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Experimental and numerical techniques to characterize structural properties of fresh concrete

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Experimental and numerical techniques to characterize structural properties of fresh concrete

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Content EXPERIMENTAL AND NUMERICAL TECHNIQUES TO CHARACTERIZE STRUCTURAL PROPERTIES OF FRESH CONCRETE RELEVANT TO CONTOUR CRAFTING by Tony Di Carlo A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (INDUSTRIAL AND SYSTEMS ENGINEERING) December 2012 Copyright 2012 Tony Di Carlo ii Dedication This dissertation is dedicated to my family and friends for their endless and enabling love, encouragement and sacrifice. Words cannot express how lucky and grateful I am to have you in my life. iii Acknowledgements Many thanks to the many mentors, sponsors and 'inspirators' who have contributed emotionally, materially and intellectually to this project - this work is a focused amalgam of their collective generosity, insights, wisdom and genius. My academic advisors: Behrokh "Berok" Khoshnevis, Anders Carlson, Steve Nutt, Yong Chen, Kurt Palmer, Qiang Huang, Nicholas J Carino. Suppliers: A&A Ready Mixed Concrete, Active Minerals International, Txi Riverside Cement Company, Txi Expanded Shale & Clay, Headwaters Resources, FabPro Oriented Polymers, Poraver North America, Associated Soils Engineering, Satellite Manufacturing, Deslauriers, Gilson, Vibco, Propex, Grace, Dow, BASF, Handy Chemicals, Holcim, Dassault Systems, Fritz Pak, Esteco. Mellissa Van Ert: a veteran concrete practitioner at A&A Ready Mixed Concrete. I was incredibly fortunate to talk to Melissa first. As I set out on this venture, Melissa was not afraid to let me know, in no uncertain terms, where I was on the learning curve. Then she proceeded to avail me with the guidance, tools and materials I needed to make the right start. Thank you Melissa! Though I’m still only 1/3 the way up or less, my journey up the curve started when I met you. Jackie de Jung: my neighbor and a master baker. It’s probably safe to say that the specialized mortar mixture developed here for Contour Crafting is unlike any mixture developed for concreting to date. To understand just how different consider the initial feedback I received from countless experts, “sounds fascinating, I hope you can do it, but probably won’t happen in my lifetime”, or some variation of this positive yet skeptical sentiment. Of all things Jackie taught me how to mix this unconventional, queer mixture. Thank you Jackie! You took me from struggle to ‘piece of cake.’ iv Mary Anna Di Carlo: my sister. Somehow Mary Anna understands fibers. After every conceivable tack failed to achieve satisfactory dispersion, Mary Anna simply knew what had to be done. Thank you Mary Anna! Although not given nearly enough credit in the narrative, the unique properties exhibited by the mortar mixture developed here owe much to those little fibers, and the most excellent dispersion achieved with your ‘technique.’ Many thanks to Stuart Shelton for his tireless devotion to this work and Contour Crafting in general. Thank you Stuart! Every experiment featured here was made possible by your charming approach towards our generous suppliers, and your ever-helping hand. Many thanks to my buddy Stephen VoPava. Thank you Steve! You deserve a gold medal in mathematical gymnastics. Many thanks to Ching-Long Hsu for generously crafting the elegant VBA code that drives our numerical simulations. Many thanks to Don Zike and Associated Soils Engineering. Finally, many thanks to my formidable army of practitioners, co-workers, family and friends: Robert Graine, Joe Hyder, Steve Cochran, Patrick Tasson, Keith Perrine, Mike Horsfield, Frank Ormond, Thor L Moody, Trent R Smith, Al Carocci, Carl Patton, David L Anderson, Drew DeCarlo, Jeffery A Ferris, Andrew W Taylor, Josh Hamilton, Don Gilbart, Jeff Ryan, Nader Fateh, Don Zike, Ron Federico, Kenneth Shelton, Craig McRae, Eric W Mastin, Rod Elderton, Erich Kunze, Susanna Cipriani, Ernesto Russo, Lisa Tchakmakian, Paul de Jung, Gabriele Di Eugenio, Philippe and Camelia Avon, Lance Hill, Mark Rivera. v Abstract This research explores experimental and numerical techniques for the analysis of fresh concrete subjected to fabrication loads. The work is relevant wherever green, or uncured, concrete must be load-bearing, and is particularly relevant to an emerging fabrication technology called Contour Crafting, which fabricates civil structures additively with layered freeform depositions of fresh cementitious extrudate. In traditional concrete construction, rigid formworks are employed, like exoskeletons, to mold, protect and support concrete, and these molds are not removed until the concrete has developed considerable load-bearing strength. Contour Crafting dispenses with the rigid formwork, and therefore, contour-crafted concrete must be independently load-bearing immediately upon placement. This research develops techniques, tools and strategies for engineering the in-process fresh concrete subjected to these unprecedented fabrication loads. vi Table of Contents Dedication …………………………………………………………………………….………………..…. ii Acknowledgements ………………………………………………….…………………………………… iii Abstract .……………………………………………………………………………………….…….….... v List of Tables ………………………………………………………………………………………......... ix List of Figures ……………………………………………………………………………………….…… xi Abbreviations .…………………………………………………………………………………………. xviii Notations .……………………………………………………………………………………………….. xix 1. Chapter One: Introduction .................................................................................................. 1 1.1 Introduction to the Problem ............................................................................................ 1 1.2 Statement of the Problem ............................................................................................... 1 1.3 Research Purpose .......................................................................................................... 9 1.4 Research Plan .............................................................................................................. 11 1.5 Importance of the Study ............................................................................................... 12 1.6 Limitations, Delimitations and Assumptions ................................................................. 13 1.7 Definitions ..................................................................................................................... 14 2. Chapter Two: Literature Review ....................................................................................... 25 2.1 Introduction ................................................................................................................... 25 2.2 Shape-Stable Concretes .............................................................................................. 25 2.3 Testing Shape-Stable Concrete ................................................................................... 32 2.4 Maturity of Shape-Stable Concrete .............................................................................. 33 2.5 Previous Attempts at Layering Shape-Stable Concrete ............................................... 36 3. Chapter Three: Mix Design............................................................................................... 40 3.1 Introduction ................................................................................................................... 40 3.2 Mix Design Criteria ....................................................................................................... 40 vii 3.3 Reference Mixtures ...................................................................................................... 41 3.4 Mix Design .................................................................................................................... 42 4. Chapter Four: Experimental Research ............................................................................. 46 4.1 Introduction ................................................................................................................... 46 4.2 Specimen Preparation .................................................................................................. 46 4.3 Green Strength Test ..................................................................................................... 49 4.4 Plate-Stacking Test ...................................................................................................... 61 4.5 Cured Cylinder Strength Test ....................................................................................... 67 4.6 Bond Strength Test ...................................................................................................... 69 5. Chapter Five: Analytical Material Models ......................................................................... 78 5.1 Predicting Mortar Maturity ............................................................................................ 78 5.2 General Maturity Model ................................................................................................ 78 5.3 Specific Maturity Model ................................................................................................ 87 6. Chapter Six: Numerical Analysis of Fresh Concrete ......................................................... 91 6.1 Elasto-Plasticity ............................................................................................................ 91 6.2 Model Selection ............................................................................................................ 96 6.3 Parameter Calibration................................................................................................. 102 6.4 Fresh Mortar Simulation ............................................................................................. 108 6.5 Numerical Simulation of Mortar Layering.................................................................... 122 7. Chapter Seven: Full-Scale Demonstration ..................................................................... 124 7.1 Introduction ................................................................................................................. 124 7.2 Mortar-Layering Apparatus ......................................................................................... 124 7.3 Full-Scale Mortar-Layering Demo ............................................................................... 125 viii 8. Chapter Eight: Conclusion and Future Work .................................................................. 135 8.1 Research Contribution ................................................................................................ 135 8.2 Implications for Practice ............................................................................................. 136 8.3 Opportunities for Future Research ............................................................................. 138 9. Bibliography.................................................................................................................... 144 10. Appendices..................................................................................................................... 149 Appendix A: M2 Mix (60 pcf) .................................................................................................. 149 Appendix B: Green Strength Test (9-25-2011) ...................................................................... 151 Appendix C: Plate-Stacking Test, M1 Mix, 1% Set Acceleration ............................................ 158 Appendix D: Plate-Stacking Test, M1 Mix, 2% Set Acceleration ............................................ 160 Appendix E: Plate-Stacking Test, M1 Mix, 3% Set Acceleration ............................................ 163 Appendix F: Consolidation (thru Plate-Stacking) of the Bond-Strength Specimens ............... 165 Appendix G: Bond-Strength Test Specimens After Compression Test .................................. 168 Appendix H: Cured Cylinder Strength, 3x6 Test Specimens .................................................. 170 Appendix I: Cured Cylinder Strength, 3x4 Test Specimens ................................................... 172 Appendix J: Failed Plate-Stacking Test Specimens ............................................................... 175 Appendix K: Exemplary Predictive Model for Contour Crafting .............................................. 182 Appendix L: Testing Shape-Stable Mortar ............................................................................. 185 Appendix M: Technical Specification Documents .................................................................. 187 Appendix N: Technical Certifications ..................................................................................... 188 Appendix O: VBA Code for ABAQUS Layer-Stacking Simulation .......................................... 190 Appendix P: ABAQUS Input Layer-Stacking Simulation ........................................................ 194 ix List of Tables Table 2.1. Properties of SikaRepair 224 ...................................................................................... 26 Table 3.1. Basic 2000 psi Poraver Concrete Formula .................................................................. 41 Table 3.2. Basic 4000 psi Poraver Concrete Formula .................................................................. 42 Table 3.3. Basic 5000 psi Poraver Concrete Formula .................................................................. 42 Table 3.4. Batching Ratios for Lightweight Concrete ................................................................... 42 Table 3.5. Study Mix M1 .............................................................................................................. 44 Table 4.1. Material Parameters as a Function of Time ................................................................. 61 Table 4.2. Plate-Stacking Schedule ............................................................................................. 63 Table 4.3. Compression Strength – 100 pcf M1 Mix .................................................................... 68 Table 4.4. Consolidation Regimen of the Bond-Strength Specimens........................................... 71 Table 4.5. Compression Strength of Cured Bond-Strength Specimens ....................................... 76 Table 5.1. Parameters for the Exponential Strength Gain Function of the M1 Mix ....................... 89 Table 6.1. Typical Fresh Concrete Properties (Ritchie, 1962) .................................................... 103 Table 6.2. Typical Fresh Concrete Properties (Alexandridis, 1981) ........................................... 104 Table 6.3. Associated Versus Non-Dilatant Flow (Abaqus User's Manual, 2009) ...................... 106 Table 6.4. Test versus FEA: Mortar Defection = f (Applied Load) .............................................. 117 Table 6.5. Notional Drucker-Prager Strain-Hardening Parameters ............................................ 118 Table 6.6. Test versus FEA: Mortar Defection = f(Mortar Age) .................................................. 121 Table 7.1. Batching Regimen for Full-Scale Mortar Layering Demo .......................................... 126 Table 7.2. Final Dimensions of Full-Scale Mortar Layering Demo ............................................. 132 Table 7.2. Predictive Material Model Development Process ...................................................... 138 Table 10.1. Compression Strength – 60 pcf M2 Mix .................................................................. 149 Table 10.2. Compression Strength – 3x6 Green Strength Test Specimens (Supplemental) ...... 170 Table 10.3. Compression Strength – 3x4 Green Strength Test Specimens (Remolded) ........... 173 Table 10.4. Compression Strength – Plate-Stacking Test Specimens (Unconfined).................. 173 x Table 10.5. Predictive Model: Tower Dimensions and Machine Weight..................................... 183 Table 10.6. Predictive Model: Mortar Strength Development ..................................................... 183 Table 10.7. Predictive Model: Mortar Maturity ............................................................................ 184 xi List of Figures Figure 1.1 Contour Crafting Technology and Prototypical Research Specimen ............................ 2 Figure 1.2. A Structure and its Contour Crafting Tool Path (Zhang, 2009) ..................................... 2 Figure 1.3. Previous Contour Crafting Material Systems ............................................................... 4 Figure 1.4. Concrete Setting and Initial Strength............................................................................ 5 Figure 1.5. Elevation of Willow Island Cooling Tower Unit No 2 (Lew et al., 1972) ........................ 6 Figure 1.6. Jump Form Construction System (Lew et al., 1972) .................................................... 7 Figure 1.7. Jump Form Material Hoisting System (Lew et al., 1972) .............................................. 7 Figure 1.8. Temperatures Prior to Collapse of the Willow Island Tower (Lew et al., 1972) ............ 8 Figure 1.9. Structural Failure of the Willow Island In-Process Concrete (Delatte, 2009) ................ 9 Figure 1.10. Target Road Stacking Rate ...................................................................................... 10 Figure 1.11. Research Objectives ................................................................................................ 12 Figure 1.12. Bolton’s Simplified Saw Blade Model of Dilatancy (Bolton, 1986) ............................ 16 Figure 1.13. Mortar Penetration Resistance versus Elapsed Time .............................................. 18 Figure 1.14. Secant Young’s Modulus (Mar, 2002) ...................................................................... 21 Figure 1.15. The Triaxial Test (Abaqus User's Manual, 2009) ..................................................... 23 Figure 1.16. Isotropic Yield Surfaces and the π-plane in 3-D Stress Space ................................ 24 Figure 2.1. Apparatus for Simulating Slip-Form Casting (Tregger, Voigt, & Shah, 2007) ............. 27 Figure 2.2. Improving Slip-Form Casting with Clay (Tregger, Voigt, & Shah, 2007)..................... 27 Figure 2.3. Shape-Stable Concrete Slab Produced without Vibration (Pekmezci et al., 2007) .... 28 Figure 2.4. Comparison of Self-Consolidatability of SF-SCC (Pekmezci et al., 2007).................. 28 Figure 2.5. Effect of Admixtures on Flowability and Green Strength of Fresh Concrete .............. 29 Figure 2.6. Manipulating Form Pressure with Sand/Aggregate Ratio (Assaad, 2004) ................. 29 Figure 2.7. Consistency of a Cement Paste with Various Fibers (Martinie et al., 2009) ............... 30 Figure 2.8. Extrusion of a Fiber-Enhanced Cement-Based Composite (Koker & Zijl, 2004) ........ 30 Figure 2.9. Internal Curing at the Contact Zone ........................................................................... 31 xii Figure 2.10. Visualizing Internal Curing (Lura et al. 2007) ........................................................... 31 Figure 2.11. Tregger Green Strength Test (Tregger et al., 2010)................................................. 32 Figure 2.12. Uniaxial Compression of Freshly Extruded Mortar (Voigt et al., 2006) ..................... 33 Figure 2.13. Power Law Development of Compressive Mortar Strength ...................................... 34 Figure 2.14. Linear-Hyperbolic Development of Compressive Mortar Strength ........................... 35 Figure 2.15. Parabolic-Hyperbolic Development of Compressive Mortar Strength ...................... 35 Figure 2.16. Exponential Development of Compressive Strength Concrete ................................ 36 Figure 2.17. Removing Hardened Rapid Set from CC Equipment (Hwang, 2005) ....................... 37 Figure 2.18. Week Bonds Between Layers using Polyacrylamide Accelerating Agent ................ 38 Figure 2.19. Curing Distinct-Layer Casting (Roussel & Cussigh, 2008) ....................................... 38 Figure 3.1. Beauty and the Beast ................................................................................................. 43 Figure 3.2. Bulk Ingredients and How They Contribute to the Suitable Mix ................................. 43 Figure 3.3. Exemplary Composite Roads ..................................................................................... 45 Figure 4.1. Drop Table and Mortar Mold ...................................................................................... 47 Figure 4.2. Measurement of Mortar Spread ................................................................................. 48 Figure 4.3. Custom Vibration Table .............................................................................................. 48 Figure 4.4. Mechanical Mixing of Mortar of Plastic Consistency (ASTM C 305) .......................... 49 Figure 4.5. Mortar Mixed to Plastic Consistency .......................................................................... 49 Figure 4.6. Apparatus for Unconfined Compressive Strength of Fresh Concrete ........................ 51 Figure 4.7. Apparatus for Preparing Fresh Mortar Specimens for Green Strength Test .............. 52 Figure 4.8. Exemplary Unconfined Compressive Strength Tests (3x4 cylinders) ......................... 54 Figure 4.9. Exemplary Unconfined Compressive Strength Test (3x6 cylinder) ............................ 55 Figure 4.10. Evolution of Unconfined Compressive Strength (3x4 cylinders) ............................... 55 Figure 4.11. Stress-Strain Diagrams of M1a Mortar Mix (2% clay, 0% NCA) ............................... 56 Figure 4.12. Exemplary Early-Age σ-ɛ Diagram of M1a Mortar Mix ............................................. 57 Figure 4.13. Exemplary Later-Age σ-ɛ Diagram of M1a Mortar Mix ............................................. 57 Figure 4.14. Modulus=f(t) ............................................................................................................. 58 xiii Figure 4.15. Compressive Yield Strength=f(t) .............................................................................. 58 Figure 4.16. Cohesion=f(t) ........................................................................................................... 58 Figure 4.17. Poisson’s Ratio=f(t) .................................................................................................. 59 Figure 4.18. Slump=f(t) ................................................................................................................ 59 Figure 4.19. Development of Very-Early Compressive Strength in the M1 Mortar ....................... 60 Figure 4.20. Typical Early-Age Slip Plane .................................................................................... 61 Figure 4.21. Apparatus for the Plate-Stacking Test ...................................................................... 62 Figure 4.22. Exemplary Plate-Stacking Test ................................................................................ 64 Figure 4.23. Evolution of Mortar Strength and Fabrication Load Over Time ................................ 66 Figure 4.24. Typical Cured Cylinder Strength Test (M1, 100 pcf specimen) ................................ 67 Figure 4.25. Cured Cylinder Strength Test (100 pcf specimen @ 24 Hrs) ................................... 68 Figure 4.26. Cured Cylinder Strength Tests (100 pcf specimen @ 3 days) ................................. 68 Figure 4.27. Cured Cylinder Strength Tests (100 pcf specimen @ 28 days) ............................... 69 Figure 4.28. Apparatus for Preparing Bond Strength Test Specimen .......................................... 70 Figure 4.29. Plate-Stacking Test (at time 1:35) ............................................................................ 72 Figure 4.30. Plate-Stacking Test (at time 4:15) ............................................................................ 73 Figure 4.31. Mix Water Forced out of Bond-Strength Specimens ................................................ 73 Figure 4.32. Exemplary Demolded Bond-Strength Specimen ...................................................... 74 Figure 4.33. Exemplary Uniaxial Compression Testing of Bond-Strength Specimen ................... 74 Figure 4.34. Exemplary Bond-Strength Specimen After Compression Test ................................. 75 Figure 4.35. Uniaxial Compression Strength of Cured Bond-Strength Specimens ...................... 76 Figure 4.36. Alternative Bond-Strength Specimen Preparation .................................................... 77 Figure 5.1. Basic Road Dimensions ............................................................................................. 79 Figure 5.2. Very Early Maturity, Max Build Rates, and Time to Critical Condition ........................ 82 Figure 5.3. Effect of Temperature on Allowable Build Rate and Time to Critical Condition .......... 84 Figure 5.4. Mortar Deflection Due to Gravity (Slump) .................................................................. 85 Figure 5.5. Fabrication Delay to Correct for Self-Weight .............................................................. 86 xiv Figure 5.6. Development of Compressive Strength in Extruded Mortar ....................................... 88 Figure 5.7. M1 Mortar Strength Development: Exponential to Linear Hyperbolic ......................... 90 Figure 5.8. M1 Mortar Strength Development: Exponential to Parabolic-Hyperbolic.................... 90 Figure 6.1. Failure Theories and Yield Surfaces in Triaxial Stress Space (Hinton, 1992) ............ 93 Figure 6.2. Plastic Flow Potential Q and Plastic Potential Gradient (Hinton, 1992) .......... 94 Figure 6.3. Associated and Non-Associated Flow Rules (Hinton, 1992) ...................................... 95 Figure 6.4. Evolution of a Yield Surface (Hinton, 1992) ............................................................... 95 Figure 6.5. Time-Dependent Discretization of the FEA Properties (Hauggaard-Nielsen, 1997) ... 96 Figure 6.6. D-P Yield Surfaces in the Meridional (d-p stress) Plane ............................................ 98 Figure 6.7. Hardening and Dilation Angle in the Linear Drucker-Prager Model ............................ 99 Figure 6.8. NAFEMS Test and Modeling Complexity Diagram .................................................. 101 Figure 6.9. Dilation Angle Limits (Famiglietti, 1994) ................................................................... 104 Figure 6.10. Image-Based Analysis of Fresh Concrete (Štemberk & Kohoutková, 2005) .......... 105 Figure 6.11. Constitutive Model Parameter Calibration .............................................................. 106 Figure 6.12. Drucker-Prager Yield Surfaces for the M1 Mortar @ 0% NCA ............................... 107 Figure 6.13. FEA of the Green Strength Test: U1 = f (Applied Load) ......................................... 110 Figure 6.14. FEA of the Green Strength Test: U2 = f (Applied Load) ......................................... 111 Figure 6.15. FEA of the Green Strength Test: S11 = f (Applied Load) ....................................... 112 Figure 6.16. FEA of the Green Strength Test: S33 = f (Applied Load) ....................................... 113 Figure 6.17. FEA of the Green Strength Test: S12 = f (Applied Load) ....................................... 114 Figure 6.18. FEA of the Green Strength Test: PEMAG = f (Applied Load) ................................ 115 Figure 6.19. FEA of the Green Strength Test: AC YIELD = f (Applied Load) ............................. 116 Figure 6.20. Test versus FEA: Mortar Defection =f(Applied Load) ............................................. 117 Figure 6.21. FEA of the Green Strength Test with Strain Hardening.......................................... 118 Figure 6.22. FEA of the Green Strength Test (M1, 0% NCA, 11 min., 6 lbf) .............................. 118 Figure 6.23. FEA of the Green Strength Test (M1, 0% NCA, 52 min., 6 lbf) .............................. 119 Figure 6.24. FEA of the Green Strength Test (M1, 0% NCA, 109 min., 6 lbf) ............................ 119 xv Figure 6.25. FEA of the Green Strength Test (M1, 0% NCA, 211 min., 6 lbf) ............................ 120 Figure 6.26. FEA of the Green Strength Test (M1, 0% NCA, 288 min., 6 lbf) ............................ 120 Figure 6.27. Test versus FEA: Mortar Defection = f(Mortar Age) ............................................... 121 Figure 6.28. Steady-State Finite Element Simulation of Plate Stacking Test ............................. 121 Figure 6.29. FEA of Full-Scale Layering Demonstration (with Aging Properties) ....................... 123 Figure 7.1. Scaffold for Full-Scale Layering Demo ..................................................................... 124 Figure 7.2. Mortar Molding and Extruding Apparatus for Full-Scale Layering Demo.................. 125 Figure 7.3. Full-Scale Layering Demo (Process)........................................................................ 127 Figure 7.4. Nominal Full-Scale Mortar Layering Demo Road Dimensions ................................. 128 Figure 7.5. Full-Scale Mortar Layering Demonstration ............................................................... 129 Figure 7.6. Full-Scale Mortar Layering Artifact (roads 15-30) .................................................... 130 Figure 7.7. Full-Scale Mortar Layering Artifact (roads 1-15) ...................................................... 131 Figure 7.8. Approx. Decomposition of Shrinkage in the Full-Scale Layered Artifact .................. 133 Figure 7.9. Full-Scale Mortar Layering Artifact (Close-ups) ....................................................... 134 Figure 8.1. Slip Lines in Assemblies of Particles in Contact (Rowe, 1962) ................................ 140 Figure 8.2. Non-Linear Mortar Response ................................................................................... 141 Figure 8.3. Non-Linearity in Hyperbolic D-P Yield Function at Low Confining Pressure ............ 142 Figure 10.1. M2 Mix Specimens Floating in Curing Tank ........................................................... 150 Figure 10.2. Cured Cylinder Strength Tests (60 pcf specimens @ 24 hrs) ................................ 150 Figure 10.3. Cured Cylinder Strength Tests (60 pcf specimens @ 3 days)................................ 150 Figure 10.4. Cured Cylinder Strength Tests (60 pcf specimens @ 28 days).............................. 151 Figure 10.5. M1 Green Strength Test (11 minutes after mixing) ................................................ 151 Figure 10.6. M1 Green Strength Test (18 minutes after mixing) ................................................ 152 Figure 10.7. M1 Green Strength Test (22 minutes after mixing) ................................................ 152 Figure 10.8. M1 Green Strength Test (26 minutes after mixing) ................................................ 153 Figure 10.9. M1 Green Strength Test (47 minutes after mixing) ................................................ 153 Figure 10.10. M1 Green Strength Test (58 minutes after mixing) .............................................. 154 xvi Figure 10.11. M1 Green Strength Test (73 minutes after mixing) .............................................. 154 Figure 10.12. M1 Green Strength Test (92 minutes after mixing) .............................................. 155 Figure 10.13. M1 Green Strength Test (99 minutes after mixing) .............................................. 155 Figure 10.14. M1 Green Strength Test (109 minutes after mixing) ............................................ 156 Figure 10.15. M1 Green Strength Test (208 minutes after mixing) ............................................ 156 Figure 10.16. M1 Green Strength Test (211 minutes after mixing) ............................................ 157 Figure 10.17. M1 Green Strength Test (283 minutes after mixing) ............................................ 157 Figure 10.18. M1 Green Strength Test (288 minutes after mixing) ............................................ 158 Figure 10.19. Plate-Stacking Test, M1 Mix, 1% Set Acceleration .............................................. 