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Characterization of Shrinkage Behavior in Concrete Materials Using Cure Reference Method

Permanent Link: http://ufdc.ufl.edu/UFE0025161/00001

Material Information

Title: Characterization of Shrinkage Behavior in Concrete Materials Using Cure Reference Method
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Chen, Tzu-Chau
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: concrete, crack, hydration, moire, moisture, shrinakge
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A novel experimental technique was developed to investigate the shrinkage behavior in cementitious materials. The Cure Reference Method (CRM), previously developed for residual strain measurements in composites, was used to determine the shrinkage that develops in concrete materials during the curing or drying process. This technique involves the replication of diffraction grating on the concrete specimen during the curing process and the use of high sensitivity moire acute interferometry. A specially-designed stage was created to help obtain a set of the consecutive phase shifted fringe patterns. Instead of the intensity-based methods, an automated fringe analysis program was used to analyze fringe patterns to obtain full-field displacement and strain information. Shrinkage as a function of time, location, humidity, temperature, water/cement (w/c) ratio and size was measured for unsealed cement paste specimens. Also, a method of combining CRM and removing drying effect was used to explore the relative contribution of non-drying shrinkage (autogenous shrinkage) to the total shrinkage in cement pastes. Furthermore, CRM technique was applied to explore the effect of fine aggregates (sand) on the shrinkage behavior. The effect of sand quantities was investigated to observe how shrinkage responded to this influential factor. The method of removing drying effect was modified to explore the relative contribution of autogenous shrinkage to the total shrinkage in the specimen with the fine aggregates (mortar specimen). The effect of coarse aggregates (gravel) on shrinkage was also displayed. An inverse method based on finite element moisture diffusion model and optimization was developed in order to obtain the material properties of cement paste from the complex geometry used in the tests. Once the material parameters were determined, they can be the inputs in finite element analysis for the predictions. The tests in different drying conditions, with different geometry of the specimens, and for the reinforced specimens were performed and their results were compared with FEA to validate the constructed model and the obtained materials properties. Ring tests were performed under both normal and extreme low humidity conditions for crack investigation. Also, the FEA of the ring test under normal humidity has shown that the numerical result had good agreement with that from the experiment. Finally, stresses were predicted in FEA model for both free shrinkage and restrained (ring test) shrinkage cases.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tzu-Chau Chen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025161:00001

Permanent Link: http://ufdc.ufl.edu/UFE0025161/00001

Material Information

Title: Characterization of Shrinkage Behavior in Concrete Materials Using Cure Reference Method
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Chen, Tzu-Chau
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: concrete, crack, hydration, moire, moisture, shrinakge
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A novel experimental technique was developed to investigate the shrinkage behavior in cementitious materials. The Cure Reference Method (CRM), previously developed for residual strain measurements in composites, was used to determine the shrinkage that develops in concrete materials during the curing or drying process. This technique involves the replication of diffraction grating on the concrete specimen during the curing process and the use of high sensitivity moire acute interferometry. A specially-designed stage was created to help obtain a set of the consecutive phase shifted fringe patterns. Instead of the intensity-based methods, an automated fringe analysis program was used to analyze fringe patterns to obtain full-field displacement and strain information. Shrinkage as a function of time, location, humidity, temperature, water/cement (w/c) ratio and size was measured for unsealed cement paste specimens. Also, a method of combining CRM and removing drying effect was used to explore the relative contribution of non-drying shrinkage (autogenous shrinkage) to the total shrinkage in cement pastes. Furthermore, CRM technique was applied to explore the effect of fine aggregates (sand) on the shrinkage behavior. The effect of sand quantities was investigated to observe how shrinkage responded to this influential factor. The method of removing drying effect was modified to explore the relative contribution of autogenous shrinkage to the total shrinkage in the specimen with the fine aggregates (mortar specimen). The effect of coarse aggregates (gravel) on shrinkage was also displayed. An inverse method based on finite element moisture diffusion model and optimization was developed in order to obtain the material properties of cement paste from the complex geometry used in the tests. Once the material parameters were determined, they can be the inputs in finite element analysis for the predictions. The tests in different drying conditions, with different geometry of the specimens, and for the reinforced specimens were performed and their results were compared with FEA to validate the constructed model and the obtained materials properties. Ring tests were performed under both normal and extreme low humidity conditions for crack investigation. Also, the FEA of the ring test under normal humidity has shown that the numerical result had good agreement with that from the experiment. Finally, stresses were predicted in FEA model for both free shrinkage and restrained (ring test) shrinkage cases.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tzu-Chau Chen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025161:00001


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1 CHARACTERIZATION OF SHRINKAGE BEHAVIOR IN CONCRETE MATERIALS USING CURE REFERENCE METHOD By TZU CHAU CHEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREM ENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 TzuChau Chen

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3 To my dearest parents, wife and son

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4 ACKNOWLEDGMENTS First of all, I give my heartfelt appreciation to my dear parents for their endless love, support, and enc ouragement throughout my life. They encourage me to believe in myself, and in my dreams. Their love has meant more than words can express. I dedicate this study especially to them. Also, I would like to express my extreme thanks to my wife for h er love and understanding. When I was chained in the lab working on my research or chained to my desk writing the dissertation, s he took care of Samuel, our beloved son, and did the house chores Moreover I have my profound appreciation to Dr. Peter Ifju my mentor, advisor and committee chair, for h is guidance and patience throughout my doctoral study. H is continued support and insights made this task much easier. And I reall y appreciate Weiqi Yin, one of the doctoral students in our laboratory, for the automated analysis system he developed. Furthermore, I want to give my thanks to Chris Ferraro and Charles Ishee in FDOT for their financial support and assistance. Finally, I would like to give my thanks to all other committee members, Dr. Bhavani Sankar, Dr. Nicolae Cristescu, and Dr. Mang Tia, for their valuable suggestions and comments on my research.

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5 TABLE OF CONTENTS ACKNOWLEDGMENTS ...............................................................................................................4 page LIST OF FIGURES .........................................................................................................................8 ABSTRACT ...................................................................................................................................12 CHAPTER 1 INTRODUCTION ..................................................................................................................14 1.1 Background .......................................................................................................................14 1.2 Literature Review .............................................................................................................15 1.2.1 Shrinkage Behavior i n Concrete Materials .............................................................16 1.2.1.1 Autogeneous shrinkage ................................................................................17 1.2.1.2 Drying shrinkage ..........................................................................................18 1.2.2 Experimental Techniques .......................................................................................18 1.2.2.1 Non full field measurements ........................................................................19 1.2.2.2 Full field measurements ...............................................................................19 1.2.3 Numerical Simulation .............................................................................................20 1.2.3.1 Moisture diffusion modeling ........................................................................20 1.2.3.2 Shrinkage modeling ......................................................................................21 1.2.3.3 Inverse method .............................................................................................21 1.3 Research Objectives ..........................................................................................................23 2 METHODOLOGY .................................................................................................................25 2.1 High Sensitivity Moir Interferometry .............................................................................25 2.2 Cure Reference Method ....................................................................................................28 2.2.1 Methodology of CRM ............................................................................................28 2.2.2 Replication of Grating ............................................................................................29 2.2.2.1 Silicone rubber grating based method without epoxy layer .........................30 2.2.2.2 Aluminized epoxy grating based method .....................................................30 2.2.2.3 Silicone rubber grat ing based method with epoxy layer ..............................31 2.3 Automated Fringe Analysis ..............................................................................................34 3 SHRINKAGE MEASUREMENTS OF CONCRETE ...........................................................39 3.1 Introduction .......................................................................................................................39 3.2 Chamber Setup ..................................................................................................................40 3.2.1 Humidity Control ....................................................................................................40 3.2.2 Temperature Control ..............................................................................................41 3.3 Experimental Setups .........................................................................................................41 3.3.1 PEMI I ....................................................................................................................41 3.3.2 PEMI II ...................................................................................................................43

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6 3.4 Experimental Results ........................................................................................................44 3.4.1 Drying Condition Eff ect (Temperature and Humidity) ..........................................44 3.4.2 W/C ratio and Size Effects .....................................................................................61 3.4.3 Aggregate Effect .....................................................................................................61 3.4.3.1 Fine aggregate ..............................................................................................62 3.4.3.2 Coarse aggregate ..........................................................................................67 3.4.4 Autogenous Shrinkage Measurements in Sealed Conditions .................................70 3.4.4.1 Sealed cement paste specimens ....................................................................70 3.4.4.2 Sealed mortar specimen ...............................................................................75 3.4.5 Ring Test for Crack Investigation ..........................................................................77 3.4.6 Swelling test ...........................................................................................................79 3.5 Conclusion & Discussion .................................................................................................80 4 NUMERICAL MODELING ..................................................................................................82 4.1 Introduction .......................................................................................................................82 4.2 Model Descript ion ............................................................................................................84 4.2.1 Axisymmetric Model ..............................................................................................84 4.2.2 Materials Properties ................................................................................................84 4.2.3 Initial Condition: ....................................................................................................84 4.2.4 Boundary Condition ...............................................................................................85 4.3 Inverse Method .................................................................................................................85 4.4 Validation of Model ..........................................................................................................89 4.4.1 Different Surrounding Humidity ............................................................................89 4.4.2 Ring Test ................................................................................................................92 4.4.3 Square Shape ..........................................................................................................94 4.4.4 Expansion on Day 1 ................................................................................................96 4.4.4.1 Inplane deformation measurement ..............................................................96 4.4.4.2 Out of plane displacement simulation .........................................................98 4.4.5 Reinforced Concrete ...............................................................................................98 4.5 Stress Development Prediction .......................................................................................103 4.5.1 Free Shrinkage ......................................................................................................103 4.5.2 Restrained Shrinkage ............................................................................................105 4.6 Results and Discussions ..................................................................................................107 5 CONCLUSIONS & FUTURE WORKS ..............................................................................109 5.1 Conclusions .....................................................................................................................109 5.2 Future Works ..................................................................................................................110 APPENDIX: CRM MOIRE FRINGE PATTERNS AND FRINGE ANALAYIS RESULTS ...112 LIST OF REFERENCES .............................................................................................................118 BIOGRAPHICAL SKETCH .......................................................................................................126

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7 LIST OF TABLES Table page 11 Categories of concrete materials .......................................................................................16 31 Substances for RH control ................................................................................................41 32 Shrinkage measurements unde r RH=0% and ..........................58 33 Shrinkage measurements under RH=100% and ......................59 41 Thermal m echanical interaction model .............................................................................83 42 Errors of optimization .......................................................................................................87

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8 LIST OF FIGURES Figure page 11 Concrete under external restraints ....................................................................................15 12 Shrinkage strain components in (a) normal strength and (b) highstrength concrete (Sakata & Shimomura 2004) .............................................................................................17 21 Scheme of moir interferometer .......................................................................................26 22 Schematic diagram of moir interferometry .....................................................................27 23 (a) Concrete fluid etched aluminum (b) concrete broke during separation ......................31 24 Concrete samples and molds .............................................................................................32 25 P rocedure to prepare diffraction grating ...........................................................................33 26 Fringe patterns from the master grating ............................................................................34 31 Chamber setup ..................................................................................................................40 32 Experimetnal setup with PEMI .........................................................................................42 33 Fringe shifting stage .........................................................................................................42 34 Ex perimental setup with PEMI II .....................................................................................43 35 U field Moir fringe patterns under 50% RH and 23 ...................................................44 36 V field Moir fringe pattern s ...................................................45 37 Full field maps in xy coordinate for day 2 ......................................................................46 38 Full field maps in polar coordinate for da y 2 ...................................................................47 39 U field Moir fringe patterns .....................................................49 310 V field Moir fringe patterns .....................................................50 311 Full field maps for day 7 under 0% RH and 23C ...........................................................50 312 U field Moir fringe patterns .......................................................51 313 V field Moir fringe patterns .......................................................52 314 Measured shrinkage from center to outer surface .............................................................55

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9 315 U field Moir fringe patterns .................................................56 316 V Field Moir fringe patterns ................................................57 317 U field displacement and strain maps for day ..................................................................58 318 Relative humidity and temperature effect .........................................................................60 319 w/c and size effects on averaged shrinkage of cement pastes ..........................................61 320 U field moir fringe patterns for mortar with s/c=37.5% .................................................62 321 Strain information for mortar with s/c=37.5% on day 2 ...................................................63 322 Displacement maps for mortar with s/c=37.5% on day 2 .................................................63 323 Moir fringe patterns for mortar with s/c=75% on day 7 .................................................64 324 Full field normal strain maps with both (a) large and (b) small gauge lengths for the mortar s pecimen of s/c=75% on Day 7 ..............................................................................65 325 A ggregate quantity and RH effects on average shrinkage of mortar specimens ..............66 326 Side and top views of gravel test ......................................................................................67 327 Day 5 moir fringe patterns for the gravel test .................................................................68 328 The Strain analysis for gravel test .....................................................................................69 329 U field moir fringe patterns for w/c =0.4 in room temperature ......................................71 330 V field moir fringe patterns for w/c =0 .4 in room temperature ......................................71 331 Day 7 U field displacement for the sealed specimen with w/c=0.4 in x y coordinate .....72 332 W/C ratio and temperature effects on sealed specimen shrinkage ...................................73 333 Day 6 displacement and strain analysis for the sealed cement paste specimen with w/c=0.4 in polar coordinate ...............................................................................................74 334 A modified sealing method ...............................................................................................75 335 Day 7 Moir fringe pattern for w/c=0.3 and s/c =37.5% ..................................................76 336 Autogenous shrinkage for mortar with w/c=0.3 and s/c=37.5% in room temperature .....76 337 Scheme of Ring Test .........................................................................................................77 338 Ring Test investigation for RH=0% and room temperature .............................................78

