Testing and Evaluation of Confined Polymer Concrete Pile with Carbon Fiber Sleeve

Transcription

1 Testing and Evaluation of Confined Polymer Concrete Pile with Carbon Fiber Sleeve Item Type text; Electronic Dissertation Authors Toufigh, Vahid Publisher The University of Arizona. Rights Copyright is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 11/05/ :06:13 Link to Item

2 1 TESTING AND EVALUATION OF CONFINED POLYMER CONCRETE PILE WITH CARBON FIBER SLEEVE By Vahid Toufigh A Dissertation Submitted to the Faculty of the DEPARTMENT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY WITH A MAJOR IN CIVIL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 2013

3 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As member of Dissertation Committee, we certify that we have read the dissertation preparation by Vahid Toufigh entitled Testing and Evaluation of Confined Polymer Concrete Pile with Carbon Fiber Sleeve and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy Hamid Saadatmanesh Date Tribikram Kundu Date Lianyang Zhang Date John M. Kemeny Date Final approval and acceptance of this dissertation is contingent upon the candidate s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Dissertation Director: Hamid Saadatmanesh Date

4 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirement for an advanced degree at The University of Arizona and is deposited in The University of Library to be made available to borrowers under rules of the Library. Brief quotation this dissertation is allowable without special permission, provided that accurate acknowledgment of source is made. Request for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interested of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Vahid Toufigh

5 4 ACKNOWLEDGEMENTS I would like to thank all those who stood behind me and supported me throughout my life. First of all, I would like to thank God. I would like to thank my parents, Saleheh Jafari and Mohammad M. Toufigh, for all their love and support through my entire life. This dissertation would not have been possible without Professor Saadatmanesh who not only served as my advisor but also encouraged and challenged me throughout my academic program. I would like to thank Professor Saadatmanesh for the use of the constitutive modeling laboratory, helping me with the laboratory test, helping me with my PhD dissertation and journal manuscripts. I would like to thank Professor Budhu for his book. I also would like to thank my friends Vahab Toufigh, Ahad Ouria, Saeed Ahmari, Ehsan Mahmoudabadi, Ehsan Kabiri and Parisa Mansorian for their help. I would like to thank Professor Desai for let us to use his device. I would like to thank all my friends and my family for their support.

6 5 TABLE OF CONTENTS LIST OF FIGURES...12 LIST OF TABLES.30 ABSTRACT CHAPTER 1, INTERODUCTION General of Introduction History and Science of Foundation Engineering Type of Foundation Shallow Foundation Spread Footing Combined Foundation Mat Foundation Deep Foundation Pile Foundation Timber Pile Steel Pile Concrete Pile General Pile Analysis General Principle of Polymer Concrete General Principle of Fiber Reinforced Polymer General Principle Interface and Durability of Piles Scope of Study 56 CHAPTER 2, LITERATURE REVIEW General 58

7 6 TABLE OF CONTENTS Continued 2.2 Compressive Strength of Confined Cement Concrete Flexure Test of Confined Cement Concrete Durability of Confined Concrete Pile with Carbon Fiber Polymer Concrete Interface Shear Test between FRP and Dense Sand Interface between Drilled Pile (Cast-in-Pile) and Soil Axial Load Test on Cement concrete Pile Lateral Load Test on Cement concrete Pile Large Lateral Load Deflection Two Ways Cyclic load.. 81 CHAPTER 3, DESCRIPTION OF MATERIALS General Aggregates Polymer Concrete Aggregate Cement concrete Aggregate Carbon Fiber Carbon Fiber Sleeve Epoxy Resin Cement Water...95 CHAPTER 4, SPECIMENT PREPARATION LABORATORY TEST SETUP General Types of Aggregates Procedure for obtaining maximum dry bulk density of aggregate blend...98

8 7 TABEL OF CONTANTS-Continued Determining of maximum dry bulk density of mix G8 and G Determining of maximum dry bulk density of mix G8 and Sand Determining of maximum dry bulk density of mix G16 and Sand Determining of maximum dry bulk density of mix G8, G16, and sand Preparation of Unconfined Polymer Concrete Samples for Compression Test Epoxy Resin and Aggregate 1:2 (Volume Ratio of epoxy resin to aggregate by weight) Epoxy Resin and Aggregate 1:3 (Volume Ratio of epoxy resin to aggregate by weight) Epoxy Resin and Aggregate 1:4 (Volume Ratio of epoxy resin to aggregate by weight) Preparation of Confined Polymer Concrete with Carbon Fiber Sleeve for Compression Test Preparation of Plain Polymer Concrete for Splitting Test Confined Polymer Concrete Pile with Carbon Fiber Sleeve Preparation for Flexure Test, One way and Two way Cycling Load Carbon Fiber Sleeve Tensile Test Preparation Interface Shear Test and Direct Shear Test Preparation Preparation Unconfined and Confined Cement concrete Samples for Compression Test CHAPTER 5, ANALYSIS OF EXPERIMENT TESTING AND RESULTS General...119

9 8 TABEL OF CONTANTS-Continued 5.2 Compression Test Results for Different Ratios of Aggregates and Epoxy Resin with SoilTest CT Splitting Test Results Plain Polymer Concrete Compression test results and Stress and Strain Diagram for Unconfined Polymer Concrete Compression test results and Stress and Strain Diagram for Confined Polymer Concrete with Carbon Fiber Sleeve Compression Test Results and Stress and Strain Diagram for Unconfined Cement Concrete Compression Test Results and Stress and Strain Diagram for Confined Cement Concrete Summery Result discussion of Compression Test Tensile Test Results for Carbon Fiber Sleeve Samples Experimental Flexure Test Results Flexure Test Results for Confined Polymer Concrete Theoretical Analyses Theoretical Analyses to calculate natural axis, bending moment and bending stress for pile polymer concrete Theoretical Analyses to calculate load-displacement curve for pile polymer concrete...159

10 9 TABEL OF CONTANTS-Continued 5.13 Experiment Program and Set up for One Way cycling Load and Two way Cycling Load One Way Cyclic Load Test Two Way Cyclic Load Test Interaction Diagram Interface and Direct Shear Test set up and Analysis CHAPTER 6, NUMERICAL AND COMPUTER MODELING OF POLYMER CONCRETE PILE General PLAXIS Computer Program Introduction Mohr-Coulomb Model and Limitation Mohr-Coulomb Model Theory Hardening Soil Model and Limitation Hardening Soil Model Theory Interface Theory in PLAXIS Compare Experiment Results with PLAXIS Model Polymer Concrete in Compression Test Model Cemented Soil in Triaxial Test Model Cement concrete Pile in PLAXIS Polymer Concrete Pile Modeled in Axial Load at Different Length Size 233

11 10 TABEL OF CONTANTS-Continued 6.5 Polymer Concrete Pile Modeled in Axial Load at Different Type of Soil Model Straight Piles in Different Type of Soil Model Belled Drilled Pile in Different Type of Soil Compare Straight Piles with Belled Drilled Piles Model Piles in Different Type of Soil on Bed Rock General of Pile Lateral Load OpeenSeesPl Computer Program Theory of Material Definition Theory of Pile Definition Theory of Pile Definition Compare Experiment Results with OpenSeesPL Model Cement concrete Pile in OpeenSeesPL Cemented and Confined Polymer Concrete Pile Modeled in Lateral Load at Different Type of Soil 266 CHAPTER 7, DESIGN GUIDE General Piles Design Procedure for Axial Load in Cohesionless Soil Example for Piles Design Procedure for Axial Load in Cohesionless Soil Piles Design Procedure for Axial Load in Cohesion Soil..284

12 11 TABEL OF CONTANTS-Continued 7.5 Example for Piles Design Procedure for Axial Load in Cohesion Soil Piles Design Procedure for Lateral Load in Cohesionless Soil Example for Piles Design Procedure for Lateral Load in Cohesionless Soil Piles Design Procedure for Lateral Load in Cohesion Soil Example for Piles Design Procedure for Lateral Load in Cohesion Soil.316 CHAPTER 8, CONCLUSIONS. 318 REFERENCES...322

13 12 LIST OF FIGURES Figure 2.1 Axial Stress-Strain Relationships for Concrete with Glass Fiber Composite [Xiao and Wu 2003]...60 Figure 2.2 Axial Stress-Strain Relationships for Concrete with Carbon Fiber Composite Jackets [Xiao and Wu 2003]..61 Figure 2.3 Load-Deflection Curves for Specimens B1, B2 and B3 [Coleand and Fam 2006]..63 Figure 2.4 Degradation of Conventional Piles: Corroded Steel Pile (Left), Degraded Concrete Pile (Middle) and Deteriorated Timber Pile (Right) [Miguel 2002]..65 Figure 2.5 Shear Stress versus Horizontal Displacement (Direct Shear Test) for Ottawa Sand [Forst 1999]...69 Figure 2.6 Shear Stress versus Horizontal Displacement (Direct Shear Test) for Valdosta blasting sand [Forst 1999]..70 Figure 2.7 Shear Stress versus Horizontal Displacement (Interface Shear Test) between Ottawa Sand and FRP [Forst 1999]...70 Figure 2.8 Shear Stress versus Horizontal Displacement (Interface Shear Test) between Valdosta blasting Sand and FRP [Forst 1999].. 71 Figure 2.9a Stress Strain Curve of Cemented Sand [Ismail 2001]...73 Figure 2.9 b Stress-Strain Curves and Failure Envelope from Drained Triaxial Test on Cemented Sand [Ismail 2001] 74 Figure 2.10 Jack Applied Load on Pile [Ismail 2001]...75 Figure 2.11 Load-Displacements for Pile in Axial Load at Pile Head [Ismail 2001] 75

14 13 LIST OF FIGURES - Continued Figure 2.12 Lateral Tests on Concrete Pile [Ismail 1990].77 Figure 2.13 Load-Displacements for Piles in Lateral Load at Pile Head [Ismail 2001] 77 Figure 2.14 Lateral Displacement of Stabilizing Pile [Song 2012]...79 Figure 2.15 General View of the Jacket Frame [Memarpour 2012]..80 Figure 2.16 Lateral Deflections along the Pile Shaft in Cyclic Loading [Memarpour 2012]..81 Figure 2.17 Layout of Concrete Filled Fiber Reinforced Polymer Tube Beam/Pile Specimens [Shao, Y., and A, Mirmiran 2005]...82 Figure 2.18 Loading Regime for Concrete Filled Fiber Reinforced Polymer Tube Beam/Pile [Shao, Y., and A, Mirmiran 2005] Figure 2.19 Normalized Load Displacement Hysteretic Curve for Beam/Pile Specimen [Shao, Y., and A, Mirmiran 2005].84 Figure 2.20 Normalize Envelop Load Deflection Curves [Shao, Y., and A, Mirmiran 2005]..85 Figure 2.21 Load Displacements Hysteretic Curve for Column Specimen [Priestley and Benzoni 1996] 86 Figure 2.22 Normalize Envelop Load Deflection Curves [Priestley and Benzoni 1996]..86 Figure 3.1 Different Types of Aggregates for Polymer Concrete under this Study.89

15 14 LIST OF FIGURES - Continued Figure 3.2 Different Types of Aggregates for Cement concrete under this Study 90 Figure 3.3 Carbon Fiber Sleeve under this Study..92 Figure 3.4 Part A (left) and Part B (right) under this Study..94 Figure 4.1 Sieve Test Machine..98 Figure 4.2 Dry Densities vs. Percent Fine Aggregate (G8, G16)..99 Figure 4.3 Dry Densities vs. Percent Fine Aggregate (G8, Sand) Figure 4.4 Dry Densities vs. Percent Fine Aggregate (G16, Sand) Figure 4.5 Dry Density vs. Percent of Fine Aggregate for all Mix Design.102 Figure 4.6 Typical Specimen: with mold (left) without cap (middle) with cap (right) 107 Figure 4.7 Typical Specimen in Side Mold (left) and Sample out of Mold after Curing Process (right)..108 Figure 4.8 Confined Polymer Concrete Sample Cut (Left) and Adjust Sample Surface (Right)..108 Figure 4.9 Unconfined Polymer Concrete Sample Cut (Left) and Adjust Sample Surface (Right)..109 Figure 4.10 Polymer Concrete without Reinforced.110

16 15 LIST OF FIGURES - Continued Figure 4.11 Carbon Fiber Sleeve in side Paper Mold before Fill Fresh Polymer Concrete in side Mold.111 Figure 4.12 Pile Polymer Concrete Reinforced with Sleeve fiber Carbon..111 Figure 4.13 Prepare sample for Tensile Stress.112 Figure 4.14 Fiber Carbon Sleeve for Tensile Test Figure 4.15 Unsaturated Carbon Fiber Sleeve on Soil Figure 4.16 Polymer Concrete on Carbon Fiber Sleeve..114 Figure 4.17 Sample with Load 250kg and 50kg (Left) and 500kg and 0kg (Right)..115 Figure 4.18 Sample after Three days under Load 115 Figure 4.19 Sample Cut and Prepare for Interface Shear Test 116 Figure 4.20 Samples for Interface Shear Test under this Study..116 Figure 4.21 Unconfined Cement concrete (Left) Confined Cement concrete (Right) 118 Figure 5.1 SoilTest CT-6200 with Sample for Measure Compression Test 121 Figure 5.2 Mode of Failure of Aggregate and Epoxy Resin 122 Figure 5.3 Samples Testing for Splitting Test.124

17 16 LIST OF FIGURES - Continued Figure 5.4 Samples after Tension Test 124 Figure 5.5 Unconfined Polymer Concrete with Extensometer under MTS Load Frame Figure 5.6 Stress-Strain Curves for Sample 1 of Unconfined Polymer Concrete Figure 5.7 Stress-Strain Curves for Sample 2 of Unconfined Polymer Concrete Figure 5.8 Stress-Strain Curves for Sample 3 of Unconfined Polymer Concrete Figure 5.9 Unconfined Polymer Concrete Samples Results in Compression Test Together..128 Figure 5.10 Mode of Failure for Unconfined Polymer Concrete.129 Figure 5.11 Confined Polymer Concrete with Extensometer under MTS Load Frame Figure 5.12 Stress-Strain Curves for Sample 1 of Confined Polymer Concrete.130 Figure 5.13 Stress-Strain Curves for Sample 2 of Confined Polymer Concrete.131 Figure 5.14 Stress-Strain Curves for Sample 3 of Confined Polymer Concrete.131 Figure 5.15 Confined Polymer Concrete Samples Results in Compression Test Together Figure 5.16 Mode of Failure for Confined Polymer Concrete.132 Figure 5.17 Unconfined Cement concrete with Extensometer under MTS Load Frame Figure 5.18 Stress-Strain Curves for Sample 1 of Unconfined Cement Concrete...134

18 17 LIST OF FIGURES - Continued Figure 5.19 Stress-Strain Curves for Sample 2 of Unconfined Cement Concrete Figure 5.20 Stress-Strain Curves for Sample 3 of Unconfined Cement Concrete..135 Figure 5.21 Unconfined Cement concrete Samples Results in Compression Test Together Figure 5.22 Mode of Failure for Unconfined Cement Concrete. 136 Figure 5.23 Stress-Strain Curves for Sample 1 of Confined Cement Concrete..138 Figure 5.24 Stress-Strain Curves for Sample 2 of Confined Cement Concrete Figure 5.25 Stress-Strain Curves for Sample 3 of Confined Cement Concrete Figure 5.26 Confined Cement concrete Samples Results in Compression Test Together..140 Figure 5.27 Mode of Failure for Unconfined Cement concrete before and after Compression Test.140 Figure 5.28 Cement and Polymer Concrete Samples Results in Compression Test Figure 5.29 MTS with Sleeve Fiber Carbon with Extensometer.143 Figure 5.30 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 1) Figure 5.31 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 2) Figure 5.32 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 3)...145

19 18 LIST OF FIGURES - Continued Figure 5.33 Carbon Fiber Sleeve Samples Results in Compression Test Together Figure 5.34 Carbon Fiber Strip Samples were failed after Tensile Test..146 Figure 5.35 Confined Polymer Concrete Pile/Beam under Flexure Test 148 Figure 5.36 Flexure Test Diagram for Confined Polymer Concrete of Sample Figure 5.37 Flexure Test Diagram for Confined Polymer Concrete of Sample Figure 5.38 Flexure Test Diagram for Confined Polymer Concrete of Sample Figure 3.39 Load Displacement Diagram for Confined Polymer Concrete Pile/Beam Samples in Flexural Test Together..150 Figure 5.40 Confined Polymer Concrete Beam/Pile Samples Failed After Flexure Test.151 Figure 5.41 Compression Stress-Strain Diagram with an Equation Figure 5.42 Tensile Stress- Strain Diagram with an Equation.154 Figure 5.43 Cross Section of Piles with Angle of θ.156 Figure 5.44 Geometry and Force Effect on Cross Section..157 Figure 5.45 Moment Curvatures Curve Figure 5.46 Moment Curvature with an Equation

20 19 LIST OF FIGURES - Continued Figure 5.47 Load-Displacement Curves for Sample Figure 5.48 Theoretical and Experimental Curves Results Together..164 Figure 5.49 Theoretical Load Displacement Curves for Sample Figure5.50 Theoretical and Experimental Curves Results Together Figure 5.51 Theoretical Load Displacement Curves for Sample Figure 5.52 Theoretical and Experimental Curves Results Together..167 Figure 5.53 Theoretical Load Displacement Curves for Average Load Value Figure 5.54 Theoretical and all Experimental Curves Results Together. 168 Figure 5.55 Loading and Unloading Regime for Confined Polymer Concrete Beam/Pile..171 Figure 5.56 Hysteric Curves for One Way Cycling Load for sample Figure 5.57 Hysteric Curves for One Way Cycling Load for sample Figure 5.58 Static (Monotonic) Flexure Test Vs. One Way Cyclic Load of Sample Figure 5.59 Static (Monotonic) Flexure Test Vs. One Way Cyclic Load of Sample Figure 5.60 Snag of Confined Polymer Concrete beam/pile for Support and the Section which is apply the Load for Two Ways Cycling Load 174

21 20 LIST OF FIGURES - Continued Figure 5.61 Compressions (Pushing) Load and Tension (Pulling) Lode Regime for Confined Polymer Concrete Beam/Pile Figure 5.62 Beam/Pile when is in Compression (Pushing) Test.176 Figure 5.63 Beam/Pile when is in Tension (Pulling) Test Figure 5.64 Hysteric Curves for Two Ways Cycling Load.177 Figure 5.65 Normalized Load Displacements Hysteretic Curve for Beam/Pile..178 Figure 5.66 Normalize Envelop Load Deflection Curves Figure 5.67 Normalized Envelop Load Deflection Curve for Confined Polymer Concrete Beam/Pile with Carbon Fiber Sleeve Vs, Confined Concrete with Longitudinal Steel Rebar 179 Figure 5.68 Reinforced Cement concrete with Steel Rebar (left) and Confined Polymer Concrete with Carbon Fiber Sleeve (right)..182 Figure 5.69 Interaction Diagram Analyses of Cement concrete and Polymer Concrete..182 Figure 5.70 CYMDOF Devices under this Study 184 Figure 5.71 CYMDOF Device with Vertical Jack (Left) and Horizontal Jack (Right) 185 Figure 5.72 Sand in Bottom Box of CYMDOF Figure 5.73 Polymer Concrete Screws on Steel Pad 186 Figure 5.74 Aluminum Block on Upper Box...186

22 21 LIST OF FIGURES - Continued Figure 5.75 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 1000N..188 Figure 5.76 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 2000 N.189 Figure 5.77 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 4000 N.189 Figure 5.78 Normal Stress vs. Maximum Shear stress for sample Figure 5.79 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 1000N..190 Figure 5.80 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 2000N..191 Figure 5.81 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 4000N..191 Figure 5.82 Normal Stress vs. Maximum Shear stress for sample Figure 5.83 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 1000N..192 Figure 5.84 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 2000N..193 Figure 5.85 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 4000N..193 Figure 5.86 Normal Stress vs. Maximum Shear stress for sample

23 22 LIST OF FIGURES - Continued Figure 5.87 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 1000N..195 Figure 5.88 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 2000N Figure 5.89 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 4000N Figure 5.90 Normal Stress vs. Maximum Shear stress for sample Figure 5.91 Direct Shear Test Results for Sand with Normal Load of 1000N 199 Figure 5.92 Direct Shear Test Results for Sand with Normal Load of 2000N Figure 5.93 Direct Shear Test Results for Sand with Normal Load of 4000N 200 Figure 5.94 Normal Stresses vs. Maximum Shear Stress for Sand. 201 Figure 6.1 The Mohr Coulomb yield surface in principle stress space [PLAXIAS b.v. 2006] 207 Figure 6.2 Hyperbolic stress-strain relation in primary loading for a standard drained triaxial test [PLAXIAS b.v. 2006] Figure 6.3 Definition of Eoedref in oedometer test results [PLAXIAS b.v. 2006].212 Figure 6.4 Representation of total yielding contour of the Hardening Soil model in Principal stress space for cohesion soil [PLAXIAS b.v. 2006] Figure 6.5 Mohr Circle for Unconfined Polymer Concrete for Calculate φ and c..218

24 23 LIST OF FIGURES - Continued Figure 6.6 Mohr Circle for Confined Polymer Concrete for Calculate φ and c Figure 6.7 Unconfined Polymer Concrete PLAXIS Model 222 Figure 6.8 Confined Polymer Concrete PLAXIS Model 222 Figure 6.9 Stress Strain Curves of Computer Model and Experiment for Unconfined Polymer Concrete Figure 6.10 Stress Strain Curves of Computer Model and Experiment for Confined Polymer Concrete.223 Figure 6.11 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 100 kpa.225 Figure 6.12 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 200 kpa.226 Figure 6.13 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 300 kpa.226 Figure 6.14 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 400 kpa.226 Figure 6.15 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 100 kpa 227 Figure 6.16 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 200 kpa 227 Figure 6.17 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 300 kpa 228

25 24 LIST OF FIGURES - Continued Figure 6.18 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 400 kpa 228 Figure 6.19 Mohr Coulomb, Hardening Soil Model and Ismail Experiment Deviatoric Stress-Strain Graph at all Horizontal Principle Stresses..229 Figure 6.20 Mohr Circle for Unconfined Cement concrete for Calculate φ and c..230 Figure 6.21 Cement Pile Model into Cemented Sand (Right), Mesh of Pile before Run the Program (Middle) and Mesh of Pile after Run the Program (Left) Figure 6.22 Load Displacement of Experiment Test (Blue Line), Hardening soil Model (Red Dash Line) and Mohr Coulomb Theory (Green Point Load)..233 Figure 6.23 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 5 m Length and 0.3 m Diameter..234 Figure 6.24 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 10 m Length and 1 m Diameter Figure 6.25 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 20 m Length and 1 m Diameter Figure 6.26 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 20 m Length and 1 m Diameter Figure 6.27 Confined Polymer Pile Model into Soil (Right), Mesh of Pile before Run the Program (Middle) and Mesh of Pile after Run the Program (Left).237 Figure 6.28 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Loose Sand 238

26 25 LIST OF FIGURES - Continued Figure 6.29 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Dense Sand 239 Figure 6.30 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Soft Clay Figure 6.31 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Stiff Clay Figure 6.32 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Hard Clay Figure 6.33 Bottom Part of Belled Drilled Cement concrete Pile in Plaxis Model.242 Figure 6.34 Bottom Part of Belled Drilled Confined Polymer Concrete Pile in Plaxis Model Figure 6.35 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Loose Sand 244 Figure 6.36 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Dense Sand Figure 6.37 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Soft Clay Figure 6.38 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Stiff Clay Figure 6.39 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Hard Clay...245

27 26 LIST OF FIGURES - Continued Figure 6.40 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Loose Sand Figure 6.41 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Dense Sand..248 Figure 6.42 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Soft Clay.248 Figure 6.43 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Stiff Clay Figure 6.44 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Hard Clay.249 Figure 6.45 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Loose Sand..252 Figure 6.46 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Dense Sand..253 Figure 6.47 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Soft Clay..253 Figure 6.48 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Stiff Clay..253

28 27 LIST OF FIGURES - Continued Figure 6.49 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Hard Clay..254 Figure 6.50 Cover Patch and Core Patch for Nonlinear Beam/Pile Element-Fiber Section [Mazzoni 2006] Figure 6.51 Multi Surface in Principle Stress Space and Deviatoric Plane [OpenSeesPL 2010] 259 Figure 6.52 Von Mises Multi Surface [OpenSeesPL 2010] 260 Figure 6.53 Finite Element Full Mesh for Ismail Pile in Cemented Sand in Cemented Sand Dome with General Mesh Definition..264 Figure 6.54 Load Displacement of Ismail Experiment Test (Red Line) and Load Displacement of OpenSees PL Computer Analysis (Dash Blue Line) 265 Figure 6.55 Model of Polymer Concrete Pile which Confined with Carbon Fiber Sleeve Figure 6.56 Finite Element Full Mesh for cement concrete pile and Confined Polymer Concrete pile in Soil Dome with General Mesh Definition.269 Figure 6.57 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Loose Sand..270 Figure 6.58 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Dense Sand Figure 6.59 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Soft Clay...270

29 28 LIST OF FIGURES - Continued Figure 6.60 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Stiff Clay.270 Figure 6.61 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Hard Clay Figure 7.1 Soil Profile and Stress Diagram for Example 1 [Prakash 1990] 281 Figure 7.2 Soil Profile for Example 2 [Prakash 1990] 289 Figure 7.3 Rotation and Translation Movement for Free Head Short Pile (left), Soil Reaction and Bending Moment in Cohesive Soils (middle) and Soil Reaction and Bending Moment in Cohesionless Soils (Right) [Broms 1964]..295 Figure 7.4 Ultimate Lateral Load Capacity and Resistance for Short Pile in Cohesionless Soil Related to Embedded Length [Broms 1964] 296 Figure 7.5 Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesionless Soils for Free Head Long Pile (left) and Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesive Soils for Free Head Long Pile (Right) [Broms 1964] Figure 7.6 Ultimate Lateral Load Capacity and Resistance for Long Pile in Cohesionless Soil Related to Ultimate Resistance Moment [Broms 1964] Figure 7.7 Rotation and Translation Movement for Fixed Head Short Pile (left), Soil Reaction and Bending Moment in Cohesive Soils (middle) and Soil Reaction and Bending Moment in Cohesionless Soils (Right) [Broms 1964]..299 Figure 7.8 Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesionless Soils for Fixed Head Long Pile (left) and Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesive Soils for Fixed Head Long Pile (Right) [Broms 1964]...300

30 29 LIST OF FIGURES - Continued Figure 7.9 Soil Profile for Example 3 [Prakash 1990].305 Figure 7.10 Ultimate Lateral Load Capacity and Resistance of Short Pile in Cohesive Soil [Broms 1964] Figure 7.11 Ultimate Lateral Load Capacity and Resistance of Short Pile in Cohesive Soil [Broms 1964] Figure 7.12 Coefficients of Moments A mc and Deflection A yc vs. Coefficients of Depth z [Davisson and Gill 1963].314 Figure 7.13 Coefficients of Moments B mc and Deflection B yc vs. Coefficients of Depth z [Davisson and Gill 1963].315

31 30 LIST OF TABLES Table 1.1: Size of Butt and Tip Related with Length of Timber Pile Foundation [Robert. E. Krieger 1987].45 Table 2.1 results of Samples from Compressive Test...61 Table 2.2 Summary of Test Matrix of Beam Specimens [Coleand and Fam 2006]..62 Table 2.3 Mechanical Properties of FRP Pile Material [Nehdi 2007] Table 2.4 Soil Friction Angle and Interface Friction Angle [Nehdi 2007] 68 Table 2.5 Friction angles between sand itself and sand/frp [Forst 1999] 71 Table 2.6 Specimen size [Shao, Y., and A, Mirmiran 2005].82 Table 3.1 Mechanical Properties of Biaxial Sleeve Carbon Fiber. 92 Table 3.2 Properties of Epoxy Resin...94 Table 4.1 Weight and Density of Each Different Mixer for G8 and G Table 4.2 Weight and Density of Each Different Mixer for G8 and Sand.. 100

32 31 LIST OF TABLES- Continued Table 4.3 Weight and Density of Each Different Mixer for G16 and Sand 101 Table 4.4 Weight and Density of Each Different Mixer for three Aggregates Table 4.5 Weight and Density of Each Different Mixer for three Aggregates Table 4.6 Trial Sample Mix.106 Table 4.7 Measure of Each Material to Make Cement concrete by Total Weight Percentage 117 Table 5.1 Result for Compression Test with Different Ratios of Aggregate and Epoxy Resin 122 Table 5.2 Maximum Load and Tension Results for each Sample Table 5.3 Compression Test Results for Unconfined Polymer Concrete 128 Table 5.4 Compression Test Results for Confined Polymer Concrete 132 Table 5.5 Compression Test Results for Unconfined Cement Concrete.135 Table 5.6 Compression Test Results for Confined Polymer Concrete 139

33 32 LIST OF TABLES- Continued Table 5.7 Compression Test Results for Cement and Polymer Concrete with and without confined Table 5.8 Summery Results of Carbon Fiber sleeve in Tensile Test Table 5.9 Results of Flexure Test for Confined Polymer Concrete Pile/Beam Table 5.10 different percentage of maximum curvature and bending moment Table 5.11 Theoretical Results of Load Displacement of Sample 1 for Flexure Test.163 Table 5.12 Theoretical Results of Load Displacement of Sample 2 for Flexure.164 Table 5.13 Theoretical Results of Load Displacement of Sample 3 for Flexure Test.166 Table 5.14 Theoretical Results of Load Displacement of Sample 3 for Flexure Test.167 Table 5.15 Loading and Unloading Procedure for Apply One Way Cyclic Load on Confined Polymer Concrete Beam/Pile Table 5.16 Compression (Pushing) Load and Tension (Pulling) Lode Procedure for Apply Two Ways Cyclic Load on Confined Polymer Concrete Beam/Pile Table 5.17 Mechanical Properties of columns.182

34 33 LIST OF TABLES- Continued Table 5.18 Load Rate of Interface Shear Test for Normal Load of 1000 N 187 Table 5.19 Load Rate of Interface Shear Test for Normal Load of 2000 N 187 Table 5.20 Load Rate of Interface Shear Test for Normal Load of 4000 N 188 Table 5.21 Normal Stress vs. Maximum Shear Stress for Sample Table 5.22 Normal Stress vs. Maximum Shear Stress for Sample Table 5.23 Normal Stress vs. Maximum Shear Stress for Sample Table 5.24 Normal Stress vs. Maximum Shear Stress for Sample Table 5.25 Load Rate of Direct Shear Test for Normal Load of 1000 N Table 5.26 Load Rate of Direct Shear Test for Normal Load of 2000 N 198 Table 5.27 Load Rate of Direct Shear Test for Normal Load of 4000 N 198 Table 5.28 Normal Stress vs. Maximum Shear Stress for Sand..200

35 34 LIST OF TABLES- Continued Table 6.1 Unconfined Polymer Concrete Parameter for Mohr Circle.217 Table 6.2 Confined Polymer Concrete Parameter for Mohr Circle.218 Table 6.3 Summery of Mechanical properties of Carbon Fiber Sleeve, Polymer concrete and Geometry of Polymer Concrete 221 Table 6.4 Mechanical Properties of Cemented Sand [Ismail 2001] 225 Table 6.5 Cement concrete Parameter for Mohr Circle Table 6.6 Summery of Mechanical properties of Cement concrete Pile and Geometry of Cement concrete Pile Table 6.7 Mechanical Properties of Different Type of Soil.238 Table 6.8 Mechanical Properties of Lime Stone..252 Table 6.9 Mechanical Properties of Cement concrete at Core and Cover Patch for Ismail Pile Table 6.10 Mechanical Properties of Steel Bar for Ismail Pile 262 Table 6.11 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element for Ismail Pile...262

36 35 LIST OF TABLES- Continued Table 6.12 Mesh Properties Base of General Definition for Lateral Load Analysis on Ismail Cement concrete Pile Table 6.13 Mechanical Properties of Cement concrete at Core and Cover Patch..266 Table 6.14 Mechanical Properties of Steel Bar Table 6.15 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element Table 6.16 Mechanical Properties of Polymer Concrete at Core and Cover Patch.268 Table 6.17 Mechanical Properties of Carbon Fiber Sleeve.268 Table 6.18 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element Table 6.19 Mesh Properties Base of General Definition for Lateral Load Analysis on Cement concrete Pile and Confined Polymer Concrete Pile Table 7.1 Value for Ks for Various Pile Types in Sands [Prakash 1989] Table 7.2 Value for Nq and φ [Prakash 1989] 275 Table 7.3 Typical Value of Coefficient C p [Prakash 1989].279

37 36 LIST OF TABLES- Continued Table 7.4 Value of N c for vs. Depth of Pile Diameter (D f /B) Ratio [Prakash 1989] Table 7.5 Values of N c for Various Pile Diameters (B) [Canadian Foundation Design Manual] 285 Table 7.6 Effective Pile Length (L e ) of Driven and Drilled Piles 286 Table 7.7 Group Efficiency Value for Vs. Pile Spacing..286 Table 7.8 Recommended Values of n h for Submerged Sand Table 7.9 Coefficient A and B for Free Head Long Pile [Matlock and Reese 1962]..303 Table 7.10 Group Reduction Factor for the Coefficient of Subgrade Reaction [Davission 1970] 304

38 37 ABSTRACT The goal of this research is to investigate the behavior of polymer concrete confined with a carbon fiber sleeve used as a pile foundation. To evaluate the behavior of a confined polymer concrete pile in this research, four steps was considered. The first step of this investigation considered the mix design of polymer concrete, polymer concrete is a new material which is a combination of epoxy resin and aggregate. Instead of using a traditional mix of cement and water to make concrete, epoxy resin is used. Three dissimilar varieties of aggregate are mixed with different ratios in order to reach the maximum bulk density to obtain the maximum strength. After discovering the optimum ratio which gives the maximum bulk density, several samples of the aggregate are mixed with different ratios of epoxy resin. Next, the samples are investigated in a compression test to observe which ratios have the maximum strength and this ratio is used for a polymer concrete mix design to create a pile foundation. The pile is a built using a cast in place method and confined with a sleeve of carbon fiber. The second part of this investigation determined the structural mechanical properties of confined polymer concrete pile material. The unconfined and confined polymer concrete was tested in compression to determine compressive strength and stress-strain behavior. Similar tests were conducted on unconfined and confined cement concrete for comparison between these materials. Additional tension tests were conducted on unconfined polymer concrete. Then, a carbon fiber sleeve was tested in compression test to determine tensile strength and tension stress-strain behavior. After these tests, the confined polymer concrete is modeled in the computer program MATTCAD which is

39 38 used to calculate the theoretical bending moment capacity and load-displacement curve. Finally, the confined polymer concrete is tested with the MTS 311 Load Frame in three point load flexure test to determine the experimentally bending moment capacity, loaddisplacement curve and compare with theoretical results. Confined polymer concrete was tested in one and two way cyclic loading to observe the ductility behavior of this material as laterally loaded piles and compared with cement concrete results in cyclic loading. The third part of this investigation determined the geotechnical mechanical properties of confined polymer concrete pile material. Cyclic Multi Degree of Freedom (CYMDOF) device was used to determine interface reaction and friction angle between confined polymer concrete and soil with interface shear test theory method. Furthermore, the same device was used to determine the friction angle of soil with direct shear test theory, and compare the friction angle results together. The last part of this investigation considered the behavior of different sized confined polymer concrete pile in different types of soil. A confined polymer concrete pile was modeled into PLAXIS and OPENSEES PL computer software to analysis pile in axial load and lateral load respectively. Furthermore, a cement concrete pile was modeled with similar software and conditions to compare these two materials.