160 Figure 10.20. Plate-Stacking Test, M1 Mix, 2% Set Acceleration .............................................. 162 Figure 10.21. Plate-Stacking Test, M1 Mix, 3% Set Acceleration .............................................. 165 Figure 10.22. Consolidation of the Bond-Strength Specimens ................................................... 167 Figure 10.23. Bond-Strength Specimen After Compression Test (10’ Stacking Interval) ........... 168 Figure 10.24. Bond-Strength Specimen After Compression Test (15’ Stacking Interval) ........... 168 Figure 10.25. Bond-Strength Specimen After Compression Test (20’ Stacking Interval) ........... 169 Figure 10.26. Bond-Strength Specimen After Compression Test (25’ Stacking Interval) ........... 169 Figure 10.27. Plate-Stacking Test Specimen (1% SA, 5 minute) ............................................... 176 Figure 10.28. Plate-Stacking Test Specimen (1% SA, 10 minute) ............................................. 176 Figure 10.29. Plate-Stacking Test Specimen (1% SA, 15 minute) ............................................. 177 Figure 10.30. Plate-Stacking Test Specimen (1% SA, 20 minute) ............................................. 177 Figure 10.31. Plate-Stacking Test Specimen (2% SA, 5 minute) ............................................... 178 Figure 10.32. Plate-Stacking Test Specimen (2% SA, 10 minute) ............................................. 178 Figure 10.33. Plate-Stacking Test Specimen (2% SA, 15 minute) ............................................. 179 Figure 10.34. Plate-Stacking Test Specimen (2% SA, 20 minute) ............................................. 180 Figure 10.35. Plate-Stacking Test Specimen (3% SA, 5 minute) ............................................... 180 Figure 10.36. Plate-Stacking Test Specimen (3% SA, 10 minute) ............................................. 181 Figure 10.37. Plate-Stacking Test Specimen (3% SA, 15 minute) ............................................. 181 xvii Figure 10.38. Plate-Stacking Test Specimen (3% SA, 20 minute) ............................................. 182 Figure 10.39. Predictive Model: Wind Tower Calculator (1 st Layer) ........................................... 184 Figure 10.40. Alternative Methods for Assessing Fresh Mortar Properties ................................ 186 xviii Abbreviations ASTM American Society for Testing and Materials CC Contour Crafting DP Drucker-Prager EL Elevation ES&C Expanded shale and clay FE Finite elements FEA Finite element analysis FEM Finite element model HRWR High range water reducer LWA Lightweight aggregate LWAC Lightweight aggregate concrete M1 Mortar mix #1 (100 pcf) M2 Mortar mix #2 (60 pcf) NCA Non-chloride (set) acceleration NWA Normal weight aggregate OD Outer diameter pcf pounds per cubic foot SA Set acceleration SAP Superabsorbent polymer additive SLA Structural lightweight aggregate SLC Structural lightweight concrete SSD Saturated surface dry VMA Viscosity-modifying admixture w/c Water-cement (or cementitious) ratio xix Notation d Cohesion p Hydrostatic or equivalent pressure stress q Deviatoric or Mises equivalent stress β Friction angle (angle of internal friction) ψ Dilation angle measured in the p-q plane ɛ Strain σ Stress σ 0 Yield limit for uniaxial stress-strain curve σ 1 Principal stress σ 2 Principal stress σ 3 Principal stress σ c Uniaxial compression yield stress σ m Hydrostatic stress E Modulus of elasticity (Young’s modulus) ν Poisson’s ratio V Volume d Vector of nodal displacements f Vector of applied nodal forces B Strain-displacement matrix D Constitutive matrix ɛ Strain tensor σ Stress tensor { ɛ} Column matrix or vector representation of strain tensor ɛ { σ} Column matrix or vector representation of stress tensor σ 1 1. Chapter One: Introduction Introduction to the Problem 1.1 This research pursues techniques, tools and strategies for engineering in-process fresh concrete subjected to unusual fabrication loads. The work is relevant wherever green, or uncured, concrete must be load-bearing, and is particularly relevant to an emerging fabrication technology called Contour Crafting, which fabricates structures additively with layered freeform depositions of fresh cementitious extrudates. Statement of the Problem 1.2 Contour Crafting, is an emerging additive fabrication technology that proposes to use computer- controlled layering of unconfined cementitious materials, to robotically manufacture homes that are more sustainable and affordable. Contour Crafting works by extruding a polymer-modified cementitious material, such as a concrete or a mortar, into successive layers that can rapidly accrue civil structures, incrementally from the bottom up. This feat is accomplished in-situ, with a robotic arm capable of traversing the construction site. The tip of the robotic arm is equipped with a swiveling nozzle, which constitutes the point of material extrusion. Material deposition follows predetermined, computer-controlled tool paths. Once a layer of material has been deposited along a fabrication path, the nozzle indexes vertically and proceeds to deposit a subsequent similar layer above. The fabricated structures are designed on a standard CAD system and ‘sliced’ into strata, during pre-construction planning. Optimization algorithms are used to convert these slices into corresponding energy and time efficient fabrication tool paths. The fabrication tool paths guide the automated layering of material depositions. The sum of the layered material depositions in turn (re)produces the total structure. Material deposition can proceed without interruption, and 2 the speed of fabrication and material accumulation is limited only by the structural integrity of the fabrication material. Figure 1.1 depicts prototypical Contour Crafting technology, and extrudate. Figure 1.2 depicts an exemplary contour-craftable structure and its corresponding fabrication tool path (Zhang, 2009). Figure 1.1 Contour Crafting Technology and Prototypical Research Specimen In the diagram to the right, each horizontal line represents a layer of extrudate. Figure 1.2. A Structure and its Contour Crafting Tool Path (Zhang, 2009) Contour Crafting is an efficient fabrication process, which embodies material, labor and energy savings achieved through paradigm shift and unprecedented reliance on automation. Material savings are achieved by eliminating formwork, and by batching according to precisely pre- programmed fabrication regimens, which when combined with computer controls and the accuracy of the extrusion process, result in minimal waste of construction material. Labor-related 3 savings are achieved with less touch labor, and less chance for construction related injury. Energy savings are achieved with compressed construction schedules, with energy-optimal tool paths, and by minimizing transportation of material and workforce. A complete description of Contour Crafting technology is beyond the scope of this research, which is limited to the material engineering challenge introduced by this new construction paradigm. However, the interested reader may learn more through the following references: (Zhang & Khoshnevis, to appear (2012)), (Zhang & Khoshnevis, 2011), (Zhang & Khoshnevis, Spring 2010), (Zhang & Khoshnevis, Summer 2010), (Yeh & Khoshnevis, 2009), (Khoshnevis, Hwang, Yao, & Yeh, 2006), (Khoshnevis, et al., January 2005), (Khoshnevis B. , January 2004), (Kwon, Bukkapatnam, Khoshnevis, & Saito, 2002), (Khoshnevis B. , Spring 2001), (Khoshnevis, Russell, Kwon, & Bukkapatnam, 2001), (Khoshnevis, Bukkapatnam, Kwan, & Sato, 2001). Contour Crafting is a rapid fabrication process, because nozzle routing is optimized to compress total construction time, and because the pace of construction is constrained only by the growing strength of the cementitious extrudate. The process is such that any given layer of construction material must support itself and every other layer subsequently deposited above it. Therefore, during fabrication each layer of the construction material is subjected to a steadily increasing applied load. The strength of the cementitious material, however also increases steadily as a function of cement hydration. Therefore, structural integrity is assured, and fabrication proceeds safely, as long as the strength gain derived from material maturation outpaces the accumulated load. If fabrication progresses slowly enough, timing the fabrication such that everywhere in the emerging structure material maturity outpaces structural loading is a trivial problem – this is the domain of applications that are not time sensitive - erecting infrastructure ahead of lunar colonization could be one such example. However, the technology is also intended to accelerate construction. For example, its developers project it will build a 2000 square foot, 2-story house in less than 24 hours, incidentally, at a cost 1/5 th that of conventional construction (ref.: 4 www.controurcrafting.org). At these hastened fabrication rates, the integrity of the in-process construction material becomes a structural challenge, which must be engineered. Figure 1.3 depicts the evolution of Contour Crafting technology with emphasis on materials and material delivery, specifically, the transition from paste extrusion to mortar pumping (Russell, 1999), (Kwon, 2002) and (Hwang, 2005). Paste extrusion can deliver very cohesive material that is very stiff and shape-stable, with process parameters similar to slip form casting. Conversely, pumping is at lower pressure; mix is necessarily more fluid; initial (or green) strength of the deposited material is diminished and thus a concern upon deposition, and during material layering – this complicates mix design and adds to the engineering challenge – materials must be pumpable and stiff enough to be independently load bearing only minutes after mixing. Figure 1.3. Previous Contour Crafting Material Systems However, the structural properties of fresh concrete, only minutes after mixing, are severely understudied, possibly because before Contour Crafting there was no practical application for Ram Extruder Pump 5 them. Comparison can be made to rammed earth, curbing and slip form casting, which however drive considerable compaction energy into mixtures that are far too stiff for pumping. Comparison can also be made to jump form construction which however uses rigid forms that support the fresh concrete for 24 hours or more, and transfer all fabrication loads into previously cast layers that are between 1 and 3 days old, and thus in terms of material maturation, well past final set - Figure 1.4. Adapted from (Schindler, 2004) and (van Breugel, 1992) Figure 1.4. Concrete Setting and Initial Strength Conversely, in terms of material maturation, contour crafted concrete begins working not hours but minutes after mixing, and therefore even before initial set, in the period commonly referred to Initial Set Final Set Mortar Strength Mortar Age (or Degree of Hydration) Hardening Dormant Period Setting Workable elasto- plastic mixture Stiffening, unworkable mixture Rigid solid strength gain with time Mixing 6 as the ‘dormant period.’ Therefore, understanding the uninvestigated structural properties of unset, unconfined concrete is perquisite to engineering a freeform-layered fabrication system like Contour Crafting. If unchecked, imposition of construction loads can lead to failure of the fabricated concrete elements. In other words, fabrication proceeds safely only if material maturation and strength gain outpaces the applied loads. The Willow Island cooling tower collapse is an apropos example of how things can go wrong when fabrication loads outpace the strength of the maturing (hydrating) concrete. The natural- draft hyperbolic concrete cooling tower (Figure 1.5) at the Pleasants Power Station at Willow Island, West Virginia collapsed while under construction on April 27, 1978, and killed 51 workers in what was then the worst construction disaster in U. S. history (Lew, Fattal, Shaver, Reinhold, & Hunt, 1979). A jump form system was being used, with the forms secured by bolts in one-day and three-day-old concrete. The forms were designed to be progressively moved up the tower as it was built - Figure 1.6 (Lew, Fattal, Shaver, Reinhold, & Hunt, 1979). Figure 1.5. Elevation of Willow Island Cooling Tower Unit No 2 (Lew et al., 1972) 7 Figure 1.6. Jump Form Construction System (Lew et al., 1972) Figure 1.7. Jump Form Material Hoisting System (Lew et al., 1972) Cross section thru the Formwork and Scaffolding Systems Static line Hoist cable Inside legs Outside legs Counterstatic line Chain hoist Pulley Steel balls Slide plate assembly Crane (cathead) Load line to crane Concrete bucket Static line Concrete loading platform Two-drum hoist 8 The safety of the slip form construction method depends on the capacity of the partially completed shell structure to resist all of the imposed construction loads, including formwork, scaffolding and material hoisting systems (Figure 1.6 and Figure 1.7). This demands that sufficient strength be developed in the previously cast shell so that structural resistance of these lower load-bearing elements exceeds the construction loads by a reasonable margin of safety (Lew, Fattal, Shaver, Reinhold, & Hunt, 1979). The night after lift 28 was poured, ambient temperature dipped into the mid-thirties, and this in turn delayed early strength gain. Figure 1.8 shows temperature variation prior to the collapse based on airport data. Figure 1.8. Temperatures Prior to Collapse of the Willow Island Tower (Lew et al., 1972) The National Bureau of Standards found that the concrete had not attained enough strength to support the imposed construction loads, and the failure analysis report concluded that the most probable cause of the collapse was the imposition of construction loads on the shell before the concrete of lift 28 had gained adequate strength to support these loads (Lew, Fattal, Shaver, Reinhold, & Hunt, 1979) - Figure 1.9 (Delatte, 2009). Temperature (⁰F) Time (days) Time of collapse End of pour, lift No. 28 Beginning of pour, lift No. 28 Temperature in the cylinder curing chamber Ambient Temperature (at the airport) 9 Figure 1.9. Structural Failure of the Willow Island In-Process Concrete (Delatte, 2009) Research Purpose 1.3 This thesis presents the foundational material engineering necessary to rapidly fabricate civil structures additively with unconfined fresh concrete, and as such, yields a crucial enabling technology for Contour Crafting. The primary purpose of the work is creation of a predictive procedure for engineering contour- crafted material which, as mentioned, is subjected to unprecedented fabrication loads. This predictive model will be based on a combination of experimental and numerical simulation methods. Ultimately, the predictive material model will be leveraged here to enable fabrication of a prototypical full-scale structure under controlled laboratory conditions, and at a commercially useful material stacking rate. The target production rate corresponds to an 8-foot tall structure erected in one day (Figure 1.10) - this is assumed to translate to practical material stacking rates on the order of 1 foot per hour, calculated as follows: H = total height of a prototypical structure = 96 inches h 0 = height of a single fabrication layer, or road = 3 inches n = number of roads required = H / h = 96 / 3 = 32 roads T = target fabrication time = 480 minutes ḣ = road layering rate = n / T = 32 / 480 = 1 road / 15 minutes ḣ = 12 inches / hour 10 Figure 1.10. Target Road Stacking Rate Three substantial topics are explored here to achieve the ultimate objective: (1) a suitable material mix, (2) a maturity model for said mix, and most importantly, (3) empirically verified timing constraints for uninterrupted but safe fabrication of prototypical contour-crafted artifacts under controlled (isothermal) laboratory conditions. A critical preliminary hypothesis is that qualitative analysis techniques will guide tailoring of a cementitious material mixture, which is (1) suitable for layered freeform fabrication, (2) adequate for erecting prototypical structures at commercially useful stacking rates (on the order of one foot per hour), and (3) capable of achieving useful structural strength once cured (ACI 213R, 2500 psi). Together, these qualities will serve to demonstrate the proposed fabrication process is both feasible and commercially useful. The pertinent research questions are as follows: 1. Can an extrudable mortar mixture be developed which satisfies the unique and structurally demanding performance requirements of a formless and layered fabrication process, such as Contour Crafting, to sustain useful fabrication rates, under prototypical isotheral conditions, with H h 11 built-in provisions for curing, which will achieve useful structural strength once cured (i.e. the suitable mix will have adequate workability and green strength during fabrication, cure properly after placement, and achieve 2500 psi strength once cured)? 2. Can standard tests be revised or novel experimental techniques be devised to characterize development over time of the pertinent structural properties of said fresh contour craftable mortar mixture (i.e. to support definition of an empirical maturity model for fresh contour craftable mortar)? 3. Can strength development (or maturity) of said prototypical mortar mixture be related to the structural demands of freeform fabrication, to produce a model which can be used to define safe material stacking regimens, in the context of a formless and layered fabrication process, such as Contour Crafting? In other words, can a simple analytical tool be developed to define the limits of safe contour craftability of simple, monolithic and homogenous civil structures (i.e. to pace fabrication such that over time and throughout the fabricated structure, material strength development always outpaces the increasing fabrication loads due to structural dead weight)? Research Plan 1.4 As mentioned, development of a suitable cementitious material is a prerequisite. This mix design leverages published reference mixtures, qualitative analysis techniques, and extensive consultation with practitioners. The subsequent work pertains to developing the sought-after predictive material engineering model. The predictive material engineering model is built on the following three research tasks: (1) development of experimental techniques to characterize the structural properties of fresh concrete relevant to Contour Crafting, (2) development of analytical structural analysis tools for Contour Crafting concreting, and (3) development of numerical (finite element) techniques for Contour Crafting concreting. 12 The experiments are central to the work because they provide parameters for the analytical modeling, and calibration and validation of the numerical simulation. The analytical model, which relates material strength gain to material stress rate, is the primary source of the sought-after critical fabrication timing constraints. This analytical model defines the limits of safe contour- craftability, and identifies the critical fabrication constraints. The numerical simulation is a supplementary building block which is used to facilitate parameter studies, to demonstrate feasibility as a material health-monitoring system, and to validate the critical timing constraints that are drawn from the analytical model. Figure 1.11 illustrates the relationships between these three building blocks. Exp.= experimental techniques; AM = analytical models; FEM = numerical methods r = parameter relations; c= calibration; v= validation Figure 1.11. Research Objectives As mentioned, the work culminates in a full-scale wall building demonstration, which serves to build confidence in this unprecedented fabrication process, and as validation. Importance of the Study 1.5 Contour-crafted structures can be subjected to sever loading during construction, i.e., before the concrete has developed adequate load-carrying capacity. If unchecked, imposition of fabrication loads can lead to failure of the structural elements, such as sagging, spalling or total collapse. AM Exp. FEM v r c,v 13 There is very little research relevant to fresh concrete working as a structural element possibly because before Contour Crafting there was no practical application for it. This research aims to fill this gap and to provide a foundation for the structural engineering of fresh concrete. Contour Crafting technology developers will benefit directly vis-à-vis the tailored material developed for this study, which is suitable for rapid freeform fabrication using Contour Crafting technology, and can thus be used as a medium for technology demonstrations and technology development. Mix designers will benefit because this research demonstrates a cementitious mixture tailored to achieve a combination of workability and shape stability suitable for rapid freeform fabrication, and because this prototypical mixture will be useful as a reference mix for future mix optimization (e.g. to reduce cost, increase strength, and increase robustness of the material system). Engineers, practitioners and policy makers will benefit from the tools introduced here for the structural analysis of fresh concrete. These tools lay the groundwork for developing the general material maturity function which will be necessary for fabrication planning and material health monitoring under variable field conditions (which must ultimately also account for inevitable material and temperature variations). Limitations, Delimitations and Assumptions 1.6 Limitations: the cementitious material studied here was constrained to be compatible with current Contour Crafting technology, which employs a progressive cavity rotor stator pump powered by a 5.5 Kw electric motor. This equipment is suited for pumping mortars (not concrete) with aggregates up to 1/8”. Delimitations: material was batched with pre-saturated light weight aggregate - this reduces one of the major advantages of lightweight aggregate concrete (LWAC), namely reduced dead weight, 14 but insures compatibility with current Contour Crafting technology, because aggregate pre- saturation is known to aid pumping (Norden & Thienel, 2000); scope was limited to monolithic homogeneous structures; experiments where performed in controlled laboratory environment, and under isothermal curing conditions; the LWAC specimens tested for compressive strength were not subjected to pumping, therefore results do not account for possible structural impact due to pumping pressure; the specific material model developed here to support erection of a prototypical full-scale wall is for a specific contour craftable material mix at room temperature (76F). Assumptions: experiments did not include full-scale pumping trials (which would have required considerably more material) – it was assumed instead that a mixture with consistency compatible with an ordinary household mixer (a 7 qt.,1000 W mixer) would also be compatible (pumpable) with the current Contour Crafting material delivery system. For the same reason, an expedient sample consolidation regime was also adopted and assumed to provide compaction comparable to that which would be achieved, thru pumping pressure, in the full-scale Contour Crafting material delivery system. Definitions 1.7 3D printing: process of making three-dimensional solid objects from a digital file (http://en.wikipedia.org/wiki/3D_printing) Additive or additive-layer manufacturing: a process of joining materials to make objects from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies; synonyms: additive fabrication, additive processes, additive techniques, additive layer manufacturing, layered manufacturing, and freeform fabrication (ASTM F2792 Rev A) Cementitious (material): an inorganic material or a mixture of inorganic materials that sets and develops strength by chemical reaction with water by formation of hydrates (ASTM C 125) 15 Concrete: a composite construction material composed primarily of aggregate, cement and water Constitutive material model: a numerical model to describe material behavior in finite element analysis; may also be thought of as a collection of sub-models where each sub-model plays a specialized representational role (e.g. to introduce elastic response or a characteristic yield surface) while collectively reproducing how the material reacts to boundary conditions and applied loads; when adequately chosen and calibrated, results in a global representation of local conditions in the material; numerically the material constitutive matrix (D) relates components of stress (σ) to components of strain (ɛ) in a multiaxial state: {σ} = D {ɛ}; in linear elastic analysis the terms of the constitutive matrix are usually expressed as functions of constant values of elasticity (E) and Poisson’s ratio (ν), and this constant D matrix leads to a constant stiffness matrix K=∫B T DBdV, Kd=f, d=K -1 f (where d represents displacement, f represents forces, and B is the strain-displacement matrix); departure from linear elasticity implies that the linear elastic constitutive equations are no longer valid, and that the material matrix D is no longer constant. This non-constant material matrix D represents the nonlinear material model, which in turn is based on generalization of experimental results. Typically, for lack of experimental evidence, nonlinear models of multiaxial material behavior rely heavily on generalizations of uniaxial concepts (Hinton, 1992) Contour-craftable: a cementitious material suitable for additive layer manufacturing using current Contour Crafting technology Cohesion: the component of shear strength of a rock or soil that is independent of interparticle friction; q-axis intercept of the Drucker-Prager linear yield function in the p-q stress plane Cold joint: a plane of weakness in concrete caused by an interruption or delay in the concreting operations Cured strength (concrete): compressive strength of cylindrical concrete specimens, such as cast cylinders and drilled cores, tested after at least 24 hours of curing 16 Dead load: includes structural loads that are relatively constant over time, including the weight of the structure itself Deviatoric (or Mises equivalent) stress: represents the shear component of the stress, i.e. the remainder of the stress after deducting the hydrostatic stress component; this division of stress is important in the theory of plasticity because of the fact (backed by experimental evidence) that the deviatoric stress is responsible for the plastic flow through the shear component, whereas the hydrostatic stress is composed of principal stresses with no shear and is thus responsible only for change in volume (but not shape) of an element of material (Becker, 2001); in terms of principal stresses, q=(1/√2)[(σ 1 -σ 2 ) 2 +(σ 2 -σ 3 ) 2 +(σ 3 -σ 1 ) 2 ] 1/2 Dilatancy: an increase in volume during shearing; Reynolds showed that dense sands expand at failure (a phenomenon he named 'dilatancy'), whereas loose sands contract during shear to failure (Reynolds, 1995); this proved that particle movements during deformation and failure are not necessarily in the direction of the applied shear stress) Dilation angle, ψ: represents the angle along which individual grains in a granular material slide up and over each other during shearing; the higher the dilation angle, the greater the degree of dilation; Bolton demonstrates Rowe’s stress-dilatancy relationship for plane shear is operationally indistinguishable from Φ’ = Φ' crit + 0.8ψ, where Φ' crit is the angle of shearing observed in a simple shear test on soil loose enough to be in a critical state, with zero dilation (Bolton, 1986); the advantage of having developed such an expression is that any angle of shearing in excess of the friction angle of loose earth is seen to be due solely to the geometry of the volumetric expansion which is necessary before shearing can take place - Figure 1.12 Figure 1.12. Bolton’s Simplified Saw Blade Model of Dilatancy (Bolton, 1986) 17 Drucker-Prager plasticity: a family of plasticity models that describes the behavior of granular materials and polymers in which the behavior depends on pressure stress in that they exhibit pressure-dependent yield (the material becomes stronger as the confining pressure increases); the inelastic deformation is often associated with frictional mechanisms such as sliding of particles across each other; these models are extensions of the original Drucker-Prager model (Drucker & Prager, 1952) Equilibrium density: as defined in ASTM 567, it is the density reached by structural lightweight concrete (low density) after exposure to relative humidity of 50 ± 5% and a temperature of 73.5 ± 3.5 °F (23 ± 2 °C) for a period of time sufficient to reach a density that changes less than 0.5% in a period of 28 days (ACI 213R-03) Expanded shale and clay: a lightweight aggregate manufactured from shale and clay heated and expanded in a rotary kiln to produce a strong, but lightweight, clinker; this clinker is then crushed and sized to meet aggregate grading requirements (http://www.txiesc.com) Factor of Safety: in general engineering terms, this is defined as the failure load divided by the design limit load; also sometimes defined as the available strength divided by the minimum strength required to just maintain equilibrium Final setting: since the setting of concrete is a gradual process, any definition of time of setting must necessarily be arbitrary (ASTM C 403); in the test method prescribed by ASTM C 403, the times required for a mortar to reach specified values of resistance to penetration are used to define times of setting; specifically, final setting occurs at a penetration resistance of 4000 psi, using the specified penetration needle and loading apparatus; phenomenologically, final setting of concrete relates to the point where stresses and stiffness start to develop in freshly placed concrete, and occurs at approximately the same degree of hydration for a particular mixture irrespective of the curing history (Schindler, 2004) - Figure 1.13; Tuthill and Cordon determined that at a penetration resistance of 4000 psi a concrete had reached a compressive strength of around 80 psi (Tuthill & Cordon, 1955) 18 Adapted from: (ASTM C403) Figure 1.13. Mortar Penetration Resistance versus Elapsed Time Finite Element Method (FEM): a numerical technique for finding approximate solutions to partial differential equations and their systems; in simple terms, FEM divides or discretizes field problems or continuous domains into a set of discrete sub-domains usually called elements, that can be solved in relation to each other Flow Rule: when the stress at any point in a material under load reaches the yield surface, the material starts to undergo plastic deformation; when material is deforming inelastically (flowing), the inelastic part of the deformation is defined by a flow rule; for some rate-independent plasticity models the direction of material flow is the same as the direction of the outward normal to the yield surface (the yield function and plastic flow potential are identical), and the flow is referred to as “associated” flow; associated flow models are useful for most metals in which the fundamental mechanism of plastic flow is atomic dislocation movement and slip; associated flow is generally 4000 psi 500 psi Elapsed Time [min] → Penetration Resistance [psi] Initial Setting Final Setting, σ c ~80 psi 19 not accurate for materials in which the inelastic deformation is primarily caused by frictional mechanisms, and which exhibit volume change during shearing; in the context of this research, the significant extension of the Drucker-Prager plasticity model (useful for the numerical analysis of the fresh mortar) is the introduction of a non-associated flow rule; nonassociated flow is also generally assumed when the model is used for polymeric materials (Abaqus User's Manual, 2009) Freeform or solid-freeform fabrication: (see additive manufacturing) Fresh (concrete or mortar): concrete which possesses enough of its original workability so that it can be placed and consolidated by the intended methods (ASTM C 125) Friction angle, β: slope of the Drucker-Prager linear yield function in the p-q stress plane Green strength: compressive strength of a concrete or mortar shortly after mixing, and before setting (also initial strength) Hydration (of cement): the chemical reaction