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10 339 Pictures of the specimen with a crack in the ring test .......................................................78 340 Moir fringe patterns before and after one day immersion ..............................................79 341 Full field displacement maps for the swelling test ...........................................................79 41 Scheme of numerical modeling ........................................................................................83 42 Boundary conditions of moisture diffusion model ...........................................................85 43 Optimiza tion results ..........................................................................................................87 44 3D model of shrinkage behavior .....................................................................................88 45 FEA results for RH=50% and room temperature .............................................................88 46 Experimental and FEA results for RH=80% and room temperature ................................89 47 Experimental and FEA results for RH=80% and room temperature on Day 3 ................90 48 Cross section view of deformations for RH=80% and room temperature on Day 3 ........91 49 U&Vfield moir fringe patterns fo r ring test under RH60% and room temperature ......92 410 Experimental (above) and FEA (below) results of ring test on Day 2 ..............................93 411 Experimental and FEA shrinkage distribution for Day 2 .................................................93 412 Experimental (above) and FEA (below) results of ring test on Day 3 ..............................94 413 U and V field moir fringe patterns for the square specimen ...........................................95 414 Distribution of normal strain in x direction along the red line .........................................95 415 Experimental (above) and FEA (below) maps for square specimen on Day 4 .................96 416 Experimental (above) and FEA (below) results for Day 1 measurement .........................97 417 FEA result for out of plane displacement .........................................................................98 418 Size and arrangement of the steel rods in cement paste ....................................................99 419 Master grating with the sheet on the back ........................................................................99 420 Moir fringe patterns for reinforced concrete .................................................................100 421 Experimental (left) and FEA (right) results for reinforced concrete on Day 2 ...............101 422 Experimental (above) and FEA (below) results for reinforced concrete on Day 3 ........102

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11 423 FEA result for stress development ..................................................................................103 424 FEA results for fullfield stress maps .............................................................................104 425 FEA results for stress maps over the cross section .........................................................104 426 FEA results for stress development in the ring test of RH=60% ....................................105 427 FEA results for fullfield stress maps in ring test ...........................................................106 428 FEA results for stress development in the ring test of RH=0% ......................................106 A 1 U field Moir fringe patterns for w/c=0.6 in sealed condition .......................................112 A 2 V field Moir fringe patterns for w/c=0.6 in sealed conditi on .......................................112 A 3 U field Moir fringe patterns under 80% RH and 23 .................................................113 A 4 V field Moir fringe patterns under 80% RH and 23 .................................................113 A 5 Additional full field maps for ring test on Day 2 ...........................................................114 A 6 Additional full field maps for ring test on Day 3 ...........................................................115 A 7 The full field strain maps of cement paste only in ring test on Day 2 ............................116 A 8 The full field strain maps of cement paste only in ring test on Day 3 ............................116 A 9 Additional full field strain maps for reinforced concrete on Day 2 ................................117

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12 Abstract of Dissertation Presented to the Gr aduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CHARACTERIZATION OF SHRINKAGE BEHAVIOR IN CONCRETE MATERIALS By Tzu Chau Chen December 2009 Chair: Peter G. Ifju Major: Mechanical Engineering A novel experimental technique w as developed to investigate the shrinkage behavior in cementitious materials. The Cure Reference Method (CRM), previously developed for residual strain measurements in composites, was used to determine the shrinkage that develops in concrete materials during the curing or drying process. Th is technique involves the replication of diffraction grating on the concrete specimen during the curing process and the use of high sensitivity moir interfe rometry. A specially designed stage was created to help obtain a set of the consecutive phase shifted fringe patterns. Instead of the intensity based methods a n automated fringe analysis program was used to analyze fringe patterns to obtain full field dis placement and strain information. Shrinkage as a function of time, location, humidity, temperature water/cement (w/c) ratio and size was measured for unsealed cement paste specimens Also a method of combining CRM and removing drying effect was used to e xplore the relative contribution of nondrying shrinkage (autogenous shrinkage) to the total shrinkage in cement pastes. Furthermore, CRM technique was applied to explore the effect of fine aggregates (sand) on the shrinkage behavior The effect of sand quantities was investigated to observe how shrinkage responded to this influential factor The method of removing drying effect was modified to explore the relative contribution of autogenous shrinkage to the total shrinkage in the

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13 specimen with the fine aggregates (mortar specimen). The effect of coarse aggregates ( gravel ) on shrinkage was also displayed A n inverse method based on finite element moisture diffusion model and optimization was developed in order to obtain the material properties of cement past e from the complex geometry used in the tests. Once the material parameters were determined, they c an be the inputs in finite element analysis for the predictions The tests in different drying conditions with different geometry of the specimens and for the reinforced specimens were performed and their results were compared with FEA to validate the constructed model and the obtained materials properties Ring tests were performed under both normal and extreme low humidity conditions for crack investigatio n. Also, t he FEA of the ring test under normal humidity has shown that the numerical result had good agreement with that from the experiment Finally, stresses were predicted in FEA model for both free shrinkage and restrained (ring test) shrinkage cases.

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14 CHAPTER 1 INTRODUCTION 1.1 Background Concrete is a material that forms the basis of our modern society. Nearly every aspect of our daily life depends directly or indirectly on concrete materials For example, we live, play, work or study directly in concrete structures or buildings to which we drive directly over concrete roads and bridges. Indirectly, our goods can be transported by trucks running on concrete freeways or by trains traveling on rails supported by concrete crossties ; water for our drin king and raising crops is stored behind the concrete dams and is distributed through the systems of concrete water ways, conduits and pipes. We take concrete for granted when we are enjoying all the activities in our daily life. However, it can be truly s aid that many achievements of our modern civilization have been attributed to concrete. Since concrete is closely related to our life, every aspect of its behavior /properties must be understood in order to thoroughly utilize it to the highest potential. O ne aspect that requires proper characterization is the shrinkage beh avior because it influences the development of tensile stress when external or internal re straints exist and causes the subsequent cracking in concrete. The case of external restraints is very straightforward and can be explained by Figure 11 [1]. On the other hand, the internal re strain t is due to nonuniform shrinkage over the cross section. It is known that larger shrinkage occurs near the outer surface and smaller shrinkage in the inne r core. In this case, tensile stress develops close to the outer surface and compressive stress in the inner core [2] Both cases can lead to subsequent cracking and reduction of its service life when the tensile stress that develops in concrete is gr eater than the tensile strength. Furthermore, i n the case of reinforced concrete, the cracking may produce a direct path for chloride ions to reach the reinforcing steel. Once chloride ions reach the steel surface, the stee l will corrode, which itself

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15 c an cause cracking, spalling, and delamination of the concrete [ 3] As a result the shrinkage behavior must be well understood in order to better evaluate the structural life of concrete or to properly control the occurrence of the shrinkage induced cracks Fig ure 11. Concrete under external re straint s 1.2 Literature Review Concrete materials exper ience volume change during their service life. The total in service volume change is the resultant of shrinkage and deformation from applied load or temperature variation. S hrinkage is typically defined as the strain measured on a load free & unrestrained concrete specimen, not including changes due to temperature variations and is commonly described in micro strains. According to the definition of concrete materials, t here are three main categories: cement paste, mo rtar and concrete [ 4] and their compositions are indicated in T able 11. But generally speaking, they are all called concrete in our daily living.

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16 Table 11. C ategories of concrete materials Category Compon ents Cement paste = Cement + water Mortar = Fine Aggregate (sand) + Cement Paste Concrete = Fine and Coarse Aggregate (gravel) + Cement Paste 1.2.1 Shrinkage Behavior in Concrete Materials There are four main types of shrinkage associated with concrete materials: plastic, carbonation, autogeneous, and drying shrinkage. Plastic shrinkage is due to moisture loss from the concrete before the concrete sets [ 57] Carbonation shrinkage is caused by the chemical reac tion of various cement hydration products with carbon dioxide present in the air [ 810] This type of shrinkage is usually limited to the surface of the concrete. Autogeneous s hrinkage is associated with the hydration of the cement which is a chemical reaction between water and cement, without water loss into the surrounding environment s This type of shrinkage tends to increase at lower water to cementitious materials ratio (w/c) and at a higher cement content of a concrete mixture In general, it is rela tively small and not distinguished from drying shrinkage for normal strength concrete materials with w/c ratio larger than 0.4 Drying shrinkage is due to drying or moisture loss of concrete into the surrounding environment s T he ratio of autogenous and dr ying shrinkage in total shrinkage of concrete is schematically illustrated as in F igure 12 [ 11, 12] The figure indicates that autogenous shrinkage already occurs before the start of drying. The start of drying is usually set as the point at which the mea surement of shrinkage is zero. Also, it can be seen that t he contribution of autogenous shrinkage to the total shrinkage is significant for high strength concrete materials. On the contrary, autogenous shrinkage in normal strength concrete contributes to t he total shrinkage insignificantly. The magnitude of the

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17 total shrinkage depends on concrete mixture proportions and material properties, method of curing, ambient temperature and humidity conditions, and geometry of the concrete element. In the analysis o f concrete structures two components, drying and autogenous shrinkage are usually taken into account because they are more associated with induced cracking in concrete materials. As a result autogeneous and drying shrinkage draw more attention from the c oncrete researchers. Therefore, it is necessary to discuss them in more detail s as below Figure 12. Shrinkage strain components in (a) normal strength and (b) highstrength concrete (Sakata & Shimomura 2004) 1.2.1.1 Autogeneous s hrinkage The shrinkage occurring in the absence of moisture exchange (as in a sealed concrete s pecimen ) due to the hydration reactions taking place inside the cement matrix is termed autogenous shr inkage [ 1 3] Autogenous shrinkage was almost never considered as a factor in the research on shrinkage before 1990. It is usually insignificant for many normal compressive

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18 strength concretes and can usually be neglected H owever f or highstrength concrete with w/c ratio less than 0.40, it may be a significant contribution to the tota l shrinkage. As a result, it has become an issue with the increasing use of highpe rformance concrete. Factors affecting autogenous shrinkage include water/cement ratio [ 14, 15] temperature [ 16] aggregate s [ 17, 18] and admixtures [ 19, 20] etc. And a utoge neous shrinkage is not one time deformation, but a time dependent behavior. 1.2.1.2 Drying s hrinkage Shrinkage occurring in a specimen that is exposed to the environment and allowed to dry is called drying shrinkage. For normal strength concrete with w/c larger than 0.4, it is usually assumed that the entire shrinkage strain is only from drying shrinkage, and any contributi on from autogenous shrinkage is neglected. Factors influencing drying shrinkage can be divided into three categories. The first cat egory is drying conditions. Much research has been devoted to the temperature, humidity and wind speed effects [ 2128]. Also, because drying shrinkage involves moisture diffusion through the material and moisture loss into the surrounding environment it depends on the geometry of the specimen which is the second category, such as the shape and size of the specimen [ 29 30]. The third category is the composition s of concrete, including the type of cement, water/cement ratio, and fine/coarse aggregate quantity etc. [ 31] Drying shrinkage is also timedependent behavior as is autogenous shrinkage 1.2.2 Experimental Techniques Some experimental techniques have been developed and used to determine the shrinkage that occurs in concrete materials during the curing and drying. There are two major categories of these experimental techniques, non full field measurements and full field measurements. They are summarized as the following.

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19 1.2.2.1 Non full field measurements The most common one is ASTM C157 standar d test method. This method measures the length change of hardened hydraulic cement mortar and concrete specimen using a comparator [ 32, 33]. However, this method is categorized into the measurement of the averaged shrinkage of concrete sample s Embedded se nsors, such as embedded strain gauges and fiber optics, are also the well known methods which are used for measuring internal shrinkage at specific locations [ 3438]. But these methods are in the category of point measurements and the gathered information is easily altered by the intrusive nature of these tests. M embrane method protocol is for the measurement of autogenous shrinkage and performed by monitoring the weight of a cement paste sample that is sealed in a membrane, submerged in paraffin oil and suspended from a highprecision balance [ 39] This method is able to obtain the averaged shrinkage in terms of volumetric strain rather than linear strain. Although the shrinkage of concrete in a fluid state can be measured, it is not significant to the de velopment of tensile stress. And the lack of a steady contact between the membrane and the cement paste is a considerable disadvantage. Rigid form method measures the shrinkage using a non contact laser to investigate the length change of a specimen in a conventional rigid steel form [ 40 ]. Likewise, this method belongs to the measurement of averaged shrinkage. Other methods, such as corrugated tube method and buoyancy method [ 41], are all averaged shrinkage measurements. Also they have their own drawbacks and limitations of use. 1.2.2.2 Full f ield measurements Some of the full field experimental techniques have been applied in the study of concrete structure inspection. Optical techniques, s uch as Grid method, Electronic Speckle Pattern I nterferometry (EPSI ) and Digital Correlation M ethod (DCM) are the most popular ones for the detection of flaws and cracks in the concrete structures [ 424 6] Moreover, moir interferometry

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20 was used to investigate Fracture of concrete [4 7, 48] However, t he full field techni ques for measuring shrinkage of concrete are scarce in the literature An o ptica l technique digital photogrammetric method, ha s been used to measure the shr inkage in concrete s amples [ 49]. Although this method offers full field measurement, it does not possess high sensitivity of displacement s and strain s measurements. Recently, a n image intensity matching technique was used to measure strain in cement pastes within an environmental scanning electron microscope [ 50]. This method is still in the stage of t he development 1.2.3 Numerical S imulation Since the us e of full field technique s to measure shrinkage is scarce in the literature, the modeling of shrinkage on a full field basis is not available Many mathematical models based on ASTM C157 standard test were proposed to predict average d shrinkage of concrete specimens. On the other hand, due to the fact that shrinkage closely relies on moisture distribution, much research has been devoted to the measurement and the modeling of moisture distribution in co ncrete materials in terms of moisture content or internal relative humidity However, they serve as the qualitative indication of shrinkage rather than quantitative 1.2.3.1 Moisture diffusion modeling M oisture diffusion models based on Ficks Law were wi dely used and solved analytically or numerically to investigate moisture distribution in concrete specimens [51 62] The majority of commercial software packages do not offer mass diffusion modules but only heat conduction modules. The governing equation of heat conduction given by Fouriers law has the generalized form similar to the equation of diffusion given by Ficks Law. Hence, the heat conduction analogy is extremely useful in practice. However, for highstrength concrete with low er w/c ratio moistu re distribution cannot be governed only by moisture diffusion. As a result, the

