this study, sh is calculated as follows: patasrhlash (65) The correction factors a pplicable to the concrete mixes ev aluated in this study are shown in Table 64. PAGE 137 138 Table 64 Correction factors for the ACI 209 model on shrinkage prediction la sh No. of Mix 7day moist 14day moist rh s a at p 7day moist 14day moist Mix1F 0.916 0.814 0.77 0.85 0.57 1.00 0.88 0.30 0.27 Mix2F 0.916 0.814 0.77 0.83 0.87 1.00 0.88 0.45 0.40 Mix3F 0.916 0.814 0.77 0.83 0.69 1.00 0.88 0.36 0.32 Mix4F 0.916 0.814 0.77 0.83 0.64 1.00 0.88 0.33 0.29 Mix5S 0.916 0.814 0.77 0.84 0.80 1.00 0.88 0.42 0.37 Mix6S 0.916 0.814 0.77 0.83 0.66 1.00 0.88 0.34 0.30 Mix7S 0.916 0.814 0.77 0.84 0.96 1.00 0.88 0.50 0.44 Mix8S 0.916 0.814 0.77 0.83 0.80 1.00 0.88 0.41 0.37 Mix9LF 0.916 0.814 0.77 0.83 0.73 1.00 0.88 0.38 0.33 Mix10LS 0.916 0.814 0.77 0.83 0.93 1.00 0.88 0.48 0.43 Mix2GF 0.916 0.814 0.77 0.83 1.13 1.00 0.88 0.58 0.52 Mix3GF 0.916 0.814 0.77 0.83 0.60 1.00 0.88 0.31 0.27 Mix5GS 0.916 0.814 0.77 0.84 0.96 1.00 0.88 0.50 0.44 Mix7GS 0.916 0.814 0.77 0.83 0.80 1.00 0.88 0.41 0.37 6.3.2 CEBFIP Model In this model, the effects of cement type, ambient relative humidity, compressive strength of concrete, and size effect of specimen on sh rinkage strain of concrete are taken into consideration. The total shri nkage strain may be estimate d by the following equation: s tt scss tt cs 0 (66) Where scstt = time dependent total shrinkage strain; 0 cs = notational shrinkage coefficient; and s (t ts) = coefficient to describe the development of shrinkage with time. 0 cs can be estimated by the following equation: RH cmo cm sc csf f 6 010 910 160 (67) wheresc a coefficient depending on the type of cem ent is equal to 5 for normal or rapid hardening cements; cmf = the mean compressive strength of concrete at the age of initial shrinkage tests. cmof is a constant, equal to 10MPa. RH can be computed as follows: PAGE 138 139 3 0 155.1 RH RH RH for %99 %40 RH (68) With RH equal to 75% in this study and 0RH equal to 100%, then, 8959.010 9101606 0 cmo cm sc csf f (69) sstt can be estimated by the following equation: 5.0 1 2 0 350 1 t s tt h h t s tt s tt s (610) Where u A hc2 = the notational size of member (in mm), where Ac is the crosssectional area (mm2) and u is the perimeter (mm) of th e member circular cross section (2 r) in contact with the atmosphere. H is equal to 1.5 for 6 12in cylinder. 0h is equal to 100 mm. 1t is equal to 1 day. Therefore, the above equation can be simplified as follows: 5.0 23.203 t t t s (611) The shrinkage strains at 91 days for all the c oncrete mixtures invest igated in this study were compared with the calcula ted results using ACI 209 model a nd C.E.BF.I.P model in Figure 67. The hollow circle indicates the predicti on by C.E.BF.I.P model, and solid black dot represents the prediction by ACI 209 model. As shown in Figure 67, C.E.BF.I.P model gives encouraging prediction in comparison with the experimental data, while ACI209 model provides extreme overestimation. PAGE 139 140 y = x 0.00E+00 1.00E04 2.00E04 3.00E04 4.00E04 5.00E04 0.00E+001.00E042.00E043.00E044.00E045.00E04 Predicted Shrinkage StrainShrinkage Strain from Experiment ACI 209 model C.E.BF.I.P model Figure 67 Comparison between the shrinkage st rain at 91 days and the shrinkage strain calculated by ACI 209 model and C.E.BF.I.P model 6.4 Prediction of Ultimate Shrinkage Strain Shrinkage of concrete lasts for a long time w ith decreasing shrinkage rate. Generally, it is assumed that concrete will shrink with time to a limiting value, called ultimate shrinkage strain, which is a very important parameter in concrete structural design. In th is study, an asymptotic equation, given as follows, was used to fit the experimental data. t t t sh (612) As can be seen from the above equation, shri nkage strain will approach its limiting value as time goes to infinite value. Thus, is the ultimate shrinkage strain. Curvefitting regression analys is was performed using Least Square Method, which is detailed as follows: PAGE 140 1416.4.1 Least Square Method of Curvefitting The method of least squares was used when f itting data. The model sel ected to relate the response data to the predictor data with two coefficients is given as follows: x x y (613) Where and are two constitutive parameters to be determined from curve fitting process; x is time variable, and y is response variable, and it is the creep strain in this study. The goal of the fitting process is to estimat e the "true" but unknown coefficients of the model. To obtain the coefficient estimates, the residual for the ith data point, i r defined as the difference between the observed response value i y and the fitted response valuei y and identified as the error associated with the data is computed by yyr (614) Then, the summed square of residuals is given by n i i y i y n i i rS 1 2 1 2 (615) Where n is the number of data points included in the fit, and S is the sum of squares error estimate. Th e least squares method minimizes the summed square of residuals, and then the optimized coefficients will be achieved. Since the model used to fit the data is the ratio of two polynom ials, it is a nonlinear equation. Therefore Nonlinear Leas t Squares Method was used to do cu rvefitting anal ysis in this study. In matrix form, nonlinear models are given by the formula PAGE 141 142 Xy f (616) Where y is an nby1 vector of responses, f is a function of and X, is a mby1 vector of coefficients, x is the nbym design matrix for the model, and is an nby1 vector of errors. Unlike linear models, the coefficients are es timated using simple matrix techniques; an iterative approach is used to estimate coefficients of nonlinear model. The fitted response value is given by bXy f (617) and involves the calculation of the Jacobian of f( X,b), which is defined as a matrix of partial derivatives taken with respect to the coeffici ents. Then, the coefficients are adjusted and determination was made as to whether the fit improves. The direction and magnitude of the adjustment depend on the fitting algorithm. In this study, Trustregion algorithm was used because it can solve difficult nonlin ear problems more efficiently th an the other algorithms, and it represents an improvement over the popular LevenbergMarquardt algorithm. Because nonlinear models can be particularly sensitive to the starting points, the initial values of the estimates should be carefully de fined to guarantee the convergence of regression analysis. 6.4.2 Evaluation Methods on the Goodness of Fit In this study, after fitting data with the model, the goodness of fit was evaluated by graphical illustration, such as a visual examination of the fitted curve and residual plot, and PAGE 142 143 numerical measures, such as goodness of fit statis tics confidence, standard error, and regression correlation coefficient (R2). In doing so, graphical illustration allows us to view the entire data set at once, and they can easily display a wide range of relationships between the model and the data. The numerical measures are more narrowly focused on a particular aspect of the data and often try to compress that information into a single number. In the following content, the methods used to evaluate the goodness of fit in this study are described briefly. The sum of squares due to error (SSE) This statistic, also called the summed square of residuals, measures the total deviation of the response values from the fit to the response values. It is usually labeled as SSE. n i i y i y i w SSE 1 2 (618) A value closer to 0 indicates a better fit. Rsquare Rsquare, also called the square of the multiple correlation coefficient and the coefficient of multiple determination, is th e square of the correlation between the response values and the predicted response values. It measures how successful the fit is in explaining the variation of the data. Rsquare is defined as the ratio of the sum of squares of the regression (labeled as SSR) and the total sum of squares (labeled as SST), also called the sum of squares about the mean. SSR is defined as n i iiyywSSR1 2 (619) And SST is defined as PAGE 143 144 n i iiyywSSESSRSST1 2 (620) Then, according to the definition, Rsquare is expressed as SST SSE SST SSESST SST SSR R 12 (621) Rsquare can take on any value between 0 and 1, with a value closer to 1 indicating a better fit. Root mean squared error (RMSE) RMSE is also known as the fit standard error and the standard error of the regression MSEsRMSE (622) Where MSE is the mean square error or the residual mean square v SSE MSE (623) A RMSE value closer to 0 indicates a better fit. Confidence and Prediction Bounds Confidence and prediction bounds define the lo wer and upper values of the associated interval, and define the width of the interval, which indicates how uncertain we are about the fitted coefficients, the predicted observation, or the predicted fit. Confidence bounds were obtained through regressi on analysis for the fitted coefficients, and prediction bounds for the fitted function. In this study, the confidence bounds are given numerically, while the prediction bounds are displayed graphically. In this study, the bounds are defi ned with a certainty of 95%. In this study, the regression analysis was car ried out using statisti c analysis software, GraphPad Prism, programmed by Gr aphPad Prism software Inc. PAGE 144 1456.4.3 Predicted Results The results of regression analysis using E quation 612 are presented in Table 65. The ultimate shrinkage strains predicted for 14 concrete mixtures, which are represented the values for are summarized in Table 65. Graphically, predicted ultimate shrinkage strain based on experimental data was compar ed with the predictions made by original ACI209 model and C.E.BF.I.P model in Figure 68. As can be seen from the graphical plots as well as Table65, the predicted ultimate shrinkage strains,, for fourteen concrete mixtures vary from 0.0002 to 0.00041, which is considerable less than the pr edicted values by ACI 209 model and C.E.BF.I.P model. 0.00E+00 1.00E04 2.00E04 3.00E04 4.00E04 5.00E04 6.00E04 0.00E+002.00E044.00E046.00E04 Calculated by C.E.BF.I.P model and ACI modelUltimate Shrinkage Strain by Curvefitting ACI 209 model C.E.BF.I.P model Figure 68 Comparison among the ultimate shrinkag e strains from curvefitting, CEBFIP model and ACI 209 model As shown in Table 65, has a value close to 1 for all concrete mixtures, while value is significantly different between fly as h concrete and slag concrete. has an average value of PAGE 145 146 1.04, and has an average value of 30.0. As can be seen from Table 65, value for the specimens moistcured for 7 days is higher than that for the sp ecimens moistcured for 14 days. This is due probably to the fact that the evapor ation rate of free water concrete becomes slower at a longer curing age when the concrete is denser. At last, based on the 14 concrete mixtures inve stigated in this study, the ultimate shrinkage strain predicted through curvefitting the threeparame ter model to experimental data is less than 3.5104 for normalweight aggregate concrete, and 4.5104 for lightweight aggregate concrete. Table 65 Results of regression analysis for pr ediction of shrinkage st rain using Equation 612 Mix SE SE SE R2 SSE 1F 0.983 1.122 0.024 0.049 2.66E04 2.27E04 2.70E06 4.31E06 31.18 31.10 1.804 3.117 0.9997 0.9992 1.20 106 1.67 106 2F 1.027 1.137 0.021 0.042 3.39E04 3.21E04 1.51E06 3.35E06 16.48 19.13 0.649 1.515 0.9998 0.9994 1.27 106 1.23 106 3F 1.011 0.920 0.022 0.031 3.03E04 2.85E04 1.69E06 3.89E06 20.05 31.74 0.869 2.545 0.9998 0.9994 1.19 106 1.81 106 4F 0.867 0.855 0.013 0.032 3.44E04 3.24E04 2.74E06 8.93E06 27.84 32.44 1.530 3.910 0.9999 0.9990 1.10 106 2.45 106 5S 0.996 0.812 0.045 0.026 2.46E04 2.29E04 1.83E06 1.86E06 12.52 20.88 1.005 1.427 0.9992 0.9994 2.02 106 1.50 106 6S 1.227 1.332 0.041 0.125 2.16E04 1.93E04 0.86E06 1.54E06 8.172 6.511 0.432 0.761 0.9997 0.9985 1.16 106 2.20 106 7S 1.196 0.910 0.028 0.034 2.55E04 2.40E04 0.93E06 2.13E06 11.37 18.89 0.449 1.429 0.9998 0.9993 0.98 106 1.74 106 8S 1.325 1.232 0.087 0.089 2.43E04 2.20E04 1.82E06 2.52E06 7.822 11.61 