between hydraulic cement and water forming new compounds most of which have strength-producing properties (ASTM C 219) Hydrostatic, equivalent (or mean) stress, p: the hydrostatic stress is composed of principal stresses with no shear and is thus responsible only for change in volume (but not shape) of an element of material (Becker 2001); in terms of principal stresses, p=(1/3)( σ 1 +σ 2 +σ 3 ); often also denoted as σ m Initial setting: since the setting of concrete is a gradual process, any definition of time of setting must necessarily be arbitrary (ASTM C 403); in the test method prescribed by ASTM C 403, the times required for a mortar to reach specified values of resistance to penetration are used to define times of setting; specifically, initial setting occurs at a penetration resistance of 500 psi, using the specified penetration needle and loading apparatus; phenomenologically, the concrete has reached the point where it has stiffened to such an extent that it can no longer be vibrated without damage; under hot weather conditions, the time to initial set will be shorter than under 20 normal temperatures, and this will affect the construction crew’s ability to consolidate and finish the in-place concrete (Schindler, 2004) - Figure 1.13 Initial strength: see green strength Internal curing: refers to the process by which the hydration of cement continues because of the availability of internal water that is not part of the mixing water; typically, this internal water is made available by the pore system in structural lightweight aggregate that absorbs and releases water (ACI 213R-03) Maturity: the extent of the development of a property of a cementitious mixture (ASTM C 1074) Maturity function: a mathematical expression that uses the measured temperature history of a cementitious mixture during the curing period to calculate an index that is indicative of the maturity at the end of that period (ASTM C 1074) Meridional plane: the p-q stress plane; p=hydrostatic or mean stress, q=deviatoric stress Mortar: a mixture of finely divided hydraulic cementitious material, fine aggregate, and water in either the unhardened or hardened state; hydraulic mortar (ASTM C 219) Plastic weight: the density, or unit weight of freshly mixed concrete Principal stress: the principal directions of a stress tensor represent the orthogonal axes which define the planes where the shear stress components of the stress vector vanish; the corresponding normal components of the stress vector are the principal stresses σ 1 +σ 2 +σ 3 ; the magnitude of the principal stresses is independent of the coordinate frame used (principal stresses are stress invariants) Proportional loading: all external loads are applied simultaneously and increase in proportion to one another throughout the loading history; if there is proportional loading with no reversal in direction it is usually acceptable to use isotropic hardening Rapid prototyping: a group of techniques used to quickly fabricate a physical part or assembly using three-dimensional computer aided design (CAD) data; construction of the part or assembly is usually done using 3D printing technology (http://en.wikipedia.org/wiki/Rapid_prototyping) 21 Road: each layer of material deposited during additive-layer manufacturing Robustness (of concrete): robustness of concrete is defined as the material's capacity to tolerate variation in material characteristics (e.g. aggregate moisture), mixture parameters (e.g. mixing time and dosage), and environmental conditions (e.g. temperature and humidity); robust concrete has lower sensitivity to such variations (Naji, Hwang, & Khayat, 2011) Saturated surface dry: the condition in which the permeable pores of aggregate particles are filled with water to the extent achieved by submerging in water for the prescribed period of time, but without free water on the surface of the particles (ASTM C 128) Secant Young’s modulus: for material like soil and fresh mortar which have a variable modulus of elasticity E, the value of E used must be either the slope of the tangent to the σ-ɛ curve or that of the secant; the secant is the line joining the origin of the curve to (for example) 50% of the failure stress point on the curve (Mar, 2002) – Figure 1.14 Figure 1.14. Secant Young’s Modulus (Mar, 2002) Setting: the process, due to chemical reactions occurring after the addition of mixing water, which results in a gradual development of rigidity of a cementitious mixture (ASTM C 125) Shape-stable: a mortar or concrete with negligible slump 22 Slump: a sample of freshly mixed concrete is placed and compacted by rodding in a mold shaped as the frustum of a cone; the mold is raised, and the concrete allowed to subside; the vertical distance between the original and displaced position of the center of the top surface of the concrete is measured and reported as the slump of the concrete (ASTM C 143) Stress invariant: a scalar function derived from the stress tensor whose magnitude does not vary as the reference coordinate axes change orientation; examples of stress variants are: p=(1/3)( σ 1 +σ 2 +σ 3 ), and q=(1/√2)[(σ 1 -σ 2 ) 2 +(σ 2 -σ 3 ) 2 +(σ 3 -σ 1 ) 2 ] 1/2 , where σ 1 , σ 2 and σ 3 are the principal stresses (which are also invariants) Structural lightweight aggregate - structural aggregate meeting the requirements of ASTM C 330 with bulk density less than 70 lb/ft3 (1120 kg/m3) for fine aggregate and less than 55 lb/ft3 (880 kg/m3) for coarse aggregate; this includes aggregates prepared by expanding, pelletizing, or sintering products such as blast-furnace slag, clay, fly ash, shale or slate, and aggregates prepared by processing natural materials such as pumice, scoria or tuff (ACI 213R-03) Structural lightweight concrete: structural lightweight-aggregate concrete made with structural lightweight aggregate as defined in ASTM C 330; the concrete has a minimum 28-day compressive strength of 2500 psi (17 MPa), an equilibrium density between 70 and 120 lb/ft3 (1120 and 1920 kg/m3); comprises lightweight aggregate or a combination of lightweight and normal-density aggregate (ACI 213R-03) Thixotropic: bodies are said to be thixotropic if (1) after a long rest when a shear stress or strain rate is applied suddenly and then held constant, the apparent viscosity is a diminishing function of the time of flow, and (2) the body recovers its initial state following a long enough interval after the cessation of the flow; this time-dependent decrease in the viscosity may be explained by a reversible change of the suspension microstructure during shear; in the absence of shear, the damaged structure rebuilds; the physical origin of this rebuilding might find its foundations in the Brownian motion that could induce a slow rearrangement of the particles’ configuration or in an evolution of the colloidal interactions between the particles, although it has to be noted that this aspect is still unclear (Rhéologie, 1990) 23 Triaxial test: a laboratory test of a cylindrical material specimen sealed inside a rubber bag surrounded by water under pressure in a cell; a load is applied by a piston to one end of the specimen via a stiff platen while loads and deformations are recorded – Figure 1.15 (a) triaxial compression, (b) triaxial tension, (c) exemplary triaxial test stress-strain curves at different levels of confinement pressure Figure 1.15. The Triaxial Test (Abaqus User's Manual, 2009) Time at rest: time elapsed after material placement (e.g. once extruded) Validation: the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model (Schwer & Rogers, 2006) Verification: the process of determining that a computational model accurately represents the underlying mathematical model and its solution (Schwer & Rogers, 2006) (a) (b) (c) 24 Water-cement ratio (w/c): the ratio of the mass of water, exclusive only of that absorbed by the aggregates, to the mass of portland cement in concrete, mortar, or grout, stated as a decimal; this term, abbreviated as w/c, is applicable only to cementitious mixtures in which the only cementitious material is portland cement; for cementitious mixtures containing blended hydraulic cement, or a combination of portland cement and separate addition of another cementitious material (such as a pozzolan), use the term water-cementitious material ratio (ASTM C 125) Yield Surface, (or yield criterion): in the theory of plasticity, a law defining the limit of elastic behavior under any possible combination of stresses π plane: a plane perpendicular to the line subtending equal angles with the coordinate axes σ 1 , σ 2 , and σ 3 ; the deviatoric stress is a vector in this plane Adapted from: (Becker, 2001) Figure 1.16. Isotropic Yield Surfaces and the π-plane in 3-D Stress Space Linear Drucker-Prager yield surface Drucker-Prager yield locus Von Mises yield surface Von Mises yield locus Hydrostatic stress, σ m π-plane 25 2. Chapter Two: Literature Review Introduction 2.1 This chapter surveys the relevant literature, with emphasis on three areas of interest: (a) research relevant to shape-stable, extrudable concrete with significant green strength, (b) early strength gain and concrete maturity, and (c) prior experience layering fresh unconfined concrete. Shape-Stable Concretes 2.2 This section explores research relevant to developing a cementitious material suitable for freeform-layered fabrication. In 1999, Richard J. Russell II completed his PhD dissertation on the strength of his research proving out the Contour Crafting fabrication paradigm, at a reduced scale and using melted polystyrene (Russell, 1999). In 2002, Russell’s work was followed by Hongkyu Kwon’s dissertation which published experiments, also performed at reduced scale, using uncured ceramic materials (Kwon, 2002). In 2005, Dooil Hwang upped the ante considerably, scaling up to 2 ft. walls and setting Contour Crafting within the context of concrete practitioners with the first references to familiar concreting terminology and industry standards (e.g. ASTM methods). Dooil’s initial mix designs produced extrusions which lacked the superb cohesion, green strength and structural integrity characteristic of the bench-scale artifacts produced by the prior generation Contour Crafting machine using uncured clay extrudate. In a characteristic moment of holistic insight Dr. Khoshnevis surmised that cohesion of a cementitious extrudate might be improved with a small addition of clay. Hence, Dooil introduced a cementitious mix design that used clay as a viscosity-modifying admixture (Hwang, 2005). Most recently, full-scale Contour Crafting laboratory tests have employed a readymade sprayable mortar developed for structural repairs and marketed by the Sika Corporation as SikaRepair 224. 26 SikaRepair 224 is a dark gray, high strength, shrinkage-compensated cementitious mortar enhanced with silica fume and fiber reinforcement. Despite its impressive 10000 psi 28 day compressive strength, SikaRepair 244 is ill suited for Contour Crafting because it combines a relatively high wet density, with a relatively low green strength, and inadequate setting times. This material is also very costly. Wet density (wet mix) 125 lbs/cu ft Initial setting time (ASTM C 266) 2 to 3 hours Final setting time (ASTM C 266) 5 to 6.5 hours 1 day compressive strength (ASTM C 109) 73°F 4,500 psi (31 MPa) 7 day compressive strength (ASTM C 109) 73°F 8,000 psi (55 MPa) 28 day compressive strength (ASTM C 109) 73°F 10,000 psi (69 MPa) Cost (as quoted by Kurt Anderson; kkasika@cox.net, May 3, 2010) $1400 per cubic yard Table 2.1. Properties of SikaRepair 224 Contour Crafting’s inauspicious history with SikaRepair is notable for its exemplary inadequacy, and to emphasize that the material performance requirements of freeform-layered fabrication are onerous, and unlikely to be satisfied by a non-specific, albeit sophisticated, material system. As mentioned earlier, a suitable mix is one which can be pumped and extruded, which can support layering at useful fabrication rates (function of both density and initial structural integrity, or green strength), which will age gracefully under less-than optimal conditions (e.g. provide for cement hydration and resistance against autogenous shrinkage cracking), and which will achieve useful structural strength once cured. SikaRepair excelled in most, but not all of these performance categories. Clearly, contour-craftable materials must be tailor made. Fortunately, a number of researchers working primarily out of Northwestern University under the tutelage of professor Shah, and in adjacent research vectors aiming for example to manipulate cement rheology to reduce formwork pressure and to simplify slip-form casting, have made significant progress towards improving the structural properties of fresh concrete, and with only slight mix manipulations, such as addition of mineral admixtures, most notably clay. 27 Tregger, Pekmezci and Voigt (Tregger, Voigt, & Shah, 2007), (Pekmezci, Voigt, Wang, & Shah, 2007), (Tregger, Pakula, & Shah, 2010) and (Voigt, Mbele, Wang, & Shah, 2010) demonstrate that fresh self-consolidating slipform concrete (SF-SCC) can be made more shape-stable with small additions of clay (Figure 2.1, Figure 2.2, Figure 2.3, Figure 2.4 and Figure 2.5). Assaad (Assaad, 2004) demonstrates that sand and coarse aggregate ratios can be manipulated to reduce formwork pressure (Figure 2.6) 1 . Martinie (Martinie, Rossi, & Roussel, 2009) and de Koker (Koker & Zijl, 2004) demonstrate how fibers modify the consistency, shape stability and extrudability of cement pastes (Figure 2.7 and Figure 2.8). Figure 2.1. Apparatus for Simulating Slip-Form Casting (Tregger, Voigt, & Shah, 2007) (a) The first photo shows consolidation and shape stability of a model pavement slab for a standard slipform mix. The rough pavement exhibits poor consolidation. (b) Consolidation and shape stability of a model pavement slab for an SF-SCC developed with fly ash. The bulging sides indicate poor shape stability, but the smooth surface indicates good consolidation. (c) Consolidation and shape stability of a model pavement slab for an SF-SCC developed with clay and fly ash. The smooth surface and straight sides indicate both acceptable consolidation and shape stability (Shah, Mondal, Ferron, Tregger, & Sun, 2008) Figure 2.2. Improving Slip-Form Casting with Clay (Tregger, Voigt, & Shah, 2007) 1 Although this work is potentially very relevant to layered freeform fabrication it was not be leveraged here to maintain compatibility with current Contour Crafting technology – the work is emphasized nonetheless because it should be tapped for future research. 28 Figure 2.3. Shape-Stable Concrete Slab Produced without Vibration (Pekmezci et al., 2007) (new concrete is plain + 1% Clay) Figure 2.4. Comparison of Self-Consolidatability of SF-SCC (Pekmezci et al., 2007) 29 Source: (Voigt, Mbele, Wang, & Shah, 2010) Figure 2.5. Effect of Admixtures on Flowability and Green Strength of Fresh Concrete (1.0-SCC= 100% sand; no coarse aggregate) Figure 2.6. Manipulating Form Pressure with Sand/Aggregate Ratio (Assaad, 2004) 30 Figure 2.7. Consistency of a Cement Paste with Various Fibers (Martinie et al., 2009) Figure 2.8. Extrusion of a Fiber-Enhanced Cement-Based Composite (Koker & Zijl, 2004) Finally, a mix suitable for layered freeform fabrication should also provide for graceful aging, and specifically for internal curing because, as alluded to, the unconfined extrudate may be exposed to less-than-optimal curing conditions. Internal curing refers to the process by which the hydration of cement occurs because of the availability of additional internal water that is not part of the mixing water. Typically, this additional internal water is made available by the pore system in structural lightweight aggregate that absorbs water prior to or during mixing, and releases water after placement – like a sponge (ACI 213R-03). Figure 2.9 and Figure 2.10 illustrate internal curing and the how moisture moves between the porous lightweight aggregate (LWA) and the cement paste to promote hygral equilibrium and cement hydration. 31 Source: http://www.escsi.org Figure 2.9. Internal Curing at the Contact Zone Colored Corona Expanding Around a Lightweight Aggregate Saturated with Ink Solution and Cast in a White Portland Cement Paste (Lura, Jensen, & Igarashi, 2007) Figure 2.10. Visualizing Internal Curing (Lura et al. 2007) 32 Testing Shape-Stable Concrete 2.3 An expedient test for evaluating the structural integrity (e.g. load-bearing capacity) of fresh mortar is necessary. The test must be expedient because the performance period of interest begins just minutes after mixing – meaning minimal time for specimen preparation, test setup, and execution. A number of approaches defined in both research and industrial specifications were considered for this purpose. The devices implemented here are patterned after Tregger (Tregger, Pakula, & Shah, 2010) and Voigt (Voigt, Malonn, & Shah, 2006). Tregger (Tregger, Pakula, & Shah, 2010) demonstrates rudimentary but very expedient strength testing of fresh concrete using cylindrical specimens, a container and sand (Figure 2.11). Figure 2.11. Tregger Green Strength Test (Tregger et al., 2010) 33 Voigt (Voigt, Malonn, & Shah, 2006) demonstrates strength testing of freshly extruded cement mortar specimens using a load cell and stiff platens. These uniaxial compression tests were performed in displacement control at a rate of 0.1 mm/s (Figure 2.12). Figure 2.12. Uniaxial Compression of Freshly Extruded Mortar (Voigt et al., 2006) A survey of other very relevant options considered but not implemented here can be found in the appendix. Maturity of Shape-Stable Concrete 2.4 As mentioned, the Contour Crafting process subjects fresh, uncured concrete or mortar to unprecedented fabrication loads. A clear understanding of initial strength and very early strength development is therefore necessary for safe fabrication. To be clear, in this context, fabrication loads are be applied just minutes after mixing – or in other words, during the initial setting period, and somewhat earlier than documented in the literature (for example, Voigt 2005). This section explores previous attempts at modeling very early strength development in cementitious materials. As noted, the performance period of interest begins just minutes after mixing when the mixture is commonly considered to be in a dormant phase. 34 A number of empirical models are considered, including power law and linear hyperbolic - Figure 2.13 and Figure 2.14 (Voigt, Malonn, & Shah, 2006); parabolic-hyperbolic - Figure 2.15 (Carino & Lew, 2001); and exponential - Figure 2.16 (Freiesleben Hansen & J., 1985), (Carino & Lew, 2001) and (Schindler, 2004). Voigt, Malonn and Shah (Voigt, Malonn, & Shah, 2006) investigated early strength development of extruded mortar specimens. In the context of that research, the compressive strength obtained from the mortar cylinders in their fresh state was referred to as the ‘green strength’ of the tested material. As illustrated in Figure 2.13 and Figure 2.14, initially, the green strength of such specimens develops very gradually. However, after a certain time, the strength values start to increase and begin to develop according to a power law. The period between the first significant increase and the beginning of the power law trend was interpreted as the transition from the green strength to an actual compressive strength. At a later age the compressive strength followed a hyperbolic trend function. Source: (Voigt, Malonn, & Shah, 2006) Figure 2.13. Power Law Development of Compressive Mortar Strength 35 Source: (Voigt, Malonn, & Shah, 2006) Figure 2.14. Linear-Hyperbolic Development of Compressive Mortar Strength Source: (Carino & Lew, 2001) Figure 2.15. Parabolic-Hyperbolic Development of Compressive Mortar Strength 36 Source: (Schindler, 2004) Figure 2.16. Exponential Development of Compressive Strength Concrete Previous Attempts at Layering Shape-Stable Concrete 2.5 In this section we explore prior research relevant to layering shape-stable unconfined concrete, with emphasis on fabrication planning and the actual layering of self-supporting cemetitious compounds. As reported by Hwang (Hwang, 2005), tool path optimization analysis defines the following relevant manufacturing constraints: Dooil Toolpath Planning Constraint #3: the lower layer must be able to support the upper layer, therefore the time interval between depositing subsequent layers cannot be shorter than the critical limit. Dooil Toolpath Planning Constraint #4: subsequent layers must be able to adhere; therefore the interval between depositing subsequent layers should not exceed the critical limit. Constraints 3 and 4 are both related to the time interval between depositing subsequent layers. This interval is equal to the overall time of constructing a layer, t r , which can be calculated once the tool path of the layer has been generated. If t r is shorter than the interval required by 37 constraint 3, the machine has to wait before depositing the next layer. If t r is longer than the interval required by constraint 4, the structure is too large to be built by a single nozzle (more nozzles are needed, and/or the tool path must be partitioned). When layers accumulate, each layer must be solidified enough to support the overall weight of layers above it. The overall weight on a layer is proportional to the number of layers above it. Hence it is proportional to the overall time of constructing a layer. Once the construction time of each layer is calculated, a chart that shows the relationship between the weight of upper layers and construction time can be used to verify this constraint. One way to satisfy constraint 3 is to exploit set acceleration. Set accelerators work by accelerating cement hydration, which results in shortened setting time and increased early age strength. Hwang (Hwang, 2005) experimented with several batches of rapid set pastes and concluded that fabrication with rapid set was unrealistic and risked paste hardening inside the equipment (Figure 2.17). Figure 2.17. Removing Hardened Rapid Set from CC Equipment (Hwang, 2005) The 2008 CRAFT Task Report (Khoshnevis B. , 2008) also documents problems associated with rapid set. The stated task objective was to find an accelerating agent that would allow a very pumpable mix (slump = 3-6 inches) to attain sufficient initial hardening to sustain the wall weight during the construction process. Although “strong interlayer bonds” were reported after topical application and subtraction of a set accelerator, this technique adds complexity, runs counter to 38 cold joint prevention regimens, and may produce less homogeneous material structure and properties, uneven curing and other unforeseen detrimental effects (Figure 2.18). Source: (Khoshnevis B. , 2008) Figure 2.18. Week Bonds Between Layers using Polyacrylamide Accelerating Agent The cold joints produced by distinct-layer casting degrade the structural strength and load- bearing capacity of the fabricated structure, and should therefore be avoided. Roussel (Roussel & Cussigh, 2008) reported a specific distinct-layer casting prevention regimen that may be relevant to Contour Crafting: (a) the interface between two layers of fresh concrete must be rough, as the roughness at the interface creates a bond between the two layers even if they do not mix, and (b) the structuration or structural build-up rate of the first layer has to be low enough to allow the stresses generated at the interface between the two layers to re-initiate flow in the first layer. In this context, structuration is defined as the material’s ability to build up a load- bearing internal structure (Figure 2.19). Examples of numerical simulation of distinct-layer casting of a thixotropic SCC (self consolidating concrete). Units are meters. (left) 300 s resting time between two layers; the two layers mix perfectly (right) 1200 s resting time between layers; the two layers do not mix at all. Figure 2.19. Curing Distinct-Layer Casting (Roussel & Cussigh, 2008) 39 Yet some set acceleration can and should be leveraged. For example, Roussel also showed that small amounts of accelerator can be used to achieve a 10x increase in structuration which was mostly thixotropic. Thixotropy is potentially useful in layered freeform fabrication because it entails reversible destructuration under flow (pumpability), and useful structuration at rest (shape- stability). Finally, it is worthwhile in this context to revisit Hwang’s formwork pressure calculations and resulting conclusions relative to allowable Contour Crafting fabrication rates (Hwang, 2005), keeping in mind that in his work, Hwang considered formwork pressure exerted by a fresh filler material (in a 2-part composite road) against a previously layered and cured outer formwork. Although ultimately relevant, these calculations do not define the minimum time between layers (the allowable fabrication rate) for Contour Crafting, in that in Hwang’s fabrication scenario minimum time between layers is constrained by how fast you can erect the outer formwork material. This prerequisite allowable mortar-stacking rate is one of the fundamental questions answered for the first time by the present work. 40 3. Chapter Three: Mix Design Introduction 3.1 This chapter describes development of a cemetitious material suitable for freeform layered fabrication. Mix design leverages published reference mixtures, qualitative analysis techniques, and extensive consultation with practitioners. Mix Design Criteria 3.2 A suitable mix is one which can be pumped and extruded, which can support layering at useful fabrication rates (function of both density and initial structural integrity, or green strength), which will age gracefully under less-than optimal curing conditions (e.g. provide for cement hydration and resistance against autogenous shrinkage cracking), and which will achieve useful structural strength once cured. Mix design was guided by the following heuristics: 1) Favor availability and locally sourced raw materials. 2) Identify and opt for synergy leveraging properties that are “already there”; for example, expanded shale and clay (ES&C) is adequate structurally, promotes shape-stability (by way of aggregate angularity), and is also good for weight, thermal insulation and internal curing. 3) Avoid material and system incompatibilities. 4) All else being equal (i.e. performance, sustainability, affordability, availability), favor appearance (for example, light-colored metakaolin instead of dark grey silica fume). Furthermore, mix design considered the following inputs, outputs and functional constraints. Mix Design Independent Variables (Inputs): 1) Lightweight aggregate (e.g. ES&C, Poraver, Elemix) 2) Mineral admixtures (Metakaolin, Calcium Carbonate fines) 41 3) Chemical admixtures (HRWR, VEAs, accelerators) 4) Fiber reinforcement (multiple lengths, diameters and material options) 5) Process variables (temperature, pressure, vibration) Mix Design Dependent Variables (Outcomes): 1) Workability 2) Green strength 3) Fresh density 4) Finish and appearance Mix Design Constraints: Compatibility with the current system (the Contour Crafting pump, which uses a Markham- Sheffield progressive cavity rotor stator pump powered by a 5.5 Kw electric motor, is suited for pumping mortar with aggregates up to 1/8”). Reference Mixtures 3.3 Study mixes were expediently modeled after designs provided by Poraver North America 2 (Table 3.1, Table 3.2 and Table 3.3). Ingredient % By Weight Cement 25.1 Fly Ash 16.7 Sand 41.8 Poraver Blend 16.4 Fresh Density 88 lbs/ft 3 Density 80 lbs/ft 3 Compressive Strength 7 d 1919 psi Compressive Strength 28 d 2000 psi Table 3.1. Basic 2000 psi Poraver Concrete Formula 2 Personal communication with Mike Horsfield, Vice President Sales & Marketing, Poraver North America, Ltd., 3/1/2010. 42 Ingredient % By Weight Cement 42.1% Sand 28.1% Fly Ash 10.5% Poraver 0.1-0.3 mm 17.5% Poraver 0.25-0.5 1.75% Density 95.8 lbs/ft 3 Compressive Strength 7 day 4071 psi Compressive Strength 28 day 5242 psi Table 3.2. Basic 4000 psi Poraver Concrete Formula Ingredient % By Weight Cement 43.6% Sand 29.0% Fly Ash 10.9% Poraver 0.1-0.3 mm 16.4% Density 104 lbs/ft3 Compressive Strength 7 days 4989 psi Compressive Strength 28 days 5969 psi Table 3.3. Basic 5000 psi Poraver Concrete Formula The Poraver designs suggested a number of useful mix ratios, which are summarized in Table 3.4. Cured Strength %cement, c %fly ash, fa %(c+fa) %sand, s %poraver, p s/p 2000 psi 25.1 16.7 41.8 41.8 16.4 2.55 4000 psi 42.1 10.5 52.6 29.9 17.5 1.71 5000 psi 43.6 10.9 54.5 29.0 16.4 1.77 6000 psi 45.1 11.3 56.4 28.2 16.4 1.72 (The 6000 psi data results from linear extrapolation; measures are percent by weight) Table 3.4. Batching Ratios for Lightweight Concrete Mix Design 3.4 The bulk ingredients were batched leveraging the batching ratios derived above. Other components and admixtures were selected favoring availability, lighter weight and color (for appearance), and dosed per the manufacturer’s recommendations. The design was fine-tuned 43 through trial and error. Figure 3.1 illustrates the first and final mortar mixtures, affectionately referred to a “beauty” and “beast” for obvious reasons. (left: the first experimental mortar mixture; right: the final M1 study mix) Figure 3.1. Beauty and the Beast Figure 3.2 summarizes the bulk ingredients and the desirable attributes which they contribute. Figure 3.2. Bulk Ingredients and How They Contribute to the Suitable Mix Table 3.5 identifies the bulk ingredients of the final 100 pcf mortar recipe, which is identified throughout this study as the M1 mix. Lightweight Internal curing Early Strength Workability (Green) Shape Stability 44 Saturated ES&C #1 3 0.366 % wt. Poraver 0.1-0.3 mm 0.216 % wt. Type III Cement 4 0.334 % wt. Class C Fly Ash 5 0.084 % wt. Clay 6 0.002 % wt. Plastic unit weight 90.1 lb/ft^3 Equilibrium weight 75.8 lb/ft^3 Table 3.5. Study Mix M1 A suitable lightweight insulating mix was also developed and tested for strength. This mix, identified in this report as M2, is a 60 pcf mix developed with the addition of expanded polystyrene beads. The lightweight insulating M2 mix may be used in combination with the lightweight structural M1 mix to fabricate composite roads with less dead load and more insulation. The reduction in dead load would allow for faster fabrication (vis-à-vis a larger green strength to weight ratio). The increased insulation would improve the energy efficiency of the fabricated structures. Figure 3.3 depicts an exemplary composite road using the M1 and M2 mortar mixtures. The M2 mix is documented in the appendix. 3 The ES&C is batched saturated to minimize slump loss due to free mix water being forced into open aggregate pores by pump pressure; the reported ES&C weight is saturated surface dry (SSD) weight. 4 Type-III early strength cement that is also light in color and relatively lightweight, supplied by Txi 5 Class C fly ash supplied by Headwaters 6 Highly purified Magnesium Alumino Silicate supplied by Active Minerals International 45 M1 = lightweight structural concrete; M2 = lightweight insulating concrete Figure 3.3. Exemplary Composite Roads M1 M2 46 4. Chapter Four: Experimental Research Introduction 4.1 This chapter describes methods for measuring the structural properties of concrete by means of various unconfined compression tests performed using fresh and cured cylindrical mortar specimens. This testing is necessary to develop empirical predictions of very early strength gain, to emulate the Contour Crafting fabrication process, and to calibrate finite element models of contour-crafted artifacts. Specimen Preparation 4.2 This section describes mortar preparation with emphasis on workability. Following the precedent set by Shah et al. at Northwestern University (Tregger, Ferrara, & Shah, 2008), relative workability was initially evaluated using a drop table (references: BS EN 12350-5, ASTM C 230, ASTM C 1611, and ASTM C 1437), and the ASTM C 230 mini-cone (72.4 in3). This approach uses flow ratio as a measure of workability, and was particularly attractive for its simplicity (Figure 4.1 and Figure 4.2). Unfortunately, this approach proved to be inadequate because it was neither sufficiently expedient nor sensitive. In this context, expediency is paramount because sample preparation, test setup and execution must occur within minutes of mixing, and without unduly delaying subsequent structural testing. Flow ratio was also marginally adequate as a measure of workability because the suitable mortar mixtures exhibited very little flow. In an attempt to overcome these difficulties, a custom vibration table was introduced to accelerate the process (Figure 4.3). Vibration was very effective, but still rather time-consuming, and a departure from practice because current Contour Crafting technology does not vibrate the mortar mixture (consolidation is achieved entirely by means of pumping pressure). 