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21 decrease in relative humidity or moisture content due to s elf desiccation needs to be considered in the moisture distribution modeling [ 6366]. 1.2.3.2 Shrinkage modeling Ther e exist many mathematical models associated with predicting shrinkage of concrete materials. A review of the literature for these types of prediction models shows that the most widely discussed and used models are Comite EuroInternational Du Beton (CEB Mo del Code 1990), Bazant and Panula (BP KX and Model B3), and American Concrete Institute (ACI 209) etc. [ 6775]. However, all these models were based on the results of ASTM C157 standard test. The models are used for the prediction of averaged shrinkage as a function of time and composition of concrete materials. The shrinkage at certain locations of interests cannot be known from these models. 1.2.3.3 Inverse m ethod The inverse methods based on optimization have been widely used to evaluate unknown coeffi cients such as material parameters or to determine the load and boundary conditions in the structural or heat transfer problems. Th ey are computed by minimizing the error between the measured values obtained experimentally and those found by finite element analysis or analytical solutions Several methods have been developed for the determination of material properties using experimentally determined displacement or strain data. T he analytical model for a circular disc in diametric compression with a linear least square updating procedure was used to determine the elastic constants using moir interferometry displacements [ 76 ] The inverse approach was applied to determine the far field or residual stresses in open hole specimens with biaxial loading [77] A nonlinear least squares solution was described for the evaluation of far field stresses, material elastic properties and residual stresses in an infinite orthotropic plate with a hole

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22 Computer generated moir interferometry displacement data was used fo r the updating procedure [ 78, 79]. T he application of the microscopic hole method was demonstrated to assess the elastic properties of polycrystalline silicon freestanding thin films employed in microelectro mechanical system (MEMS) devices The analytical model for an infinite plate with a hole with a LevenbergMarquardt updating procedure using the nanometric displacement data obtained from atomic force microscopy (AFM) was used [ 80] A n overview of the existing full field measurement techniques, their a pplication in the field of composite material characterization and identification of parameters of constitutive equations has been presented [ 81] On the other hand, s everal methods have been developed for calculating the loads from the structur al response data that are measured using a variety of experimental techniques. The measured structural response is often the displacements or strains. A n optical method of using CCD cameras to measure the displacements in a loaded structure has been descri bed Images before and after the loading are obtained and using subpixel edge detection techniques, the displacements are computed [8 2] L oads acting on a beam by modeling the load distribution using Legendre polynomials with unknown weight factors have b een computed. The unknown coefficients are computed by minimizing the erro r between the measured values of displacements obtained experimentally and those found by FEA [8 3 ] A method to identify the element stiffness parameters of a truss and framelike structures by utilizing elemental strain measurements has been proposed [84] A videogrammetric technique for determining aerodynamic loads has been developed Elastic deformations are measured optically and used to obtain the normal force and pitching moment [8 5 ] An inverse problem approach has been presented for computing or calibrating the loads and boundary conditions acting on a structure. This enables the creation of more accurate finite element models, especially for structures that

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23 have complicated l oad distribution and compliant boundary conditions. The method involves minimizing the least square error between the strains computed using the finite element model and the strains and displacements obtained experimentally by luminescent photoelastic coat ing (LPC) technique [8 6]. 1.3 Research Objectives In this research work, there are four main objectives proposed as following: First, a full field experimental technique must be developed for the measurement of in plane deformation on the surface of concr ete materials during drying. This technique is based upon the C ure Reference Method (CRM) in conjunction with the use of high sensitivity moir interferometry. Because moir interferometry requires a high quality diffraction grating on the specimen, t he mo st challenging part in developing this technique is to create a procedure of replicating the diffraction grating on the concrete specimen during the curing process Moreover, the selection of diffraction grating material is another issue. T he diffraction g rating should be able to survive in different drying conditions and should not degrade or be damage d with time so that shrinkage as time dependent deformation behavior in concrete materials can be captured Also, it should be nonreinforcing to the specim en Second, based on the experimental results, the shrinkage behavior in concrete materials should be characterized and compared with the trends documented in the literature Once they have good agreement, the technique is considered reliable and robust. T hird based on the experimental data a n inverse method must be developed in order to obtain the material properties of shrinkage in cement paste from the complex geometry use d in the tests. The method involves minimizing the least square error between the strains computed using the finite element model and the strains obtained experimentally by the moir interferometry technique Onc e the material properties are identified they can be the inputs in

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24 finite element analysis for the prediction of shrinkage behavior in concrete materials. The tests in different drying conditions or with different geometry of the specimens can be performed and the ir experimental result s can be compared with FEA to validate the constructed model and derived material properties Finally, the stress development in concrete specimen s can be simulated in FEA and the occurrence of cracking can be predicted if the tensile strength is given.

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25 CHAPTER 2 METHODOLOGY 2.1 High Sensitivity Moir Inte r ferometry M oir interferometry has matured rapidly as a powerful tool, proven by numerous industrial and scientific applications [ 8789]. It is an optical technique which has been used in the studies of composite materials, polycrystalline materials, piezoelectric materials, fracture mechanics, bi omechanics, structural elements & joints, residual stress measurements, strain gauge calibration and more recently, thermal defor mation of electronic packages. It utilizes moir phenomenon of optical interference to measure the in plane deformation of obj ects. The principle of high sensitivity moir interferometry is founded on the interference between the specimen grating and the virtual reference grating created by two laser beams. Moir interferom etry record s the data as interference fringe patterns, or contour maps of displacement fields. It is characterized by a list of excellent qualities as follow s : (a) full field technique, i.e. quantitative measurements can be made throughout the field; (b) high sensitivity to in plane displacements U and V, typically 0.417 m per fringe; (c) insensitive to out of plane displacements W; (d) high spatial resolution, meaning that measurements can be made in tiny zones; (e) high signal to noise ratio, ensuring that the fringe patterns have high contrast and excellent visibility; (f) determinat ion of shear strains as readily as normal strains; (g) real time technique, where the displacement fields can be viewed as loads are applied. (h) capability for finite el ement analysis (FEA) validation, obtaining or correcting m aterial properties or boundary condi tions required for FEA inputs The general scheme of moir interferometry is illustrated in Figure 21. A highfrequency crossline grating on the s pecimen called the specimen grating initially of frequency fs (1200 lines/mm), deforms together with the specimen. Two parallel (collimated) incident laser beams

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26 from the U field mirrors strike the specimen and are diffracted back. Since the specimen grating is deformed as a result of the applied loads or thermal deformation, these diffracted beams are no longe r collimated. Instead, they are beams with warped wav efronts, where the warpage is related to the deformation of the grating. These two coherent beams interfere in the image plane of the camera lens, producing a U field interference fringe pattern which gi ves displacement information in xdirection. Similarly, a V field interference fringe pattern produced by the beams from the V field mirrors gives displacement information in y direction. Figure 21. S cheme of moir interferomet er Another more understandable physical explanation considers a virtual reference grating, of frequency f created by two incident beams as in Figure 22. The frequency f of the virtual reference grating is determined by the angle 2 sin f (2 1)

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27 Figure 22. Schematic diagram of moir interferometry Moir interferometry utilizes a virtual reference grating of twice the initial frequency of the undeforme d 47.5. 2sff (2 2) In this case, w hen the sp ecimen grating is undeformed there will be no interference fringe s called null field. However, when the specimen is deformed in the x y plane, the virtual reference grating and the deformed specimen grating interact to form the moir fringe patterns The in plane displacement maps can be determined according to the equa tions 1 (,) 1 (,)x yUxyN f VxyN f (2 3) Also, the in plane normal strains and the in plane shear strain can be calculated with the selected gauge length by the equations

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28 1 1 1 ()x x y y y x xyN fx N fy N N fyx (2 4) where U ( x y ) and V ( x y ) are the displacements in x and y direction at the point of interest ( x y ) with respect to the chosen origin. Nx and Ny are the f ringe orders in x and y direction from the origin to the point of interest. x and y are the normal strains, and xy is the shear strain. x and y are the selected gage lengths; Nx and Ny are the fringe order difference over the selected gage length respectively. 2.2 Cure Reference Method The Cur e R eference M ethod (CRM) was originally developed for the measurements of residual strain s which develop in composites as cooling via moir interferometry [ 9094] A lso i t was already applied for the measurement of post gel chemical shrinkage in epoxy [ 95]. Un like many other methods the CRM technique i s non destructive gathers the information not altered by the intrusion of the tests and measures the deformation on a full field basis. Because of these advantages t he same methodology was adopted to investigate shrinkage beha vior in concrete materials 2.2.1 Methodology of CRM In the application of CRM to the shrinkage measurements in concrete materials, the diffraction grating is replicated from a master grating substrate unto the concrete spec imen during the curing process or at the stressfree state. The stress free state exists before the solidification of the specimen The deformation of the concrete specimen at fluid state is unable

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29 to be measured in CRM. However, it is of little significance to inducing cracks because fluid c annot carry stress After t he concrete specimen is hardened to some extent the deformation causes it to carry stress. But at this moment, t he inplane dimensions of the specimen and the frequency of the diffraction grating on its surface remain the same due to the constrain t from the rigid substrate. Once the concrete specimen is set and separated fro m the master grating substrate, the accumulated stresses are release d and the specimen as well as the diffraction grating attached to it deform s Hence, the f requen cy of the specimen grating is change d as the deformation occurs The virtual reference grating is first created by tuning the moir interferometer to reach the null field with the master grating To minimize errors that c an occur due to the misalignm ent of the gratings between the master grating and the specimen grating, the master grating i s rotated 90 counter clockwise. This operation account s for any possibility that the cross lines of the master grating are not exactly perpendicular Then b y repl acing the master grating with the deformed specimen grating, the interference fringe patterns can be obtained and the in plane full field deformation can be measured accordingly. Another advantage of CRM is that time dependent deformation in concrete materials can be determi ned. This requires the grating on the specimen not to degrade with time or in certain drying environments In routine practice, once the virtual reference grating is created it is fixed throughout the entire period of the testing. Ever y day the specimen is properly positioned in the moir interferometer, the phase shifted moir fringe patterns are recorded, and the deformation as a function of time is determined I n summary, CRM is a nondestructive, nonintrus ive, full field and resilient me t hod. 2.2.2 Replication of Grating In developing the procedure of grating replication, three major methods were attempted and they are discussed as below

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30 2.2.2.1 Silicone rubber grating based method without epoxy layer The first attempted method w as using silicon rubber grating (RTV615 A&B 10:1) as the master grating. Then concrete in fluid state was directly poured into the mold which was on top of the silicon rubber grating. Because of good contact between the mold and the master grating, leaking was not a concern. H owever, there a re many issues with respect to this method. First, it was found that there was no grating at all for concrete with lower w/c ratio. The reason for this should be that concrete fluid was too thick to fit into the space of master grating. It was difficult to deal with this problem, but resulted in the put ting a weight on concrete fluid Second the grating might disappear or degrade later during shrinkage because the grating itself is part of the concrete specimen Finally, aluminum is a must for increasing the grating efficiency. But aluminum was not well deposited unto the surface of the specimen in the vacuum deposition process. On the other hand, heat and vacuum resulting from the deposition process might accelerate the drying of the specimen which should cause significant errors on the experimental result s 2.2.2.2 Aluminized epoxy grating based method The second method wa s using an aluminized epoxy grating as the master grating was attempted Aluminum in double layers was used with a parting agent (Kodak Photoflo 200 diluted 1:300 in distilled water) in between in order to help separation of the specimen from the master grating Parting agent was applied uniformly on the surface of the first aluminum layer by using a l ens tissue prior to the deposition of the second aluminum layer T his method was forming a thin layer of epoxy on the surface of master grating and then fluid concrete was poured into the mold. After separation, t he top or second layer of aluminum with epoxy was intende d to be transferred unto the concrete specimen ; the bottom layer remained on the master grating. However, the result has shown that concrete fluid etched aluminum if it went through the thin

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31 epoxy layer as shown in F igure 23 (a). If not, the re was another issue as shown in figure 23 (b) indicating that concrete is subject to breaking during separation. (a) (b) Figure 23. (a) Concrete f luid etched aluminum (b) concrete broke during separation 2.2.2.3 Silicone rubber grating based method with epoxy layer In order to deal with all the issues addressed above, a method of using the silicone rubber RTV 6 428 grating as the master grating and f orming a thin layer of epoxy on the surface of the master grating has been developed. The procedure to prepare the diffraction grating on the specimen was described here Step 1 : A 57.1 mm x 57.1 mm silic one rubber RTV 6428 grating ( master grating) was pr epa red by replicati on from a photoresist or epoxy diffraction grating. The primer for RTV 6428 silicone rubber is SS4155, which provide s very good adherence of RTV 6428 to glass substrates. Envirotex Lite epoxy was mixed, degassed by the centrifugal and a dded to the master grating. The p ool of e poxy needs to cure for 2 hours in advance to increase its viscosity. Step 2: A clean glass plate was pushed onto the pool of epoxy to make it as thin as possible. Then the glass plate was removed horiz ontally and slowly from the master grating to prevent beads or bubbles A thin layer of epoxy of in thick ness was

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32 formed on the mast er grating. Because of the relative thickness and compliance after cure, its reinforcement to the specimen was considered negligible. Step 3 : A silicone rubber mold of 28 mm in i nner diameter was put on the master grating. Then the mixed concrete fluid was poured into the mold. The mold was made of GE RTV 6 27 silicone rubber. Step 4: 24 hours was required before the concrete was set and epoxy was cured. Epoxy needs to be well cured to become the diff raction grating of good quality. Step 5: The concrete specimen was demold ed and separated fr om the master grating Due to lower bonding between the thin epoxy layer and the master grating, t he epoxy diffraction grating was transferred onto the concrete specimen. The size of the specimen was 28 mm in diameter and 11 mm in thick ness. The same steps can be applied to replicate the diffraction grating on the specimens in the different shape or size as shown in F igure 24. The procedure to prepare the diffracti on grating on the specimen i s illustrated in Figure 2 5. Figure 24. Concrete samples and molds

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33 Figure 25. Proc edure to prepare diffraction grating Once the master gratin g wa s separated from the specimen, it was examined by observing moir fringe patterns in the moir interferometer. The U and V field moir fringe patterns in the null field and the fringe patterns with rotation carriers are shown as in Figure 26. The area in the circle was where the replication took place. T he f ringe patterns in the circled area remain th e same as those in the area outside the circle This in dicated that the deformation of the concrete specimen d id not cause any damage or distortion on the master grating. Therefore, the master grating can be used as the reference grat ing in the measurements.