0.789 1.406 0.9989 0.9984 2.42 106 2.56 106 9LF 0.836 1.018 0.030 0.030 3.95E04 3.49E04 3.09E06 4.89E06 20.53 31.49 1.220 2.756 0.9996 0.9992 2.11 106 2.51 106 10LS 1.055 0.851 0.026 0.066 4.22E04 3.96E04 3.30E06 7.12E06 21.74 21.04 1.349 2.796 0.9983 0.9995 4.42 106 2.05 106 2GF 1.105 0.053 2.83E04 3.39E06 18.09 1.632 0.9994 2.16 106 3GF 0.832 0.052 2.62E04 3.16E06 48.32 2.263 0.9999 5.93 106 5GS 0.897 0.010 2.18E04 1.96E06 18.44 1.661 0.9988 2.35 106 7GS 0.668 0.045 2.19E04 5.61E06 31.11 5.619 0.9976 3.17 106 6.5 Summary of Findings This chapter presents the results of shrinkage tests on the concrete mixtures investigated in this study. The summary of this chapter and major findings are provided as follows: PAGE 146 147 (1) Fly ash concrete mixtures had slightly highe r shrinkage strain at 91 days than slag concretes. This is due probabl y to the slow hydration rate of fly ash in comparison with that of slag. As a result of slower rate of hydration, there is more free water evaporating from the interior concrete out, which can cause concrete to shrink more. Thus, it is recommended that using a longer wet curing time would be helpful to reduce shrinkage of fly ash concrete. (2) Water content has a significant effect on dryi ng shrinkage strain of concrete. The higher the water content, the more the concrete tends to shrink. However, no clear trend can be seen on the effects of water to cementitious materials ratio on shrinkage of concrete. (3) For the four concrete mixtures with Georgia granite aggregate, shrinkage strain is slightly lower than the four corresponding concrete mixtures with Miami Oolite limestone aggregate. Lightweight aggregate concrete shrinks more than normal weight aggregate concrete. This might be explained by their difference in elastic modulus. The concrete with higher elastic modulus w ould have a stronger resistance to the movement caused by shrinkage of cement paste. (4) For the concretes tested, ther e appeared to be a relations hip between the compressive strength ('cf) at the age when shrinkage test wa s started and the shrinkage strain (sh ) at 91 days as follows: '0001.0 0005.0cf e sh Where 'cf is in unit of psi. (5) For the concretes tested, ther e appeared to have a relati onship between elastic modulus (cE) at the age when shrinkage test was started and the shrinkage strain (sh ) at 91 days as follows: c shE e 7102 0007.0 Where cE is in unit of psi. (6) According to the shrinkage test results from this study, th e C.E.BF.I.P model (as shown in Equation 66) appeared to give better predictions than the ACI 209 model (as shown in Equation 63). Using ACI 209 model may resu lt in overestimation of the ultimate shrinkage strain. (7) For the concrete investigated in this study, the ultimate shrinkage strain ranged from 1.93 104 to 3.64 104 for the concretes with Miami Oolite limestone aggregate; from 2.18 104 to 2.83 104 for the concretes with Georgia granite aggregate; and from 3.49 104 to 4.22 104 for the concretes with Stalite lightweight aggregate concrete. PAGE 147 148 CHAPTER 7 ANALYSIS OF CREEP TEST RESULTS 7.1 Introduction This chapter presents the results from creep tests on the fourteen c oncrete mixes evaluated in this study. The effects of various factors on creep behavior of concrete were analyzed. Empirical equations relating creep to other fundamental properties, such as compressive strength and elastic modulus, were established through regression analysis. Evaluation was made on C.E.BF.I.P model and ACI 209 model for their e ffectiveness and accuracy in creep prediction. Ultimate creep strain was approximated using a threeparameter asymptotic equation to fit experimental data, and ultimate creep coefficien t was computed using ultimate creep strain divided by instantaneous strain. 7.2 Analysis of Creep Test Results The measured and calculated results from the creep tests on the fourteen concrete mixes evaluated in this study were presented in Tabl e B1 in Appendix B. The results presented include the total strain, shrinkage strain, creep st rain, elastic strain, creep coefficient and creep modulus at various loading ages. 7.2.1 Effects of Curing Condition s on Creep Behavior of Concrete As shown in Figure 71 and Figure 72, the curi ng condition has a significant effect on the creep behavior of such concrete mixtures as Mix1F, Mix2F, Mix3F, and Mix4F. Generally, the concrete specimens moistcured for 14 days ha d creeping strains which were less than those moistcured for 7 days by more than 13 percen t. This observation applies to the specimens loaded at both 40% of compressive strength and 50% of compre ssive strength at the two given loading ages. Also, it is of significance to men tion that, for ultrahigh strength concrete, the effect of curing condition on creep strain is extremely important For example, the specimens PAGE 148 149 from Mix1F moistcured for 14 da ys have creep strain at 91 days over 25 percent less than those moistcured for 7 days. This is due probably to its high cementitious ma terials content, 1000 lbs per cubit yard, and low water to cementitious ratio of 0.24. Thus, longterm moist curing condition is needed to make cement hydration as complete as possible. The tremendous effects of curing conditions on creep behavior also extend to the concrete mixtures with lightweight aggregate, such as Mix9LF and Mix10LS. For example, the creep strain of Mix9LF moistcured for 14 days a nd loaded at 50% of compressive strength is 0.000749, which is 29.8% lower than that of Mix9LF moistcured for 7 days and loaded at the same loading level. The creep strain of Mix10LS moistcured for 14 days and loaded at 50% of compressive strength is 0.000776, which is 47.3% lower than that of Mi x10LS moistcured for 7 days and loaded at 50% of its compressive strength. However, no substantial effect of curing c ondition on creep strain was seen from the concrete mixtures containing gr ound granulated blastfurnace sl ag as mineral additives. For example, the creep strain of Mix5S moistcured fo r 14 days is nearly identical to that of Mix5S moistcured for 7 days. This similar situation can also be seen from Mix6S, Mix7S and Mix8S. The cause can be attributed probably to the f act that the slag concretes nearly develop their compressive strength fully in 14 days. That is to say, in comparison with the compressive strength at 14 days, slag concrete mixtures ha ve no significant increase in compressive strength at age of 28 days. That means the specimens mois tcured for 14 days has no significant change in microstructure in comparison with those moistcured for 7 days. Thus, creep strains of slag concretes obtained und er two different curing conditions show no significant difference. PAGE 149 150 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 1.40E03 1F2F3F4F5S6S7S8S9LF10LS MixtureCreep Strain at 91 days 7day moist curing 14day moist curing Figure 71 Effects of curing condition on creep of concrete loaded at 40% of compressive strength 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 1.40E03 1.60E03 1F2F3F4F5S6S7S8S9LF10LS MixtureCreep Strain at 91 days 7day moist curing 14day moist curing Figure 72 Effects of curing condition on creep of concrete loaded at 50% of compressive strength PAGE 150 151 7.2.2 Effects of Loading Condition on Creep Behavior of Concrete The effects of stress level on creep of the conc retes investigated in this study are presented in Figure 73 and Figure 74. As shown in Figure 73 and Figure 74, th e concrete specimens loaded at 50% of compressive strength develop c onsiderably higher creep strain than those loaded at 40% of compressive strength at loading age, and the signi ficant effects of stress level on creep strain can be seen from both the normal weight aggregate concretes and lightweight aggregate concretes. As shown in Table 71, for the concrete mixtur es with fly ash, after 7 days moist curing the specimens of Mix1F loaded at 50% of compressi ve strength have creep strain of 0.00093, nearly 20% higher than those loaded at 40% of compressive strength. The 7day moistcured specimens from Mix2F loaded at 40% of compressive stre ngth have creep strain at 91 days 18.5 percent less than those loaded at 50% of compressive st rength. For Mix3F and Mi x4F, creep strain of specimens moistcured for 7 days and loaded at 40% of compressive strength is 31.6% and 22.7% lower than those of the same concretes moistcured under the same condition but loaded at 50% of compressive strength. For the concrete mixtures with slag, creep st rains of Mix5S, Mix6S, Mix7S and Mix8S moistcured for 7 days and loaded at 50% of compressive strength are 22.8%, 11.9%, 17.2%, and 16.3% higher than those of the same correspond ing concretes cured under the same condition but loaded at 40% of compressive strength. Significant effects of loading c onditions on creep behavior can also be observed from the specimens moistcured for 14 days. For the fly as h concretes, the specim ens of Mix1F, Mix2F, Mix3F and Mix4F moistcured for 14 days and loaded at 50% of compressive strength creep 12.7%, 22.1%, 18.5% and 18.5% higher than thos e of the same corresponding concretes loaded PAGE 151 152 at 40% of compressive strength co rrespondingly. For slag concretes, the creep strains of Mix5S, Mix6S, Mix7S and Mix8S moistcured for 14 da ys and loaded at 50% of compressive strength are 18.3%, 16.1%, 16.4% and 18.6% higher than those of the same corresponding concretes loaded at 40% of compressive strength. In addition, significant effect of loading condition on creep beha vior can be seen from the concrete mixtures with granite aggregate. For example, in comp arison with the specimens loaded at 40 percent of compressive strength, the creep strain of the specimens loaded at 50 percent of compressive strength is over 23% higher. Similar observation can also be seen from the concrete mixtures with lightweight aggregate. 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 1.40E03 1.60E03 1F2F3F4F5S6S7S8S9LF10LS MixtureCreep Strain at 91 days 40% of compressive strength 50% of compressive strength Figure 73 Effects of stress level on creep of concrete moistcured for 7 days PAGE 152 153 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 1.40E031F 2F 3 F 4 F 5S 6 S 7 S 8 S 9 L F 1 0 LS 2GF 3GF 5 GS 7 GSMixtureCreep Strain at 91 days 40% of compressive strength 50% of compressive strength Figure 74 Effects of stress level on creep of concrete moistcured for 14 days 7.2.3 Effects of Aggregate Types on Creep Behavior of Concrete The effect of two different normal coarse aggr egates on creep behavior was investigated on four typical concrete mixtures i.e. Mix2F, Mix3F, Mix5S and Mix7S. These mixes used a Miami Oolite limestone as coarse aggregate. The four concrete mixtures with Georgia granite aggregate were labeled as Mix2GF, Mix3GF, Mix5GS, and Mi x7GS. The creep behavior of these concrete mixtures was compared under the same curing conditions and loading conditions. As shown in Figures 75 through 78, the comp arison between Mix2F and Mix2GF, Mix3F and Mix3GF, Mix5S and Mix5GS, and Mix7S and Mix7GS indicate that Mix2GF, Mix3GF, Mix5GS, and Mix7GS creep slightly mo re than the correspondi ng Mix2F, Mix3F, Mix5S and Mix7S for all loading conditions. This agrees with the findings from the study by G.E. Troxell et al [G.E. Troxell et al, 1958]. He carried out the study on the effect of six different types of aggregate on creep behavior of concrete The results indicate that the concrete with PAGE 153 154 limestone aggregate has the lowest creep strain in comparison with the concretes with other types of coarse aggregates, including quartz, granite, gravel, basalt and sandstone. In addition, the concrete mixt ures with lightweight aggregat e, such as Mix9LF and Mix10LS, do not creep as much as the concrete mixtur es with normal weight aggregate. As can be seen from Table 71, Mix9LF and Mix10LF deve lop much less creep stra in than the concrete mixtures, such as Mix2F, 3F, 4F, 5S, 6S, 7S, and 8S, even though the compressive strengths of Mix9LF and MixLS are considerab le lower than those of concrete mixtures with normal weight aggregate. These results agree with the conclu sion made by A.M. Neville [A.M. Neville, 1996], which stated that, as a general rule, the creep of structural quality lightwe ight aggregate concrete is about the same as that of concrete made with ordinary aggregate. 