47 Ultimately, mortar workability was not measured directly, but expediently assessed and somewhat consistently achieved by proxy, relative to the power of an ordinary 1000 W household mixer, and in general agreement with ASTM C 305, Standard Practice for Mechanical Mixing of Hydraulic Cement Pastes and Mortars of Plastic Consistency. Specifically, at the target degree of plasticity, the mortar mixture could be mixed at mixer power level 6 (see Figure 4.4 and Figure 4.5). Adapted from: BS EN 12350-5 Figure 4.1. Drop Table and Mortar Mold 48 Adapted from: (Tregger, Ferrara, & Shah, 2008) and BS EN 12350-5 Figure 4.2. Measurement of Mortar Spread Figure 4.3. Custom Vibration Table Vibration Isolation Mounts Vibco Vibrator (VS-130) Mold Locking Device 49 Figure 4.4. Mechanical Mixing of Mortar of Plastic Consistency (ASTM C 305) Figure 4.5. Mortar Mixed to Plastic Consistency Green Strength Test 4.3 This test method was developed to support the empirical determination of very early strength gain in a fresh contour-craftable mortar. The test is patterned after ASTM D 1266, Standard Test Method for Unconfined Compressive Strength of Cohesive Soil. The primary purpose of this 50 unconfined compression test is to quickly and expediently obtain a measure of compressive strength in specimens with enough cohesion to permit testing in the unconfined state – in other words, shape-stable concretes and mortars with very low slump. The apparatus includes a platform weighing scale, a (somewhat) constant rate loading device (a dry sand chute), and a deformation indicator to measure slump (an analog deflectometer). Mortar specimens are prepared per ASTM C 192, using an open-ended cylindrical mold that allows the specimen to be extruded after consolidation, with negligible disturbance. The extruded specimen is tested on the weighing platform, centered under a rigid loading platen. For convenience, the scale and deflectometer can be zeroed before each test such that applied load, and axial deflection can be read directly. A high-resolution digital camera is used to document the test, and to provide snapshots that record the scale and deflectometer reading 7 . Optionally, snapshots of the deformed specimen can also be digitized in post-processing with software, or manually with the aid of a superimposed grid. The setup is depicted in Figure 4.6. 7 The apparatus is simple and inexpensive, however, it is worth noting that in retrospect post-processing video frames to extract the measurements was extremely tedious and could have been easily avoided using a relatively inexpensive LVDT sensor (for example, Instron 2601 Series Deflectometers). 51 Figure 4.6. Apparatus for Unconfined Compressive Strength of Fresh Concrete Green strength is evaluated with uniaxial compression of molded 3x6, or 3x4 cylinders of fresh mortar. Specimens are prepared in the laboratory at room temperature (approximately 74F), with batching water at approximately 65F. Immediately after mixing, mortar specimens are prepared, extruded and tested as follows. An open-ended cylindrical mold equipped with a false bottom and a sealing cap is filled in 2 layers (lifts). Each layer is consolidated with either 5-10 seconds on the custom vibration table 8 , or with 3 swift drops on the workbench from a height of 4-6 inches. After each consolidation, the outside of the mold is tapped sharply 12 times with a rubber mallet to close holes and release entrapped air. After filling and consolidation, excess mortar is stricken off the top with a tapping rod. Finishing is performed with the minimum manipulation necessary to produce a flat even 8 Per ASTM C192, sufficient vibration has been applied as soon as the surface of the concrete becomes relatively smooth and large air bubbles cease to break through the top surface. Continue vibration only long enough to achieve proper consolidation of the concrete. Dummy specimen used to zero extensometer. Digital weighing platform to measure applied force. Extensometer to measure slump and axial deflection. 6 in.x12 in. cylinder guided laterally and suspended by springs. The cylinder collects sand flowing in at a constant rate from above. This charge stretches the suspension system, and is considerably larger than the resistance exerted by the compressed fresh mortar specimen - this disparity assures nearly constant axial strain rate. Vibration table used to consolidate test specimens inside extrudable cylindrical mold. Bin to hold sand used to charge the loading device. Ram used to extrude test specimens. 52 surface that is level with the rim of the mold and which has no depressions or projections larger than 1/16 in. After finishing the specimen is carefully de-molded (extruded) as illustrated in Figure 4.7. After de-molding the green strength of the unconfined fresh mortar specimen is determined by applying a vertical load-controlled force. Compression force is applied by pouring sand into a guided cylinder. The loading rate is approximately 1.8 lb/sec. (a) assemble mold, cap and false bottom, then fill with mortar and consolidate; (b) carefully remove cap and bring the filled mold with false bottom to ram extruder; (c) align mold and ram extruder; (d) slide mold down to extrude the shape-stable mortar specimen Figure 4.7. Apparatus for Preparing Fresh Mortar Specimens for Green Strength Test Figure 4.8 depicts three exemplary 3x4 cylindrical mortar specimens compressed, from left to right, at 19, 37 and 45 minutes after mixing. Figure 4.9 depicts snapshots of an exemplary test 3x4 Plastic Cylindrical Mold (Open-Ended) Plexiglas Ram Extruder False Bottom Mold Cap (a) (b) (c) (d) 53 from start to finish. Figure 4.10 illustrates evolution of mortar green strength over time, at three exemplary mortar ages: 11, 109 and 288 minutes after mixing. In Figure 4.10, the first frame depicts the start of the test; the second frame depicts the mortar specimens at approximately 12.5 lbs. of applied load. The increase in strength from early-age to later-age is readily apparent. Figure 4.11 depicts the raw force-deflection curves produced testing the prototypical mortar mix M1 at various ages spanning the range between 11 to 288 minutes after mixing 9 . The subsequent figures and tables summarize how the data obtained thru green strength testing were reduced to characterize the material properties used in the analytical and numerical models developed herein. Figure 4.12 and Figure 4.13 illustrate stress-strain diagrams for exemplary very-young and later- age mortar specimens respectively. These diagrams illustrate marked evolution in material response as specimen age increases. Since there is no evidence of an elastic limit at very early ages, a secant modulus was calculated and reported for the younger specimens. This compromise was necessary for ages up to 30 minutes. Figure 4.14 summarizes evolution of stiffness (Young’s modulus, E) as a function of time. As expected, in the plotted performance period of interest, stiffness increases exponentially. The complete set of stress-strain diagrams is documented in appendix. Figure 4.15 illustrates evolution of compressive yield strength, σ c , as a function of time. The reported trend was anchored using limit strengths evidenced in the stress-strain diagrams of the younger specimens (up to age 52 minutes), and extrapolated exponentially afterwards (as suggested by development of Young’s modulus). Figure 4.16 illustrates evolution of cohesion, d, as a function of mortar age, assuming cohesion relates to compressive yield strength (Prinja & Puri, 2005) as follow: . 9 The data are corrected to compensate for increments of deflection in the measurements due to system flexibility. The necessary correction was determined by testing a perfectly stiff specimen, and is a function of applied weight: , where d is deflection (in), and w is applied weight (lb). 54 Cohesion will be of particular interest for calibration of the material model used to analyze the fresh aging mortar numerically (by FEA). Figure 4.17 illustrates evolution of Poisson’s ratio as a function of mortar age. After Štemberk (Štemberk & Kohoutková, 2005) values were assumed to range from 0.25 to 0.20 during the plotted performance period of interest. Evolution was patterned after the evolution law published with HIPERPAV: ν = -0.017 ln(t) + 0.29 (Ruiz, et al., 2005). Figure 4.18 illustrates evolution of mortar slump as a function of time. Extrusion of the fresh and relatively delicate younger mortar samples resulted in uneven upper surfaces. These raised lips interfered with measurement of slump, insofar as slump could not be taken to be the deflectometer reading coincident with the initial measurement of applied load (the instant the platen begin transferring load to the specimen, as indicated on the weighing platform). To compensate, here we extrapolate to an equivalent slump at zero load using specimen deflections at 0.5 and 1.0 lbf. Figure 4.20 illustrates exemplary slip planes which were clearly evidenced in the youngest mortar specimens tested. These slip planes are of particular interest for calibration of the material model used to analyze the fresh aging mortar numerically (by FEA). Table 4.1 summarizes the aforementioned material properties and their respective evolution laws over the performance period of interest (up to about 4 hours after mixing). Figure 4.8. Exemplary Unconfined Compressive Strength Tests (3x4 cylinders) 55 Figure 4.9. Exemplary Unconfined Compressive Strength Test (3x6 cylinder) Figure 4.10. Evolution of Unconfined Compressive Strength (3x4 cylinders) 56 (All testing performed under isotheral conditions at a room temperature, approximately 74F) Figure 4.11. Stress-Strain Diagrams of M1a Mortar Mix (2% clay, 0% NCA) 10 10 This data was obtained testing four 3x4 specimens cast from a single batch of the M1 mortar mixture using no set acceleration (0% NCA). The first four tests were performed on virgin specimens. Subsequent tests were performed on recycled (and reconsolidated) specimens. This recycling could impact the findings. Although, the data supports the hypothesis that evolution of material properties during the dormant phase follows an exponential law, caution should be exercised when drawing conclusions as the data is limited and potentially adulterated (by the specimen recycling). Increasing Mortar Age Stress-Strain Diagram for M1 Mortar Mix at 0% NCA 57 x-axis = strain[in/in], y-axis = stress[psi] Figure 4.12. Exemplary Early-Age σ-ɛ Diagram of M1a Mortar Mix x-axis = strain[in/in] 11 , y-axis = stress[psi] Figure 4.13. Exemplary Later-Age σ-ɛ Diagram of M1a Mortar Mix 11 Note that in these σ-ɛ diagrams the run-out at approximately 1.8 psi is due to mortar settling after the maximum load allowed by the equipment has been applied – it does not necessarily indicate yielding. 58 Figure 4.14. Modulus=f(t) Figure 4.15. Compressive Yield Strength=f(t) Figure 4.16. Cohesion=f(t) y = 9.7597e 0.0096x R² = 0.9166 0 50 100 150 200 0 50 100 150 200 250 300 E [psi] Time After Mixing [min] y = 0.8099e 0.0095x R² = 0.9798 0 2 4 6 8 10 12 14 0 50 100 150 200 250 300 σc [psi] Time After Mixing [min] y = 0.5727e 0.0095x R² = 0.9798 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 100 200 300 Cohesion [psi] Time After Mixing [min] 59 Figure 4.17. Poisson’s Ratio=f(t) Figure 4.18. Slump=f(t) 12 12 As noted earlier, most of the green strength tests were performed using recycled and reconsolidated mortar specimens. This recycling interfered with characterization of initial slump mainly because a slight amount of mortar material was lost while reforming the specimens. The first few recycled tests are most impacted in this way because no attempt was made to replenish the lost material, and this resulted in inflated slump values. For this reason data for ages between 22 and 84 minutes are omitted here. Although, data reduction supports the hypothesis that evolution of the material property during the plotted period of interest follows an exponential law, caution should be exercised when drawing conclusions as the data is limited and potentially adulterated. (Štemberk & Kohoutková, 2005) y = 0.149e -0.005x R² = 0.8004 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0 50 100 150 200 250 300 Slump of 3x4 Fresh Mortar Cyl. [in] Time After Mixing [min] 60 Figure 4.19. Development of Very-Early Compressive Strength in the M1 Mortar 12.5 lbf @11 minutes 12.5 lbf @ 52 minutes 12.5 lbf @ 109 minutes 12.5 lbf @ 288 minutes 61 Figure 4.20. Typical Early-Age Slip Plane E = 9.7597e 0.0096t ; σ c = 0.8099e 0.0095t ; ν = -0.017ln(t) + 0.29; d = 0.5727e 0.0095t Table 4.1. Material Parameters as a Function of Time Plate-Stacking Test 4.4 This supplemental test was developed to overcome limitations of the green strength test, because it was simpler, and most importantly because it is most representative of the actual conditions to which the unconfined fresh mortar is subjected to during free form layered fabrication. 011 61⁰ 018 61⁰ 11 18 22 47 52 92 99 109 211 283 288 E [psi] 11.3 11.4 11.5 14.8 16.7 18.6 18.2 25.7 70 200 180 σc [psi] 0.8 0.8 1.2 1.55 1.6 1.7 1.9 2.1 5.8 12.1 12.8 ν 0.25 0.24 0.24 0.23 0.22 0.21 0.21 0.21 0.20 0.20 0.20 β=ψ 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3 d 0.6 0.6 0.8 1.1 1.1 1.2 1.3 1.5 4.1 8.6 9.0 Time After Mixing, t [min] 62 The test was designed to closely mimic a layered fabrication process, which subjects fresh cementitious extrudate to discrete increments of load. As above, the test specimens are prepared per ASTM C 192, in extrudable cylindrical molds. After consolidation the specimens are carefully extruded from the mold with negligible disturbance, and simply placed upon a sturdy surface. At regular intervals, chosen to emulate candidate fabrication regimens, metal plates are placed upon the unconfined test specimens. These metal plates are prepared to match the predetermined weight of the test specimen, and therefore provide a convenient means of emulating the fabrication load that in practice would be exerted by subsequent mortar layers. The test is exceedingly simple. Figure 4.21 illustrates the apparatus, which includes metal plates, plus needles and rulers which were incorporated to measure deflection. Table 4.2 illustrates an exemplary schedule which allows for simultaneous testing at four relevant plate-stacking rates. Figure 4.21. Apparatus for the Plate-Stacking Test 3 in. Diam. Steel Plates (machined to match the weight of one 3x4 cylinder of M1 (or M2) fresh mortar specimens Rulers and for measuring deflection Needles affixed to first plate to indicate specimen slump 63 Table 4.2. Plate-Stacking Schedule Figure 4.22 illustrates exemplary time steps during testing of the M1 mortar mixture. This test was repeated three times, at each of three levels of set acceleration: 1%, 2% and 3%. Complete test documentation is in appendix. 64 Test Time [clock / stopwatch] Plate Count (clockwise from upper right) 2:35/0:00 A single plate is applied to each mortar specimen 3:15/0:40 9 th plate on stack 1, 5 th plate on stack 2, 3 rd plate on stack 3, 3 rd plate is about to be applied to stack 4 5:05/2:30 1 st stack failed, 16 plates, 11 plates, 8 plates 6:05/3:30 1 st stack failed, 22 plates, 15 plates † , 11 plates 13 Testing ends 7 hours after t=0, when the 22nd plate is added to stack 4 (not shown) Figure 4.22. Exemplary Plate-Stacking Test As the load applied to the aging mortar increases, failure occurs when lower levels of set acceleration are combined with faster loading rates. Importantly, these distinct failures (rather sudden instabilities) allow us to anchor the mortar strength development curves (which are exponential, as predicted by the literature and corroborated by earlier green strength testing) in a very meaningful and pertinent way. 13 The last 2 plates applied to this stack in this time-step were weight-calibrated for the M2 mix, and together they conservatively apply an incremental load which is in excess of an M1 layer; this was done here and in subsequent time-steps because we ran out of M1 plates; however at each increment the total applied load was as high as or conservatively higher than scheduled for that increment. 65 Figure 4.23 compares the resulting exponential strength development curves of M1 mortar to fabrication loads associated with four road-laying regimens. In this juxtaposition, mortar strength increases monotonically (per the exponential trend), while the loading profiles are regular stepped functions, following the reasonable assumption of equal time delays between road depositions (Zhang, 2009). The juxtaposition illustrates the notion that for safe fabrication, strength must never fall below (or cross) the stepped loading function. Figure 4.23 also charts the bounds of safe Contour Crafting concreting. For example, the road- stacking regimen with 5-minute delay between layers overtakes each of the exemplary M1 strength development curves – it’s too aggressive. The M1.3pc mortar can support a 10-minute road-stacking regimen. The M1.2pc can support a 15-minute road-stacking regimen. The M1.1pc mortar, strapped by the lowest level of set acceleration, is marginal even at the slowest 20 minute stacking regimen. Here the suffix appended to the mortar designation M1, indicates percent set acceleration; for example, “.1pc” indicates 1% NCA. 66 Figure 4.23. Evolution of Mortar Strength and Fabrication Load Over Time 14 14 It’s important to note that in the actual execution of the plate-stacking test we switched the 20’ stacking schedule to an accelerated 5’ schedule after plate 11 – this can be seen in the plotted results as an abrupt shift in the loading step function – the change in pace was fortuitous because it induced failure in the stack, and hence a usable limit state data point, whereas it’s safe to conclude that no failure would have been observed in the 20’ stack had the nominal 20’ stacking interval been maintained throughout the duration of the test. Importantly, the limit state data point is used to anchor the exponential strength development curve for the M1.2pc mixture. This observation suggests a modification to the plate-stacking test. Accordingly, at the higher levels of set acceleration, which are unlikely to fail at the longer stacking intervals, the stacking interval should be chosen such that failure is likely before the test ends. In other words, the objective is to register failures throughout the time frame of interest. 67 Cured Cylinder Strength Test 4.5 Cured cylinder uniaxial compressive strength tests are performed per ASTM C 39, Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens, using standard 3x6 mortar specimens prepared and cured per ASTM C 192 15 . This section summarizes results of the ASTM C39 cured cylinder compression tests. These tests were performed at Associated Soils Engineering, in Long Beach, CA. Figure 4.24. Typical Cured Cylinder Strength Test (M1, 100 pcf specimen) Although not necessary to characterize early strength development, these tests provide data necessary to model mortar maturity past final setting, and also demonstrate that the M1 mortar mix meets requirements for structural lightweight concrete as defined by ACI 213R-03: minimum 28-day compressive strength of 2500 psi (Ries, 2003). 15 The 3x4 cylindrical specimens which did not fail in the plate-stacking test are also tested after curing in lab air (see appendix for details). 68 Table 4.3. Compression Strength – 100 pcf M1 Mix Figure 4.25. Cured Cylinder Strength Test (100 pcf specimen @ 24 Hrs) Figure 4.26. Cured Cylinder Strength Tests (100 pcf specimen @ 3 days) 1=Day 3-Day 7-Day 28-Day Specimen No. M1.1.1 M1.2.1 M1.1.2 M1.2.2 M1.1.3 M1.2.3 M1.1.4 M1.2.4 Date Tested: 21-Sep 21-Sep 23-Sep 23-Sep 27-Sep 27-Sep 18-Oct 18-Oct Specimen Size 3x6 3x6 3x6 3x6 3x6 3x6 3x6 3x6 Age [days] 1 1 3 3 7 7 28 28 Total Load [lbf] 7560 5620 13700 11200 20000 17500 28250 26250 D1 [in] 3.03 3.02 3.02 3.02 3.02 3.02 3.04 3.03 D2 [in] 3.01 3.02 3.02 3.02 3.02 3.02 3.02 3.04 Area [in 2 ] 7.16 7.16 7.16 7.16 7.16 7.16 7.21 7.23 Strength [psi] 1055 785 1913 1564 2792 2443 3918 3628 69 Figure 4.27. Cured Cylinder Strength Tests (100 pcf specimen @ 28 days) Bond Strength Test 4.6 Bond strength testing was undertaken to ensure that the combinations of set acceleration and layering intervals entertained here are not detrimental to interlayer bond strength - in other words, to insure that the recommended fabrication regime does not result in distinct layer casting, or cold joints. The test developed for this purpose is patterned after ASTM C 882, Standard Test Method for Bond Strength of Epoxy-Resin Systems Used with Concrete by Slant Shear. Figure 4.28 illustrates the apparatus. A mortar of plastic consistency is prepared as described above. Immediately after mixing an open-ended 3x6 cylinder mold equipped with a slanted dummy section, a mold-release barrier and a removable cap is filled and consolidated, as described above. Mixing of a second batch of mortar is timed such that it will be ready for filling the second half of the specimen, at the desired time, which is chosen to emulate a specific layer-stacking regimen. After consolidation of the first half, the mortar surface is leveled, finished and topped with a false bottom and a removable cap. Before the designated time for forming the second half of the specimen the dummy section is extracted. Removal of the dummy section is a delicate operation, which must be performed carefully so as to disturb the specimen as little as possible. The procedure is as follows. 70 The cap opposite the dummy section is removed and a vented eyelet bolt is threaded into the vent hole that runs the length of the dummy section (wedge). With the mold held horizontally and clocked such that the tip of the slanted mortar surface is closest to the workbench (this is the most stable position for the young mortar in the mold), the dummy section is extracted by pulling firmly on the eyelet bolt. After the dummy section and mold-release barrier are removed, the slanted surface of the specimen is inspected for damage, and carefully repaired if necessary. The second half of the specimen is filled, consolidated, finished and capped as above. The specimen is then positioned upright on the workbench with the false bottom facing up, and the removable cap is removed in preparation for loading. Metal plates are applied to the specimen to simulate the progressive weight of regular fabrication regimens. Table 4.4 illustrates a mortar mixing, specimen preparation and plate stacking schedule, which allows for the simultaneous preparation and testing of four separate stacks in the shortest possible total test time. Adapted from: ASTM C 882 Figure 4.28. Apparatus for Preparing Bond Strength Test Specimen 3x6 Cylindrical Mold (open ended) 3x6 Mold Caps Dummy ½ Section (with venting hole) Mold- Release Paper 71 Table 4.4. Consolidation Regimen of the Bond-Strength Specimens Hr Min 0 9: 30 start mixing part 1 10 9: 40 stop mixing part 1 20 9: 50 mold part 1 25 9: 55 start mixing part 2 25 9: 55 remove wedge 35 10: 05 stop mixing part 2 45 10: 15 mold part 2 50 10: 20 prep for plates Hr Min 60 10: 30 start mixing part 1 75 10: 45 add plate 1 70 10: 40 stop mixing part 1 80 10: 50 start mixing part 2 80 10: 50 mold part 1 85 10: 55 remove wedge 90 11: 00 stop mixing part 2 100 11: 10 add plate 2 100 11: 10 mold part 2 105 11: 15 prep for plates Hr Min 125 11: 35 add plate 3 125 11: 35 add plate 1 120 11: 30 start mixing part 1 130 11: 40 stop mixing part 1 135 11: 45 start mixing part 2 145 11: 55 add plate 2 140 11: 50 mold part 1 150 12: 00 add plate 4 145 11: 55 remove wedge 145 11: 55 stop mixing part 2 155 12: 05 mold part 2 165 12: 15 add plate 3 160 12: 10 prep for plates 175 12: 25 add plate 5 175 12: 25 add plate 1 Hr Min 185 12: 35 add plate 4 180 12: 30 start mixing part 1 190 12: 40 add plate 2 190 12: 40 stop mixing part 1 190 12: 40 start mixing part 2 200 12: 50 add plate 6 205 12: 55 add plate 5 205 12: 55 add plate 3 200 12: 50 mold part 1 200 12: 50 stop mixing part 2 205 12: 55 remove wedge 210 13: 00 mold part 2 220 13: 10 add plate 4 215 13: 05 prep for plates 225 13: 15 add plate 7 225 13: 15 add plate 6 225 13: 15 add plate 1 235 13: 25 add plate 5 235 13: 25 add plate 2 245 13: 35 add plate 7 245 13: 35 add plate 3 250 13: 40 add plate 8 250 13: 40 add plate 6 255 13: 45 add plate 4 265 13: 55 add plate 8 265 13: 55 add plate 7 265 13: 55 add plate 5 275 14: 05 add plate 9 275 14: 05 add plate 6 280 14: 10 add plate 8 285 14: 15 add plate 9 285 14: 15 add plate 7 295 14: 25 add plate 9 295 14: 25 add plate 8 300 14: 30 add plate 10 305 14: 35 add plate 10 305 14: 35 add plate 9 310 14: 40 add plate 10 315 14: 45 add plate 10 325 14: 55 add plate 11 325 14: 55 add plate 11 325 14: 55 add plate 11 325 14: 55 add plate 11 335 15: 05 add plate 12 340 15: 10 add plate 12 345 15: 15 add plate 12 345 15: 15 add plate 13 350 15: 20 add plate 12 355 15: 25 add plate 13 355 15: 25 add plate 14 365 15: 35 add plate 13 365 15: 35 add plate 15 370 15: 40 add plate 14 375 15: 45 add plate 13 375 15: 45 add plate 16 385 15: 55 add plate 14 385 15: 55 add plate 15 385 15: 55 add plate 17 395 16: 05 add plate 18 400 16: 10 add plate 14 400 16: 10 add plate 16 405 16: 15 add plate 15 405 16: 15 add plate 19 415 16: 25 add plate 17 415 16: 25 add plate 20 425 16: 35 add plate 15 425 16: 35 add plate 16 425 16: 35 add plate 21 430 16: 40 add plate 18 435 16: 45 add plate 22 445 16: 55 add plate 17 445 16: 55 add plate 19 450 17: 00 add plate 16 460 17: 10 add plate 20 465 17: 15 add plate 18 475 17: 25 add plate 17 475 17: 25 add plate 21 485 17: 35 add plate 19 490 17: 40 add plate 22 500 17: 50 add plate 18 505 17: 55 add plate 20 525 18: 15 add plate 19 525 18: 15 add plate 21 545 18: 35 add plate 22 550 18: 40 add plate 20 575 19: 05 add plate 21 600 19: 30 add plate 22 15' LAYS 10' LAYS 20' LAYS 25' LAYS 72 This section summarizes results of the interlayer bond strength tests. Bond-strength specimens were consolidated by means of plate-stacking at 10, 15, 20 and 25 minute intervals. Results suggest no apparent sensitivity to minimum time between layers, over the tested range of interest. However it would be unrealistic to draw extensive conclusions given the scarcity of data, and the fact that these specimens were consolidated in molds and thus with confining pressure, whereas in practice this would not be the case for freestanding layered depositions. Figures below are exemplary. Full documentation of the plate-stacking test is in appendix. (mortar layering/plate stacking intervals from left to right: 10’, 15’ 20’ and 25’) Figure 4.29. Plate-Stacking Test (at time 1:35) 73 (mortar layering/plate stacking intervals from left to right: 10’, 15’ 20’ and 25’) Figure 4.30. Plate-Stacking Test (at time 4:15) (mortar layering/plate stacking intervals from left to right: 10’, 15’ 20’ and 25’) Figure 4.31. Mix Water Forced out of Bond-Strength Specimens 74 Figure 4.32. Exemplary Demolded Bond-Strength Specimen Figure 4.33. Exemplary Uniaxial Compression Testing of Bond-Strength Specimen 75 (10-minutes between mortar layers; 10-minute consolidation-stacking intervals) Figure 4.34. Exemplary Bond-Strength Specimen After Compression Test Figure 4.34 illustrates an exemplary bond-strength specimen after compression test. Table 4.5 and Figure 4.35 reported the bond strength calculated by dividing the load carried by the specimen at failure by the area of the bonded surface 16 . 16 As specified by ASTM C 882, the theoretical area of the elliptical bonding surface in this test method is 14.13 in2, but should be adjusted to the actual area based on measuring the lengths of the two axes [0.7854 a b]. The area of the bonded surface should also be reduced by that of any voids found in the bond on inspection after test. Neither of these corrections was implemented here. 76 Table 4.5. Compression Strength of Cured Bond-Strength Specimens Figure 4.35. Uniaxial Compression Strength of Cured Bond-Strength Specimens Is the bond strength insensitive to layering interval? Aside from the cautionary note required by the scarcity of the data, the bond strength specimens were subjected to confining pressure during consolidation, and though the plate-stacking schedule mimicked the expected fabrication loading, in practice roads are unconfined. What happens to bond strength when unconfined mortar layers are consolidated by freeform layering remains essentially unknown. However, it’s not necessarily worse than the preliminarily encouraging results reported here. In fact it’s easy to imagine that slight displacement at the boundaries between layers (as material shears under load) could improve the interlocking at the boundaries, and thus increase post-cured bond strength. These 10 15 20 25 Specimen No. T10 T15 T20 T25 Age [days] 28 28 28 28 Total Load [lbf] 14000 13100 14100 19200 D1 [in] 3.05 3.05 3.05 3.05 D2 [in] 3.05 3.05 3.04 3.04 Area [in 2 ] 7.31 7.31 7.28 7.28 Compression Strength [psi] 1916 1793 1936 2637 Plate-Stacking Interval T10 1916 T15 1793 T20 1936 T25 2637 0 500 1000 1500 2000 2500 3000 5 10 15 20 25 30 Compressive Strength [psi] Time Delay between Layers [minutes] 77 tests should be repeated with unconfined specimens. Alternatively the artifact produced during the full-scale mortar layering demo could also be cored (diagonally) and tested for this purpose. Leveraging the lessons learned, an alternative, and more apropos method for preparing bond strength specimens is proposed and illustrated in Figure 4.36. This simpler and more representative approach would also make it easy to investigate the effects of surface roughness, which Roussel reported to be beneficial (Roussel & Cussigh, 2008). (a) mortar and load plate stacking (4.25” tall roads; metal plates calibrated to match the road weight), (b) cure and cut specimen at 45⁰, (c) core out 3x6 cylinders, (d) bond strength cylinders ready for compression testing Figure 4.36. Alternative Bond-Strength Specimen Preparation 78 5. Chapter Five: Analytical Material Models Predicting Mortar Maturity 5.1 This chapter describes the analytical models developed here for the structural analysis of freeform-layered fabrication using free-standing, unconfined and self-supporting fresh mortar. Two models are developed: (1) a general model with dependencies on material density, set acceleration, and temperature, and (2) a specific isothermal model for the M1 mix. The specific model is used later to plan a full-scale freeform layering demonstration, which in turn serves as empirical validation of this work. The engineering tools developed here for the analysis of fresh concrete pertain to a specific specialized mortar mixture prepared and placed under controlled laboratory conditions (most notably at room temperature and with carefully controlled moisture content). In practice temperature and moisture (w/c) will be quite variable, and this variability will greatly influence the outcome. General Maturity Model 5.2 This section represents the first investigation of the maximum vertical fabrication rate allowable in freeform layering of unconfined and self-supporting fresh mortar. The objective here is to identify a maximum sustainable fabrication rate for freeform layered deposition of unconfined and self-supporting fresh mortar. To do this we contrast mortar maturity and structural stress (due to self-weight). To simplify the work, both functions are initially assumed to increase monotonically. We begin with mortar maturity. A maturity model is necessary to define development (over time) of the compressive strength of the extruded mortar. As demonstrated, the very early (before final setting) strength development of the M1 mortar mixture, under isothermal curing may be represented as: 79 (1) where, S = material strength (aka σ c ) (psi) t = fabrication time; starts when 1 st layer is deposited (min) t 0 = age of the mix at t=0 (min) m = material rate constant (1/s) Next we consider structural stress. A number of stress measures may be relevant to Contour Crafting concreting, for example, shear stress and compression stress. This model considers engineering compression stress per the familiar P/A relation, as follows: (assume constant road height h) Figure 5.1. Basic Road Dimensions (2a) ̇ ̇ (2b) where, r = road h H W L r 1 r 2 r n 80 P = compressive force applied to r 1 (lbf) A = road cross sectional area (in 2 ) V = volume of structure (in 3 ) L = road length (in) W = road width (in) H = total height of deposition (in) δ = material density (lb/in 3 ) σ = road r 1 stress (psi) and, ̇ (3) where, h t = fabricated height at time t (in) h 0 = height of a single road (in) Here h 0 is the height of a single road, which should factor into this derivation because in this context stress due to material self-weight is not negligible. However, to simplify the derivation h 0 is initially assumed to be zero. We’ll return to this simplification once a more intuitive result is obtained, by way of the simplification. Naturally, the critical measure of interest is the difference between strength and stress (∆): (4) Thus, the critical condition occurs when , and ∆ is at a minimum. ∆ is at a minimum when, ̇ ̇ ̇ (5) If we define t c as the critical time t when ( , and ∆ is at a minimum), then, c ≡ @ t c, S c ≡ S @ t c c ≡ @ t c = δ ḣ t c 81 If we also define, , we can rewrite eq. (1) as, [ ] (6a) ̇ (6b) where, S 0 = initial mortar strength (psi) at mix age 0 Ś 0 = mortar strength at fabrication time t = 0 Combining (2b), (5) and (6b), and solving for t c , ̇ (7a) [ ̇ ] (7b) If we now combine (4) and (7b), and solve for ḣ such that (∆>0), i.e. (S c -σ c >0), ḣ [ ̇ ] ḣ [ ̇ ] ḣ ḣ [ ̇ ] [ ̇ ] ḣ ḣ ḣ So, ḣ (8) Importantly, equation (8) defines the maximum vertical build rate ḣ max as a function of material strength at time t=0, material rate constant, and material density. Combining (7b) and (8), [ ] (9) 82 The important implication of this intermediate (isothermal) result is that the critical time t c is independent of both the initial mortar strength, S 0 and the age of the mix when fabrication begins, t 0 . In other words, at constant temperature, increasing S 0 and/or t 0 allows for faster fabrication, but the time to reach the critical condition (when the difference between strength and stress is critical) remains the same. Figure 5.2 illustrates this result for two exemplary initial mix ages, t 0 . A comparison varying initial mix strength, S 0 would be similar. Figure 5.2. Very Early Maturity, Max Build Rates, and Time to Critical Condition So far the derivation of critical time, t c assumed a singular isothermal condition. We now extend the work slightly to allow for arbitrary isotherms. To do this we incorporate the age conversion factor, ɣ proposed by Freiesleben and Hansen (Freiesleben & Pedersen, 1977): (10) where, E = apparent activation energy (J/mol) (Carino N. , 1984) 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 120 140 160 180 200 Strength (S), Stress (σ) [psi] Time from Start of 1st Road, t 0 (min) Effect of Initial Age of Mix on Allowable Build Rate Strength (Initial Age of Mix = 30 min) Stress (@ Max Allowable Build Rate = 1.4 ft/hr) Strength (Initial Age of Mix = 10 min) Stress (@ Max Allowable Build Rate = 1.1 ft/hr) Tcritical = 100 min 83 R = universal gas constant, 8.314 J/mol-K T = average absolute temperature of the concrete during the interval (Kelvin) T r = absolute reference temperature (Kelvin) In European practice, reference temperature is usually taken to be 20 ⁰C, whereas in North American practice it is usually taken to be 23 ⁰C (Carino & Lew, 2001). In this work the reference temperature is 24 ⁰C (75 F). Applying age conversion, (11a) (11b) where, t e = the equivalent time t at the average temperature T (min) t 0e = the equivalent time t 0 at the average temperature T (min) Combining (11a), (11b) and (1), and defining m e ≡ mɣ, (12) Clearly, equation (12) is in the same format as the original equation (1). The implication is temperature simply alters the rate constant. Figure 5.3 illustrates this result for 3 exemplary isotherms. 