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34 Fig ure 26. Fringe patterns from the master gratin g 2.3 Automated Fringe Analysis T raditionally the fringe patterns are analyzed manually by choosing the positions of interest and counting the fringe numbers within the selected gauge lengths. This is an intensity based and point wise method. A lthough this method can be repeated on multiple data points, it is time consuming and causes error s because of the uncertainty in dete rmining the exact loc ation s of fringe s M ethods based on extraction of the underlying phase distribution are becom ing popular since they have significant advantages over the intensitybased methods: data is obtained U field V field + rotation carriers U field + rotation carriers i V field

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35 over the full f iel d, not just at the fringe maxima and minima the sign of the deformation is given and immunity from noise is normally better [ 96] A n automated fringe analysis system based on phase shifting theory was developed to obtain the full field displacement and strain information. T he automated fringe ana lysis system was developed by Weiqi Yin in the UF ESA Lab to obtain the full field displacement and strain map s automatically. T here are five basic steps of this system listed as below Step 1: Fringe pattern recording A stage specially for phase shifting was designed in the Experimental Stress Analysis (ESA) L ab at the University of Florida [ 97] I t appl ies a phase ramp to the U and V direction after calibration T he Insight Firewire charged coupled device (CCD) camera and a PC based frame grabber were acquired from Diagnostic Instruments Inc. The CCD camera is used to scan the fringe pattern and the frame grabber is used to digitize the image and store it into the computer. T he combination of CCD camera, frame grabber and computer can output images with h igh resolution of 16bits and maximum size of 10001000 pixels. Step 2: Noise filtering A n a ppropriate noise reduction algorithm is needed since n oise exists in all fringe patterns. The noise in the fringe pattern is considered as a random noise with a Ga ussian distribution in our research. Gaussian Low Pass Filter (GLPF) in the frequency domain was chosen to remove the noise [ 98] before phase shifting step and the results showed that it was an effective way to reduce the noise. Step 3: Phase shifting Mo ir fringe patterns are developed by interference caused by two light sources reflecting off a common location. W ithin that interference there is a corresponding intensity and phase

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36 associated at each location (pixel) within the fringe image which can be m athematically expressed as Eq. ( 25), ,,(,)cos,bmIxyIxyIxyxy (2 5) where Ixy is the recorded intensity of each pixel ,bIxy is the background intensity, ,mIxy is the fringe amplitude, an d xy is the phase function to be measured. Based on the expression above, it is generally impossible to obtain a unique phase distribution from a single fringe pattern. P ositive phase cannot be distinguished from negative without more information. T he solution to this problem is to add to the phase function of known phase ramp which is linear in either tim e or position as shown in Eq. ( 26). ,,(,)cos, 0,1,2......1bmIxyIxyIxyxynnN (2 6) where n is the added known phase ramp, N is the total number of phase shifted and n is the order of the phase shifting pattern. The wrapped phase xy can be extracted by N phase shifted fringe patterns using Eq. ( 27), 1 0 1 0(,)sin(2/) (,) (,)cos(2/)N n n N n nIxynN xyarctg IxynN (2 7) Step 4: Phase unwrapping guided by quality A Phase unwrapping algorithm based on the quality map of the wrapped phase was develope d to obtain the natural unwrapped pha se. Quality maps are arrays of values that define the quality or goodness of each pixel of the wrapped phase. In a quality map, the areas with low quality represent unreliable phase data. There are many quality maps available such as

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37 correlation, pseudoco rrelation, phase derivative variance (PDV) etc [ 99] In this paper PDV map was utilized as the quality map. PDV map is used to lead the phase unwrapping algorithm star t ing from the pixel with high quality to the pixel with poor quality. A fter phase unwr apping, the whole field phase information which can be easily converted into displacement and strain information via Eq ( 28). 1 2 1 ,, 2 1 1 2 ,, 2 ,, 1 22U xx U V yy V UV xyxy xy fx Uxyxy f xy xy fy Vxyxy f xyxy xy fyx (2 8) Step 5: Calculation of displacement and strain T he displacement or unwrapped phase field conta ins optical and electrical noise. T he noise may not significantly affect the displacement field; however, it can result in large errors when calculating strain. Generally, the deformation of the specimen measured via m oir Interferometry is continuous, whi ch indicates that the unwrapped phase, displacement, strain and should also be continuously distributed. H owever, the noise from an optical or electric device might break the continuity and incorporate significant error in strain calculation. The tradition al method to calculate the strain is highly sensitive to the existence of noise in the phase map. A t the same time, the selection of the gage length will also greatly affect the result. The idea of using global s urface fit technique to smooth the unwrapped phase map can effectively attenuate the noise. A nd most importantly, it can calculate gradient (strain) analytically. Thin plate spline (TPS) is chosen because it is insensitive to noise in the data and it has high capability of constructing complex surfa ce shapes. Theoretically, all the pixels recorded by the CCD camera can be used in TPS surface fit to maintain the spatial and strain resolution. However, the estimation of

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38 parameters of TPS [100 103] is time consuming or even fails for large images. O ne s olution to this problem is to use the subset of the data, which can reduce spatial resolution somehow. A trade off between the resolution and computational efficiency has to be made to obtain reasonable results for large images. TPS technique was used to a nalyze the numerically simulated fringe pattern or the experimental fringe patterns. The results show the effective performance and accuracy of this method.

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39 CHAPTER 3 S H RINKAGE MEASUREMENT S OF CONCRETE 3.1 Introduction Using the Cure Ref erence Method which was described in the previous chapter some tests were performed and their results were characterized and compared with the trends of shrinkage behavior recorded in the literature Because a large number of factors can influence the shrinkage in concrete materials, in every test only one factor was set as a variable and the others were fixed in order to investigate the specific effect. Among these factors, temperature and relative humidity are the most important ones to be properly contr olled because they are not quite stable in the surrounding environment s Without accurate contro l of them in the tests, the experimental results c an be greatly affected. As a result a n environmental chamber for controlling the temperature and humidity was created In the concrete shrinkage measurements, once the specimen had been demolded, the master grating was positioned in the moir interferometer as the reference grating for the tuning of the moir interferometer to a null field which is regarded as the absolute reference of nondeformation. Then by replacing the master grating with the specimen grating, a set of the initial (day 1) fringe patterns can be captured by the CCD camera. After that, the specimen was stored in the environmental chamber which establishes the specific drying condition for the duration of six days. Every 24 hours in this period, the specimen was removed from the chamber and positioned in the moir interferometer, a set of the consecutive phase shifted moir fringe patterns was recorded and the specimen was stored back after the measurement. Precautions to accurately position the specimen were taken so that the location and orientation were repeatable. These procedures are discussed in detail in ref [9 1]. An automated strain anal ysis system based on phase shifting theory was used to obtain the full field displacement and strain maps for the

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40 measurements from day 1 to day 7. Shr inkage as a function of time, location and other factors was determined accordingly. 3.2 Chamber Setup A 100% air tight food storage container served as the chamber ( Figure 3 1) The picture shows that the desiccant fills the bottom side of the container to provide low humidity drying environment to the specimen. The size of the container is around 10x10x15c m The hygrometer with an accuracy of % RH and 1C was used to check the temperature and humidity i nsi de of the chamber. Figure 31. Chamber setu p 3.2.1 Humidity Contro l Water, saturated salt solutions [ 104 ] or desiccates w ere inserted into the chambe r to create differing level s of relative humidity inside the chamber. 0.5 pounds of Drierite desiccants are inserted to create 0~2% relative humidity (RH) inside of the chamber. On the other hand, 100% RH is easily maintained only by replacing desiccates w ith a cup of 80c.c water. 200c.c. potassium carbonate saturated salt solution is mixed and filled the bottom of the chamber for creating 502% RH. T able 3 1 shows the substances for the control of RH inside of the chamber

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41 Table 3 1. Substances for RH co ntrol Substance Desiccate Potassium carbonate Magnesium nitrate Sodium chloride Water RH (%) 0~2 502 602 802 100 3.2.2 Temperature Control 23 C was room temperature which was very stable in the laboratory. The oven was used to create higher temperatu re such as 40 C and 45 C The refrigerator was used to provide 5 C. The chamber was p laced in the oven or the refrigerator if the specific temperature other than room temperature as needed. 3.3 Experimental Setup s In this research, tw o experimental setup s are introduced here They are the first and second generations of Portable Engineering Moir Interferometers (PEMI) respectively 3.3.1 PEMI I The experimental setup with PEMI I is shown in Figure 32. It includes a moir interferometer, a stage for phaseshifting a power supply, a specimen fixture an xy z stage, a CCD camera and a desktop. The moir interferometer is put on the stage which is controlled by the power supply. When the stage is moving, the fringe patterns are shifted and recorded via t he CCD camera which is controlled by the software in the desktop. A set of the consecutive phase shifted fringe patterns is able to be recorded with some interval time. The Figure 33 shows a clo seup view of this specially design ed stage for fringe shift ing. This was designed in the Experimental Stress Analysis (ESA) lab at the University of Florida T he stage is composed of two aluminum plates and four aluminum tubes. The four tubes were precisely machined and attached to the bottom and top plates at 45o. Magnetic wires of 0.007 in diameter with special enamel coating for high temperature were wrapped exactly 200 times around the center of each

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42 of the four aluminum tubes then connected together with strain gage wire to complete the circuit. A 0~35 V, 0 ~5 A adjustable power supply, from Pyramid, model PS 32 lab was connected to the circuit. By turning on the power and increasing the voltage, the current passed through the magnetic wire circuit. The aluminum tubes are hence heated and have elongation in t he 45degree direction. This then moves the entire moir interferometer in the 45 degree direction. Therefore, the displacements of the moir interferometer in both horizontal and vertical directions remain the same. This provides the same phase to both U and V field fringe patterns. 1 2 3 4 5 6 7 1 6 5 4 3 2 7Specimen fixture IBM PEMI moir interferometer CCD camera X-Y -Z stage PC Power supply Stage for phase shifting Figure 32. Experimetnal setup with PEMI Specially designed stage for fringe shifting Aluminum Tube Magnetic wire circuit Fig ure 33. F ringe shifting stage

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43 3.3.2 PEMI II The experimental setup with PEMI II is shown in Figure 34 This setup is much more compact, versatile, portable, and friendly to us e rs because of the combination of all components as one system and extremely easy alignment Also, there is no need for traditional dark room. The PEMI II has built in phase shifting hardware that utilizes a custom designed piezo electric transducer. The c ompact design of the phase shifting device offers optimu m stability and repeatability. S witching between U and V fields is achieved without touching the interferometer, eliminating the possibility of a disturbance that c an modify the fringe patterns. The phase shifting hardware and the high resolution CCD camera are controlled through the software in the computer A set of the consecutive phase shifted fringe patterns are obtained in the format of 1000x1000 pixels and can be analyzed immediately through the automatic fringe analysis system in the computer Fig ure 34. E xperimental setup with PEMI I I

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44 3.4 Experimental Results Since there are numerous factors influencing the shrinkage of concrete materials, the testing can be performed by controlling some oth er factors in order to investigate the specific effect Some examples of the moir fringe patterns are shown and analyzed. And then their results are compared with one another and interpreted. 3.4.1 Drying Condition Effec t (Temperature and Humidity) The cement paste specimens were made by mixing ASTM C150 type I Portland cement with water in w/c ratio of 0.5 Shrinkage in different drying environments was measured Initial fringe patterns (day 1) which were obtained right after the specimen was demolded rev ealed some swelling effect, but this was not significant and was able to be explained by FEA in the next chapter Some example s of the U and V field moir fringe patterns in different drying conditions are shown and analyzed Case1: 50% RH and room tempera Figure 35. U field Moir fringe patterns under 50% RH and 23

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45 Figure 36. V f ield Moir fringe patterns Obviously, Figure 35 and 36 have shown that the V field fringe patterns are similar to the U field except the rotation of 90 degree This is due to the axis ymmetric conditions of the specimen Moreover, the number of fringe s increases with time and the fringe density is larger in the area close to the outer surface than in the inner core. Although the fringe densi ty i s too high to show here, the inset shows the quality and contrast are high. The full field maps for each day were obtained via the automated fringe analysis system. Only the day 2 full field information i s shown as Figure 37 in xy coordinate and Figu re 3 8 in polar coordinate. In the automated fringe analysis system, the center of the specimen i s set as the point of zero displacement. The displacement and strain fields in polar coordinates a re obtained by the transformation of those in rectangular co ordinates. From the displacement maps in both coordinate systems, the overall in plane deformation of the specimen i s shrinkage. In the normal strain maps, it can be seen that shrinkage was larger in the area close to the outer surface. This is due to the fast drying in the volume close to the exposed surface.

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46 Displacement: U field (m) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -6 -4 -2 0 2 4 6 Displacement: V field ( m) Pixel Pixel 0 200 400 600 800 1000 1000 800 600 4000 200 0 -6 -4 -2 0 2 4 6 Strain xx ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 Strain yy ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 Shear Strain xy ( ) Pixel Pixel 0 200 400 600 800 1000 1000 800 600 400 200 0 -300 -200 -100 0 100 200 300 Figure 37. Full field maps in xy coordinate for day 2

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47 Displacement: R field (m) PixelPixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -6 -4 -2 0 Displacement: field (m) PixelPixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -0.3 -0.2 -0.1 0 0.1 0.2 Strain rr ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 Strain ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -550 -500 -450 -400 -350 -300 -250 -200 -150 Strain r ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -80 -60 -40 -20 0 20 40 60 Figure 38. Full field maps in polar coordinate for day 2

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48 The shear strain map in x y coordinate shows the maximum shear str ain near the outer surface occurred in 45 and 135 degree directions. Also, along the vertical and horizontal centerlines, the value of the shear stain i s zero. This can be easily explained by using Mohr s circle or shown later by finite element analysis In polar coordinate, the angular displacement and shear strain should be zero due to axisymmetry. The result has shown their values are insignificant compared with those in other fields. However, their maps ar e not uniform due to noise. Case2: 0% RH and room temperature In this case, a generous amount of desiccates was used in the chamber to create as low RH as 0%. The moisture diffusing out of the specimen was absorbed by desiccates continuously, which maintained the RH 0% in the chamber. Figure 39 and 310 are the U and V field fringe patterns under 0% and room temperature. Likewise, both the fields have shown similar fringe distributions because of axi symmetry Apparently, the fringe density or the number of fringes was mu ch higher compared with the case of RH50%. This is due to the faster drying in the case of lower humidity. Likewise, the number of fringes increased with time A lso the fringe density was higher in the area close to the outer surface than in the inner core from day 2 U & V field fring e patterns. T he inset has shown the quality and contrast a re still high. Only day 7 full field strain information i s shown here as Figure 3 12. The automatic strain analysis system was still capable of resolving such fringe patterns of very high fringe density. The radial strain is as high as around 5000 t Also, t he shear strain map in x y coordinate shows the maximum shear strain occu r s near the outer surface in 45 and 135 degree directions T he value of the shear stain in x y coo rdinate i s zero along the vertical and horizontal centerlines. The shear strain i n polar coordinate was not significant.

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49 Figure 39. U field Moir fringe patterns under 0% RH and 23

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50 Figure 310. V field Moir fringe patterns under 0% RH and 23 x x ( ) -4800 -4600 -4400 -4200 -4000 -3800 -3600 -3400 y y ( ) -4800 -4600 -4400 -4200 -4000 -3800 -3600 -3400 xy ( ) -500 -400 -300 -200 -100 0 100 200 300 400 500 rr ( ) -4800 -4600 -4400 -4200 -4000 -3800 -3600 -3400 ( ) -3900 -3800 -3700 -3600 -3500 -3400 -3300 r ( ) -100 -50 0 50 100 150 Figure 311. Full field maps for day 7 under 0% RH and 23C

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51 Case3: 0% RH and In this example, the chamber of 0% RH was maintained in the refrigerator. T he low temperature of was very stable in the refrigerator. After the specimen was removed from the chamber, the measurement was not started immediately. Instead, it was placed on the optical table for around 5 minutes. This is to make the specimen retur n to room temperature and to reduce deformation from the thermal effect. Figure 312 and 13 are U & V field moir fringe The fringe density and the fringe number are not as large as those in the case of RH 0% and room temperature. It can be explained by the fact that low temperature reduces the rate of drying. Also, t his example makes the fringe densit ies near the outer surface and in the inner core more distinguishable than the case of RH 0% and room temperature It can be seen that the fringe density was higher near the outer surface. Figure 312. U field Moir fringe patt erns under 0% RH and 5

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52 Figure 313. V field Moir fringe patterns under 0% RH and 5 The moir fringe patterns in the case of 0% and 40 patterns, it can be followed that drying is accelerated in high temperature environment. Likewi se, the specimen was left on the optical table for about 5 minutes before the measurement. Figure 314 shows the measured shrinkage from the center of the specimen to the outer surface on the grating surface for different combinations of humidity and temperature. Shrinkage on day 1 was not recorded because it is insignificant. Here, shrinka ge is defined as the radial strain ( rr) Obviously, the results indicate that larger shrinkage occurred in the area close to the outer surface and shrinkage increased with time Also, shrinkage is very sensitive to the drying conditions. In the hot and cold temperature conditions, the speci men might take at least 20 minutes rather than 5 minutes to return to room temperature. The experimental results in these two cases must incorporate some errors due to thermal effect. The typical value of thermal expansion coefficient for cement paste with w/c =0.5 is 18 Therefore, the results for the cold and hot conditions are demonstrated with the consideration of the errors.

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53

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54

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55 Figure 314. Measured s hrinkage from center to outer surface

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56 The evolution of the shrinkage in the case of related to the temperature variation over the cross section. The heat generated from the hydration outer surface. This temperature variation would lead to differential material properties of shrinkage over the cross section. However, this phenomenon might not be influential in room temperature condition. Case4: This example is wo rthy to be discussed here because the fringe distribution is quite different from the previous cases. The U and V field moir fringe patterns in Figure 3 15 and Figure 316 have show n that c ompared with RH=0 or 50%, there are not many fringes. That means t he overall deformation is quite small. Also, t he fringes curve outwardly instead of curving inwardly in the other cases Furthermore, t here are the enclosed fringes close to the outer surface from Day 5 Figure 315. U field Mo i r fringe patterns under 1

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57 Figure 316. V Field Moir fringe patterns In order to understand the strain distribution in this special case, the U field fringe pattern on day7 was analyzed. The result is shown in F igure 317 with the full field displacement and strain information, and the plot of the strain distribution along the horizontal centerline Globally, the concrete experienced shrinkage which is determined according to the U field displacement map Locally, swelling occurred in the ar ea close to the outer surface, which is due to the moisture gain from the surrounding environment. The inner core still experienced the shrinkage because of the hydration process. The locations of zero strain approximately correspond to the centers of the enclosed fringes. They are the positions to separate the swelling zone and the shrinkage zone.

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58 Shrinkage Swelling Swelling N=0 3 2 1 -1 -2 -3 0 200 400 600 800 1000 -200 -100 0 100 200 Pixel Strain x x U-field displacement (m)PixelPixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1 -0.5 0 0.5 1 Strain xx ( )PixelPixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -150 -100 -50 0 50 100 Figure 317. U field displacement and strain maps for day Three tests were attempted for both drying conditions of RH=0% and 100% in room temperature. Their results are recorded in Table 3 2 and 33 separately The data strongly indicated the repeatability of this experimental technique. Table 3 2. Shrinkage measurements under RH=0% and RH=0% Specimen 1 Specimen 2 Specimen 3 F r i nge number Shrinkage ) F r i nge number Shrinkage Fringe number Shrinkage Day1 0 0 0 0 1 14.88 Day2 80 1190.47 88 1309.52 87 1294.64 Day3 147 2187.5 0 156 2321.42 158 2351.19 Day4 175 2604.16 183 2723.21 186 2767.85 Day5 197 2931.54 206 3065.47 209 3110.11 Day6 210 3125 .00 217 3229.16 224 3333.33 Day7 225 3348.21 230 3422.61 238 3541.66

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59 Table 3 3. Shrinkage measurements under RH=100% and RH=100% Specimen 1 Specimen 2 Specimen 3 F r i nge number Shrinkage ) F r inge number Shrinkage F r i nge number Shrinkage Day1 0 0 0 0 2 29.76 Day2 4 59.52 2 29.76 2 29.76 Day3 5 74.40 4 59.52 3 44.64 Day4 6 89.28 6 89.28 3 44.642 Day5 7 104.16 7 104.16 4 59.52 Da y6 8 119.04 8 119.04 5 74.40 Day7 12 178.57 8 119.04 5 74.40 The experimental results can be displayed in terms of the average d shrinkage or overall shrinkage The average d shrinkage was determined by dividing the diameter change by the original diameter (28mm) The diameter change was derived by counting the number of fringes within the horizontal centerline in the U field or within the vertical centerline in the V field, and then multiplying it with 0.417 m/per fringe. Figure 318 are the result s con cerning relative humidity and temperature effect s on the shrinkage behavior of cement pastes. Figure 3 19 were the result s regarding to W/C ratio and size effects on the shrinkage behavior of cement pastes. The data points are the measurements of the averaged shrinkage. From the results, it can be known that in the surrounding environment of low humidity and high temperature concrete experiences larger shrinkage. As a result, larger tensile stress is developed when the concrete structure is constrained. Th is increases the possibility of cracking occurrence in the structure and reduces the durability of the structure.

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60 Figure 318. Relative humidity and temperature ef fect

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61 3.4.2 W/C ratio and Size E ffects Figure 319. w/c and size effects on averaged shrinkage of cement pastes 3.4.3 Aggregate Effect The shrinkage behavior of the specimens with aggregates was explored in t he same experimental technique. Either fine or coarse aggregates (sand or gravel ) were added to cement

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62 pastes to investigate how aggregates affected moir fringe patterns and shrinkage behavior. Some examples of moir fringes patterns were shown and analyzed. Both a ggregate quantity and humidity effect s were tested. 3.4.3.1 Fine aggregate The mortar specimens were made by adding ASTM C 778 sand to cement pastes (w/c=0.5). The specimen s were stored in the drying conditions of relative humidity 0% and room temperature. Figure 320 was The U field mo ir fringe patterns for sand/cement ratio (s/c) of 37.5%. The V field fringe patterns were not shown here due to the same shape as U field except 90 rotation The inset revealed the fringes were affected by the existence of the sand particle s Sands seem to lower the fringe density or reduce the shrinkage locally. However, hand counting the number of fringe s was not an issue while determining the average d shrinkage. Figure 320. U field moir fringe patterns for mortar with s/c=37.5% The strain analysis for Day 2 fringe patterns was shown as Figure 321. The maps might be too smooth to reflect the actual strain information. However, it was stil l acceptable and

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63 reasonable while only considering the strain distribution in a more global sense. Likewise, shrinkage was larger in the area close to the outer surface than in the inner core. Strain yy ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1400 -1200 -1000 -800 -600 -400 -200 Strain xx ( ) Pixel Pixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -1400 -1200 -1000 -800 -600 -400 -200 0 Fi gure 321. Strain information for mortar with s/c=37.5% on da y 2 The displacement maps in both coordinate systems were shown in Figure 322. The radius displacement field was used to verify the angular strain field by the equation Ur /r. Figure 322. D isplacement map s for mortar with s/c=37.5% on day 2 The specimen with s/c= 75% was also tested. D ay 7 U & Vfield moir fringe patterns and fringe patterns with rotation carriers were shown as in Figure 323. The inset revealed counting

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64 fringes became ch allenging due to the irregularity and distortion of the fringes. However, the r otation carriers could be added to make it possible to count fringes for the det ermination of the average d shrinkage. Also, this would not change the full field strain distribution if ch oosing the moir fringe patterns with rotation carriers for analysis. Fig ure 323. Moir fringe patterns for mortar with s/c=75% on day 7 Theoretically, t he full field strain map s could be obtained with different sizes of gauge lengths in the automatic fringe analysis system However, if the selected gauge length is too large the maps will be too smooth to exactly reflect real local information like the maps in the previous case of s/c=37.5%. Therefore, in this case, Day 7 moir fri nge patterns were analyzed with both small and large gauge lengths The result shown in Figure 324 revealed two things.

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65 First ly there still existed larger shrinkage in the area close to the outer surface. Secondly from 324(b), t he shrinkage at many local point s was smalle r due to the existence of t he randomly distributed sands. The strain information from the analysis with the small gauge length might display the strain distribution more properly. Strain xx ( ) -1850 -1800 -1750 -1700 -1650 -1600 -1550 -1500 -1450 -1400 Strain yy ( ) 200 400 600 800 1000 -1850 -1800 -1750 -1700 -1650 -1600 -1550 -1500 -1450 -1400 -1350 (a) Large gauge length (25 pixels) (b) Small gauge length (8 pixels) Figur e 324. Full field normal strain maps with both (a) large and (b) small gauge lengths for the mortar specimen of s/c=75% on Day 7 Figure 325 shows both fine aggrega te quantity and RH effects on the average d shrinkage of mortar specimens Obviously, the more the quantities of sands, the lower the measured averaged shrinkage. Also, averaged shrinkage increased with the decreased relative humidity.

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66 Figure 325. A ggrega te quantity and RH effects on average shrinkage of mortar specimens

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67 3.4.3.2 Coarse a ggre gate Gravel was embedded into the cement paste (w/c=0.5), but did not contact with the grating. The arrangement of th e gravel is shown as Figure 3 26 with the side view and the top view The specimen was stored in relative humidity 0% and room temperatur e Figure 326. S ide and top views of gravel test The m oir fringe patterns from Day 1 to Day 5 were recorded. But only day 5 U & Vfield moir fringe patterns are shown here in Figure 3 27. There were some areas of the lower fringe density as remarked by the blue boxes. T he insets indicated the fringes in the blue box. These areas correspond ed to the locations of the embedded gravels. There was a crack going on in the area circled by the red line. This was due to the constraint from the embedded gravels

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68 Figure 327. Day 5 moir fringe patterns for the gravel test

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69 The s train analysis was performed and the results were shown in Figure 328. Clearly, the locations of the gravels have the lower shrinkage. The plots just displayed the normal strain dist ributions along the horizontal centerline in U fie ld and along the vertical centerline in V field. Strain xx ( ) Pixel Pixel 0 200 400 600 800 1000 1000 800 600 400 200 0 -3000 -2500 -2000 -1500 -1000 0 100 200 300 400 500 600 700 800 900 1000 3500 3000 2500 2000 1500 1000 500 Position Shrinkage Strain yy ( ) 0 200 400 600 800 1000 1000 800 600 400 200 0 -3000 -2500 -2000 -1500 -1000 0 200 400 600 800 1000 3500 3000 2500 2000 1500 1000 500 Position Shrinkage Figure 328. The Strain analysi s for gravel test

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70 3.4.4 Autogenous Shrinkage Measurements in Sealed Conditions In order to explore Autogenous shrinkage only, drying shrinkage from moisture loss needs to be prevented. A method of combining CRM and the sealing of the entire specimen was used to measure autogenous shrinkage. This method could offer the information concerning the contribution of autogenous shri nkage to overall shrinkage Therefore, instead of placing the specimen inside of the chamber after demold, the entire specimen was sealed with aluminum sheets first and then plastic wrap to prevent the exchange of moisture with the surrounding environments Many sealing methods have been attempted, but this one could prevent the grating on the surface of the specimen from damage. Every day the specimen was unsealed, a quick measurement was taken and then the specimen was sealed again after testing Humidit y is no longer a factor to autogenous shrinkage measurement, but temperature is still an influential one. The tests were done on both the sealed cement paste specimens and the mortar specimen. For the test on the mortar specimen, one modified sealing method was used which could work out some issues in the original sealing method. 3.4.4.1 Sealed c ement paste specimens According to literature, autogenous shrinkage is not significant when w/c ratio is above 0.4. Hence, the cement paste specimen with w/c rati o=0.4 was tested first. The U&Vfield moir fringe patterns for w/c=0.4 in room temperature were shown as Figure 329 and 330. It was noticed that the fringes were quite uniformly spaced in both the fields. That was because drying shrinkage which is diffe rential over the cross section no longer existed in this case and the measured shrinkage only came from the hydration process The day 7 U field fringe pattern was analyzed as in Figure 3 31. Exactly uniform strain maps could not be obtained through the a utomated fringe analysis because of noise. However, the normal strain map in U field has shown very uniform strain over the entire field when the

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71 scale was enlarged. Furthermore, by obtaining displacement fields and plotting displacement distribution along the horizontal centerline in U field, it was found that the slope was very close to constant, which means the strain was very uniform. And the shear strain was very uniform and close to zero over the entire field when the scale was enlarged. Figure 329. U field moir fringe patterns for w/c =0.4 in room temperature Figure 330. V field moir fringe patterns for w/c =0.4 in room temperature