40 39 CHAPTER 1 INTRODUCTION 1.1 General of Introduction The purpose of this chapter is to review and study differing types of foundations common to civil engineering. The main goal of this research is to investigate the behavior of Confined Polymer Concrete with carbon fiber sleeve and used as a pile foundation. 1.2 History and Science of Foundation Engineering Humans first used foundations to improve and stabilize their homes. Early foundations were made of clay mud which helped anchor the home and provided better construction. The earliest foundations date back to 2000 BC and were a part of the great Egyptian empire. The great pyramids were built on foundations. In 500 BC, the Romans built giant statues on foundations to increase their structural integrity. Foundation engineering is a branch of civil engineering which is derived from structural engineering and geotechnical engineering. Foundation engineering is used to describe the connection and transfer of loads between the structure and soil or rock. A foundation helps prevent the structure from settling, rotating, or sliding. Foundations are considered to be a structure and they are typically constructed from concrete, steel and wood. Before designing a foundation, several properties need to be noted. These include the type of soils near the foundation, the location of rock and bed rock, and type of structure and load that will be placed on the foundation.

41 40 The properties of the soil beneath the foundation are related to the physical and chemical behavior of soil and rock. The forces generated by soil and rock will have an effect on the foundation. There have been numerous studies and investigations on the behavior of soil and rock on foundations. This is what is known as the branch of civil engineering called geotechnical engineering. The properties of the structure needed for foundation design is related to the physical behavior and weight of the structure. The foundation will support the structure and all loads are transferred to the foundation and foundation transfer load to soil or rock below. 1.3 Type of Foundation The skill and art of designing foundations that are the most functional and economical for a project are derived from careful investigation by the engineer. Excellent knowledge in soil mechanics, geology engineering and structural engineering and experience are necessary for a well-designed foundation. Civil Engineers design foundations based on soil/rock properties, weight of the structure, and economical decisions. Several types of natural loads such as wind loads, seismic, and environmental factors can also have an effect on foundations. Different types of foundations provide better design alternatives for differing situations. Differing foundation type, size and shape will provide multiple ways to transfer the load from the structure to the soil. There are two types of foundations that are very common to civil engineering. The first type is referred to as a shallow foundation which includes foundations such as spread footings, combined footings and mat foundations. The second type is known as deep foundations and these include pile and pier foundations and caissons.

42 Shallow Foundation A shallow Foundation is a type of foundation that transfers load from the structure close to the surface of the earth. Shallow foundations rely solely on the bearing capacity of the soil beneath them. As previously mentioned, there are several types of shallow foundations. In this section different types of shallow foundations are briefly discussed Spread Footing Spread footing are constructed with concrete and reinforced with steel bar (reinforced concrete). They usually have the shape of a square and are sometimes rectangular. Spread foundations typically have a length (L) to width (B) ratio less than 1.5. Spread footings are sometimes referred to as isolated foundations or individual foundations. Spread footings transfer the column load of a structure to the soil beneath the footing. If structure has six columns, each column could potentially have an individual spread footing to individually transfer the load from the columns to the soil beneath the footings. In this condition, each footing is working independently from the other footings. In this type of situation there can be different amounts of settlement between the foundations and the amount of settlement should not exceed allowable limits for total and differential settlement. Footings are typically designed with reinforced concrete cast straight onto the soil, and are typically embedded into the ground to penetrate through the zone of frost and obtain additional bearing capacity. In foundation design, geotechnical engineers focus primarily on the bearing capacity and estimation of settlement, while structural engineers focus on the type of concrete and rebar needed for a sufficient foundation.

43 Combined Foundation If a spread footing overlaps with another spread footing, the two can be combined to form a combined foundation. When the soil under a structure has a low or medium compressibility, and differential settlement between each column has to be controlled within certain limits, civil engineers should design combined footing instead of spread footings. Combined foundations are designed by engineer as a beam between columns on soil. Columns are modeled as a point load on the combined foundation (beam) and soil reacts on the combined foundation as distributed load. In this type of foundation design there are several imported aspects for the engineer to consider such as the bearing capacity, settlement, and type of concrete and rebar Mat Foundation A mat foundation is a combined foundation that covers all the area under a structure and supports all loads from the structure. Engineers should design mat foundations instead of combined foundation when the soil under structure has a high or very high compressibility, the allowable soil pressure is small and the structure above soil is heavy. Mat foundations are also used to reduce the settlement of structures. For geotechnical engineers, the design of mat foundations is similar to the design of spread footings. For structural engineers, the design of mat foundations is the same as the design of concrete slabs. Mat foundations are typically very large and are there not very economical to use. Usually pile and pier foundations are preferable in high rise buildings and bridges.

44 Deep Foundation Deep foundations are used for heavy structures when shallow foundations cannot provide enough capacity due to size and structure limitations. They may also be used to transfer building loads past weak or compressible soil layers. While shallow foundations rely solely on the bearing capacity of the soil beneath them, deep foundations can rely on end bearing resistance, friction resistance along their length, or both in developing the required capacity. Geological engineers typically use in situ tests to estimate the properties of the soil. The most popular and common test for the design of foundations is the Standard penetration test (SPT) and Cone penetration test (CPT). The SPT is used to estimate the description of soil, unit weigh, relative density and friction angle. The CPT is used to estimate the amount of skin and end bearing resistance available in the surface. They are several types of deep foundations used today such as pile or pier foundations and caisson foundations. This research focused on the investigation of pile foundations composed of polymer concrete Pile Foundation Pile foundations are the most widespread type of deep foundation and they consist of a long and slim column shape. The scale of the pile depends on the soil properties beneath the structure and the loads. The structural loads are transferred deep into the ground by the piles. Engineers use pile foundations to significantly decrease the structural settlement. Piles are designed to work together as a group to transfer load from the pile cap (shallow foundation) to deep soil or rock. Most bridges are designed with pile foundations because piles transfer the load to the supporting stratum below the water table.

45 44 When surface soil has a low bearing capacity and the compressibility of the soil is found to be high. Engineers use pile foundations to transfer the load through the surface soil to deeper soil or rock strata for adequate bearing capacity and stiffness, with smaller vertical displacement. Pile foundations are efficient and more economical than shallow foundations carried to the same depth in the form of a block. When the depth of weak soil near the surface is greater than 4 meters, engineers typically recommend pile foundations. Piles that are hammered into the soil or rock are known as driven piles and piles that are installed in a predrilled hole is a drilled pile. [Zdenek B, 1979] Timber Pile Wooden or timber piles are the oldest pile foundation type. They were used for many centuries. In some areas of the world, timber piles are still more common and easier to construct than the other types of pile foundations (steel and concrete). The use of timber piles typically correlate to large regions of forest or with cheap imported lumber. They are commonly used in North America, Europe, china, Southeast Asia and Scandinavia Timber piles are made with the trunks of tall trees, usually the center of tree trunk, it is stronger than the periphery. Timber piles can have differing cross sections, most likely circular or sometimes they can be square. Timber piles are usually circular or square at the top and at the bottom they have a narrow tip. Timber pile foundations are assembled in the field by driving them into soil with drop hammers. To protect the timber pile during installation, two methods are used. The first method uses steel shoes under the piles around the tip to only protect around the tip section. The second method uses a steel

46 45 pipe around the wood section to protect all sections of the timber pile. [Robert. E. Krieger 1987] Timber piles have a several disadvantages, timber cannot be suitable for large scale loads and timber pile s material (wood) is not a homogeneous material. Strength and geometry of timber piles is not constant; furthermore timber piles are driven piles, and dropping heavy hammers on the pile can cause cracks. One of the disadvantages of timber pile foundations is the limitation to the length of the pile. This limitation depends on the type of wood; which is usually between 10 to 30 meters or 30 to 100 feet. Although with Douglas fir timber, the engineer can increase a piles length to 40 meters or 130 feet. As mentioned before, a timber pile has a circular cross section at top and at bottom they have a tip shape, the size of timber piles are tabled below related by length of piles as Table 1.1 [Peck B 1974][ Robert. E. Krieger 1987]. Length of Piles (m, ft) Diameter of pile at Butt (cm, in) Diameter of pile at Tip (cm, in) 12, , , , , , , , , Table 1.1: Size of Butt and Tip Related with Length of Timber Pile Foundation [Robert. E. Krieger 1987] The main advantages of timber pile foundations is that they can stay underground in water and survive for long time compared to other types of pile foundations (steel and concrete). In Venice, Italy timber piles were used four hundred years ago and they still are functional. Timber piles also have some advantages to the environment and they are easy to assemble and economical when compared to other types of pile foundations.

47 Steel Pile Foundation Piles foundations are needed when soil and ground conditions are not suitable to support the structure. Steel pile foundations are used as deep foundations to transfer the axial and lateral loads from structure to soil and rock. One of the most common driven pile foundations is a steel pile or steel column. This type of pile has the same strength as a structural column. Steel piles give the highest load value compared to any other type of pile foundation. [Robert. E. Krieger 1987] Steel pile foundations are able to transfer heavy loads with small cross sections and long lengths deep into the soil. The recommended maximum stress and length to use steel piles is 60 MPa (8.7 ksi) and 30 m (98.4 ft) respectively. Steel piles foundations are suitable for driving in long lengths. Steel piles have a relatively small cross section area and combined with their high strength it makes their penetration easier and safer in stiff soil or rock. Steel piles have minimum damage during driving and a small cross section compared to other types of driven pile foundations (concrete and timber). Steel piles can be easily cut off or joined by welding and they are the best type of pile foundation for end bearing in rock. Steel is an expensive material to use as a long pile foundation and it is more economical to use concrete and timber as the materials for a pile foundation. One of the main disadvantages for steel piles is corrosion. Steel piles can corrode in saturated soils and at the ground surface and this can be especially dangerous in seismic loads. Usually, the corrosion process damages piles for up to 50 years. Normally the speed of corrosion is mm/year ( in/year), but in design, engineers estimate the speed of corrosion to be 1 mm/year (0.04 in/year).

48 47 Steel pile foundations have several shapes. The most common shape is a steel H- pile (H beam) and steel pipe pile. Steel H piles are used for structure designs in bridges. Steel H beam piles are penetrated into hard soil very easily. AISC recommends the maximum stress for H-piles for design is MPa ( ksi). Another type of steel pile foundation is a pipe pile foundation which is a cylinder shape. Pipe pile foundations are driven into soil either open ended or close ended. Engineers use open end pipe foundations to allow soil to enter from the bottom into the pipe pile. Closed end pipe piles are designed by covering the bottom of the pile with steel shoe (steel plate). Often engineers use closed end pipe piles to increase the moment generated by filling concrete in the pipe pile. Pipe piles are calculated based on steel strength and concrete strength if filled Concrete pile Foundation These types of pile foundations are made by concrete and reinforced with steel bars. The engineer uses concrete piles instead of timber piles based on three conditions. 1. Under super structures where timber piles are not suitable to be used because of their insufficient bearing capacity, concrete piles are stronger than timber piles. 2. Where ground water conditions make the use of timber piles undesirable for example; if the groundwater table is deep below the ground surface or groundwater table has a fluctuation 3. In places where timber piles are not available

49 48 Normally the engineer uses two types of foundations for design; precast or readymade piles which are driven piles and cast in place concrete piles which are drilled piles. [Robert. E. Krieger 1987] Precast concrete piles are reinforced concrete columns penetrated into the soil. These types of piles are referred to as prestressed concrete piles, cylindrical concrete piles and solid concrete piles. Precast concrete pile foundations are the most common pile foundations to use throughout the world over; they are suitable for bridge foundations, structural foundations and marine construction. Based on geological conditions, this type of foundation is easily driven into the loose and soft soil. Precast concrete piles have a disadvantage. The main disadvantage is that they can easily be damaged during penetration. Another disadvantage of precast concrete piles is their fixed length which cannot be varied to suit the varying levels of the bearing stratum and must, therefore, be modified by cutting. This type of pile is not like steel piles which are easily cut and welded. Precast concrete piles must have a symmetric cross section because bending is apt to occur in any inclined plane. Precast concrete piles are economical to use around 12 m (39.37 ft) length. [Zdenek Bazant 1979] Another type of concrete pile is a cast in place concrete pile which is a drilled pile. Engineers excavate soil from the ground which is the same size of the pile and insert concrete mortar cast inside the excavation to the exact length required. There are many types of cast in place concrete piles, engineers used them in designed to satisfy geological and other conditions. Cast in places concrete piles are suitable to carry heavy loads compared to precast concrete pile.

50 49 Advantages of cast in place piles are that, these types of foundations have excellent wall friction due to chemical bond between fine grain soil and cement. There is no hammer noise during the construction. When piles are driven by hammer, the ground vibration may cause damage to a nearby structure, which the use of drilled shafts avoids. [Zdenek Bazant 1979]. 1.4 General Pile Analysis Piles are generally used in groups. However, the allowable or design load is always determined from a single pile. In most situations, behavior of a single pile is different from that of a pile group. Therefore, procedures will be developed to determine the allowable loads of a pile group from that of the single pile. The design load may be determined either from consideration of shear failure or settlement and is lower of the following two values; allowable load obtained by dividing the ultimate failure load with a factor of safety and load corresponding to an allowable settlement of the pile. The most important loads applied to a pile is axial load and lateral load. Axial load or vertical load was applied as a large scale load from the structure above into the pile, this load is sheared between the bearing at pile tip and shaft friction around the pile perimeter. For example, if Q v is the axial compressive ultimate load on pile foundation is shared by the pile tip, Qp, and by the friction resistance, Qf, around the pile shaft. This can be represented by the following relationship, [Prakash, S. 1989] Q v = Qp + Qf (1.1)

51 50 Pile foundations are frequently required to carry inclined loads which are the resultant of the dead load of the structure and horizontal load from wind, water pressure and earthquake on the structures. For these type of loads engineers need to design and analyze the lateral load capacity for piles [Tomlinson 1967]. The lateral load of a pile may be divided broadly into the two categories of active loading, where external loads are applied to the pile, with the soil resisting the load, and passive loading, where movement of the soil subjects the pile to bending stress. [Fleming 1985] 1.5 General Principle of Polymer Concrete Civil engineers have always considered cement concrete to be one of the most common construction materials. Cement concrete is a composite material consisting of fine and coarse aggregates bonded together with cements and water paste. The main disadvantages of concrete are 1) it takes around one month to fully cure, and 2) it is extremely weak in tension when compared to compression. Today, there are new materials that are available which allow concrete to be stronger in tension when compared to its compression, and it takes only few hours to fully cure, depending on the temperature. Polymer concrete behaves stronger under compression than regular concrete. Concrete containing epoxy resin is a combination of two types of chemical materials; part A, Medium Viscosity Epoxy resin and part B, Epoxy Hardener. Instead of using only cement and water to formulate the concrete mixture, epoxy resin is used to hold the aggregates together. 1.6 General Principle of Fiber Reinforced Polymer

52 51 In the past few decades, Fiber Reinforced Polymer (FRP) composites have been developed and utilized in civil engineering, construction, automotive, marine and aerospace industries, just to name a few. Research and applications have proven that FRP composites are far more efficient and highly advantageous for retrofitting techniques than conventional materials. Some common applications are as follows: 1. Increasing the structural integrity and strength to withstand underestimated loads or correcting design errors/omissions 2. Increasing the load bearing capacity 3. Compensating for lost materials due to deterioration 4. Eliminating premature failure due to inadequate detailing It has been observed and universally accepted that replacing conventional materials with FRP composites eliminates many issues associated with strengthening concrete and steel structures due to such characteristics as the high strength to weight ratio, resistance to corrosion, excellent fatigue strength, versatility, and economics. However, there are issues that affect the material properties of the FRP; primarily the problems associated with environmental conditions, e.g. the effects of thermal loading on the effective lifespan and mechanical properties of FRP, along with the FRP/substrate interfacial bond strength. A fiber reinforced polymer (FRP) is a composite material comprising a polymer matrix reinforced with fibers. The fibers are usually carbon, glass, and/or aramid, while the polymer is usually an epoxy resin, vinyl ester or polyester thermosetting plastic. A composite structural material contains high strength fibers embedded in a resin matrix

53 52 which together develops mechanical properties greatly superior than those of the individual components. The fiber reinforced polymer (FRP) industry today is experiencing significant growth as more products are made from reinforced plastic for greater durability, strength and life. Thousands of products are now manufactured from reinforced plastics including building materials, sporting equipment, appliances, automotive/aircraft parts, boat and canoe hulls, and bodies for recreational vehicles. In this study the polymer concrete was coated by carbon fibers or fiber glass (Fiber Reinforced Polymers) for use as a pile foundation. In the early 1960 s, fiber reinforcement started with the use of smooth and straight fibers. This type of reinforcement has improved throughout the years with the use of different fiber materials with a coat around the body of structural column, beam and pile. The factors that control the performance of Fiber Reinforced Polymer Concrete (FRPC) are the properties of fibers, characteristics of the matrix, and the bonding strength between the fibers and matrix. In the samples used for these tests, fibers carbons or fiber glass are bounded around body of column or pile to made polymer concrete stronger, and it is generally impossible to achieve a high fiber carbon reinforcement ratio. 1.7 General Principle of Interface and Durability of piles Drilled pill foundations have been extensively used throughout world. In the last decade the improvement of drilling augers and drilling machines has made it possible to drill economically a pile in to the standard size. there are two types of drilled pile, the straight pile and the belled shaft. For belled shaft, the base resistance and uplift resistance are increased. The load on a drilled shaft is transferred to the surrounding soil, as in a driven pile, by shaft side resistance and bottom resistance. The amount of load carried by

54 53 shaft side resistance and bottom resistance is dependent on the size of the pile and on the shear strength of the supporting soil. Since a drilled pile is made of cast in place cement concrete, a certain amount of water will penetrate into the surrounding soil from the fresh concrete. The amount of water from fresh concrete penetrated to soil is not well known. The relationship between soil and water has been of interest since the earliest time of human life. Agronomists and agriculturists have been studying soil water plant relations since the first days of agriculture. The soil water relation has been considering the most important factor affecting the behavior of soil, especially its mechanical properties. The water content native soil varies with both location and time. It is rarely static. The distribution and penetration of water in soil are a function of many known and unknown factors, such as gravitational, osmotic, and ionic gradients. In soil, moisture transfer can be divided into saturated and unsaturated flow. Water movement underground water level ids classified as saturated flow, water movement above the grand water level is classified as unsaturated flow. In general, most of water movement in soil is classified as unsaturated flow. The degree and amount of cement water that penetrated from fresh cement concrete is dependent on many factors. The pressure head that might be built up from fresh concrete, soil properties; water cement ratio and underground temperature all affect the water penetration between fresh cement concrete and soil. The pressure head that might be built up from fresh concrete during placing is influenced by several factors, including the flowing: water-cement ratio, velocity of

55 54 concrete placing, properties of the fresh concrete, temperature of the concrete and total depth of placement and rate of hardening. The study of pressure from fresh concrete is a difficult and complicated problem. If one considers a certain depth near the bottom of a drilled excavation, the pressure of fresh concrete against the soil will increase as the fresh concrete continues to be poured into the excavation. Meanwhile, the concrete starts to set after a certain period of time, and the pressure of the concrete will reach a maximum and will then drop. Concrete usually takes an initial set in less than 60 minutes and a final set in less than tem hours; therefore, the pressure gradients causing the water flow into the soil last only a short time. One part of this research is to investigate the interface between polymer concrete with carbon fiber sleeve (FRP) and soil and to see how epoxy resin liquid penetrates to the soil and increase interface. The one of the biggest advantages of a carbon fiber sleeve is it has longer durability compared to other pile materials and, as previously mentioned, this type of pile is a composite cast in place pile which is a new topic for this research. Foundation engineering has historically involved the use of wood, concrete, steel, and composite materials; during the last 20 years geosynthetics have been increasingly used. Many of the conventional materials have been found to deteriorate with time. For example, when steel is placed in certain subsurface environments such as marine environments and contaminated, corrosion can be a potential problem. According to Chandler (1976) rate of corrosion at marine environment, is 0.60 mm/year ( in/year) in the splash zone above high tide level, which is almost twice the rate of

56 55 corrosion for a steel pile below low tide level where the pile remains submerged all the time. According to Fleming 1992, attack on cement concrete occurs when there are high sulfate and chloride concentrations and low ph levels in the soils and ground water. Wright reported (1995) about deterioration of wooden piles in New York Harbor due to microorganisms. Fiber reinforced polymer composites are potentially suitable alternatives for use in many of these harsh environments [Forst 1999]. During the last 30 years, there has been a significantly increased demand for the use of fiber reinforced polymer (FRP) composite materials in civil engineering construction and furthermore in the rehabilitation and strengthening of existing structures [Zureick 1997]. Extensive research has been conducted since then to develop a range of composite materials that are noncorrosive and nonconductive, lightweight, have high specific strength and stiffness, exhibit good thermal stability, and have a high specific damping capacity. The development of these materials has been accompanied by an increase in the applications for which they are being used. Recently, interest in the use or potential use of composite materials in structures, foundation and highways applications has increased. Recent estimates have indicated that about 2.7x10 5 tones of composites was transported for use in the construction market in 1994, and use is growing at a rate in excess of 10% per year (Tarricone 1995). In Japan both the private sector and the government consider fiber reinforced polymer (FRP) composites to be a significant enabling technology for the construction industry [Li 1995]. Fiber reinforced polymer has had limited use in geotechnical engineering applications to date, and thus there is a lack of information regarding the behavior of

57 56 systems that include these materials. To provide some insight into the interface behavior between a fibers reinforced polymer and soil, an experimental study was performed to evaluate the importance of various factors. Many studies show that most failures happen in the interface between soil and other materials for composite pile. In this research, the interface between reinforced polymer concrete with fiber reinforced polymer and soil is investigated. The main advantage of this configuration is the interface between reinforced polymer concrete and soil is cast in place and failure is not occurring in the interface between the two materials. Failure is occuring in the soil because epoxy resin in polymer concretes penetrates to the soil and makes the soil a part of the pile. This process increases the shaft resistance in the pile foundation. 1.8 Scope of this Study The main goal of this research is to use polymer concrete reinforced with carbon fiber sleeve under a confined condition in piles under axial and lateral load. In order to determine the general behavior of piles with this new material, different experiments in advance should be adopted to evaluate the final performance. In this research experiments were used on polymer concrete, carbon fiber sleeves and soil to determine the mechanical behavior of these materials according to ASTM. These tests include; Unconfined compression tests on polymer concrete and compare the results with cement concrete. Confined compression tests on polymer concrete and compare the results with cement concrete.

58 57 Splitting test on unconfined polymer concrete Tension test on sleeve of carbon fiber. Flexure tests on confined polymer concrete pile/beam (lateral loading) and compare with theoretical analysis. One way and two way cycling load tests on confined polymer concrete pile/beam. Direct shear test of soil materials in large scale testing equipment. Interface between polymer concrete material and soil in large scale testing equipment. After determining mechanical properties of materials in the above testing conditions, a computer program for pile modeling should be used under various conditions. To show the actual behavior of confined polymer concrete pile in axial load and lateral load, the data from tests for material behavior as input for the computer models of PLAXIS and OpenSees PL were used for axial and lateral load analysis respectively. Calibrations of computer programs, PLAXIS and OpenSees PL were done based on field test data for a known cement concrete pile to compare with experimental results and computer model. Then the calibrated models were used for confined polymer concrete pile in two different types of soil to observe and compare with various conditions of piles.

59 58 CHAPTER 2 LITERATURE REVIEW 2.1 General During the last 50 years, researchers have been investigating the behavior of fiber composite materials. Concrete composite with FRP has been an exception to these studies. Several research projects have been attempted to determine the mechanical properties of concrete composite with FRP. The objective of these projects has been to examine the behavior of polymer concrete composite with carbon fiber sleeve. Generally fiber carbon (FRP) were wrapped around concrete material in different shape and size but, in this research polymer concrete material is filled in side of a carbon fiber sleeve and used as a drilled pile foundation. The common tests to determine the major characteristics of confined polymer concrete pile are compression test, tension test and flexure test, one way and two way cycling load test, direct shear test, interface share test and review of durability of polymer material. A summary of the behavior of carbon fiber (FRP) with respect to some of these tests, as reported by several researchers, is discussed in the following section. This summary is not exhaustive, but is given to provide an insight into the behavior and characteristics of confined polymer concrete with carbon fiber sleeve. 2.2 Compressive Strength of Confined Cement Concrete The compressive strength of composite polymer concrete is an important property. The effect of carbon fiber reinforcement polymer (CFRP) on the compressive strength of composite concrete was a topic research of Xiao and Wu (2003). This paper summarizes the experimental results from a comprehensive research program to study the fundamental stress strain behavior

60 59 of concrete confined by various types of glass and carbon fiber composite jackets. More than 20 concrete samples with several types of FRP composite jackets were tested under axial compression. The impact of different design parameters including plain concrete unconfined strength, types of composites as well as jacket thickness were considered in this paper. The strength enhancement and ductility improvement of specimens confined with FRP composite jackets were discussed. In addition, a new stress strain model to predict the behavior of axial members jacketed with FRP composites is presented. Comparisons between the analytical results using their proposed model and test results were also presented. Two types of FRP with different layer thickness for jacketing systems were investigated in the ongoing research. A total of 20 standard concrete cylinders with the diameter of 152mm (6 in) and height of 300mm (12 in) were tested under uniaxial compression loading. The composite jacket systems investigated in this paper involved both hand lay-up and machine-wound of unidirectional fabrics saturated with different epoxy resins. The composite jackets had a fiber orientation configured along the circumferential direction of the cylinders. The following are the installation procedures used for applying the composite jackets using the hand lay-up method: The cylinders concrete surfaces were cleaned. A thin layer of low-viscosity epoxy primer was applied to the cleaned concrete surface. The low-viscosity epoxy primer was allowed to cure for about 3 hours at the ambient temperature. The cut-to-size unidirectional fabrics were fully saturated with resin and were applied on the cylinders surface.

61 60 After the resin-impregnated fabrics were installed, epoxy was applied again and the overflow was squeezed away using a flat plastic scraper. After the required laminates were installed, the FRP jacket was cured at the laboratory ambient condition. Figures 2.1 and Figure 2.2, show axial stress versus axial and transverse strains for specimens with different unconfined concrete strength and jacket layers. The axial stress strain relationships obtained for unconfined concrete stub columns are also shown in Figures 2.1 and Figure 2.2. As shown in the figures, the initial portions of stress strain responses of confined concrete essentially followed the curves of unconfined concrete up to the stage close to the peak strength. The summaries of results from compressive tests were recorded as Table 2.1 [Xiao and Wu 2003]. Figure 2.1 Axial Stress-Strain Relationships for Concrete with Glass Fiber Composite [Xiao and Wu 2003]

62 61 Figure 2.2 Axial Stress-Strain Relationships for Concrete with Carbon Fiber Composite Jackets [Xiao and Wu 2003] ID Fiber Number f c Stress Max axial Max lateral Type of Layer MPa, ksi MPa, ksi strain strain Sample 1 Glass , , Sample 2 Glass , , Sample 1 Carbon , , Sample 2 Carbon , , Sample 3 Carbon , , Table 2.1 Summery result of compression test [Xiao and Wu 2003] According to Xiao and Wu results, shows by adding of glass fiber on concrete were increasing straight 15% and 42% with one layer and two layers respectively compare to without confined and confined polymer concrete with carbon fiber shows by adding of glass fiber on concrete were increasing straight 12%, 48% and 51% with one layer, two layers and three layers

63 62 respectively compare to without confined. By adding of glass fiber on concrete were increasing maximum axial strain 79% and 86% with one layer and two layers respectively compare to without confined and confined polymer concrete with carbon fiber shows by adding of glass fiber on concrete were increasing maximum axial strain 56%, 78% and 80% with one layer, two layers and three layers respectively compare to without confined. 2.3 Flexure Test of Confined Cement Concrete The behavior of a reinforced concrete was a topic research of Cole and Fam (2006). This paper focused on the flexural performance of concrete. Three concrete beams were tested with different material properties and named as B1, B2 and B3. These beams had internal longitudinal reinforcement including two control specimens without glass fiber reinforced polymer (GFRP) tubes (B1 and B2), and one concrete filled GFRP tubes (B3), as shown in Table 2.2. All specimens were 2.43 m (100 in) long and 220 mm (9 in) diameter. Specimen B2 included steel spiral reinforcement, whereas B1 did not include any transverse reinforcement. B1 was used as a reference specimen to examine the contributions of both steel spirals and GFRP tube. Specimen B3 included six Number 15 bars (Canadian standard) and a GFRP tube. Figure 2.3 shows the results of flexure test [Fam and Rizkalla 2002] [Coleand and Fam 2006] Specimen Confinement Diameter Longitudinal Rebar Cross-Section type mm, in rebar Area (mm 2, in 2 ) B1 None 203, 8.0 Steel 1200, 1.8 B2 Steel spiral 203, 8.0 Steel 1200, 1.8 B3 GFRP tube 219, 8.6 Steel 1200, 1.8 Table 2.2 Summary of Test Matrix of Beam Specimens [Coleand and Fam 2006]

64 63 Figure 2.3 Load-Deflection Curves for Specimens B1, B2 and B3 [Coleand and Fam 2006] According to Coleand and Fam Results, when steel rebar in beams are reaches to yield point, Beam 1 and Beam 2 are almost failed but, in Beam 3 which confined with glass are not failed after steel rebar reaches to yield point and beam 3 is 43 % stronger than Beam 1 and Beam 2 at failure point. 2.4 Durability of Confined Concrete Pile with Carbon Fiber The state of the practice review in confined concrete with fiber reinforced polymer was the topic of research addressed by Iskander and Hassan (1998). This paper noted considerable problems associated with the use of traditional piling material in corrosive soil and marine environments. Concrete durability, steel corrosion, and vulnerability of timber make the construction of piles in these environments difficult. Creosote-treated timber poses a threat to marine life and is also a growing environment disposal problem. Composite materials such as fiber reinforced polymer (FRP) can offer several performance advantages in comparison to timber, steel and concrete. Composite piles can be designed to perform well in difficult

65 64 environments. However, composites face many obstacles because they do not have a long history of use in civil engineering applications. A comprehensive review of the research, testing, design, and practice of composite piles is presented in the Iskander paper. The technical and economic viability of composite piles is discussed. Emphasis is given to material properties, durability, drivability and soil confined pile interaction. A composite pile with FRP was recently developed in the past 15 years. This material provided many performance advantages for use in aggressive and marine environments. Composite pilling has been used primarily in marine settings and light bearing applications. Composite materials have a number of advantages and disadvantages. Advantages include excellent durability and improved environmental consequences. Disadvantages include higher costs, high compressibility, and the lack of a long term track record as a proven material. [Iskander and Hassan 1998] Traditional pile materials for bridge foundations include steel, concrete, and timber. These pile materials have limited service life and high maintenance costs when used in harsh marine environments due to corrosion, degradation, and marine borer attack. Problems associated with traditional pile materials used in harsh environments include concrete durability, steel corrosion, and marine borer attack or degradation of timber piles as show in Figure 2.4. Lampo 1996 it has been estimated that repair and replacement of piling systems costs the U.S. over $1 billion annually.