84 Figure 5.3. Effect of Temperature on Allowable Build Rate and Time to Critical Condition We now return to the earlier simplification, h 0 =0. As mentioned, h 0 is the height of a road, and it should factor into this derivation because in this context, unlike other ‘mechanics of materials’ problems, stress due to material self-weight is not negligible. As it turns out we can simply delay fabrication a bit to make the necessary ‘correction.’ Recall t c was defined as the time to reach the critical condition when the difference between mortar strength and stress is critical. We now revise t c as follows: ́ (13) where t delay is required to correct our model for the unaccounted for self-weight effect. This required delay depends on the effect that a layer’s weight has upon the layer itself. An estimate is made comparing increments of load and deflection. To make the comparison we equate deflection induced by gravity (D g ; a body force) to deflection induced by an applied load 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 120 140 160 180 200 Strength (S), Stress (σ) [psi] Time from Start of 1st Road, t0 [min] Effect of Temperature on Allowable Build Rate Strength (T = 85 F) Strength (T = 75 F) Strength (T = 65 F) Stress (@ Max Allowable Build Rate = 1.7 ft/hr) Stress (@ Max Allowable Build Rate = 1.2 ft/hr) Stress (@ Max Allowable Build Rate = 0.8 ft/hr) Tcritical 85 (D P ; a boundary load) with the familiar expression for elastic uniaxial deformation (δ = PL/AE), as follows: Deflection due to Gravity, D g : , [ ] , [ ∫ ∫ ] δ Deflection due to Applied Load, D P : Equating D g and D P , and solving for P, yields the following equivalency: where, g = gravity H = height of the specimen (also L) δ = mortar density E = modulus of elasticity P = applied load (equivalent) W = specimen weight ( Figure 5.4. Mortar Deflection Due to Gravity (Slump) This implies the ‘gravity effect’ is analogous to an applied load equal to ½ a road weight, assuming as we did that the responses are linear. Thus, the effective load, W e due to a layer’s self-weight, W is assumed to be W/2: 0 H (L) δH D Before gravity After gravity 1g h 86 (14) We can also safely assume that fabrication rate is at its maximum, ḣ max , in which case the minimum time to lay a road, t r,min is: ḣ (15) In other words, at the maximum allowed fabrication rate, one increment of W (and corresponding induced stress) is applied every t r,min increments of time. Therefore, if fabrication is to be delayed to account for the effective self-weight, and the effect of self-weight is half the effect of one in increment of road weight, then the required delay is simply: (16) Figure 5.5 illustrates the t delay correction graphically. Figure 5.5. Fabrication Delay to Correct for Self-Weight t Ś 0 δḣ max 1 t r /2 t r t c t delay σ r1 σ r2 σ r3 87 Finally, to complete the model we calculate the critical deposition, N c , or the layer deposited at critical time ť c . Again referring to Figure 5.5, it is easy to see that: [ ] (17) Specific Maturity Model 5.3 This section develops a model for strength development of the specific M1 mix at 3% NCA, to be used isothermally at room temperature (74 to 75 ⁰F). This specific model is critical to the remainder of the work because it will be relied upon to pace the layering of a full-scale vertical structure. As emphasized throughout this report, a clear understanding of very early strength development is necessary for safe fabrication. To be clear, in this context, fabrication loads are applied just minutes after mixing – or in other words, during the initial setting period, and somewhat earlier than documented in the literature - for example Voigt (Voigt, Malonn, & Shah, 2006). Voigt, Malonn and Shah (Voigt, Malonn, & Shah, 2006) investigated early strength development of extruded mortar specimens. In the context of that research, the compressive strength obtained from the mortar specimens in their fresh state was referred to as the ‘green strength’ of the tested material. As illustrated in Figure 5.6, initially, the green strength of such specimens develops very gradually. However, after a certain time, the strength values start to increase and begin to develop according to a power law. The period between the first significant increase and the beginning of the power law trend was interpreted as the transition from the green strength to an actual compressive strength. Incidentally, at a later age the compressive strength has been reported as linear hyperbolic (Carino & Lew, 2001) and (Voigt, Malonn, & Shah, 2006), or parabolic-hyperbolic (Carino & Lew, 2001). 88 Source: (Voigt, Malonn, & Shah, 2006) Figure 5.6. Development of Compressive Strength in Extruded Mortar One primary objective of this work is to flesh out the uninvestigated gap that precedes the mortar aging trends illustrated above. As demonstrated earlier, in the very early stages (including well before final set), strength develops as follows: S =Ce mt (18) where, t is mortar age (measured in minutes), C and m are material-dependent parameters, and curing is assumed to be isothermal and at 74 to 75 ⁰F. The specialized mortar mixture identified throughout this report as M1 is a highly workable, shape-stable, no-slump, lightweight structural mix prepared with lightweight aggregate (including expanded shale and clay) and small additions of fly ash and clay to increase both workability and shape-stability. This prototypical mix was tested in section at three discrete levels of set acceleration, identified here as M1.1pc, M1.2pc, M1.3pc. The subscripts refer to set accelerator 89 dosage, which was 1%, 2% and 3% of the cement content by weight. Table 5.1 tabulates the corresponding early-age (exponential) maturity function parameters. Set Accelerator [% of cement wt.] C m M1.1pc 1% 4 0.0057 M1.2pc 2% 6 0.0060 M1.3pc 3% 8 0.0068 S =Ce mt Table 5.1. Parameters for the Exponential Strength Gain Function of the M1 Mix The simplistic exponential strength development model (equation 18) is adequate for most Contour Crafting situations in which the critical deposition N c is deposited before final set (for example, layer 6 or 7 deposited about 100 minutes after t 0 ). The model can also extended for applications where the in-process contour-crafted structure must also carry the weight of the fabricator (which can be substantial), and/or suddenly applied supplemental fabrication loads, such as a floor beams and headers. In such cases, the critical difference between strength and stress is revised as follows: (19) where, σ M is introduced to represent the supplemental stress introduced by the supplemental construction weight W M (i.e. machine weight). Since the simple exponential trend traced by equation (18) deviates from actual strength development after final set, we next explore options for extending the model vis-à-vis transition to supplementary later-age strength gain relations. As mentioned, to integrate this extension we consider the power, linear hyperbolic and hyperbolic trends reported in the literature. As it turns out, transition to a power law was not supported by the data, and thus is not reported further here. Figure 5.7 illustrates transition from the simple exponential strength model to a subsequent linear hyperbolic phase. Note that data used to plot the later phase derive from cured cylinders of the same mix, tested per ASTM C 39. Similarly, Figure 5.8 illustrates transition from the simple 90 exponential strength model to a subsequent parabolic-hyperbolic phase. Further testing would be necessary to discriminate between these two options. Figure 5.7. M1 Mortar Strength Development: Exponential to Linear Hyperbolic Figure 5.8. M1 Mortar Strength Development: Exponential to Parabolic-Hyperbolic 91 6. Chapter Six: Numerical Analysis of Fresh Concrete This chapter presents numerical methods useful for analysis and engineering of Contour Crafting concreting. Elasto-Plasticity 6.1 The finite element method can be leveraged to evaluate and compare alternative fabrication strategies, to study interaction between the layered mortar and adjacent construction elements, to simulate the various stages of construction and predict the critical stages in the loading history, to determine overall structural stability, to identify the most critical failure mechanism and corresponding factor of safety, to investigate the deleterious effects of material nonhomogeneity, and generally whenever analytical methods are deemed to be too simplistic to provide realistic results. These simulations can be useful before construction begins, for example, to evaluate and compare alternative fabrication strategies, and during construction, as a material health monitoring system. As a material health monitoring system the numerical model would run in real time (synchronously during fabrication) accounting for, among other variables, non-isothermal curing and concomitant material strength development (maturity). Such a numerical model can be easily implemented with commercially available finite element analysis (FEA) programs, like ABAQUS, using Drucker-Prager (DP) plasticity, which Famiglietti (Famiglietti & Prevost, 1994) and others have demonstrated to be adequate for modeling fresh concrete. We begin with a cursory review of numerical elasto-plasticity, with enough detail to allow the reader to appreciate the idiosyncrasies of this technique, and the necessary parameter calibration. This discussion is limited to rate-independent material nonlinearity (plasticity), hence no sudden loads and creep effects assumed to be negligible. 92 A basic assumption of elasto-plastic models is that that total strain can be divided into an elastic part and an inelastic (or plastic) part, as follows: ɛ = ɛ e + ɛ p where the superscripts e and p refer to the elastic and plastic components respectively. The elastic part of the behavior can be modeled as linear elastic per the familiar Hooke’s law. The plastic part requires the following key modeling elements: (1) a yield criterion, (2) a yield surface (in triaxial stress space), (3) a material flow rule, and (4) an evolution law that defines material strain-hardening, if relevant. The yield criterion simply postulates that yielding in an elasto-plastic material occurs when a designated measure reaches a designated limiting value. The yield surface generalizes the concept of “yield load” into a testable function that can be used to determine the loci in stress space (and indirectly, in physical space) where the material responds plastically. The flow rule defines the inelastic deformation that occurs at the yield surface where the material is no longer responding purely elastically - it dictates which way the material there flows. Hardening defines how the yield surface and the flowing evolve. Yield Criterion. Material yielding is governed by a scalar function, F, which is written such that elastic behavior occurs if F<0, and plastic yielding occurs if F=0. In other words, at each increment of load, this test is repeated for every material point within the tributary volume of the mathematical model, to ascertain whether the point is responding elastically or elasto-plastically. Yield Surface. A yield surface defines the various stress states where linear elasticity ceases to hold, and thus indirectly charts the boundaries between portions of the material responding elastically and those responding elasto-plastically. If a material is assumed to be initially isotropic, then the yield surface can be described and graphically represented in terms of any set of three stress invariants, for example, σ 1 , σ 2 and σ 3 . Thus, recalling the yield criterion mentioned above, in triaxial stress space a yield surface is defined by the following condition: F(σ 1 , σ 2 and σ 3 )=0 93 Very often a failure theory bolstered by phenomenological reasoning is expediently adopted 17 . Figure 6.1 illustrates a few familiar failure theories by plotting their failure surfaces in principal stress space (Hinton, 1992). In each of these models all the stress points which lay inside the space bound by the yield surface are assumed to be associated with elastic stress states, whereas all the points that lay on the yield surface are assumed to represent plastic stress states. It’s important to note that by definition no points are allowed to lay outside the yield surface. Figure 6.1. Failure Theories and Yield Surfaces in Triaxial Stress Space (Hinton, 1992) 17 The notion of yield limit for a one-dimensional elasto-plastic material model is represented by a point on the (uniaxial) stress axis indicating the onset of a definite change in the material behavior (e.g. a turning point in a stress-strain curve, and/or a significant deviation from linearity). A single uniaxial experiment can provide all the information necessary to calibrate such a material model. The multiaxial problem is a little more complicated. With vast resources and a great number of multi-axial experiments conducted following a variety of loading paths it would be possible to map enough points in triaxial stress space to mechanically trace a yield surface for the multi-axial plasticity model. 94 Flow Rule. Yield criterion and surface define when and where plasticity will occur (within the tributary volume of the mathematical model), but say nothing about the nature of the plasticity, and more specifically, say nothing about how the “plastic zone” grows, and in which direction the material flows. A plastic flow rule is required to define the constitutive relationship between the stress increment and the plastic strain increment. Figure 6.2. Plastic Flow Potential Q and Plastic Potential Gradient (Hinton, 1992) Figure 6.2 illustrates the flow rule which is formulated in terms of a flow potential, Q, differentiated by a stress, σ, and scaled by a positive scalar factor of proportionality, , to give a plastic strain increment as follows (Hinton, 1992): As illustrated by Figure 6.3, the plastic flow potential Q and the yield function F can be identical or different (Hinton, 1992). If the flow potential Q and the yield function F are identical then the flow rule is called an associated flow rule. Associated flow rules are valid for most metals. Models that exhibit hydrostatic sensitivity tend to use non-associated flow rules. 95 associated flow; (b) non-associated flow Figure 6.3. Associated and Non-Associated Flow Rules (Hinton, 1992) Hardening. Finally, to progress an elasto-plastic analysis, in addition to defining initial yield surface and flow rule, we need to also describe how the yield surface and flow are to change as plastic strains accumulate. In other words, we need a (yield) surface evolution law. For example, it is necessary to define whether as a result plastic straining the yield surface expands, moves or shifts in stress space, or whether it morphs into a new shape – see Figure 6.4 (Hinton, 1992). Figure 6.4. Evolution of a Yield Surface (Hinton, 1992) Since the material properties of an aging fresh concrete are a function of time, and thus evolving during the FEA analysis time steps, the constitutive model will also require age-related time- dependent discretization. Since the hydration process is assumed independent of stress, development of the properties between analysis time-steps is known in advance. Within each 96 time step average properties are used, as illustrated by Figure 6.5. In the discretization to a final time step, use of average properties is an approximation, but with small time steps and corresponding small changes of the properties, the error introduced by the differences should be negligible (Hauggaard-Nielsen, 1997). Figure 6.5. Time-Dependent Discretization of the FEA Properties (Hauggaard-Nielsen, 1997) Note the ironic confounding of ‘hardening.’ The term is used to denote the familiar outcome of cement hydration (age-related hardening), but it is also used to denote an essential component in the mortar’s material constitutive model (strain-related hardening). Although the two are distinct concepts, they are actually comingled (perhaps for the first time) in the implementation of the numerical model, because a single parameter is effectively employed to represent both. Model Selection 6.2 Is non-linear analysis necessary? Strictly speaking it may not be. If the objective is to engineer freeform-layered artifacts with useful dimensional integrity (i.e. straight walls), then every part of the structure must remain well below the material limit state throughout fabrication (and the simulation thereof). Since this is indeed the application at hand, and since there is no load ratcheting (proportional monotonic loading), and since we are intentionally ignoring the effects of creep (assuming they are negligible), then elastic analysis should be adequate. t = time E = stiffness 97 To be sure the strains of interest here are significantly less (and deformed shapes significantly less dramatic) than those in the concrete slump tests studied in the research referenced above. There are two reasons for this: (1) the M1 study mix exhibits essentially no slump, and (2) as alluded to above, allowable strains will be defined relatively low (e.g. 5% or less) to preserve the dimensional integrity of the fabricated product. Considering this, an elastic constitutive model might have proved adequate as we expect negligible plasticity at design limit load, by definition. However, the general solution is necessarily elasto-plastic, relevant to the eventual characterization of safety margin, and therefore was considered a worthwhile pursuit nonetheless, if for no other reason than to lay the groundwork for future work. The next step is to select a proper elasto-plastic material model which can also be adequately supported by test results. As mentioned, Famiglietti (Famiglietti & Prevost, 1994) and others have demonstrated Drucker-Prager plasticity to be adequate for modeling fresh concrete. The Drucker-Prager family of plasticity model describes the behavior of granular materials and polymers in which the yield behavior depends on the equivalent pressure stress (the material becomes stronger as the confining pressure increases), and in which inelastic deformation is often associated with frictional mechanisms such as sliding of particles across each other. D-P Yield Surface (F). In ABAQUS Drucker-Prager plasticity is available with three different yield criteria. The differences in the criteria stem from the shape of the assumed yield surface in the meridional (p-q stress) plane. As illustrated by Figure 6.6 the options are linear, hyperbolic and general exponent (Abaqus User's Manual, 2009). (linear yield criterion) √ – (hyperbolic yield criterion) (general exponent yield criterion) where, q = deviatoric or Mises equivalent stress 98 p = hydrostatic or equivalent pressure stress β = friction angle of the material (slope of the linear yield surface in the p-q stress plane) d = cohesion of the material Adapted from: (Abaqus User's Manual, 2009) Figure 6.6. D-P Yield Surfaces in the Meridional (d-p stress) Plane 18 18 The ABAQUS linear Drucker-Prager model also provides for a possibly noncircular yield surface in the deviatoric plane, to match different yield values in triaxial tension and compression. This feature is not implemented here (K=ratio of yield stress in triaxial tension to the yield stress in triaxial compression=1), and diagrams are modified to reflect the simplification. 99 D-P Flow Rule (and Dilation Angle). A geometric interpretation of flow and associated dilation angle (ψ) for a linear Drucker-Prager model is shown in the p-q diagram of Figure 6.7. As indicated, the dilation angle, ψ, and the material friction angle, β, may be different, so the model may or may not be associated in the p-q plane, meaning the flow is assumed to be normal to the yield surface in the π-plane but possibly at an angle to the q-axis in the p–q plane, where usually ψ<β, as illustrated. Incidentally, if ψ=β, the model is fully associated in the p-q plane, and is then of the type first introduced by Drucker and Prager (Drucker & Prager, 1952). If ψ=0 the material is nondilational. For granular and polymeric materials the linear model is normally used with nonassociated flow. Source: (Abaqus User's Manual, 2009) Figure 6.7. Hardening and Dilation Angle in the Linear Drucker-Prager Model D-P Hardening. As mentioned, hardening provides for evolution of the yield surface. If the material can exhibit unlimited flow when the stress reaches yield, then the yield surface can be used as a failure surface and the behavior is called perfectly plastic. Alternatively, it can be assumed that plastic flow causes the yield surface to change size uniformly, and this behavior is called isotropic hardening. In ABAQUS this evolution of the yield surface with plastic deformation is described in terms of an equivalent stress measure, which can be chosen as either the uniaxial q 100 compression yield stress (σ c ), the uniaxial tension yield stress (σ t ), or the shear (cohesion) yield stress (τ). For the linear yield criterion (which will be selected used here), , where if hardening is defined by uniaxial compression yield stress σc if hardening is defined by uniaxial tension stress σt √ if hardening is defined by shear yield stress The choice of model to be used depends largely on the experimental data available for calibration of the model parameters, and the stresses that the material is likely to experience in the application. Material model complexity should be as simple as possible considering the available experimental evidence. In other words, a more complicated model would require more test dimensions to fully calibrate all the material parameters in a meaningful way, as illustrated by the complexity diagram in Figure 6.8. It is common to have triaxial test data at different levels of confining pressure, but this is not the case here. For the present purpose, test complexity (or lack thereof) dictates that for the time being we limit consideration to the linear Drucker-Prager model, because it’s the only one of the three available options which can be calibrated in a meaningful way (for example, the other models require an initial hydrostatic tension strength, which we have not characterized for the M1 mortar). 101 Adapted from: (Järvtråt, 2004) Figure 6.8. NAFEMS Test and Modeling Complexity Diagram As for stresses, the linear model is in fact intended primarily for applications where the stresses are for the most part compressive, and this is of course consistent with freeform layering of unconfined mortar 19 . Finally, when the experimental data are already calibrated in terms of a cohesion and a friction angle, and these parameters are provided for a Mohr-Coulomb model (which they often are), they can be easily converted to the corresponding Drucker-Prager parameters as follows (for associated flow): √ √ and √ √ and 19 It may be worth noting that according to the ABAQUS documentation (Abaqus User's Manual, 2009), the accuracy with which the linear model can represent actual material behavior may be limited by the fact that it assumes linear dependence of deviatoric stress on pressure stress (the straight line in p-q space). Conversely, although the hyperbolic model makes a similar assumption at high confining pressures, it provides a nonlinear relationship between deviatoric and pressure stress at low confining pressures, and this nonlinear relationship may achieve a better match of the triaxial experimental data (and presumably also material behavior in the field). This refinement may be worth investigating in future research. Material Test Complexity Too complex Too simple Good Model Complexity Good Too Complex Too simple Danger! Unexpected behavior outside tested region Good Overly expensive Tests (but results OK) Sever Danger! Highly unrealistic or unphysical behavior may occur outside tested region Inaccurate Results 102 where Φ and c are Mohr-Coulomb friction angle and cohesion, and α is the material slip plane angle. These relations will be used shortly to estimate the Drucker-Prager friction angle, β 20 . In summary, the parameters necessary to calibrate the elasto-plastic material model are as follows: E, ν, d=(σ c ), β and ψ. The next section will discuss calibration of these parameters. Parameter Calibration 6.3 As mentioned, the veracity, and thus usefulness, of any numerical model is also predicated on the parameters used to bring the simulation into agreement with the experiments. Here we summarize this critical parameter calibration and reiterate which parameters are estimated from our rudimentary testing, which parameters can be assumed, and how we arrive at an adequate if not the appropriate material flow rule. Mortar modulus, cohesion (expressed thru an estimate of compression yield stress), and Poisson’s ratio have already been characterized by means of the green strength test data, and typical values reported in the literature. What remain to be addressed here are internal friction and dilation angles (β and ψ). Alexandridis (Alexandridis & N.J.Gardner, 1981) describes green concrete strength as a combination of paste cohesion and intergranular friction. Importantly, intergranular friction is considered an inherent property of the mix that does not change over time (including the dormant and setting phases), and which can be manipulated in mix design, for example, thru aggregate grading and angularity. Conversely, cohesion is a property which evolves during hydration. Importantly, this dictates constant internal friction angle (β), and evolving paste cohesion (d). In other words, there is no need to develop a maturity model for the mortar friction angle β. 20 Derivations are reported by Rowe (Rowe, 1962), Prinja (Prinja & Puri, 2005), and the ABAQUS documentation (Abaqus User's Manual, 2009). 