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72 Figure 331. Day 7 U field displacement for the sealed specimen with w/c=0.4 in xy coordinate Two influential factors, w/c ratio and temperature, were investigated and the results were shown in Figure 332. It can be seen that the use of concrete with w/c below 0.4 or in higher temperature might face an issue. Autogenous shrinkage in s uch cases has significant contribution. As a consequence, this might induce cracking in the concrete structure and reduces its durability. Strain xx ( ) 0 200 400 600 800 1000 1000 800 600 400 400 0 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 Shear Strain xy ( ) PixelPixel 0 200 400 600 800 1000 0 200 400 600 800 1000 -400 -300 -200 -100 0 100 200 300 400 Displacement: U field (m) Pixel Pixel 200 400 600 800 1000 0 200 400 600 800 1000 -6 -4 -2 0 2 4 6 0 200 400 600 800 1000 -8 -6 -4 -2 0 2 4 6 8 PixelPixel U-field Displacment

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73 Figure 332. W/C ratio and temperature effects on sealed specimen shrinkage The results show autogenous s hrinkage increased with decreased w/c ratio and with increased temperature. For w/c=0.3, the shrinkage increased significantly. Even the measurement on day 1 showed the shrinkage rather than the swelling. This was due to strong hydration process in the ear lier time of curing. For w/c=0.5 or 0.6, the shrinkage is not significant. The fringe

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74 patterns for w/c=0.6 included in the appendix were to show the insignificant deformations The results correspond to the trend of autogenous shrinkage documented in the l iterature. Therefore, the contribution of chemical shrinkage to overall shrinkage increases with the decrease in the w/c ratio. The autogenous shrinkage is a concern in the use of high performance concrete materials. On the other hand, higher temperature c ould accelerate the hydration process and induce larger shrinkage. The day 6 fringe patterns are analyzed and the full field maps are shown in terms of polar coordinate in Figure 5. The radial displacement and shear strain maps are not shown here because t hey are suppose to be zero. Also, it can been seen that the radial strain is similar to the angular strain. Displacement: R field (m)PixelPixel 0 200 400 600 800 1000 1000 800 600 400 200 0 -6 -5 -4 -3 -2 -1 0 Strain ( )PixelPixel 0 200 400 600 800 1000 1000 800 600 400 200 0 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 Strain rr ( )PixelPixel 0 200 400 600 800 1000 1000 800 600 400 200 0 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 Figure 333. Day 6 displacement and strain analysis for the sealed cement paste specimen with w/c=0.4 in polar coordinat e

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75 3.4.4.2 Seal ed m ortar specimen A modified sealing method i s illustrated in Figure 3 33 and also described as following : Figure 334. A modified sealing method Step 4 : 4 hours after concrete was poured into the mold, concrete was hardened a little bit. It is good time to seal the top side of the specimen with the tape This prevents the moisture loss from that side afterwards. Another 18 hours later, the mold was removed and the side was sealed with the tape Step 5 : The specimen was separated from the master grating. Th ere is no need to seal the bottom side with the grating. The epoxy grating is already a block to the moisture diffusion. This method avoids repeating the sealing and unsealing steps for the measurement of everyday. And the top side is sealed earlier to mi nimize the error from the moisture loss. D ay 7 U field moir fringe pattern and the fringe pattern with rotation carriers for w/c=0.3 and s/c =37.5% in room temperature were shown as in Figure 334

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76 Figure 335. D ay 7 M oir fringe pattern for w/c=0.3 and s/c =37.5% It can be easily seen from the fringe pattern with rotation carriers that the fringes are close the uniformlyspaced distribution. Also, the fringes seem to be affected by the particles of the sand. Figure 335 shows the evolution of the autogenous shrinkage. The autogenous shrinkage is reduced if comparing this result with that without sands. Therefore, aggregates can lower the chemical shrinkage. Figure 336. Autogenous shrinkage for mortar with w/c=0.3 and s/c=37.5% in room temperature

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77 3.4.5 Ring Test for Crack Investigation Since cracks could happen due to shrinkage and existence of constraints the ring test as shown in figure 333 was performed to induce cracks on the concrete specimen. In the test, the thin epoxy layer was formed on silicone rubber grating, and then the steel rod was placed in the middle of the mold. The position s of the mold and the steel rod were marked on the back side of the silicon rubber grating in advanced. C ement paste fluid (w/c=0.5) was poured into the space formed by the mold and the steel rod. Likewise, the specimen with the steel rod was demolded after 24 hours. Then t he chamber with drying condition of RH0% and room temperature was used t o store the specimen. RH0% was chosen to induce large shrinkage to i nitiate cracks. F igure 337. Scheme of Ring Test The specimen was stored in the chamber for one day and then removed from the chamber for the measurement. Moir fringe patterns on day 1 and day 2 were recorded as in figure 334. Day 1 m oir fringe pa tterns indicated the deformation was not significant because the specimen has not been stored in the chamber. Day 2 moir fringe pattern has shown cracks occurred due to shrinkage and constraint from the steel rod as the insets in both U and V fields indic ated. The pictures of the specimen in figure 335 demonstrated the crack from the top, bottom and side view s Cracks seemed to propagate along the radius direction.

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78 V fieldDay 1UfieldDay 1 Day 2 Day 2 Crack opening=86 m Figure 338. Ring Test investigation for RH=0% and room temperature Top view Bottom view Side view Figure 339. P ictur es of the specimen with a crack in the ring test

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79 3.4.6 Swelling test Instead of being placed into the chamber under drying, the specimen was fully immersed into water for 24 hours after demold. But the grating was covered with dental material before immers ion so that it was not allowed for direct contact with water. The fringe patterns before and after immersion as in figure 3 39 are compared. The result in figure 340 showed the specimen absorbed water and swelle d. However, the deformation due to the absor pt ion of water was insignificant. Fi gure 340. Moir fringe patterns before and after one day immersion Figure 341. Full field displacement maps for the swelling test

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80 3.5 Conclusion & Discussion The experimental technique to measure shrinkage which develops in concrete materials during drying is very repeatable and the process to prepare grating on the specimen is not complicated. The following conclusions can be drawn The experimental technique to measure the shrinkage of concrete materials on a full field basis was developed based on the methodology of curing reference method. A method of combining CRM and the sealing of the entire specimen was used to explore the relative contribution of nondrying shrinkage (chemical shrinkage) to the overall s hrinkage in concrete materials. Phase shifting technique was used to analyze the moir fringe patterns to obtain the full field displacement and strain maps in both xy and polar coordinates. The experimental results demonstrated the same trend of shrinkag e behavior as documented in literature T he following conclusions can be drawn for shrinkage behavior in concrete For the cement paste specimens, Shrinkage increases with the decrease of relative humidity. Shrinkage decreases as temperature decreases. Shr inkage increases with time. Shrinkage near the exposed surface is larger than that in the inner core. For RH=100%, swell up occurs near the outer surface, but shrinkage in the inner core Specimens in small size have larger shrinkage (rate) than the ones i n large size. Shrinkage increases as w/c ratio goes up. The specimen experiences the swelling after the immersion into water but not significant For the specimens with fine or coarse aggregates, The r otation carriers are helpful in obtaining the average shrinkage and the full field shrinkage information. Shrinkage increases with time. Shrinkage near the exposed surface is larger than that in the inner core. Shrinkage decreases as increasing fine aggregates Fine and coarse aggregates both affect the shri nkage locally.

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81 For the sealed specimens, Chemical shrinkage increases with the decrease of w/c ratio. Chemical shrinkage above w/c=0.4 was not significant. Chemical shrinkage increases with the increase of temperature. Chemical shrinkage decrease with th e increase of aggregate quantity. For r ing test, cracks occurred and propagated in the radial direction in the drying condition of RH0% and room temperature. The experimentally obtained shrinkage measurements seem very useful in characterizing shrinkage behavior under different influencing factors However, f rom the experiment one cannot directly measure the shrinkage coefficient, which is a material property of cement paste. Material properties must be independent of specimen geometry but dependent on the composition of cement paste, such as cement type and w/c ratio. The FEA model will be used to match the boundary conditions with the experiment to determine the shrinkage coefficient using an inverse approach.

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82 CHAPTER 4 NUMERICAL MODELING 4.1 Introd uction According to literature, the shrinkage in concrete materials is not uniform over the entire specimen but highly dependent upon the distribution of moisture content As known, m oisture distribution is mainly governed by moisture diffusion during drying, which is here described by Ficks law and self desiccation in the hydration process. Also, m oisture distribution is generally described with relative humidity instead of moisture concentration. From the results of the experiments or previous research shrinkage from self desiccation or shrinkage under sealed conditions was negligible for w/c ratio =0.5. In this case, t he measured shrinkage could be assumed as drying shrinkage only. Therefore, only drying effect or moisture diffusion was considered in th e model if w/c=0.5 was used In other words, if w/c is below 0.4, shrinkage from self desiccation must be considered. The scheme of the inverse approach to obtain the material properties from the complex geometry in the tests is depicted in Figure 41. F inite element model as the forward model was cr eated based on thermal mechanical interaction because this was a multi physics problem. In this coupled model, moisture diffusion was modeled as heat transfer a nd shrinkage behavior was modeled as thermal ex pan sion. Table 4 1 gave the details of the analogy regarding to the model T wo materials parameters, film coefficient and shrinkage coefficient, were defined and to be determined. Optimization in conjunction with the constructed finite element model was used to fit experimentally determined shrinkage in order to determine these two material parameters. This was the inverse method to solve this inverse problem. Once they are obtained, they can be the inputs for finite element analysis to predict the shrinkage under different drying or geometric conditions. The other tests can be performed and their results can be compared with FEA.

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83 Figure 41. S cheme of numerical modeling Table 4 1. Thermal mechanical interaction model Thermal Mechanical Interaction Model Thermal Mod el Mechanical Model Heat Transfer vs. Moisture Diffusion Thermal Expansion vs. S hrinkage Temperat ure vs. Relative Humidity Thermal Expansion coefficient vs. Shrinkage coefficient Conductivity vs. Diffusity Surface coefficient vs. Fil m c oefficient

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84 4.2 Model Description 4.2.1 Axisymmetric M odel In order to obtain the defined material properties, the finite element model was created an d took advantage of axisymme try because the geometry of the specimen in the tests was in the shape of the cylindrical disk. The use of the a xisymmetric model could save running time in each iteration while using the inverse method to determine material properties. Eight node quadrati c qua drilateral mesh es were used in the model. 4.2.2 Materials Properties According to literature, the expression of moisture diffusion coefficient shown as below was used in the thermal model: 11 *( ) 1 1() 1n cDD h h (4 1) Where D1 is the maximum of D(h) for h = 1.0, D0/D1, D0 is the minimum of D(h) for h = 0.0, hc is the pore relative humidity when D(h) = 0.5D1. Here D1 = 25mm2/day, 0.1, n=6, and hc =0.72 are approximately assum ed [ 105 ] The values of these parameters are only applicable to ASTM Portland cement type I with w/c=0.5 in room temperature condition. Typical values E=2.5 GP a cementitious materials in the mechanical model The s hrinkage coefficien t in the mechanical model and film coefficient in the thermal model are two unknown material properties to be determined by the inverse approach. 4.2.3 Initial C ondition: Moisture diffusion from the bottom side which is the opposite side to the top side with the grating, to the environment started before the specimen was demolded However, i t was assumed negligible due to the long process of drying in the tests. Also, the specimen took some

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85 time to cure and get hardened from the fluid phase Therefore, i t was assumed that the whole specimen has h=1 or 100% when t =0 which referred to Day 1. 4.2.4 Boundary Condition The boundary conditions in moisture diffusion model were described in figure 42. The grating on top of the specime n was assumed as the insulat ion to moisture flux. The insulation on the boundary along the symmetrical line wa s automatically assumed. The flux on other two boundaries was assumed as convection type which is described by the equation in figure 42. Here, f represents film coefficient. J represents moisture flux hs represent relative humidity on the surface. hen represents ambient relative humidity No boundar y conditions need to be defined in the mechanical model because the specimen in the experiment s was in the condition of free sh rinkage Figure 42. Boundary conditions of moisture diffusio n model 4.3 Inverse Method In the inverse method, t he finite element model described above was the forward model created in COMSOL This forward model was interfaced with the optimization code which was developed in Matlab to obtain the shrinkage coefficient and film coefficient. The s hrinkage coefficient and the film coefficient were two variables in the optimization code. In each of

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86 iterations, the optimization code specified the values of t hese two variables, called the forward model to solve the problem and then computed the value of the objective function. When the value of the objective function was minimized, which indicated the fitting of the FEA result with the experimental data was o ptimized the shrinkage coefficient and the film coefficient were hence determined. The optimization code was based upon the nonlinear least square s method and the GaussNewton algorithm was adopted. The objective function was defined as the following equatio n: 2 11(,)()mn ijij jiFfee (4 2) In the above formulation, there are two unknown coefficients represented by constant as the shrinkage coefficient and represented by constant f as the film coefficient. eij in equation ( 42) is the i th radial strain on jth drying day obtained experimentally and eij* is the radial at the same point computed using finite element analysis. It is assumed that there are n such experimentally obtained radial strain s at n positions from the center to the circumference on the surface with the grating. Here, n is equal to 6 and the measurement positions are equally spaced. Hence, t he di stance betw een two neighboring positions is 2.8mm. And m represents the total drying duration in the chamber in unit s of day. Here m is equal to 6, which corresponds to drying duration of 6 days in the experiments Using the experimentally obtained radial strains u nder RH=50% and room temperature at six locations from Day 2 to Day 7, the estimation of the se two material parameters was perf ormed through the inverse approach mentioned above T he curve fitting result was shown in Figure 43. The shrinkage coefficient =53.8 / C and the film coefficient f = 2.12 mm/day were obtained.