66 65 Figure 2.4 Degradation of Conventional Piles: Corroded Steel Pile (Left), Degraded Concrete Pile (Middle) and Deteriorated Timber Pile (Right) [Miguel 2002] Miguel 2002 describes a durability methodology proposed to assess the long-term structural capacity of concrete-filled tubular FRP piles, and presents the durability experimental results to date. Base on Miguel results, a simplified model for predicting the long-term axial and flexural capacity of a concrete-filled FRP pile exposed to marine environment moisture has been presented. The use of the model was illustrated using available experimental data applied to a simple example. Based on the simplified example presented, it appears that the degradation of the FRP properties has a greater impact on the long-term flexural capacity of the pile. For the example presented, the long-term axial and flexural capacities were estimated to be 5 and 24 percent lower than the short-term capacities respectively. 2.5 Polymer Concrete The behavior of a polymer concrete, combination of epoxy resin and aggregate was a topic research of Toufigh and Saadatmanesh (2009). This paper focused on the experimental evaluation of the properties of polymer concrete reinforced with chopped glass and steel fiber

67 66 elements. Chopped glass and steel fiber with different fiber contents (0.5, 1 and 1.5 % by weight) and (2.5, 5 and 7.5 % by weight) were considered, respectively. Polymer concrete with different amounts of chopped steel fiber and chopped glass fiber were tested. They were tested in compression; 0.5% glass fiber and 7.5% steel fiber (% by weight) provided the maximum compressive strength (11.3 ksi and 11.8 ksi, respectively). The samples with different types of fibers and other samples without fibers were almost identical in maximum compressive strength. Samples were then tested for tensile strength using a splitting test. Based on the results, 1.5% glass fiber and 5.0% steel fiber (% by weight) gave the maximum tensile stress (1.4 ksi and 1.7 ksi, respectively). These samples are almost 6 to 8 times weaker in tension when compared to compression. Based on the compression test results, reinforced polymer concrete with chopped glass and steel is 3 times stronger than plain concrete. Based on the splitting test results, reinforced polymer concrete with chopped glass is 2.5 times stronger than plain concrete, and reinforced polymer concrete with chopped steel is 3 times stronger than plain concrete. After obtaining the samples which had the maximum tensile strength, samples with this optimal ratio were tested in an impact energy process. 1.5% glass with polymer concrete were observed at 573 lbs-ft until it failed and 5.0% steel with polymer concrete were observed at 862 lbs-ft until it failed. Therefore, steel fiber and glass fiber play a large role in impact energy. [Toufigh and Saadatmanesh 2009] 2.6 Interface Shear Test between FRP and Dense Sand The friction resistance at the interface between pile foundation and surrounding soil constitutes a considerable component of the pile capacity in compression and is considered the soil mechanism in resisting uplift loads of piles installed in granular soils. Studies on the

68 67 interface behavior between soil and pile material such as wood, steel and concrete were many research topics. However information on interface between FRP and soils is scarce. The interface between saturated FRP plate and dense sand was research topics of M. Nehdi, M. Sakr and H. El Naggar (2007). They used interface shear test to evaluate the characteristics of FRP and dense sand interface furthermore, they determined the surface roughness of the pile material with a Taylor Hobson profile meter. Two different fiber reinforced polymer (FRP): FRP-I and FRP-II and a steel material were used in the study to determine interface between them. FRP-I tubes were made of commercially available FRP pipes fabricated using two layers of glass filamentwound at ply angles of 55 and 55. The glass fiber was impregnated with laminating resin at a volumetric ratio of 60/ 40. The FRP-I pile shells have a tensile strength of 193 MPa (28 ksi) and an elastic modulus of 8.5x10 3 MPa ( ksi). The FRP-II with a wall thickness of 7.8 mm (0.3 in) consisted of a structural laminate with a layup in the form of (CSM/03 /90 /CSM). The exterior chopped strand mat (CSM) was used to increase the surface roughness. The E-glass fiber was impregnated with two-part epoxy: resin and hardener at a volumetric ratio of 60/ 40. The cylindrical steel pile was an open ended model made of a cold drawn steel tube with diameter of 168 mm (6.6 in) in diameter, a young modulus of 2.15x10 5 MPa (31183 ksi), a thickness of 6.35 mm (0.25 in) and with length of m (60 in). Table 2.3 shows mechanical properties of FRPs Property Density Glass Compression Young Tensile Flexure Surface Mg/m3 content % Strength modulus Strength Strength Roughness MPa, ksi GPa, ksi MPa, ksi MPa, ksi μm FRP-I , , , 28 76, FRP-II , , , , Table 2.3 Mechanical Properties of FRP Pile Material [Nehdi 2007]

69 68 Surface roughness profile for the different materials was tested. The average roughness for FRP-II was an order of magnitude higher than that of FRP-I and steel. FRP-I and steel surfaces had almost similar average surface roughness. The values of the average surface roughness of FRP-I, FRP-II, and the steel pile material were about 1.66 μm, μm, and 1.05 μm, respectively. The interface shear test results showed that the relative roughness of the FRP composite material had a significant effect on the interface between FRP and dense sand behavior during interface shear tests. Rough FRP surface coupled with rounded sand resulted in a brittle interface behavior and strain softening at high displacement levels. Peak and residual interface friction angles for different materials are summarized in Table2.4. Soil properties FRP-II/Sand FRP-I/Sand Steel/Sand φp φr δp δr δp δr δp δr Table 2.4 Soil Friction Angle and Interface Friction Angle [Nehdi 2007] According to Nehdi, the results show that the friction between FRPs and sand is higher than the friction between steel and sand. The reason is FRPs has higher values of the average surface roughness compared to steel which is an advantage of using FRP tube for a pile. However, the main disadvantage is the friction of the soil itself is higher than any friction between FRP/steel and soil. Conventional construction materials used in foundations can encounter serious durability problems in contaminated subsurface or marine environments. Fiber-reinforced polymer (FRP) composites are potentially suitable for these harsh environments due to their chemical and corrosion resistant properties. Quantification of the interface behavior between FRP composites and soils is a necessary precursor to the adoption of these new materials in geotechnical

70 69 engineering practice. J. D. Forst and J. Han (1999) describe the results of an experimental study that was conducted to investigate the behavior of sand-frp interfaces. The term direct shear test is used herein to refer to tests performed on granular materials only, whereas the term interface shear test refers to tests performed using a modified direct shear test apparatus to study the shearing of granular materials on the surface of FRP or steel materials. The direct shear test specimens had a diameter of 6.35 cm (2.5 in) and a height of approximately 2.54 cm (1 in). The interface shear test specimens had the same diameter but a height of only 1.52 cm (0.6 in), except for the tests used to specifically study the effect of specimen thickness. In them research, they were used two type of sand Ottawa sand and Valdosta blasting sand the results of direct and interface shear test between sand itself and FRP/sands were graphed From Figure 2.5 to Figure 2.8, and friction angles between sands itself and sand/frp are tabled at Table 2.5. Figure 2.5 Shear Stress versus Horizontal Displacement (Direct Shear Test) for Ottawa sand [Forst 1999]

71 70 Figure 2.6 Shear Stress versus Horizontal Displacement (Direct Shear Test) for Valdosta blasting sand [Forst 1999] Figure 2.7 Shear Stress versus Horizontal Displacement (Interface Shear Test) between Ottawa Sand and FRP [Forst 1999]

72 71 Figure 2.8 Shear Stress versus Horizontal Displacement (Interface Shear Test) between Valdosta blasting Sand and FRP [Forst 1999] Otw sand/otw sand Val sand/val sand Otw sand/frp Val sand/frp φp φr φp φr δp δr δp δr Friction angles between sand itself and sand/frp [Forst 1999] According to Forst results Shows the friction between FRP and sand is almost 50% smaller than friction for sand itself. 2.7 Interface between Drilled Pile (Cast-in-Pile) and Soil The drilled pile foundation is made of cast in place concrete; a certain amount of water will penetrate into the surrounding soil from uncured concrete. The amount of water that penetrated to soil is not well known and interface between fresh concrete and soil was the research topic of Chuang and Reese (1969), Beech and Kulhawy (1987) and Reese and O Neill (1988).

73 72 Chuang and Reese (1969) performed laboratory experiments by placing a layer of concrete over remolded soil samples. They found that water transfer from the fresh concrete to the soil samples increased with increasing water/cement ratio. Testing of the resulting specimens in a direct shear device showed that failure did not occur at the concrete/soil interface but rather within the soil at about 3 to 6 mm from the interface. Beech and Kulhawy (1987) conducted load tests on model drilled pile foundation and observed that the failure surface was independent of the construction procedure and is rather linked to the soil type and roughness of the shaft surface. Typical failures occurred between 6 and 19 mm away from the shaft. They argued that shafts with large irregularities such as pieces of aggregate, force the failure surface away from the shaft. Reese and O Neill (1988) reported that results of direct shear tests on partially saturated clays revealed that some kind of chemical bonding occurs between clay particles and cement in the concrete. Higher shear strengths were measured at the clay-cement interface than the shear strength of the clay itself. In summary, observations in the field and modeling suggest that the failure surface occurs in the soil and not at the concrete-soil interface. The distance at which failure occurs is small and varies depending on soil properties and shaft roughness. This indicates that even though water does penetrated from concrete to the soil around the shaft, there appear to be some benefits with regards to strength resulting from a small amount of chemical bonding between the soil and cement. The higher strength of the soil-cement interface forces the shear failure away from the shaft.

74 Axial Load Test on Cement concrete Pile Many investigators was examined and tested in detail of single and group piles, Ismail (2001) tested single drilled cement concrete pile in axial test in cemented sand with diameter of 0.1m (3.93 in) and length of 2.25m (7.4 ft). The cemented sand strength parameters were determined by drained triaxial compression tests. Undisturbed samples were trimmed from block samples taken from the cemented sand deposit for testing. The peak strength parameters such as friction angle, φ and cohesion were 35⁰ and 20 kpa (2.9 psi) respectively. Furthermore, Figure 2.9 a and b shows the stress strain curves and the failure envelop as determined from triaxial test results on cemented sand at a depth of 2 m (6.5 ft). Figure 2.9a Stress Strain Curve of Cemented Sand [Ismail 2001]

75 74 Figure 2.9 b Stress-Strain Curves and Failure Envelope from Drained Triaxial Test on Cemented Sand [Ismail 2001] The installation of Ismail pile was carried out under favorable ground condition. The holes were dry upon auguring, and no groundwater was encountered. No casing was needed, since no caving or collapse occurred within a depth of 5 m (16.4 ft). for the reaction piles; the steel reinforcing cage was lowered into position after completion of the hole. Concrete was poured by free fall to the level of the tip of the central rod that was then positioned in place, after which the concrete pouring was continued in the top. For the test pile the central reinforced rod was position along the full from ground level. To apply load on the Ismail pile a jack was used. The jack was manufactured by B.V Holmator, Holland, and Figure 2.10 shows the jack applying load to the pile.

76 75 Figure 2.10 Jack Applied Load on Pile [Ismail 2001] After an hour the results were recorded and strain gauges were installed on top of the pile and the load was recorded with a jack gauge. Figure 2.11 shows Load- Settlement of Ismail pile. Figure 2.11 Load-Displacements for Pile in Axial Load at Pile Head [Ismail 2001]

77 Lateral Load Test on Cement concrete Pile Many investigators examined and tested in detail single and group piles. Ismail (1990) tested a single drilled cement concrete pile in lateral load test. The test was in cemented sand with a diameter of 0.3m (11.8 in) and length of 5.0 m (16.4 ft). The cemented sand strength parameters were determined by drained triaxial compression tests which is mentioned in section 6.3. The friction angle and cohesion of cemented sand from the ground surface to depth of 3 m (10 ft) was 35⁰ and 20 kpa (2.9 psi) respectively and the friction angle and cohesion of cemented sand from 3 m depth to depth of 5 m (16.4 ft) was 43⁰ and 0.0 kpa (0.0 psi) respectively. Ismail assembled four piles in cemented sand with 5 m (16.4 ft) long, 0.3 m (11.8 in) diameter and had a reinforcing cage 0.25 m (9.8 in) in diameter consisting of six No. 22 mm reinforcing bars. The pile protruded 0.3 m (11.8 in) above ground level for applying jack on the pile to creative load. Figure 2.12 shows lateral test on concrete pile and Figure 2.13 shows concrete piles load-displacement curve after lateral test at pile head.

78 77 Figure 2.12 Lateral Tests on Concrete Pile [Ismail 1990] Figure 2.13 Load-Displacements for Piles in Lateral Load at Pile Head [Ismail 2001] 2.10 Large Lateral Deflection of Pile

79 78 In this section large pile deflections were considered based on experimental results and computer program results. Song (2012) and Memarpour (2012) were considered of large laterally deflection with experiment and computer modeling respectively. Song. Y.S., Hong. P.Y., and Woo. K, S., (2012) considered the behavior of stabilizing piles installed in a cut slope is investigated using a field measurement system and analyzed considering the infiltration depth of environmental rainfall. There is a slope located on an express highway construction site in Donghae, Korea and it was selected for the study. As the primary method of slope enforcement, stabilizing piles were created, and a series of field monitoring systems was installed to measure the movements of the stabilizing piles and the slope. According to the field monitoring results, the deflection of the stabilizing piles and the deformation of the slope were significantly affected by heavy rainfall. The stabilizing piles were constructed as compound piles to increase the section force and protect slop stability from failure. The compound pile is steel pipe piles (φ508) in which H-Piles (250mm x 255mm x 14mm x 14 mm) were inserted, and void is filled with cement grouting and strain gage were installed in side of pile. These gauges recorded pile deflection during the rain and the rainfall after two days was 900 mm (35.4 in). Figure 2.14 shows the maximum lateral displacement for stabilizing the pile is around 118 mm (4.64 in).

80 79 Figure 2.14 Lateral Displacement of Stabilizing Pile [Song 2012] Fixed offshore platforms supported by pile foundations are always subjected to lateral cyclic loads due to environmental conditions. Pile-supported coastal and offshore structures in marine soil deposits are always subjected to large lateral loads. Usually, the critical lateral forces on piles used in coastal structures are due to berthing and mooring forces, whereas piles in offshore jacket platforms are subjected to cyclic lateral loads due to waves. Memarpour, M.M., (2012) modeled a jacket frame with the ABAQUS computer program. Figure 2.15 shows a two dimensional frame of a pile supported jacket type

81 80 Figure 2.15 General View of the Jacket Frame [Memarpour 2012] Platform used in the study. This platform is a four-legged jacket with single diagonal bracing at each bay on the vertical frames and one through leg pile at each corner. The jacket dimensions in the horizontal plane at the top (deck-leg work point) and bottom (seabed level) are 13.7 m (44.9 ft) and 26.5 m (86.9 ft) respectively. The mean water depth is 39.1 m (128.3 ft), the jacket total height is 44.0 m (144.3 ft) and the piles are driven to total depth of 57.0 m (187.0 ft) below seabed. The outside diameters and wall thickness of the piles below seabed level are cm (32 in) and 3.18 cm (1.25 in) respectively. The topside as a whole is a four-story space frame on top of a one-story deck. The soil profile consists of three horizontal soil layers of clay, sand and clay from top to bottom with respective depth of 28.0 m (91.8 ft), 15.0 m (49.2 ft) and 14.0 m (45.9 ft).

82 81 Figure 2.16 Lateral Deflections along the Pile Shaft in Cyclic Loading [Memarpour 2012] The ABAQUS computer result for a jacket frame in cycling load shows the maximum lateral deflection for pile is around 200 mm (4.7 in) and Figure 2.16 shows lateral deflections along the pile shaft in cyclic loading Two Ways Cyclic Load Strength and structural integrity of concrete bridge pier columns and piles are adversely affected in dynamic load through earthquake, wind and etc. A survey of damaged structures and foundation in recent earthquakes indicates that catastrophic failure of an entire structure and foundation may result from failure of a few columns in a chain action. Since it may not be economical to design columns and piles to respond in their elastic range to most earthquake loads, dissipation of energy by post elastic deformation is desired. Although FRP materials are

83 82 generally known for their linear elastic and elastic response, furthermore, confinement of concrete core with FRP is known to improve its ductility. Shao, Y., and A, Mirmiran (2005) tested confined steel reinforced concrete with FRP tube in two way cycling load to obtain the behavior of this material in seismic region. They tested six types of beam/pile in a two way cyclic load. The sample which was considered for this research is shown at Figure The size and dimension of the sample are shown in Table 2.6. Figure 2.17 shows steel rebar is reinforced inside the concrete from support to m (30 in) inside the beam for both sides and the middle of the span is without any steel reinforcement. The whole beam/pile samples are confined with FRP tubes. Figure 2.17 Layout of Concrete Filled Fiber Reinforced Polymer Tube Beam/Pile Specimens [Shao, Y., and A, Mirmiran 2005] Data Dimension Span Length, L (mm, in) 2743, 96 Core Diameter, D (mm, in) 312, 12.3 Tube Thickness, t (mm, in) 5.08, 0.2 Length to Diameter (L/D) Ratio 8.8 Longitudinal Steel Reinforcement 4#4 and 4#5 Table 2.6 Specimen size [Shao, Y., and A, Mirmiran 2005]

84 83 After 28 days, they tested the sample in cycling load at the North Carolina State University structures lab. The cyclic lateral load was applied by a hydraulic actuator reacting on the specimen and Figures 2.18 shows the specimen with upward and downward deflection. A limit of 127 mm was imposed on the actuator displacement to avoid large end rotation which could result in lateral instability of the axial loading system. Figure 2.18 Loading Regime for Concrete Filled Fiber Reinforced Polymer Tube Beam/Pile [Shao, Y., and A, Mirmiran 2005] The specimen failed at a deflection of 259 mm (10 in). Figure 2.19 shows the load displacement hysteretic curve for beam/pile specimen. The data is normalized to remove the effect of different cross sections, span lengths, and concrete strengths. The lateral load is normalized as, where P is the total applied load in the transverse direction, f c is 28 day

85 84 compressive strength of concrete, D is a concrete core diameter and α is The deflection is normalized as, δ is a midspan deflection and L is a span length. The envelope curves for the beam/pile specimen are plotted in Figure Figure 2.19 Normalized Load Displacement Hysteretic Curve for Beam/Pile Specimen [Shao, Y., and A, Mirmiran 2005]

86 Normalized Load αp/(f"c D 2 ) Normalized Displacement δ/l Figure 2.20 Normalize Envelop Load Deflection Curves [Shao, Y., and A, Mirmiran 2005] Shao and Mirmiran compared their results with reinforced concrete with steel bar. Priestley, M, J, N, and Benzoni, G, (1996) tested reinforced concrete with steel bar column in two way cyclic load. The specimen was 610 mm (24 in) diameter and span length was 2286 mm (90 in) and them specimen was reinforced with steel rebar. Longitudinal reinforcement for the specimen consisted of 12 # 4 (12.7 mm) diameter Grade 60 longitudinal steel rebar. Figure 2.21 and Figure 2.22 shows hysteretic curve and normalize envelop load deflection curves for column specimen respectively.

87 Normalized Load αp/(f''c D 2 ) 86 Figure 2.21 Load Displacements Hysteretic Curve for Column Specimen [Priestley and Benzoni 1996] Normalized Displacement δ/l Figure 2.22 Normalize Envelop Load Deflection Curves [Priestley and Benzoni 1996] According to Priestley and Benzoni, the results show that the specimen failed after ten cycles with values of 50.8 mm (2 in) and 90 kn (20 kips). In this research the normalize envelop

88 87 load deflection curves for Priestley and Shao will compare with the normalize envelop load deflection curves for a confined polymer concrete pile in Chapter 5.

89 88 CHAPTER 3 DESCRIPTION OF MATERIALS 3.1 General as: This chapter deals specifically with the materials that have been used in this study. Such Aggregate Polymer Concrete Aggregate Cement concrete Aggregate Carbon Fiber Carbon Fiber Sleeve Epoxy Resin Part A Part B Cement Water 3.2 Aggregates The importance of using the right type and quality of aggregates cannot be ignored as they generally occupy about 80% of the polymer concrete volume and strongly influence the fresh and hardened concrete behavior. Natural gravel and sand that were dug or dredged from pits or rivers were washed and used in the study. Usually, two types of aggregates are used and they are considered as fine and coarse aggregate.

90 Polymer Concrete Aggregate In this research three types of aggregates were used for making Polymer concrete: G8 with gravel size of mm ( in), G16 with gravel size of mm ( in) and mortar sand. The three different types aggregate for polymer concrete considered in this study are shown in Figure 3.1. Figure 3.1 Different Types of Aggregates for Polymer Concrete under this Study Cement concrete Aggregate For cement concrete in this research, fine aggregate and coarse aggregate were used. Coarse aggregate is ¾ in maximum size gravel (ASTM C33) with an oven dry specific gravity of 2.86, absorption of 0.5% (moisture content at SSD condition). Fine aggregate is natural sand

91 90 (ASTM C33) with oven dry specific gravity of 2.64 and absorption of 7%. Figure 3.2 shows the aggregate used for cement concrete. Figure 3.2 Different Types of Aggregates for Cement concrete under this Study 3.3 Carbon Fiber In 1958, Roger Bacon created high performance carbon fibers at the Union Carbide Parma Technical Center (UCPTC), now GrafTech International Holdings, Inc., located outside of Cleveland, Ohio. Those fibers were manufactured by heating strands of rayon until they carbonized. This process proved to be inefficient, as the resulting fibers contained only about 20% carbon and had low strength and stiffness properties. In the early 1960s, a process was developed by Dr. Akio Shindo at Agency of Industrial Science and Technology of Japan, using polyacrylonitrile (PAN) as a raw material. This had produced a carbon fiber that contained about 55% carbon. During the 1970s, experimental work to find alternative raw materials led to

92 91 the introduction of carbon fibers made from a petroleum pitch derived from oil processing. These fibers contained about 85% carbon and had excellent flexural strength. Carbon fiber is most notably used to reinforce composite materials, particularly the class of materials known as carbon fiber or graphite reinforced polymers. Non-polymer materials can also be used as the matrix for carbon fibers. Due to the formation of metal carbides and corrosion considerations, carbon has seen limited success in metal matrix composite applications. Reinforced carbon-carbon (RCC) consists of carbon fiber reinforced graphite, and is used structurally in high-temperature applications. The fiber also finds use in filtration of high-temperature gases, as an electrode with high surface area and impeccable corrosion resistance, and as an anti-static component. Molding a thin layer of carbon fibers significantly improves fire resistance of polymers or thermo set composites because a dense, compact layer of carbon fibers efficiently reflects heat. [Bazant 1979] The properties of carbon fibers such as high flexibility, high tensile strength, low weight, high temperature tolerance and low thermal expansion make them very popular in aerospace, civil engineering, military and motor sport along with other competition sports. However, they are relatively expensive when compared to similar fibers for example glass fibers or plastic fibers. Carbon fibers are usually combined with other materials to form a composite. When combined with a plastic resin and wound or molded it forms carbon fiber reinforced plastic (often referred to also as carbon fiber) which is a very high strength-to-weight, extremely rigid, although somewhat brittle material. However, carbon fibers are also composed with other materials, such as with graphite to form carbon-carbon composites, which have a very high heat tolerance.

93 Carbon Fiber Sleeve There are several types of carbon fiber that exist. In this research a biaxial sleeve of fiber carbon was used. A biaxial sleeve of carbon fiber is a weave of carbon in two directions and it has a circular cross section. It is also referred to as a tube of carbon fiber. A sleeve of carbon fiber is shown in Figure 3.2 and Table 3.1 gives the mechanical properties of a biaxial sleeve of carbon fiber. Diameter (in-cm) Type Thickness (in-mm) Weight (oz/yd sq-g/m sq) Heavy Table 3.1 Mechanical Properties of Biaxial Sleeve Carbon Fiber Figure 3.3 Carbon Fiber Sleeve under this Study

94 Epoxy Resin In chemistry, epoxy or polyepoxide is a thermosetting epoxide polymer that cures (polymerizes and crosslinks) when mixed with a catalyzing agent or hardener. Most common epoxy resins are produced from a reaction between epichlorohydrin and bisphenol-a. The first commercial attempts to prepare resins from epichlorohydrin were made in 1927 in the United States. Credit for the first synthesis of bisphenol-a-based epoxy resins is shared by Dr. Pierre Castan of Switzerland and Dr. S.O. Greenlee of the United States in Dr. Castan's work was licensed by Ciba, Ltd. of Switzerland, which went on to become one of the three major epoxy resin producers worldwide. Ciba's epoxy business was spun off and later sold in the late 1990s and is now the advanced materials business unit of the Huntsman Corporation of the United States. Dr. Greenlee's work was for the firm of Devoe-Reynolds of the United States. Devoe-Reynolds, which was active in the early days of the epoxy resin industry, was sold to Shell Chemical (now Hexion, formerly Resolution Polymers and others). Epoxy resin usually combines with carbon and glass reinforcement and produces fiber composite laminates with exceptional strength, durability and chemical resistance. Epoxy resin is a 100% solid formation with low toxicity and low odor during cure. The cure time depends on temperature and usually takes 72 hours; therefore, the curing time is nine times faster than concrete. The density of the epoxy resin is approximate 1.1kg/L. In practice, a hardener is referred to as part B and the resin is part A. In this study, a proportion of two parts component A to one part component B by volume was mixed, and the properties this epoxy resin are shown in. The properties for Parts A and B are shown in Figure3.4.

95 94 EPOXY PROPERTIES Color Part A is pigmented syrup Part B is amber liquid Viscosity at 25 1,400 1,700 cps Pot Life at 25 C 3 4 hours (thin film set time) Full cure time 3 days Density at 20 C Part A: 9.4 lbs/gal (1.13 kg/l) Part B: 8.3 lbs/gal (1.00 kg/l) Tensile Strength (ASTM D-638) 8,915 psi (61.5 MPa) Tensile Modulus (ASTM D-638) 378,228 psi (2,608 MPa) Compressive Strength (ASTM D-695) 14,011 psi (96.6 MPa) Compressive Modulus (ASTM D-695) 618,706 psi (4,266 MPa) Flexural Strength (ASTM D-790) 17,583 psi (121.2MPa) Flexural Modulus (ASTM D-790) 415,234 psi (2,863 MPa) Shear Strength (ASTM D-3165) Unable to force a shear failure mode; samples fail in tension. Water absorption (% gain) in 24 hours < 1% Expansion Coefficient [-37.4 to 40.1 C] m/m C Expansion Coefficient [120 to 222 C] m/m C Table 3.2 Properties of Epoxy Resin Figure 3.4 Part A (left) and Part B (right) under this Study 3.5 Cement In this research, normal cement (Portland Cement Type II) was used. The specific gravity of the Portland cement was 3.1. The necessary amount of cement for the entire study was ordered from the

96 95 retailer at on time and kept in a dry place time and kept in dry place to prevent deterioration. All batches of concrete were made within a week to eliminate any possible change in cement property. In other to prepare the concrete with 20 to 30 MPa (2.9 to 4.3 ksi), 600 lb of cemented in every cubic yard (386 kg/m 3 ) of cement concrete was used. 3.6 Water Water containing less than 2000 ppm of total dissolved solids can generally be used for making concrete. Normal Tucson tap water was used in the concrete mixture. The ratio between water and cement for making concrete was kept almost the same for all different batches to avoid changes in strength due to this parameter.

97 96 CHAPTER 4 SPECIMEN PREPARATION AND LABORATORY TEST SETUP 4.1 General As previously mentioned, to determine the mechanical behavior of confined polymer concrete pile, a computer program was used. To model polymer concrete, the mechanical properties of confined polymer concrete material were determined by experimental testing. This chapter covers specimen preparation and laboratory test setup. Over seventy samples were made allowing this research to investigate properties of all samples including; 1. The preparation of aggregates for polymer concrete to obtain desired maximum dry bulk density. 2. Combination of different amounts of aggregates mixed with epoxy resin (Polymer Concrete). 3. Unconfined polymer concrete was crated for compression test and tension test. 4. Polymer concrete was reinforced with carbon fiber sleeve to create for compression test tension test, maximum tensile strength flexure test one way and two way cycling load. 5. Laboratory specimen preparation for unconfined and confined cement concrete with carbon fiber sleeve. 6. Laboratory specimen preparation for interface shear test and direct shear test between soil itself and polymer concrete and soil and

98 97 7. Laboratory specimen preparation for carbon fiber sleeve in tension test. 4.2 Types of Aggregates Three different types of aggregate were used to find the maximum dry density. The three aggregate types were Gravel8 (G8), Gravel16 (G16) and sand. G8 and G16 were obtained from a sieve analysis indicated in (Figure 4.1). The soils used were obtained from storage bins and measured accordingly. The soil type is fine aggregate which is commonly used for making concrete in various civil engineering projects. The sieves (#4 #8 #16) were cleaned with a brush and were inspected for excessive wear and damage before being used. The specified sieves were stacked in order (Top-down) from largest to smallest. The sample was placed in the top sieve and a cover plate was attached to the top. The sieves were locked in place by screwing down the cover attached to the mechanical sieve shaker. The mechanical sieve shaker was turned on for approximately five minutes. Each soil size from the sieve was taken out from the mechanical shaker and stockpiled in buckets. The part of the sample remaining on sieve #8 was deemed as G8 and likewise the sample which remained on sieve #16 was G16. The sand for this investigation was obtained locally.

99 98 Figure 4.1 Sieve Test Machine 4.3 Procedure for obtaining maximum dry bulk density of aggregate blend Three types of aggregates were mixed together as follow below according to ASTM C29 1. G8 and G16 2. G8 and Sand 3. G16 and Sang 4. G8, G16 and Sand Determining of maximum dry bulk density of mix G8 and G16 G8 and G16 were mixed in different ratios to obtain the maximum dry bulk density. In this process the larger size of aggregates stayed constant and smaller size of aggregate was increased until the maximum density was reached. The mass of G8 (which stayed constant) and

100 99 the increasing mass of G16 are shown in table 4.1. For the 30% G16 / 70% G8 blend, 1.95 kg (4.3 lb). of G16 and 4.53 kg (10 lb). of G8 were used. For the 40% G16 / 60% G8 blend and subsequent blends, the proportion of G8 remained constant at 4.53 kg (10 lb) while the proportion of G16 was changed to achieve the necessary ratio. To obtain a 40/60 ratio, 3.03 kg (6.7 lb) of G16 and 4.53 kg (10 lb) of G8 was required. Thus, the 40/60 blend can be obtained from the 30/70 blend by simply adding 1.08 kg (2.4 lb) of G16. 30% of G16 and 70% of G8 were thoroughly mixed in a large container. The method of compaction used is referred to as rodding procedure in which 1/3 of a bucket ( m3, 0.1 ft3) was filled with this sample, and then compacted using a steel rod dropped 25 times. 2/3 of the bucket was filled and rodded 25 times again. Finally, the bucket was completely filled and rodded again in the manner previously mentioned. The final step levels the surface of the filled bucket in such a way that any slight projections of aggregate above the rim are balanced by the voids below the rim. The compacted sample is then weighed. This process was repeated for the other percentages mentioned above. Table 4.1 shows the weight and density of G16 and G8 and Figure 4.2 shows dry density vs. percent fine aggregate ( G8, G16). Determination Percent (% finer particle) Weight of G#16 (kg, Ib) 1.95, , , , , 17.5 Weight of G#8 (kg, Ib) 4.53, , , , , 10 weight of blend (kg, Ib) 4.25, , , , , 9.28 Dry density (m 3,ft 3 ) 2.65, , , , , 92.8 Table 4.1 Weight and Density of Each Different Mixer for G8 and G16

101 Dry Density (Kg/m^3) Percent of Fine Aggregate Figure 4.2 Dry Densities vs. Percent Fine Aggregate (G8, G16) Determining of maximum dry bulk density of mix G8 and Sand The process in this section is identical to section except sand was used instead of G16. Table 4.2 shows the weights and bulk density of each different percentage. Figure 4.3 shows dry density vs. percent fine aggregate (G8, Sand). Determination Percent (% finer particle) Weight of Sand (kg, Ib) 1.95, , , , , 17.5 Weight of G#8 (kg, Ib) 4.53, , , , , 10 weight of blend (kg, Ib) 4.68, , , , , Dry density (m 3,ft 3 ) 2.92, , , , , Table 4.2 Weight and Density of Each Different Mixer for G8 and Sand

102 Dry Density (Kg/m^3) Percent of Fine Aggregate Figure 4.3 Dry Densities vs. Percent Fine Aggregate (G8, Sand) Determining of maximum dry bulk density of mix G16 and Sand The process for this section is the same as section the only difference being G16 was used instead of G8. Table 4.3 shows the weight and bulk density of each mixer. Figure 4.4 shows dry density vs. percent fine aggregate (G16, Sand). Determination Percent (% finer particle) Weight of Sand (kg, Ib) 1.95, , , , , 17.5 Weight of G#16 (kg, Ib) 4.53, , , , , 10 weight of blend (kg, Ib) 4.51, , , , , 9.69 Dry density (m 3,ft 3 ) 2.81, , , , , 96.9 Table 4.3 Weight and Density of Each Different Mixer for G16 and Sand

103 Dry Density (Kg/m^3) Dry Density (Kg/m^3) Percent of Fine Aggregate Figure 4.4 Dry Densities vs. Percent Fine Aggregate (G16, Sand) Figure 4.5 shows dry density vs. percent of fine aggregate for all mix design to observe which mix design it has higher dray density. According to Figure 4.5, in order to get the best mix results for polymer concrete, 40% of sand and 60% of G8, it has higher dry density compared to other mix designs Percent of Fine Aggregat G8-Sand G16-Sand G8-G16 Figure 4.5 Dry Density vs. Percent of Fine Aggregate for all Mix Design

104 Determining of maximum dry bulk density of mix G8, G16, and sand For this part of the experiment, three different types of aggregate were combined together to reach maximum bulk density and then compared to the results obtained with the other previous combinations kg (5 lbs) of G8, 2.26 kg (5 lbs) of G16 and 2.26 kg (5 lbs) of sand were mixed and the bulk density was then calculated. The mixing process was the same as mixing G8 and G16. By incrementally increasing the weight of G8 from 2.26 kg to 4.53 kg (5 lbs to 10 lbs) the bulk density also gradually increases until it reaches a maximum blend weight of lbs. As shown in Table 4.4 the corresponding weights of sand and G16 that contributed to the maximum blend weight were 3.17 kg (7 lbs) and 3.62 kg (8 lbs) respectively. After the maximum weight was achieved, it was shown that any change in the combination of soil weights decreased the overall weight of the blend. Table 4.4 and 4.5 show all the soil combinations that were tried as well as their respective mixed weights and dry densities. sand (kg, Ib) G16 (kg, Ib) G8 (kg, Ib) Weight of blend (kg, Ib) Dry density (m 3,ft 3 ) 2.26, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Table 4.4 Weight and Density of Each Different Mixer for three Aggregates

105 104 sand (kg, Ib) G16 (kg, Ib) G8 (kg, Ib) Weight of blend (kg, Ib) Dry density (m 3,ft 3 ) 0.9, , , , , , , , , , , , , , ,1 4.53, , , , , , , , Table 4.5 Weight and Density of Each Different Mixer for three Aggregates The mix design of 40% of sand and 60% of G8, has higher dry density compared to other mix design of mixing G8, G16 and Sand together. Therefore in this research the latter one was used for making polymer concrete. 4.4 Preparation of Unconfined Polymer Concrete Samples for Compression Test In this section, different types of aggregate and epoxy resin were mixed together with volume ratio of 1:2, 1:3 and 1:4 epoxy resin and aggregate respectively Epoxy Resin and Aggregate 1:2 (Volume Ratio of epoxy resin to aggregate by weight) In this setup, aggregate and epoxy resin were mixed in a volume ratio of 2:1, respectively. The aggregate mix was obtained from the maximum sample weight shown in Table 4.2. This mix contained 40% sand and 60% G8. Part A and part B of epoxy resin were mixed with an electrical drill for approximately three minutes. The weight of aggregate and epoxy resin were then measured with a scale and then combined. Then epoxy resin and aggregate were

106 105 mixed again for 5 minutes. The fresh epoxy resin and aggregate (polymer concrete) was then placed into 7.62x15.24 cm (3x6 in) cylindrical plastic molds. The inside of these molds were coated with oil to ease sample extraction. The sample was filled in thirds with each layer being rodded 25 times. The side of the mold was tapped in order to prevent large surface voids. The top surface of the specimen was smoothed and marked for identification. Three samples were made by this process. The samples were then allowed to cure at room temperature for 5 days. The final sample mixture contained 2.85 kg (6.30 lbs) G8, 1.9 kg (4.20 lbs) sand, and 1.52 kg (3.37 lb) epoxy resin. After the 5 days of curing, a small hole was made at the bottom of the mold in order to remove the samples from molds. A compressed air hose was inserted into the holes and the samples were extracted. For distribution of equally loading on samples surfaces, the bottom and top of these samples were capped with Sulfur (S) material for compression testing [ASTM C617] Epoxy Resin and Aggregate 1:3 (Volume Ratio of epoxy resin to aggregate by weight) In this section, aggregate and epoxy resin were combined together in a volume ratio of 3:1, respectively. The samples were prepared in the same manner as section The only difference was that the ratio of the aggregate was increased to 3. Three samples were made using 7.62x15.24 cm (3x6 in) cylindrical molds kg (6.30 lbs) G8, 1.9 kg (4.20 lbs) sand and 1.00 kg (2.25 lbs) epoxy resin were used. After mixing all the particles of the sample, one-third of the mold was filled with the epoxy resin/aggregate mix (polymer concrete) and the rodded 25 times. Two-thirds of the mold was filled and the sample was again rodded 25 times. The mold was then completely filled and the rodding procedure repeated. The top surface was then

107 106 smoothed. The three samples stayed at room temperature for 5 days to cure. The samples were again removed from the molds using air pressure. The top and bottom of some of the samples were capped for compression test Epoxy Resin and Aggregate 1:4 (Volume Ratio of epoxy resin to aggregate by weight) In this section, aggregate and epoxy resin were mixed together in a volume ratio of 4:1, respectively. The samples were prepared almost as the same as section The only difference is that the ratio of the aggregate increased to kg (6.30 lbs) G8, 1.9 kg (4.20 lbs) sand, and 0.76 kg (1.68 lb) epoxy resin were used for making three necessary samples of size of 7.62x15.24 cm (3x6 in) test cylinders. The fresh epoxy resin and aggregate (polymer concrete) were placed in plastic molds in the same fashion as section The three samples stayed at room temperature for 5 days to cure. After removing the samples from the molds with high air pressure, the top and bottom of the samples that were to undergo compression testing were capped with sulfur. Capping was not needed for splitting and impact testing. Table 4.6 shows the weight of each particle that was needed to make each particular sample. Figure 4.6 shows the sample in mold, the sample itself, and sample after it was capped. Ratio by Volume Number of samples size of mold weight of G#8 weight of sand weight of epoxy resin day of cure 1 epoxy resin to 2 aggregate x15.24cm, 3x6 in 2.85 kg 6.30 lb 1.90 kg 4.20 lb 1.52 kg, 3.37 lb 5 1 epoxy resin to 3 aggregate x15.24cm, 3x6 in 2.85 kg 6.30 lb 1.90 kg 4.20 lb 1.00 kg 2.25 lb 5 1 epoxy resin to 4 aggregate x15.24cm, 3x6 in 2.85 kg 6.30 lb 1.90 kg 4.20 lb 0.78 kg, 1.68 lb 5 Table 4.6 Trial Sample Mix

108 107 Figure 4.6 Typical Specimen: with mold (left) without cap (middle) with cap (right) 4.5 Preparation of Confined Polymer Concrete with Carbon Fiber Sleeve for Compression Test In this section, aggregate and epoxy resin were combined together in a ratio of 3:1, respectively. The samples were prepared in the same manner as section Three samples were made using 7.62x15.24 cm (3x6 in) cylindrical molds kg (6.30 lbs) G8, 1.9 kg (4.20 lbs) sand, and 1.00 kg (2.25 lbs) epoxy resin were used. Inside the molds, a sleeve fiber carbon with a diameter of 7.62 cm (3 in) was installed producing a reinforced polymer concrete. After mixing all the particles of the sample, one-third of the mold was filled with the epoxy resin/aggregate mix (polymer concrete) and the rodded 25 times. Two-thirds of the mold was filled and the sample was again rodded 25 times. The mold was then completely filled and the rodding procedure repeated. The top surface was then smoothed. The three samples stayed at room temperature for 5 days to cure. The samples were again removed from the molds using air pressure. For these samples preparation, the samples were not capped for compression since the extensometer was attached on polymer concrete specimens to measure strain with MTS 311 load frame. An extensometer is very sensitive equipment to measure strain. The strain obtained with

109 108 an extensometer for cut samples is more accurate compared to capped samples. Furthermore, the unconfined polymer concrete samples were cut and the strain measured by extensometer. Figure 4.7 shows sample reinforced with carbon fiber sleeve, and Figure 4.8 and Figure 4.9 shows the cut sample to make smooth surface for confined and unconfined polymer concrete respectively. Figure 4.7 Typical Specimen in Side Mold (left) and Sample out of Mold after Curing Process (right) Figure 4.8 Confined Polymer Concrete Sample Cut (Left) and Adjust Sample Surface (Right)

110 109 Figure 4.9 Unconfined Polymer Concrete Sample Cut (Left) and Adjust Sample Surface (Right) 4.6 Preparation of Plain Polymer Concrete for Splitting Test In this section, aggregate and epoxy resin were combined together in a ratio of 3:1, respectively. The samples were prepared in the same manner as section Three samples were made using 7.62x15.24 cm (3x6 in). Cylindrical paper molds 2.85 kg (6.30 lbs) G8, 1.9 kg (4.20 lbs) sand, and 1.00 kg (2.25 lbs) epoxy resin was used. After mixing all the particles of the sample, one-third of the mold was filled with the epoxy resin/aggregate mix (polymer concrete) and then rodded 25 times. Two-thirds of the mold was filled and the sample was again rodded 25 times. The mold was then completely filled and the rodding procedure repeated. The top surface was then smoothed. The three samples stayed at room temperature for 5 days to cure. The samples were again removed from the molds to prepare for splitting test. Figure 4.10 shows samples of polymer concrete without reinforcement.