103 Friction angle would normally be measured in triaxial compression, however as noted in Figure 4.20, the younger mortar specimens showed clear evidence of a constant slip plane at 61 degrees. This slip plane was readily equated to a Drucker-Prager friction angle of 41.3 degrees by means of the transformations noted in the preceding section. Table 6.1 (Ritchie, 1962) and Table 6.2 (Alexandridis & N.J.Gardner, 1981) show this to be consistent with values reported in the literature. Table 6.1. Typical Fresh Concrete Properties (Ritchie, 1962) 104 Table 6.2. Typical Fresh Concrete Properties (Alexandridis, 1981) Dilation angle is a little more challenging and for lack of data we will be forced into conservatively assuming ψ=β, but first some discussion. As noted earlier, the dilation angle is expected to be: 0<ψ≤β (greater than zero because granular and polymeric materials are known to dilate during shearing (Rowe, 1962), and less than or equal to β, the limit for associated flow). These limits are investigated by Famiglietti and illustrated in Figure 6.9 (Famiglietti & Prevost, 1994). Figure 6.9. Dilation Angle Limits (Famiglietti, 1994) 105 The green strength tests could also be mined for useful insights into mortar dilation. Specifically, snapshots of the deformed mortar shape could be post-processed to estimate the change in mortar volume associated with material shearing. Štemberk reports relevant image-processing techniques, which were used in a similar context to estimate the Poisson’s ratio of young and hardening concrete specimens - Figure 6.10 (Štemberk & Kohoutková, 2005). A similar approach was implemented to estimate dilatancy of the M1 mix, but ultimately not leveraged because it was deemed to be inconclusive, laborious and unnecessary. Instead, the aforementioned conservative assumption was adopted. This expedient approach is consistent with practice, and likely adequate as indicated by the sensitivity study summarized in Table 6.3 (Abaqus User's Manual, 2009). Figure 6.10. Image-Based Analysis of Fresh Concrete (Štemberk & Kohoutková, 2005) 106 Table 6.3. Associated Versus Non-Dilatant Flow (Abaqus User's Manual, 2009) Figure 6.11 summarily illustrates how green strength test data were leveraged for parameter calibration, and also importantly reiterates that parameters might have also been characterized in triaxial compression. Figure 6.12 graphically illustrates the linear Drucker-Prager yield surfaces (in p-q stress space) of the M1 mortar mixture at 0% NCA, between 10 and 320 minutes after mixing. GST = green strength test TCT = triaxial compression test (option) Figure 6.11. Constitutive Model Parameter Calibration TCT GST d=f(σ c ,t) GST β=C1 0<ψ=C2≤β TCT GST 107 Figure 6.12. Drucker-Prager Yield Surfaces for the M1 Mortar @ 0% NCA Mortar Age [min] Hydrostatic Stress, p [psi] Equivalent Stress, q [psi] p q d β Ψ=β Shear Failure hardening 108 Fresh Mortar Simulation 6.4 This section presents numerical simulations of fresh mortar specimens loaded in axial compression at specific mortar maturities. The finite element analyses us the linear Drucker- Prager elasto-plastic model calibrated in section 6.3. Figure 6.13 thru Figure 6.19 illustrate simulation of a green strength test using the M1 mortar mixture at 0% NCA, and at a mortar age of 11 minutes (after mixing). Figure 6.13 illustrates axial deflection as a function of applied load. Figure 6.14 illustrates lateral deflection as a function of applied load. Figure 6.15 illustrates lateral stress (σ x ) as a function of applied load. Figure 6.16 illustrates hoop stress (σ z ) as a function of applied load. Figure 6.17 illustrates shear stress (σ xy ) as a function of applied load. Figure 6.18 illustrates plastic strain as a function of applied load. Figure 6.19 illustrates yield flag as a function of applied load. In these simulations the applied load is arbitrarily chosen in increments of road weight (1 road, 2 roads, etc.), and mortar age is constant - meaning the mortar does not age as the load increases. As a result, the later cases are progressively more extreme, as up to the equivalent of 6 road weights is applied instantaneously. Figure 6.20 and Table 6.4 summarize the results comparing the measured axial deflection to the simulated axial deflection. Simulation is in excellent agreement with test up to the equivalent of 4 road weights, and diverges sharply thereafter. Importantly, Figure 6.19, which plots the yield flag, indicates plastic straining throughout the specimen at the equivalent of 4 applied road weights. These results suggest the calibrated constitutive material model is adequate (without strain-hardening) in the range of practical interest (plastic strain less than 2%). Although not explored thoroughly here, results at large strains are readily brought into excellent agreement with test, by implementation of a simple strain-related hardening rule. Table 6.5 illustrates notional Drucker-Prager hardening parameters for the M1 mortar mixture (dependence of yield stress on plastic strain). Figure 6.21 illustrates a simulation of the green strength test which implements this hardening rule. With hardening implemented, the simulation predicts 0.75 109 inches of axial deflection at the extreme applied load of 12.5 lbf (the equivalent of 8 road weights) – the result is within 1% of the tested deflection. Figure 6.22 thru Figure 6.26 illustrate simulation of several green strength specimens at increasing ages. In each of these simulations the mortar is the M1 mixture at 0% NCA, and the applied load is 6 lbf (the equivalent of 4 road weights). Figure 6.22 illustrates axial and lateral deflection for a specimen loaded 11 minutes after mixing. Figure 6.23 illustrates axial and lateral deflection for a specimen loaded 52 minutes after mixing. Figure 6.24 illustrates axial and lateral deflection for a specimen loaded 109 minutes after mixing. Figure 6.25 illustrates axial and lateral deflection for a specimen loaded 211 minutes after mixing. Figure 6.26 illustrates axial and lateral deflection for a specimen loaded 288 minutes after mixing. As expected, specimen deflections decrease drastically as the mortar ages. Figure 6.27 and Table 6.6 summarize the results comparing the measured axial deflection to the simulated axial deflection. Simulation is in excellent agreement with test throughout the investigated performance period of interest. Finally, Figure 6.28 illustrates numerical simulation of the plate-stacking test. In this test, which is at considerably lower strain and clearly far more representative of the practical application, axial deflection and lateral strain are in excellent agreement with experiment. 110 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (U1 = axial deflection; mix =M1, 0% NCA, mortar age = 11 min) Figure 6.13. FEA of the Green Strength Test: U1 = f (Applied Load) 111 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (U2 = lateral deflection; mix =M1, 0% NCA, mortar age = 11 min) Figure 6.14. FEA of the Green Strength Test: U2 = f (Applied Load) 112 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (S11 = σ x stress-; mix =M1, 0% NCA, mortar age = 11 min) Figure 6.15. FEA of the Green Strength Test: S11 = f (Applied Load) 113 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (S33 = σ z stress (hoop); mix =M1, 0% NCA, mortar age = 11 min) Figure 6.16. FEA of the Green Strength Test: S33 = f (Applied Load) 114 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (S12 = σ xy stress (shear); mix =M1, 0% NCA, mortar age = 11 min) Figure 6.17. FEA of the Green Strength Test: S12 = f (Applied Load) 115 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (PEMAG = plastic strain; mix =M1, 0% NCA, mortar age = 11 min) Figure 6.18. FEA of the Green Strength Test: PEMAG = f (Applied Load) 116 F=1.5 lbf (1 road) F=3.0 lbf (2 roads) F=4.5 lbf (3 roads) F=6.0 lbf (4 roads) F=7.5 lbf (5 roads) F=9.0 lbf (6 roads) (AC YIELD = yield flag; mix =M1, 0% NCA, mortar age = 11 min) Figure 6.19. FEA of the Green Strength Test: AC YIELD = f (Applied Load) 117 Note: mix = M1, 0% NCA; mortar age = 11 minutes; deflections are net (total deflection – slump) Figure 6.20. Test versus FEA: Mortar Defection =f(Applied Load) Load Case Applied Load [lbf] Test Deflection (in) FEA Deflection (in) 1-plate 1.5 0.09 0.08 2-plate 3.0 0.17 0.16 3-plate 4.5 0.23 0.24 4-plate 6.0 0.31 0.33 5-plate 7.5 0.38 0.58 6-plate 9.0 0.48 0.85 7-plate 10.5 0.62 1.09 8-plate 12.0 0.76 1.32 Note: mix = M1, 0% NCA; mortar age = 11 minutes; deflections are net (total deflection – slump) Table 6.4. Test versus FEA: Mortar Defection = f (Applied Load) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Mortar Deflection [inches] Applied Load [lbf] Test Deflection (in) FEA Deflection (in) 118 Yield Stress [psi] Absolute Plastic Strain [in/in] 0.9 0.00 1.0 0.02 2.0 0.12 Table 6.5. Notional Drucker-Prager Strain-Hardening Parameters (mix =M1, 0% NCA, mortar age = 11 min, notional strain-hardening parameters) Figure 6.21. FEA of the Green Strength Test with Strain Hardening Figure 6.22. FEA of the Green Strength Test (M1, 0% NCA, 11 min., 6 lbf) 119 Figure 6.23. FEA of the Green Strength Test (M1, 0% NCA, 52 min., 6 lbf) Figure 6.24. FEA of the Green Strength Test (M1, 0% NCA, 109 min., 6 lbf) 120 Figure 6.25. FEA of the Green Strength Test (M1, 0% NCA, 211 min., 6 lbf) Figure 6.26. FEA of the Green Strength Test (M1, 0% NCA, 288 min., 6 lbf) 121 Note: mix = M1, 0% NCA; net applied load = 6 lbf; deflections are net (total deflection – slump) Figure 6.27. Test versus FEA: Mortar Defection = f(Mortar Age) Mortar Age [minutes] Deflection [inches] Test FEA 11 0.31 0.329 52 0.21 0.222 109 0.15 0.124 211 0.05 0.050 288 0.02 0.020 Note: mix = M1, 0% NCA; net applied load = 6 lbf; deflections are net (total deflection – slump) Table 6.6. Test versus FEA: Mortar Defection = f(Mortar Age) Figure 6.28. Steady-State Finite Element Simulation of Plate Stacking Test 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 50 100 150 200 250 300 Mortar Deflection [inches] Mortar Age [minutes] Test Deflection (in) FEA Deflection (in) 122 In the next section we extend the numerical simulation to include time-dependent material properties. This lays the groundwork for (1) simulating the Contour Crafting fabrication process, and (2) for implementing a material health monitoring system. Numerical Simulation of Mortar Layering 6.5 Our next challenge is a numerical simulation of unconfined mortar solved in discreet time steps, and with material properties updated at each time step to match the concurrent strength and stiffness of the aging mortar. Naturally, we accomplish this by integrating the time-dependent properties developed earlier, and summarized in Table 4.1. The simulation is implemented with ABAQUS, Excel and some custom VBA code. Figure 6.29 illustrate an exemplary fresh mortar stacking simulated using this tool. The associated VBA code is documented in appendix. This simulation tool allows for user-controlled incremental analysis, post-processing and visualization of the entire fabrication process. This tool can be used, for example, to explore and appreciate which roads are critical at any given stage of the layering. The feedback is color- coded as follows: green for [(allowed/applied) > 1.2], yellow for [1 < (allowed/applied) < 1.2], and red for [(allowed/applied) < 1]. An alternative simulation, which does not require the VBA engine, can be performed in ABAQUS using material dependency and field variable linked to total time amplitude (to update material properties as the simulation progresses). An ABAQUS input file configured to accomplish this at a single stage of fabrication is also included in appendix. 123 Figure 6.29. FEA of Full-Scale Layering Demonstration (with Aging Properties) FOS 2 Road Height (h) 3.0 in. Current Road # 32 Delay Between Roads 15 min Current Time 475 Mix Time 10 min N xo yo ∆x ∆y xt yt σ Allow. Allow/σ ti δ β K ψ d (σ c ) εp E ν 66 10 96 0.0 -2.1 10.0 93.9 -10.0 465 0.051 41.3 1 41.3 0.9 0 9.6 0.25 64 10 93 0.0 -2.1 10.0 90.9 -0.08 -0.4 5.8 -10.0 450 0.051 41.3 1 41.3 1.0 0 11.2 0.24 62 10 90 0.1 -2.0 10.1 88.0 -0.23 -0.5 2.3 -10.1 435 0.051 41.3 1 41.3 1.2 0 13.0 0.23 60 10 87 0.1 -1.9 10.1 85.1 -0.38 -0.6 1.6 -10.1 420 0.051 41.3 1 41.3 1.4 0 15.1 0.22 58 10 84 0.1 -1.8 10.1 82.2 -0.53 -0.7 1.3 -10.1 405 0.051 41.3 1 41.3 1.6 0 17.5 0.22 56 10 81 0.1 -1.7 10.1 79.3 -0.68 -0.8 1.2 -10.1 390 0.051 41.3 1 41.3 1.9 0 20.4 0.21 54 10 78 0.1 -1.6 10.1 76.4 -0.83 -0.9 1.1 -10.1 375 0.051 41.3 1 41.3 2.2 0 23.6 0.21 52 10 75 0.1 -1.5 10.1 73.5 -0.98 -1.1 1.1 -10.1 360 0.051 41.3 1 41.3 2.5 0 27.5 0.21 50 10 72 0.1 -1.4 10.1 70.6 -1.13 -1.3 1.1 -10.1 345 0.051 41.3 1 41.3 2.9 0 31.9 0.21 48 10 69 0.1 -1.3 10.1 67.7 -1.28 -1.5 1.1 -10.1 330 0.051 41.3 1 41.3 3.4 0 37.1 0.21 46 10 66 0.1 -1.1 10.1 64.9 -1.43 -1.7 1.2 -10.1 315 0.051 41.3 1 41.3 4.0 0 43.1 0.20 44 10 63 0.1 -1.0 10.1 62.0 -1.58 -2.0 1.3 -10.1 300 0.051 41.3 1 41.3 4.6 0 50.1 0.20 42 10 60 0.1 -0.9 10.1 59.1 -1.74 -2.3 1.3 -10.1 285 0.051 41.3 1 41.3 5.3 0 58.2 0.20 40 10 57 0.1 -0.8 10.1 56.2 -1.89 -2.7 1.4 -10.1 270 0.051 41.3 1 41.3 6.2 0 67.6 0.20 38 10 54 0.1 -0.8 10.1 53.2 -2.04 -3.1 1.5 -10.1 255 0.051 41.3 1 41.3 7.2 0 78.5 0.20 36 10 51 0.1 -0.7 10.1 50.3 -2.19 -3.6 1.6 -10.1 240 0.051 41.3 1 41.3 8.4 0 91.2 0.20 34 10 48 0.0 -0.6 10.0 47.4 -2.35 -4.2 1.8 -10.0 225 0.051 41.3 1 41.3 9.7 0 106.0 0.20 32 10 45 0.0 -0.5 10.0 44.5 -2.50 -4.9 1.9 -10.0 210 0.051 41.3 1 41.3 11.3 0 123.1 0.20 30 10 42 0.0 -0.5 10.0 41.5 -2.66 -5.7 2.1 -10.0 195 0.051 41.3 1 41.3 13.2 0 143.1 0.20 28 10 39 0.0 -0.4 10.0 38.6 -2.81 -6.6 2.3 -10.0 180 0.051 41.3 1 41.3 15.3 0 166.2 0.20 26 10 36 0.0 -0.3 10.0 35.7 -2.96 -7.6 2.6 -10.0 165 0.051 41.3 1 41.3 17.8 0 193.1 0.20 24 10 33 0.0 -0.3 10.0 32.7 -3.12 -8.9 2.8 -10.0 150 0.051 41.3 1 41.3 20.6 0 224.4 0.20 22 10 30 0.0 -0.3 10.0 29.7 -3.27 -10.3 3.2 -10.0 135 0.051 41.3 1 41.3 24.0 0 260.7 0.20 20 10 27 0.0 -0.2 10.0 26.8 -3.42 -12.0 3.5 -10.0 120 0.051 41.3 1 41.3 27.9 0 302.9 0.20 18 10 24 0.0 -0.2 10.0 23.8 -3.58 -13.9 3.9 -10.0 105 0.051 41.3 1 41.3 32.4 0 351.9 0.20 16 10 21 0.0 -0.1 10.0 20.9 -3.73 -16.2 4.3 -10.0 90 0.051 41.3 1 41.3 37.6 0 408.8 0.20 14 10 18 0.0 -0.1 10.0 17.9 -3.89 -18.8 4.8 -10.0 75 0.051 41.3 1 41.3 43.7 0 475.0 0.20 12 10 15 0.0 -0.1 10.0 14.9 -4.04 -21.8 5.4 -10.0 60 0.051 41.3 1 41.3 50.7 0 551.9 0.20 10 10 12 0.0 -0.1 10.0 11.9 -4.20 -25.4 6.0 -10.0 45 0.051 41.3 1 41.3 59.0 0 641.2 0.20 8 10 9 0.0 0.0 10.0 9.0 -4.35 -29.5 6.8 -10.0 30 0.051 41.3 1 41.3 68.5 0 745.0 0.20 6 10 6 0.0 0.0 10.0 6.0 -4.50 -34.3 7.61 -10.0 15 0.051 41.3 1 41.3 79.6 0 865.5 0.20 4 10 3 0.0 0.0 10.0 3.0 -4.66 -39.8 8.54 -10.0 0 0.051 41.3 1 41.3 92.5 0 ##### 0.20 2 10 0 0.0 0.0 10.0 0.0 -4.81 -46.2 9.61 -10.0 Material Properties (Age-Dependent) 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 -20 -10 0 10 20 Run All Run Once 10 10.1 124 7. Chapter Seven: Full-Scale Demonstration Introduction 7.1 This section presents a mortar-layering demonstration which was undertaken to demonstrate that full-scale freeform layering of unconfined and self-supporting fresh mortar is feasible and safe when properly engineered. An 8-foot structure is erected with 30 layers of highly workable, yet shape-stable mortar. The remarkable thing is that the mortar is fresh and unconfined, meaning each free-standing 'brick' is gaining strength, as it cures, just fast enough to support on its own, the increasing weight of the other layers accumulating above it. The demonstration essentially mimics the freeform-layered fabrication proposed by Contour Crafting except that with the Contour Crafting system the process is fully automated, and the material is pumped and extruded into a continuous ribbon. Mortar-Layering Apparatus 7.2 Figure 7.1 and Figure 7.2 illustrate the test apparatus, including scaffold and molding equipment. Figure 7.1. Scaffold for Full-Scale Layering Demo 96” 80/20 T-Slotted Frame Pre-Cast Pedestal Rails (height-adjustable) 125 Figure 7.2. Mortar Molding and Extruding Apparatus for Full-Scale Layering Demo Full-Scale Mortar-Layering Demo 7.3 The test is performed in the laboratory under isothermal conditions (at room temperature, approximately 74F). In order to emulate the process with fidelity, each mortar layer is batched separately. Table 7.1 illustrates the batching regimen required to layer 30 roads at 15-minute intervals. 126 Table 7.1. Batching Regimen for Full-Scale Mortar Layering Demo Figure 7.3 illustrates the mortar layering process, which proceeds as follows. (A) and (B): assemble mold and insert, fill with mortar, consolidate (as noted earlier) and finish (C) and (D): using removable handles extract insert from mold and position over scaffold rails (E) and (F): while holding extruder firmly in place slide insert laterally to extrude specimen (G) and (H): raise scaffold 3 inches to prepare for next mortar layer Starting Time 11:55 Hours Delay 0:00 7:30 Stacking Interval 0:15 Mixing Time 0:05 Road No. Mixing Start Time Mixing Stop Time 1 11:55 12:00 2 12:10 12:15 3 12:25 12:30 4 12:40 12:45 5 12:55 13:00 6 13:10 13:15 7 13:25 13:30 8 13:40 13:45 9 13:55 14:00 10 14:10 14:15 11 14:25 14:30 12 14:40 14:45 13 14:55 15:00 14 15:10 15:15 15 15:25 15:30 16 15:40 15:45 17 15:55 16:00 18 16:10 16:15 19 16:25 16:30 20 16:40 16:45 21 16:55 17:00 22 17:10 17:15 23 17:25 17:30 24 17:40 17:45 25 17:55 18:00 26 18:10 18:15 27 18:25 18:30 28 18:40 18:45 29 18:55 19:00 30 19:10 19:15 Starting Time 11:55 Delay 0:00 Stacking Interval 0:15 Mixing Time 0:05 Hours 7:30 127 A. B. C. D. E. F. G. H. Figure 7.3. Full-Scale Layering Demo (Process) 128 Figure 7.4 illustrates the molding equipment developed to prepare the mortar layers, and the individual mortar layer nominal dimensions. Figure 7.5 depicts key moments in the execution of the full-scale layering demonstration. Figure 7.6 and Figure 7.7 document the full-scale artifact which was successfully produced during this demonstration. Table 7.2 reports the final dimensions of the full-scale artifact. This data provides an indication of slump, deflection and autogenous shrinkage. Figure 7.8 decomposes the total axial deformation of the artifact into components dues to (1) distortion during mortar extrusion, (2) mortar slump, and (3) creep and autogenous shrinkage. Although only approximate, this estimate supports the hypothesis that creep and autogenous shrinkage are negligible (the cured artifact is 3.29” shorter than the combined nominal road heights; mortar stretching during specimen extraction accounts for approximately 1.95” of the vertical shrinkage; slump accounts for an additional 1.34”). Figure 7.9 shows exemplary artifact close-ups to emphasize dimensional stability of the layered product. Figure 7.4. Nominal Full-Scale Mortar Layering Demo Road Dimensions w L h ho 3.02 in wo 4.86 in Lo 15.08 in 129 a) mortar mixing b) plastic mortar c) mold filling d) mold filling e) mold drops f) mold tapping g) mortar troweling h) mortar ready for layering j) extruding the road k) removing mold pan l-m) full-height stack o) celebration Figure 7.5. Full-Scale Mortar Layering Demonstration a b c d e f g h i j k l m n o 130 Figure 7.6. Full-Scale Mortar Layering Artifact (roads 15-30) 131 Figure 7.7. Full-Scale Mortar Layering Artifact (roads 1-15) 132 Table 7.2. Final Dimensions of Full-Scale Mortar Layering Demo w L h Layer # h w1_L w1_R w1_avg w2_L w2_R w2_avg L 30 2.92 4.92 4.86 4.89 4.93 4.84 4.89 15.34 29 2.94 4.91 4.98 4.95 4.88 4.88 4.88 15.39 28 2.94 4.93 4.89 4.91 4.84 4.98 4.91 15.44 27 2.94 4.91 4.94 4.92 4.89 4.88 4.89 15.49 26 2.94 4.95 4.95 4.95 4.88 4.84 4.86 15.39 25 2.94 4.93 4.99 4.96 4.86 4.90 4.88 15.42 24 2.90 4.92 5.01 4.96 4.89 4.94 4.91 15.60 23 2.91 4.98 4.99 4.98 4.91 4.93 4.92 15.39 22 2.96 4.93 4.92 4.92 4.89 4.96 4.92 15.44 21 3.02 5.01 4.92 4.96 4.88 4.87 4.87 15.35 20 2.95 4.91 5.03 4.97 4.88 4.89 4.88 15.56 19 2.95 5.01 5.10 5.05 4.86 4.94 4.90 15.66 18 2.84 4.97 5.03 5.00 4.87 4.88 4.87 15.73 17 2.87 5.07 5.01 5.04 4.91 4.88 4.89 15.72 16 2.91 5.05 5.02 5.04 4.79 4.91 4.85 15.36 15 2.85 4.99 4.99 4.99 4.85 4.93 4.89 15.30 14 2.80 5.12 5.00 5.06 4.90 4.85 4.88 15.33 13 2.77 5.08 5.00 5.04 4.80 4.93 4.86 15.55 12 2.79 4.93 4.98 4.96 4.91 4.78 4.85 15.62 11 2.89 5.05 4.96 5.00 4.82 4.85 4.84 15.30 10 2.88 5.01 5.08 5.04 4.88 4.82 4.85 15.59 9 2.90 4.99 5.02 5.01 4.85 4.92 4.88 15.59 8 2.83 4.94 5.02 4.98 4.89 4.82 4.85 15.32 7 2.96 4.92 4.98 4.95 4.93 4.87 4.90 15.27 6 3.01 4.99 4.93 4.96 4.81 4.87 4.84 15.27 5 2.84 4.99 5.03 5.01 4.84 4.87 4.86 15.52 4 2.91 5.04 5.01 5.02 4.85 4.86 4.85 15.76 3 3.02 4.91 4.96 4.94 4.81 4.83 4.82 15.25 2 3.01 4.96 4.94 4.95 5.06 5.13 5.10 15.31 1 3.00 5.45 5.34 5.39 4.81 4.78 4.79 14.24 widest width (near bottom of road) narrowest width (top of road) 133 (a) (b) (a) correlation between the extruded road length (L) and height (h) visually confirms the assumption that a portion of axial shrinkage may be attributed to the stretch unintentionally imparted during mortar extrusion (b) decomposition of axial deflection suggests 60% of the measured deflection can be attributed to process- induced initial distortion, 40% to slump (estimated equating road volumes and sectional areas, respectively) Figure 7.8. Approx. Decomposition of Shrinkage in the Full-Scale Layered Artifact 14.0 15.0 16.0 0.0 1.0 2.0 3.0 4.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Road Length (L), [in] road height (h), [in] Road No. (1 is the first layer) h L 134 . . . Figure 7.9. Full-Scale Mortar Layering Artifact (Close-ups) 135 8. Chapter Eight: Conclusion and Future Work This chapter summarizes the research results and outlines important opportunities for future work. Research Contribution 8.1 This research demonstrates that a specially formulated mortar mixture may be safely layered at useful fabrication speeds and without formwork, maintaining structural integrity during freeform fabrication and achieving useful structural load-carrying capacity once cured. The prototypical mortar mix specifically developed for this unique and unprecedented application, leveraging a combination of lightweight bulk ingredients, viscosity-modifying admixtures, and provisions for internal curing and set acceleration, provides a suitable medium for technology development, and a baseline for industrial mix optimization, which may be undertaken to reduce material cost, reduce minimum time between layer depositions, increase cured strength and reduce sensitivity to process parameter (increase robustness). The research also contributes to the heretofore severely understudied structural properties of fresh concrete minutes after mixing. Analytical tools are developed to guide the safe layering of a specific cementitious mortar mixture under isothermal conditions. Numerical tools are also developed which are suitable for structural analysis (engineering) the freeform layering of fresh concretes and mortars into arbitrary configurations, as a tool for fabrication planning, and as basis for a material health monitoring system. Importantly, as noted earlier the allowable fabrication rate previously reported by Hwang (Hwang, 2005) was never the limiting rate for Contour Crafting. True limits on fabrication rate are investigated and reported for the first time here. This sustainable vertical fabrication rate is on the order of 12 inch/hour, using the specially developed M1 mortar mixture (at constant w/c and temperature=74F). Incidentally, this rate is consistent with fabrication rates achieved in slip form casting (Slip Form). In this context we should emphasize that, although perhaps counterintuitive, 136 the n th mortar layer is not likely to be critical at layer (n+1) when the n th layer is at its youngest. Typical evolution of mortar maturity and loading rates associated with regular stacking intervals are such that the critical moment (point in time where the two curves are closest to each other) is more likely to occur well after the (n+1) layer has been deposited – for example, when (n+6) layer is deposited. This was demonstrated mathematically, and can also be explored and verified interactively using the numerical simulation tool. In summary the research contributes: (a) a novel cementitious material system suitable for freeform-layered fabrication, (b) an isothermal maturity model for said material, (c) pertinent relevant structural analysis tools, including empirically verified timing constraints for uninterrupted but safe fabrication of prototypical artifacts under controlled laboratory conditions, and (d) a process for systematic design of materials suitable or Contour Crafting. Implications for Practice 8.2 The work demonstrates that a special class of structural lightweight mortar can develop sufficient independent load-carrying capacity to safely fabricate layered structures without the aid of external formwork. We developed a prototypical mortar mix using ES&C because this unique material synergizes a preponderance of characteristics that are desirable in this context. Namely, ES&C can promote internal curing, can increases internal friction (and hence initial strength) by means of aggregate angularity, can be used to achieved final structural strength, is lightweight and can be used to produce a mortar that is visually pleasing. But in practice material availability and cost constraints may apply, therefore it’s important to understand how to generally approach development of suitable materials. To this end we outline a process which may be followed to engineer materials for Contour Crafting, given certain prevailing constraints, such as cost, material availability, machine limitations, performance requirements, and environmental conditions. 137 The first thing to consider is that, as demonstrated, vertical build rate is solely a function of (a) material initial strength, (b) material rate constant, and (c) material wet density. Furthermore, build rate is directly proportional to initial strength and rate constant; and indirectly proportional to the wet density. Meaning, deficiencies introduced by one factor may be offset by another. As an example, the negative impact of being forced to incorporate higher density aggregate, say NWA, can be offset by boosting initial strength and/or the material rate constant. To implement such tradeoffs it’s important to appreciate how each of the three aforementioned driving parameters can be manipulated. Material initial strength is primarily a function of w/c, aggregate grading (as demonstrated in literature), VMA, fines, and aggregate angularity. Material rate constant is primarily a function of set acceleration, cement content (presumably), and temperature. Wet density is primarily a function of aggregate weight, weight-compensating additives, air voids, and total water content. With this preface in mind a suitable material model, which is mindful of locally prevailing conditions and the intended application, may be developed as follows: 1 Carefully consider the complete tradeoff matrix implied by each of the functional dependencies listed above, to minimize overall negative effects, and maximize overall positive effects of the constrained inputs. In other words, stack the deck to favor contour-craftability. For example, if forced to incorporate NWA, an angular (e.g. crushed) NWA would be preferable to a round NWA (internal friction and resulting increase in initial strength compensating for the unfavorable aggregate weight). 2 Design mix proportions leveraging available industry guidelines, and/or using the mix ratios developed and presented here. 3 Set w/c and HRWR to produce a mixture which is as stiff as possible but still compatible with the currently available material delivery system (pump, ram extruder, etc.). 4 If necessary, feasible and/or affordable modulate material shape-stability and initial strength by means of additives, most notably VMA and fines, as reported extensively both here and in literature. (continued) 138 5 If necessary and feasible manipulate process parameters, most notably mixing regimen, compaction energy, and temperature. 6 Incorporate provisions for curing, which can be aided internally as was done here (options include saturated aggregate and/or specialty additives like SAP), or provide for curing externally (options include wetting, moisture barriers, and/or environmental controls). 7 Measure material initial strength and material rate constant by means of plate- stacking test developed and described herein. 8 Using the limit-state data points obtained through plate-stacking, calibrate the specific material maturity model, assuming the general exponential strength development trend substantiated and presented here. 9 Optionally, improve results iteratively through judicious trial and error, and/or by means of a formal mix optimization. Table 8.1. Predictive Material Model Development Process Opportunities for Future Research 8.3 Due to the groundbreaking nature of this work, for every question answered, a crop of new ones emerged. The unanswered questions define a number of opportunities for future research. Experimental results have been leveraged to develop recommendations (or regimens) for safe layering of prismatic unconfined mortar extrudate. Further testing is required to make generic recommendations for layer deposition regimens as a function of road height, width, and mix design (including w/c) at other than the isothermal conditions available in a controlled laboratory environment. Maturity models are proposed here to characterize mortar maturity from inception to final cured strength. The models can be configured to also account for critical dependency on moisture content (w/c) and temperature, which will vary appreciably in practice, but which were omitted for 139 scope and simplicity from the material experiments performed here. Further testing is required to investigate sensitivity to moisture and temperature. Further testing and analysis is also required to investigate variability in very early concrete behavior to develop design limits for Contour Crafting and other techniques of early structural loading without formwork. Further research is also necessary to evaluate the bond strength between extrudate layers, since this could be the limiting factor for post-hardened load carrying capacities. More work is necessary to verify that numerical simulation of unconfined mortar stacking scenarios can be implemented with sufficient ease and fidelity to be useful for design, fabrication planning, in material health monitoring, and to generally explore stacking effects on the time- dependent cementitious materials used in this type of layered freeform fabrication. As demonstrated, the M1 mortar mixture is adequate but not necessarily optimal, and importantly, constrained by limitations imposed by current Contour Crafting equipment - namely the pump, which is limiting in pumping pressure and aggregate size. Yet there is ample evidence that aggregate angularity and grading contribute significantly to that portion of the initial green strength which is contributed by particle friction. This important improvement can and should be investigated (decoupling cohesion), possibly following the approach developed by Rowe for his seminal work with assemblies of particles in contact (Rowe, 1962) - Figure 8.1. 140 Figure 8.1. Slip Lines in Assemblies of Particles in Contact (Rowe, 1962) During mortar sample preparation and testing we observed marked non-linearity in the initial response - meaning slump, or response to self-weight, was not in proportion to the response exhibited to the load increment applied initially in uniaxial compression. In fact, the slump (witnessed immediately upon sample extrusion) was proportionally much larger. Incidentally, we were able to appreciate this behavior only because the apparatus we developed for specimen preparation allowed us to see it – it happened right in front of our eyes. This was fortuitous because had we used a more sophisticated ram extruder for specimen preparation, such as the one used by Voigt (Voigt, Malonn, & Shah, 2006), this phenomenon might have been obscured. This unanticipated non-linearity was cause for some unwarranted concern initially, because a proportional response suggested the mortar would have deflected excessively when loaded. Instead, a marked initial stiffening was observed. As an example we consider the very young M1 mortar specimen strength-tested only 11 minutes after mixing. This specimen slumped between 0.11 and 0.15 inches under gravity 21 . Conversely, the first increment of W/2=0.75 lb applied load 21 While this small deflection may seem to be barely perceptible in a 3x4 cylinder, it’s worth noting that the ‘physical straining’ in the material was quite palpable. The range is due to the measurement uncertainty. 141 resulted in an incremental axial deflection between 0.05 and 0.06 inches 22 – about half the deflection predicted for a linear response. Clearly the initial response is far from linear. A similar insight is illustrated in the material stress-strain curve (Figure 8.2). In this diagram the darker trace does not account for stress due to gravity, and does not include slump. Conversely, the lighter trace includes stress due to gravity (set equivalent to stress due to W/2) and initial slump. Figure 8.2. Non-Linear Mortar Response This stiffening, which could perhaps also be described as a form of material structuration, warrants further investigation. Recall also that granular and polymeric materials are known to be pressure-sensitive, in that they exhibit pressure-dependent yield. In other words, the material becomes stronger under pressure. Although our specimens were tested without confinement (and thus with no externally enforced confining pressure) it may be worthwhile to consider whether this familiar mechanism is 22 Furthermore, the first increment of W=1.5 lb applied load resulted in an incremental axial deflection of only 0.09 inches. 