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87 Figure 43. Optimization results The errors of the optimization were calculated and shown in table 4 2. The goodness of fit can be evaluated by the value of R square value. The value indicated the fitting between the experimentally obtained data and FEA results is good. The discrepancy mainly results from the day 4 data. Table 4 2. Errors of optimization Mean TSS SSR SSE Erms R2 1515.995 13159522.14 13005106.88 154415.26 4289.31 0.9883 Once the shrinkage coefficient and the film coefficient were determined, 3 D model was created to mo del shrinkage behavior of the entire specimen in xy coordinate as figure 44. This made it easy to compare between FEA results and experimental resul ts from moir interferometry in xy coordinate

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88 Figure 44. 3D model of shrinkage behavior The top surface of 3D model which the grating was on was selected and the shrinkage maps on this surface were drawn as figure 45. The full field strain infor mation in both xy and polar coordinates is shown. The shear strain in polar coordinate is automatically assumed zero in the finite element analysis. Figure 45. FEA results for RH=50% and room temperature

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89 4.4 Validation of Model In order to validate the constructed model and the obtained material properties, some other tests were performed and their results were compared with FEA. D ifferent surrounding relative humidity, different size and s hape of the specimen, ring test, shrinkage before d emold and reinforced cement paste were tested and discussed 4.4.1 Different Surrounding Humidity The same material p arameters were used to predict the shrinkage under the drying condition of RH=80% and room temperature. The size of the specimen and w/c ra tio remained the same. The moir fringe patterns for RH80% and room temperature are covered in A ppendix. The experimental and FEA result s are shown as Figure 46. F or each day measurement, t he experimental result did not match perfectly with FEA result. Ho wever, they a re very similar in the trend and the range of the magnitude The full filed experimental and FEA maps on Day 3 are compared as Figure 4 7. The maps indicated that the results from the experiment and FEA have very good agreement. Figure 46. E xperimental and FEA results for RH=80% and room temperatur e

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90 Figure 47. E xperimental and FEA results for RH=80% and room temperature on Day 3

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91 The experimental technique can only measure the deformation on the surface of t he specimen. In order t o investigate the true shrinkage b ehavior inside of the concrete specimen, the cross section view s of the deformations in cylindrical coordinate in FEA are used to address t he 3D effect through the thickness as Fig ure 48. The top a nd left sides represent the surface with the grating and the central axis of the specimen individually. The shear components are not shown here due to their insignificance in magnitude. The normal components reveal the maximum shrinkage occurs in the area near the bottom side and close to the outer surface. On the other hand, the minimum shrinkage occurs near the central axis of the specimen and close to the surface with the grating. Figure 48. C ross section view of deformations for RH=80% and room tem perature on Day 3

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92 4.4.2 Ring Test Ring test was performed again, but this time the test was under room temperature and RH60% which was achieved in the laboratory The U and V field m oir fringe patterns from D ay 1 to D ay 3 were recorded as figure 4 9. Ap parently, the deformation of the steel rod was insignificant according to the fringe patterns on the surface of the steel rod Also, no cracks are observed from the fringe patterns because the shrinkage induced stress is not high enough to initiate cracks. Figure 49. U&Vfield moir fringe patterns for ring test under RH60% and room temperature The Day 2 and Day 3 moir f ringe patterns were analyzed through the a utomatic fringe analysis system and the fullfield maps in xy coordinate s were shown as figu re 4 10 for D ay 2 and figure 4 12 for D ay 3. A 3 D composite model with steel rod and cement paste was created in finite element analysis with the typical values E=200 GPa test. FEA results were also included in the figures for the purpose of comparisons.

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93 Figure 410. E xperimental (above) and FEA (below) results of ring test on Day 2 From figure 410 or 411, the experiment al result and FEA result matched well except in the magnitude around the interface between the steel rod and the cement paste. T he shrinkage distribution along the horizontal centerline in the was plotted as figure 4 13. Clearly, the re is larger discrepancy in magnitude around the interface. -14 -8.4 -7 -2.8 2.8 7 8.4 14 -200 0 200 400 600 800 1000 1200 Shrinkage ( ) Position (mm) FEA Experimental Figure 411. Experimental and FEA shrinkage distribution for Day 2

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94 From figure 412, it can be seen that the maximum normal and shear strains moved toward the steel rod instead of remaining near the outer surf ace. The experimental result had good agreement with the result from FEA. Figure 412. E xperimental (above) and FEA (below) results of ring test on Day 3 The experimental and FEA full field strain information on the cement paste only ( the inf ormation on the steel ring not included) are shown as figure A 8 for Day 2 and figure A 9 for Day3 in Appendix. 4.4.3 Square Shape The square shape cement paste specimen with w/c=0.5 was made with the size of 25 mm in length and 14 mm in thickness. The sam e process was used to prepare grating on the surface the specimen. The specimen was stored in the chamber of 80% RH and room temperature for three day3 after demold The U and V field moir fringe patterns from Day 1 to D ay 4 were recorded as figure 4 13. The distribution of the normal strain in x direction along the red line

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95 which was indicated in figure 413 was plotted as shown in figure 414. The full field experimental and FEA maps for Day 4 were shown as figure 4 15. However, the displacement and nor mal strain in y direction are no t shown here due to symmetry. Figure 413. U and V field moir fringe patterns for the square specimen Figure 414. Distribution of normal strain in x direction along the red line

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96 From figure 414, t he experimental result did not match well with FEA result for every day measurements. However, they are similar in the range of the magnitude and the trend. Figure 415 show s the maximum in plane normal strain occurred in the four corners of the specimen. The maximum shear strain did not occur exactly in the corners but near the corners. FEA and the experimental results had good agreement in the displacement field. Displacement: U field (m) -8 -6 -4 -2 0 2 4 6 8 Figure 415. Experimental (above) and FEA (below) maps for square specimen on Day 4 4.4.4 Ex pansion on Day 1 4.4.4.1 In plane deformation measurement Instead of the measurement of shrinkage on Day 1, the measurement of expansion was obtained using CRM In order to acc ount for this phenomenon, FEA was performed and the boundary condition for drying effect was modified. The top surface was the surface with the diffraction grating where the moisture flux was blocked by the master grating. The side surface of the specimen was covered with the silicone rubber mold. Hence, the moisture fluxes only

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97 diffused from the bottom surface of the specimen within day 1. 12 hour was assumed as drying duration. FEA result was compared with the result from the experiment of RH=50% and room temperature as figure 4 1 6. Figure 416. Experimental (above) and FEA ( below) results for Day 1 measurement The results show the U field displacement map from the experiment has good agreement with that from FEA The experimental U field strain map was not smooth due to the difficulty in analyzing the fringe pattern with few fringes. However, it still indicates shrinkage occurred near the outer surface and expansion in the middle as FEA shows. Overall, it can be seen from the displacement map that the top surface of the specimen experien ced the expansion once it was demolded. The explanation is that the bottom surface experience larger shrinkage than the top surface due to the fact that the drying started from the bottom surface Th e differential shrinkage

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98 through the thickness should cause the bending to the specimen. The top surface should experience some tension and the bottom surface compression. 4.4.4.2 Out of plane displacement simulation In order to further prove the measurement of expansion on day 1 or bending effect out of plane displacement was simulated by FEA as in figure 417 In the model, the top surface faced the positive zdirection. The map clearly shows the top surface has the convex shape. This was caused due to the bending of the specimen. Figure 417. FEA result for out of plane displacement 4.4.5 Reinf orced Concrete Previously, the gravels were embedded into the cement paste in the gravel test. The result reflected the effect of gravels on the fringe densities at the positions of gravels However, it i s difficult to model the test with FEA not only beca use of the irregular shape and size of the gravels but also because of the unknown exact positions of the gravels. T he cement paste specimen was reinforce d with the four steel rods. The arrangement and the size of the rods are shown in figure 418. The pos itions of the steel rods in the mold are printed on the paper sheet The sheet was attached on the back side of the master grating as shown in figure 4 20. Therefore, the rods and the mold could be located at the specific positions.

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99 Figure 418. Size and arrangement of the steel rods in cement paste Figure 419. Master grating with the sheet on the back The specimen was first stored in the drying conditions of RH80% and room temperature for one day. Then it was stored under RH60% and room temperature for another day. The moir fringe patterns from Day 1 to Day 3 are shown in figure 420. The Day 2 and Day 3 moir fringe patterns were analyzed through the automatic fringe analysis system and the full field strain maps in xy coordinates were shown as f igure 422 for Day 2 and figure 4 23 for Day 3. A 3D composite model with 4 steel rod s and cement paste was created in finite element analysis with

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100 are also included in the figures for the purpose of comparisons. However, the full field maps do not show infor mation concerning the steel rods not only because they are not the focus in the research but also because their deformation is insignificant compared with the portion of the cement paste according to the fringe patterns. Figure 420. Moir fringe pattern s for reinforced concrete The displacement fields in both xy and polar coordinates and the strain field s in polar coordinate for Day 2 are not shown here but included in A ppendix. From figure 421, the trend in the experimental result is similar to that in FEA From figure 4 22, it can be seen that the experimental result and FEA result also matched well except in the area around the crack.

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101 Figure 421. Experimental (left ) and FEA ( right ) results f or reinforced concrete on Day 2

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102 Figure 422. Experimental (above) and FEA (below) results for reinforced concrete on Day 3

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103 4.5 Stress Development Prediction As known, shrinkage influences the development of stress in concrete materials when internal and external constraints exist. Through the prediction of the stress, whe re and whe n cracks may occur can be predicted if tensile stress is available. Therefore, in this section, s tress was predicted in both cases of free shrinkage and restrained shrinkage. 4.5.1 Free Shrinkage The development of str ess was modeled for the specimen under room temperature and RH80%. There were no external constraints in this case so that the specimen experienced shrinkage freely. Due to nonuniform shrinkage over the entire specimen, the stress should be distributed nonuniformly. The stresses developing on the surface with the grating were modeled as figure 4 2 3 with the plot of the stress distribution in polar coordinate from the center to the outer surface of the specimen and as figure 4 24 with the full field maps o f stresses in both x y and polar coordinates for day 3 only. The r adius stress was compressive near outer surface and was tensile stress in the middle. Also, the angular stress was larger than the radius stress. If cracks occur, they should initiate near t he outer su rface and propagate in radial direction at earlier time Figure 423. FEA resul t for stress development

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104 From full field maps in xy coordinate, the normal stress distribution was different from the normal strain distribution. Figure 424. FEA results for full field stress maps It was also interesting to investigate the stress distribution in polar coordinate over the cross section of the specimen as figure 4 25. The FEA result shows the tensile stresses developed near the outer surface and the compressive stresses in the inner core of the specimen This is due to the effect of internal constraint s or the effect of stress self equilibrating Figure 425. FEA results for stress maps over the cross section

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105 4.5.2 Restrained Shr inkage In this section, the ring test was used as the example of the restrained specimen. There were external constraints from the steel rod in the center so that the specimen did not experience shrinkage freely. The development of stress was modeled for t he specimen under room temperature and RH60% in the ring test. The stresses developing on the surface with the grating were modeled as figure 4 26 with the plot s of the stress distribution in polar coordinate from the inner surface to the outer surface of the specimen from day 2 to day 7 and as figure 4 27 with the full field maps of stresses in both xy and polar coordinates for day 3 only. The radius stress was tensile near the inner surface of the specimen and compressive in the rest area. T he angular st ress was always tensile stress and increased with time. Also the angular stress was larger near the inner surface of the specimen If cracks occur, they should initiate near the inner surface and in radial direction. Figure 426. FEA results for stress development in the ring test of RH=60% From the full field maps, the shear stress distribution in xy coordinate was quite similar to the shear strain distribution. However, the normal stress distribution was different from the normal strain distribution

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106 Figure 427. FEA results for full field stress maps in ring test The stress development was also predicted for the ring test under room temperature and RH0% because the crack s occurred in this experiment The stresses developing on the surface with the grating were modeled as figure 4 28 with the plots of the stress distribution in polar coordinate from the inner surface to the outer surface of the specimen. But only the development with first day drying was shown because the crack s occurred during t his period (between day 1 and day 2) in the experiment. In the experiment, the fact that the crack initiated near the outer surface and propagated in the radial direction was proved by this FEA Figure 428. FEA results for stress development in the ring test of RH=0%

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107 4.6 Results and Discussion s The inverse approach of combining FEA and optimization was used to determine the materials properties of shrinkage behavior in cement paste with w/c=0.5 under room temperature. The obtained materials properties were used to be the inputs in finite element model to predict the shrinkage behavior of cement paste in different conditions, such as different drying, geometric, or boundary conditions. The results from FEA and experiments match quite well in both the magnitude and the trend. Moreover, instead of modeling the shrinkage behavior in mortar or in the gravel test, the shrinkage behaviors in both the ring test and in the case of reinforced concrete were modeled using the composite models. The FEA results als o show the good agreement with those from the experiments. Furthermore, the stress development in cement paste under drying was simulated using FEA. This c an serve as the prediction of cracking occurrence if the tensile strength is given. To be summarized, t he constructed FEA model with the obtained material properties is suitable for the simulation of shrinkage behavior in concrete materials according to the validation of the experimental results. However, the material properties of shrinkage in concrete materials are very complicated and even unknown in many aspects. As a result, m any things need to be considered and discussed here for constructing a more complete model in the future First, the material properties of cement paste should be dependent upon the composition, such as w/c ratio and cement type. The combination of t he CRM and the inverse method can be applied to determine the shrinkage coefficient corresponding to their compositions. But the model needs to consider chemical shrinkage from hydra tion when w/c is below 0.4. That means the overall shrinkage cannot be modeled only by the phenomenon of moisture diffusion in the case of lower w/c ratio. The developed method combining CRM and the sealing of the specimen can be used to investigate the contribution of chemical shrinkage to total shrinkage or the ratio

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108 between drying and chemical shrinkage. That will be useful in modeling the overall shrinkage in cement paste with lower w/c ratio. Second, the shrinkage coefficient might not be constant, but dependent upon moisture content or relative humidity. But in the FEA model it was assumed constant for RH50~100% This assumption was based on literature survey. Nevertheless, shrinkage coefficient may not be regarded as a constant for RH0 ~50%. Therefore t he complete understanding of shrinkage coefficient as a function of relative humidity is needed in the future so that the shrinkage behavior can be more accurately predicted for surrounding humidity below 50%. The last but not the least the materials properties may be temperaturedependent. However, the variation of temperature inside of the specimen was not considered in the FEA model due to the small size of the specimen Hence, in the model t he temperature is assumed constant over the entire specimen as surrounding temperature. In the future study, t he further investigation of shrinkage coefficient as a function of temperature and the temperature variation inside of the specimen is needed so that the shrinkage behavior can be more accurately predicted for the specimen in larger size. T he more thorough FEA model including heat transfer should be used later.