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 0102030405060708090100 Time (days)Creep Strain Georgia granite40%28day curing Georgia granite50%28day curing Miami Oolite limestone40%28day curing Miami Oolite limestone50%28day curing Figure 75 Effects of aggregate t ype on creep behavior of Mix2F PAGE 154 155 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 0102030405060708090100 Time (days)Creep Strain Georgia granite40%28day curing Georgia granite50%28day curing Miami Oolite Limestone40%28day curing Miami Oolite limestone50%28day curing Figure 76 Effects of aggregate t ype on creep behavior of Mix3F 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 0102030405060708090100 Time (days)Creep Strain Georgia granite40%28day curing Georgia granite50%28day moist curing Miami Oolite limestone40%28day curing Miami Oolite limestone50%28day curing Figure 77 Effects of aggregate t ype on creep behavior of Mix5S PAGE 155 156 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 0102030405060708090100 Time (days)Creep Strain Georgia granite40% loading level Georgia granite50% loading level Miami Oolite limestone40% loading level Miami Oolite limestone50% loading level Figure 78 Effects of aggregate t ype on creep behavior of Mix7S 7.2.5 Effects of Water to Cement Rati o and Air Content on Creep Strain The main component of creep in concrete is from creep of the hydrat ed cement paste. Creep is related to internal movement of absorb ed or intracrystalline water, i.e. to internal seepage [A.M.Neville, 1996]. Gl ucklichs study has shown that concrete from which all evaporable water has been removed exhibits pr actically no creep [J. Glucklich, 1962]. Thus, water to cementitious materials ratio gives a signi ficant effect on the magnitude of creep strain. Also, voids in the concrete play a critical role in influencing cr eep behavior of concrete because internal seepage of water from the absorbed layers to voids such as capillary voids is quite possible. A.M.Neville [A.M.Neville, 1996] stated that creep appears to be a function of the relative amount of the unfilled space, and that the voids in the gel govern creep in concrete. The effects of water to cementitious materials ratio and air content on creep of concrete are illustrated in Figures 79 through 712. From these figures, it can be seen that creep of concrete PAGE 156 157 increases as water to cementitious materials ratio increases. It can also been seen from these figures that the creep strain in creases with increase of air cont ent of fresh concrete, even though air content of fresh concrete may not be directly related to the void content of hardened concrete. 7.2.6 Relationship between Compre ssive Strength and Creep Strain It is always desirable in practice to find th e relationship between co mpressive strength and creep strain. If a simple relationship can be found between compressive st rength and creep, it is not necessary to consider the effect of type of cement, aggregate content and aggregate type, water to cement ratio, air content and age on cr eep behavior separately In addition, possible accurate estimation on creep strain based on characteristic strength of concrete will make us free from timeconsuming creep test. In Figure 713, compressive streng th of concrete at 14 days is plotted against creep strain at 91 days for the concretes moistcured for 7 da ys and loaded at 40% and 50% of compressive strength. In Figure 714, the compre ssive strength of conc rete at 28 days is plotted against creep strain at 91 days for the conc retes moistcured for 14 days an d loaded at 40% and 50% of compressive strength. As seen from Figure 713 and Figure 714, the creep strain decreases with increase of compressive strength of concrete. Regression analysis was performed to determine the relationship between compressive strength and creep strain at 91 days using following simple linear function c cf91 (71) The results of the regression analys is are presented in Table 72. As shown in Table 72, loading condition has a significant influence on the slope and interception of the above linear equation, while curing age ha s nearly no effect on the slope and interception. That is to say, the relationship between compressive st rength and creep strain PAGE 157 158 obtained under the load at 40% of compressive strength can be expressed as one single linear equation regardless of what curi ng condition was applied to the specimens. The same conclusion also applies to concrete specimens loaded at 50% of compressive strengt h. The above hypothesis is confirmed by the results of re gression analysis given in Table 71, and also shown in Figure 715. In addition, instantaneous stra ins of normalweight aggregate concrete are plotted against compressive strength of concrete at corresponding curing ages in Figure 716. It indicates that instantaneous strain measured in creep test in creases with increase of compressive strength of concrete. 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 1.40E03 0.200.250.300.350.400.450.50 Water to Cementitious Materials RatioCreep Strain at 91 days high air content low air content Figure 79 Effects of water to cementitious materi als ratio and air content on creep of concrete moistcured for 7 days and loaded at 40% of compressive strength PAGE 158 159 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 0.200.250.300.350.400.450.50 Water to Cementitious Materials RatioCreep Strain at 91 days high air content low air content Figure 710 Effects of water to cem entitious materials ratio and ai r content on creep of concrete moistcured for 7 days and loaded at 50% of compressive strength 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 0.200.250.300.350.400.450.50 Water to Cementitious Materials RatioCreep Strain at 91 days high air content low air content Figure 711 Effects of water to cem entitious materials ratio and ai r content on creep of concrete moistcured for 14 days and loaded at 40% of compressive strength PAGE 159 160 0.00E+00 4.00E04 8.00E04 1.20E03 1.60E03 2.00E03 0.200.250.300.350.400.450.50 Water to Cementitious Materials RatioCreep Strain at 91 days high air content low air content Figure 712 Effects of water to cem entitious materials ratio and ai r content on creep of concrete moistcured for 14 days and loaded at 50% of compressive strength Table 71 Regression analysis on relationship between compressive strength and creep strain using Equation 71 Curing condition Loading condition 95% Confidence Interval 95% Confidence Interval R2 Sy.x 40% 8.57E08 1.19E07 ~ 5.29E08 1.54E03 1.28E03 ~ 1.81E03 0.69 8.38E05 7day moist curing 50% 1.20E07 1.62E07 ~ 7.75E08 1.98E03 1.65E03 ~ 2.32E03 0.72 1.08E04 40% 9.27E08 1.23E07 ~ 6.29E08 1.59E03 1.35E03 ~ 1.84E03 0.70 8.70E05 14day moist curing 50% 1.11E07 1.46E07 ~ 7.62E08 1.95E03 1.67E03 ~ 2.24E03 0.71 1.01E04 40% 8.99E08 1.10E07 ~ 6.94E08 1.57E03 1.41E03 ~ 1.74E03 0.70 8.33E05 All curing conditions 50% 1.13E07 1.39E07 ~ 8.80E08 1.95E03 1.75E03 ~ 2.16E03 0.71 1.03E04 PAGE 160 161 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 400050006000700080009000100001100012000 Compressive Strength at loading ageCreep Strain at 91 days 7day40% 7day50% Figure 713 Relationship between compressive strength and creep stra in of concrete moistcured for 7 days 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 50006000700080009000100001100012000 Compressive Strength at loading ageCreep Strain at 91 days 14day40% 14day50% Figure 714 Relationship between compressive strength and creep stra in of concrete moistcured for 14 days PAGE 161 162 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 400050006000700080009000100001100012000 Compressive Strength (psi)Creep Strain at 91 days 40% loading level 50% loading level Figure 715 Relationship between compressive strength and creep st rain of concrete under all curing conditions 0.00E+00 2.00E04 4.00E04 6.00E04 8.00E04 1.00E03 1.20E03 50006000700080009000100001100012000 Compressive Strength (psi)Instantaneous Strain from Creep Test 40% of compressive strength 50% of compressive strength Figure 716 Relationship of compressi ve strength to instantaneous st rain measured in creep test PAGE 162 163 7.3 Creep Coefficient Creep coefficient, which is calc ulated by dividing creep strain by elastic strain, is a very important parameter in prestressed concrete design. Creep coefficient is si gnificantly affected not only by those factors influencing creep strain, but also by the el astic property of concrete. 7.3.1 Effects of Loading Conditions on Creep Coefficient For the specimens moistcured for 7 days, the creep coefficients obtained from two different stress levels are plotte d in Figure 717 for ten concrete mixtures. It shows that two different stress levels have nearly no effect on the creep coefficien t of all the concrete mixtures. The same observation can be seen from the specime ns moistcured for 14 days as well, as shown in Figure 718. In this study, two stress levels includ e 40% of compressive strength and 50% of compressive strength. Thus, the conclusion can be arrived that the ratio of creep strain to instantaneous strain of concretes investigated in this study is pr oportional to the stress applied up to 50% of compressive stre ngth at loading age. 7.3.2 Effects of Curing Condi tions on Creep Coefficient Curing conditions have some effects on creep coefficient. As shown in Figure 719, the effects of curing conditions on creep coefficients of Mix1F, Mix2F, and Mi x3F are substantial. For example, the creep coefficient of Mix1F mois tcured for 14 days is 0.81 at 91 days, which is 35.8% lower than that of Mix1 moistcured for 7 days. Also, the creep coefficients of Mix2F and Mix3F moistcured for 14 days are 23.9% and 17.7% lowe r than those of the same corresponding concretes mo istcured for 7 days. However, for some concrete mixtures, such as Mix6S, Mix7S, Mix8S, and Mix4F, the effects of curing conditions on creep coefficient are not very appreciable. For instance, the creep co efficients of Mix6S, Mix7S, Mix8S and Mix4F moistcured for 14 days are ju st about 10% lower than those of them moistcured for 7 days. PAGE 163 164 The cause can be attributed to the fact th at there was not too much additional strength development from the age of 14 days to the age of 28 days for the slag concretes. 0.50 0.00 0.50 1.00 1.50 2.00 1F2F3F4F5S6S7S8S9LF10LS MixtureCreep Coefficient at 91 days 40% of compressive strength 50% of compressive strength Difference Figure 717 Effects of stress leve l on creep coefficient of concrete moistcured for 7 days 0.50 0.00 0.50 1.00 1.50 2.001F 2 F 3 F 4 F 5S 6S 7 S 8S 9 LF 10 L S 2 GF 3GF 5GS 7 GSMixtureCreep Coefficient at 91 days 40% of compressive strength 50% of compressive strength Difference Figure 718 Effects of stress leve l on creep coefficient of concrete moistcured for 14 days PAGE 164 165 The effects of curing condition on creep coeffici ent of lightweight aggregate concrete are very significant. For instance, the creep coeffici ent of Mix9LF moistcure d for 14 days is about 1.14, nearly 18% lower than that of Mix9LF moistcured for 7 days. Also, the specimens of Mix10LS moistcured for 14 days has creep coefficient of 1.13, which is over 42% lower than 1.61, creep coefficient of Mix6 moistcured for 7 days. Thus, apparently, longer curing time can decrease creep coefficient tremendously for lightweight aggregate concrete. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1F2F3F4F5S6S7S8S9LF10LS MixtureCreep Coefficient at 91 days 7day moist curing 14day moist curing Figure 719 Effects of cu ring condition on creep coefficient of concrete 7.3.3 Effects of Water Cont ent on Creep Coefficient Since water content of fresh concrete affect significantly drying creep of concrete, they should have considerable effects on creep coeffici ent as well. As can be seen from Figure 720, water content of fresh concrete have significant effects on creep coefficient of concrete at 91 days. Creep coefficient at 91 days increases as water content of fresh concrete increases. PAGE 165 166 0.00 0.50 1.00 1.50 2.00 2.50 100150200250300350400 Water Content (lbs/yard3)Creep Coefficient at 91 days Miami Oolite limestone Georgia granite Stalite lightweight aggregate Figure 720 Effects of wa ter content on creep coefficient at 91 days 7.3.4 Effects of Compressive Strength at Loading Age on Creep Coefficient As shown in Table 71, the higher the compress ive strength of concrete is at the loading age, the lower the creep coeffici ent is. For example, for the concrete mixtures with Miami Oolite limestone aggregate, Mix1 has the highest comp ressive strength, and it has the lowest creep coefficient. Also, it is of great importance to see that the creep coefficient is not affected by the loading conditions, i.e. the creep coefficient obtained under the loading condition of 40% of compressive strength is iden tical to that obtained under th e loading condition of 50% of compressive strength. To find out how the compressive strength of conc rete at loading age is related to the creep coefficient at 91 days, compressive strength at loading age was plotted against corresponding creep coefficient at 91 days in Figure 721 and Fi gure 722, for specimens loaded at 14 days and PAGE 166 167 28 days, respectively. Then linear regression analysis using Equation 72 was performed, and the analyzed results are displayed in Table 72. c cf (72) Where c = creep coefficient at 91 days; fc = compressive strength; and = the slope and interception of linear equation. Table 72 Regression analysis on re lationship of compressive strength to creep coefficient using Equation 72 Curing condition 95% Confidence Interval 95% Confidence Interval R2 Sy.x 14day curing 2.02E04 2.39E04 ~ 1.64E04 3.016 2.717 ~ 3.316 0.9041 0.0951 28day curing 2.06E04 2.43E04 ~ 1.69E04 3.077 2.774 ~ 3.379 0.8855 0.1071 All curing conditions 2.03E04 2.28E04 ~ 1.79E04 3.042 2.842 ~ 3.242 0.8919 0.0999 As can be seen from Table 72 as well as Figure 721 and Figure 722, compressive strength of concrete at loading age is nearly linearly related to the creep coefficient at 91 days. This situation is true for the specimens under two different curing conditions. Also, it is to be noted that the slope and intercep tion of the linear regres sion equations are nearly identical to one another for the specimens under tw o different curing conditions. That is to say, once compressive strengths of specific concrete mixtures are given, the creep coefficient can be computed using the linear relationship between compre ssive strength and creep coeffici ent at 91 days regardless of what curing condition was applied to the specimens. Therefore, linear regression analysis was car ried out on the experimental data obtained from both curing conditions, and th e analyzed results are plotted in Figure 723 and presented in Table 72 as well. As can be seen from Table 72, the slope and intercep tion of linear regression equation from combined analysis are approxi mately equal to the average of slopes and interceptions from separate analyses. PAGE 167 168 0.00 0.50 1.00 1.50 2.00 2.50 2000400060008000100001200014000 Compressive strength at 14 days (psi)Creep Coefficient Second phase First phase Figure 721 Relationship between compressive strength and creep coefficient for specimens loaded at 14 days 0.00 0.50 1.00 1.50 2.00 2.50 400060008000100001200014000 Compressive Strength at 28 Days (psi)Creep Coefficient Second phase First phase PAGE 168 169 Figure 722 Relationship between compressive strength and creep coefficient for specimens loaded at 28 days 0.00 0.50 1.00 1.50 2.00 2.50 400060008000100001200014000 Compressive Strength (psi)Creep Coefficient at 91 days Limestone Granite Figure 723 Relationship between compressive strength at loading age and corresponding creep coefficient at 91 days 7.3.5 Relationship between Elastic Modulus at Loading Age and Creep Coefficient After realizing the close relati onship between compressive strength and creep coefficient, it is not difficult to note that because, for a gi ven concrete, compressive strength and elastic modulus is related, creep coefficient and elastic modulus should be related as well. As shown in Figure 724, elastic modulus was plotted against creep coefficient at 91 days for the concrete with normalweight aggregate. A linear regression analysis was performed using Equation 73. c cE (73) The results of the regression analysis are show n in Table 73. As can be seen from Figure 724, for the normalweight aggregate concrete, creep coefficient at 91 days is linearly related to PAGE 169 170 the elastic modulus at the loading age, while for lightweight aggregate conc rete creep coefficient can not be related to elastic modulus using the linear equation from normalweight aggregate concrete. More data from creep test on lightweight a ggregate concrete are needed to establish reliable relationship between el astic modulus and creep coeffici ent for lightweight concrete. In addition, creep coefficient at 91 days wa s plotted against the ratio of compressive strength and elastic modulus in Figure 725. It indicates that creep coefficient at 91 days is linearly related to the ratio of compressive strength to elastic modulus of concrete at loading age. A linear regression analysis was performed to relate creep coefficient to the ratio of compressive strength to elastic modulus by the following equation: c c cE f (74) The results of the regression analys is are presented in Table 74. 0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.00E+063.00E+064.00E+065.00E+066.00E+067.00E+068.00E+06 Elastic Modulus at Loading Ages (psi)Creep Coefficient at 91 days Normal weight aggregate Lightweight aggregate Figure 724 Effects of Elastic modulus at lo ading age on creep coefficient at 91 days PAGE 170 171 0.00 0.50 1.00 1.50 2.00 2.50 00.00050.0010.00150.0020.00250.003 fc/ECreep Coefficient at 91 days Miami Oolite limestone Georgia granite Figure 725 Relationship between cree p coefficient at 91 days and fc/E Table 73 Regression analysis on relationship of elastic modulus to creep coefficient using Equation 73 95% confidence interval 95% confidence interval R2 SSE 4.55E07 5.67E07 ~ 3.43E07 3.725 3.151 ~ 4.299 0.6671 0.1742 Table 74 Regression analysis on re lation of creep coefficient to fc/E using Equation 74 95% confidence interval 95% confidence interval R2 SSE 1132 1609 ~ 1014 3.485 3.010 ~ 3.959 0.7026 0.1647 7.3.6 Effects of Coarse Aggre gate Type on Creep Coefficient As can be seen from Figure 726, the creep co efficients of concretes made with Georgia granite is higher than those of concretes with Miami Oolite limestone aggregate. This is due probably to the lower elastic deformation of concretes with Georgia granite aggregate in comparison with those with Miami Oolite limestone aggregate. Therefore, the ratio of creep PAGE 171 172 strain to elastic strain is larger for Georgia granite aggregate concrete However, lightweight aggregate concrete behaves in a different way in comparison with Georgia granite aggregate concrete. Since the elastic deformation of lightwei ght aggregate concrete is significantly higher than that of Georgia granite aggregate concrete and Miami Oolite limestone aggregate concrete, the ratio of creep strain to elastic strain is lower for lightweight aggregate concrete. This observation is in agreement with the conclusion given by Neville [A.M. Neville, 1996]. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 Mix2Mix3Mix5Mix7 MixtureCreep Coefficient at 91 days Miami Oolite limestone Georgia granite Figure 726 Effects of coarse aggregate type on creep coefficient at 91 days 7.4 Creep Modulus Creep modulus, defined as the ratio of stress applied to concrete specimen to the total strain excluding shrinkage strain, reflects the decay of stiffness with time. Apparently, this parameter is of great important in inelastic stru ctural material analysis to obtain timedependent elastic modulus so that accurate deformation of material can be computed correctly using the PAGE 172 173 reduced elastic modulus. Figure 727 presents a typical decay curve of concrete mixture investigated in this study. As can be seen from Table 71, for the fl y ash concrete mixtures, curing condition has significant effects on the creep modulus as a function of time. That is to sa y, the decay of creep modulus of specimen moistcured fo r 14 days is considerably less th an that of the same concrete moistcured for 7 days. The same observation can also be made on the lightweight aggregate concrete as well. This indicates that curing cond ition plays a very significant role in decreasing creep strain of fly ash concrete and lightweight aggregate concrete. However, for the slag concrete mixtures, no appreciable effects of curing condition on creep modulus can be observed. This means that a longer curing time beyond 14 days has no significant influence on the creep behavior of slag concrete. 0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06 0102030405060708090100 Time (days)Creep Modulus (psi) 7day moist curing40% of compressive strength 7day moist curing50% of compressive strength 14day moist curing40% of compressive strength 14day moist curing50% of compressive strength Figure 727 Typical decay curves of creep modulus with time PAGE 173 174 7.5 Prediction of Ultimate Creep Strain It is often assumed that creep rate for a c oncrete material decreases with time, and the creep strain will approach a lim iting value after an infinite ti me under load. The study by G.E. Troxell et al [G.E.Troxell et al, 1958] indicates that th e average value of cr eep strain after 30 years is 1.36 times the oneyear creep strain. In engineering practical point of view, it is often assumed that the 30year creep strain represents the ultimate creep stain. The ultimate creep strain of concrete invest igated in this study was determined using asymptotic equation, given as follows to fit the experimental data. t tc (75) This equation is the ratio of two polynomials. As the time variable approaches infinity, the ratio of two polynomials will be equal to 1. Th erefore, ultimate creep strain is equal to In this equation, and are two parameters to be determined from curvefitting, and which is the factor borrowed fr om CEBFIP Equation, reflects the effect of geometrical characteristics of specimen and relative humidity on creep behavior of concrete. The relative humidity was controlled at 75% in this study. "12"6 cylindrical specimens were used for creep tests. The geometric characteris tic of the test specimen, h, can be computed as follows: mm in u A hc2.763 6 32 22 (76) Then, can be obtained as follows: 15005.381250 100%100 %75 2.1115018 h (77) Thus, the equation used to fit the experimental data becomes PAGE 174 175 5.381 t tc (78) Least Squares Method of curve fitting as described in Chapter 6 was used to determine two unknown parameters, and Ultimate creep strains and ultimate creep coefficient after regression analysis for 14 concrete mi xtures are presented in Table 75. Table 75 The predicted ultimate creep strain and creep coefficient Predicted items Ultimate creep strain ultimate creep coefficient Curing conditions curing condition 1 Curing c ondition 2 curing condition 1 Curing condition 2 Loading conditions 40% 50% 40% 50% 40% 50% 40% 50% Mix1F 1.06E03 1.30E03 0.88E03 1.03E03 1.48 1.55 1.14 1.16 Mix2F 1.93E03 2.08E03 1.66E03 2.11E03 2.91 2.59 2.37 2.44 Mix3F 1.45E03 1.86E03 1.39E03 1.56E03 2.30 2.40 2.11 1.90 Mix4F 1.37E03 1.59E03 1.24E03 1.63E03 2.28 2.14 2.14 2.32 Mix5S 1.40E03 1.84E03 1.25E03 1.64E03 2.10 2.17 1.74 1.84 Mix6S 1.68E03 1.87E03 1.55E03 1.75E03 2.51 2.23 2.23 2.05 Mix7S 1.41E03 1.69E03 1.46E03 1.60E03 2.71 2.71 2.61 2.46 Mix8S 1.58E03 1.97E03 1.45E03 1.95E03 2.57 2.72 2.21 2.34 Mix9LF 1.11E03 1.40E03 0.99E03 1.16E03 1.78 1.83 1.46 1.49 Mix10LS 0.94E03 1.19E03 0.76E03 0.97E03 1.61 1.45 1.32 1.26 Mix2GF 1.80E03 2.10E03 2.99 2.70 Mix3GF 1.57E03 1.81E03 2.96 2.72 Mix5GS 1.42E03 1.77E03 2.51 2.55 Mix7GS 1.49E03 1.76E03 2.89 2.69 As shown in Table 76, it is to be pointed out that most of the concretes investigated in this study have an ultimate creep coefficient higher than 2.0. 