111 110 Figure 4.10 Polymer Concrete without Reinforced 4.7 Confined Polymer Concrete Pile with Carbon Fiber Sleeve Preparation for Flexure Test, One way and Two way Cycling Load In this section, aggregate and epoxy resin were combined together in a ratio of 3:1, respectively. Three samples were made using 7.62 x 91.4 cm (3x36 in). cylindrical paper molds kg (37.8 lbs) G8, kg (25.2 lbs) sand, and 6.12 kg (13.5 lbs) epoxy resin were used. Inside the molds, a carbon fiber sleeve was installed with a diameter of 7.62 cm (3 in). After mixing all the particles of the sample, one-third of the mold was filled with the epoxy resin/aggregate mix (polymer concrete) and rodded 5 times. Two-thirds of the mold was filled and the sample was again rodded 5 times. The mold was then completely filled and the rodding procedure repeated. The top surface was then smoothed. The three samples stayed at room temperature for 5 days to cure. The samples were again removed from the molds to prepare for flexure tests. Figure 4.11 shows carbon fiber sleeve in side paper mold before fill fresh polymer concrete in side mold. Figure 4.12 shows a sample reinforced with a carbon fiber sleeve.

112 111 Figure 4.11 Carbon Fiber Sleeve in side Paper Mold before Fill Fresh Polymer Concrete in side Mold Figure 4.12 Pile Polymer Concrete Reinforced with Sleeve fiber Carbon 4.8 Carbon Fiber Sleeve Tensile Test Preparation In this section three samples of carbon fiber sleeve with cm (12 in) of height and 7.62 cm (3 in) diameter were cut. Then carbon fiber sleeves were placed on clean Mylar to keep dust from sticking to the fiber during saturation. Figure 4.13 shows samples were cut and prepared for tensile stress test.

113 112 Figure 4.13 Prepare sample for Tensile Stress The carbon fiber sleeve samples were saturated with epoxy resin which is formed from a 2:1 ratio resin and hardener respectively. Resin and hardener were measured by volume using a measuring cup and they were mixed together for three minutes. Then the epoxy resin was applied to the one side of the carbon fiber sleeve samples with a squeegee. The squeegee was moved in a direction to the parallel to the fibers. After fully saturating one side of the carbon fiber sleeve it was flipped over and the same process was applied for other side of the carbon fiber sleeve samples. Both sides of the carbon fiber sleeve samples were covered by clean Mylar and left outside to fully cure for five days. Then 10 pound steel plates with a uniform thickness were applied on the saturated carbon fiber sleeve and were used to compress the sample in order to remove the majority of air pockets between the epoxy resin and fiber. After five days, the carbon fiber sleeve samples became fully cured. The samples were removed from the Mylar and were ready for the tensile test. Figure 4.14 shows the cured samples for tensile tests.

114 113 Figure 4.14 Fiber Carbon Sleeve for Tensile Test 4.9 Interface Shear Test and Direct Shear Test Preparation This section covers specimen preparation and laboratory test setup for interface shear test and direct shear test. For interface testing, four unsaturated carbon fiber sleeve were flattened on soil, then polymer concrete was poured on unsaturated the carbon fiber sleeve to determine the effect of epoxy resin liquid penetration from polymer concrete to the soil. As mention before polymer concrete was made by 1 volume of epoxy resin an 3 volumes of aggregate (40% of sand and 60%). First carbon fiber sleeves were cut and flattened on soil with dimensions of 20x20 cm2 (7.84x7.84 in2). The thickness of the soil was 5 cm (1.96 in). After that, fresh polymer concrete was poured on the carbon fiber sleeve. Figure 4.15 and Figure 4.16 shows a carbon fiber sleeve on soil and fresh polymer concrete on the fiber carbon sleeve respectively.

115 114 Figure 4.15 Unsaturated Carbon Fiber Sleeve on Soil Figure 4.16 Polymer Concrete on Carbon Fiber Sleeve Four different samples were made for the effect of epoxy penetration. Sample 1 has zero load, sample 2 has 50 kg (0.11 kips), sample 3 has 250 kg (0.5 kips) and sample 4 has 500 kg (1.1 kips) load on the polymer concrete uncured material to observe how much epoxy resin would penetrate in the soil. Figure 4.17 shows samples with the applied load.

116 115 Figure 4.17 Sample with Load 250kg and 50kg (Left) and 500kg and 0kg (Right) After 3 days samples were cured and the loads on the samples were removed. Then samples were cut with a circular cross section to fit into the interface shear test device. The diameter of sample was almost 17 cm (6.69 in). Figure 4.18 shows the sample after three days curing under load and Figure 4.19 shows sample cutting preparation for interface shear test device. Figure 4.18 Sample after Three days under Load

117 116 Figure 4.19 Sample Cut and Prepare for Interface Shear Test The main reason to put load on the samples is to observe how much of the epoxy liquid would penetrate into the soil. The idea of applying such load is due to uncured polymer concrete weight in practice while poured into the carbon fiber sleeve for actual cast in place piling. According to Figure 4.20, it shows the penetrated epoxy resin into soil for sample of 0 kg to 500 kg load is almost same as each other, and this will be discussed further in Chapter 5. The effect of epoxy penetration would have an influence on friction and cohesion between polymer pile sample and soil at interface. Figure 4.20 Samples for Interface Shear Test under this Study

118 117 Sample preparation for direct shear test on soil using the CYMDOF device and the results will be presented in Chapter Preparation Unconfined and Confined Cement concrete Samples for Compression Test In this research, cement concrete samples were constructed according to the Lab Manual at the University of Arizona for compression test to compare compression results with polymer concrete compression test results. Table 4.7 shows the measure of each material to make cement concrete by total weight percentage. Material Total Weight % Coarse Aggregate 46% Fine Aggregate 31% Water 15% Cement 8% Table 4.7 Measure of Each Material to Make Cement concrete by Total Weight Percentage According to table above for this cement concrete, water cement ratio (w/c) was 0.55 with a slump of 7.62 cm (3 in) and compressive strength of 20 to 30MPa (2.9 to 4.3 ksi). After mixing cement concrete material together, the fresh cement concrete was placed in to the mold with a size of 7.62 x 15.24cm (3x6 in) and left at room temperature for one day. After one day, the sample was removed from the mold by air pressure and left in a moisture room for 28 days to reach the maximum compressive strength. After 28 days, some of the

119 118 samples were reinforced with a carbon fiber sleeve and cut at the top and bottom of the sample to create a smooth surface. Figure 4.21 shows unconfined and confined cement concrete. Figure 4.21 Unconfined Cement concrete (Left) Confined Cement concrete (Right)

120 119 CHAPTER 5 ANALYSIS OF EXPERIMENTAL TESTING AND RESULTS 5.1 General After performing the experiments the next step was to measure the parameters which were the objective of the study. These parameters such as compression, Tension, flexure, one way and two way cycling load, interface and direct shear test were compared in order to illustrate any significant difference among specimens. In order to calculate the parameters of interest ASTM specifications were used. The results were then compared by employing a series of statistical procedures. In this analysis, two important goals were pursued. The first goal was to show the homogeneity of different specimens and the second goal was to determine if the difference between the average values of the specimens was more significant than the variation within the group of specimens. 5.2 Compression Test Results for Different Ratios of Aggregates and Epoxy Resin with SoilTest CT-6200 In this section samples with different ratios of aggregates and epoxy resin were tested and the sample that achieved the maximum compressive strength was selected as the ratio for polymer concrete. A compression test determines behavior of materials under crushing loads. The specimen is compressed and deformation at various loads is recorded. Compressive stress and strain are calculated and plotted as a stress-strain diagram which is used to determine elastic limit, proportional limit, yield point, yield strength and, for some materials, compressive strength.

121 120 The compressive strength of a material that fails by a shattering fracture can be defined within fairly narrow limits as an independent property. However, the compressive strength of materials that do not shatter in compression must be defined as the amount of stress required to distort the material an arbitrary amount. Compressive strength is calculated by dividing the maximum load by the original cross-sectional area. To measure the maximum strength of the samples in compression, ASTM C 39/C 39M (Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens) was used. This test method covers determination of compressive strength of cylindrical concrete specimens such as molded cylinders and drilled cores. The values stated in either English or SI units are to be regarded separately. The SI units are shown in brackets. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. The test method consisted of applying a compressive axial load to a molded polymer concrete cylinder at a constant rate within a prescribed range. The specimens were 3x6 in molded cylinders in which the top and bottom of the samples were capped with sulfur. Sulfur caps allow the load to be uniformly applied across the cross section of the sample. The testing machine was a SoilTest CT-6200 (Compression Machine) with a maximum capacity of 450 kips, controlled by a panel to operate test in load control status. The machine was equipped with two hardened steel bearing blocks. On the top block a supplementary bearing plate was attached to a ball joint support to allow complete freedom of rotation. The load was applied in compression in the top and bottom of the samples with 0.89 to 1.33 KN/sec ( lb/sec) load ratio. The loading was controlled and monitored using the aforementioned control panel.

122 121 In this case, nine samples of the epoxy resin and aggregate mix (polymer concrete) were tested in compression with the SoilTest CT To measure the maximum strength in compression, the load was applied on the top and bottom of the specimens with a 0.89 to 1.33 KN/sec ( lb/sec) load rate. Figure 5.1 shows the testing machine with a sample. Figure 5.1 SoilTest CT-6200 with Sample for Measure Compression Test Three set of samples were tested with different ratio of resins (refer to section 4.4) to distinguish the maximum compression stress. Three samples with ratios 1:4 are shown in Table 5.1, sections A, B and C. This table gives values for the diameter, weight, and peak load of each the samples and also illustrates the maximum and average stress. Sections D, E and F in Table 5.1 report the same characteristics and have a ratio of 1:3 and sections G, H and I in Table 5.1 have a ratio of 1:2. Figure 5.2 shows the summary of the maximum compression strength vs. different aggregate and epoxy resin ratios.

123 122 Ratio 4 to 1 4 to 1 4 to 1 3 to 1 3 to 1 3 to 1 2 to 1 2 to 1 2 to 1 Max Load (MN, Kips) 267.3, , , , , , , , , 65.3 Stress (MPa, ksi) 58.6, , , , , , , , , 9.23 Average (MPa, ksi) 61.9, , , 9.20 Table 5.1 Result for Compression Test with Different Ratios of Aggregate and Epoxy Resin Based on Table 5.1, the maximum compression strength is 65.5 MPa (9.49 ksi) which has a corresponding ratio of 3:1, and the minimum compression strength is 61.9 MPa (8.98 ksi) for the ratio of 4:1. Based on these results, the maximum compressive strength mix ratio of 3:1 was selected for compaction testing. This ratio was also used for pile samples. Figure 5.2 shows the mode of failure of one of the nine samples. All these samples (with different ratios) failed in shear. Figure 5.2 Mode of Failure of Aggregate and Epoxy Resin

124 Splitting Test Results Plain Polymer Concrete Splitting tensile strength is generally greater than direct tensile strength and lower than flexural strength (modulus of rupture). Splitting tensile strength is used in the design of structural lightweight concrete members to evaluate the shear resistance provided by concrete and to determine the development length of reinforcement. Only maximum loading was applied during the split cylinder tests. The ASTM C496 method was used to calculate the maximum strength of the sample in tension. This test method covers the determination of the splitting tensile strength of cylindrical concrete specimens, such as molded cylinders and drilled cores. The values can be stated in either British units or SI units and should be regarded separately. The values stated in each system may not be the exact equivalents; therefore each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the given standard. According to ASTM C496, the value of splitting tensile strength of the specimen (T) can be calculated as: (5.1) Where: P = maximum applied load during the test; l = length of sample; and d = diameter of sample.

125 124 In this section three samples were tested, in tension, with the SoilTest CT To measure the sample s tension capacity, the load was applied in compression along the length of the samples with load rate 0.22, 0.44 kn/sec (50 to 100 lb/sec). Figure 5.3. Shows the SoilTest CT-6200 with a sample loaded for the Splitting Test. Figure 5.3 Samples Testing for Splitting Test After a few minutes the samples failed. Table 5.2 shows the maximum load tension results for each sample. Figure 5.4 shows a sample that failed in tension Figure 5.4 Samples after Tension Test

126 125 Maximum Load (KN, k) Tension (MPa, ksi) Sample , , 1.56 Sample , , 1.32 Sample , , 1.37 Average 178.4, , 1.40 Table 5.2 Maximum Load and Tension Results for each Sample 5.4 Compression test results and Stress and Strain Diagram for Unconfined Polymer Concrete In this section the MTS 311 Load Frame testing machine was used to measure the compression strength of the samples. The standard test method for compressive strength of cylindrical concrete specimens was used. Comparing the results from the MTS 311 Load Frame with the SoilTest CT-6200, the MTS 311 Load Frame is more accurate and MTS 311 Load Frame was record strain of each material by extensometer. In this section, three samples of epoxy resin and aggregate mix with a ratio of 3:1 (polymer concrete) were tested in compression with the MTS. To measure the stress-strain diagram and compressive strength, the load was applied on the top and bottom of the specimens with a mm/sec (0.001 in/sec) load rate. Figure 5.5 shows the MTS 311 Load Frame with a sample.

127 Compression Stress (MPa) 126 Figure 5.5 Unconfined Polymer Concrete with Extensometer under MTS Load Frame 311 After a few minutes the samples failed and the stress and strain diagrams were recorded. Figures 5.6, 5.7 and 5.8 shows stress and strain diagrams for these samples. 70 Sample Strain Figure 5.6 Stress-Strain Curves for Sample 1 of Unconfined Polymer Concrete

128 Compression Stress (MPa) Compression Stress (MPa) Sample Strain Figure 5.7 Stress-Strain Curves for Sample 2 of Unconfined Polymer Concrete 70 Sample Strain Figure 5.8 Stress-Strain Curves for Sample 3 of Unconfined Polymer Concrete According to figure above and the MTS 311 Load Frame, the results are tabled at table 5.3, figure 5.9 shows unconfined polymer concrete samples results in compression test together. All samples failed in shear as show in figure 5.10.

129 Compression Stress (MPa) Strain Figure 5.9 Unconfined Polymer Concrete Samples Results in Compression Test Together Unconfined Polymer Compressive Strength Strain Corresponding Failure strain Modulus of Elasticity Concrete Samples MPa, ksi to ultimate stress GPa, ksi Sample , , 2590 Sample , , 2270 Sample , , 2250 Average 63.6, , 2370 Table 5.3 Compression Test Results for Unconfined Polymer Concrete

130 129 Figure 5.10 Mode of Failure for Unconfined Polymer Concrete 5.5 Compression test results and Stress and Strain Diagram for Confined Polymer Concrete with Carbon Fiber Sleeve To generate the stress-strain diagrams and compressive strength results of the samples in compression for confined polymer concrete, the MTS 311 Load Frame was used. In this section three samples were mixed with a ratio of 3:1 (polymer concrete) and were reinforced with a carbon fiber sleeve. These three samples were tested in compression with the MTS 311 Load Frame, Figure 5.11 shows the MTS 311 Load Frame with a sample. To measure the stress-strain curves and compressive strength, the load was applied on the top and bottom of the specimens with a mm/sec (0.001 in/sec) load rate. Figures 5.12, 5.13 and 5.14 show the stress and strain curves of these three samples.

131 Compression Stress (MPa) 130 Figure 5.11 Confined Polymer Concrete with Extensometer under MTS Load Frame 311 Sample Strain Figure 5.12 Stress-Strain Curves for Sample 1 of Confined Polymer Concrete

132 Compression Stress (MPa) Compression Stress (MPa) Sample Strain Figure 5.13 Stress-Strain Curves for Sample 2 of Confined Polymer Concrete Sample Strain Figure 5.14 Stress-Strain Curves for Sample 3 of Confined Polymer Concrete According to figure above and the MTS 311 Load Frame, the results are tabled at table 5.4 and figure 5.15 shows confined polymer concrete samples results in compression test together All samples failed in shear as show in figure 5.16.

133 132 Confined Polymer Compressive Strength Strain Corresponding Failure strain Modulus of Elasticity Concrete Samples MPa, ksi to ultimate stress GPa, ksi Sample , , 3368 Sample , , 2690 Sample , , 2419 Average 65.7, , 2825 Table 5.4 Compression Test Results for Confined Polymer Concrete Figure 5.15 Confined Polymer Concrete Samples Results in Compression Test Together Figure 5.16 Mode of Failure for Confined Polymer Concrete

134 Compression Test Results and Stress and Strain Diagram for Unconfined Cement Concrete To generate the stress-strain diagrams and compressive strength results of the samples in compression for unconfined cement concrete, the MTS 311 Load Frame was used. In this section three samples were tested in compression with the MTS 311 Load Frame. Figure 5.17 shows the MTS 311 Load Frame with a sample. To measure the stress-strain curves and compressive strength, the load was applied on the top and bottom of the specimens with a mm/sec (0.001 in/sec) load rate. Figures 5.18, 5.19 and 5.20 show the stress and strain curves of these three samples. Figure 5.17 Unconfined Cement concrete with Extensometer under MTS Load Frame 311

135 Compression Stress (MPa) Compression Stress (MPa) 134 Sample Strain Figure 5.18 Stress-Strain Curves for Sample 1 of Unconfined Cement Concrete 30 Sample Strain Figure 5.19 Stress-Strain Curves for Sample 2 of Unconfined Cement Concrete

136 Compression Stress (MPa) 135 Sample Strain Figure 5.20 Stress-Strain Curves for Sample 3 of Unconfined Cemente Concrete According to figure above and the MTS 311 Load Frame, the results are tabled at table 5.5 and figure 5.21 shows unconfined cement concrete samples results in compression test together All samples failed in cone and shear as show in figure Unconfined Cement Compressive Strength Strain Corresponding Failure strain Modulus of Elasticity concrete Samples MPa, ksi to ultimate stress GPa, ksi Sample , , 3665 Sample , , 4100 Sample , , 3360 Average 23.9, , 3708 Table 5.5 Compression Test Results for Unconfined Cement Concrete `

137 Stress (MPa) Strain Figure 5.21 Unconfined Cement concrete Samples Results in Compression Test Together Figure 5.22 Mode of Failure for Unconfined Cement concrete 5.7 Compression Test Results and Stress and Strain Diagram for Confined Cement Concrete To generate the stress-strain diagrams and compressive strength results of the samples in compression for unconfined cement concrete, the MTS 311 Load Frame was used. In this section three samples were tested in compression with the MTS 311 Load Frame. The figure for

138 137 confined cement concrete under MTS load frame is same as Figure To measure the stressstrain curves and compressive strength, the load was applied on the top and bottom of the specimens with a mm/sec (0.001 in/sec) load rate. Figures 5.23, 5.24 and 5.25 show the stress and strain curves of these three samples.

139 Compression Stress (MPa) Compression Stress (MPa) sample strain Figure 5.23 Stress-Strain Curves for Sample 1 of Confined Cement Concrete Sample Strain Figure 5.24 Stress-Strain Curves for Sample 2 of Confined Cement Concrete

140 Compression Stress (MPa) Sample Strain Figure 5.25 Stress-Strain Curves for Sample 3 of Confined Cement Concrete According to figure above and the MTS 311 Load Frame, the results are tabled at table 5.6 and Figure 5.26 shows unconfined cement concrete samples results in compression test together All samples after compression test are show in figure Confined Cement Compressive Strength Strain Corresponding Failure strain Modulus of Elasticity concrete Samples MPa, ksi to ultimate stress GPa, ksi Sample , , 4821 Sample , , 4687 Sample , , 4667 Average 42.5, , 4728 Table 5.6 Compression Test Results for Confined Polymer Concrete

141 Compression Stress (MPa) Strain Figure 5.26 Confined Cement concrete Samples Results in Compression Test Together Figure 5.27 Mode of Failure for Unconfined Cement concrete before and after Compression Test 5.8 Summery Result discussion of Compression Test In this section were discuses of compression test result and compare cemented and polymer material together. Figure 5.28 shows and compression test results for cemented and polymer concrete with and without confined are tabled at table 5.7.

142 Compression Stress (MPa) Confined Polymer Concrete Unconfined Polymer Concrete Confined Cemented Concrete Unconfined Cemented Concrete Strain Figure 5.28 Cemented and Polymer Concrete Samples Results in Compression Test Samples Ultimate Stress MPa, ksi Strain in/in corresponding to ultimate stress Failure Strain E Gpa, ksi Uncf CC , , 3665 Uncf CC , , 4100 Uncf CC , , 3360 Conf CC , , 4821 Conf CC , , 4687 Conf CC , , 4667 Uncf PC , , 2590 Uncf PC , , 2270 Uncf PC , , 2250 Conf PC , , 3368 Conf PC , , 2690 Conf PC , , 2419 Table 5.7 Compression Test Results for Cemented and Polymer Concrete with and without confined From the stress strain curve in Figure 5.28, it is seen that polymer concrete samples are stronger than regular cement concrete, according to table 5.7, the average value for unconfined cement concrete for ultimate stress, strain corresponding to ultimate stress, failure strain and young modulus is 23.9 MPa (3.45 ksi), , and 25.6 GPa (3708 ksi) respectively. The average value for confined cement concrete for ultimate stress, strain corresponding to ultimate

143 142 stress, failure strain and young modulus is 42.5 MPa (6.16 ksi), , and 32.6 GPa (4728 ksi) respectively. The average value for unconfined polymer concrete for ultimate stress, strain corresponding to ultimate stress, failure strain and young modulus is 63.6 MPa (9.23 ksi), , and GPa (2340 ksi) respectively. The average value for confined polymer concrete for ultimate stress, strain corresponding to ultimate stress and young modulus is 65.7 MPa (9.53 ksi), , and 19.5 GPa (2828 ksi) respectively. According to compression test results, confined polymer concrete is 3%, 64% and 35% stronger than unconfined polymer concrete, unconfined cement concrete and confined cement concrete in compression which shows. The samples with carbon fiber sleeve and those with no carbon fiber sleeve were almost identical in maximum compression strength. Confined polymer concrete has a modulus of elasticity that is a 16% higher than unconfined polymer concrete. In cement concrete, confined cement concrete is 44% stronger than unconfined cement concrete, confined cement concrete has a modulus of elasticity that is 21% higher than unconfined cement concrete. In this test confined cement concrete had a failure strain of 98%, 80% and 70% which is higher than the values for unconfined cement concrete, unconfined polymer concrete and confined polymer concrete respectively. Confined cement concrete has almost 1.5 in displacement in compression test and figure 5.27 shows sample before and after compression test. The large strain values seen for the cement concrete samples is due to the fact that the carbon fiber sleeve confined the sample during the compression test which allowed for large strains to transfer into the sample. Also, the carbon sleeve that is used does not have any seem or weak area which is the point where failure could originate. The confine polymer concrete samples are stronger and therefore the samples do not fail gradually. They tear the carbon fiber sleeve with a brittle type failure. 5.9 Tensile Test Results for Carbon Fiber Sleeve Samples

144 143 In this section three samples with a carbon fiber sleeve were tested with the MTS 311 Load Frame. In these tests, the samples were held in place by gripping mechanisms at the top and bottom of the MTS. An extensometer was placed in the middle of the fiber specimens. To prevent any sliding of the samples from the grip, a slip resistant grip was used. A deformation controlled testing procedure was then performed. ASTM D3039 was used for all three tests. For some of the tensile tests the displacement rate was varied. According to the ASTM D3039 method, to measure the tensile stress and tensile strain diagram, the load is applied at the top and bottom of the specimens with mm/sec (0.001 in/sec) load rates. A strain gauge was attached to each to measure strain. Figure 5.29 shows the MTS with a carbon fiber sleeve and with extensometer. Figure 5.29 MTS with Sleeve Fiber Carbon with Extensometer Minutes later, the samples reached failure and the tensile stress and strain diagrams were recorded. Figures 5.30, 5.31 and 5.32 show the tension stress and strain diagrams for these samples.

145 Tensile Stress (MPa) Tension Stress (MPa) Sample Strain Figure 5.30 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 1) Sample Strain Figure 5.31 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 2)

146 Tension Stress (MPa) Sample Strain Figure 5.32 Tension Stress and Strain Diagrams for Carbon Fiber Sleeve (Sample 3) According to the figure above and the MTS results, the maximum tensile for samples 1, 2 and 3 are MPa (44.6 ksi), (44.34 ksi), 314.3, (45.58 ksi) respectively. The maximum strain for samples 1, 2 and 3 are 0.058, and respectively and table 5.8 shows the summery results for FRP in tension test. Figure 5.33 shows carbon fiber sleeve samples results in tension test together and Figure 5.34 shows the carbon fiber sleeves after failure. FRP Ultimate Stress Strain Corresponding Modulus of Elasticity Samples (MPa, ksi) to ultimate stress (GPa, ksi) Sample , , 3800 Sample , , 3585 Sample , , 3712 Average 309.2, , 3698 Table 5.8 Summery Results of Carbon Fiber sleeve in Tensile Test

147 Tensile Stress (MPa) Strain (in/in) Figure 5.33 Carbon Fiber Sleeve Samples Results in Compression Test Together Figure 5.34 Carbon Fiber Strip Samples were failed after Tensile Test The average values of a carbon fiber sleeve in ultimate tensile stress, strain corresponding to ultimate stress and young modulus in the tension test is MPa (44.84ksi), and25.5 MPa (3698 ksi) respectively. Usually engineers use a steel bar in cement concrete to make concrete stronger in tensile stress, because concretes are very weak in tensile force. To strengthen polymer concrete in tension, a carbon fiber sleeve is used. The advantage of carbon

148 147 fiber compared to a steel bar is that the steel bar is heavier than fiber carbon. The ultimate tensile stress for a steel bar is between MPa (40-60 ksi) but a carbon sleeve fiber is almost 310 MPa (45 ksi). Polymer concrete is week in tensile force according to section 5.3. The tensile stress of polymer concrete is 9.6 MPa (1.4 ksi) which is very week compared to polymer concrete in compressive stress. Carbon fiber sleeve is more ductile material compare to steel rebar because the modulus of elasticity of fiber carbon is 25.5 GPa (3698 ksi) and for steel is 200 MPa (29000 ksi) Experimental Flexure Test Results The flexure test method measures behavior of materials subjected to simple beam loading ASTM D7264. It is also called a transverse beam test with some materials. Maximum fiber stress and maximum strain are calculated for increments of load. Results are plotted in a stressstrain diagram. Flexural strength is defined as the maximum flexure stress or bending stress, in the outermost fiber. This is calculated at the surface of the specimen on the convex or tension side. Flexural modulus is calculated from the slope of the stress vs. deflection curve. If the curve has no linear region, a secant line is fitted to the curve to determine slope. A flexure test produces compression stress in the concave side of the specimen and tensile stress in the convex side. This creates an area of shear stress along the midline. To ensure the primary failure comes from tensile or compression stress the shear stress must be minimized. This is done by controlling the span to depth ratio; the length of the outer span divided by the depth (height) of the specimen. Flexure testing is often done on relatively flexible materials such as concrete, steel, polymers, wood and composites. There are two test types one point load and tow point load. In one point load, load was applied in middle of beam. In two point load, loads were applied at two point of beam.