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109 CHAPTER 5 CONCLUSIONS & FUTURE WORKS 5.1 Conclusion s The methodology of CRM has been successfully applied to the measurement of overal l shrinkage which develops in concrete materials during drying and hydration, and also to the measurement of nondrying shrinkage which develops in sealed concrete materials. The proc edure to prepare diffraction grating on the specimen, which is the key par t in the CRM, has been well developed. The process of grating replication is simplified to the uttermost and thus is very repeatable. The use of RTV 6 428 silicone rubber master grating provides the weak bonding between the master and the specimen gratings. This helps the separation of the specimen from the master substrate and prevents the damage on the specimen grating. Also, the RT V 6 428 master gratings are easier to be replicated in better quality and with higher hardness than RTV 615. More importantly, the use of RTV 6428 reduc es the possibility of the bubbles on the specimen grating The experimental setup of PEMI II helped align the gratings and obtain the phase shifted fringe patterns more precisely. The chamber setup provides stable drying conditions and is easy for other researchers to recreate. There are many advantages in the CRM technique such as non destruction nonintrusion highsensitivity and non reinforcement Although this technique is nondestructive, a thin layer of epoxy grating covered on the surface of the concrete specimen may prevent the diffusion of moisture. The result is different with the actual strain distribution of a natural concrete specimen without epoxy layer quantitatively D igital image correlation (DIC) would be a techni que to not avoid moisture exchange with the environments However, this technique would not help when the shrinkage measurement is less than 500 m icrostrains, such as in the drying condition of high humidity in the measurement of mortar with high aggregat e quantity or in the chemical

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110 shrinkage measurement under higher w/c ratio Therefore, high sensitivity moir interferometry is a more sound technique to investigate shrinkage behavior in concrete materials. On the other hand, the automated fringe analys is system is a nice tool to help obtain the full field displacement and strain information. This image processing method not only reduce much time in analyzing the data but also provided a way to compare between experimental and FEA results in the forms of the full field maps Although CRM gave a fine piece of the experimental results the materials properties of shrinkage were not able to be directly obtained from the 2D in plane deformation measurement on the surface of the specimen Hence, the 3D FEA model was created under some assumptions to match the boundary conditions and the geometry of the specimen with the experiment s Due to the geometry of the specimen in the tests, the advantage of axisymmetry was used in the FEA model Then an inverse approach was developed to fit the experimental results with the numerical results from FEA to determine the materials properties. The constructed FEA model w as further validated through some other experiments And the stress development can be simulated automat ically in the FEA model That is very useful in predicting when and where cracks could occur. Also the deformation in the 3 D views or in the cross section views can be demonstrated in the FEA model This is for the investigation of shrinkage behavior ins ide of the specimen 5.2 Future Works Some works are brought out here for the future research in both the experimental and numerical aspects. Experimentally t he more tests can be performed to explore the other influential factors on shrinkage such as wi nd speed, admixture, and cement type, by using the CRM. Moreover digital image correlation is a potential technique due to the recent improvements and

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111 developments in optical equipments and image processing technique Likewise, the FEA model can be created with the modified boundary condition on the speckled surface. The result s from FEA can be compared with DIC result s Another advantage is that DIC can provide out of plane deformation information which cannot be obtain ed in moir interferometry Numeric ally, chemical shrinkage as a function of w/c ratio, aggregate quantity, temperature and time can be modeled with the mathematical expression. But it requires more tests for abundant experimental data. Also, the composite model of cement paste and randomlydistributed sands can be created to simulate the shrinkage behavior in mortar s Mortars are considered as composite materials. Sands act like fibers, and cement pastes like matrix. B ut the size and the mechanical properties of sand particles need to be de termined first. The simulating results can be compared with the results from the CRM.

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112 APPENDIX CRM MOIRE FRINGE PAT TERNS AND FRINGE ANALAYIS RESULTS Figure A 1. U field Moir fringe patterns for w/c=0.6 in sealed condition Figure A 2. V f ield Moir fringe patterns for w/c=0.6 in sealed condition

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113 Figure A 3. U field Moir fringe p atterns under 8 Figure A 4. V field M oir fringe patterns under 8

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114 Figure A 5. Additional full field maps for ring test on Day 2

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115 Figure A 6. Additional full field maps for ring test on Day 3

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116 Experimental FEA Figure A 7. The full field strain maps of cement paste only in ring test on Day 2 Experimental FEA Fig ure A 8. The full field strain maps of cement paste only in ring test on Day 3

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117 Figure A 9. Additional f ull field strain maps for reinforced concrete on Day 2

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118 LIST OF REFERENCES 1. ACI 224R 01 Control of cracking in concrete s t ructures. ACI committee report. 2. Sa C., Benboudjema F, Thiery M, Sicard J (2008) Analysis of m ic rocrack ing induced by differential drying shrinkage Cement and Concrete Composites 30:947956. 3. Mokarem D W (2002) Development of concrete shrinkage performance s pecification Dissertation, Academic, Virginia Polytechnic Institute and State University Civi l and Environmental Engineering. 4. Mindess S Young JF, Darwin D (2003) Concrete Second Edition, Prentice Hall, New Jersey 5. Mangat PS Azari MM (1990) Plast ic shrinkage of steel f ib e r reinforced c oncrete Materials and S tructures 23( 135):186 195. 6. Shaeles CA, Hoover KC (1988) Influence of mix proportions on plastic shrinkage cracking in thin s labs ACI Mater J 85: 495504. 7. Branch J, Hannant DJ Mulheron M (2002) Factors affecting the p lastic shrinkage cracking of high strength concrete Mag azine of Concrete Research 54( 5 ):347354. 8. Erlin B William H (2004) Carbonation of c oncrete Concrete ConstructionWorld of Concrete. 49( 8):22 9. Fumiaki M Yoshimichi A Sumio S (2004) Calcium silicate structure and sarbonation s hrinkage of a tobermorite based m aterial. Cem ent and Concrete Research 34( 7):1251 1257. 10. Shideler JJ (1963) Carbonation shrinkage of concrete masonry units Research and Development Laboratories Journal 5( 3):36 51. 11. Sakata K, Shimomura T (2004) Recent progress in r esearch on and evaluation of concrete creep and shrinkage in Japan. Journal of Advanced Concrete Technology 2( 2): 133140. 12. Viktor V Gintaris K, Darious B (2008) Shrinkage in r einfo rced concrete structure: a computational aspect Journal of Civil Engineering and Management 14( 1):49 60. 13. Jensen OM, Bentz DP, Lura P (2004) Autogenous deformation of c oncrete American Concrete Institute Michigan. 14. Zhang M.H T am CT, Leow MP (2003) E ffect of water to cementitious materials ratio and silica fume on the autogenous shrinkage of c oncrete Cement and Co ncrete Research 33(10):1687 1694.

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119 15. Veronique B B Pierre M Abdelhafid M Ahmed L Noureddine R (2006) Autogenous deformati ons of cement pastes: Part II. w/c effects, micro macro correlations, and threshold values Cement and Concrete Resear ch 36(1):123 136 16. Pierre M Veronique BB Ahmed L Abdelhafid K (2006) Autogenous deformat ions of cement pastes: Part I. t emperature effects at early age and micro macro correlations Cement and Concrete Research 36(1):110122. 17. Kohno K, Okmoto T, Iskawa Y, Sibata T Mori H ( 1999) Effects of artificial lightweight aggregate on autogenous shrinkage of concrete Cement and Concrete Research 29( 4):611 614 18. Tazawa E, Miyazawa S (1997) Influence of constituents and composition on autogenous shrinkage cementitious materials Magazine of Concrete Research 49(178):1522. 19. Tazawa E Miyazawa S (1995) Influence of cement and admixture on autogenous shrinkage of cement paste. Cement and Concrete Research 25(2):281 287. 20. Millard MJ, Kurtis KE (2008) Effects of lithium nitrate admixture on early age cement hydration. Cement and Concrete Research 38(4):500510. 21. Bhal NS, Mital MK (1996) Effect of relative humidity on creep and shrinkage of c oncrete The Indian C oncrete Journal 2127. 22. Masami S Shuichi S (1987) E ffect of wind action on early shrinkage of c oncrete. Proceedings of The Japan Congress on Materials Research 161 170. 23. Azenha M, Maekawa K, Ishida T (2007) Drying of induced moisture losses from mortar to the environment. Part I: experimental research Materials and Structures 40:801811. 24. Barr B Hoseinian S B Beygi M.A (2003) Shrinkage of concrete stored in natural e nvironments Cement and Concrete Composites 25(1):19 29. 25. Alshamsi, M. Imran, H.D., Bushlaibi, A. (2005) Drying S hrinkage of C oncrete Samples Exposed to Extreme Hot W eather Proceedings of the International Conference on Cement Combinations for Durable Concrete 357 362. 26. ACI 209.1R 05 Report on Factors Affecting Shrinkage and Creep of Hardened Concrete. 27. Bissonnette B Pierre P Pigeon M (1999) Influence of key parameters on drying shrin kage of cementitious materials. Cement and Concrete Research 29:16551622. 28. Barr B Hoseinian S B Beygi M A (1984) Evaporation of water from fresh mortar and concrete at different environmental conditions ACI Journal 81(42):560 565. 29. Almudaiheem JA Hansen W (1987) Effect of specimen size and shape on d rying shrinkage of concrete. ACI Materials Journal 84( 2):130135.

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120 30. Saleh AA, Rajeh Z A (2006) Effects of drying conditions, admixtures and speci men size on shrinkage strains. Ce ment and Concrete Research 36:1985 1991. 31. Zhou M Wang J Zhu L (2008) Effects of manufactured sand on dry shrinkage and creep of highs trength concrete Journal Wuhan University of Technology, Materials Science Edition 23(2):249253. 32. ASTM C157/C157M 06 Standard Test Method for Length Change of Hardened Hydraulic Cement Mortar and Concrete. 33. Mokarem D W Weyers R E Lane DS (2005) Developme nt of a shrinkage performance specifications and prediction model analysis for supplemental cementitio us material concrete mixtures. Cement and Conc rete Research 35:918 925 34. Kim J K Lee CS (1998) Prediction of drying shrinkage in concrete. Cement and Concr ete Research 28:985994. 35. Yang Y Sato R Kawai K (2005) Autogenous shrinkage of high strength concrete containing silica f ume under drying at early ages. Cement and Concrete Research 35:449 456. 36. Habel WR, Hofmann D Hillemeier B (1997) Deformation measurem ents of mortars at early ages and of large concrete components on site by means of embedded fiber optic m icr ostrain sensors. Ceme nt and Concrete Composites 19:81102. 37. Volker S Evelyn S Thomas K (2004) Experimental investigation into early age shrinkage of cement paste by using fibre bragg g ratings Cement and Concrete Composites 26: 473479. 38. Allan CL Childs P A Berndt R Macken T, Peng GD Gowripalan N (2007) Simultaneous measurement of shrinkage and temperature of reactive powder concrete at early age us ing fibre bragg grating sensors. Cement and Concrete Composites, 29:490497. 39. Lura P, Jensen OM (2005) Measuring techniques for autogeneous strain of cement paste. Proc Knud Hojgaard Conference on A dvanced Cement Based Materials, Lyngby, Denmark, June 40. Pease BJ Hossain AB, Weiss WJ (2004) Quantifying volume change stress development and cracking due to self desiccation, In ACISP 220: Autogenous deformation of c oncrete, American Concrete In stitute, Farmington Hills, Mich 41. Sant G Lura P, Weiss J (2006) Measurement of volume change in cementitious materials at early age review of testing protocols and interpretation of results. Transportation Research Record 197:21 29.

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121 42. Avril S Ferrier E Vautrin A Hamelin P Surrel Y (2004) A full field optical method for th e experimental analysis of reinforced concrete beams repaired with composites. Composites, Part A 35:873884. 43. Avril S Vautrin A Hamelin P Surrel Y (2005) A multiscale approach for crack width prediction in reinforced beams repaired with composites Composites Science and Technology 65:445455. 44. Avril S Vautrin A Surrel Y (2004) Grid method: application to the characterization of c racks Experimental Mechanics 44( 1):37 43. 45. Cao SY Chen JF Pan JW Sun N (2007) EPSI measurement of bondslip relations hips of FRP concrete i nterface. J ournal of Composites for Construction 11( 2):150 160. 46. Chen J Jin G Meng L (2007) Application of digital correlation method to structure i nspection. Tsinghua Science and Technology 12(3):237 243. 47. He S, Feng Z Rowlands RE ( 1997) Fracture process zone analysis of concrete using moir interferometry Experimental Mechanics 37(3): 367 373 48. Yu CT, Kobayashi AS, Hawkins NM (1993) Energydissipation m echanism s associated with rapid fracture of c oncrete Experimental Mechanics 37( 5 ) :205211. 49. Yilmazturk F Kulur S Pekmezci BY (2003) Measurement of shrinkage in concrete samples using digital photogrammetric methods. The International Archives of the Photogrammtry, Remote Sensing and Spatial Information Sciences 34 Part XXX. 50. Neubeuer CM B ergstrom TB Sujata K XI Y G aboczie EJ Jennings H M (1997) Drying shrinkage of cement paste as measured in an environmental scanning electron microscope and comparison with m icrostructural models Journal of Material Science 32:64156427. 51. Bazant ZP, Najjar L J (1971) Drying of concrete as a nonlinear diffusion problem. Cem ent and Concr ete Res earch 1( 1):461 73. 52. Wittmann FH (1977) The fundamentals of a model for the descript ion of concrete characteristics. Schriftenreihe Deutscher Ausschuss ft ir Stahlbe ton, Heft 290, Berlin:43101. 53. Wittmann X Sadouki H Wittmann FH (1989) Numerical evaluation of drying test data. Transactions 10th Int. Conf. on Struct. Mech. in Rea ctor Technology, SMiRT 10, R: 7189. 54. Bazant ZP Najjar LJ (1972) Nonlinear water dif fusion in nonsaturated concrete. Materials and Structures 5(25): 3 20. 55. Sakata K (1983) A study on moisture diffusion in drying a nd drying shrinkage of concrete. Cement and Concrete Research 13(2): 216 224.

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126 B IOGRAPHICAL SKETCH Tzu Chau Chen from Taipei, Taiwan, wa s a doctoral student in Mechanical Engineering at University of Florida. He completed his undergraduate study in mechanical enginee ring at National Taiwan University in 2000. After receiving his bachelor s degree Chen performed his military service in R.O.C Army until March, 2002 In August, 2003, Chen went to UCLA and majored in MEMS. He received his master s degree in spring, 2005. In fall, 2005, he transferred to University of Florida to pursue his doctoral degree specializing in experimental stress analysis Chens research interests include moir interferometry digital image correlation, c oncrete & composite materials, and fi nite element analysis.