142 responsible for some or all of the aforementioned initial material structuration 23 . Incidentally, this also serves to underline how the linear Drucker-Prager model may not be entirely adequate, and how further consideration should be given to the hyperbolic or general exponent models which can represent non-linear pressure-dependent yielding at low confining pressures, as illustrated by the yield surface depicted in Figure 8.3. Source: (Abaqus User's Manual, 2009) Figure 8.3. Non-Linearity in Hyperbolic D-P Yield Function at Low Confining Pressure A general cautionary note on creep is warranted. For simplicity we assumed that the material characteristics, environmental conditions and loading rate were such that it was reasonable to neglect it. Although measurements taken of the full-scale demonstration artifact (after curing) seem to corroborate this hypothesis, generalization is not warranted. Creep is potentially detrimental and warrants further investigation. Other opportunities for future research include: mix optimization; non-isothermal extension of the M1 material model; expanding the role of health-monitoring in Contour Crafting; effects of stacking load on pore pressure, free water migration, cement hydration and structural strength; effects of pumping (LWA) on structural strength 24 ; material robustness 25 ; large aggregate; in-line 23 For example, imagine the external mortar layer (near the OD) participating like formwork by means of the non-negligible cohesion in the M1 mix, and thus exerting an increment of hydrostatic pressure upon the inner core. 24 BE96-3942/R11, March 2000, Pumping of lightweight aggregate concrete based on expanded clay in Europe, would be an apropos reference for this. 143 tests for green strength and structural buildup; not pre-soaking the LWA 26 ; test for cured mortar strength using 3x6 cores extracted from the artifact produced during the full-scale mortar layering demo; test bond strength between layers of the full-scale layering demo. 25 e.g. the capacity of the material to tolerate certain variation in the material characteristics, mixture parameters, environmental conditions, mixing, pumping – robust concrete has lower sensitivity to such variations. 26 This would demand higher pumping pressure because moisture would be forced into the aggregate voids by the pumping pressure, but could also produce a stiffer extrudate with greater green strength, lower w/c, and possibly higher cured strength if provision for adequate curing are also made 144 9. 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Retrieved August 19, 2012, from MPA, The Concrete Center: http://www.concretecentre.com/technical_information/building_solutions/formwork/slip_for m.aspx Štemberk, P., & Kohoutková, A. (2005). Image-Analysis-Based Measuring of Lateral Deformation of Hardening Concrete. Materials Science, 292-296. Tregger, N. A., Pakula, M. E., & Shah, S. P. (2010). Influence of clays on the rheology of cement pastes. Cement and Concrete Research, 40, 384–391. Tregger, N., Ferrara, L., & Shah, S. P. (2008, December). Identifying Viscosity of Cement Paste from Mini-Slump-Flow Test. American Concrete Institute. Tregger, N., Voigt, T., & Shah, S. (2007). Improving the slipform process via material manipulation. In C. U. Grosse, & C. U. Grosse (Ed.), Advances in Construction Materials 2007 (pp. 539-546). Springer Berlin Heidelberg. Tuthill, H. L., & Cordon, A. W. (1955). Properties and Uses of initially Retarded Concrete. Proceedings of the American Concrete Institute (pp. 273-286). ACI. van Breugel, K. (1992). Numerical Simulation of Hydration and Microstructural Development in Hardening Cement-Based Materials. HERON, 37(2). Voigt, T., Malonn, T., & Shah, S. P. (2006). Green and early age compressive strength of extruded cement mortar monitored with compression tests and ultrasonic techniques. Cement and Concrete Research, 36, 858–867. Voigt, T., Mbele, J.-J., Wang, K., & Shah, a. S. (2010). Using Fly Ash, Clay, and Fibers for Simultaneous Improvement of Concrete Green Strength and Consolidatability for Slip- Form Pavement. Journal of Materials in Civil Engineering, 22(2), 196-206. Wikipedia. (n.d.). 3D Printing. Retrieved July 28, 2012, from http://en.wikipedia.org/wiki/3D_printing Yeh, Z., & Khoshnevis, B. (2009). Geometric Conformity Analysis for Automated Fabrication Processes Generating Ruled Surfaces-Demonstration for Contour Crafting. Rapid Prototyping Journal, 15(5), 361-369. Zhang, J. (2009, August). Contour Crafting Process Planning and Optimization. Los Angeles: University of Southern California. 148 Zhang, J., & Khoshnevis, B. (2011). Toolpath Planning Optimization for Single and Multiple Gantry Contour Crafting System. International Journal of Advanced manufacturing Systems, 13(1), 61-74. Zhang, J., & Khoshnevis, B. (Spring 2010). Contour Crafting Process Plan Optimization - Part I: Single-Nozzle Case. Journal of Industrial and Systems Engineering, 4(1), 33-46. Zhang, J., & Khoshnevis, B. (Summer 2010). Contour Crafting Process Plan Optimization - Part II: Multi–Machine Cases. Journal of Industrial and Systems Engineering, 4(2), 77-94. Zhang, J., & Khoshnevis, B. (to appear (2012)). Optimal Machine Operation Planning for Construction by Contour Crafting. Journal of Automation in Construction. 149 10. Appendices Appendix A: M2 Mix (60 pcf) This section describes a supplementary lightweight insulating mortar mixture developed as part of this research, which is also suitable for layered freeform fabrication. This mortar mix is identified here as M2. The M2 mix is patterned after the M1 structural lightweight mix, but with 4% (by weight) of the ES&C aggregate replaced with Elemix concrete additive (expanded polystyrene). A contour craftable lightweight structural mix may be useful in composites roads to reduce dead load, and increase insulation and the energy efficiency of the fabricated structures. Table 10.1 summarizes compression strength of the M2 mix at 1, 3, 7 and 28 days after casting. Figure 10.1 illustrates how this 60 pcf material floats in water. Figure 10.2, Figure 10.3, and Figure 10.4 illustrate exemplary cured cylinder strength testing of the M2 mix at 24 hours, 3-days, and 28- days, respectively. Table 10.1. Compression Strength – 60 pcf M2 Mix 1-Day 3-Day 7-Day 28-Day Specimen No. M2.1.1 M2.2.1 M2.1.2 M2.2.2 M2.1.3 M2.2.3 M2.1.4 M2.2.4 Date Tested: 21-Sep 21-Sep 23-Sep 23-Sep 27-Sep 27-Sep 18-Oct 18-Oct Specimen Size 3x6 3x6 3x6 3x6 3x6 3x6 3x6 3x6 Age [days] 1 1 3 3 7 7 28 28 Total Load [lbf] 2060 1560 3850 3320 6050 4640 8470 8500 D1 [in] 3.02 3.02 3.02 3.02 3.02 3.02 3.04 3.04 D2 [in] 3.02 3.01 3.02 3.02 3.02 3.02 3.03 3.05 Area [in 2 ] 7.16 7.14 7.16 7.16 7.16 7.16 7.23 7.28 Strength [psi] 288 219 537 463 845 648 1171 1167 150 Figure 10.1. M2 Mix Specimens Floating in Curing Tank Figure 10.2. Cured Cylinder Strength Tests (60 pcf specimens @ 24 hrs) Figure 10.3. Cured Cylinder Strength Tests (60 pcf specimens @ 3 days) 151 Figure 10.4. Cured Cylinder Strength Tests (60 pcf specimens @ 28 days) Appendix B: Green Strength Test (9-25-2011) Here we report stills and stress-strain curves produced during room temperature green strength testing of the M1 mix at 0% NCA. Figure 10.5. M1 Green Strength Test (11 minutes after mixing) 152 Figure 10.6. M1 Green Strength Test (18 minutes after mixing) Figure 10.7. M1 Green Strength Test (22 minutes after mixing) 153 Figure 10.8. M1 Green Strength Test (26 minutes after mixing) Figure 10.9. M1 Green Strength Test (47 minutes after mixing) 154 Figure 10.10. M1 Green Strength Test (58 minutes after mixing) Figure 10.11. M1 Green Strength Test (73 minutes after mixing) 155 Figure 10.12. M1 Green Strength Test (92 minutes after mixing) Figure 10.13. M1 Green Strength Test (99 minutes after mixing) 156 Figure 10.14. M1 Green Strength Test (109 minutes after mixing) Figure 10.15. M1 Green Strength Test (208 minutes after mixing) 157 Figure 10.16. M1 Green Strength Test (211 minutes after mixing) Figure 10.17. M1 Green Strength Test (283 minutes after mixing) 158 Figure 10.18. M1 Green Strength Test (288 minutes after mixing) Appendix C: Plate-Stacking Test, M1 Mix, 1% Set Acceleration This section includes complete documentation of the plate-stacking test, using the M1 mortar mixture at 1% set acceleration. A snapshot is included for each increment of loading. At each increment, a 1.5 lb plate is added to one or more stacks as summarized in Table 4.2. (continued) 159 (continued) 160 Figure 10.19. Plate-Stacking Test, M1 Mix, 1% Set Acceleration Appendix D: Plate-Stacking Test, M1 Mix, 2% Set Acceleration This section includes complete documentation of the plate-stacking test, using the M1 mortar mixture at 2% set acceleration. A snapshot is included for each increment of loading. At each increment a 1.5 lb plate is added to one or more stacks as summarized in Table 4.2. The mortar specimens performed better than anticipated, so towards the end of the test we ran out of the 1.5 lb plates and began improvising with lighter plates originally slated for testing the lighter 60 pcf mix, and other lab weights. However, at each increment the total stack load was as high as or conservatively higher than scheduled for that increment. (continued) 161 (continued) 162 Figure 10.20. Plate-Stacking Test, M1 Mix, 2% Set Acceleration 163 Appendix E: Plate-Stacking Test, M1 Mix, 3% Set Acceleration This section includes complete documentation of the plate-stacking test, using the M1 mortar mixture at 3% set acceleration. A snapshot is included for each increment of loading. At each increment a 1.5 lb plate is added to one or more stacks as summarized in Table 4.2. The mortar specimens performed better than anticipated so towards the end of the test we ran out of the 1.5 lb plates and began improvising with lighter plates originally slated for testing the lighter 60 pcf mix, and other lab weights. However, at each increment the total stack load was as high as or conservatively higher than scheduled for that increment. (continued) 164 (continued) 165 Figure 10.21. Plate-Stacking Test, M1 Mix, 3% Set Acceleration Appendix F: Consolidation (thru Plate-Stacking) of the Bond-Strength Specimens This section includes complete documentation of the consolidation (effected thru plate-stacking) of the bond-strength specimens. A snapshot is included for each increment of loading. At each increment a 1.5 lb plate is added to one or more stacks as summarized in Table 4.4. Towards the end of the test we ran out of the 1.5 lb plates and began improvising with lighter plates originally slated for testing the lighter 60 pcf mix, and other lab weights. However, at each increment the total stack load was as high as or conservatively higher than scheduled for that increment. (continued) 166 (continued) 167 Figure 10.22. Consolidation of the Bond-Strength Specimens 168 Appendix G: Bond-Strength Test Specimens After Compression Test Figure 10.23. Bond-Strength Specimen After Compression Test (10’ Stacking Interval) Figure 10.24. Bond-Strength Specimen After Compression Test (15’ Stacking Interval) 169 Figure 10.25. Bond-Strength Specimen After Compression Test (20’ Stacking Interval) Figure 10.26. Bond-Strength Specimen After Compression Test (25’ Stacking Interval) 170 Appendix H: Cured Cylinder Strength, 3x6 Test Specimens This section documents supplemental cured cylinder strength tests. These supplemental cured specimens are M1 Mix (100 pcf), 3x6 cylinders that were cast using the same material batched for the unconfined plate-stacking tests. These specimens were cured normally (in a wet bath) and tested at 28 days. Only one specimen was produced at each of the three levels of set acceleration (1%, 2% and 3%). A correlation between level of set acceleration and 28-day strength is observed, however it would be unrealistic to make extensive conclusions due to the scarcity of the data. Still, it’s very satisfying to see the M1 mix breaking the 4000 psi barrier. Table 10.2. Compression Strength – 3x6 Green Strength Test Specimens (Supplemental) Specimen No. 1%NCA 2%NCA 3%NCA Date Tested: 21-Nov 28-Nov 28-Nov Specimen Size 3x6 3x6 3x6 Age [days] 28 28 28 Total Load [lbf] 24700 27750 31000 D1 [in] 3.04 3.05 3.04 D2 [in] 3.05 3.04 3.05 Area [in 2 ] 7.28 7.28 7.28 Strength [psi] 3392 3811 4257 171 (3392 psi; Type 3 fracture pattern) Figure 96. Cured Cylinder Strength, 3x6 Test Specimen, M1-1%SA (3811 psi; Type 3 fracture pattern) Figure 96. Cured Cylinder Strength, 3x6 Test Specimen, M1-2%SA 172 (4257 psi; Type 3 fracture pattern) Figure 96. Cured Cylinder Strength, 3x6 Test Specimen, M1-3%SA Appendix I: Cured Cylinder Strength, 3x4 Test Specimens This section documents supplemental cured cylinder strength tests performed on shorter 3x4 cylindrical specimens of the M1 Mix (100 pcf). The specimens derive from 2 sources: (1) the green strength test (GST), and (2) the unconfined plate-stacking test (UST). The GST specimens, which were subjected to a number of loading cycles while curing, were remolded and consolidated after the last green strength test, more than 4 hours after mixing. These specimens were cured as molded in unconditioned lab air. The UST specimens, which were subjected to significant plate-stacking loads (33 lbs) while curing, were cured most unfavorably, free-standing and bare, in unconditioned lab air. The reported strengths are corrected for length to diameter ratio (L/d) as specified by ASTM C 43. 173 Table 10.3. Compression Strength – 3x4 Green Strength Test Specimens (Remolded) Table 10.4. Compression Strength – Plate-Stacking Test Specimens (Unconfined) 3-Day 14-Day 21-Day Specimen No. M1a-1 M1a-2 M1a-3 M1a-4 M1a-5 Date Tested: 28-Sep 12-Oct 12-Oct 18-Oct 18-Oct Specimen Size 3x4 3x4 3x4 3x4 3x4 Age [days] 3 14 14 21 21 Total Load [lbf] 14900 24500 26750 28000 26750 D1 [in] 3.05 3.04 3.04 3.04 3.04 D2 [in] 3.05 3.05 3.05 3.05 3.04 Area [in 2 ] 7.31 7.28 7.28 7.28 7.26 Strength [psi] 2039 3364 3673 3845 3685 Height [in] 4.20 4.15 4.13 4.16 4.16 L/D 1.40 1.38 1.38 1.39 1.39 Correction for Height 0.94 0.95 0.95 0.95 0.95 Corrected Strength [psi] 1917 3196 3490 3653 3501 Source of specimen GST GST GST GST GST 28-Day Specimen No. M1.1pc.15M1.1pc.20M1.3pc.10M1.3pc.15M1.3pc.20 Date Tested: 21-Nov 21-Nov 28-Nov 28-Nov 28-Nov Specimen Size 3x4 3x4 3x4 3x4 3x4 Age [days] 28 28 28 28 28 Total Load [lbf] 19800 23200 24250 23750 24250 D1 [in] 3.25 3.23 3.24 3.21 3.17 D2 [in] 3.2 3.18 3.26 3.18 3.21 Area [in 2 ] 8.17 8.07 8.30 8.02 7.99 Strength [psi] 2424 2876 2923 2962 3034 Height [in] 4.07 4.07 4 4 4 L/D 1.36 1.36 1.33 1.33 1.33 Correction for Height 0.94 0.94 0.94 0.94 0.94 Corrected Strength [psi] 2278 2703 2748 2785 2852 Source of specimen UST UST UST UST UST 174 Figure 96. Cured Cylinder Strength, 3x4 Test Specimen, M1.1pc.15 Figure 96. Cured Cylinder Strength, 3x4 Test Specimen, M1.1pc.20 Figure 96. Cured Cylinder Strength, 3x4 Test Specimen, M1.3pc.10 175 Figure 96. Cured Cylinder Strength, 3x4 Test Specimen, M1.3pc.15 Figure 96. Cured Cylinder Strength, 3x4 Test Specimen, M1.3pc.20 Appendix J: Failed Plate-Stacking Test Specimens This section documents the 3x4 cylindrical mortar specimens which failed in unconfined compression testing (as noted earlier, the specimens that did not fail were cured and retested for compression strength). This photographic evidence is included here because knowing how these specimens failed under unconfined axial compression may be useful in the future for limit state analysis, for example, to push the FEA towards such critical states and failure modes, and thus support characterization of structural margin of safety. 176 Figure 10.27. Plate-Stacking Test Specimen (1% SA, 5 minute) Figure 10.28. Plate-Stacking Test Specimen (1% SA, 10 minute) 177 Figure 10.29. Plate-Stacking Test Specimen (1% SA, 15 minute) Figure 10.30. Plate-Stacking Test Specimen (1% SA, 20 minute) 178 Figure 10.31. Plate-Stacking Test Specimen (2% SA, 5 minute) Figure 10.32. Plate-Stacking Test Specimen (2% SA, 10 minute) 179 Figure 10.33. Plate-Stacking Test Specimen (2% SA, 15 minute) 180 Figure 10.34. Plate-Stacking Test Specimen (2% SA, 20 minute) Figure 10.35. Plate-Stacking Test Specimen (3% SA, 5 minute) 181 Figure 10.36. Plate-Stacking Test Specimen (3% SA, 10 minute) Figure 10.37. Plate-Stacking Test Specimen (3% SA, 15 minute) 182 Figure 10.38. Plate-Stacking Test Specimen (3% SA, 20 minute) Appendix K: Exemplary Predictive Model for Contour Crafting This section illustrates an exemplary predictive model relating overall fabrication rate to mortar maturity and associated structural strength. The model leverages the empirical results produced herein, and is formatted to be used as a decision tool. The practical application is the free-form layering of tall structures (for example wind towers), which during fabrication are subjected to both dead loads (e.g. structural self-weight), machine loads (the fabricated structure must also support the Contour Crafting machine), and live fabrication loads (for example, as imparted by the material delivery system). Since fabrication uses a climbing robot, an additional strength check must be made to identify which cured layers are strong enough to support the dead and live machinery loads. Table 10.5, Table 10.6 and Table 10.7 illustrate input-output for dimensions, material parameters, and mortar maturity. Figure 10.39 graphically illustrates the corresponding 183 safe fabrication rate, and where (within the pre-built layers) the machinery loads can be safely transferred. As indicated in this example, given the specified parameters, the machine weight can be transferred to the first mortar layer (road) after 270 minutes. In other words, the machine must reach 1.3 meters below the nozzle plane to anchor itself to pre-fabricated structure. These estimates apply only to the lower layers, and do not allow for point loading and/or pressure required to transfer machinery loads to the fabricated structure thru friction. As the structure narrows, stress will increase proportionally, and either fabrication rate will decrease or the anchors will be lowered, for example 1.5 meters below the nozzle plane. (σm = stress on 1 st layer due to machine weight) Table 10.5. Predictive Model: Tower Dimensions and Machine Weight Table 10.6. Predictive Model: Mortar Strength Development H 100 m OD 8.00 m 315 in ID 7.3 m 287 in in Area 13038 in 2 Machine weight, M 6000 kg 13228 lbs σm 1.015 psi (eq. 1): Exponential (up to t=720 min) y 1 =C 1 e mt where, t = age, in minutes y = strength of mortar, in psi C 1 = C/7.07 C1 1.2 m 0.007 (eq. 2): Linear Hyperbolic model fcu 4500.0 k 0.0001798 t 0 500.6 fab. rate, r 11.5 in/hr fab. rate, r 0.2 in/min plastic density, δ 100 lb/ft 3 plastic density, δ 0.0579 lb/in 3 SF 2 184 Table 10.7. Predictive Model: Mortar Maturity Figure 10.39. Predictive Model: Wind Tower Calculator (1 st Layer) time [min] ht [in] ht [m] σc σc+σm fc fc' fc'-σc 0 0.0 0.00 0.0 0.00 1.2 0.6 0.6 100 19.2 0.49 1.1 1.11 2.5 1.2 0.1 200 38.3 0.97 2.2 2.22 4.9 2.5 0.2 300 57.5 1.46 3.3 4.004 9.9 5.0 1.6 400 76.7 1.95 4.4 5.113 20.0 10.0 5.6 500 95.8 2.43 5.5 6.222 40.3 20.1 15 600 115 2.92 6.7 7.331 81.1 40.6 34 700 134 3.41 7.8 8.441 163 82 74 1000 192 5 11.1 11.768 371 185 174 2000 383 10 22.2 22.860 956 478 456 3000 575 15 33.3 33.952 1395 698 664 185 Appendix L: Testing Shape-Stable Mortar The following supplemental tests were considered potentially useful for characterizing workability of the M1 fresh mortar mixture. These alternatives are summarized here because they may be relevant to future research, for example, for insights into developing an in-line test which would be capable of providing the fabrication system with real-time material property measurements. (a) slump test, reference: Fifty-cent rheometer for yield stress measurements, from slump to spreading flow (Roussel & Coussot, 2005) (b) direct vane rheometer, reference: ASTM D4648 Standard Test Method for Laboratory Miniature Vane Shear Test for Saturated Fine-Grained Clayey Soil, ASTM D2573 Standard Test Method for Field Vane Shear Test in Cohesive Soil, and (Saaka, Jennings, & Shah, 2004) (c) Nordenswan ‘blood pressure’ test, reference: (Nordenswan, 2002) (d) IC-Tester, reference: (Koehler & Fowler, 2003) (e) triaxial compression test, reference: ASTM D4757 Standard Test Method for Consolidated Undrained Triaxial Compression Test for Cohesive Soils, and ASTM WK3821 New Test Method for Consolidated Drained Triaxial Compression Test for Soils (under development) (f) direct shear test, reference: ASTM D3080 Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions 186 (a) (b) (c) (d) (e) (f) Sources: (Roussel & Coussot, 2005), (Saaka, Jennings, & Shah, 2004), (Nordenswan, 2002), (Koehler & Fowler, 2003), http://www.isotop.co.il, and ASTM D3080 Figure 10.40. Alternative Methods for Assessing Fresh Mortar Properties 187 Appendix M: Technical Specification Documents The following technical specifications are referenced and leveraged in this research: ACI 213R-03, Guide for Structural Lightweight-Aggregate Concrete ASTM C 39, Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens ASTM C 42, Standard Test Method for Obtaining and Testing Drilled Cores and Sawed Beams of Concrete ASTM C 109, Standard Test Method for Compressive Strength of Hydraulic Cement Mortars ASTM C 125, Standard Terminology Relating to Concrete and Concrete Aggregates ASTM C 128, Standard Test Method for Density, Relative Density, and Absorption of Fine Aggregate ASTM C 138, Standard Test Method for Density (Unit Weight), Yield, and Air Content of Concrete ASTM C 143, Standard Test Method for Slump of Hydraulic-Cement Concrete ASTM C 192, Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory ASTM C 219, Standard Terminology Relating to Hydraulic Cement ASTM C 230, Standard Specification for Flow Table for Use in Tests of Hydraulic Cement ASTM C 266, Standard Test Method for Time of Setting of Hydraulic-Cement Paste by Gillmore Needles ASTM C 330, Standard Specification for Lightweight Aggregates for Structural Concrete ASTM C 305, Std. Practice for Mech. Mixing of Hydraulic Cement Pastes and Mortars of Plastic Consistency ASTM C 403, Standard Test Method for Time of Setting of Concrete Mixtures by Penetration Resistance ASTM C 567, Standard Test Method for Determining Density of Structural Lightweight Concrete ASTM C 882, Std. Method for Bond Strength of Epoxy-Resin Systems Used with Concrete by Slant Shear ASTM C 1074, Standard Practice for Estimating Concrete Strength by the Maturity Method ASTM C 1437, Standard Test Method for Flow of Hydraulic Cement Mortar ASTM C 1583, Standard Test Method for Tensile Strength of Concrete Surfaces and the Bond Strength or Tensile Strength of Concrete Repair and Overlay Materials by ASTM C 1611, Standard Test Method for Slump Flow of Self-Consolidating Concrete ASTM D 2573, Standard Test Method for Field Vane Shear Test in Cohesive Soil ASTM D 3080, Standard Test Method for Direct Shear Test of Soils under Consolidated Drained Conditions ASTM D 4648, Std. Method for Lab. Miniature Vane Shear Test for Saturated Fine-Grained Clayey Soil ASTM D 4757, Std. Test Method for Consolidated Undrained Triaxial Compression Test for Cohesive Soils ASTM F 2792, Standard Terminology for Additive Manufacturing Technologies 188 ASTM WK 3821, New Test Method for Consolidated Drained Triaxial Compression Test for Soils BE96-3942/R11, Pumping of lightweight aggregate concrete based on expanded clay in Europe BS EN 12350-5, Testing Fresh Concrete, Part 5: Flow Table Test Appendix N: Technical Certifications This section documents the professional certifications attained to prepare for working with and testing concrete. The benefits of certification included: (1) fluency with test methods and equipment, (2) proficiency with industry-standard test methods to ensure consistent and meaningful test results, and (3) significant immersion in concreting culture. Fluency in concreting culture was instrumental for: (a) facilitating discovery and thus informing the work with the wealth of wisdom that is available in industry, (b) properly framing the work within its intended operational context, and (c) facilitating dissemination and acceptance, by a professional cadre which accepts change reluctantly, for good reasons. Emphasis is on standard-driven field and laboratory testing. The standards are leveraged to drive consistency into test results. This forms a basis for comparison across experiments and with outside research. The following certifications and associated proficiencies were deemed relevant: ACI Concrete Field Testing Technician, 3/13/2010 ASTM C 1064 - Temperature of Freshly Mixed Portland-Cement Concrete ASTM C 172 - Sampling Freshly Mixed Concrete ASTM C 143 - Slump of Hydraulic Cement Concrete ASTM C 138 - Unit Weight, Yield, and Air Content (Gravimetric) of Concrete ASTM C 231 - Air Content of Freshly Mixed Concrete by the Pressure Method ASTM C 173 - Air Content of Freshly Mixed Concrete by the Volumetric Method ASTM C 31 - Making and Curing Concrete Test Specimens in the Field 189 ACI Concrete Strength Testing Technician, 3/25/2010 ASTM C 617 - Capping Cylindrical Concrete Specimens ASTM C 1231 - Unbonded Caps for Concrete Cylinders ASTM C 39 - Compressive Strength of Cylindrical Concrete Specimens ASTM C 78 - Flexural Strength of concrete ACI Aggregate Testing Technician – Level 1, 6/8/2010 ASTM T2 / D75 - Sampling Aggregates ASTM T248 / C702 - Reducing Samples of Aggregate to Testing Size ASTM T11 / C117 - Materials Finer Than 75-µm (No. 200) Sieve in Mineral Aggregates by Washing ASTM T27 / C136 - Sieve Analysis of Fine and Coarse Aggregates ASTM T85 / C127 - Specific Gravity and Absorption of Coarse Aggregate ASTM T84 / C128 - Specific Gravity and Absorption of Fine Aggregate ASTM T255 / C566 - Total Moisture Content of Aggregate by Drying ASTM T21 / C40 - Organic Impurities in Fine Aggregate for Concrete ACI Concrete Laboratory Testing Technician - Level 1, 6/8/2010 ASTM C617 - Capping Cylindrical Concrete Specimens ASTM C1231 - Unbonded Caps for Concrete Cylinders ASTM C39 - Compressive Strength of Cylindrical Concrete Specimens ASTM C78 - Flexural Strength of Concrete (Using Simple Method with Third-Point Loading) ASTM T2 / D75 - Sampling of Aggregates ASTM T248 / C702 - Reducing Samples of Aggregate to Testing Size ASTM T11 / C117 - Materials Finer Than 75-µm (No. 200) Sieve in Mineral Aggregates by Washing ASTM T27 / C136 - Sieve Analysis of Fine and Coarse Aggregates ASTM T85 / C127 - Specific Gravity and Absorption of Coarse Aggregate ASTM T84 / C128 - Specific Gravity and Absorption of Fine Aggregate ASTM T255 / C566 - Total Evaporable Moisture Content of Aggregate by Drying ASTM T21 / C40 - Organic Impurities in Fine Aggregates for Concrete 190 Appendix O: VBA Code for ABAQUS Layer-Stacking Simulation This section documents the VBA-code which links ABAQUS and Excel, and drives the numerical simulation of mortar layering with the age-dependent material properties described in section 6.5. Sub runAbaqus() updateMaterial Shell "C:\Users\Tony\Documents\Contour_Crafting\MEM_vSE\1_Aging_Properties\runAbaqus.bat" onQue getResults Sheets("IO").Select End Sub Function Is_File(filename) 'MsgBox "function: Is_File" ' This function doesn't work if the current directory isn't already set (e.g. with a file, open) Is_File = False Set fs = CreateObject("Scripting.FileSystemObject") If fs.FileExists(filename) Then Is_File = True End If End Function Sub onQue() 'MsgBox "sub: onQue" Application.StatusBar = "job submitted >> " & Now() newHour = Hour(Now()) newMinute = Minute(Now()) newSecond = Second(Now()) + 5 waitTime = TimeSerial(newHour, newMinute, newSecond) Application.Wait waitTime Do While Is_File("mem.lck") Application.StatusBar = "running ...." & Now() Loop End Sub Function readFile(fno) 'MsgBox "function: readFile" Dim aa() nlines = 0 Open fno For Input As #1 Do While Not EOF(1) 191 nlines = nlines + 1 ReDim Preserve aa(1 To nlines) Line Input #1, aa(nlines) Application.StatusBar = nlines Loop Close #1 readFile = aa End Function Sub getResults() 'MsgBox "sub: getResults" Dim myDir As String, fn As String, ff As Integer, txt As String, a() Dim x, i As Long, n As Long, b(), t As Long myDir = "C:\Users\Tony\Documents\Contour_Crafting\MEM_vSE\1_Aging_Properties\" 'Have to input this path manually fn = Sheets("AutoRun").Range("fn_Out") fno = (myDir & fn) ' MsgBox myDir ' MsgBox fn ' MsgBox fno aa = readFile(fno) nlines = UBound(aa) jobCompletetionFlag_N = False jobCompletetionFlag_E = False ' get displacement Set idRange = Sheets("IO").Range("NodeIDs") Sheets("IO").Range("deltaXY").ClearContents For i = 1 To nlines ' MsgBox aa(i) If InStr(aa(i), "NODE") = 8 Then jobCompletetionFlag_N = True istart = i + 3 For ii = istart To nlines If Len(aa(ii)) < 30 Then GoTo EndOfDisp nid = Int(Mid(aa(ii), 7, 5)) dx = Mid(aa(ii), 17, 12) dy = Mid(aa(ii), 29, 12) addr = searchAddr(nid, idRange) If addr <> "" Then Sheets("IO").Range(addr).Offset(0, 3) = dx Sheets("IO").Range(addr).Offset(0, 4) = dy End If 192 Next ii End If Next i EndOfDisp: ' get stress Set idRange = Sheets("IO").Range("EID") Sheets("IO").Range("stress").ClearContents For i = 1 To nlines ' MsgBox aa(i) If InStr(aa(i), "ELEMENT") = 5 Then jobCompletetionFlag_E = True 'MsgBox "jobCompletetionFlag_E = True" istart = i + 3 For ii = istart To nlines If Len(aa(ii)) < 60 Then GoTo EndOfStress eid = Mid(aa(ii), 1, 12) s11 = Mid(aa(ii), 19, 12) s22 = Mid(aa(ii), 31, 12) s33 = Mid(aa(ii), 43, 12) s12 = Mid(aa(ii), 56, 12) addr = searchAddr(eid, idRange) If addr <> "" Then Sheets("IO").Range(addr).Offset(0, 18) = s22 End If Next ii End If Next i EndOfStress: If Not jobCompletetionFlag_N Then MsgBox " job failed" ElseIf Not jobCompletetionFlag_E Then MsgBox " job failed" Else Application.StatusBar = " Job Completed" End If End Sub Sub updateMaterial() 'MsgBox "sub: updateMaterial" 193 Dim myDir As String, fn As String, ff As Integer, txt As String, a() Dim x, i As Long, n As Long, b(), t As Long myDir = "C:\Users\Tony\Documents\Contour_Crafting\MEM_vSE\1_Aging_Properties\" 'Have to input this path manually fn = Sheets("AutoRun").Range("fn_In") fni = (myDir & fn) ' MsgBox myDir ' MsgBox fn ' MsgBox fni aa = readFile(fni) nlines = UBound(aa) ' get material properties Set eidRange = Sheets("IO").Range("EID") For i = 1 To nlines If InStr(aa(i), "Material, name=") Then newid = Mid(aa(i), 20) addr = searchAddr(newid, eidRange) If addr <> "" Then delta = Sheets("IO").Range(addr).Offset(0, 2) beta = Sheets("IO").Range(addr).Offset(0, 3) pt = Sheets("IO").Range(addr).Offset(0, 4) psi = Sheets("IO").Range(addr).Offset(0, 5) d = Sheets("IO").Range(addr).Offset(0, 6) epsilon = Sheets("IO").Range(addr).Offset(0, 7) E = Sheets("IO").Range(addr).Offset(0, 8) nu = Sheets("IO").Range(addr).Offset(0, 9) ' MsgBox delta & " " & beta & " " & pt & " " & phi & " " & d & " " & epsilon & " " & E & " " & nu aa(i + 2) = delta & ", " aa(i + 4) = beta & ", " & pt & ", ," & psi & " " aa(i + 6) = d & ", " & epsilon & ", " aa(i + 8) = E & ", " & nu & ", " End If End If Next i ' updates input file Open fni For Output As #1 For i = 1 To nlines Print #1, aa(i) Next i Close #1 194 End Sub Function searchAddr(id, Rng) 'MsgBox "function: searchAddr" For Each x In Rng If Val(x.Value) = Val(id) Then searchAddr = x.Address Exit Function End If Next searchAddr = "" End Function Appendix P: ABAQUS Input Layer-Stacking Simulation This section documents an input file that illustrates a simple way to implement age-dependent material properties in ABAQUS. ** % Wall-Building Simulation: ** % 30 layers of fresh mortar ** % ** % Version: v4 ** % Date: 19 Aug 2012 ** % ** % Limitations: ** % 1) only modulus matures over time, w/notional linear trend ** % ** % UNITS: IN-Inch (pound f) ** % ... LENGTH : inch ** % ... TIME : sec ** % ... MASS : lbf-sec**2/in ** % ... FORCE : pound (lbf) ** % ... TEMPERATURE : deg Fahrenheit ** %========================================== *Heading ** Job name: Job-v3 Model name: Building_the_Wall_v3 ** Generated by: Abaqus/CAE Student Edition 6.11-2 *Preprint, echo=NO, model=NO, history=NO, contact=NO 195 [model…] ** %========================================== ** % MATERIAL DATA ** %========================================== ** % *Material, name=ROADMAT1 *Density 0.00012, *Drucker Prager 64., 0.,64. *Drucker Prager Hardening, type=SHEAR 0.8,0. *Elastic, dependencies=1 10., 0.25, , 0. 70., 0.25, , 30. ** % *Material, name=ROADMAT2 *Density 0.00012, *Drucker Prager 64., 0.,64. *Drucker Prager Hardening, type=SHEAR 0.8,0. *Elastic, dependencies=1 10., 0.25, , 1. 68., 0.25, , 30. [other layer materials…] ** %========================================== *Amplitude, name=TIME, time=TOTAL TIME 0., 0., 30., 30. ** %========================================== […] ** %========================================== ** % STEPS ** %========================================== ** % ** STEP: Step-1 *Step, name=Step-1, nlgeom=YES, inc=1000 *Static 0.1, 1., 1e-05, 1. ** 196 ** LOADS ** Name: GRAVITY-1 Type: Gravity *Dload ALLELEMENTS, GRAV, 1e-06, 0., 0., -1. *End Step ** ** STEP: Step-2 ** *Step, name=Step-2, nlgeom=YES, inc=1000 *Static 0.1, 1., 1e-05, 1. ** ** LOADS ** Name: GRAVITY-2 Type: Gravity *Dload PART-1-1.ROAD1, GRAV, 386.09, 0., 0., -1. ** *End Step ** ---------------------------------------------------------------- [other STEPS…]