149 Flexure Test Results for Confined Polymer Concrete In this section three reinforced polymer concrete samples were tested in one point load flexure with MTS 311Load Frame and load rate of mm/sec (0.001 in/sec). The confined polymer concrete pile/beam under flexure test is shows at Figures Figures 5.36, 5.37 and 5.38 show the graphs for Load-displacement for confined polymer concrete pile/beam samples. The neutral axis for this section is 1.6 cm (0.62 in) from the top of pile sample. Figure 5.35 Confined Polymer Concrete Pile/Beam under Flexure Test

150 Load (KN) Load (KN) Load (KN) Displacement (mm) Figure 5.36 Flexure Test Diagram for Confined Polymer Concrete of Sample Displacement (mm) Figure 5.37 Flexure Test Diagram for Confined Polymer Concrete of Sample Displacment (mm) Figure 5.38 Flexure Test Diagram for Confined Polymer Concrete of Sample 3

151 Load (KN) 150 According to figure above and the MTS results of the bending moment, displacement and bending stress for the Confined polymer concrete beam/pile for samples 1, 2 and 3 are recorded in Table 5.9. Figure 5.39 shows load displacement diagram for confined polymer concrete pile/beam samples in flexural test together and Figure 5.40 shows the confined polymer concrete beam/pile sample after test. Max Load (KN, kip) Displacement (cm, in) Bending Moment (KN-m, k ) Sample , , , Sample , , , Sample , , , average 16.1, , , Table 5.9 Results of Flexure Test for Confined Polymer Concrete Pile/Beam Displacement (mm) Figure 3.39 Load Displacement Diagram for Confined Polymer Concrete Pile/Beam Samples in Flexural Test Together

152 151 Figure 5.40 Confined Polymer Concrete Beam/Pile Samples Failed After Flexure Test 5.12 Theoretical Analyses The goal of this section is used theory method to find neutral axis, bending moment, moment curvature and load-displacement curve, and compare theory results with experiment results Theoretical Analyses to calculate natural axis, bending moment and bending stress for pile polymer concrete In this section, the reinforced pile polymer concrete was analyzed to calculate the neutral axis of reinforced pile polymer concrete. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression. There is a compressive (negative) strain at the top of the beam or pile, and a tensile (positive) strain at the bottom of the beam or pile. Therefore by the Intermediate Value Theorem, there

153 152 must be some point in between the top and the bottom that has no strain, since the strain in a beam or pile is a continuous function. In this research the cross section of the piles is circular. To calculate the neutral axis, static equilibrium for the compressive and tensile effect on the cross section and the computer based program, MATHCAD, were used. As mentioned before the reinforced pile polymer concrete is a polymer concrete which is a reinforced with a carbon fiber sleeve. Polymer concrete was designed for compressive forces and the carbon fiber sleeve was designed for tensile forces, there is a small amount of polymer concrete that is used in tension which is ignored. The carbon fiber sleeve is analogous to concrete reinforced with steel bar. To calculate the neutral axis, the stress-strain diagram for compression and stress-strain diagram for tensile strength were needed. Figure 5.13 from Section 5.5 and Figure 5.31 from Section 5.9 were used for the stress-strain diagrams for compression and tensile strength respectively. The pile has a 7.62 cm (3 in) diameter and the fiber has a mm (0.03 in) thickness. For calculation purposes, the thickness of fiber was taken as 1.27 mm, 0.05 in (t FRP =0.05in) due to the extra thickness from the epoxy resin. To find the compression equation from Figure 5.13, interpolation function were used and Figure 5.41 shows compression stress-strain diagram with an equation

154 Compression Stress (MPa) y = x x x x x Strain Figure 5.41 Compression Stress-Strain Diagram with an Equation According to the Figures above, the maximum compressive strength is 65.5 MPa (9.5 ksi) (σ PL =65.5 MPa) and failure strain is 0.04 (ε PLfailure = 0.04). The compression equation is: σ = ε ε ε ε ε (5.2) Equation (5.1) can be summarized as σ = a 5 ε 5 + a 4 ε 4 + a 3 ε 3 +a 2 ε 2 + a 1 ε +a 0 a 5 = a 4 = a 3 = a 2 = a 1 = a 0 = Equation (5.2) was then input into MATHCAD with the compressive stress as a function of strain for the stress-strain diagrams from Figure (5.13)

155 Tensile Stress (MPa) 154 PL ( ) a 5 5 a 4 4 a 3 3 a 2 2 a 1 a 0 if PLfailure 0 otherwise (5.3) For the tensile stress equation, Figure 5.32 from Section 5.9 (Tensile Test Results for Sleeve Fiber Carbon Samples) was used. According to Figure 5.32 was used to estimate the maximum strain which is (ε FRPfailure = 0.051) and maximum tensile stress, MPa (45.58 ksi) (σ FRP = ksi). Figure 5.42 shows the tensile stress-strain diagram with an equation. The equation came from spreadsheet calculations with a regression analysis y = 5,120,146.10x 3-529,597.72x ,020.66x Strain (in/in) Figure 5.42 Tensile Stress- Strain Diagram with an Equation According the Figure 5.27 above the tensile equation is: σ = ε ε ε (5.4) Eq (5.3) can be summarized as σ = c 3 ε 3 + c 2 ε 2 + c ε + c 0 c 3 = c 2 = c 1 =

156 155 Equation (5.4) was inputted into MATHCAD, which is tensile stress for fiber carbon sleeve is a function of strain for stress-strain diagram from Figure (5.31). FRP Te nsion ( ) c 3 3 c 2 2 c 1 c 0 if FRPfailure (5.5) 0 otherwise As previously mentioned, the samples have a circular cross section. Within this cross section, a portion of the polymer concrete is designed for compression strength. The carbon fiber sleeve with a smaller portion of polymer concrete is designed for tensile strength. In this section, the strain of compression ε C (θ) and strain of sleeve fiber carbon ε T (θ) were calculated. The compression strain and tensile strain are functions of the angle between the center of the cross section and the assumed neutral axis c. This angle is defined as θ. Figure 5.43 shows the cross section of the piles with an angle of θ.

157 156 Sleeve Fiber Carbon Polymer Concrete c Neutral Axis D=3 in θ Center of Cross section Figure 5.43 Cross Section of Piles with Angle of θ To calculate the strain in compression and tension, first the strain of polymer concrete must be calculated when the carbon fiber sleeve reaches maximum strain which is defined as ε PLtop. Equation (5.5) is used to calculate ε PLtop as show below: c PLtop FRPfailure 2r c (5.6) In the above equation, c is the neutral axis, r is the radius of the cross section and ε FRPfailure is the failure strain of the carbon fiber sleeve which is After calculating ε FRPtop, to calculate the compression strain and tensile strain two condition must be considered. The Equations (5.6) and (5.7) calculated strains using these two conditions.

158 157 The first condition, when ε PLtop > ε PLfailure means that polymer concrete failed first. The second condition, when ε PLtop < ε PLfailure means that carbon fiber sleeve initially failed. [ c ( r r sin( ) )] C ( ) PLfailure if c PLtop PLfailure [ c ( r r sin( ) )] FRPfailure otherwise 2r c (5.7) ( r c r sin( ) ) T ( ) PLfailure if c PLtop PLfailure ( r c r sin( ) ) FRPfailure otherwise 2r c (5.8) The Figure 5.44 shows the geometry and force effect on cross section. Figure 5.44 Geometry and Force Effect on Cross Section Tensile force and compression force were calculated by integration of the tension zone and compression zone. Equation 5.8 and Equation 5.9 were used to calculate the tensile force and compression force

159 158 2 Tensile asin ( r c) r r FRP T ( ) 2 t FRP d (5.9) 2 Compression asin ( r c) r PL C ( ) r 2 r cos ( ) d (5.10) To find the neutral axis c, the difference between the tensile force and compression force should be zero, and then in MATHCAD a trial and error method was used to find the exact neutral axis. According to MATHCAD, the neutral axis is around 1.6 cm (0.62 in) from the top of the pile sample, which is an area where the tensile force and compression force is zero. The magnitude of the forces for tension and compression is 95.5 MPa (13.85 ksi). With the neutral axis now calculated, a new neutral axis is calculated for the bending moment and bending stress (flexure stress). The theoretical results and compared with the experimental result. In order to find the bending moment, it is necessary to calculate the moment for tension and compression then by adding between the tension moment and compression moment gives the bending moment. According to the definition of moment, moment is a force times the length. The force which is the tension and compression force and the length is from each point of force to the top of the pile sample. Equations (5.8) and (5.9) are used to calculate tensile moment and compression moment.

160 159 2 M T r FRP FRP ( ) 2 t FRP ( r r sin( ) ) d asin ( r c) r 2 M C asin ( r c) r PL PL ( ) r 2 r cos ( ) ( r r sin( ) ) d (5.11) (5.12) The summation of two equations above are the bending moment which is M T + M C = 3.97 KN-m (35.2 kip-in). According to bending moment formula, σ = Mc/I, σ is a bending stress, M is the bending moment, c is the neutral axis and I is the moment of inertia. The bending stress is MPa (5.5 ksi) Theoretical Analyses to calculate load-displacement curve for pile polymer concrete In this section, the reinforced pile polymer concrete was analyzed to calculate and graph the load-displacement curve of reinforced pile polymer concrete. To calculate and graph loaddisplacement curve same process of section were fallowed, but institute of Eq (5.6) and Eq (5.7), Eq (5.10) and Eq (5.11) were used as show below, κ is a curvature. In this section to calculate compressive and tensile strain used C ( ) [ c ( r r sin( ) )] T ( ) ( r c r sin( ) ) (5.13) (5.14)

161 160 To calculate load-displacement curve, these process should be fallow; 1. Calculate moment curvature curve, first needed to calculate maximum curvature which is a κ max = εc (π/2)/c, in this case c = m (c = 0.62 in) and κ max = 0.82 (κ max = ) 2. Used process as mention before with maximum curvature κ max = 0.82 (κ max = ) to find bending moment. The bending moment with maximum curvature is 3.97 KN-m (35.2 k ) 3. With different value of curvature from 0% to 100% of maximum curvature, bending moments were calculated. The value of different percentage of maximum curvature and bending moment are tabled at table Percentage of κ max Bending moment Percentage of κ max Bending moment (KN-m, K ) (KN-m, K ) 0% x κ max 0.0, % x κ max 3.02, % x κ max 0.48, % x κ max 3.14, % x κ max 0.92, % x κ max 3.26, % x κ max 1.32, % x κ max 3.36, % x κ max 1.67, % x κ max 3.44, % x κ max 1.98, % x κ max 3.52, % x κ max 2.25, % x κ max 3.60, % x κ max 2.48, % x κ max 3.68, % x κ max 2.69, % x κ max 3.77, % x κ max 2.86, % x κ max 3.85, % x κ max 3.96, Table 5.10 different percentage of maximum curvature and bending moment

162 Curvature (1/m) Curvature (1/m) Different value of curvature and bending moments, curvature moment curve is show at Figure 5.45 and Moment (KN-m) Figure 5.45 Moment Curvatures Curve 5. To find the moment curvature equation from Figure 5.44, interpolation function were used and Figure 5.46 shows moment curvature curve with equation y = x x x x Moment (KN-m) Figure 5.46 Moment Curvature with an Equation According to figure 5.45, the moment curvature equation is a: κ = M M M M (5.15)

163 In this problem to fined bending moment for pile polymer concrete was assumed, beam with a simply support, according to the beam with simply support, the moment formula is, P is a load and x is a length of beam. Insistent of M in eq (5.15), Px/2 was used, then the equation became; κ = (Px/2) (Px/2) (Px/2) (Px/2) (5.16) 7. To calculate load-displacement formula needed to use second integration of Eq (5.16) according to Eq (5.17), y is a displacement and x is a length of beam. κ = dy 2 /dx 2 dy 2 = κ dx 2 y = κ dx 2 (5.17) The Eq (5.18) is a main formula to calculate load-displacement carves: y = 7.7E-06 P 4 x 6 6.1E-05 P 3 x E-04 P 2 x Px 3-5.5E-04 x E-07P 4 x E-05 P 3 x 1.07 E-04 P 2 x Px+5.06 E-04x (5.18) 8. To graph load-displacement curve, needed to replace length and load in to Eq (5.15). The value of length and load which are obtained from experiment results. Length was 0.46 m (18 in) (x=0.46 m) because, the load was apply at middle of beam according to Figure 5.34 one point load flexure test, piles polymer concrete were tested in this research, they were 0.92 m (36 in) length.

164 Load (KN) 163 As mention before, three samples of pile polymer concrete were test at flexure test, according to section 5.8. The maximum loads for samples 1, 2 and 3 in a flexure test are 15.8 KN (3.56 k), 16.2 KN (3.66 k) and 16.3 KN (3.67 k) respectively. To graph theoretical loaddisplacement curve for each sample needed to replace a different load number from 0 kips to maximum load of each samples in to the Eq (5.15) which is P and length is constant value which is equal to 0.45 m (18 in) (x=0.46 m). The load number for sample 1 is a between 0 kip to 15.8 KN (3.56 k) and different load displacement value are tabled at table 5.11 which is calculated from Eq (5.15) with length is equal to 0.45 m (18 in). Figure 5.47 shows theoretical load-displacement curve for sample 1 and Figure 5.48 shows the theoretical and experimental curve results together for sample 1. Load 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15.8, (KN,k) Dis (mm,in) Table 5.11 Theoretical Results of Load Displacement of Sample 1 for Flexure Test Displacement(mm) Figure 5.47 Load-Displacement Curves for Sample 1

165 Load (KN) Sample Experiment Analysis Theory Analysis Displacement(mm) Figure 5.48 Theoretical and Experimental Curves Results Together According to Figure 5.48, error between experiment and theory results is a 10% at maximum displacement. The load number for sample 2 is a between 0 kip to 16.2 KN (3.66 kips) and different load displacement value are tabled at table 5.12 which is calculated from Eq (5.15) with length is equal to 0.45 m (18 in) 0.46 m (18 in). Figure 5.49 shows theoretical load-displacement curve for sample 2 and Figure 5.50 shows the theoretical and experimental curve results together. Load 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.2, (KN,k) Dis (mm,in) Table 5.12 Theoretical Results of Load Displacement of Sample 2 for Flexure Test

166 Load (KN) Load (KN) Displacement(mm) Figure 5.49 Theoretical Load Displacement Curves for Sample 2 Sample Experiment Analysis Theory Analysis Displacement(mm) Figure5.50 Theoretical and Experimental Curves Results Together According to Figure 5.50, error between experiment and theory results is a 9% at maximum displacement. The load number for sample 3 is a between 0 kip to 16.3 KN (3.67 kips) and different load displacement value are tabled at table 5.13 with length is equal to 0.45 m (18 in). Figure

167 Load (KN) shows theoretical load-displacement curve for sample 3 and Figure 5.52 shows the theoretical and experimental curve results together. Load 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.3, (KN,k) Dis (mm,in) Table 5.13 Theoretical Results of Load Displacement of Sample 3 for Flexure Test Displacement(mm) Figure 5.51 Theoretical Load Displacement Curves for Sample 3

168 Load (KN) Sample 3 Experiment Analysis Theory Analysis Displacement(mm) Figure 5.52 Theoretical and Experimental Curves Results Together According to figure 5.52, error between experiment and theory results is a 2% at maximum displacement. The load number for average load value of flexure test for confined polymer concrete pile/beam at Table 5.9 is a between 0 KN (0 kip) to 16.1 KN (3.62 kips) and different load displacement value are tabled at table 5.14 which is calculated from Eq (5.15) and the length was a 0.46 m (18 in). Figure 5.53 shows theoretical load-displacement curve for average load value and Figure 5.54 shows the theoretical and experimental curve results for all experiment test together. The average error between theory and experiment results is a 7% according to Figure Load 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.1, (KN,k) Dis (mm,in) Table 5.14 Theoretical Results of Load Displacement of Sample 3 for Flexure Test

169 Load (KN) Load (KN) Displacement(mm) Figure 5.53 Theoretical Load Displacement Curves for Average Load Value Experiment Analysis Theory Analysis Displacement(mm) Figure 5.54 Theoretical and all Experimental Curves Results Together To analyze the flexural capacity of the confined polymer concrete sample, the samples were studied using theoretical methods with MATTCAD to calculate the bending moment in samples with 7.62 cm (3 in) diameter and cm (36 in) length. To calculate the bending moment in the theoretical analysis, the tensile strength of the carbon fiber sleeve was calculated. The average value of tensile strength in a carbon fiber sleeve is 310 MPa (45 ksi) and this value

170 169 is used as the strength of fiber in a confined polymer concrete pile. From the flexure theoretical analysis, the bending moment for a confined polymer concrete was 3.97 kn-m (35.2 kip-in). After determining the theoretical bending moment, the confined polymer concrete pile was tested with the MTS 311 Load Frame and these results were compared to the theoretical results. From the experimental test results, the bending moment for the samples was 3.69 kn-m (32.67 kip-in). In theoretical bending moment results, the theoretical results are slightly larger than the experiment results but, they are very similar. According to Figure 5.53 shows average load displacement curve for theoretical part is almost 8% different with experiment result at maximum deflection 5.13 Experiment Program and Set up for One Way cycling Load and Two way Cycling Load The confined polymer concrete was evaluated in this study. The static (monotonic) flexural test and theory of flexure test were previously reported. A total of three confined polymer concrete samples were tested in cycling load, two of the samples were tested in one way cyclic load and one of them was tested in two way cyclic load One Way Cyclic Load Test The samples were tested with MTS 311 Load Frame for one way cyclic load. The setup procedure is the same as the static flexural test with load rate of mm/sec ( in/sec). In MTS, there is a program which allows the user to be able to design a program for one way cycling load.

171 170 In the MTS, a program was designed to apply loading and unloading on a beam/pile as one way cyclic load. Figure 5.55 and Table 5.15 shows how MTS applies loading and unloading on confined polymer concrete beam/pile according to ICC-AC 125. Number of Cycling Loading for Cycle 1 Unloading for Cycle 1 Loading for Cycle 2 Unloading for Cycle 2 Loading for Cycle 3 Unloading for Cycle 3 Loading for Cycle 4 Unloading for Cycle 4 Loading for Cycle 5 Unloading for Cycle 5 Loading for Cycle 6 Unloading for Cycle 6 Loading for Cycle 7 Unloading for Cycle 7 Loading for Cycle 8 Unloading for Cycle 8 Loading for Cycle 9 Unloading for Cycle 9 Loading for Cycle 10 Unloading for Cycle 10 Appling Load Apply load from 0 mm to 5.08 mm (0.2 in)with displacement control Unloading load from 5.08 mm (0.2 in) to 0 mm with load control Apply load from 0 mm to mm (0.4 in)with displacement control Unloading load from mm (0.4 in) to 0 mm with load control Apply load from 0 mm to mm (0.6 in)with displacement control Unloading load from mm (0.6 in) to 0 mm with load control Apply load from 0 mm to mm (0.8 in)with displacement control Unloading load from mm (0.8 in) to 0 mm with load control Apply load from 0 mm to 25.4 mm (1.0 in)with displacement control Unloading load from 25.4 mm (1.0 in) to 0 mm with load control Apply load from 0 mm to mm (1.2 in)with displacement control Unloading load from mm (1.2 in) to 0 mm with load control Apply load from 0 mm to mm (1.4 in)with displacement control Unloading load from mm (1.4 in) to 0 mm with load control Apply load from 0 mm to mm (1.6 in)with displacement control Unloading load from mm (1.6 in) to 0 mm with load control Apply load from 0 mm to mm (1.8 in)with displacement control Unloading load from mm (1.8 in) to 0 mm with load control Apply load from 0 mm to 50.8 mm (2.0 in)with displacement control Unloading load from 50.8 mm (2.0in) to 0 mm with load control Table 5.15 Loading and Unloading Procedure for Apply One Way Cyclic Load on Confined Polymer Concrete Beam/Pile

172 Load (kn) Displacment (mm) Number of Cycle Figure 5.55 Loading and Unloading Regime for Confined Polymer Concrete Beam/Pile According to Table 5.15, MTS was set to apply load by displacement control of mm/sec ( in/sec) and for unloading, it was set by load control. The placing of confined polymer concrete beam/pile in MTS is the same as Figure 5.34 at section 5.8. After two hours the samples failed and Figure 5.56 and 5.57 shows hysteric curves for one way cycling load Displacment (mm) Figure 5.56 Hysteric Curves for One Way Cycling Load for sample 1

173 Load (kn) Displacment (mm) Figure 5.57 Hysteric Curves for One Way Cycling Load for sample 2 According to the figure above both samples failed in cycle number eight in sample 1 and failed at kn (2.86 kips) and 38.8 mm (1.52 in) of load and displacement respectively. Sample 2 failed at kn (2.92 kips) and 39.3 mm (1.54 in) load and displacement respectively. Figures 5.58 and 5.59 show the difference between static flexure test and one way cyclic load test (dynamic). For sample 1, one way cyclic load is 23% and 22% weaker than static flexure test in load and displacement respectively. For sample 2, one way cyclic load is 16% and 20% weaker than static flexure test in load and displacement respectively.

174 Load (kn) Load (kn) Static (monotonic) flexur test One way cycling load Displacment (mm) Figure 5.58 Static (Monotonic) Flexure Test Vs. One Way Cyclic Load of Sample Static (monotonic) flexural test One way cycling load Displacment (mm) Figure 5.59 Static (Monotonic) Flexure Test Vs. One Way Cyclic Load of Sample Two Way Cyclic Load Test The samples were tested with MTS 311 Load Frame for two way cyclic load. The setup procedure is the same as static flexural test and one way cyclic load with load rate of mm/sec ( in/sec) as in compression test. During the tensions test when sample was pulled

175 174 up, the sample needed to be attached at supports to apply the load from MTS. The supports were attached to the sample by 25.4 mm (1 in) diameter steel bar. The configuration of the sample in the tension test is as shown in Figure 5.60 Figure 5.60 Snag of Confined Polymer Concrete beam/pile for Support and the Section which is apply the Load for Two Ways Cycling Load In MTS a program was designed to apply load in compression and tension (pushing and pulling) on a beam/pile as two way cyclic load. Figure 5.61 and Table 5.16 show how MTS applies load in compression and tension on confined polymer concrete beam/pile according to ICC-AC 125. Number of Cycling Compression Load (pushing) for Cycle 1 Tension loading (pulling) for Cycle 1 Compression Load (pushing) for Cycle 2 Tension loading (pulling) for Cycle 2 Compression Load (pushing) for Cycle 3 Tension loading (pulling) for Cycle 3 Compression Load (pushing) for Cycle 4 Tension loading (pulling) for Cycle 4 Appling Load Apply compression load (pushing) from 0.0 mm to mm (-0.2 in)with displacement control Apply tension load (pulling) from mm (-0.2 in) to 5.08 mm (0.2 in)with displacement control Apply compression load (pushing) from 5.08 mm (0.2 in) to mm (-0.4in)with displacement control Apply tension load (pulling) from mm (-0.4 in) to mm (0.4 in)with displacement control Apply compression load (pushing) from mm (0.4 in) to mm (-0.6in)with displacement control Apply tension load (pulling) from mm (-0.6in) to mm (0.6in)with displacement control Apply compression load (pushing) from mm (0.6 in) to mm (-0.8in)with displacement control Apply tension load (pulling) from mm (-0.8in) to mm (0.8in)with displacement control

176 Displacment (mm) 175 Compression Load (pushing) for Cycle 5 Apply compression load (pushing) from 20.23mm (0.8 in) to mm (-1.0 in)with displacement control Tension loading (pulling) for Cycle 5 Apply tension load (pulling) from mm (-1.0 in) to 25.4 mm (1.0 in)with displacement control Compression Load (pushing) for Cycle 6 Apply compression load (pushing) from 25.4mm (1.0 in) to mm (-1.2 in)with displacement control Tension loading (pulling) for Cycle 6 Apply tension load (pulling) from mm (-1.2 in) to mm (1.2 in)with displacement control Compression Load (pushing) for Cycle 7 Apply compression load (pushing) from mm (1.2 in) to mm (-1.4 in)with displacement control Tension loading (pulling) for Cycle 7 Apply tension load (pulling) from mm (-1.4 in) to mm (1.4 in)with displacement control Compression Load (pushing) for Cycle 8 Apply compression load (pushing) from mm (1.4 in) to mm (-1.6 in)with displacement control Tension loading (pulling) for Cycle 8 Apply tension load (pulling) from mm (-1.6 in) to mm (1.6 in)with displacement control Compression Load (pushing) for Cycle 9 Apply compression load (pushing) from mm (1.6 in) to mm (-1.8 in)with displacement control Tension loading (pulling) for Cycle 9 Apply tension load (pulling) from mm (-1.8 in) to mm (1.8 in)with displacement control Compression Load (pushing) for Cycle 10 Apply compression load (pushing) from 45.75mm (1.8 in) to mm (-2.0 in)with displacement control Tension loading (pulling) for Cycle 10 Apply tension load (pulling) from mm (-2.0 in) to 50.8 mm (2.0 in)with displacement control Tension loading (pulling) for Cycle 10 Apply tension load (pushing) from 50.8 mm (-2.0 in) to 0.0 mm with displacement control Table 5.16 Compression (Pushing) Load and Tension (Pulling) Lode Procedure for Apply Two Ways Cyclic Load on Confined Polymer Concrete Beam/Pile Number of Cycle Figure 5.61 Compressions (Pushing) Load and Tension (Pulling) Lode Regime for Confined Polymer Concrete Beam/Pile

177 176 According to Table 5.16, for compression (pushing) loading part MTS was set for apply load by displacement control of mm/sec ( in/sec) and for tension (pulling) loading part MTS was set for apply load by displacement control of mm/sec ( in/sec). The Figure 5.62 and Figure 5.63 shows the beam/pile sample when are in compressions (pushing) load and tension (pulling) load respectively. After two and half hour samples were filed and Figure 5.64, Figure 5.65 and Figure 5.66 shows hysteric curves for two ways cycling load, normalize hysteric curves (Chapter 2 section 2.11) and normalize envelop load deflection curves for confined polymer concrete pile/beam sample respectively. Figure 5.62 Beam/Pile when is in Compression (Pushing) Test

178 Load (kn) 177 Figure 5.63 Beam/Pile when is in Tension (Pulling) Test Displacment (mm) Figure 5.64 Hysteric Curves for Two Ways Cycling Load

179 Normalized Load Normalized Displacment Figure 5.65 Normalized Load Displacements Hysteretic Curve for Pile/Beam Figure 5.66 Normalize Envelop Load Deflection Curves According to Figure 5.64, it shows the samples failed at cycle number eight with kn (3.7 kips) and 38.3 mm (1.51 in) for load capacity and displacement respectively. Figure 5.67 shows the difference between a normalized envelope load deflection curve for confined polymer

180 Normalized Load 179 concrete beam/pile with carbon fiber sleeve and confined concrete with longitudinal steel rebar [Priestley and Benzoin 1996] Normalized Displacement Reinforced concrete with steel bar Confined polymer comcrete with Carbon fiber sleeve Figure 5.67 Normalized Envelop Load Deflection Curve for Confined Polymer Concrete Beam/Pile with Carbon Fiber Sleeve Vs, Confined Concrete with Longitudinal Steel Rebar In this section, research results were compared to experiment results of confined polymer concrete beam/pile in two way cyclic load with Priestley and Benzoin reinforced cement concrete with steel rebar in two way cyclic load. During the flexure test and two way cyclic load, cement concrete and polymer concrete failed at the beginning of the test when the sample is in tension because concrete is weak at tension. In tension test, steel rebar were used for tensile load in reinforced cement concrete with steel rebar and carbon fiber sleeve was used to for tension support for polymer concrete. According to Figure 5.67, it shows steel rebar in reinforced cement concrete from zero point at normalize displacement and normalize load to normalized displacement and

181 normalized load. Steel bars react as elastic material when the beam/pile is in tension load from MTS (pulling) and normalize displacement and normalize load from zero to normalized displacements and normalized load steel bars react as elastic material when beam/pile is at compression load from MTS (pushing). This point is a yielding point of steel bars in the Priestley and Benzoin reinforced cement concrete results. After the yielding point, steel rebar material reacts as a plastic material and failed at failure point of normalized displacements and normalized loads when the sample is in tension load (pulling). After reaching the yielding point in compression (pushing), the sample reacts plastically and failed at normalized displacement and normalized load. In reinforced cement concrete, steel bars are reacting as elastic material before the yield point and reacts as plastic material after the yielding point. In carbon fiber sleeve material it reacts as elastoplastic material. Confined polymer concrete failed at a failure point of for normalized displacement and for normalized load when the sample is at tension load (pulling) and failure point of for normalized displacement and for normalized load when the sample is in compression load (pushing). According to maximum displacement, a carbon fiber sleeve deflects 62% more than the steel rebar at the same load. Carbon fiber and steel rebar failed at almost the same load. Confined polymer concrete is more ductile compared to reinforced cement concrete with steel bar, the main reason is because the modulus of elasticity of carbon fiber is 25.5 GPa (3698 ksi) and steel rebar is 200 GPa (29000 ksi) which means the modulus of elasticity of carbon fiber is 7-8 times weaker than steel rebar. So, fiber carbon has more deflection compared to steel rebar at the same load.

182 Interaction Diagram In this section, two columns were modeled with the same geometry, concrete mechanical properties and reinforcing area. The difference is in the reinforcing part. First the columns are modeled as polymer concrete with compressive strength of 63.6 MPa, (9.23 ksi) according to section 5.4, reinforced with steel rebar and the second column is polymer concrete with compressive strength of same as first column and confined with a carbon fiber sleeve. To achieve the interaction diagram, a SAP computer model was used. First, the column was modeled with a 50.8 cm (20 in) diameter of polymer concrete and reinforced with 6-#7 bars. The reinforcing layer of polymer concrete was cm (18 in). Figure 5.68 shows reinforced polymer concrete with steel rebar. The second column was 50.8 cm (20 in) diameter of polymer concrete and confined with a carbon fiber sleeve. Carbon fiber was modeled around of column in the computer model, and defined mechanical properties of the carbon fiber are the same as section 5.9. Figure 5.68 shows confined polymer concrete with carbon fiber sleeve. In this model the reinforced area for two columns are same as each other and yielding stress of steel rebar is assumed 310 MPa (45 ksi) with is the same as carbon fiber failure strength. The main goal is to compare column 1 and column 2 with the same material condition and to observed difference between confined column and unconfined column in interaction diagram. Table 5.17 shows the mechanical properties of two columns. Figure 5.69 shows interaction diagram analysis of cement concrete and polymer concrete and compare the result together.

183 Axis Load P (kn) 182 Column Number Column 1 Column 2 Concrete Strengths (MPa, ksi) 65.7, , 9.52 Reinforced Strength (MPa. Ksi) 310, , 45 Reinforcing Area (cm 2, in 2 ) 23.2, , 3.6 Modulus of Elasticity of Concrete (GPa, ksi) 19.5, , 2828 Modulus of Elasticity of Reinforcing(GPa, ksi) 200, , 3698 Reinforcing Diameter (cm, in) 45.72, , 20 Table 5.17 Mechanical Properties of columns Figure 5.68 Reinforced Cement concrete with Steel Rebar (left) and Confined Polymer Concrete with Carbon Fiber Sleeve (right) Confined Unconfined Moment (kn-m) Figure 5.69 Interaction Diagram Analyses of Cement concrete and Polymer Concrete

184 183 According to figure above shows the confined material is stronger than unconfined material. The axial load of confined concrete is 11% and moment is 14 % stronger than unconfined column because, the carbon fiber sleeve which is confined column. It was able to increase compressive strength of concrete material and also, the reinforced diameter of confined column is larger than unconfined material. The columns confined with a carbon fiber sleeve indicate that this strengthening method can be used to increase effectively the strength and ductility compared to columns reinforced with steel rebar. [Saadatmanesh 1994] 5.15 Interface and Direct Shear Test set up and Analysis This section discuses the interface and direct shear test to determine the interface between confined polymer concrete and uniform sand. The cyclic multi degree of freedom (CYMDOF) device was used. This device was originally designed and developed by Desai and was used by Desai and his coworkers (Drumm 1983, Desai and Rigby 1997, Fishman 1988, and Desai et. al. 2005). The present device which was conceived and redesigned over the period of ten years was modified and fabricated by Desai and Rigby (1997). The modified shear device was built with a provision for undrained interface testing. Figure 5.70 shows the CYMDOF device. The CYMDOF device was used to determine the interface between two materials such as concrete and soil, steel and soil, soil itself and any other material.

185 184 Figure 5.70 CYMDOF Devices under this Study CYMDOF was used in this research to determine the interface between confined polymer concrete and uniform sand. To determine the interface shear testing between these two material, confined polymer concrete was installed above the box and sand is placed at the bottom of the box. The bottom of the box was constant and the upper box move horizontally by a lateral jack. This jack applied lateral load to the sample and normal load was applied on top of the sample with a vertical jack. Figure 5.71 shows that the CYMDOF device with a vertical and lateral jack.

186 185 Figure 5.71 CYMDOF Device with Vertical Jack (Left) and Horizontal Jack (Right) To assemble the sample on the CYMDOF, first you need to turn on the device at zero pressure. After fifteen minutes, the bottom of the box was filed with sand until it reached the edge level of the box. Then it is rodded and compacted at the surface of the sample to make a smooth surface. Figure 5.72 shows sand in the bottom box. Figure 5.72 Sand in Bottom Box of CYMDOF Confined polymer concrete disk was screwed on a steel pad, then the steel pad was placed on upper box, so that the polymer sample was face down and attached to soil on the bottom box. Figure 5.73 shows sample screwed on a steel pad and steel pad on the upper shear

187 186 box. Then the aluminum block was placed on top of the upper box and vertical load which is connected to a vertical jack was applied on the aluminum block. Also, the upper shear box was connected to a lateral jack which applied lateral load. Figure 5.74 shows the aluminum block on the upper box Figure 5.73 Polymer Concrete Screws on Steel Pad Figure 5.74 Aluminum Block on Upper Box After placing the sample into the CYMDOF device, the device is ready to begin running. To run CYMDOF device, a computer program which was made by Material Test System (MTS), called Test Start is run. In this research four types of samples were tested. Each sample was

188 187 tested in interface shear test for normal load of 1000 N (224 lb), 2000 N (448 lb) and 4000 N (896 lb) to determine the shear resistance and friction angle. CYMDOF device first applied normal load on the sample then normal load stayed on the sample for around 20 seconds. Then lateral load was applied to the sample by a vertical jack with load rate of 0.02 mm/sec ( in/sec). In the computer program, maximum horizontal displacement was selected as 8 mm (0.31 in). In this case, CYMDOF device applied horizontal load until the upper shear box with sample moves 8 mm (0.31 in). After that the device stops applying load and starts to reload normal and shear loads. The load rate for each test is tabulated in Table 5.18, 5.19 and Table 5.18 shows load rate for normal load of 1000 N, Table 5.19 shows load rate for normal load of 2000 N and Table 5.20 shows load rate for normal load of 4000 N Max Load (N, lb) 1000, 224 Normal Stress (kpa, psi) 50, 7.25 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection (sec) 1 Table 5.18 Load Rate of Interface Shear Test for Normal Load of 1000 N Max Load (N, lb) 2000, 448 Normal Stress (kpa, psi) 100, 14.5 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection 1 Table 5.19 Load Rate of Interface Shear Test for Normal Load of 2000 N

189 Shear Stress (kpa) 188 Max Load (N, lb) 4000, 896 Normal Stress (kpa, psi) 200, 29 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection 1 Table 5.20 Load Rate of Interface Shear Test for Normal Load of 4000 N After testing these samples, all samples data were recorded and graphed. Figure 5.75, 5.76 and 5.77 shows the curve of interface shear test for sample 1 (0 kg load) for normal load of 1000N, 2000 N and 4000N respectively. 40 Sample 1 with Normal Load of 1000 N Displacemente (mm) Figure 5.75 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 1000N

190 Shear Stress (kpa) Shear Stress (kpa) 189 Sample 1 with Normal Load of 2000 N Displacment (mm) Figure 5.76 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 2000 N Sample 1 with Normal Load of 4000 N Displacment (mm) Figure 5.77 Interface Shear Test Results between Sample 1 and Sand with Normal Load of 4000 N According to the figures above, it shows shear strength and displacement for normal load of 1000 N, 2000 N and 4000 N. Table 5.21 shows normal stress and shear stress for each normal load at maximum shear strength point. The normal and shear stress is normal and shear load divided by area of the sample 1 (16.7 cm, 6.57 in) respectively. Figure 5.78 shows normal stress and shear stress point curve with best fitting curve to calculate friction angle between sample 1 and sand. According to Figure 5.78, the friction angle for sample 1 is a degree, and assumes the cohesion is zero because the sample was sand.

191 Shear Stress (kpa) Shear Stress (kpa) 190 σ (kpa) τ(kpa) Table 5.21 Normal Stress vs. Maximum Shear Stress for Sample Interface Shear Test for sample Normal Stress (kpa) Figure 5.78 Variation of maximum shear stress vs. normal stress for sample 1 Figures 5.79, 5.80 and 5.81 shows the curve of the interface shear test for sample 2 (50 kg, 110 lb load) for normal loads of 1000N, 2000 N and 4000 N, respectively. 40 Sample 2 with Normal Load of Displacment (mm) Figure 5.79 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 1000N

192 Shear Stress (kpa) Shear Stress (kpa) 191 Sample 2 with Normal Load of Displacment (mm) Figure 5.80 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 2000N Sample 2 with Normal Load of Displacment (mm) Figure 5.81 Interface Shear Test Results between Sample 2 and Sand with Normal Load of 4000N According to the figures above, it shows shear strength and displacement for normal load of 1000 N, 2000 N and 4000 N. Table 5.22 shows normal stress and shear stress for each normal load at maximum shear strength point. The normal and shear stress is normal and shear load divided by area of sample 2 (16.8 cm, 6.61 in) respectively. Figure 5.82 shows normal stress and shear stress point curve with best fitting curve to calculate friction angle between sample 2

193 Shear Stress (kpa) Shear Stress(kPa) 192 and sand. According to Figure 5.82, the friction angle for sample 2 is a degree, and assumes the cohesion is zero because the sample was sand. σ (kpa) τ(kpa) Table 5.22 Normal Stress vs. Maximum Shear Stress for Sample Interface Shear Test for sample Normal Stress (kpa) Figure 5.82 Variation of maximum shear stress vs. normal stress for sample 2 Figures 5.83, 5.84 and 5.85 shows the curve of the interface shear test for sample 3 (250 kg, 551 lb load) for normal load of 1000N, 2000 N and 4000N respectively Sample 3 with Normal Load of Displacment (mm) Figure 5.83 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 1000N

194 Shear Stress (kpa) Shear stress (kpa) 193 Sample 3 with Normal Load of Displacment (mm) Figure 5.84 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 2000N 120 Sample 3 with Normal Load of Displacment (mm) Figure 5.85 Interface Shear Test Results between Sample 3 and Sand with Normal Load of 4000N According to the figures above, they show shear strength and displacement for normal load of 1000 N, 2000 N and 4000 N. Table 5.23 shows normal stress and shear stress for each normal load at maximum shear strength point. The normal and shear stress is normal and shear load divided by area of sample 3 (17.0 cm, 6.7 in) respectively. Figure 5.86 shows normal stress and shear stress point curve with best fitting curve to calculate friction angle between sample 3

195 Shear Stress (kpa) 194 and sand. According to Figure 5.86, the friction angle for sample 3 is a degree, and assumes the cohesion is zero because the sample was sand. σ (kpa) τ(kpa) Table 5.23 Normal Stress vs. Maximum Shear Stress for Sample Interface Shear Test for sample Normal Stress (kpa) Figure 5.86 Variation of maximum shear stress vs. normal stress for sample 3 Figures 5.87, 5.88 and 5.89 shows the curve of the interface shear test for sample 4 (500 kg, 1102 lb load) for normal load of 1000N, 2000 N and 4000N respectively.

196 Shear Stress (kpa) Shear Stress (kpa) Shear Stress(kPa) 195 Sample 4 with Normal Load of Displacement (mm) Figure 5.87 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 1000N Sample 4 with Normal Load of Displacment (mm) Figure 5.88 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 2000N Sample 4 with Normal Load of Displacment (mm) Figure 5.89 Interface Shear Test Results between Sample 4 and Sand with Normal Load of 4000N

197 Shear Stress (kpa) 196 According to the figures above, they show shear strength and displacement for normal load of 1000 N, 2000 N and 4000 N. Table 5.24 shows normal stress and shear stress for each normal load at maximum shear strength point. The normal and shear stress is normal and shear load divided by area of sample 4 (16.9 cm, 6.65 in) respectively. Figure 5.90 shows normal stress and shear stress point curve with best fitting curve to calculate friction angle between sample 4 and sand. According to Figure 5.90, the friction angle for sample 4 is degrees, and assumes the cohesion is zero because the sample was sand. σ (kpa) τ(kpa) Table 5.24 Normal Stress vs. Maximum Shear Stress for Sample Direct Shear Test for sample Normal Stress (kpa) Figure 5.90 Variation of maximum shear stress vs. normal stress for sample 3 According to results on the interface shear test, the friction angle between confined polymer concrete and sand for 0 kg, 50 kg, 250 kg and 500 kg are 31.34⁰, 30.27⁰, 30.42⁰ and 30.16⁰ respectively, which is almost same as each other.

198 197 One main purpose in this research was to use different loads on the sample to see how much epoxy resin liquid penetrated into soil, according to Figure 4.20, it shows the penetration of epoxy resin into sand for sample 1 (0 kg) to sample 4 (500 kg) in both cases, the penetration was the same as each other which is almost 3 mm (0.11 in). Before preparation of samples, it was expected that sample 4 would penetrate more into the soil/sand compare to other samples. The reason sample 4 penetrated the same as other ones is that the samples were compacted and this pushed particles of sand/soil together. This created a minimum void ratio between each particle of sand/soil and did not let epoxy resin liquid penetrate more. After determining the friction angle between reinforced polymer concrete and sand with interface shear test, CYMDOF device was used to calculate the friction angle of sand itself. In this test, sand was tested in direct shear test with normal load of 1000 N (224 lb), 2000 N (448 lb) and 4000 N (896 lb). CYMDOF device first applied normal load on the sample then normal load stayed on the sample around 20 seconds. Then lateral load was applied on sample by vertical jack with load rate of 0.02 mm/sec ( in). In the computer program, the maximum horizontal displacement was selected 8 mm (0.31 in), in this case CYMDOF device apply horizontal load until the upper shear box moves 8 mm (0.31). After that the device stopped applying load and started to reload normal and shear load. The load rate for each test is tabulated in Tables 5.25, 5.26 and Table 5.25 shows load rate for normal load of 1000 N, Table 5.26 shows load rate for normal load of 2000 N and Table 5.27 shows load rate for normal load of 4000 N.

199 198 Max Load (N, lb) 1000, 224 Normal Stress (kpa, psi) 50, 7.25 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection (sec) 1 Table 5.25 Load Rate of Direct Shear Test for Normal Load of 1000 N Max Load (N, lb) 2000, 448 Normal Stress (kpa, psi) 100, 14.5 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection 1 Table 5.26 Load Rate of Direct Shear Test for Normal Load of 2000 N Max Load (N, lb) 4000, 896 Normal Stress (kpa, psi) 200, 29 Normal load rate (N/sec, lb/sec) 100, 22.4 Hold (sec) 20 Horizontal Load rate (mm/sec, in/sec) 0.02, 8E-4 Max Horizontal Displacement (mm, in) 8, 0.31 Normal unload Rate (N/sec, lb/sec) 200, 44.9 Horizontal Unload Rate (N/sec, lb/sec) 50, 11.2 Data Collection 1 Table 5.27 Load Rate of Direct Shear Test for Normal Load of 4000 N

200 Shear Stress (kpa) Shear Stress (kpa) 199 After testing the sand sample, all samples data were recorded and graphed. Figure 5.91, 5.92 and 5.93 shows curve of direct shear test for sand sample with normal load of 1000N, 2000 N and 4000N respectively. 25 Sand with Normal Load of Displacment (mm) Figure 5.91 Direct Shear Test Results for Sand with Normal Load of 1000N Sand with Normal Load of Displacment (mm) Figure 5.92 Direct Shear Test Results for Sand with Normal Load of 2000N

201 Shear Stress (kpa) Sand with Normal Load of Displacment (mm) Figure 5.93 Direct Shear Test Results for Sand with Normal Load of 4000N According to the figures above, they show shear strength and displacement for normal load of 1000 N, 2000 N and 4000 N. Table 5.28 shows normal stress and shear stress for each normal load at maximum shear strength point. The normal and shear stress is normal and shear load divided by area of upper box (21 cm, 8.26 in) respectively. Figure 5.94 shows normal stress and shear stress point curve with best fitting curve to calculate friction angle of sand. According to Figure 5.94, the friction angle for sand is 29.5 degrees, and assumes the cohesion is zero because the sample was sand. τ (kpa) σ (kpa) Table 5.28 Normal Stress vs. Maximum Shear Stress for Sand

202 Shear Stress (kpa) 201 Direct Shear Test for sand Normal Stress (kpa) Figure 5.94 Normal Stresses vs. Maximum Shear Stress for Sand In direct shear test results for sand itself, the friction angle is a 29.5⁰ which is almost the same as the friction angle between reinforced polymer concrete and sand. According to Chuang and Reese (1969), Beech and Kulhawy (1987) and Reese and O Neill (1988), they concluded that a dilled confined cement pile failed due to the interface between the pile and soil. In this research, computer modeling assumed that the interface between the confined polymer concrete pile and soil is rigid and failure never occurs between the interface of pile and soil (skin friction).

203 202 CHAPTER 6 NUMERICAL AND COMPUTER MODELING OF POLYMER CONCRETE PILE 6.1 General The desire to understand the physical world and to be able to describe it using mathematical concepts and numbers has long been a goal of scientists and engineers. This desire has been evident since at least the time of Pythagoras. The discipline of geotechnical engineering is no exception, as first researchers and non-practitioners routinely make use of mathematical models and computer technology in their day-to-day work, trying to understand and predict their world of geomaterials. For example, simple numerical procedures have been used for many years in geotechnical practice in the assessment of strength, analysis of soil consolidation, estimation of slope stability and foundation behavior. With the introduction of electronic computers after World War II came the opportunity for engineers to make much more use of numerical procedures to solve the equations governing their practical problems. This new computing power has made possible the solution of quite complicated non-linear, timedependent problems, boundary and initial value problems that were once too tedious and intractable using hand methods of calculation. The ready availability of desktop and portable computers has meant that these numerical tools for the solution of boundary and initial value problems are no longer the preserve of academic and research engineers. With the spectacular improvements in hardware have come major developments in software and very sophisticated packages for solving geotechnical problems are now available commercially. This includes a wide range of software for solving

204 203 problems from the more routine type, such as limiting equilibrium calculations, to the most powerful non-linear finite element analyses [Carter and Desai, 2001]. The availability of this powerful hardware and sophisticated geotechnical software has allowed geotechnical engineers to examine many problems in much greater depth than was previously possible. In particular, they have allowed the possibility of using numerical methods to examine the important mechanisms that control the overall behavior in many problems. Further, they can be used to identify the key parameters in any problem, thus indicating areas that require more detailed and thorough investigation. These developments have also meant that generally better quality field and laboratory data are required as inputs to the various models; furthermore mathematical models are also becoming increasingly important in the workplace. Businesses use model to optimize their future plans [Kim, Cho 2006] [Terzopoulos 1999]. However, in this chapter, computer program such PLAXIS and OPENSEES PL were used to consider axial and lateral behavior of polymer concrete pile in different type of soil and compare polymer concrete pile with traditional cement concrete pile. The Plaxis computer program were used for axial behavior of pile and Opensees PL were used for lateral behavior of pile. In this thesis were adopted from PLAXIS manual V8 and OPENSEES PL version 0.6 user manual 6.2 Plaxis Computer Program Introduction Plaxis is a special two dimensional finite element computer program that has been developed specifically for the analysis of deformation and stability in geotechnical engineering project. The simple graphical input procedures enhanced output facilities provide a detailed

205 204 presentation of computational results. The calculation itself is fully automated and base on robust numerical procedures. Real situation may be modeled either by a plane strain or an axisymmetric model. The program uses a convene graphical user interface that enable users to quickly generate a geometry model and finite element mesh based on a representative vertical cross section of the situation. In this part of study, PLAXIS V8 Professional version Manual were used to model polymer concrete pile in to soil, [PLAXIAS b.v. 2006]. In this study, two type of material models were used; Mohr-Coulomb Model, and Hardening Soil Model Mohr-Coulomb Model and Limitation Mohr-Coulomb Model (MC) is a linear-elastic- perfectly-plastic MC model involves five input parameters, i.e. the modulus of elasticity, E and the poison ratio, ν for soil elasticity; friction angle, φ and the cohesion, c, for soil plasticity and ψ as an angle of dilatancy. This MC model represents a first-order approximation of soil or rock behavior. It is recommended to use this model for first analysis of the problem considered. For each layer on estimates a constant average stiffness. Due to this constant stiffness, computations tend to be relatively fast and obtain a first impression of deformations. Besides the model parameters mentioned above, the initial soil conditions play an essential role in most soil deformation problems. Initial horizontal soil stresses have to be generated by selecting proper K 0 values. MC model has limitation; model is a first order model that includes only a limited number of features that soil behavior shows in realty. Although the increase of stiffness with depth can be taken into account, the Mohr-Coulomb model dose neither includes stressdependency nor stress-path dependency of stiffness or anisotropic stiffness. In general, stress

206 205 states at failure in drained conditions are quite well described using the Mohr-Coulomb failure criterion with effective strength parameter φ and c. However, care must be taken in undrained conditions, since the effective stress path that is followed by the Mohr-Coulomb model may not be realistic. This is particularly the case for soft soils like normally consolidated clays and peat, and also for very stiff, very dense or highly over-consolidated soils. In such cases the effective stress path followed may be incorrect, in turn resulting in an incorrect assessment of the resulting shear strength. Alternatively, the Mohr-Coulomb model may be used with the friction angle φ set to 0 and the cohesion c set to c u (s u ), to enable a direct control of undrained shear strength. In that case notes that the model does not automatically includes the increase of shear strength with consolidation Mohr-Coulomb Model Theory Plasticity is associated with the development of limits allowable stress state and it irreversible strain. In order evaluate whether or not plasticity occurs in a calculation, a yield function, f, is introduction as a function of stress and strain. Plastic yielding is related with the condition yielding function is equal to zero. This condition can often be presented as a surface in principle stress space. A perfectly plastic model is a constitutive model with a fixed yield surface, a yield surface that is fully defined by model parameters and not affected by straining. For stress states represented by points within the yield surface, the behavior is purely elastic and all strains are reversible. The basic principle theory of elastoplasticity the total strain rates can separate in to elastic strain (ε e ) and plastic strain (ε p ). As show in equation 6-1 ε= ε e + ε p (6.1)

207 206 For elastic strain rates Hooke s law is used which show at equation 6-2a and for plastic strain rate is proportional to the derivative of the yield function with respect to the stress according to the classical theory of plasticity [Hill 1950]. This theory means the plastic strain rate can be represented as vectors perpendicular to the surface of yield. This classical form of the theory is referred to as associated plasticity. However, From MC type yield function, the theory of associate plasticity leads to an overproduction of dilatancy. Therefore, in additional to the yield function, a plastic potential function, g, is introduced. The case g is not equal to f is denoted as non-associated plasticity. In general, the plastic strain rate as written as equation 6-2b. ε e = (6.2a) ε p =λ (6.2b) In equation 6-2b, λ is a plastic multiplier, if λ is equal to zero which means pure elastic behavior, if λ is positive, it means plastic behavior. The MC yield condition is an extension of coulomb s friction law to general state of stress. In fact, this condition ensures that Coulomb s law is obeyed in any plane within a material element. The full MC model of yield condition consists of six yield function when formulated in terms of principal stresses [Smith, Griffith 1982], these function are shows from equation 6-3a to 6-3f. These equations were adapted from PLAXIS V8 manual. f 1a = (σ 2 -σ 3 ) + (σ 2 +σ 3 ) sinφ c cosφ <= 0 (6.3a)

208 207 f 1b = (σ 3 -σ 2 ) + (σ 3 +σ 2 ) sinφ c cosφ <= 0 (6.3b) f 2a = (σ 3 -σ 1 ) + (σ 3 +σ 1 ) sinφ c cosφ <= 0 (6.3c) f 2b = (σ 1 -σ 3 ) + (σ 1 +σ 3 ) sinφ c cosφ <= 0 (6.3d) f 3a = (σ 1 -σ 2 ) + (σ 1 +σ 2 ) sinφ c cosφ <= 0 (6.3e) f 3b = (σ 2 -σ 1 ) + (σ 2 +σ 1 ) sinφ c cosφ <= 0 (6.3f) The two plastic model parameters; friction angle φ and the cohesion c are appearing in the yield function. When the condition yield function equal to zero, all yield functions together represent a hexagonal cone in principle in principal stress space as shown in Figure 6-1 Figure 6.1 The Mohr Coulomb Yield Surface in Principle Stress Space [PLAXIAS b.v. 2006]

209 208 In additional to the yield function (f), six plastic potential functions (g) are defined for the MC model and shows from equation 6-3g to 6-3l. These equations were adapted from PLAXIS V8 manual. g 1a = (σ 2 -σ 3 ) + (σ 2 +σ 3 ) sinψ (6.3g) g 1b = (σ 3 -σ 2 ) + (σ 3 +σ 2 ) sinψ (6.3h) g 2a = (σ 3 -σ 1 ) + (σ 3 +σ 1 ) sinψ (6.3i) g 2b = (σ 1 -σ 3 ) + (σ 1 +σ 3 ) sinψ (6.3j) g 3a = (σ 1 -σ 2 ) + (σ 1 +σ 2 ) sinψ (6.3k) g 3b = (σ 2 -σ 1 ) + (σ 2 +σ 1 ) sinψ (6.3l) The Plastic potential function contains a third plastically parameter, the dilatancy angle (ψ). This parameter is to mode plastic volumetric strain increments as actual observed for dense and stiff soils. Discuses of the entire model parameters used in MC model are given at the end of this section Hardening Soil Model and Limitation The hardening soil model is advance model to simulate any type of soil such as soft soil and stiff soil [Schanz, Vermeer 1998]. Mohr-Coulomb model has limiting states of stress are described by means of the friction angle (φ), cohesion (c) and dilatancy angle, (ψ). However, soil stiffness is described much more accurately by using three different input stiff nesses such as Triaxial loading stiffness, triaxial unloading stiffness and oedometer loading stiffness which

210 209 shows by E 50, E ur and E oed respectively. As average values for various soil types, we have E ur 3 E 50 and E oed E 50, but both very stiff soils tend to give other ratios of E oed / E 50. In constant to the Mohr-Coulomb model, the Hardening Soil model also accounts for stress dependency of stiffness moduli. This means that all stiff nesses moduli. This means that all stiffnesses increase with pressure. Hence, all three input stiffnesses relate to a reference stress, being usually taken as 100kPa. Besides the model parameters mentioned above, the initial soil conditions, such as reconsolidation, play an essential role in most soil deformation problems. These can be taken in to account in the initial stress generation. Hardening soil model has limitation; it is a hardening model that does not account for softening due to soil dilatancy and debonding effects Hardening Soil Model Theory The Hardening soil (HS) model uses two failure criteria and plastic potentials, a family of Mohr-Coulomb criterion for deviatoric failure and elliptic cap for volumetric failure are used in Hardening Soil model. Some properties of Hardening Soil model as follow: - Stress dependent stiffness according to a power law with input parameter m - Plastic straining due to primary deviatoric loading with input parameter E 50 ref - Plastic straining due to primary compression with input parameter E oed ref - Elastic unloading / reloading with input parameters E ur ref, v ur - Failure according to the Mohr-Coulomb model with parameters c, ϕ, and ψ

211 210 A formulation of hardening soil model is the hyperbolic relationship between the vertical strain ε 1 equation 6.4 and the deviatoric stress, q, in primary triaxial loading. Standard drained triaxial tests tend to yield curves that can be described by; for q < q f (6.4) The initial stiffness equation 6.5 and q a is the asymptotic value of the shear strength (6.5) This relationship is plotted in Figure 6.2. The parameter E 50 is the confining stress dependent stiffness modulus for primary loading and given by the equation. Instead of the initial modulus, E i, for small strain, E 50, is used as tangent modulus according to Figure 6.2. E 50 is given by the equation 6.6. (6.6) is a reference stiffness modulus corresponding to the reference stress p ref. The actual stiffness depends on the minor principle stress, σ 3, which is the effective confining pressure in triaxial test, and amount of stress dependency is given by the power m. for soft clay, the power should take equal to 1.0 and Janbu (1963) reported value of m around 0.5 for Norwegian sand [Janbu 1963], furthermore Von Soos (1980) reports various different values in the range 0.5 < m < 1.0. as secant modulus E 50,ref is calculated from a triaxial stress-strain graph for mobilization of 50% of the maximum shear strength, which is show in Figure 6.2 The ultimate deviatoric stress, q f, and the quantity q a is:

212 211 (6.7) (6.8) The above equations for q f are derived from the Mohr-Coulomb failure criterion, which involves the strength parameters such as friction angle (φ) and cohesion (c). When q reaches to q f failure criterion is satisfied and perfectly plastic yielding occurs. The failure ratio R f is ratio between q f and q a which is often equal to 0.9. For unloading and reloading stress paths, another stress-dependent stiffness modulus is used; E ur is a young modulus for unloading and reloading according to Equation 6.9 and Figure 6.2. (6.9) Figure 6.2 Hyperbolic stress-strain relation in primary loading for a standard drained triaxial test [PLAXIAS b.v. 2006]

213 212 After calculated E 50 by Equation 6.6, it is now important to calculate the oedometer stiffness, E oed, to calculate oedometer stiffness Equation 6.10 was used. (6.10) is a tangent stiffness modulus as show in figure 6.3. Hence, is a tangent stiffness at major principle stress of σ 1 = p ref. Note that, used σ 1 rather than σ 3 and that was consider primary loading. Figure 6.3 Definition of E oed ref in oedometer test results [PLAXIAS b.v. 2006] For triaxial test the yielding function are defined as, f, and show in equation f = ƒ - γ p (6.11) Where ƒ is a function of stress and γ p (superscript p is used to denote plastic strain) is a function of plastic strain, which shows at equation 6.12 and Here the measure of the plastic

214 213 shear strain γ p according to equation 6.13 is used as the relevant parameter for friction hardening [Schanz 1999]. (6.12) γ p = - (2ε 1 p ε v p ) -2ε 1 p (6.13) In reality, plastic volumetric strains ε p v will never be precisely equal to zero, but for hard soils plastic volume changes tend to be small when compared with the axial strain, so that approximation in equation 6.13 will be generally be accurate. For a given constant value of the hardening parameters, γ p, the yield condition ƒ =0 can be visualized in p -q plane by means of a yield locus. When plotting such yield loci, one has to use equation 6.11 as well as equation 6.6 and 6.9 for E 50 and E ur respectively. Shear yield surfaces do not explain the plastic volume strain that is measured in isotropic compression. A second type of yield surface must therefore be introduced to close the elastic region in the direction of the p-axis. The triaxial modulus largely controls the shear yield surface and the oedometer modulus controls the cap yield surface. The definition of the cap yield surface is as follow [PLAXIAS b.v. 2006]. f c = + p 2 p p 2 (6.14) Where α is an auxiliary model parameter that relates to which is the value for normal consolidation. p and q are related to mean and deviatoric stresses.

215 214 The yield surface of a hardening plasticity model can expand due to plastic straining as show in Figure 6.4. Distinction is made between two main types of hardening, namely shear hardening and compression hardening. Shear hardening is used to model irreversible strains due to deviatoric loading. Compression hardening is used to model irreversible plastic strains due to compression in oedometer loading and isotropic loading [Schanz, Vermeer 1998]. Further information about the Hardening model can be found in Plaxis material manual [PLAXIAS b.v. 2006]. Figure 6.4 Representation of total yielding contour of the Hardening Soil model in Principal stress space for cohesion soil [PLAXIAS b.v. 2006] Interface Theory in PLAXIS Interface elements are typically modeled by using a bilinear Mohr-Coulomb model. When a more advanced model is used for the matching cluster material data set, the interface element will only pick the relevant data for the Mohr-Coulomb model. Therefore stiffness is

216 215 taken to be the elastic soil stiffness. Hence, E=E ur where E ur is stress level dependent, following a power law with E ur proportional to σ m [PLAXIAS b.v. 2006]. Interface elements are often modeled by means of the bilinear Mohr-Coulomb model. In such case, the interface stiffness is taken to be the elastic stiffness. Hence, E= E ur, where E ur is stress level dependent, following a power law with E ur proportional to σ m [PLAXIAS b.v. 2006]. The Mohr-Coulomb yield condition is an extension of Coulomb s friction law to general state of stress. This condition ensures that Coulomb s friction law is obeyed in any plane within a material element. The full Mohr-Coulomb yield condition consists of six yield functions when formulated in terms of principal stresses which show at equation 6.3a to 6.3e. The two plastic model parameters appearing in the yield functions are the well-known friction angle φ and cohesion c. The yield functions together represent a hexagonal cone in principal stress space Figure 6.1. An elastic-plastic model is used to describe the behavior of interfaces for the modeling of soil-structure interaction. However, the coulomb criterion is used to distinguish between elastic behavior, where small displacements can occur within the interface, and plastic interface behavior when permanent slip may occur. For the interface to remain elastic the shear stress τ is given by: < σ n tan φ + c (6.15a) And for plastic behavior τ is given by: = σ n tan φ + c (6.15b) Where φ and c are the friction angle and cohesion of the interface, the strength properties of interfaces are linked to the strength properties of a soil layer. Each data set has an associated strength reduction factor for interfaces (R inter ). The polymer concrete pile is simulated by a linear

217 216 elastic - perfectly plastic model [PLAXIAS b.v. 2006]. In this research were rigid interface (R=1), because failure will happen in to soil. As mention before epoxy resin from polymer concrete were move in to soil and soil around of pile make part of pile body and make interface between pile and soil are stronger than soil interface. 6.3 Compare Experiment Results with PLAXIS Before modeling polymer concrete pile with PLAXIS in Mohr-Coulomb and Hardening Soil model, it is necessary to calibrate PLAXIS computer model with experimental testing. Then a comparison between the PLAXIS computer results and the experimental results can be drawn the accuracy of computer model can be verified. To observe the accuracy of PLAXIS, three types of experiment tests were modeled with PLAXIS such as modeling polymer concrete in compression test, modeling of cemented sand (Ismail 2001) in triaxial test and modeling of cement concrete pile (Ismail 2001) in PLAXIS with Mohr Coulomb and Hardening Soil model Model Polymer Concrete in Compression Test In this section unconfined and confined polymer concrete were modeled in PLAXIS to determine the stress strain curve and compare the plaxis results with experiment results of the stress strain curve of unconfined and confined polymer concrete, which was determined in Chapter 5. For the unconfined polymer concrete, sample 2 (Figure 5.7) was selected and for confined polymer concrete sample 1 (Figure 5.12) was selected. To model polymer concrete in PLAXIS, an axisymmetry model was used. The reason this computer analysis used an axisymmetry model is it has a circular cross section and the end the compression and load results from plaxis were times 2πr (r = radius). To analyze the unconfined and confined polymer concrete in plaxis, the material mode is Mohr-Coulomb and

218 217 the unit weight of polymer concrete is a 21 kn/m 3 (7.73E-05 kci) (Toufigh and Saadatmanesh, 2009), the modulus of elasticity of plain and reinforced polymer concrete are GPa (2340 ksi) and 19.5 GPa (2828 ksi) respectively. The poison ratio of polymer concrete is 0.24 (Rise, 2005). In using Mohr Coulomb theory to calculate stress strain diagram at compression test for polymer concrete, two main parameters were needed. These parameters are friction angle, φ and cohesion, c. To calculate the friction angle and cohesion, Mohr circle theory was used to calculate each circle of unconfined and confined polymer concrete. Equation 6.16a and equation 6.16b for regular cement concrete were used [Macgregor and Wight 2009]. σ 1 = f c + 2 σ 3 (6.16a) σ 1 = f c σ 3 (6.16b) Table 6.1 and Table 6.2 shows unconfined and confined polymer concrete parameter to achieve of Mohr circle respectively, which σ 1 and σ 3 are vertical and horizontal principle stress and f c is ultimate compression stress. Figure 6.5 and Figure 6.6 shows Mohr circle of unconfined and confined polymer concrete respectively. Unconfined Polymer Concrete σ 3 (ksi, MPa) f'c (ksi, MPa) σ1(ksi, MPa) 1.0, , , , , , , , , , , , Table 6.1 Unconfined Polymer Concrete Parameter for Mohr Circle

219 218 Confined Polymer Concrete σ 3 (ksi, MPa) f' c (ksi, MPa) σ 1 (ksi, MPa) 1.0, , , , , , , , , , , , Table 6.2 Confined Polymer Concrete Parameter for Mohr Circle Figure 6.5 Mohr Circle for Unconfined Polymer Concrete for Calculate φ and c

220 Figure 6.6 Mohr Circle for Confined Polymer Concrete for Calculate φ and c According to the tables above, horizontal stress (σ 3 ) was chosen randomly from 1 ksi to 4 ksi and ultimate compression stress (f' c ) was determined by experimental test from chapter 5. These parameter were used in equation 6.16 a and b to calculate friction angle and cohesion. Figure 6.5 and 6.6 shows Mohr circle of unconfined and confined polymer concrete respectively. One of the main reasons to determine friction and cohesion of polymer concrete is that friction and cohesion for a solid material in plaxis assumes the material is plastic and it has plastic reaction. According to figures above, they show inclination lines which are tangent to the circle. The friction angle can be found from the inclination line. The vertical axis is cohesion of unconfined and confined polymer concrete. The friction angle and cohesion for unconfined

221 220 polymer concrete is 18.5⁰ and 3.15 ksi (2.17E4 kpa) and, the friction angle and cohesion for confined polymer concrete is 19.0⁰ and 3.2 ksi (2.2E4 kpa). In the plaxis computer program, a carbon fiber sleeve was model for confined polymer concrete and modeled in the Geogrids section of plaxis. The material type was defined as elastoplastic, because as mentioned in chapter 5, the stress strain graph for the tensile test of carbon fiber sleeve was not linear. For elastoplastic materials in Geogrids, plaxis needs to define EA and N p. These parameters are calculated below. EA = E x t x unite length = 25.5 E 6 kpa x m x 1 = kn/m. N p = σ x t x unite length = kpa x m x 1 = 394 kn/m. E is a modulus of elasticity of carbon fiber sleeve, which is 25.5 GPa (3698 ksi). σ is a compressive strength of carbon fiber sleeve, which is kpa (45 ksi). t is a thickness of carbon fiber sleeve, which is (0.05 in). Unit length is thickness times by unit length. It can be in the units of meters or inches. The polymer concrete was modeled in plaxis, it has geometry of 6 in (15.24 cm) length and 1.5 in (3.81 cm) width. The reason the width in computer model of polymer concrete is half of the experiment model is because, in the plaxis was defined as axisymmetry model. Table 6.3 shows the summery of mechanical parameters of polymer concrete, sleeve fiber carbon and geometry of polymer concrete model.

222 221 Parameter Unconfined Polymer Concrete Confined Polymer Concrete Width 3.81 cm, 1.5 in 3.81 cm, 1.5 in Length cm, 6 in cm, 6 in EA kn/m, 185 k/in N P kn/m, 2.25 k/in E GPa, 2340 ksi 19.5 GPa, 2828 ksi ɣ 21 kn/m 3, 7.73E-05 kci 21 kn/m 3, 7.73E-05 kci v c 2.17E04 kpa, 3.15 ksi 2.20E04 kpa, 3.20 ksi φ 18.5⁰ 20⁰ Table 6.3 Summery of Mechanical properties of Carbon Fiber Sleeve, Polymer concrete and Geometry of Polymer Concrete Figures 6.7 and 6.8 shows unconfined and confined polymer concrete modeled in plaxis respectively, to calculate stress strain curve. The arrows at the top show the sample controlled by displacement or strain. In this model, plaxis calculated the stress strain curve by maximum displacement or strain of 0.24 in (6.1 mm) or 0.04 in/in, which means plaxis calculated the stress strain curve until the sample model reached 0.24 in (6.1 mm) or 0.04 in/in. Figures 6.9 and 6.10 shows the stress strain curve for the computer model and experimental tests. Figures 6.7 and 6.8 at point 0 were defined as horizontally fixed. Point 1 was defined as free and point 2 was defined as vertically fixed. Point 3 was defined as horizontal and vertical fixed. Line 0 to 3 was defined as vertical fix, line 2 to 3 was defined as vertical and horizontal fix and lines of 0 to 1 and 1 to 2 were defined as free.

223 222 Figure 6.7 Unconfined Polymer Concrete PLAXIS Model Figure 6.8 Confined Polymer Concrete PLAXIS Model

224 Compression Stress (ksi) Compression Stress (ksi) unconfined polymer concrete Experiment Results PLAXIS Results Strain (in/in) Figure 6.9 Stress Strain Curves of Computer Model and Experiment for Unconfined Polymer Concrete Confined Polymer Concrete Experiment Results PLAXIS Results Strain (in/in) Figure 6.10 Stress Strain Curves of Computer Model and Experiment for Confined Polymer Concrete According to Figure 6.9 the maximum compression stress of the experiment result and plaxis results are 9.2 ksi (63.5 MPa) and 8.1 ksi (55.9 MPa) respectively, which is a 12% difference between the strain corresponding to maximum compression stress of the experiment result. The plaxis results are and respectively which is 62% difference. According to Figure 6.10 the maximum compression stress of the experimental results and plaxis results are 9.9 ksi (68.2MPa) and 8.7 ksi (59.9MPa) respectively, in there is a 12% difference

225 224 between them. The strain corresponding to maximum compression stress of experimental result and plaxis results are and respectively which is 65% difference. According to Figure 6.9 and 6.10, there is a big deference between the experiment and plaxis results at the strain corresponding to maximum compression stress. This is due to the fact that in plaxis the material model is Mohr-Coulomb. As mentioned before, Mohr-Coulomb theory was calculated as liner elastic material until the model reached the yield point. After the yield point Mohr-Coulomb assumed perfectly plastic Model Cemented Soil in Triaxial Test In this section, cemented sand was modeled in plaxis with Mohr Coulomb and Hardening Soil model and compared the plaxis results with experimental results (Ismail 2001). The mechanical properties of cemented sand are tabled in table 6.4. Furthermore, this section compared Mohr Coulomb theory with hardening soil theory to observe which model is closer to experimental results. Ismail 2001 test cemented sand in triaxial test with horizontal principle stresses (σ 3 ) with 100, 200, 300 and 400 kpa as shown in Figure 2.9a. This model used the same horizontal principle stresses in Mohr Coulomb and hardening soil model to determine deviatoric stress-strain graph.

226 deviatoric stress (kpa) 225 Identification cemented sand Material Model Mohr-Coulomb Hardening Soil ɣ unsat 19 kn/m 3, 120 pcf 19 kn/m 3, 120 pcf ɣ sat 20 kn/m 3, 127 pcf 20 kn/m 3, 127 pcf E ref 56 MPa, 8.1 ksi - E 50 ref E oed ref - 30 MPa, 4.35 ksi - 30 MPa, 4.35 ksi - 90 MPa, ksi v c 20 kpa, 2.9 pcf 20 kpa, 2.9 pcf φ 35⁰ 35⁰ Table 6.4 Mechanical Properties of Cemented Sand [Ismail 2001] E ur ref Figures 6.11, 6.12, 6.13 and 6.14 shows the hardening soil model with horizontal principle stresses of 100, 200, 300 and 400 kpa, respectively. Furthermore these figures were compared with experimental results which are discussed in Section 2.8. The x axis shows strain (%) and in y axis shows deviatoric stress (kpa). 400 σ 3 = 100 kpa Ismail Experiment PLAXIS-M C strain (%) Figure 6.11 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 100 kpa

227 deviatoric stress (kpa) deviatoric stress (kpa) deviatoric stress (kpa) σ 3 = 200 kpa Ismail Experiment PLAXIS-M C strain (%) Figure 6.12 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 200 kpa 1000 σ 3 = 300 kpa Ismail Experiment PLAXIS-M C 0 10 strain (%) Figure 6.13 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 300 kpa σ 3 = 400 kpa Ismail Experiment PLAXIS-M C strain (%) Figure 6.14 Mohr Coulomb Analysis and Ismail Experiment Deviatoric Stress Strain Graph at σ3 = 400 kpa

228 deviatoric stress (kpa) deviatoric stress (kpa) 227 Figures 6.15, 6.16, 6.17 and 6.18 shows hardening soil model with horizontal principle stresses of 100, 200, 300 and 400 kpa, respectively. Furthermore these figures were compared with experiment results which are discussed in Section 2.8. The x axis shows strain (%) and in y axis shows deviatoric stress (kpa). 400 σ 3 = 100 kpa Ismail Experiment PLAXIS-H S strain (%) Figure 6.15 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ 3 = 100 kpa σ 3 = 200 kpa Ismail Experiment PLAXIS-H S 0 10 strain (%) Figure 6.16 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ 3 = 200 kpa

229 deviatoric stress (kpa) deviatoric stress (kpa) σ 3 = 300 kpa Ismail Experiment PLAXIS-H S strain (%) Figure 6.17 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ 3 = 300 kpa 1400 σ 3 = 400 kpa Ismail Experiment PLAXIS- HS 0 10 strain (%) Figure 6.18 Hardening Soil Model and Ismail Experiment Deviatoric Stress Strain Graph at σ 3 = 400 kpa Figure 6.19 shows Mohr coulomb, hardening soil model and Ismail deviatoric stressstrain graphs at all horizontal principle stresses to observe which models are close to experiment results.

230 deviatoric stress (kpa) 229 Ismail Experiment 1200 Mohr Coulomb 1000 Hardening Soil strain (%) Figure 6.19 Mohr Coulomb, Hardening Soil Model and Ismail Experiment Deviatoric Stress-Strain Graph at all Horizontal Principle Stresses In the Figure above, the red dashed line shows the Ismail experiment result. The blue lines show the Mohr coulomb theory analysis, and the green line represents the hardening soil model. The horizontal principle stresses, 100, 200, 300, 400 kpa were applied to the graph from bottom to top respectively. According to Figure 6.19 shows hardening soil model is very close to experimental results because, the hardening soil model analyzed as a elastoplastic material but, mohr coulomb theory analyzed only as linear elastic Model Cement Concrete Pile in PLAXIS In this section, Ismail cement concrete pile was modeled in plaxis in mohr coulomb and hardening soil model to compare with experimental test results for two purposes. The first purpose was to calibrate the plaxis results with experiment results and the second purpose observed which theory (mohr coulomb and hardening soil model) was closer to experimental results.

231 230 To use the plaxis computer program, soil properties in Table 6.4 were used. In the Ismail paper, it does not mention about concrete properties, therefore in this section, the mechanical properties of concrete from chapter 5 were used. Equation 6.16b and mohr circle theory were used to determine friction angle and cohesion of cement concrete. Table 6.5 shows cement concrete parameters for mohr circle which is determined by equation 6.16b and Figure 6.20 Mohr circle of cement concrete. Cement Concrete σ 3 (ksi, f'c (ksi, σ 1 (ksi, MPa) MPa) MPa) 1, , , , , , , , , , , , Table 6.5 Cement Concrete Parameter for Mohr Circle Figure 6.20 Mohr Circle for Unconfined Cement Concrete for Calculate φ and c

232 231 The table above, horizontal principle stresses (σ 3 ) were selected randomly from 1 to 4 kpa as mention at section According to figure above friction angle and cohesion of cement concrete are 37⁰ and 4800 kpa (0.7 ksi) respectively. The cement concrete pile were model in to plaxis, it has geometry of 7.4 ft (2.25 m) length and 2 in (5 cm) width, the reason of width of computer model of cement concrete pile is half of the experiment model is because, in the plaxis was define as axisymmetry model. The Table 6.6 shows the summery of mechanical parameter of cement concrete pile and geometry of cement concrete model. For cemented sand Table 6.4 was used. Parameter Width Length E Cement Concrete Piles 5 cm, 2 in 2.25 m, 7.4 ft 25.6 GPa, 3712 ksi ɣ 24 kn/m 3, 8.85E-05 kci v 0.25 c 4800 kpa, 0.7 ksi φ 37⁰ Table 6.6 Summery of Mechanical properties of Cement Concrete Pile and Geometry of Cement Concrete Pile Figure 6.21 shows a cement pile in plaxis. Before running the program, some properties of plaxis should be consider such as axisymmetry mode, size of mesh which was medium size, and the last part which cannot be ignored, defines two phases. To calculate the piles first phase, the pile is analyzed with self-weight and second phase analyzed the pile with applying load. In this case the reset displacement to zero icon was on and it means plaxis calculated first the load displacement through pile weight then calculated pile displacement with the applied load. In this model plaxis calculated load displacement curves by maximum displacement of 1.18 in (30 mm), which means plaxis calculated load displacement curve until the cement concrete pile model reached 1.18 in (30 mm).

233 232 In Figure 6.21, the dashed line around pile is interface but, in this research as previously mentioned in earlier chapters, failure never occurs in the interface between concrete pile and soil because, the mortar of concrete (water and cement) moves in to the soil around pile making that soil a part of soil. Failure will happen in the soil itself. In this section the interface selected is rigid which means R=1, R=. δ is the friction between pile and soil and φ is soil friction angle. In cement concrete piles, Figure 6.21, the line 0-1 is defined as vertical and horizontal fixed. Line 0-3 and 1-2 are defined as horizontal fixed. Point 2 and 3 are defined as horizontal fixed and point 0 and 1 are defined as vertical and horizontal fixed. Figure 6.21 Cement Pile Model into Cemented Sand (Right), Mesh of Pile before Run the Program (Middle) and Mesh of Pile after Run the Program (Left)

234 Load (kn) 233 Figure 6.22 shows the load displacement model curve of Ismail concrete pile. According to this figure the experimental curve is shown as a blue line, hardening soil model is shown as red dash line and green point line is representing Mohr coulomb theory. According to Figure 6.22, the hardening soil model is closer to the experimental test compared to mohr coulomb theory Mohe Cloulomb Hardening Soil Experiment Displacment (mm) Figure 6.22 Load Displacement of Experiment Test (Blue Line), Hardening soil Model (Red Dash Line) and Mohr Coulomb Theory (Green Point Load) 6.4 Polymer Concrete Pile Modeled in Axial Load at Different Length Size In this part of the research, cement and confined polymer concrete was modeled in axial load with the plaxis computer program in a hardening soil model. Cement and confined polymer concrete piles were modeled in cemented sand with different of pile lengths to observe mechanical behavior of piles.

235 Load (kn) 234 Different sizes of cement concrete and confined polymer concrete pile were modeled in cemented sand. The mechanical properties of polymer concrete, cement concrete and cemented sand were described in pervious sections. The cemented and polymer concrete parts were defined in plaxis in plastic mode and used friction and cohesion parameters for plaxis. Figure 6.23 shows cement and polymer concrete with size of 5 m length and 0.3 m diameter and set the plaxis computer program to calculate load displacement at 0.3 m. Figure 6.24 shows cement and polymer concrete with size of 10 m length and 1 m diameter and set the plaxis computer program to calculate load displacement at 0.5 m. Figure 6.25 shows cement and polymer concrete with size of 20 m length and 1 m diameter and set plaxis computer program to calculate load displacement at 0.5 m. Figure 6.26 shows cementd and polymer concrete with size of 30 m length and 1 m diameter and set plaxis computer program to calculate load displacement at 0.5 m Polymer Concret Cemented Concrete Displacment (mm) Figure 6.23 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 5 m Length and 0.3 m Diameter

236 Load (kn) Load (kn) Load (kn) Polymer Concrete Cmented Concrete Displacment (mm) Figure 6.24 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 10 m Length and 1 m Diameter Polymer Concrete Cemented Concrete Displacment (mm) Figure 6.25 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 20 m Length and 1 m Diameter Polymer Concrete Cemented Concrete Displacment (mm) Figure 6.26 Cement (Blue Dash Line) and Confined Polymer Concrete (Red Line) with Size of 30 m Length and 1 m Diameter

237 236 Figure 6.23 and 6.24 shows confined polymer concrete is not suitable for a short pile. The results are the same as cement concrete pile but, in Figures 6.25 and 6.26 polymer concrete is stronger than a regular cement concrete pile. 6.5 Polymer Concrete Pile Modeled in Axial Load at Different Type of Soil In this section, cement and confined polymer concrete was modeled in different types of soil to observe and compare mechanical strength of cement concrete pile with confined polymer concrete pile. The piles were modeled under three conditions. 1. Model straight piles in different type of soil. 2. Model belled drilled piles in different type of soil. 3. Compare straight piles with belled drilled piles 4. Model piles in different type of soil on bed rock Model Straight Piles in Different Type of Soil In this part, long cylinder cement and confined polymer concrete piles with diameter of 1 m and length of 30 m were modeled into plaxis with hardening soil model. Piles were modeled in five different types of soil and mechanical properties of each soil are tabled at table 6.7 [Das 1999]. In this model, piles were modeled in medium mesh. Figure 6.27 shows confined polymer concrete with meshes and the cement concrete pile meshes Figure is the same as Figure In Material Type at Table 6.7 for sands was defined as drained material and for clays was defined as undrained material. Figures 6.28, 6.29, 6.30, 6.31 and 6.32 are load-displacement curves of cement and confined polymer concrete straight pile in loose sand, dense sand, soft clay, stiff clay and hard clay respectively.

238 237 In this model, plaxis was used to calculate load displacement at 1 m (39.4 in). Although the 1 m displacement for a pile is not applicable in engineering field, a manual such as Canadian Foundation Manual states that the maximum pile displacement is 10% of pile diameter, this model s is 10 cm (39.4 in). This research considered piles at failure point and 10 % of pile diameter displacement. Figure 6.27 Confined Polymer Pile Model into Soil (Right), Mesh of Pile before Run the Program (Middle) and Mesh of Pile after Run the Program (Left)

239 Load (kn) 238 Soil Type Loss Sand Dense Sand Soft Clay Stiff Clay Hard Clay Material Type Drained Drained Undrained Undrained Undrained ɣ unsat 16 kn/m 3, 18 kn/m 3, 15 kn/m 3, 17kN/m 3, 17kN/m 3, 101 pcf 115 pcf 95 pcf 118 pcf 118 pcf ɣ sat 19 kn/m 3, 20 kn/m 3, 17kN/m 3, 19 kn/m 3, 19 kn/m 3, 121 pcf 127 pcf 118 pcf 121 pcf 121 pcf E ref kpa, kpa, kpa, kpa, kpa, 2.9 ksi ksi 2.17 ksi 11.6 ksi 21.7 ksi ref kpa, kpa, 10000kPa, kpa, kpa, E ksi 6.81 ksi 1.45 ksi 7.83 ksi 14.5 ksi ref kpa, kpa, kpa, kpa, kpa, E oed 1.88 ksi 6.81 ksi 1.74 ksi 9.42 ksi 17.4 ksi ref kpa, kpa, kpa, kpa, kpa, E ur 5.83 ksi ksi 4.35 ksi ksi 43.5 ksi C 5 kpa, 5 kpa, 40 kpa, 100 kpa, 200 kpa, 0.72 psi 0.72 psi 5.8 ksi 14.5 ksi 29.0 ksi Φ 32⁰ 40⁰ 5⁰ 5⁰ 5⁰ Table 6.7 Mechanical Properties of Different Type of Soil Displacment (m) Figure 6.28 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Loose Sand

240 Load (kn) Load (kn) Load (kn) Displacment (m) Figure 6.29 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Dense Sand Displacment (m) Figure 6.30 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Soft Clay Displacment (m) Figure 6.31 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Stiff Clay

241 Load (kn) Displacment (m) Figure 6.32 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Hard Clay According to loose sand load displacement results, confined polymer concrete straight pile is slightly stronger than cement concrete straight pile in loose sand after failure point. However, before failure point, both materials have almost the same result. In cement concrete straight pile the failure point was 13 cm (5.11 in) in kn (3417 k) and for 10% pile diameter displacement which is 10 cm (3.9 in) load capacity was kn (3260 k). The failure point of confined polymer concrete straight pile was unknown because after 1 m (39.4 in) plaxis showed that the polymer material did not fail. However, at 10% pile diameter displacement, which is 10 cm (3.9 in), load capacity was kn (3260 k) which is the same as cement material pile, which are the same as cement material at load capacity at failure point of cement concrete straight material. According to dense sand load displacement results, confined polymer concrete straight pile is stronger than cement concrete straight pile. In cement concrete straight pile, the failure point was 4.1 cm (1.61 in) in kn (3529 k) and the failure point of confined polymer concrete straight pile was 75 cm (29.5 in) in kn (11240 k) which is 68% stronger than

242 241 cement concrete straight pile at failure point. However, 75 cm pile displacement in engineering field is too high and it is not acceptable in engineering design. In polymer concrete pile for displacement at 10% of pile diameter 10 cm (3.9 in) the load capacity was kpa (5058 k) which is 30% stronger than cement concrete straight pile at failure point and cement concrete failed at 4.1 cm (1.61 in). According to soft clay load displacement results, confined polymer concrete straight pile and cement concrete straight pile have the same load displacement curve results in soft clay. In both materials, the failure point was 15 cm (5.9 in) in 9280 kn (2086 k) load capacity and for 10 % of pile diameter displacement for both materials load capacity was 8910 kn (2003 k). According to stiff clay load displacement results, confined polymer concrete had a slightly higher strength compared to cement concrete straight pile in stiff clay. In cement concrete straight pile, the failure point was 3.7 cm (1.45 in) in kn (3641 k) and the failure point of confined polymer concrete straight pile was 7.1 cm (2.8 in) in kn (4293 k), which is 15% stronger than cement concrete straight pile at failure point. According to hard clay load displacement results, confined polymer concrete straight pile is stronger than cement concrete straight pile. In cement concrete straight pile, the failure point was 4.55 cm (1.8 in) in kn (3844 k) and the failure point of confined polymer concrete straight pile was 9.5 cm (3.74 in) in kn (7890 k), which is 51% stronger than cement concrete straight pile at failure point Model Belled Drilled Pile in Different Type of Soil

243 242 A belled drilled pile or belled drilled shaft consists of a straight shaft with the bell at the bottom, which rests on good bearing soil. The bell can be constructed in the shape of dome or it can be angled. For angled bells, the under reaming tools commercially available can make 30⁰ to 45⁰ angle with the vertical [Das 1999]. In this section, to increase the load capacity of straight piles at section 6.5.1, belled drilled piles were used. The belled drilled pile has larger area at the bottom of pile compare to straight pile; as long as the area of the pile bottom is larger, the tip resistant is higher. In this model the angle for the bell was 45⁰. Figures 6.33 and 6.34 shows the bottom part of cement concrete belled pile and confined polymer concrete belled pile in plaxis model respectively. In this model at the bell section, it was not defined as carbon fiber sleeve for confined polymer concrete pile because is not applicable at this area. All mechanical properties of cement concrete, polymer concrete and soil are discussed at section Figure 6.33 Bottom Part of Belled Drilled Cement concrete Pile in Plaxis Model

244 243 Figure 6.34 Bottom Part of Belled Drilled Confined Polymer Concrete Pile in Plaxis Model To analyzed belled piles with plaxis, all mechanical properties of cement concrete, polymer concrete and soil from section and medium mesh were used. Figures 6.35, 6.36, 6.37, 6.38 and 6.39 are load-displacement curves of cement and confined polymer concrete belled pile in loose sand, dense sand, soft clay, stiff clay and hard clay respectively. Furthermore, in these models, plaxis calculated load displacement at 1 m (39.4 in). Although the 1 m displacement for pile is not applicable in the field, displacement of 10% of the pile diameter which is 10 cm (39.4 in) is used. This research considered piles at failure point and 10 % of pile diameter displacement.

245 Load (kn) Load (kn) Load (kn) Ddisplacment (m) Figure 6.35 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Loose Sand Ddisplacment (m) Figure 6.36 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Dense Sand Ddisplacment (m) Figure 6.37 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Soft Clay

246 Load (kn) Load (kn) Ddisplacment (m) Figure 6.38 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Stiff Clay Ddisplacment (m) Figure 6.39 Load Displacement Curve of Cement concrete Belled Pile (Dash Blue Line) and Confined Polymer Concrete Pile (Red Line) in Hard Clay According to loose sand load displacement results, confined polymer concrete belled pile is slightly stronger than cement concrete belled pile in loose sand. In cement concrete belled pile the failure point was 13 cm (5.11 in) in kn (3641 k) and for 10% pile diameter displacement which is 10 cm (3.9 in) load capacity was kn (3260 k). The failure point of confined polymer concrete belled pile was unknown because after 1 m (39.4 in) in the plaxis analysis, the polymer material did not fail. However, at 10% pile diameter displacement which is 10 cm (3.9 in), load capacity was kn (3754 k) which is 13% stronger than cement concrete belled pile at 10% pile diameter displacement.

247 246 According to dense sand load displacement results, confined polymer concrete belled pile is stronger than cement concrete belled pile. In cement concrete belled pile the failure point was 4.1 cm (1.61 in) at kn (6181 k) and the failure point of confined polymer concrete belled pile was 42 cm (16.5 in) at kn (11240 k) which is 68% stronger than cement concrete straight pile at failure point. However, 42 cm pile displacement in practice is too high and it is not acceptable in engineering design. In confined polymer concrete belled pile for displacement at 10% of pile diameter 10 cm (3.9 in) the load capacity is kn (5979 k), which is 41% stronger than cement concrete belled pile at failure point. According to soft clay load displacement results, confined polymer concrete belled pile and cement concrete belled pile, it has the same load displacement curve results in soft clay. In both materials the failure point was 16 cm (6.3 in) in kn (2472 k) load capacity and for 10 % of pile diameter displacement for both materials load capacity was kn (2360 k). According to stiff clay load displacement results, confined polymer concrete belled pile, had a slightly higher strength compare to cement concrete belled pile in stiff clay. In cement concrete straight pile, the failure point was 3.7 cm (1.45 in) at kn (3641 k) and the failure point of confined polymer concrete straight pile was 9.5 cm (3.7 in) at kn (5103 k), which is 29% stronger than cement concrete belled pile at failure point. According to hard clay load displacement results, confined polymer concrete belled pile is stronger than cement concrete belled pile. In cement concrete straight pile the failure point was 4.55 cm (1.8 in) at kn (3844 k) and the failure point of confined polymer concrete straight pile was 16.5 cm (6.5 in) at kn (9510 k), which is 60% stronger than cement concrete belled pile at failure point cm displacement is not acceptable in practice. In confined

248 Load (kn) 247 polymer concrete belled pile for displacement at 10% of pile diameter 10 cm (3.9 in) the load capacity was kn (5979 k), which is 58% stronger than cement concrete belled pile at failure point Compare Straight Piles with Belled Drilled Piles In this section, belled drilled piles are compared with straight piles in load capacity at different types of soil. Figures 6.40, 6.41, 6.42, 6.43 and 6.44 are load-displacement curves of belled drilled piles and straight piles in loose sand, dense sand, soft clay, stiff clay and hard clay respectively. These curves clearly show the difference between belled drilled piles and straight piles Ddisplacment (m) Figure 6.40 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Loose Sand

249 Load (kn) Load (kn) Ddisplacment (m) Figure 6.41 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Dense Sand Ddisplacment (m) Figure 6.42 Load Displacement Curve of Cement and Polymer Concrete in Straight condition (Dash Red Line) and Confined Polymer and Cement concrete in Belled Pile (Red Line) in Soft Clay

250 Load (kn) Load (kn) Ddisplacment (m) Figure 6.43 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Stiff Clay Displacment (m) Figure 6.44 Load Displacement Curve of Cement concrete Belled and Straight Pile (Dash Blue Line), Confined Polymer Concrete Straight Pile (Dash Red Line) and Confined Polymer Concrete Belled Pile (Red Line) in Hard Clay According to loose sand load displacement results, for cement concrete material in two condition; straight and belled pile, it has same load displacement curve results. In loose sand condition the cement concrete failed. When cement concrete reached the failure point, the curve changed to perfect strength forward line or perfect plastic line. The failure point was 13 cm (5.11 in) pile displacement. Belled pile is 13% stronger than straight pile in load capacity at 10% of

251 250 pile diameter displacement. According to Figure 6.45 polymer concrete and loose sand material were not failed at a 1 m plaxis analysis. For loose sand and unaggressive soil material condition (confined polymer concrete has longer durability compare to cement concrete), it is better to use cement material because it is a more common material compared to polymer material. According to dense sand load displacement results, for cement concrete material in two conditions; straight and belled pile, it has similar load displacement results. In dense sand condition, cement concrete failed when concrete material reached failure at the point when the load displacement curve changed to perfect strength forward line or perfect plastic line. At the failure point was 4.14 cm (1.62 in) of pile displacement. In confined polymer concrete at dense sand, the belled pile is 15% stronger than strength pile in load capacity at 10% of pile diameter displacement. According to figure 6.46 confined polymer straight and belled pile failed when polymer piles reached the failure point. After the failure point the load displacement curve changed to perfect strength forward line or perfect plastic line. The failure point of straight and belled pile was 42 cm (16.5 in) and 75 cm (29.5 in) of piles displacement respectively. According to soft clay load displacement results, cement concrete pile and confined polymer concrete pile in straight condition, it has same load displacement curve because, soft clay failed before cement concrete field. Soft clay failed when piles reach 15 cm pile displacement. Furthermore, cement concrete pile and confined polymer concrete pile in belled condition, has the same load displacement curve because, soft clay failed sooner Soft clay failed when piles reach 16 cm pile displacement. For soft clay and unaggressive soil material condition (confined polymer concrete has longer durability compare to cement concrete), it is better to use cement material because it is more common material compared to polymer material.

252 251 According to stiff clay load displacement results, for cement concrete material in two conditions: straight and belled pile, it has the same load displacement curve results. In stiff clay condition, when cement concrete reached to failure point, the load displacement curve changed to perfect strength forward line or perfect plastic line. The failure point was 3.7 cm (1.45 in) pile displacement. In confined polymer concrete, belled pile is 16% stronger than straight pile. In this condition, stiff clay was failed before polymer concrete failed. The failure point of confined polymer concrete in straight and belled condition is 7.1 cm (2.8 in) and 9.5 cm (3.75 in) pile displacement respectively. According to hard clay load displacement results, for cement concrete material in two condition: straight and belled pile, it has similar load displacement curve results. In hard clay condition when cement concrete reached the failure point, the curve changed to perfect strength forward line or perfect plastic line. The failure point was 4.55 cm (1.8 in) pile displacement. The confined polymer concrete belled pile is 14% stronger than confined polymer straight pile. When confined polymer belled pile reached to 10% of pile diameter displacement 10 cm (3.9 in) and polymer concrete belled pile is 17% stronger than confined polymer straight pile when confined polymer belled pile reach to failure point which was 16.5 cm (6.5 in). In this condition, hard clay failed before polymer concrete failed Model Piles in Different Type of Soil on Bed Rock According to previous section, it shows that polymer material acted stronger in dense and hard conditions compared to cement material. In this section, a confined polymer concrete straight pile and cement concrete straight pile are modeled on bed rock to observe mechanical behavior and compare cement pile and polymer pile material on bed rock.

253 Load (kn) 252 In this part, the mechanical properties of polymer material, cement material, and soil material are found in Tables of 6.3, 6.6 and 6.23 respectively. This section used hardening soil model and plaxis analysis model for 1 m (39.4 in) displacement. In this research, lime was used and the mechanical properties are tabled at table 6.7 [Goodman 1980] Figures 6.45, 6.46, 6.47, 6.48 and 6.49 are load-displacement curves of straight piles on lime stone in loose sand, dense sand, soft clay, stiff clay and hard clay respectively. These curves clearly show the difference between cement concrete straight pile and polymer concrete straight pile. Parameter Material Type ɣ unsat ɣ sat E ref Lime Stone Mohr-coulomb 24.5 kn/ m pcf 24.5 kn/ m pcf 45 GPa, 6530 ksi ν 0.25 c φ 30 MPa, 4.35 ksi 35⁰ Table 6.8 Mechanical Properties of Lime Stone Loose sand on rock Confined Polymer Concrete Cemented Concrete Displacment (m) Figure 6.45 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Loose Sand

254 Load (kn) Load (kn) Load (kn) Denes sand on rock Confined Polymer Concrete Cemented Concrete Displacment (m) Figure 6.46 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Dense Sand Soft clay on rock Confined polymer Concrete Cemented concrete Displacment (m) Figure 6.47 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Soft Clay Stiff clay on rock Confined Polymer Concrete Cemented Concrete Displacment (m) Figure 6.48 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Stiff Clay

255 Load (kn) Hard clay on rock Confined polymer concrete Displacment (m) Figure 6.49 Load Displacement Curve of Cement concrete Straight Pile (Dash Blue Line) and Confined Polymer Concrete Straight Pile (Red Line) on Lime Stone in Hard Clay According to loose sand with lime stone results, it shows cement concrete pile and confined polymer concrete failed. The failure point of cement concrete pile for loose sand on lime stone is a 3.1 cm pile displacement and with load capacity of kn. The failure point of confined polymer concrete pile for loose sand on lime stone is 8.6 cm pile displacement and with load capacity of kn. Polymer concrete pile is 67% stronger than cement concrete pile. According to dense sand with lime stone results, it shows cement concrete pile and confined polymer concrete failed. The failure point of cement concrete pile for dense sand on lime stone is a 2.7 cm pile displacement with load capacity of kn and the failure point of confined polymer concrete pile for dense sand on lime stone is a 8.33 cm pile displacement and with load capacity of kn. Polymer concrete pile is 68% stronger than cement concrete pile. According to soft clay with lime stone results, it shows cement concrete pile and confined polymer concrete failed. The failure point of cement concrete pile in soft clay on lime stone is a 2.9 cm pile displacement and with load capacity of kn and the failure point of confined

256 255 polymer concrete pile in soft clay on lime stone is a 9.6 cm pile displacement and with load capacity of kn. Polymer concrete pile is 68% stronger than cement concrete pile. According to stiff clay with lime stone results, it shows cement concrete pile and confined polymer concrete failed. The failure point of cement concrete pile in stiff clay on lime stone is a 2.2 cm pile displacement and with load capacity of kn and the failure point of confined polymer concrete pile in stiff clay on lime stone is an 8.1 cm pile displacement and with load capacity of kn. Polymer concrete pile is 68% stronger than cement concrete According to hard clay with lime stone results, it shows cement concrete pile and confined polymer concrete failed. The failure point of cement concrete pile in hard clay on lime stone is a 3.6 cm pile displacement and with load capacity of kn and the failure point of confined polymer concrete pile in hard clay on lime stone is an 6.6 cm pile displacement and with load capacity of kn. Polymer concrete pile is 66% stronger than cement concrete pile. According to result discussions pile on bed rock, it appears that the failure point is the same and polymer material is 67% stronger than cement material in all soil conditions. This means, when the pile is assembled on bed rock soil axial load is not resisted by skin friction resistance. All axial load is transferred to the tip point of pile which is above bed rock. 6.6 General of Pile Lateral Load After considering and discussing piles under axial load, this section considers cement and polymer piles under lateral load. Structural foundations on piles is sometimes subjected to lateral loads which may come from seismic, wind, traffic and earth pressures. Moment may come from

257 256 the eccentricity of the vertical force, fixity of the structure to the pile or piles and the pile or the piles and the location of the lateral forces on the pile with reference to the ground surface. In this research as mentioned before, for analysis of piles OpenSees PL was used. In modeling of piles it has to be modeled in three dimensions because, by applying load on top of the pile, the pile can move in three dimensions. 6.7 OpeenSeesPl Computer Program OpenSeesPL computer program is a finite element software which is developed by Jinchi Lu, Zhaohui Yang and Ahmed Elgamal from University of California, San Diego and California Department of Transportation (Caltrans). OpenSeesPL is a three dimensional (3D) software to analyze static and dynamic lateral load on pile. The openseespl graphical interface is focused on facilitating a wide class of three dimensional studies with additional capabilities yet under development. Openseespl has the capability for simulations for any size of pile diameter and pile length. The pile cross section can be square or circular, defining for linear and nonlinear material properties for cement concrete, steel and soil, model a pile in to different layer and type of soil and model a pile which is extended above the ground and supporting a bridge deck [OpenSeesPL 2010]. 6.8 Theory of Material Definition In this section were discussed the theory of material which is used in this research such as cement concrete pile, confined polymer concrete pile, different type of sand and different type of clay Theory of Pile Definition

258 257 In openseespl computer program to define pile material, three type of theory models were exist at model input in pile parameter section of openseespl computer program, these models are linear beam/pile element, nonlinear beam/pile element-aggregator section and nonlinear beam/pile element-fiber section. If in openseespl computer program, linear beam/pile materials were selected. Openseespl computer program were analysis pile as an elastic material and the material properties of the pile for the linear beam element are defined by parameters such as modulus of elasticity (E) of pile, mass density of pile and moment of inertia (I) of pile cross section. The main disadvantage of this theory, pile materials was calculating as elastic material which same as mohr coulomb theory at plaxis computer program. If in openseespl computer program, nonlinear beam/pile materials were selected. Openseespl computer program were analyses pile material as an elastoplastic material. Two type of model were existing in openseespl for nonlinear material: aggregator section and finer section. Aggregator section is defined by the following parameter in openseespl, this parameter is: Flexural Rigidity (EI), Yield Moment, Shear Rigidity (GA), Torsion Rigidity (GJ) and Axial Rigidity. The fiber section which is advance model compare to aggregator section. in fiber section at opensees computer program need to defined cement concrete, polymer concrete, steel and carbon fiber sleeve martial properties such as modulus of elasticity, compressive and tensile strength, number of reinforcing bar and etc. The mechanical properties of fiber section and how to model were discuses later on this chapter.

259 258 In fiber section divided pile cross section in two parts of core patch and cover patch which shows at Figure 6.50, according to figure below core patch area is from center of pile to any point of pile cross section usually this point selected on reinforcing layer this distance called internal radius and cover patch area is from core patch perimeter to pile perimeter and this distance called external radius. To analysis pile in fiber section, cover and core patch area were divided in to small element, these elements have square or rectangular cross section and size of these element were defined in number of subdivision in circumferential direction and number of subdivision in the radial direction at fiber section of openseespl computer program. Detail information of fiber section can be found in opensees user manual [Mazzoni 2006]. Figure 6.50 Cover Patch and Core Patch for Nonlinear Beam/Pile Element-Fiber Section [Mazzoni 2006]

260 Theory of Pile Definition In openseespl, the soil model for cohesionless soil is developed within the frame work of multi-yield surface plasticity (Prevost 1985) and Figure 6.51 shows multi surface in principle stress space and deviatoric plane. In this model, emphasis is placed on controlling the magnitude of cycle by cycle permanent shear strain in loose to dense sands (Parra 1996 and Yang 2000). Furthermore, appropriate loading unloading flow rules were devised to reproduce the observed strong dilation tendency, and resulting increase in cyclic shear stiffness and strength. The material type for the cohesionless soils in openseespl is called Pressure Depend Multi Yield [OpenSeesPl manual 2010]. Figure 6.51 Multi Surface in Principle Stress Space and Deviatoric Plane [OpenSeesPL 2010] Clay material is modeled as a nonlinear hysteretic material (Parra 1996 and Yang 2000) with a Von Mises multi surface (Iwan 1967, Mroz 1967) Figure 6.52 shows Von Mises multi surface. In this regard, focus is on reproduction of the soil hysteretic shear response. In this material, plasticity is exhibited only in the deviatoric stress strain response is linear elastic and is independent of deviatoric responses. This constitutive model simulates monotonic or cyclic

261 260 responses of materials whose shear behavior is insensitive to the confinement change. Plasticity is formulated base on the multi surface concept, with an associative flow rule. In the clay model, the nonlinear shear stress-strain back bone curve is represented by the hyperbolic relation (Kondner 1963), defined by the two material constants, low strain shear modulus and ultimate shear strength. The material type for the cohesive soils opensees is called Pressure in depend Multi Yield. Detail information of theory of soil can be found in openseespl user manual [OpenSeesPL 2010]. Figure 6.52 Von Mises Multi Surface [OpenSeesPL 2010] 6.9 Compare Experiment Results with OpenSeesPL In this section before modeling polymer concrete pile with openseespl in soil, it is necessary to calibrate the openseespl computer model with experimental tests and compare the openseespl computer results with experiment results and observed accuracy of computer model. To observe accuracy of openseespl, cement concrete pile [Ismail 1990] was modeled in openseespl. Furthermore in this section, the bending moment of Ismail cement concrete pile was calculated.

262 Model Cement concrete Pile in OpeenSeesPL In this section Ismail cement concrete was modeled into openseespl. This pile was 5 m long and 0.3 m diameter. In openseespl computer program model the mechanical properties were defined for cover patch and core patch separately and for concrete material at fiber section (nonlinear). This mechanical property is: concrete compressive strength, concrete strain at maximum strength, concrete crushing strength and concrete strain at crushing strength. Table 6.9 shows mechanical properties of cement concrete which is captured from experiment test at chapter 5. To defined steel rebar in openseespl computer program, mechanical properties of steel bar needed to defined these mechanical properties is; yield strength, modulus of elasticity, number of reinforced steel bars along layer, area of individual reinforced bar and radius of reinforced layer. Table 6.10 shows mechanical properties of steel bar. In openseespl computer program at fiber section require dividing pile cross sections into small elements (fiber section) and the size of the element can be determined by number of subdivisions in circumferential and radial direction for core patch area and cover patch area and define internal and external radius to separate core patch area and cover patch area. In this research the internal radius is the same as reinforcing radius and Table 6.11 shows number of subdivisions in circumferential and radial direction for fiber section element. Material Properties Core Cover Concrete Compressive Strength 25 MPa, 3.6 ksi 25 MPa, 3.6 ksi Concrete Strain at Maximum Strength Concrete Crushing Strength 17 MPa, 2.5 ksi 17 MPa, 2.5 ksi Concrete Strain at Crushing Strength Table 6.9 Mechanical Properties of Cement concrete at Core and Cover Patch for Ismail Pile

263 262 Material Properties Steel Bar Yield Strength 400 MPa, ksi Modulus of Elasticity 200 GPa, ksi Number of Reinforcing Bars 6 Area of Individual Steel Bars 380 mm 2, 0.61 in 2 Radius of Reinforcing Layer 0.25 m, 9.8 in Table 6.10 Mechanical Properties of Steel Bar for Ismail Pile Material Properties Core Cover Number of Subdivision in the Circumferential Direction Number of Subdivision in the Radial Direction 4 4 Internal Radius , 0.82ft External Radius 0.25, 0.82ft 0.3, 0.98 ft Table 6.11 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element for Ismail Pile After defined cement concrete pile in openseespl, soil domain and mesh scaling were defined in openseespl computer program. Soil material was cement sand and mechanical propriety of cemented soil were tabled at table 6.4 (Mohr-Coulomb) at section In this research soil material was defined as nonlinear material. The mechanical properties of cement concrete were tabled at table 6.6 at section To define finite element mesh in soil domain and size of soil domain at openseespl computer program needs to define general definitions. These general definitions are described below: Mash Scale: the mesh scale can be full mesh, half mesh or quarter mesh, in this research to analyze cement concrete pile and confined polymer concrete, full mash was used for fiber section according to openseespl manual. Number of Slices: The numbers of mesh slices were defined at circumferential direction (about z direction).

264 263 Horizontal Meshing: The number of layers, size of layers and number of mash layers were defined at horizontal axis. Vertical Meshing: The number of layers, height of layers and number of mash layers were defined at vertical axis. Figure 6.53 shows finite element mesh for Ismail pile in cemented sand with general mesh definition and Table 6.12 shows mesh properties based on the general definition for lateral load analysis on Ismail cement concrete pile. According to Table 6.12, in Ismail model analysis for lateral load two and three layer was defined for horizontal axis and vertical axis respectively. The size of soil dome for this analysis is 10 m (32.8 ft) high at z direction and m (62.8 ft) length at x and y direction. Mesh Scale Full Mesh Number of Slices 16 Axis Horizontal Axis Vertical Axis Size and Number of Mesh Size of Layer # of mesh Size of Layer # of mesh 1st Layer 0.15 m, 0.5 ft 6 5 m, 16 ft 6 2nd Layer 1 m, 3.3 ft 6 5 m, 16 ft 6 3nd Layer 18 m, 59 ft Table 6.12 Mesh Properties Base of General Definition for Lateral Load Analysis on Ismail Cement concrete Pile

265 264 Figure 6.53 Finite Element Full Mesh for Ismail Pile in Cemented Sand in Cemented Sand Dome with General Mesh Definition To run openseespl computer program for lateral load analysis, first it is necessary to define displacement. Openseespl computer program calculates and analyzes the pile until the pile displacement reaches the displacement amount. In Ismail cement concrete openseespl was set to analyze and calculate load displacement for 22 mm (0.86 in). Openseespl defined the displacement value in the pushover analysis section and named pushover analysis. Calculating and analyzing the pile in openseespl involves four runs which are conducted in sequence in order to achieve convergence and simulate the actual pile loading situation. These four runs are described below.

266 Load (kn) st run: Gravity of soil domain is applied in this run; all soil materials are prescribed as linear during this run. 2 nd run: Soil elements are changed to nonlinear if Nonlinear is chosen in analysis options. 3 nd run: Pile elements are added and gravity of the pile structure is applied in this run. 4 nd run: Pushover analysis is started After the openseespl computer program analysis for Ismail cement concrete pile in cemented sand, load displacement curves are shown in Figure 6.54 and this figure shows difference between experimental test and openseespl analysis Experiment Test OpeenSees PL Displacment (mm) Figure 6.54 Load Displacement of Ismail Experiment Test (Red Line) and Load Displacement of OpenSees PL Computer Analysis (Dash Blue Line) According to the figure above, it shows openseespl computer program analysis of a nonlinear material is very close to Ismail cement concrete experiment test. In this research, the openseespl computer program analysis and a model for confined polymer concrete pile and compared with cement concrete pile in lateral load.

267 Cement and Confined Polymer Concrete Pile Modeled in Lateral Load at Different Type of Soil In this part of the research, cement and confined polymer concrete were modeled in different types of soil to observe and compare mechanical strength of cement concrete piles with confined polymer concrete pile in lateral load analysis with openseespl. To model cement concrete pile and confined polymer concrete in opensees computer program it is necessary to define mechanical properties of concretes and soil material, type of mesh and defined push over analyses. In this analysis for cement and polymer pile size is 1 m (3.3 ft) diameter and 30 m (98.5 ft) length same as axial load analysis Mechanical properties of cement and confined polymer material were mentioned before in section and respectively. The soil material is the same material that was used for axial load analysis in section This soil was loose sand, dense sand, soft clay, stiff clay and hard clay. The main material which controls lateral load for a pile is reinforced material which is steel rebar for cement concrete material and carbon fiber sleeve for polymer concrete. To defined steel rebar for these analysis used 12 rebar number 22 (22 mm or 0.86 in diameter) with reinforcing diameter of 0.85 m (2.78 ft), the mechanical properties of cement concrete, steel rebar and number of subdivisions in circumferential and radial direction for fiber section element for defined cement concrete pile at openseespl computer program are tabled at Table 6.13, 6.14 and 6.15 respectively. Material Properties Core Cover Concrete Compressive Strength 23.9 MPa, 3.45 ksi 23.9 MPa, 3.45 ksi Concrete Strain at Maximum Strength Concrete Crushing Strength 17 MPa, 2.5 ksi 17 MPa, 2.5 ksi Concrete Strain at Crushing Strength Table 6.13 Mechanical Properties of Cement concrete at Core and Cover Patch

268 267 Material Properties Steel Bar Yield Strength 400 MPa, ksi Modulus of Elasticity 200 GPa, ksi Number of Reinforcing Bars 12 Area of Individual Steel Bars 380 mm 2, 0.61 in 2 Radius of Reinforcing Layer 0.85 m, 2.78 ft Table 6.14 Mechanical Properties of Steel Bar Material Properties Core Cover Number of Subdivision in the Circumferential Direction Number of Subdivision in the Radial Direction 4 4 Internal Radius m, 2.78 ft External Radius 0.85m, 2.78 ft 1.0 m, 3.3 ft Table 6.15 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element To define carbon fiber sleeve for confined polymer concrete pile in this research, it has a different process. Carbon fiber sleeves were divided in to small elements in size of m x m (0.05 in x 0.05 in), which was the thickness of the carbon fiber sleeve. The perimeter of the pile divided by thickness of carbon fiber sleeve to determine how many carbon rebar needed to defined around polymer concrete pile (with reinforcing diameter of pile diameter, 1 m), the number of carbon fiber for this analysis is Figure 6.55 shows model of polymer concrete pile which confined with carbon fiber sleeve and Table 6.16, 6.17 and 6.18 shows the mechanical properties of polymer concrete, carbon fiber and number of subdivisions in circumferential and radial direction for fiber section element for defined confined polymer concrete pile at openseespl computer program respectively.

269 268 Figure 6.55 Model of Polymer Concrete Pile which Confined with Carbon Fiber Sleeve Material Properties Core Cover Concrete Compressive Strength 65.7 MPa, 9.53 ksi 65,7 MPa, 9.53 ksi Concrete Strain at Maximum Strength Concrete Crushing Strength 46 MPa, 6.7 ksi 46 MPa, 6.7 ksi Concrete Strain at Crushing Strength Table 6.16 Mechanical Properties of Polymer Concrete at Core and Cover Patch Material Properties Carbon Fiber Sleeve Yield Strength 310 MPa, 45 ksi Modulus of Elasticity 26 GPa, 3770 ksi Number of Reinforcing Bars 2500 Area of Individual Steel Bars 1.6E-6 mm 2, 2.56E-9 in 2 Radius of Reinforcing Layer 1.0 m, 3.3 ft Table 6.17 Mechanical Properties of Carbon Fiber Sleeve Material Properties Core Cover Number of Subdivision in the Circumferential Direction Number of Subdivision in the Radial Direction 4 4 Internal Radius m, 3.3 ft External Radius 1.0 m, 3.3 ft 1.0 m, 3.3 ft Table 6.18 Number of Subdivisions in Circumferential and Radial Direction for Fiber Section Element According to Figure 6.54, it shows the fiber carbon sleeve divided into 2500 small

270 269 elements around polymer concrete pile and mechanical properties of carbon fiber were taken from experimental tests in chapter 5. Figure 6.56 shows finite element mesh for pile in soil with general mesh definition and Table 6.12 shows mesh properties based on general definition for lateral load analysis on cement concrete and confined polymer concrete pile. According to Table 6.19, in cement concrete and confined polymer concrete pile analysis for lateral load two and three layer was defined for horizontal axis and vertical axis respectively. The size of soil dome for this analysis is 60 m (196.9 ft) high at z direction and m (62.8 ft) length at x and y direction. Figure 6.56 Finite Element Full Mesh for cement concrete pile and Confined Polymer Concrete pile in Soil Dome with General Mesh Definition

271 Lateral Load (kn) 270 Mesh Scale Full Mesh Number of Slices 16 Axis Horizontal Axis Vertical Axis Size and Number of Mesh Size of Layer # of mesh Size of Layer # of mesh 1st Layer 0.15 m, 0.5 ft 6 30 m, 98.4 ft 6 2nd Layer 1 m, 3.3 ft 6 30 m, 98.4ft 6 3nd Layer 18 m, 59 ft Table 6.19 Mesh Properties Base of General Definition for Lateral Load Analysis on Cement concrete Pile and Confined Polymer Concrete Pile After running cement concrete pile and confined polymer concrete pile in different types of soil with openseespl computer program, the results of piles in loose sand, dense sand, soft clay, stiff clay and hard clay are shown in Figures 6.57, 6.58, 6.59, 6.60 and 6.61 respectively Loose Sand Polymer Concrete Cemented Concrete Dicplacement (mm) Figure 6.57 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Loose Sand

272 Load (kn) Load (kn) Lateral Load (kn) Dense Sand Cemented Concrete Polymer Concrete Dicplacement (mm) Figure 6.58 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Dense Sand 200 Soft Clay Cemented Concrete Polymer Concrete Dislplacment (mm) Figure 6.59 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Soft Clay Stiff Clay Cemented Concrete Polymer Concrete Dislplacment (mm) Figure 6.60 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Stiff Clay

273 Lateral Load (kn) Hard Clay Cemented Concrete Polymer Concrete Dicplacement (mm) Figure 6.61 Load Displacement Curve of Cement concrete Straight Pile (Blue Line) and Confined Polymer Concrete Pile (Dash Red Line) in Hard Clay In loose sand, cement concrete pile failed at 174 kn (40 kips) and 50 mm (2 in) in load and displacement respectively and for polymer concrete pile failed at 200 kn (45 kips) and 200 mm (7.8 in) in load and displacement respectively. In dense sand, cement concrete pile failed at 227 kn (51 kips) and 50 mm (2 in) in load and displacement respectively and for polymer concrete pile failed at 453 kn (102 kips) and 200 mm (7.8 in) in load and displacement respectively. In soft clay, cement concrete pile failed at 170 kn (38 kips) and 50 mm (2 in) in load and displacement respectively and for polymer concrete pile failed at 158 kn (35 kips) and 200 mm (7.8 in) in load and displacement respectively. In stiff clay, cement concrete pile failed at 188 kn (42 kips) and 50 mm (2 in) in load and displacement respectively and for polymer concrete pile failed at 200 kn (45 kips) and 200 mm (7.8 in) in load and displacement respectively. In hard clay, cement concrete pile failed at 311 kn (70 kips) and 50 mm (2 in) in load and displacement respectively and for polymer concrete pile failed at 540 kn (122 kips) and 200 mm (7.8 in) in load and displacement respectively.

274 273 According to the figures and results above, it shows polymer concrete has stronger reaction in dense and hard soils compared to cement concrete. Furthermore, confined polymer pile has more deflection in material compared to cement concrete with same process as Figure 5.66 at Section In lateral load of the pile, the main pile material which resists lateral load is reinforced material which is steel rebar at cement concrete pile and carbon fiber sleeve in polymer concrete pile. Confined polymer concrete is more ductile compared to reinforced cement concrete with steel bar, the main reason is because the modulus of elasticity of carbon fiber is 25.5 GPa (3698 ksi) and steel rebar is 200 GPa (29000 ksi) which means modulus of elasticity of carbon fiber is 7-8 times weaker than steel rebar at modulus of elasticity. So, fiber carbon has more deflection compared to steel rebar at same load. The other reason is that in some soils such as loose sand and soft clay, polymer concrete is weaker than the cement concrete is because of strength of reinforced material, the yielding strength of steel bar is 400 MPa (58 ksi) and strength of carbon fiber sleeve is a 310 MPa (45 ksi) where carbon fiber is 23 % weaker than steel rebar. Confined polymer concrete can be used in special cases where piles failed due to large deflection such as stabilized pile, offshore pile, harbors, micropiles, liquefaction, etc.

275 274 CHAPTER 7 DESIGN GUIDE 7.1 General The engineering design process (guide) is the formulation of a plan to help an engineer build a product with a specified performance goal. This process involves a number of steps, and parts of the process may need to be repeated many times before production of a final product can begin. In this chapter is consider of design procedure (guide) for confined polymer concrete pile foundation in axial and lateral load at cohesion and cohesionless soil and the most part of this design process are adopted form Pile Foundations in Engineering Practice [Prakash 1990], [Tomlinson 1977] and Canadian Foundation Manual 7.2 Piles Design Procedure for Axial Load in Cohesionless Soil The design procedure consists of the flowing five steps: Step 1: Soil Profile, from proper soils investigations, establish the soil profile and groundwater levels, and note soil properties on the soil profile based on the profile based on the field and laboratory test. Step 2: Pile Dimension and Allowable Bearing Capacity, Select a pile type, length and diameter and calculate allowable bearing capacity base on the formulas use for the available soil parameters as follows: (a) Static analysis by utilizing soil strength (Q v ) ult = Q p + Q f (7.1)

276 275 (Q v ) ult = A p σ v N q + p K s tan δ σ vl ΔL (7.2) Q p : Pile tip resistance Q f : Pile friction resistance A p: Pile tip area σ v: Effective overburden pressure at the pile tip σ vl : Effective vertical stress at a point along the pile length p: Pile perimeter K s: Earth pressure coefficient, determined from Table 7.1 N q: Bearing capacity factor, determined from Table 7.2 δ: 2/3φ L: Pile length Pile Type K s Bored pile 0.5 Driven H pile Driven displacement pile Table 7.1 Value for Ks for Various Pile Types in Sands [Prakash 1989] φ⁰ N q (driven) N q (drilled) Table 7.2 Value for N q and φ [Prakash 1989]

277 276 (b) Empirical analysis utilizing the standard penetration test value For Sands Point Baring (Q p ) Q p (tons) = D f A p < 4 N A p (7.3) For Nonplastic Silt Q p (tons) = D f A p < 3 N A p (7.4) N = C N N (7.5) C N = 0.77 log (7.6) N: Standard penetration test value N : Average of the observed standard penetration test value Shaft Friction (Q s ) Q f = (f s ) (perimeter) (embedment length) (7.7) Where f s in tons per square foot is given by the following equation: f s = < 1 tsf (7.8) The ultimate capacity (Q v ) ult is then the summation of Q p and Q f. These equations are for driven piles. For drilled piles use one-third of Q p and one-half of Q f from these equation. (c) Empirical analysis utilizing the cone penetration test value Q p = A p q c (7.9) Q f = (f s )(perimeter)(embedment length) (7.10)

278 277 The (Q v ) ult is then the summation of Q p and Q f. These equations are for driven piles. For drilled piles, use one half of the above value. Because of the uncertainties in soil parameters and the semi empirical nature of bearing formulas, a factor of safety of 3 should be used to obtain the allowable bearing capacity used in the design is then the lowest of these values. Step 3: Number of Piles and Their Arrangement, Determine the number of piles required by dividing the column load with the allowable bearing capacity of a pile and arrange the piles in that pile spacing is three to four times the piles diameter. Establish pile cap size with reference to column spacing and other space restrictions. If the pile cap becomes too large, increase pile geometry (length or diameter) and repeat to second step to obtain reasonable pile dimensions and capacity. Determine pile group capacity by simply adding the individual pile capacities. Step 4: Settlement of a Single Pile, Estimate the settlement of a single pile by the following methods: (a) Semi empirical method S t = S s + S p + S ps (7.11) S t: Total pile top settlement for a single pile. S s: Settlement due to axial deformation of a pile shaft. S p: Settlement of pile base or point caused by load transmitted at the base. S ps: Settlement of pile caused by load transmitted along the pile shaft. Ss = (7.12) Q pa : Actual base or point load transmitted to the pile base in working stress range.

279 278 Q fa : Actual shaft friction load transmitted to the pile base in working stress range. L: Pile length. A p A p : Pile area. E p : Modulus of elasticity α: A number that depends on distribution of skin friction along the pile shaft. According to Vesic (1977) α = 0.5 for the uniform or the parabolic skin friction along the pile shaft. For triangular skin friction distribution is α = Sp = (7.13) Sps = (7.14) C p : Empirical coefficient Table 7.3 C s : C p (7.15) Q pa : net point load under working conditions or allowable. Q fa : pile shaft load under working conditions or allowable. q p : ultimate end- bearing capacity B: pile diameter D f = L: embedded pile length

280 279 (b) Empirical method Soil Type Drive Pile Bored Pile Sand (dense to loose) Clay (stiff to soft) Silt (dense to loose) Table 7.3 Typical Value of Coefficient C p [Prakash 1989] S t = (7.16) S t : Settlement of pile head, in B: Pile diameter, in Q va : Applied pile load, lb A p : Area of cross-section of pile, in 2 L: pile length, in E p : modulus of elasticity of pile material, lb/in 2 The settlement is then higher of the values obtained from the foregoing methods. 1. Settlement of Pile Group and Check on Design. Estimate pile group settlement by using the following method. (a) Vesic s method S G = S t (7.17)

281 280 (b) Meyerhof s method, Standard penetration (N) values S G = 2p (7.18) I = (1- ) > 0.5 (7.19) (c) Meyerhof s method, Static cone penetration (q c ) values S G = (7.20) I = [1- D f /8b ] > 0.5 (7.21) S G : Group settlement at load per pile equal to that of the single pile b : Width of pile group. p: Net foundation pressure, in tons/ft 2 The largest of the value obtained from Vesic and Meyerhof s methods should be equal to or less than the allowable settlement value. 7.3 Example for Piles Design Procedure for Axial Load in Cohesionless Soil A 236 kip (1050 kn) vessel is to be supported on a confined polymer concrete pile foundation in an area where soil in investigation indicated soil profile Figure 7.1 Design a pile foundation and calculate total displacement? φ=36⁰ B(diameter)= 1 ft (0.3 m) Step 1 soil profile is showed at Figure 7.1

282 281 Figure 7.1 Soil Profile and Stress Diagram for Example 1 [Prakash 1990] Step 2 pile dimension and allowable bearing capacity. Static analysis by utilizing soil strength Q v ) ult = Q p + Q f (Q v ) ult = A p σ v N q + p K s tan δ σ vl ΔL N q = 30 for φ=36⁰ from table 7.2 A p = π*(2) 2 /4=3.14 ft 2 ( 0.29 m 2 ) P= πb= π(2)= 6.28 ft (1.91 m) K s = 0.5 from table 7.1 (Q v ) ult = 3.14*1690* *0.5* tan (36)*[ +1690*10] = kips kips = kips (1096 kn)

283 282 (Q v ) all = = = kips ( kn) Empirical analysis utilizing the standard penetration test value Average N value near pile tip = = 12 σ v near pile tip = 440+ ( )*30= 2315 psf (15.96 MPa) (1.15 tsf) C N = 0.77 log 10 [ ] 1.00 N =N C N = 1.00*12=12 For sand: Point Baring (Q p ) Q p (ton) = * 30 * 3.14 = tons kips ( kn) 4*N * A p = 4*12*3.14 = tons kips ( kn) Q p > tons therefore, use Q p = tons and for drilled pile Q p is a one third according to Step 2. So Q p for this example is tons kips (446.8 kn) Shaft Friction (Q s ) Average N value along pile shaft = = 7.2 or 7.0 f s = = 0.14 < 1 tsf therefore, Q f = 0.14 *6.28 * 30 = tons (127.5 kn) and for drilled pile Q f is a half according to Step 2. So Q f for this example is 13.2 tons 26.4 kips ( kn) (Q v ) ult = Q p + Q f = = kips ( kn),

284 283 (Q v ) all = = = kips (187.9 kn) The allowable bearing capacity will be the lower of the value obtained previously. Therefore, (Q v ) all = 42.26kips (187.9 kn) Q p =33.5 kips (150 kn) Q f =8.8 kips (39.1kN) Step 3 Number of pile and their arrangement Number of pile = = = 5.6 Use nine piles 3x3 b =b-1=10-1=9ft (2.74 m) Pile cap weight=3*10*10*0.15=45 kips (200 kn) Total weight on pile group = =281 kips (1250 kn) Load per pile = = 31 kips < 42 kips Pile group capacity = 42*9=378 kips ( kn) > 281 kips (1250 kn) Step 4 Settlement of single pile S t = S s + S p + S ps (Q p ) actual = [ = kips (110 kn) (Q f ) actual = 8.8 [ = 6.5 kips (28.9 kn) q p = = = 32 ksf 0.22 ksi (1516 kpa) assume α=0.5 C p = from table 7.3 S p = = = 0.7 in (17.7 mm)

285 284 S ps = C s = ( )* = 0.21 S ps = = in (0.43 mm) S t = = 0.72 in (18.3 mm) Step 5 Settlement of pile group Used Vesic s method S G = S t = 0.72 = 1.52 in (38.6 mm) In this section Meyerhof s method was ignored. 7.4 Piles Design Procedure for Axial Load in Cohesion Soil The design procedure consists of the flowing five steps: Step 1: Soil profile from proper soils investigations, establish the soil profile based on the field and laboratory test. Step 2: pile dimension and allowable bearing capacity, select pile type, pile geometry and determine allowable bearing capacity of a single pile base of equation below. (Q v ) ult = A p c u N c + p c a ΔL (7.22) A p : Pile point (base) area

286 285 c u: The minimum undrained shear strength of clay at pile point level cohesion of the bearing stratum (c = c u = S u = ) N c: The bearing capacity factor which is obtained from Table 7.4 and 7.5. B: Pile Diameter D f or L: embedded pile length L e : Effective pile length which is obtained from Table 7.6 and seasonal variation is between 3 to 5 ft. c a : For straight sided shaft = 0.6 and for belled shaft = 0.3 Df/B Nc >4 9 Table 7.4 Value of N c for vs. Depth of Pile Diameter (D f /B) Ratio [Prakash 1989] Drilled Pile Base Diameter Nc Less than 0.5m ( 1.5 ft) 9 Between 0.5 to 1 m ( 1.5 to 3 ft) 7 Greater than 1m ( 3ft) 6 Table 7.5 Values of N c for Various Pile Diameters (B) [Canadian Foundation Design Manual]

287 286 Type of Pile L e Driven and Straight Shaft Drilled L-(depth of seasonal variation) Belled Shaft Drilled L-(depth of seasonal variation + 2 pile shaft Diameter) Table 7.6 Effective Pile Length (L e ) of Driven and Drilled Piles Step 3: Calculate the number of piles, to determine the number of piles required by dividing the column load with the allowable load or bearing capacity of the single pile. Arrange the pile in the group such that pile spacing is three to four times the pile diameter. Establish pile cap size with reference to column spacing and other space restrictions. If it becomes too large, increase pile length and diameter repeat item, to obtain reasonable pile dimensions and arrangement. The pile group capacity is then the lower of the values obtained by the equation below. G e : Pile Group Efficiency which is determined by Table 7.7 (Q vg ) ult = c u N c (b ) c u (b ) L e (7.23) (Q vg ) ult = G e n (Q v ) ult (7.24) b : Width of Pile Group n: Number of Pile Pile spacing (s) 3B 4B 5B 6B 8B Ge Table 7.7 Group Efficiency Value for Vs. Pile Spacing

288 287 Step 4: Settlement of piles. The settlement of pile in cohesive soils is the sum of the short term and the long term settlements. For short term settlement the settlement of a single pile is first calculated. Then this value is used to estimate the short term settlement of pile group. Short term settlement (a) Semiempirical Method S t = S s + S p + S ps (7.25) Ss = (7.26) Sp = (7.27) Sps = (7.28) The parameter above were discussed at section 7.2 at step 4 (b) Empirical Method S t = (7.29) The settlement is then higher of the value obtained from Semiempirical and empirical method. The settlement of a pile group is then determined from the following below: S G = S t (7.30) Long term settlement (consolidation) The long term settlement for normal consolidation clay is determined from the following. ΔH = [C c / (1+e 0 )] [H- ]*log 10 [ ] (7.31)

289 288 ΔH: Consolidation Settlement σ v : present effective overburden pressure at the middle of the layer (H- ), H cohesion soil depth. Δ σ v : Increased pressure from pile load at the middle of the layer (H - ). C c : Coefficient of consolidation. e 0 : Initial void ratio of the soil. The long term settlement for overconsolidation clay is determined from the following: ΔH = ΔH 1 + ΔH 2 (7.32) ΔH 1 = ( ) (H - ) log 10 ( ) (7.32) ΔH 2 = ( ) (H - ) log 10 ( ) (7.33) ΔH 1 : Settlement due to applied load in the recompression zone ΔH 2 : Settlement due to applied load in the virgin curve zone p c = Preconsolidation Pressure The Δσ v is calculated at depth z = and at z = H by using the following equations. The Δσ v values at any intermediate depth can then be obtained by interpolation. (Δσ v ) z=2l/3 = (Q vg ) all /(b *l ) (7.34)

290 289 (Δσ v ) z=h = (Q vg ) all /(b + H - ) (b + H - ) (7.35) 7.5 Example for Piles Design Procedure for Axial Load in Cohesion Soil In an industrial project one column of a steel frame supporting heavy equipment carries an axial load of 500 kips (2225 kn). Soils investigation indicated the soil profile as show in Figure 7.2. Design a confined polymer concrete pile? Step 1 Soil Profile, the soil profile and laboratory test are show below. Figure 7.2 Soil Profile for Example 2 [Prakash 1990] Step 2: pile dimension and allowable bearing capacity B b = 30 in (0.76 m) Bs = 20 in (0.51 m) D f = 31 ft (9.45 m)

291 290 (Qv) ult = Ap cu Nc + p ca Δ A p = * = 4.9 ft in 2 (0.45 m 2 ) c u = [ = 1357 psf (64.9 kpa) c u = = 6576 psf (314.8 kpa) = = 12.4 B b = 30 in 2.5 ft (76.3 cm) N c = 9 from Table 7.4 N c = 7 from Table 7.5 The lower of these two N c values is 7 and will be used in this problem. P = π* = 5.24 ft (1.6 m) = 0.3 for belled pile c a = 0.3*c u = 0.3*1357 = psf (19.5 kpa) L e = for belled shaft drilled, L - (depth of seasonal variation + 2 pile shaft Diameter) L e = 31 [5 + 2* ] = 22.7 ft (6.92 m) (Q v ) ult = 4.9*6576*7+5.24*407.1*22.7= = kips say 274 kips ( kn) Q p = kips ( kn) Q f = kips (215.4 kn) (Q v ) ult = 274 kips ( kn) (Q v ) all = = = 91.3 kips (406.1 kn) Step 3: Calculate the number of piles

292 291 n = = = Use nine piles for this example and assume pile cap is 12.5 ft x 12.5 ft x 4 ft (3.81 m x 3.81 m x 1.21 m), b = 12.5 ft (3.81 m) and b = = ft (3.55 m) Pile weight cap = 12.5 * 12.5 * 4 * 0.15 = kips say 94 kips (418 kn) (Q vg ) all = c u N c (b ) c u (b ) L e = = = 2.48 N c = 8.5 from Table 7.4 (b + ) = 12.5 ft (3.81 m) N c = 6 from Table 7.5 In this example used lower value of N c = 6 (Q vg ) alt = 6576 * 6 * * 1357 * * 22.7 = 5373 kips kips = 6811 kips (30.3 MN) (Q vg ) all = = 2270 kips (10.1 MN) (Q vg ) alt = G e n (Q v ) alt assume s= 5 ft (1.52 m) Bs = 20 in 1.67 ft (0.5 m) = = 3 G e = 0.7 from Table 7.8 (Q v ) alt = 274 kips ( kn) (Q vg ) alt = 0.7* 9 * 274 = kips (0.77 MN) (Q vg ) al1 = = kips (2560 kn) Use lower value of (Q vg ) al1 = kips (2560 kn)

293 292 Total load on pile group = = 594 kips ( kn) > (Q G ) al1 = kips OK. Step 4: Settlement of piles Short term settlement Semiempirical Method St = Ss + Sp + Sps Ss = Total load on pile group = 594 kips therefore, load per pile = = 66 kips (293 kn) Q p = kips therefore, (Q p ) all = = kips (334.3 kn) Q f = 48.1 kips therefore, (Q f ) all = = kips (71.8 kn) Total allowable load = = 91.3 kips (406.1 kn) (Q p ) actual = [ ] = kips (241.6 kn) (Q f ) actual = [ ] = kips (51.86 kn) Modulus of elasticity of confined polymer concrete is 2800 ksi (19.3 GPa) Assume α = 0.5 A p = Ss = = in (0.53 mm) Sp = C p = 0.03 from Table 7.3 B p = B b = 30 in (76.2 m) q p = = q p = 46 ksf 0.17 in (2202 kpa) Sp = = 0.17 in (4.32 mm)

294 293 Sps = C s = ( )*0.03 = Sps = = in (0.12 mm) S t = = in (4.97 mm) Empirical Method S t = + = = = in (5.7 mm) Used settlement of empirical method because is higher compare to Semiempirical method Group pile settlement S G = S t = = 1.0 in (25.4 mm) Long term settlement (consolidation) according to step 1 soil profile Figure 7.2 both clays (clay tide and clay shales) are highly overconsolidation since their overconsolidation ratio is 4 or more. As, an example Δσ v at pile base is equal to 11 ksf while p c at that level is 14.5 ksi. Therefore, the Long term settlement (consolidation) never happen [Budhu 2007]. 7.6 Piles Design Procedure for Lateral Load in Cohesionless Soil The design procedure consists of the following step which describe below Step 1, Soil Profile: from proper soils investigations, establish the soil profile and groundwater levels and note soil properties on the profile based on field and laboratory tests. Step 2, Pile dimension and arrangement: normally, pile dimensions and arrangements are established from axial compression loading requirements. The ability of these piles dimensions

295 294 and their arrangement to resist imposed lateral load and moment is then checked by following procedure. Step 3, Calculation of ultimate lateral resistance and maximum bending moment: Single Pile Determine n h from Table 7.8 and calculate relative stiffness T=. Determine the ratio and check if it is a short ( 2) or long ( 4) pile. Relative Density Loose Medium Dense n h, (Terzaghi 1955) n h, (Recommended) Table 7.8 Recommended Values of n h for Submerged Sand D f or L: Pile length E: Modulus of elasticity I: Moment of inertia N h : Constant of modulus of subgrade reaction Calculate the ultimate lateral resistance Q u, the allowable lateral resistance, Q all, and maximum bending moment M for the applied loads by Broms method: Broms method for free head pile Short pile: for short pile ( 2), the possible failure mode and the distribution of ultimate soil resistance and bending moment are shown in Figure 7.3.

296 295 Figure 7.3 Rotation and Translation Movement for Free Head Short Pile (left), Soil Reaction and Bending Moment in Cohesive Soils (middle) and Soil Reaction and Bending Moment in Cohesionless Soils (Right) [Broms 1964] Since the point of rotation is assumed to be near the tip of the pile, the high pressure acting near tip of the pile, high pressure acting near tip can be replaced with concentrated force. Taking the moment about the toe give the following relationship: Q u = (7.36) This relationship is plotted using no dimensional terms versus in Figure 7.4. From this figure, Q u can calculated if the calculate if the value of L, e, B, K P = and ɣ are known. The maximum moment occurs at depth of x 0 below ground. At this point, the shear force equal zero.

297 296 Figure 7.4 Ultimate Lateral Load Capacity and Resistance for Short Pile in Cohesionless Soil Related to Embedded Length [Broms 1964] Q u = 1.5ɣ B (7.37) x 0 = 0.82 (7.38) M max = Q u (e+1.5x 0 ) (7.39) Long piles: For long piles ( the possible failure mode and the distribution of ultimate soil resistance and bending moments are shown in Figure 7.5. for cohesionless soils. Since the maximum bending moment concedes with the point of zero shear, the value of x 0 is given by x 0 =0.82. The corresponding maximum moment (M max ) and the point of zero moment, Q u are given by below equation:

298 297 M max = Q(e+0.67 x 0 ) (7.40) Q u = (7.41) Figure 7.5 Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesionless Soils for Free Head Long Pile (left) and Rotation, Translation Movement, Soil Reaction and Bending Moment in Cohesive Soils for Free Head Long Pile (Right) [Broms 1964] M u is the ultimate moment capacity of the pile shaft. Figure 7.6 can be used to determine the Q u value by using versus plot.

299 298 Figure 7.6 Ultimate Lateral Load Capacity and Resistance for Long Pile in Cohesionless Soil Related to Ultimate Resistance Moment [Broms 1964] Broms method for fix head pile Short Piles: For these piles, the possible failure mode is shown on Figure 7.7. Since failure of these pile is assumed by using horizontal equilibrium conditions which is shown in the equation below. Q u = 1.5ɣ L 2 BK p (7.42) M max = ɣ L 3 BK p (7.43)

300 299 Figure 7.7 Rotation and Translation Movement for Fixed Head Short Pile (left), Soil Reaction and Bending Moment in Cohesive Soils (middle) and Soil Reaction and Bending Moment in Cohesionless Soils (Right) [Broms 1964] Long piles: Figure 7.8 shows the failure mode for fix head long piles in cohesion soils. Q u and M max for cohesionless soils can be determined from the following relationship: Q u = (7.44) x 0 = 0.82 (7.45) M u = Q u (e+0.67x 0 ) (7.46)