7.6 Evaluation on Creep Prediction Models The effectiveness of other creep prediction models, such as Burgers model, C.E.BF.I.P model and ACI 209 model, were evaluated in this study. Burgers model Burgers Model or fourelement model, as show n in Figure 728, was also used to fit the experimental data to evaluate the feasibility of the Burgers model to predict creep strain of concrete at a later time, based on the expe rimental data obtain ed in three months. PAGE 175 176 Figure 728 Burgers Model The total strain predicted by the Burgers model can be considered as the sum of the strain responses of each element under the applied lo ad, and can be expressed by the following equation: 321 (79) Where 1 is the elastic strain of spring in a Maxwell model, and it can be given as 1 1R (710) 2 is viscous flow of dashpot in a Maxwell model, and its rate type formul a can be expressed as 1 2' (711) 3 is the strain of a Kelvin unit, and it can be related to the applied stress as 2 3 2 2 3' R (712) Eliminating 1, 2, and 3 from the above four equations, the constitutive relationship between and in the Burgers model can be expressed as R1 1 R2 2 1 2 3 0 t 1 t 0 B A` 3 C A 2 1 D O PAGE 176 177 "'"'2 21 1 21 21 2 2 2 1 1 1 R RRRRR (713) Solving the above second order differentia l equation with init ial conditions of 2 0 1 0 32 1 0 1' 0 0 R t (714) The creep behavior of Burgers model under the constant stress can be derived as: t R R t R t2 2 2 0 1 0 1 0exp1 (715) In this study, only creep strain was considered. Thus, we can eliminate the first term in Equation 79. Therefore, the strain in the Burgers model becomes: t R R tt2 2 2 0 1 0exp1 (716) Three material constants, R2, 1 and 2, can be easily determined by curvefitting Equation 716 to the experimental data. As can be seen from Equation 716, after a ce rtain time, the second term on right side of equation will decay and approaches 2 0R and the creep rate will become a constant value, i.e. 1 0 So, after a long time, the expression for the strain from the Burgers model can be simplified as follows: 2 0 1 0R tt (717) PAGE 177 178 Burgers model with constitutive parameters determined from regression analysis was plotted in Figure 729. As can be seen from Figure 729, Burgers model is very capable to simulate the development trend of creep of concrete. However, it indicates that the extrapolation made by Burgers model results in overestimation of the ultimate creep strain. This is due the lack of longterm creep data from this study. It is not possible to dete rmine the constitutive parameters accurately without longterm creep data. 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 020406080100 Time (days)Creep Strain 14day40% 14day50% Regression analysis Burger's Model Figure 729 Prediction of strain using the Burgers model C.E.BF.I.P Model (1990) C.E.BF.I.P Model is an empirical model re commended by Europe Union in 1990. In this model, the creep strain can be predicted based on the information from ultimate compressive strength and modulus of elastic ity at loading age, and a time function determined according to the mechanical properties of specific concrete mixture, the geometry of specimen, and the curing conditions applied to the specimen, and so on. The general equation is given as follows: PAGE 178 179 ),( )( ),(0 0 0tt E t ttci ci c cr (718) For the detail description about C.E.BF.I.P mode l, please refer to the literature review in Chapter 2. Finally, combining all the equations together and simplifying them, we have the following equation used to predict the development of creep strain with time. 3.0 10 10 2.0 10 3/1 0 0 0 0/)( /)( )/(1.0 1 / 3.5 )/(46.0 /1 1 )( ),( ttt ttt tt ff hh RHRH E t ttH cmo cm ci c cr (719) In this study, the relative humidity is controlled at 75%. For "12"6 cylinder, the geometrical characteristic of the test sp ecimen, h, can be computed as follows: mm in u A hc2.763 6 32 22 (720) Then,h can be obtained as follows: 15005.381250 100 2.76 %100 %75 2.1115018 H (721) Then, the prediction formula can be simplified as follows: For concrete cured for 14 days: 3.0 14 0 0)14(5.381 )14(55.18 )( ),( t t f E t ttcm c c cr (722) The above equation is an asymptotic function. As time approaches infinity, creep strain will reach ultimate creep strain cm ci cf E t 55.18 )(0. Similarly, for the concrete specimen cured for 28 days, the prediction equation becomes PAGE 179 180 3.0 28 0 0)28(5.381 )28(55.18 )( ),( t t f E t ttcm c c cr (723) As can be seen from the above equation, this asymptotic equation approaches a limiting value as time approaches infinity. Therefore, u ltimate creep strain can be computed by the following formula: cm c c ultf E t 55.18 )(28 0 (724) To evaluate the effectiveness of the C.E. BF.I.P model, the C.E.BF.I.P Equation was plotted in Figure 730. It indica tes that C.E.BF.I.P model gives very good prediction. To verify this conclusion, the creep strain at 91 days from experimental measurem ents is plotted against the creep strain computed according to C.E.BF.I. P model in Figure 731. It clearly shows that the measurements match very well with the predictions made by the C.E.BF.I.P model. 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 0102030405060708090100 Time (days)Creep Strain 14day40% 14day50% Regression analysis CEBFIP model ACI 209 model Figure 730 Comparison on the effectiveness of C.E.BF.I.P model and ACI model PAGE 180 181 y = x 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 0.00E+003.00E046.00E049.00E 041.20E031.50E031.80E03 Predicted Creep Strain at 91 daysCreep Strain at 91 days First phase Second Phase Figure 731 Comparison between the creep strain at 91 days from experimental data and the predicted creep strain using CEBFIP model Also, in order to verify if there is simple linear relationship between creep strain and cmfE the creep strain at 91 days was plotted against cmfE in Figure 731, where is stress applied to the specimen ; E is elastic modulus of concrete at loading age; and fcm is characteristic strength of concrete at loadi ng age. Then, a linear regression analysis was performed to determine the relationship between creep strain at 91 days and cmfE and the analyzed results are shown in Table 76. As can be seen from Figure 731, creep strain at 91 days is linearly related to cmfE The regression equation is given as follows: 4 9110758.1 40.13 cm cfE (725) PAGE 181 182 Table 76 Regression analysis on re lation of creep coefficient to cmfE 95% confidence interval 95% confidence interval R2 SSE 13.40 11.21 ~ 15.58 1.758E04 3.649E04 ~ 1.333E04 0.6848 1.193E04 In addition, the ultimate creep strains predicted by curvefitti ng to experimental data were plotted against the creep strains ca lculated using the original C.E.BF.I.P model in Figure 732. It indicates that original C.E.BF.I.P model gives very good creep strain prediction for the normalweight concrete mixtures i nvestigated in this study. 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 0.00E+003.00E056.00E059.00E051.20E041.50E04 c/(E fcm^0.5)Creep Strain at 91 days Figure 732 Relationship between creep strain and mechanical properties at loading age PAGE 182 183 y = x 0.00E+00 5.00E04 1.00E03 1.50E03 2.00E03 2.50E03 3.00E03 0.00E+005.00E041.00E031.50E032.00E032.50E033.00E03 Predicted Ultimate Creep Strain by CEBFIP modelUltimate Creep Strain by Curvefitting Second phase First phase Figure 733 Comparison between the ultimate creep strain calculated by C.E.BF.I.P model and that by curvefitting ACI209R model The evaluation on ACI 209 model was performed in this study. ACI 209 (1992) model is given as follows: 6.0 0 6.0 0 0 028)(10 )( )(),( tt tt ttt (726) Where ),(028tt Creep coefficient at time t; )(0t Ultimate creep coefficient; 0t Time of loading. In this study, 140 t days for concrete cured for 14 days before loading; and 280 t days for concrete cured for 28 days before loading. The ultimate creep coefficient can be expressed as: ct )(0 (727) PAGE 183 184 The constant 35.2 is recommended. The correction factors c consist of the following terms: a satRHlac (728) Where la Correction factor for loading age, which is equal to 0.916 for specimen cured for 14 days, and 0.814 for specimen cured for 28 days. RH Correction factor for ambient relative humidity. In this study, the ambient relative humidity is 75%, then77.0RH s Correction factor for slump of fresh concrete. l sS 00264.082.0 (lS is slump in mm). Correction factor for fine to total aggregate ratio. a 0024.088. 0 (a is fine to total aggregate ratio) a Correction factor for air content. a aa 09.046.0 (aa is air content) at Correction factor for thickness of member In this study, the volumesurface ratio method is used to obtain at )(0213.013.11 3 2s v ate (729) Where s v = Volume to surface ratio in mm. The correction factors based on the concrete mixtures, geometry of specimen and ambient conditions employed in this study for the ACI 209 model are provided in Table 77. PAGE 184 185 Table 77 Correction factors for the ACI 209 model la c Mix 7day moist 14day moist rh s a at p 7day moist 14day moist Mix1F 0.916 0.814 0.77 1.34 0.57 1.00 0.88 0.30 0.27 Mix2F 0.916 0.814 0.77 1.32 0.87 1.00 0.88 0.45 0.40 Mix3F 0.916 0.814 0.77 0.92 0.69 1.00 0.88 0.36 0.32 Mix4F 0.916 0.814 0.77 1.02 0.64 1.00 0.88 0.33 0.29 Mix5S 0.916 0.814 0.77 1.31 0.80 1.00 0.88 0.42 0.37 Mix6S 0.916 0.814 0.77 1.05 0.66 1.00 0.88 0.34 0.30 Mix7S 0.916 0.814 0.77 1.09 0.96 1.00 0.88 0.50 0.44 Mix8S 0.916 0.814 0.77 1.00 0.80 1.00 0.88 0.41 0.37 Mix9LF 0.916 0.814 0.77 0.82 0.73 1.00 0.88 0.38 0.33 Mix10LS 0.916 0.814 0.77 0.82 0.93 1.00 0.88 0.48 0.43 Mix2GF 0.916 0.814 0.77 1.12 1.13 1.00 0.88 0.58 0.52 Mix3GF 0.916 0.814 0.77 0.99 0.60 1.00 0.88 0.31 0.27 Mix5GS 0.916 0.814 0.77 1.26 0.96 1.00 0.88 0.50 0.44 Mix7GS 0.916 0.814 0.77 0.97 0.80 1.00 0.88 0.41 0.37 As can be seen from Figure 734, ACI 209 model greatly underestimates the creep strain of the concretes investigated in this study. y = x 0.00E+00 3.00E04 6.00E04 9.00E04 1.20E03 1.50E03 1.80E03 0.00E+003.00E046.00E049.00E041.20E031.50E031.80E03 Calculated Creep strain at 91 daysCreep Strain at 91 days from Experiment ACI209 C.E.BF.I.P Figure 734 Evaluation on ACI209 model and C.E.BF.I.P model PAGE 185 186 7.7 Summary of Findings This chapter presents the results from the creep tests in this study. The following is a summary of m ajor findings from the creep tests: (1) Curing condition has some effect on creep of fly ash concrete and lightweight aggregate concrete, while its effect is very slight on slag concrete. (2) For the stress levels used (40 and 50% of compressive st rength), the measured creep strain and instantaneous strain were linearly proportional to the stress applied. Thus, the computed creep coefficients were not aff ected by the stress le vel in this study. (3) Water to cementitious materials ratio has some effects on creep behavior of concrete. The higher the water to cementitious materials ratio, the more the concrete creeps. (4) For the concrete with identical water to cem entitious materials ratio, the higher the air content of fresh concrete, the more the concrete creeps. (5) The concretes with granite aggregate creeps sl ightly more than the concretes with Miami Oolite limestone aggregate and lightweight aggregate under the same stress level. However, due to the much lower elastic modul us of lightweight a ggregate concrete, the creep coefficient of lightweight aggregate co ncrete is much lower than that of normal weight aggregate concrete. Due to the hi gher elastic modulus of granite aggregate concrete, creep coefficient of granite concrete was much higher than that of the concretes with Miami Oolite limestone aggregate. (6) A simple linear relationship was established between compressive strength at loading age and creep strain at 91 days. (7) A linear relationship was also found betw een creep coefficient at 91 days and compressive strength (' cf ), elastic modulus (cE ), and the ratio of compressive strength and elastic modulus. The regre ssion equation related compressive strength at loading age to creep coefficient at 91 days (91 c ) is given as follows: 91 c cf (72) Where is equal to 2.03 104 and equal to 3.042; cf is in unit of psi. The regression equation relating el astic modulus to creep coefficient at 91 days is given as follows: c cE91 (73) Where is equal to 4.55 107 and equal to 3.725; cE is in unit of psi. PAGE 186 187 The equation related creep coefficient at 91 da ys to the ratio of co mpressive strength to elastic modulus is given as follows: c c cE f' 91 (74) With equal to 1132 and equal to 3.485. Among these regression equations, E quation 72 gave the best prediction. (8) Ultimate creep coefficient of some of the concretes appeared to exceed 2.0. These concrete mixtures included Mix2F, Mix3F, Mix4F, Mix5S, Mix6S, Mix7S, Mix8S, Mix2GF, Mix3GF, Mi x5GS and Mix7GS. (9) CEBFIP model (as shown in Equation 717) ap peared to give better prediction on the creep behaviors of concretes investigated in this study than ACI 209 model (as shown in Equation725). PAGE 187 188 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Design of Creep Apparatus Perform ance and characteristics of creep appara tus designed for this st udy are presented as follows: 1) The creep apparatus designed in this study is capable of applying and maintaining a load up to 145,000lbs on the test specimens w ith an error of less than 2%. 2) Three specimens can be stacked for simultaneous loading. 3) When a maximum load of 145,000lbs is applied, the deflection of bearing surfaces of the header plates is less than 0.001in, and th e pressure distributio n on the test specimen varies by less than 0.026%, or 1.5psi. 4) The creep testing procedures developed in this study was foun d to work very well. They are given in detail in Section 4.3. 8.2 Findings from This Study 8.2.1 Strength and Elastic Modulus 1) Splitting tensile strengths of the concre te m ixtures using granite aggregate were significantly lower than thos e using Miami Oolite limestone aggregate. This is due probably to the poor bonding condition betw een hardened cement paste and granite aggregate. 2) Compressive strengths of c oncretes with granite aggregate were comparable to or lower than those of concretes with Miami Oolite limestone aggregate. 3) The concrete with granite aggregate had hi gher elastic modulus than that with Miami Oolite limestone aggregate, while the lightweight aggregate concretes had lower elastic modulus than the normal weight concretes. 4) Fly ash concretes develop compressive strength and splitting tensile st rength at a slower rate than the slag concretes. Fly ash conc rete shows significant strength gain after 28 days, while this was not seen fr om the slag concrete mixtures. 5) The ACI 209 Equation for prediction of compressive strength () ('tfc) at various curing age from compressive strength at 28 days ( )(' 28tfc), which is given as follows, was modified to give better strength prediction fo r the various mixtures. PAGE 188 189 28 85.00.4 )( c f t t t c f The modified equation has the following form for the concrete with different coarse aggregates: 28 )( c f t t t c f The value of was found to vary from 1.1 to 2.6 for the concretes with Miami Oolite limestone aggregate, from 2.6 to 5.3 for th e concretes with Georgia granite aggregate, and from 4.2 to 6.7 for lightweight aggregate concretes; the value of was found to vary from 0.82 to 0.93 for the concretes with Miam i Oolite limestone aggregate, from 0.82 to 0.89 for the concrete with Georgia granite aggregate, and from 0.74 to 0.82 for lightweight aggregate co ncrete in this study. 6) The relationship between compressive strength (' cf ) and splitting tensile strength (ctf ) is established for the concrete mixtures investigated in this study. The Carino and Lew model, given as follows, 73.0 c f ct f was modified to the following equation: 7185.0 c f ct f Where cf and ctf are in units of psi. 7) The relationship between compressive strength and modulus of elasticity was refined in this study using Least Square of Curvefitting Technique. The ACI 31889 Equation, which is '57000cf c E was modified to the following equation: cf c E Where is equal to 55,949 for Miami Oolite lim estone aggregate; 62,721 for Georgia granite aggregate; and 43,777 for Stalite lightweight aggregate. cf and cE are in units of psi. 8) For all three aggregate t ypes investigated in this study, a modified ACI 31895 prediction equation was developed: 484200 16.30'5.1cfw E Where w is the density of c oncrete in pound per cubit foot. cf and cE are in units of psi. PAGE 189 190 8.2.2 Shrinkage Characteristic s of Concretes I nvestigated 1) Fly ash concrete mixtures had slightly hi gher shrinkage strain at 91 days than slag concretes. This is due probably to the slow hydration rate of fly ash in comparison with that of slag. As a result of slower rate of hydration, there is more free water evaporating from the interior of the concrete, which can cause the concrete to shrink more. Thus, it is recommended that using a longer wet curing time would be helpful to reduce shrinkage of fly ash concrete. 2) Water content has a significant effect on dryi ng shrinkage strain of concrete. The higher the water content, the more the concrete tends to shrink. However, no clear trend can be seen on the effects of water to cementitious materials ratio on shrinkage of concrete. 3) For the four concrete mixtures with Georgia granite aggregate, shrinkage strain is slightly lower than the four corresponding concrete mixtures with Miami Oolite limestone aggregate. Lightweight aggregate concrete shrinks more than normal weight aggregate concrete. This might be explained by their difference in elastic modulus. The concrete with a higher elastic modulus would have a st ronger resistance to the movement caused by shrinkage of cement paste. 4) For the concretes tested, there appeared to be a relations hip between the compressive strength (' cf ) at the age when shrinkage test wa s started and the shrinkage strain (sh ) at 91 days as follows: '0001.0 0005.0cf e sh Where cf is in unit of psi. 5) For the concretes tested, ther e appeared to be a relations hip between elastic modulus (cE ) at the age when shrinkage test was started and the shrinkage strain (sh ) at 91 days as follows: c shE e 7102 0007.0 Where cE is in unit of psi. 6) According to the shrinkage test results from this study, the C.E.BF.I.P model (as shown in Equation 66) appeared to give better prediction than the ACI 209 model (as shown in Equation 63). Using ACI 209 model may resu lt in overestimation of the ultimate shrinkage strain. 7) For the concrete investigated in this study, the ultimate shrinkage strain ranged from 1.93104 to 3.64 104 for the concretes with Miami Oolite limestone aggregate; from 2.18104 to 2.83 104 for the concretes with Georgia granite aggregate; and from 3.49104 to 4.22 104 for the concretes with Stalite lightweight aggregate concrete. PAGE 190 191 8.2.3 Creep Characteristics of Concretes Investigated 1) Curing condition has som e effects on creep of fly ash concrete and lightweight aggregate concrete, while its effect on slag concrete is very small. 2) For the stress levels used (40 and 50% of compressive strength) the measured creep strain and instantaneous strain were linearly proportional to the stress applied. Thus, the computed creep coefficients were not aff ected by the stress le vel in this study. 3) Water to cementitious materials ratio has some effects on creep behavior of concrete. The higher the water to cementitious materials ratio, the more the concrete creeps. 4) For the concrete with identical water to cem entitious materials ratio, the higher the air content of fresh concrete, the more the concrete creeps. 5) The concretes with granite aggregate creeps slightly higher than the concretes with Miami Oolite limestone aggregate and lightweig ht aggregate under the same stress level. However, due to the much lower elastic modul us of lightweight a ggregate concrete, the creep coefficient of lightweight aggregate co ncrete is much lower than that of normal weight aggregate concrete. Due to the hi gher elastic modulus of granite aggregate concrete, creep coefficient of granite concrete was much higher than that of the concretes with Miami Oolite limestone aggregate. 6) A simple linear relationship was established between compressive strength at loading age and creep strain at 91 days. 7) A linear relationship was also found betw een creep coefficient at 91 days and compressive strength (' cf ), elastic modulus (cE ), and the ratio of compressive strength and elastic modulus. The regression equation, which relates compressive strength at loading age to creep coefficient at 91 days (91 c ) is given as follows: 91 c cf (72) Where is equal to 2.03 104 and equal to 3.042. And' cf is in unit of psi. The regression equation, which relates elastic modulus to creep coefficient at 91 days is given as follows: c cE91 (73) Where is equal to 4.55 107 and equal to 3.725. And cE is in unit of psi. The equation related creep coefficient at 91 da ys to the ratio of co mpressive strength to elastic modulus is given as follows: PAGE 191 192 c c cE f' 91 (74) With equal to 1132 and equal to 3.485. Among these regression equations, Equati on 72 gave the best prediction. 8) Ultimate creep coefficient of some of the concretes appeared to exceed 2.0. These concrete mixtures included Mix2F, Mix3F, Mix4F, Mix5S, Mix6S, Mix7S, Mix8S, Mix2GF, Mix3GF, Mi x5GS and Mix7GS. 9) CEBFIP model (as shown in Equation 717) ap peared to give better prediction on the creep behaviors of concretes investigated in this study than ACI 209 model (as shown in Equation725). 8.3 Recommendations Based on this study, the f ollowing recomme ndations are given for the further study: 1) Study on effects of aggregate gradation on sh rinkage and creep of concrete. Since the gradation of aggregate has a great effect on the compressive st rength of concrete [A.M.Neville, 1996] [Larry C. Muszynski et al, 1997] and compressive strength was found to be related to shrinkage and creep in this study, the effects of aggregate gradation on shrinkage and creep behavior of concrete should be studie d in order to have a better understanding of this factor on sh rinkage and creep of concrete. 2) Study on the optimization of mix proportion. The optimization of mix proportion should be studied to reduce shrinka ge and creep of concrete. 3) Study on the interfacial characte ristics between coarse aggr egate and mortar paste in order to have a better interpretation on the e ffects of different aggr egate types on strength of concrete. 4) Study on rheological properties of concrete unde r sustained load in order to have a better understanding about the creep behavior of concrete. PAGE 192 193 APPENDIX A MEASUREMENTS FROM STRENGTH TESTS PAGE 193 194Table A1 Results of compre ssive strength tests (psi) Age of Testing (days) 3 7 14 28 56 91 No. of mix 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1F 8018 8091 8123 8556 8554 8607 8929 8869 9182 9319 9811 9479 10665 10799 10847 11123 11302 11376 2F 4110 4195 3927 4660 4680 4635 6053 6032 5999 6499 6268 6752 6661 6604 6648 7631 7582 7609 3F 5325 5424 5118 6448 6449 6512 7475 7649 7578 8229 8147 8349 8479 8400 8468 9415 9496 9366 4F 5669 5783 5684 7075 6762 6922 7224 7208 6910 7038 7509 7160 8668 8994 9325 9273 9072 9467 5S 5351 5772 5539 7059 7739 6908 7995 8208 8541 8684 8924 8888 9071 9255 9092 9348 9615 9406 6S 6300 6402 6423 7776 7316 8004 8211 8481 8169 8684 9127 9223 9604 9540 9593 9779 9734 9770 7S 4323 4482 4166 5311 5435 5375 5993 5902 5886 6346 6441 6389 6773 6812 6798 6990 6837 6923 8S 4415 5017 4954 5831 6202 6308 6879 6967 6971 7544 7282 7749 7856 8253 8249 8262 8148 8214 9LF 3019 3007 3092 3911 3939 3974 5039 5174 5194 5981 5999 5806 6655 6953 6462 7043 7092 6750 10LS 1486 1411 1504 2175 2310 2088 2749 2860 3201 3760 3811 3660 4496 4204 4236 4863 4725 4595 2GF 3982 3867 3807 4922 5046 4888 5874 5812 5735 6440 6388 6579 6887 7001 6969 7387 6909 7308 3GF 2960 2865 3099 4810 4612 4655 5468 5778 5829 6816 7075 7134 7818 7801 7943 7862 7915 8105 5GF 3746 3861 3847 5098 5211 5145 6196 6087 6127 7000 7409 7377 7895 7683 7769 8047 8090 7986 7GF 2249 2205 2346 4433 4178 4298 5308 5182 5175 6601 6603 6632 7072 6629 7176 7226 7200 7273 PAGE 194 195Table A2 Normalized compressive streng th development characteristics of th e concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag 3 7 14 28 56 91 Mix1F 0.24 20% 0.72 0.76 0.80 0.85/0.93* 0.96 1 Mix2F 0.33 20% 0.54 0.61 0.79 0.86/0.87* 0.90 1 Mix3F 0.41 20% 0.56 0.69 0.80 0.87/0.85* 0.90 1 Mix4F 0.37 20% 0.62 0.75 0.77 0.78/0.87* 0.97 1 Mix5S 0.33 50% 0.59 0.77 0.87 0.93/0.99* 0.97 1 Mix6S 0.36 50% 0.66 0.80 0.89 0.94/0.95* 0.99 1 Mix7S 0.41 70% 0.63 0.78 0.86 0.92/0.93* 0.98 1 Mix8S 0.44 50% 0.58 0.74 0.85 0.92/0.92* 0.99 1 Mix9LF 0.31 20% 0.44 0.57 0.74 0.85/0.84* 0.96 1 Mix10LS 0.39 60% 0.31 0.46 0.62 0.79/0.85* 0.91 1 Mix2GF 0.33 20% 0.54 0.69 0.81 0.90 0.97 1 Mix3GF 0.41 20% 0.47 0.64 0.76 0.90 0.97 1 Mix5GS 0.33 50% 0.37 0.58 0.70 0.86 0.97 1 Mix7GS 0.41 70% 0.31 0.59 0.72 0.91 0.93 1 Note: Data from the replication tests. PAGE 195 196Table A3 Results of splitting tensile strength tests (psi) Age of Testing (days) 3 7 14 28 56 91 No. of Mix 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1F 621 573 582 657 613 614 673 768 706 823 794 770 833 826 844 863 834 851 2F 397 428 401 501 484 468 551 521 515 545 542 539 650 596 617 675 645 658 3F 503 527 510 550 502 568 579 541 567 644 620 608 678 673 671 740 722 731 4F 480 434 459 604 440 517 581 455 663 678 684 647 776 737 764 796 748 766 5S 492 429 405 567 557 599 724 507 677 757 615 697 716 704 713 748 772 695 6S 607 523 580 633 586 589 616 755 575 696 658 663 711 654 707 728 708 719 7S 430 415 434 467 476 475 553 509 493 567 604 473 489 657 625 572 602 616 8S 324 383 409 428 512 557 555 530 564 617 603 681 702 691 686 696 709 704 9LF 283 369 399 425 350 438 470 460 416 472 486 512 563 549 542 579 601 552 10LS 211 203 222 316 295 253 366 351 376 413 404 400 433 401 420 444 433 414 2GF 350 340 366 425 429 408 518 446 502 541 557 535 557 550 539 585 606 595 3GF 283 288 276 433 411 417 442 522 422 521 508 547 516 646 611 617 646 684 5GS 364 410 372 381 391 456 507 509 494 563 564 553 621 600 578 652 642 659 7GS 234 258 245 363 353 371 411 418 460 540 582 515 566 623 607 555 584 593 PAGE 196 197Table A4 Normalized Splitting tensile st rength development characteristics of the concrete mixtures evaluated (psi) Age of Testing (days) Mix Number W/C Fly ash Slag 3 7 14 28 56 91 Mix1F 0.24 20% 0.70 0.74 0.84 0.94/0.86* 0.98 1.00 Mix2F 0.33 20% 0.62 0.73 0.80 0.82/0.87* 0.94 1.00 Mix3F 0.41 20% 0.70 0.74 0.77 0.850.83* 0.92 1.00 Mix4F 0.37 20% 0.59 0.68 0.74 0.87/0.80* 0.99 1.00 Mix5S 0.33 50% 0.60 0.78 0.86 0.93/0.92* 0.96 1.00 Mix6S 0.36 50% 0.79 0.84 0.90 0.94/0.87* 0.96 1.00 Mix7S 0.41 70% 0.71 0.79 0.87 0.92/0.87* 0.99 1.00 Mix8S 0.44 50% 0.53 0.71 0.78 0.90/0.93* 0.99 1.00 Mix9LF 0.31 20% 0.61 0.70 0.78 0.85/0.88* 0.95 1.00 Mix10LS 0.39 60% 0.49 0.67 0.85 0.94/0.82* 0.97 1.00 Mix2GF 0.33 20% 0.59 0.71 0.82 0.89 0.92 1.00 Mix3GF 0.41 20% 0.59 0.63 0.77 0.86 0.92 1.00 Mix5GS 0.33 50% 0.43 0.65 0.71 0.81 0.91 1.00 Mix7GS 0.41 70% 0.42 0.63 0.75 0.87 0.96 1.00 Note: Data from the replication tests PAGE 197 198Table A5 Results of elastic modulus tests ( 106psi) Age of Testing (days) 3 7 14 28 56 91 No. of Mix 1 2 1 2 1 2 1 2 1 2 1 2 1F 4.71 4.77 4.92 4.94 5.20 5.25 5.37 5.43 5.56 5.52 5.57 5.59 2F 3.47 3.38 3.72 3.82 4.11 4.04 4.28 4.34 4.46 4.40 4.77 4.50 3F 4.37 4.42 4.87 4.83 5.02 5.07 5.08 5.19 5.38 5.18 5.66 5.73 4F 4.50 4.47 4.63 4.59 4.85 4.90 4.98 5.03 5.16 5.14 5.33 5.25 5S 4.11 4.11 4.53 4.78 4.86 4.89 5.06 5.12 5.19 5.26 5.23 5.22 6S 4.42 4.11 4.97 4.86 5.08 5.28 5.23 5.67 5.48 5.75 5.54 5.78 7S 3.99 3.80 4.30 4.30 4.53 4.51 4.59 4.61 4.75 4.71 4.78 4.74 8S 3.87 4.04 4.43 4.35 4.90 4.78 5.02 4.98 5.14 5.12 5.16 5.15 9LF 2.71 2.81 2.94 2.90 3.16 3.10 3.29 3.25 3.34 3.36 3.69 3.31 10LS 1.77 1.73 2.01 1.74 2.40 2.32 2.73 2.65 3.07 2.94 2.98 3.09 3GF 3.61 3.99 4.10 4.33 4.59 4.63 4.85 5.07 5.17 5.06 5.25 5.12 4GF 4.08 4.21 4.28 4.95 5.56 5.48 5.62 5.59 5.83 6.03 5.95 5.97 5GS 3.24 3.06 3.66 3.97 4.54 4.76 5.42 4.92 5.48 5.26 5.47 5.64 7GS 2.63 2.74 3.28 3.48 4.05 4.14 5.17 5.33 5.64 5.56 5.77 5.68 PAGE 198 199 APPENDIX B MEASURED AND CALCULATED RESULTS FROM CREEP TESTS PAGE 199 200Table B1 Measured and calcula ted results from creep tests Age of testing (days) No. of Mix Curing condition Load level Strain 3 7 14 28 56 91 Total 0.001160 0.001240 0.001330 0.001460 0.001600 0.001700 Shrinkage 0.000021 0.000043 0.000076 0.000120 0.000160 0.000200 Elastic 0.000716 0.000716 0.000716 0.000716 0.000716 0.000716 Creep 0.000430 0.000480 0.000540 0.000620 0.000720 0.000780 Creep coefficient 0.60 0.68 0.76 0.87 1.00 1.10 40% Creep modulus 3.44E+06 3.16E+06 3.07E+06 2.88E+06 2.65E+06 2.52E+06 Total 0.001310 0.001420 0.001520 0.001660 0.001840 0.001970 Shrinkage 0.000021 0.000043 0.000076 0.000120 0.000160 0.000200 Elastic 0.000804 0.000804 0.000804 0.000804 0.000804 0.000804 Creep 0.000450 0.000530 0.000610 0.000700 0.000840 0.000930 Creep coefficient 0.54 0.64 0.72 0.84 1.00 1.13 7day moist cure 50% Creep modulus 3.32E+06 3.24E+06 3.02E+06 2.84E+06 2.65E+06 2.52E+06 Total 0.001070 0.001150 0.001230 0.001340 0.001450 0.001550 Shrinkage 0.000014 0.000033 0.000063 0.000100 0.000140 0.000170 Elastic 0.000760 0.000760 0.000760 0.000760 0.000760 0.000760 Creep 0.000290 0.000350 0.000400 0.000470 0.000550 0.000620 Creep coefficient 0.38 0.46 0.53 0.62 0.72 0.81 40% Creep modulus 3.78E+06 3.58E+06 3.44E+06 3.26E+06 3.06E+06 2.84E+06 Total 0.001250 0.001340 0.001420 0.001530 0.001660 0.001760 Shrinkage 0.000014 0.000033 0.000063 0.000100 0.000140 0.000170 Creep 0.000350 0.000420 0.000480 0.000550 0.000640 0.000710 Elastic 0.000880 0.000880 0.000880 0.000880 0.000880 0.000880 Creep coefficient 0.40 0.48 0.54 0.62 0.73 0.81 1F 14day moist cure 50% Creep modulus 3.71E+06 3.51E+06 3.35E+06 3.16E+06 2.98E+06 2.92E+06 PAGE 200 201 Table B1. Continued Total 0.001141 0.001313 0.0015 0.001724 0.001961 0.002115 Shrinkage 0.000051 0.000097 0.000154 0.000210 0.000261 0.000286 Elastic 0.000663 0.000663 0.000663 0.000663 0.000663 0.000663 Creep 0.000427 0.000553 0.000683 0.000851 0.001037 0.001166 Creep coefficient 0.64 0.83 1.16 1.28 1.56 1.76 40% Creep Modulus 2.21E+06 1.98E+06 1.80E+06 1.61E+06 1.46E+06 1.37E+06 Total 0.001471 0.001614 0.001811 0.002057 0.002306 0.002471 Shrinkage 0.000051 0.000097 0.000154 0.000210 0.000261 0.000286 Elastic 0.000803 0.000803 0.000803 0.000803 0.000803 0.000803 Creep 0.000617 0.000714 0.000854 0.001044 0.001242 0.001382 Creep coefficient 0.77 0.89 1.07 1.30 1.55 1.72 7day moist cure 50% Creep Modulus 2.10E+06 1.97E+06 1.80E+06 1.59E+06 1.42E+06 1.32E+06 Total 0.001114 0.001244 0.00139 0.001601 0.001834 0.001955 Shrinkage 0.000031 0.000069 0.000112 0.000173 0.000233 0.000258 Elastic 0.000669 0.000669 0.000669 0.000669 0.000669 0.000669 Creep 0.000414 0.000506 0.000609 0.000759 0.000932 0.001028 Creep coefficient 0.62 0.76 0.91 1.13 1.39 1.54 40% Creep Modulus 2.45E+06 2.28E+06 2.09E+06 1.85E+06 1.66E+06 1.55E+06 Total 0.001385 0.001557 0.00176 0.001972 0.002232 0.002398 Shrinkage 0.000031 0.000069 0.000112 0.000173 0.000233 0.000258 Elastic 0.000842 0.000842 0.000842 0.000842 0.000842 0.000842 Creep 0.000512 0.000646 0.000806 0.000957 0.001157 0.001298 Creep coefficient 0.61 0.77 0.96 1.14 1.37 1.54 2F 14day moist cure 50% Creep Modulus 2.45E+06 2.23E+06 2.02E+06 1.85E+06 1.66E+06 1.55E+06 PAGE 201 202 Table B1. Continued Total 0.001032 0.001165 0.001318 0.001477 0.001669 0.001796 Shrinkage 0.000040 0.000073 0.000124 0.000177 0.000221 0.000248 Elastic 0.000609 0.000609 0.000609 0.000609 0.000609 0.000609 Creep 0.000383 0.000483 0.000585 0.000691 0.000839 0.000939 Creep coefficient 0.61 0.77 0.93 1.10 1.33 1.49 40% Creep modulus 3.05E+06 2.77E+06 2.53E+06 2.33E+06 2.09E+06 1.96E+06 Total 0.001221 0.00139 0.001575 0.001764 0.00199 0.002132 Shrinkage 0.000040 0.000073 0.000124 0.000177 0.000221 0.000248 Elastic 0.000751 0.000751 0.000751 0.000751 0.000751 0.000751 Creep 0.000430 0.000566 0.000700 0.000836 0.001018 0.001133 Creep coefficient 0.57 0.75 0.93 1.11 1.36 1.51 7day moist cure 50% Creep modulus 3.20E+06 2.87E+06 2.61E+06 2.38E+06 2.14E+06 2.01E+06 Total 0.000957 0.001093 0.001217 0.001381 0.001557 0.001686 Shrinkage 0.000021 0.000047 0.000087 0.000137 0.000182 0.000217 Elastic 0.000633 0.000633 0.000633 0.000633 0.000633 0.000633 Creep 0.000303 0.000413 0.000497 0.000611 0.000742 0.000836 Creep coefficient 0.48 0.65 0.79 0.97 1.17 1.32 40% Creep modulus 3.52E+06 3.15E+06 2.92E+06 2.76E+06 2.41E+06 2.27E+06 Total 0.001254 0.001389 0.001537 0.001700 0.001890 0.002023 Shrinkage 0.000021 0.000047 0.000087 0.000137 0.000182 0.000217 Elastic 0.000776 0.000776 0.000776 0.000776 0.000776 0.000776 Creep 0.000457 0.000566 0.000674 0.000787 0.000932 0.001030 Creep coefficient 0.59 0.73 0.87 1.01 1.20 1.33 3F 14day moist cure 50% Creep modulus 3.34E+06 3.07E+06 2.84E+06 2.72E+06 2.41E+06 2.27E+06 PAGE 202 203 Table B1. Continued Total 0.001060 0.001200 0.001340 0.001510 0.001680 0.001810 Shrinkage 0.000037 0.000073 0.000120 0.000170 0.000230 0.000270 Elastic 0.000600 0.000600 0.000600 0.000600 0.000600 0.000600 Creep 0.000420 0.000530 0.000630 0.000740 0.000850 0.000940 Creep coefficient 0.71 0.89 1.05 1.24 1.42 1.57 40% Creep modulus 2.95E+06 2.68E+06 2.47E+06 2.28E+06 2.09E+06 1.98E+06 Total 0.001400 0.001523 0.001642 0.001804 0.001984 0.002120 Shrinkage 0.000037 0.000073 0.000120 0.000170 0.000230 0.000270 Elastic 0.000703 0.000703 0.000703 0.000703 0.000703 0.000703 Creep 0.00066 0.000747 0.000819 0.000931 0.001051 0.001147 Creep coefficient 0.94 1.06 1.17 1.32 1.50 1.63 7day moist cure 50% Creep modulus 2.79E+06 2.52E+06 2.32E+06 2.13E+06 1.96E+06 1.85E+06 Total 0.001078 0.001166 0.001259 0.001386 0.001543 0.001654 Shrinkage 0.000021 0.000042 0.000080 0.000132 0.000186 0.000223 Elastic 0.000571 0.000571 0.000571 0.000571 0.000571 0.000571 Creep 0.000486 0.000553 0.000608 0.000683 0.000786 0.000860 Creep coefficient 0.85 0.97 1.06 1.20 1.38 1.51 40% Creep modulus 3.90E+06 2.68E+06 2.47E+06 2.31E+06 2.09E+06 1.98E+06 Total 0.001208 0.001361 0.001518 0.001699 0.001886 0.002020 Shrinkage 0.000021 0.000042 0.000080 0.000132 0.000186 0.000223 Elastic 0.000702 0.000702 0.000702 0.000702 0.000702 0.000702 Creep 0.000485 0.000617 0.000736 0.000865 0.000998 0.001095 Creep coefficient 0.69 0.88 1.05 1.23 1.42 1.56 4F 14day moist cure 50% Creep modulus 3.90E+06 2.68E+06 2.47E+06 2.30E+06 2.09E+06 1.98E+06 PAGE 203 204 Table B1. Continued Total 0.001168 0.001299 0.001423 0.001587 0.001744 0.00184 Shrinkage 0.000044 0.000088 0.000130 0.000170 0.000201 0.000216 Elastic 0.000669 0.000669 0.000669 0.000669 0.000669 0.000669 Creep 0.000455 0.000542 0.000624 0.000748 0.000874 0.000955 Creep coefficient 0.409 0.580 0.683 1.101 1.320 1.476 40% Creep modulus 2.99E+06 2.69E+06 2.49E+06 2.28E+06 2.09E+06 1.98E+06 Total 0.001455 0.00162 0.001783 0.001977 0.002175 0.002299 Shrinkage 0.000044 0.000088 0.000130 0.000170 0.000201 0.000216 Elastic 0.000846 0.000846 0.000846 0.000846 0.000846 0.000846 Creep 0.000565 0.000686 0.000807 0.000961 0.001128 0.001237 Creep coefficient 0.67 0.81 0.95 1.14 1.33 1.46 7day moist cure 50% Creep modulus 2.99E+06 2.69E+06 2.49E+06 2.28E+06 2.09E+06 1.98E+06 Total 0.001222 0.001323 0.001439 0.001594 0.001747 0.001834 Shrinkage 0.000043 0.000074 0.000110 0.000149 0.000178 0.000193 Elastic 0.000718 0.000718 0.000718 0.000718 0.000718 0.000718 Creep 0.000461 0.000531 0.000611 0.000727 0.000851 0.000923 Creep coefficient 0.64 0.74 0.85 1.01 1.19 1.29 40% Creep modulus 3.00E+06 2.79E+06 2.60E+06 2.38E+06 2.19E+06 2.11E+06 Total 0.001464 0.001596 0.001747 0.001937 0.002118 0.002212 Shrinkage 0.000043 0.000074 0.000110 0.000149 0.000178 0.000193 Elastic 0.000889 0.000889 0.000889 0.000889 0.000889 0.000889 Creep 0.000532 0.000633 0.000748 0.000899 0.001051 0.001130 Creep coefficient 0.62 0.74 0.87 1.04 1.22 1.31 5S 14day moist cure 50% Creep modulus 2.99E+06 2.79E+06 2.60E+06 2.38E+06 2.19E+06 2.11E+06 PAGE 204 205 Table B1. Continued Total 0.000975 0.001105 0.001255 0.001405 0.001600 0.001758 Shrinkage 0.000042 0.000082 0.000123 0.000157 0.000183 0.000196 Elastic 0.000670 0.000670 0.000670 0.000670 0.000670 0.000670 Creep 0.000263 0.000353 0.000462 0.000588 0.000747 0.000892 Creep coefficient 0.39 0.54 0.70 0.90 1.15 1.34 40% Creep modulus 3.58E+06 3.22E+06 2.91E+06 2.65E+06 2.38E+06 2.36E+06 Total 0.001194 0.001391 0.001550 0.001707 0.001901 0.002048 Shrinkage 0.000042 0.000082 0.000123 0.000157 0.000183 0.000196 Elastic 0.000837 0.000837 0.000837 0.000837 0.000837 0.000837 Creep 0.000325 0.000472 0.000570 0.000713 0.000891 0.001015 Creep coefficient 0.41 0.54 0.69 0.87 1.08 1.25 7day moist cure 50% Creep modulus 3.54E+06 3.15E+06 2.89E+06 2.62E+06 2.31E+06 2.30E+06 Total 0.001037 0.001164 0.001291 0.001448 0.001648 0.001796 Shrinkage 0.000038 0.000076 0.000114 0.000141 0.000163 0.000177 Elastic 0.000692 0.000692 0.000692 0.000692 0.000692 0.000692 Creep 0.000307 0.000396 0.000485 0.000615 0.000793 0.000927 Creep coefficient 0.43 0.57 0.71 0.89 1.11 1.27 40% Creep modulus 3.70E+06 3.40E+06 3.15E+06 2.87E+06 2.56E+06 2.21E+06 Total 0.001263 0.001467 0.001567 0.001727 0.001941 0.002104 Shrinkage 0.000038 0.000076 0.000114 0.000141 0.000163 0.000177 Elastic 0.000854 0.000854 0.000854 0.000854 0.000854 0.000854 Creep 0.000371 0.000537 0.000599 0.000732 0.000924 0.001073 Creep coefficient 0.44 0.57 0.70 0.87 1.06 1.21 6S 14day moist cure 50% Creep modulus 3.69E+06 3.35E+06 3.12E+06 2.85E+06 2.51E+06 2.10E+06 PAGE 205 206 Table B1. Continued Total 0.000907 0.001094 0.001264 0.001399 0.001561 0.001656 Shrinkage 0.000039 0.000080 0.000126 0.000170 0.000202 0.000223 Elastic 0.000519 0.000519 0.000519 0.000519 0.000519 0.000519 Creep 0.000349 0.000495 0.000619 0.00071 0.00084 0.000914 Creep coefficient 0.67 0.95 1.19 1.37 1.62 1.76 40% Creep modulus 2.66E+06 2.33E+06 2.11E+06 1.92E+06 1.74E+06 1.65E+06 Total 0.001101 0.001285 0.001486 0.001664 0.001836 0.001941 Shrinkage 0.000039 0.000080 0.000126 0.000170 0.000202 0.000223 Elastic 0.000616 0.000616 0.000616 0.000616 0.000616 0.000616 Creep 0.000446 0.000589 0.000744 0.000878 0.001018 0.001102 Creep coefficient 0.72 0.96 1.21 1.43 1.65 1.79 7day moist cure 50% Creep modulus 2.78E+06 2.45E+06 2.17E+06 1.98E+06 1.81E+06 1.72E+06 Total 0.000948 0.001081 0.001209 0.001384 0.001556 0.001651 Shrinkage 0.000038 0.000073 0.000111 0.000148 0.000183 0.000204 Elastic 0.000546 0.000546 0.000546 0.000546 0.000546 0.000546 Creep 0.000364 0.000462 0.000552 0.00069 0.000827 0.000901 Creep coefficient 0.67 0.85 1.01 1.26 1.51 1.65 40% Creep modulus 2.84E+06 2.57E+06 2.36E+06 2.09E+06 1.89E+06 1.79E+06 Total 0.001160 0.001308 0.001466 0.001646 0.001821 0.001921 Shrinkage 0.000038 0.000073 0.000111 0.000148 0.000183 0.000204 Elastic 0.000643 0.000643 0.000643 0.000643 0.000643 0.000643 Creep 0.000479 0.000592 0.000712 0.000855 0.000995 0.001074 Creep coefficient 0.74 0.92 1.11 1.33 1.55 1.67 7S 14day moist cure 50% Creep modulus 2.78E+06 2.52E+06 2.30E+06 2.08E+06 1.90E+06 1.82E+06 PAGE 206 207 Table B1. Continued Total 0.001131 0.001263 0.001409 0.000157 0.001762 0.001914 Shrinkage 0.000073 0.000123 0.000161 0.000194 0.000228 0.000250 Elastic 0.000614 0.000614 0.000614 0.000614 0.000614 0.000614 Creep 0.000443 0.000526 0.000633 0.000761 0.000920 0.001050 Creep coefficient 0.72 0.86 1.03 1.24 1.50 1.71 40% Creep modulus 2.71E+06 2.53E+06 2.34E+06 2.04E+06 1.82E+06 1.68E+06 Total 0.001296 0.001438 0.001606 0.001821 0.002048 0.002227 Shrinkage 0.000073 0.000123 0.000161 0.000194 0.000228 0.000250 Elastic 0.000722 0.000722 0.000722 0.000722 0.000722 0.000722 Creep 0.000500 0.000592 0.000722 0.000904 0.001098 0.001254 Creep coefficient 0.69 0.82 1.00 1.25 1.52 1.74 7day moist cure 50% Creep modulus 2.56E+06 2.38E+06 2.17E+06 1.97E+04 1.77E+06 1.63E+06 Total 0.001140 0.001262 0.001394 0.001549 0.001733 0.001889 Shrinkage 0.000050 0.000098 0.000136 0.000169 0.000202 0.000230 Elastic 0.000654 0.000654 0.000654 0.000654 0.000654 0.000654 Creep 0.000436 0.000510 0.000604 0.000726 0.000877 0.001004 Creep coefficient 0.67 0.78 0.92 1.11 1.34 1.53 40% Creep modulus 2.92E+06 2.68E+06 2.51E+06 2.26E+06 2.02E+06 1.87E+06 Total 0.001374 0.001524 0.001677 0.001881 0.002118 0.002294 Shrinkage 0.000050 0.000098 0.000136 0.000169 0.000202 0.000230 Elastic 0.000831 0.000831 0.000831 0.000831 0.000831 0.000831 Creep 0.000493 0.000596 0.000710 0.000881 0.001084 0.001233 Creep coefficient 0.59 0.72 0.85 1.06 1.30 1.48 8S 14day moist cure 50% Creep modulus 2.71E+06 2.53E+06 2.34E+06 2.14E+06 1.93E+06 1.78E+06 PAGE 207 208 Table B1. Continued Total 0.001118 0.001231 0.001380 0.001528 0.001684 0.001792 Shrinkage 0.000049 0.000096 0.000162 0.000226 0.000288 0.000322 Elastic 0.000626 0.000626 0.000626 0.000626 0.000626 0.000626 Creep 0.000443 0.000510 0.000592 0.000677 0.000771 0.000844 Creep coefficient 0.71 0.82 0.95 1.08 1.23 1.35 40% Creep modulus 1.99E+06 1.85E+06 1.74E+06 1.62E+06 1.51E+06 1.43E+06 Total 0.001337 0.001487 0.001642 0.001811 0.001987 0.002112 Shrinkage 0.000049 0.000096 0.000162 0.000226 0.000288 0.000322 Elastic 0.000767 0.000767 0.000767 0.000767 0.000767 0.000767 Creep 0.000521 0.000624 0.000713 0.000819 0.000932 0.001023 Creep coefficient 0.68 0.81 0.93 1.07 1.22 1.33 7day moist cure 50% Creep modulus 1.92E+06 1.81E+06 1.69E+06 1.58E+06 1.47E+06 1.40E+06 Total 0.001169 0.001272 0.001392 0.001507 0.001633 0.001714 Shrinkage 0.000046 0.000081 0.000137 0.000189 0.000239 0.000276 Elastic 0.000677 0.000677 0.000677 0.000677 0.000677 0.000677 Creep 0.000447 0.000514 0.000579 0.000641 0.000718 0.000762 Creep coefficient 0.66 0.76 0.86 0.95 1.06 1.13 40% Creep modulus 2.29E+06 2.12E+06 2.00E+06 1.91E+06 1.79E+06 1.72E+06 Total 0.001297 0.001433 0.001564 0.001691 0.001836 0.001940 Shrinkage 0.000046 0.000081 0.000137 0.000189 0.000239 0.000276 Elastic 0.000777 0.000777 0.000777 0.000777 0.000777 0.000777 Creep 0.000474 0.000576 0.000651 0.000726 0.000820 0.000888 Creep coefficient 0.61 0.74 0.84 0.93 1.06 1.14 9LF 14day moist cure 50% Creep modulus 2.21E+06 2.08E+06 1.98E+06 1.88E+06 1.79E+06 1.72E+06 PAGE 208 209 Table B1. Continued Total 0.001206 0.001314 0.001433 0.001559 0.001694 0.001789 Shrinkage 0.000070 0.000130 0.000198 0.000260 0.000319 0.000360 Elastic 0.000546 0.000546 0.000546 0.000546 0.000546 0.000546 Creep 0.000590 0.000639 0.000690 0.000753 0.000830 0.000883 Creep coefficient 1.08 1.17 1.26 1.38 1.52 1.62 40% Creep modulus 1.16E+06 1.10E+06 1.04E+06 0.97E+06 0.92E+06 0.88E+06 Total 0.001517 0.001648 0.001780 0.001939 0.002098 0.002224 Shrinkage 0.000070 0.000130 0.000198 0.000260 0.000319 0.000360 Elastic 0.000721 0.000721 0.000721 0.000721 0.000721 0.000721 Creep 0.000726 0.000797 0.000861 0.000958 0.001058 0.001143 Creep coefficient 1.01 1.10 1.19 1.33 1.47 1.59 7day moist cure 50% Creep modulus 1.03E+06 0.99E+06 0.95E+06 0.90E+06 0.85E+06 0.82E+06 Total 0.000874 0.000898 0.000941 0.000997 0.001062 0.001116 Shrinkage 0.000038 0.000090 0.000152 0.000209 0.000279 0.000320 Elastic 0.000781 0.000898 0.001083 0.001123 0.001274 0.001377 Creep 0.000276 0.000337 0.000380 0.000486 0.000501 0.000554 Creep coefficient 0.62 0.74 0.82 0.93 1.05 1.16 40% Creep modulus 1.67E+06 1.58E+06 1.51E+06 1.42E+06 1.33E+06 1.26E+06 Total 0.001169 0.001286 0.001406 0.001539 0.001694 0.001809 Shrinkage 0.000038 0.000090 0.000152 0.000209 0.000279 0.000320 Elastic 0.000713 0.000713 0.000713 0.000713 0.000713 0.000713 Creep 0.000418 0.000482 0.000540 0.000617 0.000702 0.000776 Creep coefficient 0.59 0.68 0.76 0.87 0.99 1.09 10LS 14day moist cure 50% Creep modulus 1.67E+06 1.58E+06 1.51E+06 1.42E+06 1.33E+06 1.26E+06 PAGE 209 210 Table B1. Continued Total 0.001023 0.001173 0.001333 0.001532 0.001750 0.001873 Shrinkage 0.000032 0.000061 0.000109 0.000161 0.000204 0.000229 Elastic 0.000601 0.000601 0.000601 0.000601 0.000601 0.000601 Creep 0.000390 0.000511 0.000623 0.000769 0.000944 0.001043 Creep coefficient 0.65 0.85 1.04 1.28 1.57 1.74 40% Creep modulus 2.61E+06 2.33E+06 2.11E+06 1.89E+06 1.67E+06 1.57E+06 Total 0.001334 0.001494 0.001690 0.001992 0.002171 0.002323 Shrinkage 0.000032 0.000061 0.000109 0.000161 0.000204 0.000229 Elastic 0.000777 0.000777 0.000777 0.000777 0.000777 0.000777 Creep 0.000526 0.000657 0.000804 0.000984 0.001190 0.001318 Creep coefficient 0.68 0.85 1.04 1.27 1.53 1.70 2GF 14day moist cure 50% Creep modulus 2.48E+06 2.26E+06 2.05E+06 1.84E+06 1.64E+06 1.54E+06 Total 0.000811 0.000931 0.001084 0.001243 0.001428 0.001541 Shrinkage 0.000024 0.000047 0.000076 0.000113 0.000157 0.000183 Elastic 0.000530 0.000530 0.000530 0.000530 0.000530 0.000530 Creep 0.000257 0.000354 0.000479 0.000600 0.000741 0.000828 Creep coefficient 0.48 0.67 0.90 1.33 1.40 1.56 40% Creep modulus 3.69E+06 3.28E+06 2.88E+06 2.57E+06 2.29E+06 2.14E+06 Total 0.001043 0.001187 0.001362 0.001549 0.001747 0.001879 Shrinkage 0.000024 0.000047 0.000076 0.000113 0.000157 0.000183 Elastic 0.000666 0.000666 0.000666 0.000666 0.000666 0.000666 Creep 0.000353 0.000474 0.000621 0.000770 0.000924 0.001030 Creep coefficient 0.53 0.71 0.93 1.16 1.39 1.55 3GF 14day moist cure 50% Creep modulus 3.56E+06 3.19E+06 2.82E+06 2.53E+06 2.28E+06 2.14E+06 PAGE 210 211 Table B1. Continued Total 0.001024 0.001163 0.001296 0.001454 0.001615 0.001690 Shrinkage 0.000039 0.000064 0.000104 0.000140 0.000168 0.000184 Elastic 0.000556 0.000556 0.000556 0.000556 0.000556 0.000556 Creep 0.000429 0.000543 0.000636 0.000758 0.000891 0.000950 Creep coefficient 0.77 0.98 1.14 1.36 1.60 1.71 40% Creep modulus 2.87E+06 2.57E+06 2.35E+06 2.13E+06 1.94E+06 1.86E+06 Total 0.001261 0.001427 0.001594 0.001783 0.001977 0.002084 Shrinkage 0.000039 0.000064 0.000104 0.000140 0.000168 0.000184 Elastic 0.000703 0.000703 0.000703 0.000703 0.000703 0.000703 Creep 0.000519 0.000660 0.000787 0.000940 0.001106 0.001197 Creep coefficient 0.74 0.94 1.12 1.34 1.57 1.70 5GS 14day moist cure 50% Creep modulus 2.85E+06 2.55E+06 2.35E+06 2.13E+06 1.94E+06 1.84E+06 Total 0.000953 0.001078 0.001213 0.001383 0.001551 0.001627 Shrinkage 0.000043 0.000074 0.000100 0.000131 0.000162 0.000181 Elastic 0.000517 0.000517 0.000517 0.000517 0.000517 0.000517 Creep 0.000393 0.000487 0.000597 0.000736 0.000872 0.000929 Creep coefficient 0.76 0.94 1.15 1.42 1.69 1.80 40% Creep modulus 2.91E+06 2.64E+06 2.38E+06 2.11E+06 1.90E+06 1.83E+06 Total 0.001208 0.001361 0.001517 0.001708 0.001899 0.001977 Shrinkage 0.000043 0.000074 0.000100 0.000131 0.000162 0.000181 Elastic 0.000652 0.000652 0.000652 0.000652 0.000652 0.000652 Creep 0.000512 0.000634 0.000764 0.000924 0.001084 0.001143 Creep coefficient 0.79 0.97 1.17 1.42 1.66 1.75 7GS 14day moist cure 50% Creep modulus 2.84E+06 2.57E+06 2.33E+06 2.10E+06 1.90E+06 1.84E+06 PAGE 211 212 LIST OF REFERENCES AASHTO, 2001. 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E ffect of coarse aggreg ate on elastic modulus and compressive strength of high performance concrete. Cement and Concrete Research, Vol. 25, No. 1, pp.177186. Zia, P., Leming, M.L., Ahmad, S.H. 1991. Hi ghPerformance Concrete : A StateoftheArt Report. Strategic Highway Res earch Program, National Resear ch Council, Washington, D. C., (SHRPC/FR91103; PB92130087), pp.251. Zia, P., Ahmad, S.H., Leming, M.L., Schemmel, J. J., Elliott, R.P. 1993. Mechanical Behavior of High Performance Concretes. Volume 5: Very High Strength Concre te. Strategic Highway Research Program, National Research Counc il, Washington, D. C., xi, (SHRPC365), pp.101. PAGE 217 218 BIOGRAPHICAL SKETCH Liu Yanjun, born in 1973 in China, is a civil engineer. He went to Shenyang Architectural and Civil En gineering Institute in 1993. Four years later, he earned his bachelors degree in civil engineering in 1997. Then, he got scholarship from China Building Materials Academy and worked on his Masters study in Material Science and Engineering. After three years, in 2000, he earned his Masters degree at China Building Materials Academy in Material Science and Engineering with minor focus on cement and concrete materials. After that, he worked for China Building Materials Academy for 2 years. Then, he obtained full schola rship from Civil and Coastal Engineering Department of University of Florida and involved PhD program on the research on cement and concrete materials. At la st, he achieved his PhD at the University of Florida in 2007. 