Abstract (if available)

Abstract This research explores experimental and numerical techniques for the analysis of fresh concrete subjected to fabrication loads. The work is relevant wherever green, or uncured, concrete must be load-bearing, and is particularly relevant to an emerging fabrication technology called Contour Crafting, which fabricates civil structures additively with layered freeform depositions of fresh cementitious extrudate. In traditional concrete construction, rigid formworks are employed, like exoskeletons, to mold, protect and support concrete, and these molds are not removed until the concrete has developed considerable load-bearing strength. Contour Crafting dispenses with the rigid formwork, and therefore, contour-crafted concrete must be independently load-bearing immediately upon placement. This research develops techniques, tools and strategies for engineering the in-process fresh concrete subjected to these unprecedented fabrication loads.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Di Carlo, Tony (author)

Core Title Experimental and numerical techniques to characterize structural properties of fresh concrete

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publication Date 04/30/2013

Defense Date 09/11/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3D printing,additive-layer manufacturing,Concrete,contour crafting,Drucker-Prager plasticity,finite element analysis,green strength,Maturity,mortar,OAI-PMH Harvest,rapid prototyping,structural lightweight concrete

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Khoshnevis, Behrokh (committee chair), Carlson, Anders (committee member), Chen, Yong (committee member)

Creator Email tdicarlo@usc.edu,tony@dicarlo.us

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-107132

Unique identifier UC11288747

Identifier usctheses-c3-107132 (legacy record id)

Legacy Identifier etd-DiCarloTon-1262.pdf

Dmrecord 107132

Document Type Dissertation

Rights Di Carlo, Tony

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA