BEHAVIOR OF ULTRA - HIGH PERFORMANCE CONCRETE BEAMS UNDER FIRE CONDITIONS B y Srishti Banerji A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Civil Engineering - Doctor of Philosop hy 2021 ABSTRACT BEHAVIOR OF ULTRA - HIGH PERFORMANCE CONCRETE BEAMS UNDER FIRE CONDITIONS By Srishti Banerji Ultra - high performance concrete (UHPC) is a novel class of concrete that has superior mechanical properties and durability characteristics as compared to that of conventional concrete. When structural members made of UHPC are used in building construction, the provision of appropriate fire resistance is a key safety consideration. Since UHPC is a new construction material, there is limited in formation, as well as limited research on the fire performance of UHPC members. Preliminary research at the material and structural level have shown that UHPC members exhibit comparatively poor fire performance as compared to conventional concrete due to f ire - induced spalling resulting from its dense microstructure as well as faster degradation of mechanical properties with temperature. At present, there is a lack of experimental data and numerical models for evaluating the fire resistance of UHPC structura l members. To overcome some of the current knowledge gaps, the behavior of UHPC under fire conditions is studied at both the material and structural levels. As part of material characterization, thermal and mechanical property tests were carried out in the 20 - 800°C temperature range on two types of UHPC mixes (with and without polypropylene (PP) fibers). Data from measured property tests were utilized to propose empirical relations for high - temperature material properties of UHPC. As part of structural leve l characterization, four UHPC beams were tested under simultaneous application of loading and fire exposure. The test variables included the presence of polypropylene fibers, load level, and type of fire exposure. As part of the numerical study, a macrosco pic finite element (MFE) model, originally developed to evaluate the fire resistance of reinforced concrete (RC) beams made of conventional concrete, was extended to predict the thermo - mechanical response of UHPC beams under fire conditions. The novelty of the developed numerical model lies in the consideration of stresses resulting from pore pressure, structural loading, and thermal gradients for evaluation of spalling, instead of evaluating spalling based on only stresses due to pore pressure as in the pr evious studies. Further, the fire resistance analysis model was also modified to carry out a member - level structural analysis rather than an analysis of a single critical section. In addition, an expression for variation in permeability of concrete resulti ng from cracking patterns across the cross - section is proposed. The program also accounts for permeability variation due to the addition of polypropylene fibers. The model was validated by comparing thermal and structural response, the extent of spalling, and fire resistance predictions against measured test data on UHPC beams. The validated model was further applied to conduct a set of parametric studies to quantify the effect of critical parameters on the fire response of UHPC beams. Results from the stu dies indicate that load level, fire scenario, cover thickness, specimen shape, sectional dimensions, and dosage of steel and polypropylene fibers have a significant influence on the fire response of UHPC beams. Further, among beams of different concrete ty pes, the fire resistance of UHPC beams was significantly lower due to higher spalling levels resulting from their lower permeability, than normal strength concrete (NSC) and high strength concrete (HSC) beams, where permeability is relatively higher. Final ly, results from the studies are used to develop a set of broad guidelines for the fire design of UHPC beams. By adopting the design guidelines, spalling in UHPC beams can be minimized and fire resistance can be improved. iv This dissertation is dedicated to all lives touched by fire . v ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my Ph.D. advisor, Dr. Venkatesh Kodur for his invaluable guidance, constant support , and encouragement. He has continuously supported me for my academic growth and I thank him wholeheartedly for providing me this opportunity to pursue my research. I want to sincerely thank the members of my committee Dr. Nizar Lajnef, Dr. Weiyi Lu, and Dr. Lik - Chuan Lee for their insightful comments, suggestions, guidance , and su pport. I would like to extend my gratitude to Dr. Parviz Soroushian for his guidance on UHPC mix design and fabrication of the test specimens. I would like to thank my peers and friends; Roya Solhmirzaei, Ankit Agrawal, Saleh Mohammad Alogla, Pratik Bhatt, Mohannad Naser, Svetha Venkatachari, Puneet Kumar, Augusto Masiero Gil, and Derek Hibner f or their help and support. I would like to express my gratefulness to Mr. Siavosh Ravanbakhsh , the manager of Civil Infrastructure Laboratory , and Mr. Charles Meddau gh for their support and kindness during the trying times in the laboratory. My warmest thanks to my colleagues in Applied Engineering Sciences; Dr. Laura Genik and Jason Smith for their constant encouragement and understanding . I would like to thank Laura Taylor, Laura Post, Margaret Conner, and Bailey Weber for their administrative assistance. I am grateful for the support from the Department of Civil and Environmental Engineering and the College of Engineering for providing several resources during my gr aduate studies. In addition, I acknowledge the funding from United States Agency for International Development, U.S. Airforce Research Laboratory (AFRL) , and Metna Company. I would like to thank my husband , Harshal, for years of patience, love, unwavering support, and encouragement. I would like to express my deepest gratitude to my parents for their constant support , inspiration, and motivation . Special thanks to my puppy, Jasper, for his endless affection and positivity. vi TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ..................... ix LIST OF FIGURES ................................ ................................ ................................ ................... xi LIST OF SYMBOLS ................................ ................................ ................................ ............. xviii CHAPTER 1 ................................ ................................ ................................ ................................ ... 1 1. Introduction ................................ ................................ ................................ ............................. 1 1.1. Background ................................ ................................ ................................ ...................... 1 1.2. Behavior of Reinforced Concrete Beams under Fire Exposure ................................ ....... 3 1.3. High - Temperature Properties of UHPC ................................ ................................ ........... 6 1.4. Fire - induced S palling Phenomenon in Concrete ................................ .............................. 8 1.5. Research Approach ................................ ................................ ................................ ........ 11 1.5.1. Hypothesis ................................ ................................ ................................ ............... 11 1.5.2. Research Objectives ................................ ................................ ................................ 11 1.5.3. Research Methodology ................................ ................................ ........................... 12 1.6. Layout ................................ ................................ ................................ ............................. 13 CHAPTER 2 ................................ ................................ ................................ ................................ . 15 2. State - of - the - art Review ................................ ................................ ................................ ......... 15 2.1. General ................................ ................................ ................................ ........................... 15 2.2. High - Temperature Properties of UHPC ................................ ................................ ......... 16 2.2.1. Thermal Properties ................................ ................................ ................................ .. 16 2.2.2. Mechanical Properties ................................ ................................ ............................. 25 2.2.3. Transport Properties ................................ ................................ ................................ 43 2.3. Experimental Studies on UHPC Members ................................ ................................ ..... 48 2.4. Numerical Studies on UHPC members ................................ ................................ .......... 52 2.5. Provisions in Standards and Codes on Fire Resistance of Concrete Members .............. 59 2.6. Cost of UHPC ................................ ................................ ................................ ................. 62 2.7. Knowledge Gaps ................................ ................................ ................................ ............ 62 CHAPTER 3 ................................ ................................ ................................ ................................ . 65 3. Experimental studies ................................ ................................ ................................ ............. 65 3.1. General ................................ ................................ ................................ ........................... 65 3.2. Mix Design of UHPC ................................ ................................ ................................ ..... 66 3.3. Design and Fabrication of UHPC Specimens and Beams ................................ .............. 70 3.4. Instrumentation ................................ ................................ ................................ ............... 75 3.5. High Temperature Property Tests on UHPC ................................ ................................ .. 77 3. 5.1. Thermal Properties ................................ ................................ ................................ .. 78 3.5.2. Mechanical Properties ................................ ................................ ............................. 97 3.6. Fire Resistance Tests on UHPC Beams ................................ ................................ ....... 121 3.6.1. Test Set - Up and Procedure ................................ ................................ ................... 121 3.6.2. Results and Discussion ................................ ................................ ......................... 125 3.7. Summary ................................ ................................ ................................ ...................... 140 vii CHAPTER 4 ................................ ................................ ................................ ............................... 143 4. Numerical Model ................................ ................................ ................................ ................ 143 4.1. General ................................ ................................ ................................ ......................... 143 4.2. Analysis Procedure ................................ ................................ ................................ ....... 144 4.2.1. Evaluation of fire temperatures: ................................ ................................ ............ 147 4.2.2. Evaluation of sectional temp eratures: ................................ ................................ ... 148 4.2.3. Evaluation of spalling: ................................ ................................ .......................... 151 4.2.4. Structural response calculations: ................................ ................................ ........... 153 4.3. Procedure for Modeling Fire - Induced Spalling ................................ ........................... 157 4.3.1. Criteria for determining spalling: ................................ ................................ .......... 160 4.3.2. Stress due to pore pressure: ................................ ................................ ................... 163 4.3.3. Stress due to thermal gradients: ................................ ................................ ............ 168 4.3.4. Stress due to structural loading: ................................ ................................ ............ 170 4.3.5. Permeability simulation: ................................ ................................ ....................... 170 4.4. Model Validation ................................ ................................ ................................ .......... 174 4.4.1. Analysis Details ................................ ................................ ................................ .... 177 4.4.2. Material Properties ................................ ................................ ................................ 177 4.4.3. Validation under Ambient Conditions ................................ ................................ .. 184 4.4.4. Validation under Fire Conditions ................................ ................................ .......... 186 4.5. Summary ................................ ................................ ................................ ...................... 208 CHAPTER 5 ................................ ................................ ................................ ............................... 210 5. Parametric Studies ................................ ................................ ................................ .............. 210 5.1. General ................................ ................................ ................................ ......................... 210 5.2. Factors influencing Fire Resistance ................................ ................................ ............. 210 5.3. Parametric studies ................................ ................................ ................................ ........ 211 5.3.1. Selection of beam ................................ ................................ ................................ .. 212 5.3.2. Range of parameters ................................ ................................ ............................. 213 5.3.3. Analysis details ................................ ................................ ................................ ..... 217 5.3.4. Results of parametric studies ................................ ................................ ................ 217 5.3.5. Summary ................................ ................................ ................................ ............... 266 CHAPTER 6 ................................ ................................ ................................ ............................... 268 6. Design Recommendations ................................ ................................ ................................ .. 268 6.1. General ................................ ................................ ................................ ......................... 268 6.2. Critical factors governing fire performance of UHPC beams ................................ ...... 269 6.3. Current provisions for fire design of NSC and HSC beams ................................ ........ 277 6.4. Design recommendations for UHPC beams ................................ ................................ . 279 6.4.1. Guidelines for enhancing the fire resistance of UHPC beams .............................. 280 6.4.2. Guidelines for minimizing spalling ................................ ................................ ...... 281 6.4.3. Guidance for advanced analysis ................................ ................................ ............ 282 6.5. Limitations ................................ ................................ ................................ ................... 284 6.6. Summary ................................ ................................ ................................ ...................... 285 CHAPTER 7 ................................ ................................ ................................ ............................... 286 7. Conclusions ................................ ................................ ................................ ......................... 286 7.1. General ................................ ................................ ................................ ......................... 286 viii 7.2. Key Findings ................................ ................................ ................................ ................ 287 7.3. Research impact ................................ ................................ ................................ ........... 290 7.4. Recommendations for Future Research ................................ ................................ ....... 291 APPENDICES ................................ ................................ ................................ ............................ 293 APPENDIX A. Design calculations for UHPC test beam s ................................ ........................ 294 APPENDIX B. Illustration of condition of beams during fire tests ................................ ........... 301 APPENDIX C. Evaluation of fire performance of a UHPC beam t hrough advanced analysis numerical example ................................ ................................ ................................ ...................... 303 APPENDIX D. Material properties at elevated temperatures ................................ .................... 312 REFERENCES ................................ ................................ ................................ ........................... 319 ix LIST OF TABLES Table 2 - 1. Test standards for evaluation of thermal properties. ................................ ................... 19 Table 2 - 2. Reported high - temperature thermal property tests on UHPC. ................................ .... 25 Table 2 - 3. Test standards for evaluation of mechanical properties. ................................ ............. 34 Table 2 - 4. Reported high - temperature mechanical property tests on UHPC. .............................. 38 Table 2 - 5. Reported fire tests on UHPC members. ................................ ................................ ...... 50 Table 2 - 6. Reported numerical studies on fire - induced spalling. ................................ ................. 54 Table 3 - 1. Mix proportions in UHPC batch mixes. ................................ ................................ ...... 67 Table 3 - 2. Properties of steel and polypropylene fibers used in UHPC batch mix. ..................... 69 Table 3 - 3. Sectional dimensions and reinforcement details in UHPC beams. ............................. 71 Table 3 - 4. Test matrix of specimens utilized for high temperature material property tests. ........ 72 Table 3 - ................................ . 85 Table 3 - 6. Thermal property relations of UHPCs generated utilizing data from tests. ................ 91 Table 3 - 7. Mechanical property relations of UHPC generated utilizing data from te sts. ........... 114 Table 3 - 8. Variables in tested UHPC beams. ................................ ................................ ............. 124 Table 3 - 9. Summary of fire test results. ................................ ................................ ...................... 135 Table 4 - 1. Summary of test parameters and results from fire resistance analysis. ..................... 175 Table 5 - 1. Properties of reference beam UHPC - B0 used in the parametric study. .................... 213 Table 5 - 2. Critical parameters investigated in parametric study. ................................ ............... 215 Table 5 - 3. Effect of varying content of steel fibers on strength of UHPC. ................................ 256 Table 5 - 4. Effect of varying content of polypropylene fibers on strength of UHPC. ................. 259 Table 5 - 5. Summary of varied parame ters and results from parametric study. .......................... 264 Table 6 - 1. Minimum width and cover thickness requirements of unrestrained RC beam for achieving fire resistance adopted from ACI 216.1 [98] ................................ .............................. 278 Table 6 - 2. Minimum width and cover thickness of UHPC beam for achieving fire resistance. 281 x Table 6 - 3. Range of limits for applicability of proposed guidelines. ................................ ......... 284 Table D - 1 . Values for the Main Parameters of the Stress - strain Relationships of Reinforcing Steel at Elevated Temperatures (Eurocode 2). ................................ ................................ ..................... 317 xi LIST OF FIGURES Figure 1.1. Behavior of typical RC beam under fire exposure. ................................ ...................... 4 Figure 1.2. Schematic illu stration of spalling mechanism in a fire exposed concrete slab: (a) Pore pressure; (b) Thermal stress. ................................ ................................ ................................ ......... 10 Figure 2.1. Variation of thermal conductivity in different concrete types with rise in te mperature. ................................ ................................ ................................ ................................ ....................... 23 Figure 2.2. Variation of specific heat in different concrete types with rise in temperature. ......... 23 Figure 2.3. Variation of thermal expansion in different concrete types with rise in temperature. 24 Figure 2.4. Variation of mass loss in different concrete types with rise in temperature. ............. 24 Figure 2.5. Variation of compressive strength with temperature for NSC [17]. .......................... 27 Figure 2.6. Variation of compressive strength with temperature for HSC [17]. .......................... 27 Figure 2.7. Variation of tensile strength with temperature [17]. ................................ .................. 28 Figure 2.8. Variation of elastic modulus with temperature [17]. ................................ .................. 29 Figure 2.9. Stress - strain response of NSC at elevated temperatures [17]. ................................ .... 31 Figure 2.10. Stress - strain response of HSC at elevated tem peratures [17]. ................................ .. 31 Figure 2.11. Schematic of testing regime for mechanical property evaluation at elevated temperature. ................................ ................................ ................................ ................................ .. 33 Figure 2.12 . Testing regimes for evaluating mechanical properties of concrete at high temperature. ................................ ................................ ................................ ................................ ....................... 33 Figure 2.13. Compiled data on variation in compressive strength of UHPC with temperature. .. 39 Figure 2.14. Compiled data on variation in elastic modulus of UHPC with temperature. ........... 39 Figure 2.15. Compiled data on variation in tensile streng th of UHPC with temperature. ............ 40 Figure 2.16. Residual stress - strain curves of UHPC with 2% steel fibers as a function of temperature [49]. ................................ ................................ ................................ ........................... 40 Figure 2.17. Residual stress - strain curves of UHPC with 2% steel fibers as a function of temperature [52]. ................................ ................................ ................................ ........................... 41 Figure 2.18. Stress - strain curves of UHPC with (a) steel and PP fibers (b) on ly PP fibers, as a function of temperature [54]. ................................ ................................ ................................ ........ 42 xii Figure 2.19. Permeability of UHPCs as a function of temperature [67]. ................................ ...... 47 Figure 2. 20. Porosity of different concrete types as a function of temperature. ........................... 48 Figure 3.1. F ibers: (a) Steel (b) Polypropylene (PP). ................................ ................................ ... 70 Fig ure 3.2. Layout and cross section of UHPC beams (All units are in mm). ............................. 71 Figure 3.3. (a) Formwork for UHPC beams, (b) Casting of beams, (c) Curing of beams using insulation blankets and lining. ................................ ................................ ................................ ...... 74 Figure 3.4. Compression strength test results for each UHPC mix. ................................ ............. 75 Figure 3.5. Tension strength test results for each UHPC mix. ................................ ..................... 75 Figure 3.6. Location of strain gauges and thermocouples at various cross - sections in (a) beams U - B1, U - B2, and U - B10, (b) beam B - 11 (All units are in mm). ................................ ...................... 77 Figure 3.7. Specimens for thermal property tests: (a) 50×50×25 mm; (b) 10×10×18 mm. ......... 78 Figure 3.8. Exploded specimen during (a) TMA test; and (b) damaged glass specimen h older from TMA test; and (c) mass loss test. ................................ ................................ ................................ .. 79 Figure 3.9. Measured thermal expansion for each UHPC mix. ................................ .................... 80 Figure 3.10. Measured the rmal properties for each UHPC mix: (a) Thermal conductivity; (b) Specific heat; and (c) Mass loss. ................................ ................................ ................................ ... 81 Figure 3.11. Measured thermal properties as a function of temperature for three UHPC types: ( a) Thermal conductivity; (b) Specific heat; (c) Mass loss; and (d) Thermal expansion. .................. 83 Figure 3.12. Comparison between thermal properties of UHPC with NSC and HSC. ................. 95 Figure 3.13. Test equipment for evaluating high - temperature mechanical properties: (a) Electric furnace; (b) Forney strength test machine. ................................ ................................ ................... 98 Figure 3.14. Spall ed UHPC - S2 specimen during heating for mechanical property test. .............. 99 Figure 3.15. Schematic of testing procedure followed for mechanical property evaluation of UHPC at elevated temperature. ................................ ................................ ................................ .............. 100 Figure 3.16. Oven drying of UHPC specimens. ................................ ................................ ......... 100 Figure 3.17. Temperature progression in UHPC - S2 specimen for target temperature of 750°C at a heating rate of: (a) 0.5°C/min; (b) 2°C/min. ................................ ................................ ............... 102 Figure 3.18. Testing of the heated specimen: (a) Compression; (b) Tension. ............................ 103 xiii Figure 3.19. Variation in compressive strength as a function of temperature: (a) Absolute; (b) Relative. ................................ ................................ ................................ ................................ ...... 105 Figure 3.20. Variation in elastic modulus as a function of temperature: (a) Absolute; (b) Relative. ................................ ................................ ................................ ................................ ..................... 107 Figure 3.21. Variation in splitting tensile strength as a function of temperature: (a) Absolute; (b) Relative. ................................ ................................ ................................ ................................ ...... 109 F igure 3.22. High temperature stress - strain response of: (a) UHPC - S2; (b) UHPC - H. ............. 111 Figure 3.23. Comparison of stress - strain response of UHPC - S2 and UHPC - H following heating rates: (a) 0.5°C/min ; (b) 2°C/min. ................................ ................................ .............................. 113 Figure 3.24. Comparison between mechanical properties from design codes and fitted test data. ................................ ................................ ................................ ................................ ..................... 117 Figure 3.25. Brid ging effects from steel fiber in UHPC specimen subjected to splitting tensile strength test. ................................ ................................ ................................ ................................ 120 Figure 3.26. Structural fire test setup at MSU: (a) Furnace (b) Observation viewport. ............. 122 Figure 3.27. Time - temperature curves for fire scenarios used in the fire tests. .......................... 123 Figure 3.28. Loading set up during tests on UHPC beams (Al l units are in mm). ..................... 124 Figure 3.29. Temperature progression at various depths in UHPC beams: a) U - B1, b) U - B2, c) U - B10, d) U - B11. ................................ ................................ ................................ ............................ 126 Figure 3.30. Schematic illustration of spalling pattern in tested UHPC beams. ......................... 128 Figure 3.31. Comparison of (a) rebar, (b) concrete temperatures as a function of fire exposure time. ................................ ................................ ................................ ................................ ..................... 130 Figure 3.32. Midspan deflection as a function of time in (a) all UHPC beams, (b) beam U - B11. ................................ ................................ ................................ ................................ ..................... 133 Figure 3.33. Fire test results: (a) state o f UHPC beams after fire tests, (b) bottom surface in tested beams, (c) schematic illustration of spalling and cracking pattern in tested beams. .................. 136 Figure 3.34. Localized compression zone failure in UHPC beam. ................................ ............. 139 Figure 4.1. Flow chart illustrating steps for spalling calculation and fire resistance analysis of a typical RC beam. ................................ ................................ ................................ ......................... 145 Figure 4.2. Typical beam layout and discretization of beam into segments and elements. ........ 147 Figure 4.3. Time - temperature curves for standard and design fire scenarios. ............................ 148 xiv Figure 4.4. Illustration of evolution of stresses and spalling in RC beam at each time step of analysis. ................................ ................................ ................................ ................................ ....... 158 Figure 4.5. Illustration of two - step spall ing phenomenon. ................................ ......................... 162 Figure 4.6. Variation of permeability as a function of temperature and mechanical damage. ... 172 Figure 4.7. Tensile stress - strain curves with damage values for permeability: (a) UHPC (with steel fibers); (b) plain NSC/HSC. ................................ ................................ ................................ ........ 173 Figure 4.8. Elevation and cross - section of the analyzed RC beams. ................................ .......... 176 Figure 4.9. Time - temperature curves adopted for fire exposure in the tests of analyzed RC beams. ................................ ................................ ................................ ................................ ..................... 176 Figure 4.10. Stress - strain response of reinforc ............. 178 Figure 4.11. Stress - polypropylene fibers) under compression. ................................ ................................ .................. 179 Figure 4.12. Stress - polypropylene fibers) under tension. ................................ ................................ .......................... 18 0 Figure 4.13. C omparison of predicted and measured (a) load - deflection, (b) load - strain response of UHPC beam U - B3 under ambient conditions. ................................ ................................ ....... 185 Figure 4.14. Comparison of predicted and measured temperatures fo r UHPC beams: (a) U - B1; (b) U - B2; (c) U - B10; (d) U - B11. ................................ ................................ ................................ ...... 188 Figure 4.15. Measured and predicted corner rebar temperatures as a function of time for UHPC beams. ................................ ................................ ................................ ................................ ......... 191 Figure 4.16. Measured and predicted corner rebar temperatures as a function of time for NSC and HSC beams. ................................ ................................ ................................ ................................ . 192 Figure 4.17. Measured and predicted extent of spalling as a function of time for analyzed beams. ................................ ................................ ................................ ................................ ..................... 194 Figure 4.18. Comparison of predicted pore pressure as a function of time in NSC, HSC, and UHPC beams. ................................ ................................ ................................ ................................ ......... 195 Figure 4.19. Spalling predictions along the length of the beam: (a) UHPC U - B1; (b) HSC B5. 197 Figure 4.20. Cross - sectional analysis results at mid - span for UHPC beam U - B1. .................... 200 Figure 4.21 . Cross - sectional analysis results at mid - span for HSC beam B5. ............................. 201 Figure 4.22. Measured and predicted mid - span deflection s of UHPC beams. ........................... 205 xv Figure 4.23. Measured and predicted mid - span deflections of NSC and HSC beams. .............. 206 Figure 5.1. Sectional configur ation and elevation of reference UHPC beam UHPC - B0 analyzed for parametric study (Units: mm). ................................ ................................ .............................. 212 Figure 5.2. Time - temperature curves for different fire scenarios. ................................ .............. 214 Figure 5.3. Effect of load ratio on temperature rise at corner rebar and mid - depth of UHPC beams. ................................ ................................ ................................ ................................ ..................... 218 Figure 5.4. Effect of load ratio on extent of spalling in U HPC beams. ................................ ...... 219 Figure 5.5. Effect of load ratio on deflection of UHPC beams. ................................ .................. 220 Figure 5.6. Effect of fire scenario on temperature ri se at corner rebar and mid - depth of UHPC beams. ................................ ................................ ................................ ................................ ......... 222 Figure 5.7. Effect of fire scenario on extent of spalling in UHPC beams. ................................ . 224 Figur e 5.8. Effect of fire scenario on deflection of UHPC beams. ................................ ............. 225 Figure 5.9. Effect of tensile reinforcement ratio on deflection of UHPC beams. ....................... 227 Figure 5.10. Effect of cover thickness on temperature rise at corner rebar in UHPC beams. .... 228 Figure 5.11. Effect of cover thickness on deflection of UHPC beams. ................................ ...... 229 Figure 5.12. Cross - section of the analyzed beams with varying concrete type. ......................... 230 Figure 5.13. Effect of concrete type on temperature rise at corner re bar and mid - depth in beams. ................................ ................................ ................................ ................................ ..................... 231 Figure 5.14. Effect of concrete type on extent of spalling in beams. ................................ ......... 232 Figure 5.15. Effect of concre te type on pore pressure in beams. ................................ ................ 233 Figure 5.16. Effect of concrete type on deflection in beams. ................................ ..................... 234 Figure 5.17.Details of I - shape UHPC beam tested by Hasgul et al. [192] . ................................ 236 Figure 5.18. Predicted and measured load - deflection response for I beam. ............................... 236 Figure 5.19 . Cross - sectional details of UHPC beams of different shapes. ................................ . 237 Figure 5.20. Effect of specimen shape on temperatures at rebar and mid - depth of UHPC beams. ................................ ................................ ................................ ................................ ..................... 239 Figure 5.21. Effect of specimen shape on extent of spalling in UHPC beams. .......................... 240 xvi Figure 5.22. Effect of specimen shape on deflections in UHPC beams. ................................ .... 241 Figure 5.23. Effect of specimen dimensions on temperature rise at corner rebar and mid - depth of UHPC beams. ................................ ................................ ................................ .............................. 242 Figure 5.24. Effect of specimen dimensi ons on extent of spalling in UHPC beams. ................. 243 Figure 5.25. Effect of specimen dimensions on deflection of UHPC beams. ............................ 243 Figure 5.26. D eflections of beam with dimensions 150 mm x 230 mm made using different concrete types. ................................ ................................ ................................ ............................. 244 Figure 5.27. Deflections of UHPC beams with varying sectional sizes and cover thicknesses. 246 Figure 5.28. Effect of span length on corner rebar temperatures at L/5 from support in UHPC beams. ................................ ................................ ................................ ................................ ......... 249 Figure 5.29. Effect of span length on extent of spalling in UHPC beams. ................................ . 249 Figure 5.30. Effect of span length on deflection of UHPC beams. ................................ ............ 250 Figure 5.31. Uniformly distr ibuted loading on UHPC beam. ................................ ..................... 252 Figure 5.32. Two p oint loading on UHPC beam. ................................ ................................ ....... 253 Figure 5.33. Effect of loading type on deflection of UHPC beams. ................................ ........... 254 Figure 5.34. Bending moment along span length of UHPC beams under different loading type. ................................ ................................ ................................ ................................ ..................... 255 Figure 5.35. Effect of steel fibers on temperature rise at corner rebar and mid - depth of UHPC beams. ................................ ................................ ................................ ................................ ......... 257 Figure 5.36. Effect of steel fibers on extent of spalling in UHPC beams. ................................ .. 257 Figure 5.37. Effect of steel fibers on deflection of UHPC beams. ................................ ............. 258 Figure 5.38. Effect of polypropylene fibers on temperature rise at corner rebar and mid - depth of UHPC beams. ................................ ................................ ................................ .............................. 260 Figure 5.39. Effect of polypropylene fibers on extent of spalling in UHPC beams. .................. 261 Figure 5.40. Effect of polypropylene fibers on pore pressure in UHPC beams. ........................ 262 Figure 5.41. Effect of polypropylene fibers on deflection of UHPC beams. .............................. 263 Figure A. 1. Cross section and loading set up of UHPC beams (All dimensions are in mm). ... 294 Figure A. 2. Schematic of shear force and bending moment diagram for tested UHPC beams. 295 xvii Figure A. 3. Design assumptions for analysis of reinforced concrete beams with steel fibers. . 296 Fig ure B. 1. Typical UHPC beam just prior to fire exposure. ................................ .................... 301 Figure B. 2. UHPC beam U - B1 with only steel fibers (no polypropylene fibers) after 40 minutes into fire exposure. ................................ ................................ ................................ ....................... 301 Figure B. 3. UHPC beam U - B11 with both steel and polypropylene fibers after 40 minutes into fire exposure. ................................ ................................ ................................ ............................... 302 Figure C. 1. Cross - section and elevation of UHPC beam used in the illustration for advanced analysis (All dimensions are in mm). ................................ ................................ ......................... 303 Figure C. 2. Discretization of beam into segments along length and disc retization of cross - section into elements. ................................ ................................ ................................ .............................. 304 Figure C. 3. Time - temperature curve for standard fire scenario used in the analysis. ............... 304 Figure C. 4. Cross - sectional temperatures as a function of time in the analyzed UHPC beam. . 305 Figure C. 5. Cross - sectional temperature contours at mid - span in the analyzed UHPC beam after 10 m inutes into fire exposure. ................................ ................................ ................................ ..... 306 Figure C. 6. Pore pressure distribution at mid - span in the analyzed UHPC beam after 10 minutes into fire exposure. ................................ ................................ ................................ ....................... 307 Figure C. 7. Cross - sectional thermal stress contours at mid - span in the analyzed UHPC beam after 10 minutes into fire exposure. ................................ ................................ ................................ ..... 307 Figure C. 8. Cross - sectional mechanical stress contours at mid - span in the analyzed UHPC beam after 10 minutes into fire exposure. ................................ ................................ ............................ 308 Figure C. 9. Extent of spalling as a function of time in the analyzed UHPC beam. ................... 309 Figure C. 10. Moment curvature curves at various fire exposure times for the analyzed UHPC beam. ................................ ................................ ................................ ................................ ........... 309 Figure C. 11. Variation of moment capacity for the anal yzed UHPC beam as a function of fire exposure time. ................................ ................................ ................................ ............................. 310 Figure C. 12. Variation of deflection for the analyzed UHPC beam as a function of fire exposure time. ................................ ................................ ................................ ................................ ............ 311 xviii LIST OF SYMBOLS A = Cross - sectional area of the beam f c = Compressive strength of concrete at room temperature f cT n y and n z = Components of outward normal vector to the surface in the plane of the cross section i cr = Creep strain in concrete D = Damage variable for concrete permeability d = Effective depth of the beam L = Density of liquid wat er V = Density of water vapor in the concrete boundaries = Density of water vapor in the surrounding environment d f = Diameter of fiber D 0 = Diffusion coefficient of water vapor at the boundaries of the beam s = Distance along the boundary y = Dis tance from geometrical centroid of beam cross - section to the center of the element V = Dynamic viscosity of water vapor h = Time step E c = Elastic modulus of concrete at room temperature E cT = = Emissivit y factor F e = Equivalent nodal heat flux for elements xix F = Equivalent nodal heat flux vector T f = Fire temperature R = Gas constant M = Global mass matrix K = Global stiffness matrix q = Heat flux h con = Heat transfer coefficient convective h rad = Hea t transfer coefficient radiative h f = Incremental rise in permeability during melting of polypropylene fibers Q = Internal heat source k D = Intrinsic permeability of concrete accounting for damage k 0 = Initial undamaged permeability of concrete = Lapl acian differential operator l f = Length of fiber L = Span length of the beam E = Mass of evaporated water J = Mass flux of water vapor m LW0 = Mass of liquid water at t =0 (initial mass of liquid water) m L = Mass of liquid water at any time t m D = Mass of liquid water formed due to dehydration m V = Mass of water vapor M e = Mass matrix for each element = Mechanical damage parameter for concrete permeability xx T me = Mechanical strain in concrete mes = Mechanical strain in steel me = Mechanical stress in concrete M - = Moment - curvature I = Moment of inertia of the beam n V = Number of moles of water vapor = Parameter tracing the shape of the - k 1 - k 2 - ion of UHPC c = Peak strain (strain at peak stress) at room temperature cT k T = Permeability of concrete at temperature, T k f = Permeability of fiber tunnels k fm P = P ermeability of fibers a nd concrete matrix when they are in parallel with fluid flow k fm NP = P ermeability of fibers and concrete matrix when they are in series with fluid flow PPF = Polypropylene fiber content by % of volume P V = Pore pressure = Pore pressure variation p arameter for concrete permeability P = Pore pressure stress in concrete 0 p = Probability of percolation of polypropylene fiber tunnels xxi RH = Relativ e humidity in the concrete P S0 = Initial saturation pressure in concrete N = Shape functions vector v = Shear reinforcement ratio c = Specific heat = Stefan - Boltzman constant = 5.67 x 10 - 8 (W/m 2 . K 4 ) - = Stress - strain K e = Stiffness matrix for each element 0 = Strain at the geometrical centroid of beam cross - section SF = Steel fiber content by % of volume T = Temperature = Temperature derivative with respect to time T E = Temperature of the environment depending on exposure conditions = Temperature gradient parameter for concrete permeability t = Tensile reinforcement ratio f t = Tensile strength of concrete at room temperature f tT t = Time k t = Thermal conductivity th = Thermal st ress in concrete t = Total strain in concrete ts = Total strain in steel th = Thermal strain in concrete xxii ths = Thermal strain in steel tr = Transient strain in concrete T V V = Volume fraction of water v apor V L = Volume fraction of liquid water V S0 = Initial volume fraction of solid V D = Volume fraction of dehydrated liquid water f y = Yield strength of steel at room temperature f yT = Yield strength of steel 1 CHAPTER 1 1. Introduction 1.1. Background Concrete is one of the most extensively used building materials in the construction industry due to its excellent properties , such as strength, versatility, durability, non - combustion properties, ease of fabrication, and readily available raw m aterials. In recent years, r esearch and development in the field of concrete technology have led to the development of ultra - high performance concrete (UHPC). UHPC is characterized as an advanced cementitious material typically made with very low water to binder ratio, high fineness admixtures, steel fibers, and without any coarse aggregate s . UHPC has higher compressive (above 150 MPa) and tensile strength (5 MPa or higher), enhanced toughness , and increased durability than that of conventional normal stre ngth concrete (NSC) or high strength concrete (HSC) [1,2] . Owing to the superior mechanical properties of UHPC, it has gained popularity in structural applications such as bridges, and to a limited extent in high - rise buildings. Fire is one of the most serious threats that buildings can be exposed to and thus, a key consideration in building design is the fire resistance of structural members . Fire resistance is the duration during which a structural membe r exhibits resistance with respect to insulation, integrity, and stability criteria [ 3] . Concrete structures exhibit excellent fire resistance , and this is attributed to the low thermal conductivity and high thermal capacity of concrete, as well as to slower degradation of its strength and modulus properties with temperature. However, few p reliminary studies have indicated that UHPC structural members do not exhibit the same level of fire resistance as that of NSC and HSC members. This is mainly due to the faster degradation of strength and modulus properties of UHPC with temperature, as w ell as its high susceptibility to fire - induced spalling. In 2 addition , although most of the high - temperature material properties have been widely studied for NSC and HSC, only a scarce amount of data is available for UHPC. Fire - induced s palling is the break - up of chunks of concrete from a concrete member under severe fire exposure . Spalling can lead to loss of cross - section, thereby increasing heat penetration to inner concrete layers and steel reinforcement, leading to a decrease in the overall fire resista nce of the structural member. Therefore, it is critical to consider spalling while evaluating the capacity of fire - exposed reinforced concrete ( RC ) members . Only limited studies in the literature have focused on developing approaches to assess and predict spalling of concrete under fire conditions. Even where advanced analysis methods are adopted for fire resistance analysis, fire - induced spalling is often not included in calculations for evaluating fire resistance. The current lack of spalling evaluation m ethods is due to the complexity of the spalling phenomenon and limited test methods and equipment to generate required data for validation of associated numerical models. T he current fire design provisions in codes assign fire resistance ratings to concret e members based on their sectional dimensions and cover thickness to steel reinforcement. These ratings are based on fire tests predominantly conducted on NSC members subjected to standard fire exposure and do not specifically consider fire - induced spallin g that can take place in a concrete member. Hence, they might not be directly applicable to UHPC members. Thus, a rational approach that accounts for realistic fire exposure scenarios, loading conditions, high - temperature material properties, and fire - indu ced spalling is needed for reliable prediction of fire resistance of UHPC structural members. RC beams function in a building as essential load - bearing structural members and the complexities involved in tracing the fire response of beams are discussed bel ow to gain a better understanding of the problem. 3 1.2. Behavior of Reinforced Concrete Beams under Fire Exposure When exposed to fire, a reinforced concrete ( RC ) beam experiences a rise in sectional temperatures with time due to heat transmission from the fire - exposed surface s of the beam to the interior section . The increased sectional temperatures will influence the structural behavior of the beam and can result in loss of capacity and stiffness in the beam, which in turn can lead to failure of the beam. The behavior of a typical RC beam under fire exposure is illustrated in Figure 1 . 1 (a) . Beams are exposed to fire from three sides as shown in Figure 1 . 1 (b), as typically a slab is present on the top side of the beam. The beam has a flexural capacity of M 0 at ambient conditions. With increasing fire exposure time, the temperature rises within the beam cross - section (see Figure 1 . 1 (c)) thr ough the heat conduction process and depends on the variation in the thermal properties of concrete and rebars with increasing temperature. The applied moment due to external load remains constant with progression in fire exposure time . However, t he increa sing sectional temperatures lead to gradual degradation of strength and modulus properties (mechanical properties) in concrete as well as reinforcing steel , which in turn leads to a decrease in moment capacity (M 0 to M 3 ) of the beam with time (T 0 to T 3 ) as shown in Figure 1 . 1 (d) . In addition, the beam experiences increasing deflection as a result of a reduction in modulus properties of constituent materials (concrete and reinforcing steel), and also due to high - temp erature creep effects, which become significant in the later stages of fire exposure. When the moment due to applied structural load exceeds the decreasing moment capacity of the beam, the beam experiences failure at that time (see Figure 1 . 1 (e)) , and the fire exposure time to attain failure is taken as the fire resistance of the beam. In addition, concrete members can experience spalling under fire exposure. I f spalling of concrete occurs in RC beams, it can lead t o loss of cross - section, which in turn can accelerate temperature 4 propagation and result in faster degradation of properties in concrete and steel, lowering the overall fire resistance of the beam. The effect of spalling is usually neglected in the fire de sign of NSC beams, as they are less prone to spalling. However, spalling can be a major problem in structural members made of HSC and UHPC, due to the built - up of high pore pressure as a result of its impermeable and dense microstructure. Further, owing to its significant higher strength, UHPC members have reduced sectional size (less thermal mass) and lower cover thickness as compared to structural members made of conventional concrete (NSC or HSC). Therefore, in the fire resistance evaluation of UHPC stru ctures, all the influencing factors , and temperature - dependent material properties must be given due consideration. Figure 1 . 1 . Behavior of typical RC beam under fire exposure. 5 Figure 1.1. 6 Figure 1.1. 1.3. High - Temperature Properties of UHPC Fire resistance is defined as the duration of time during which a structural member withstands the adverse effects of fire without failure. For theoretically evaluating the fire resistance o f a structural member, information o n propert y variation of constituent materials (namely concrete, steel, etc.) at elevated temperatures is required. The properties of concrete that are needed for fire resistance analysis are thermal, mechanical, and spec ific properties for distinct phenomen a such a s fire - induced spalling. Thermal properties that include thermal conductivity, specific heat, thermal expansion, and mass loss determine the level of temperature rise in structural members, while the mechanical p roperties that include strength and modulus , as well as high temperature creep govern the extent of loss of sectional capacity and progression of deflections under fire exposure. In addition, fire - induced spalling that occurs in concrete under certain con ditions deteriorates the performance of a reinforced concrete member. For predicting such spalling, related properties such as permeability , moisture content, and tensile strength of concrete at high temperatures are 7 required . Previous research has shown t hat adding polypropylene (PP) and steel fibers are added to the concrete batch mix can minimize the extent of spalling . Addition of steel fibers enhance s the tensile strength of concrete and helps to withstand higher tensile stress generated due to pore pr essure developed at elevated temperatures, thus reducing spalling mainly in high strength concrete (HSC) members. On the other hand, polypropylene (PP) fibers melt when sectional temperatures in concrete under fire exposure reach about 160°C. This melting of PP fibers constructs channels and enhance s permeability inside concrete, resulting in dissipation of high pore pressure generated within the concrete, and thus prevent ing the occurrence of spalling. Accordingly, the influence of fibers on the properties of concrete needs to be known to evaluate the fire response of fiber - reinforced concrete (such as UHPC) structural members. The thermal, mechanical, and special properties of concrete vary with temperature and are also influenced by the type of concrete m ix (i.e. strength, aggregate type, and presence of fibers ). Establishing the behavior of UHPC at the material level and characterizing their high - temperature properties is important for quantifying the fire resistance of UHPC structural members. A good amo unt of data and well - established property relations are present for the high temperature thermal and mechanical properties of conventional concretes (NSC and HSC). However, a very limited amount of data is available on high - temperature material properties of UHPC. Moreover, at present , there are no standardized test methods for evaluating the properties of UHPC at elevated temperatures. Further, there is a lack of standardized testing procedure s and instrumentation to measure spalling - related characteristic s ( such as pore pressure) and transport properties (such as porosity, permeability) at high temperatures. 8 1.4. Fire - induced S palling Phenomenon in Concrete Many experimental and numerical studies have been conducted in the last decades to gain an understanding of the driving mechanisms for spalling in concrete under fire exposure . Based on these studies, fire - induced spalling can be theorized to occur based on either of the two mechanisms, namely: (i) pore (or vapor) pressure development or , (ii) thermal stress generation. These two spalling mechanisms are schematically illustrated in Figure 1 . 2 for the case of a reinforced concrete (RC) slab subjected to one - dimensional heating (fire) from the bottom surface. As per the pore pressure mechanism [4,5] , spalling occurs when stresses g enerated from temperature - induced pore pressure exceed the tensile strength of concrete. When a concrete member is subjected to high temperatures, as in the case of fire, moisture present in concrete turns into vapor and this vapor moves inwards or outward s of the member depending on temperature and pressure gradients developed in the section. Depending on the permeability of concrete, a part of the vapor escapes through the heated surface and the remaining portion of the vapor moves towards the inner cool er regions of concrete, where the vapor condenses back to liquid water. With the progression of fire exposure time, the processes of concrete drying, moisture migration, and vapor condensation result in the formation of a saturated layer at a certain dista nce away from the prevents further migration of water vapor towards inner regions, resulting in a build - up of pore (or vapor) pressure near the heated surface as s hown in Figure 1 . 2 (a) - (iii). At the locations where pore pressure is accumulated, tensile stresses are generated in the member. When the stress from temperature - induced pore pressure exceeds the tensile strength of concrete (which is decreasing with temperature), spalling occurs in the concrete member. The transfer and movement of moisture [6] . The development 9 of thermal gradients, pore pressure as well as resulting spal ling in the section of the slab are schematically illustrated in Figure 1 . 2 (a). As per the thermal stress mechanism [7,8] , spalling is said to occur due to fracture of concrete resulting from therm al stresses. The rise of temperature in the outer layers closer to a fire exposed face of the concrete member occurs at a considerably faster rate than the inner layers (core) of the concrete member (away from the fire - exposed surface), due to high thermal inertia of concrete (i.e. low thermal conductivity and high specific heat). This variation in temperature between the outer and inner concrete layers results in the development of high thermal gradients along the cross - section of the fire exposed concrete member. The large thermal gradients cause non - uniform expansion of the hotter parts, which is restrained by the cooler inner regions. Due to this restraint to thermal expansion, significant thermal stresses are induced in the member, resulting in compress ive stresses parallel to the heated surface and tensile stresses in the cooler regions as shown in Figure 1 . 2 (b) - (iii). The compressive stresses in the heated concrete surface induce transverse tensile stresses and when these transverse tensile stresses exceed the tensile strength, brittle fracture of concrete (pieces) occurs. This phenomenon is explained based on fracture mechanics principles [9,10] . The build - up of thermal gradients, stress, a nd the resulting spalling in a slab are illustrated in Figure 1 . 2 (b). If the concrete member is subjected to structural loading during a fire incident, the applied loading generates an additional component of stres s (mechanical), and this may amplify the stress developed from thermal expansion and pore pressure, which in turn can lead to accelerated spalling. However, the effect of load - induced stress on spalling is ignored in most previous studies. 10 Figure 1 . 2 . Schematic illustration of spalling mechanism in a fire exposed concrete slab: (a) Pore pressure; (b) Thermal stress. Some research studies also indicate that spalling is a combined action of both the pore pre ssure and thermal stress mechanisms. Despite a number of experimental and numerical studies on fire - induced spalling in concrete members in the past three decades, there is still a lack of accurate numerical approaches for modeling spalling. Further, among the different concrete types, UHPC and HSC are more susceptible (than conventional NSC), to fire - induced spalling, specifically UHPC due to its extremely dense microstructure. Therefore, for realistic fire resistance evaluation of UHPC members, a validate d spalling model is imperative . 11 1.5. Research Approach 1.5.1. Hypothesis To overcome some of the current knowledge gaps and develop a better understanding o f the fire behavior of UHPC beams, this research project is developed with a hypothesis stated as follows: response of UHPC beams under fire conditions is significantly influenced by temperature - dependent thermo - mechanical properties of constituent materials and also the occurrence of fire - induced spalling. Therefore, a realistic assessment of fire performance of UHPC beams requires proper consideration to temperature - dependent properties of UHPC and reinforcement, as well as a realistic fire - induced spalling criterion 1.5.2. Research Objectives This study aims to develop a comprehensive understanding o f the perfor mance of UHPC beams under fire conditions and develop a rational approach for the fire design of UHPC beams. As part of this thesis , the following specific objectives will be addressed: Carry out a state - of - the - art review on the behavior of UHPC structural members under fire conditions. This include s reviewing studies on the effect of temperature on material properties of UHPC , and also structural fire tests and numerical studies carried out on UHPC members . Undertake material level tests on UHPC specimens at elevated temperature s to quantify the effect of high temperature on the thermal and mechanical properties of UHPC. Conduct fire resis tance experiments on UHPC beams to evaluate their fire behavior, as well as spalling progression under fire conditions. Extend a macroscopic finite element based numerical model to trace the response of UHPC beams under fire conditions. The model will incorporate fire - induced spalling analysis 12 through an improved spalling sub - model, which will consider the stresses resultin g from pore pressure, thermal gradients , and structural loading in concrete member s to evaluate spalling . In addition, the numerical model will account for material nonlinearities and temperature - dependent property degradation in constituent materials. Uti lize data generated from fire resistance tests to validate the developed numerical model. The validation will be carried out by comparing thermal, structural , and spalling predictions from the model with measured results in fire tests. Conduct parametric s tudies applying the validated numerical model to quantify the influence of various critical factors influencing the behavior of UHPC beams under fire conditions . Develop rational design guidelines for fire resistance design of UHPC beams based on the data generated from fire tests and parametric studies. 1.5.3. Research Methodology The above - stated research objectives will be realized through experimental and numerical studies on UHPC members under fire conditions. Experiments will be carried out on UHPC at both material and structural levels. At the material level, a comprehensive testing program will be undertaken on UHPC to generate data on high temperature thermal and mechanical properties. At the structural level, four RC beams made of UHPC will be designed, fabricated, and tested under structural loading and fire conditions. As part of the numerical study, a macroscopic finite element based model originally developed by Dwaikat and Kodur [11] for NSC and HSC beams will be extended and u pgraded to evaluate the fire - response of UHPC beams. An improved spalling sub - model will be incorporated into the macroscopic numerical model. Spalling will be based on the stresses arising from the effects of 13 pore pressure, thermal gradients, and structur al loading generated in a concrete member during fire exposure. In addition, the numerical model will also be modified to carry out a member level analysis rather than analysis of a single critical section and accounts for spalling pattern s resulting from the variation of stresses along the fire exposed length of the beam. Furthermore, t he numerical model will account for high - temperature stress - strain curves (including strain hardening and softening) of concrete and steel, temperature - dependent thermal and mechanical properties, and permeability variations of concrete. Data from fire tests will be used to validate the developed numerical model for thermal, structural, and spalling analysis. The validated numerical model will be applied to conduct detailed p arametric studies to quantify the effect of critical factors on the fire performance of UHPC beams. Results from parametric studies will be utilized to develop guidelines for the fire design of UHPC beams. 1.6. Layout The research undertaken as part of this di ssertation is presented in seven chapters. Chapter 1 provides a general background on the characteristics of UHPC, fire response of reinforced concrete beams , and fire - induced spalling phenomenon. Chapter 1 also lays out the research objectives and methodo logy of this study. Chapter 2 summarizes a state - of - the - art review o f the behavior of UHPC beams exposed to fire. The review includes a summary of reported experimental and numerical studies undertaken on UHPC members, as well as presents fire design provi sions for RC structural members in current codes of practice. This chapter also reviews the high - temperature material property tests undertaken o n concrete needed for modeling the fire response of beams. Chapter 3 presents the fire resistance experiments c onducted on UHPC beams with different types of fiber reinforcement, tested under combined effects of fire and structural loading. This chapter also presents the undertaken high - temperature material property tests on UHPC and the development 14 of e mpirical re lations based on test data, for predicting high - temperature properties over a wide temperature range. Chapter 4 provides details on the macroscopic finite element based numerical model for fire resistance analysis and spalling prediction in UHPC beams. Ext ension of the numerical model , as well as validation of the extended numerical model, are also presented in this chapter. Chapter 5 presents the results from the parametric study on the impact of critical parameters on the fire response of UHPC beams . This chapter describes A detailed discussion on the trends along with the ranges of parameters governing the fire resistance of UHPC beams is described in this chapter . Chapter 6 provides fire design guidelines to mitigate fire - induced spalling and improve the fire resistance of UHPC beams. Finally, conclusions and recommendations for future research are summarized in Chapter 7 . 15 CHAPTER 2 2. State - of - the - art Review 2.1. General Fire is one of the most severe hazards to which structural members may be subjected durin g their lifetime and hence the provision of fire resistance to structural members is a key requirement in building design. Unlike steel structures, concrete structures possess a high level of fire resistance and this is due to the superior thermal and mech anical properties of concrete at elevated temperatures. However, preliminary studies have shown that ultra - high performance concrete ( UHPC ) members, unlike conventional normal strength concrete (NSC) members, do not exhibit good fire resistance due to fast er degradation of thermal and mechanical properties and also due to high susceptibility of UHPC to fire - induced spalling. To mitigate such fire - induced spalling, the addition of different types of fibers, such as steel and polypropylene (PP) is often recom mended for high - strength concrete mixes . At present , there is very limited data on fire resistance of UHPC members, as well as the effectiveness of fibers in mitigating spalling in UHPC members. Fire resistance evaluation of reinforced UHPC members require s a detailed analysis of the thermal and structural response of the member, which in turn requires an input of properties of UHPC (and steel reinforcement) as a function of temperature. Thermal and mechanical properties of UHPC are probable to vary differe ntly at elevated temperatures as compared to conventional normal strength concrete ( NSC ) and high strength concrete ( HSC ) , due to microstructural differences . Currently, only l imited studies have been reported on the high - temperature properties of UHPC and the fire behavior of UHPC structural members. Further, there is a lack of information on the transport properties of UHPC required for the prediction of spalling, such as porosity, permeability, and so on. 16 This chapter presents a state - of - the - art review o f the currently available information on the high - temperature properties of UHPC at a material level. Besides , previous experimental and numerical studies on the response of UHPC structural members under fire conditions are reviewed . Also , the existing nu merical model s and approaches for predicting fire - induced spalling in concrete , which can be a dominating factor for the fire performance of UHPC members , are discussed . Finally, a review of design provisions in current codes and standards for fire design of concrete members is presented . 2.2. High - Temperature Properties of UHPC Temperature - dependent thermal and mechanical properties of concrete and steel reinforcement have been extensively studied in the literature [12 14] . Further empirical relations defining the temperature dependence of these properties are specified in a few codes, st andards , and manuals (such as ASCE manual [15] and Eurocode2 [16] ) . However, the information available regarding the temperature - dependent properties of UHPC is rather limited. A review of the informa tion available on these properties is presented in the following sections. Typically, UHPC is made with steel fibers, which contributes to its high ductility and tensile strength properties. However, some innovative UHPC mixes do not contain steel fibers a nd previous tests on such mixes (plain UHPC) are also included in the literature review for the sake of completeness. 2.2.1. Thermal Properties 2.2.1.1. General Typically, building fires can reach temperature s up to 1000°C. Thus, in typical fire scenarios, the sectional temperature in a concrete member will be in the range of 20 800°C. Therefore, for analytically evaluating the fire resistance of a structural member , the variation of material properties is to be known in the temperature range of 20 800°C. Thermal properti es, namely, 17 t hermal conductivity, specific heat, thermal expansion, and mass loss are needed for predicting the temperature profiles and subsequent thermo - mechanical analysis in concrete structures under fire exposure. The thermal properties of concrete ar e significantly influenced by the batch mix proportions of concrete , type of aggregate, and moisture content. The t emperature - dependent thermal properties of NSC and HSC have been extensively studied by numerous test programs in the literature [17] . Data generated in the reported tests have been used to develop temperature - dependent thermal property relations of concrete and these are specified in the ASCE manual [15] , Eurocode 2 [16] , and other guidance documents. To start with, thermal conductivity is the amount of heat flow under a unit temperature gradient across a ny material and thus, indicate s the rate at which a given material transfers heat. The room temperature thermal conductivity of NSC and HSC ranges between 1.4 and 3.6 W/m K, and 2.4 and 3.6 W/m K [17 19] . Typically, the t hermal conductivity of HSC is highe r than that of NSC due to a low water - cement ratio (w/c) and the incorporation of different binders (such as slag and silica fume) in HSC [20,21] . Also, concretes made of siliceous aggregates have higher conductivity than those made of carbonate aggregates [22] . The thermal conductivity of concrete decreases with temperature due to loss of moisture with an increase in temperature. The second thermal property is specific heat which describes the amount of heat requ ired to raise a unit mass of material a unit temperature. The specific heat of NSC at room temperature is in the range of 840 J/kg K and 1800 J/kg K, whereas that of HSC is in the range of 700 and [18,20] . Similar to thermal conductivity, the specific heat is also highly influenced by moisture content , aggregate type, and mix proportions. The specific heat of carbonate aggregate concrete is higher than that of silic eous aggregate concrete in the 600 - 800ºC temperature range due to the substantial amount of heat needed for dissociation of dolomite in the carbonate aggregates [23] . The third property, thermal 18 expansion characterizes the percentage change in the length of a concrete specimen when subjected to elevated temperatures. T he thermal expansion of concrete increases from zero at room temperature to about 1.3% at 700°C and then generally remains constant through 1000°C [17 ] . The variation in thermal expansion with temperature in HSC and NSC are similar and mainly dependent on w/c ratio , moisture content, and aggregate type [22] . Concrete made with siliceous aggregate has a higher thermal expansion than concrete made with carbonate aggregate [17 ] . The fourth thermal property, mass loss depicts the decrease in mass of concrete with increasing temperature resulting from loss of moisture. Mass loss can affect the enthalpy and amount of latent heat for water evaporation which directly affects all th e other material properties of concrete. HSC exhibits a similar trend in the temperature - dependent mass loss as that of NSC. The mass loss is minimal for both carbonate and siliceous aggregate concretes up to about 600°C. Beyond 600°C, carbonate aggregate concrete exhibits significantly higher mass loss due to the dissociation of dolomite [17,19] . The temperature variation of thermal properties of concrete, apart from depending on the batch mix proportions, also relies on the specimen con ditions and test procedure (such as the size of sample and moisture content) adopted in undertaking property tests [3,24,25] . Thus, a review of test methods and proce dures specified in standards for evaluating high temperature thermal properties of concrete is presented in the following sub - section. 2.2.1.2. Test methods for high - temperature thermal properties The thermal properties of concrete, especially at elevated temperat ures, can vary significantly based on test procedures, conditioning of specimens, and equipment (instrument) used to measure these properties. S tandardized test methods and procedures are required to minimize the variations in measured thermal properties a rising from test methods, testing parameters, and equipment. To address this requirement, a review was undertaken to determine the suitable high - temperature test 19 standards for property evaluation. Test procedures provided in current test standards for meas uring thermal properties are mostly focused on room temperature conditions and only limited standardized test procedures exist for evaluating thermal properties at elevated temperature s, as summarized i n Table 2 - 1 . It can be seen that there is a lack of test methods and procedures in American Society for Testing and Materials (ASTM) standards for evaluating thermal conductivity of concrete beyond the temperature of 85 º C and specific heat beyond 600 º C [25] . Table 2 - 1 . Test standards for evaluation of thermal properties. Thermal property Temperature range Test standards Thermal conductivity Ambient temperature to 85 °C ASTM C177, ASTM C1363 ISO 8302 Elevated temperature (upto 1000°C) No ASTM standard ISO 22007 - 2 Specific heat Ambient temperature to 600 °C ASTM E1269 ISO 11357 Elevated temperature (upto 1000°C) ISO 22007 - 2 Thermal expansion Ambie nt to elevated temperature (upto 1000 °C) ASTM E831 ISO 11359 - 2 Mass loss Ambient to elevated temperature (upto 1000 °C) ASTM E1131 ISO 11358 T he t est procedure for measuring the thermal conductivity of concrete at room temperature is outlined in ASTM C17 7 [26] and ASTM C1363 [27] standards. ASTM C177 [26] provisions specify that thermal conductivity can be measured through guarded hot - plate apparatus. This test involves the construction of a hot plate apparatus abiding by the design requi rements specified in the standard. The principle involved is to establish a temperature difference across a concrete sample of known thickness and to calculate thermal conductivity from the direct measurement of steady - state power required to maintain this temperature difference. However, the ASTM C177 test procedure is applicable only for measuring thermal c onductivity at room temperature (±10 º C). ASTM C1363 [27] provisions specify design guidelines for hot box apparatus in order to measure 20 the thermal conductivity of building materials but it is limited to temperatures up to 85 º C. ASTM C1363 me thod is analogous to the ASTM C177 test procedure, except it is meant to be used for testing large specimens whose dimensions are controlled by the design of the hot box apparatus. It is noteworthy that ASTM standards do not prescribe specific test methods and procedures for measuring thermal conductivity at elevated temperatures, beyond 85 º C. Standard ISO 8302 [28] also provides provisions for th ermal conductivity measurements, which are similar to ASTM C177 provisions, whereas ISO test standard 22007 2 [29] spec ifies transient plane heat source (TPS) or hot disc method for measuring thermal conductivity in the temperature range of 20 to 1000 º C. The TPS method is base d on the principles of measuring the resistance of a transiently heated plane sensor fitted in between two test specimens. For measuring the specific heat of concrete, ASTM E1269 [30] recommend s using the differential scanning calorimetry method (DSC) in the range of room temperature to 600 º C. ISO 11357 4 [31] standard also recommends the DSC method. DSC technique is based on the principle of measuring the thermal energy necessary to establish a nearly zero temperature difference between a te st specimen and a specimen of inert reference material. The accuracy of the DSC technique in determining the specific heat may not be particularly good and sometimes can range as high or as low as ±20% [17] . ISO 22007 - 2 [ 29] recommends the transient plane heat source (TPS) or hot disc method for the evaluation of specific heat up to a temperature range of 1000 º C. For determining the thermal expansion of construction materials, a standardized test method is specified by AS TM E831 14 [32] . This method utilizes the thermo - mechanical analysis technique for room temperature as well as high - temperature measurements. The principle is based on evaluating the coefficient of linear thermal expansion by measuring the change in test specimen length as a function of temperature at a constant heating rate. This test method is similar to ISO 21 11359 - 2 [33] , but is different in technical detail (such as maximum heating rate and specimen size) and focuses more on plastic materials. For measuring the mass loss of construction materials, ASTM E1131 [34] specifies the thermo - gravimetric pr ocedure in the temperature range up to 1000 º C. ISO 11358 [35] also recommends the thermo - gravimetric method for mass loss measurement, but ASTM E1131 is more de tailed and specific. The working principle of the thermo - gravimetric method is heating a specimen of known mass to a target temperature at a constant rate and measuring its mass continuously as a function of temperature and time . 2.2.1.3. Previous studies on high - temperature thermal properties While numerous test programs have been undertaken for characterizing the high - temperature thermal properties for normal strength concrete (NSC) and high - strength concrete (HSC), only a scarce amount of data is present on the variation of thermal properties with elevated temperature for ultra - high performance concrete ( UHPC ) and fiber - reinforced UHPC . From a review of literature, published test data on high - temperature t hermal properties of UHPC is plotted in Figure 2 . 1 - Figure 2 . 4 along with test data [20,21,25] , Eurocode 2 [16] and ASCE manual [22] relations for conventional concrete types . The ASCE relations w ere developed for NSC only, whereas the Eurocode 2 relations were developed for both NSC and HSC [36] . The r eported studies on thermal properties of UHPC at high temperatures are tabulated in Table 2 - 2 and it is evident that an almost negligible amount of data has been reported on thermal properties of UHPC. Ju et al. [37] examined the effects of varying steel fiber content on the evolution of thermal conductivity, sp ecific heat, mass loss, and thermal expansion in the 20 - 250ºC temperature range, which covers lower temperatures relative to those encountered in a typical fire scenario. The test data showed that specific heat and thermal expansion decrease with increasin g steel fiber content, 22 whereas thermal conductivity and mass loss were similar for UHPCs with various fiber contents. Further, the temperature - dependent variation of thermal conductivity and thermal expansion of UHPC were found to be similar to HSC but hig her than NSC. Specific heat and mass loss of UHPC were observed to be lower than NS C and HSC. Zheng et al. [38] evaluated thermal expansion for three batches of UHPC mixes with different volume fractions of steel fibers at 20, 200, 400, 600, and 800°C. The study reported that the thermal expansion of UHPC with steel fibers was higher than that of NSC with siliceous aggregate in the 20 - 600°C range. Above 600°C, the thermal expansion of UHPC with steel fibers was lower than that of concretes wit h siliceous aggregates. In addition, the results showed that the thermal expansion of UHPC increases with an increase in steel fiber co ntent at elevated temperatures. Sanchayan and Foster [39] evaluated mass loss in 20 - 300°C and thermal expansion in 20 - 600°C for plain UHPC and steel - reinforced UHPC. In the study, the average mass loss was about 5% at 300°C and test specimens experienced violent explosive spalling around 300°C. The thermal strain of UHPC with steel fibers was found to be similar to that of the siliceous - aggregate NSC model in Eurocode2 [16] . 23 Figure 2 . 1 . Variation of thermal conductivity in different concrete types with rise in temperature . Figure 2 . 2 . Variation of specific heat in different concrete types with rise in temperature. 24 Figure 2 . 3 . Variation of thermal expansion in di fferent concrete types with rise in temperature. Figure 2 . 4 . Variation of mass loss in different concrete types with rise in temperature. 25 Table 2 - 2 . Reported hi gh - temperature thermal property tests on UHPC. Reference Fibers (dosage %) Compressive strength (MPa) Temperature range High - temperature property Ju et al. (2011) No fibers Steel (1%) Steel (2%) Steel (3%) 157 169 179 191 20 - 250°C Thermal conductivity Sp ecific heat Mass loss Thermal expansion Zheng et al. (2015) Steel (1%) Steel (2%) Steel (3%) 143 155 159 20 - 800°C Thermal expansion Sanchayan and Foster (2016) No fibers Steel (2%) 144 170 20 - 300°C 20 - 600°C Mass loss Thermal expansion 2.2.2. Mechanical Proper ties 2.2.2.1. General Mechanical properties needed for fire resistance evaluation of concrete structural members include compressive strength, tensile strength, elastic modulus, creep, and stress - strain relations. The compressive (or tensile) strength is the abili ty of a material to resist corresponding stresses arising from compression or (tension) loading. The stress - strain response of a material captures incremental deformation (strain) under applied loading (stress). The peak stress from the stress - strain respo nse is taken as the strength of the material and the slope of the stress - strain curve in the linear range is taken as the elastic modulus. Generally, concrete up to a compressive strength of 70 MPa is classified as normal - strength concrete (NSC), concrete with compressive strength in the range of 70 - 150 MPa is referred to as HSC, while concrete with compressive strength above 150 MPa is designated as UHPC [36,40] . Mechanical properties of all types of concrete d egrade with a rise in temperature due to temperature - induced microstructural changes, which are mainly influenced by the moisture content, mix proportions , and volume of admixtures in concrete . A good amount of high - temperature mechanical properties test d ata is available for both NSC and HSC with different types 26 of aggregates. The most widely adopted temperature - dependent concrete property relations are provided by ASCE Manual [22] and Eurocode 2 [16] . T he ASC E material model was devel oped for NSC and the Eurocode model was developed for both NSC and HSC. In addition to these property relations, a widely accepted material model for HSC was developed by Kodur et al. [13,41] , which is an extension to the ASCE relations for NSC. T he compressive strength of NSC gets minimally deteriorated by exposure to high temperatures up to 400°C , beyond which NSC exhibits gradual loss in compressive strength as shown in Figure 2 . 5 . This slow degradation of strength in NSC can be attributed to the low volumes of fine supplementary cementitious materials in conventional NSC batch mix, which results in high permeability allowing easy diffusion of pore pressure developed as a result of moisture evaporation . On the contrary , HSC experiences a rapid degradation in compressive strength with temperature retaining a bout 60 - 70 % of its initial compressive strength as shown in Figure 2 . 6 . HSC batch mix utilizes admixtures, binders, and silica fume to produce a dense and superior microstructure, which results in faster degradation of strength . Additionally, the compact microstructure of HSC prevents the escape of moisture and leads to a build - up of pore pressure, thereby increasing the propensity of HSC to spall. 27 Figure 2 . 5 . Variation of compressive strength with temperature for NSC [17] . Figure 2 . 6 . Variation of comp ressive strength with temperature for HSC [17] . 28 T he ambient tensile strength of concrete is much lower than the compressive strength of concrete, however, it can be crucial under fire conditions. Primarily, tensile strength is important because it resists tensile stresses and can control crack propagation in the member. In addition, higher tensile strength helps to withstand tensile str esses generated from pore pressure and can prevent fire - induced spalling in concrete. Figure 2 . 7 shows compiled data on the tensile strength of concrete at elevated temperature s from different codes of practice and previous studies [17] . A t 300°C, NSC loses about 20% of its initial tensile strength and a bove 300°C, the tensile strength in NSC drops at a rapid ra te due to extensive thermal damage in the form of microcracks. HSC also exhibits a similar trend in loss of tensile strength with temperature due to the development of thermal stresses and pore pressure in its dense microstructure [42] . There are relatively f ewer studies on the tensile behavior of concrete at elevated temperature, as compared to compressive strength. Figure 2 . 7 . Variation of tensile strength with temperature [17] . 29 The modulus of elasticity of concretes at room temperature varies over a wide range of 5 35 GPa and degrades rapidly with a rise in temperature. As shown in Figure 2 . 8 , t he degradation of elastic modulus with temperature of HSC is similar to that of NSC , with a majority of the degradation in elastic modulus occurring beyond 400°C. At around 600°C, elastic modulus losses about 8 0% of its room temperature value for both NSC and HSC . Beyond 600°C, concrete softens significantly, and elastic modulus is marginal as reported by test data. The loss of elastic modulus in both NSC and HSC can be attributed to the disintegration of hydrat ed cement products and the breakage of chemical bonds in the cement paste in the concrete microstructure. Figure 2 . 8 . Variation of elastic modulus with temperature [17] . The high temperature compressive stress - strain behavior of concrete is of significant importance in the fire resistance analysis of RC structural members as they are helpf ul to trace the structural response. The stress - strain curve of concrete becomes flatter with increasing temperature, due to a 30 decrease in compressive strength and elastic modulus, and an increase in ductility of concrete. As elastic modulus decreases, str ain at a given stress level increases at high temperatures. The stress - strain curves at elevated temperatures of NSC and HSC are shown in Figure 2 . 9 and Figure 2 . 10 respectiv ely. Previous studies have pointed out that HSC has steeper and more linear stress - strain curves in comparison to NSC in the 20 ºC - 800°C temperature range. The descending branch of the stress - strain curve of concrete also softens due to temperature - induced plastic deformations, and result in higher ultimate strain values with increasing temperature. HSC specimens exhibit brittle post peak response at low temperatures (100 ºC - 300ºC). Although a large number of data points have been reported for mechanical pr operties of concrete at high temperatures, there exists significant variability in the reported data. Much of this variation is due to the differences in test procedures, specimen conditions, test equipment used, and instrumentation adopted for undertaking the property tests by researchers. This is mainly due to the lack of standardized test methods for high - temperature property evaluation, as well as awareness o f the significant influence of test conditions and procedures on the high - temperature properties of concrete , specifically HSC and UHPC . For reliable evaluation of high - temperature mechanical properties of concrete, standardized test methods and procedures are required. 31 Figure 2 . 9 . Stress - strain respons e of NSC at elevated temperatures [17] . Figure 2 . 10 . Stress - strain response of HSC at elevated temperatures [17] . 32 2.2.2.2. Test methods for high - temperature mechanical properties There are three testing regime s to determine hi gh - temperature mechanical properties : unstressed, stressed, and residual . The procedures for these three test regimes are schematically shown in Figure 2 . 11 and are illustrated graphically in Figure 2 . 12 [3,25] . In the unstressed testing regime, the specimen is heated to a target temperature without the application of any preload. Once the uniform temperature is reached throughout the specimen, the load i s applied on the specimen till failure. In the stressed regime, the specimen is preloaded before initiation of heating , and that preload is sustained during the entire heating phase. Once the specimen reaches thermal equilibrium, it is further loaded to fa ilure. In the residual test regime, the specimen is subjected to heating, (with or without any preload) to a desired temperature until attaining a steady state. The specimen is cooled down to ambient temperature upon stabilization of temperature in the spe cimen and thereafter, it is loaded till failure. While the stressed and unstressed test conditions represent the behavior of heated concrete during fire, the residual test method is representative of the behavior of concrete following cool down after fire exposure. For mechanical property measurements at room temperature, specific test procedures are given in test standards [43,44] . However, test standards do not provide any guidance for evaluating the mechanical properties of concrete at el evated temperatures. Only RILEM recommendations provide procedures for evaluating the mechanical properties of concrete at high temperatures in the range of 20 750°C [4 5] . The specific test standards for mechanical property evaluation are tabulated in Table 2 - 3 . 33 Figure 2 . 11 . Schematic of testing regime for mechanical property evalua tion at elevated temperature. Figure 2 . 12 . Testing regimes for evaluating mechanical properties of concrete at high temperature. 34 Table 2 - 3 . Test standards for ev aluation of mechanical properties . Mechanical property Temperature range Test standards Compressive strength Ambient temperature ASTM C39 Elevated temperature (upto 750°C) No ASTM standard RILEM 200 - HTC Tensile strength Ambient temperature ASTM C78 (Fl exural) ASTM C1583 (Direct) ASTM C496 (Splitting) Elevated temperature (upto 750°C) No ASTM standard RILEM 200 - HTC In the literature, researchers have evaluated t he compressive strength of concrete at elevated temperature as per the procedure outlined in RILEM recommendations or by e xtending the room temperature proce dure laid out in ASTM C39 [43] . But ASTM C39 does not provide guidance on heating rate, and so he ating of specimen to target tem perature is to be carried out as per RILEM testing procedure. However, these high - temperature test procedures specified in RILEM are developed based on property tests on convent ional concretes , and hence, they may not be practicable and fully applicable for higher strength concretes, such as UHPC. For evaluating compressive strength, a fter following the heating scheme as per the selected testing regime, a compressive load is to b e applied in the direction of the central axis of the specimen at a constant rate till failure occurs. The load at failure of the specimen is to be recorded and the average failure load divided by the area of specimen is the resulting compressive strength at that temperature. The re corded incremental load and dis placement data at each temperature can be used to plot the stress - strain response of concrete at the tested temperature. The temperature - dependent modulus can be evaluated as the slope of the linear part of the stress - strain curve plotted at any given temperature . The modulus at each temperature can be extracted from the stress - strain relation as per ASTM - C469/C469M [46] guidance . 35 T he t ensile strength of concrete at ambient temperatures is measured in three forms as flexural, direct, and splitting tensile strength. Flexural tensile strength can be obtained as per A STM C78 [47] procedure through subjecting a small concrete be am to third - point flexural load ing. The direct tensile strength can be measured as per ASTMC1583 [48] procedure through testing cylinder or prism specimens by applying axial tensile load in a suitable test machine until specimen breaks in direct tension. Direct tension te st is less reliable as the spec imen holding devices (grips) introduce secondary stresses leading to unreliable strength data. Splitting tensile strength is evaluated as per ASTM C496 [44] by applying a diametri cal compressive load on a cylin drical concrete specimen along its length till failure occurs through the splitting of the specimen along the vertical diameter. For conventional concretes, splitting tensile strength at am bient temperature is usually 1.2 times of direct tension strength, whereas it is 0.6 times of flexure tensile strength. There is very limited guidance for tensile strength tests at elevated temperature since it is often neglected in the design and analysis . T ensile strength tests at elevated temperature s can be carried out by extending room temperature test procedures. But since ASTM does not have any guidance on heating condi tions, RILEM heating procedure recommendations for compressive strength tests can be adopted. However, most of the studies on high - temperature properties continue to adopt non - standardized conditions (such as specimen size, moisture content, heating rate, load level) without any con sideration to limited specifica tions present in RILEM. Due to the application of different test procedures, there is s ignificant variation in measured test data from the previous studies as shown in Figure 2 . 5 - Figure 2 . 8 . To thi s end, there is a dire need for standardized test procedures for generating reliable data for the characterization of mechanical properties of concrete at elevated temperatures . 36 2.2.2.3. Previous studies on high - temperature mechanical properties A review of the li terature indicates that high - temperature mechanical properties of UHPC have been studied somewhat more widely than the thermal properties of UHPC and the details of the reported studies are summarized in Table 2 - 4 . The published test data on high - temperature mechanical properties of UHPC is plotted in Figure 2 . 13 - Figure 2 . 15 along with Eurocode 2 [16] and ASCE manual [22] relations for NSC and HSC . Tai et al. [49] evaluated the residual compressive strength, elastic mod ulus, and stress - strain response of UHPC cylinders made with different volume fractions of steel fibers. Experimental results indicated that the residual compressive strength of UHPC after heating from 20 200°C increased slightly (about 15%) than that at r oom temperature and beyond 300°C, the compressive strength decreased significantly. The reduction in residual compressive strength of UHPC was found to be lower than NSC till 500°C and UHPC followed a similar trend in strength loss as NSC beyond 500°C. The elastic modulus decreased with increasing temperature with 70% of modulus loss at 500°C. The stress - strain response of UHPC with steel fiber content 2% by volume, reported by Tai et al. [49] is plotted in Figure 2 . 16 . The peak stress decreased while the peak strain increased with increasing temperatures, and the UHPC specimens with higher steel fiber content exhibited higher peak strain. Zheng et al. [50 52] evaluated high - temperature m echanical properties of UHPC extensively, following unstressed and residual test regimes. Their study shows that compressive strength decreases at 100°C, increases at temperatures from 200 to 400°C, and decreases at temperatures above 400°C. The study show s that below 300°C, the compressive strength of UHPC increased as the steel fiber content increased, but decreased between 400 to 800°C with an increase in steel fiber content. The compressive strength of UHPC lowered with higher PP fiber dosage below 37 200° C but increased between 300 to 800°C as the PP fiber content increased. The elastic modulus of UHPC initially increased till 200°C and then decreased with a further rise in temperature. The tensile strength of UHPC decreases at temperatures from 20 to 200° C, remains constant at temperatures ranging from 200 to 300°C, and decreases at temperatures above 300°C. The tensile strength of UHPC increased as steel fiber content increased at temperatures below 600°C, but above 600°C, tensile strength decreased as st eel fiber content increased. The stress - strain response of UHPC with steel fiber content 2% by volume, reported by Zheng et al. [52] is plotted in Figure 2 . 17 . The evolution of stress - strain response with increasing temperature for UHPC with different steel fiber contents is similar. The stress - strain response of UHPC in the 20 - 300°C range is almost identical and above 300°C, the stress - str ain curves become flatter with an increase in peak strain and ultimate strain values. Sanchayan and Foster [39] evaluated compressive strength and elastic modulus of plain and steel fiber reinforced UHPC at elevated temperature. In this study, an initial increase in compressive strength was observed up to a temperature of 200°C, followed by a drastic drop with a further rise in temperature. No considerable change in modulus of elasticity was reported until 300°C; thereafter, elastic modulus decreased to 50% of the room temperature value at 400°C and to 20% at 600°C. In these reported experimental studies [39,49 52] , the increase in compressive strength of UHPC upon heating till 200°C is attributed to the completion of pozzolanic reactions and hydration of the unhydrated cement products in the microstructure. 38 Table 2 - 4 . Reported high - temperature mechanical pr operty tests on UHPC. Reference Specimen dimensions Fibers (dosage %) Compre ssive strength (MPa) Test procedure High - temperature propert y Tai et al. (2011) 50 x 100 mm Cylinder Steel (1%) Steel (2%) Steel (3%) 150 168 156 Oven dried Heating at 2°C/min Tem p. range: 20 - 800°C Residual test regime Compressive strength Stress - strain response Elastic modulus Zheng et al. (2012, 2013) 70.7 x 70.7 x 228 mm Prism Steel (1%) Steel (2%) Steel (3%) 143 155 159 Oven dried Heating at 4°C/min Temp. range: 20 - 900°C Resi dual test regime Compressive strength Stress - strain response Elastic modulus 70.7 x 70.7 x 70.7 mm Cube Steel (2%) + PP(0.1%) Steel (2%) + PP(0.2%) Steel (1%) + PP(0.2%) Not mention ed Oven dried Heating at 4°C/min Temp. range: 20 - 900°C Residual test reg ime Compressive strength 150 x 75 mm Dogbone Steel (1%) Steel (2%) Steel (3%) 143 155 159 Oven dried Heating at 5°C/min Temp. range: 20 - 800°C Unstressed test regime Tensile strength Sanchayan and Foster (2016) 100 x 200 mm Cylinder No fibers Steel (2%) 144 170 Oven dried Heating at 5°C/min Temp. range: 20 - 700°C Residual test regime Compressive strength Elastic modulus Li and Liu (2016) 40 x 40 x 160 mm Prism for flexure 150 x 75 mm Dogbone for tension Steel (2%) + PP(0.1%) Steel (2%) + PP(0.2%) Steel (1%) + PP(0.2%) Not mention ed Oven dried Heating at 4°C/min Temp. range: 20 - 900°C Residual test regime Flexural strength Tensile strength Abid et al. (2019) 70.7 x 70.7 x 70.7 mm Cube Steel (2%) PP(0.3%) Steel (2%) + PP(0.2%) 154 117 151 Oven dried Heati ng at 5°C/min Temp. range: 20 - 900°C Unstressed test regime Compressive strength Stress - strain response Elastic modulus Tensile strength Flexural strength 39 Figure 2 . 13 . Compiled data on variation in compressi ve strength of UHPC with temperature. Figure 2 . 14 . Compiled data on variation in elastic modulus of UHPC with temperature. 40 Figure 2 . 15 . Compiled data on varia tion in tensile strength of UHPC with temperature. Figure 2 . 16 . Residual s tress - strain curves of UHPC with 2% steel fibers as a function of temperature [49] . 41 Figure 2 . 17 . Residual stress - strain curves of UHPC with 2% steel fibers as a function of temperature [52] . Li and Liu [53] measured the direct and flexural (bending) tensile s trength of UHPC made with hybrid (steel and polypropylene) fibers. The results indicated that steel fibers can improve the tensile performance of hybrid fiber - reinforced UHPC, whereas polypropylene (PP) fibers did not exhibit any evident effect on the tens ile performance. This study also concluded that both direct and flexural tensile strengths of UHPC significantly linearly decreased with increasing temperature. Abid et al. [54] evaluated the effect of steel, polypropylene (PP), and hybrid (steel + PP) fibers on high - temperature mechanical properties of UHPC. The high - temperature compressive strength of all UHPCs sta rted to decrease till 120°C; recovered slightly up to 300°C and gradually decreased above 300°C. The split - tensile strength, flexural strength, and elastic modulus gradual ly decreased with increasing temperature without any effect of various fibers in the different mixes . The stress - strain response of UHPC with steel and hybrid fibers was found to be ductile, whereas the stress - strain response of UHPC with only PP fibers was brittle as can be 42 observed in Figure 2 . 18 . Further, the compressive strength of UHPC mix with only PP fibers and no steel fibers was very low, around 100 MPa. (a) (b) Figure 2 . 18 . S tress - strain curves of UHPC with (a) steel and PP fibers (b) only PP fib ers, as a function of temperature [54] . The literature review shows that only a limited amount o f test data with a notable range of variation is available on high - temperature material properties of UHPC. Currently, there is a lack of procedures in test standards for measuring mechanical properties of concrete at elevated 43 temperatures [25] . As a result, there is significant variation in the test setup and test procedures including specimen size, heating rate, concrete mix proportions adopted in the reported studies to measure p roperties of UHPC at elevated temperatures. Moreover, UHPC is highly susceptible to fire - induced spalling even at lower heating rates due to its dense microstructure and low permeability. Hence, all of the reported strength tests were conducted after oven drying the specimens at 105°C to minimize spalling by avoiding pressure build - up resulting from the moisture. However, oven - drying does not reflect practical situations and might not be appropriate for evaluating realistic properties of UHPC. Further resea rch is needed to address the aforementioned variations and scarcity of data. 2.2.3. Transport Properties 2.2.3.1. General In addition to thermal and mechanical properties, transport properties are required for fire resistance analysis as transport properties determine mo isture migration, which results in pore pressure build - up and fire - induced spalling . Spalling results in faster transmission of high temperatures to inner layers of concrete and steel reinforcement, thereby leading to a faster decrease in capacity of the s tructural member. Fire - induced spalling is dependent on a number of material properties including permeability, porosity, moisture content, and tensile strength of concrete. The pore volume is characterized by porosity and the connectivity of pores is deno ted by permeability. Thus, the ability of a material to transfer fluids (gas and liquid) under pressure gradient can be evaluated mainly by measuring porosity and permeability . Various experimental and numerical studies have indicated that modern concretes with low permeability or porosity due to their dense microstructure , such as UHPC and HSC are more susceptible to spalling than 44 traditional NSC. Previous studies mainly focused on the effect of high temperature on porosity and permeability of NSC and HSC , with few studies on UHPC [55 58] . Further, v ery limited studies have been carried out on heated specimens at elevated temperatures (hot state) due to a lack of instrumentation and guidance. Majority of the previous studies measured porosity and permeability in the residual state, i.e. after cooling the specimens to room temperature. However, residual values are different and usually higher than porosity or permeability measured at elevated temperatures [59] . 2.2.3.2. Test methods for high - temperature transport properties There are very few standardized procedures for evaluating the transport properties of concrete at room temperature. ASTM standards do not provide any guidance for measuring gas permeability. For measuring chloride diffusivity of concrete, which can be indicative of concrete permeability, ASTM C1202 [60] provides rapid chloride ion penetration test procedures. According to ASTM C1202 test procedures, the concrete specimens should be initially water - saturated and then injected with NaCl and NaOH solutions sepa rately into positive and negative terminals respectively. The total charge passing through the specimens is recorded and converted to the effective chloride diffusion coefficient of concrete through empirical relation. However, t he ASTM C1202 test procedur e may not be suitable for concrete that contains electrically conductive material such as steel fibers in UHPC . It is because the presence of conductive material in concrete, in the case of steel fiber, can allow more current to pass through the specimen l eading to incorrectly high diffusivity values [61] . Another representative metric for permeability is concrete sorptivity , which quantifies the tendency of a material to absorb, desorb, and transfer liquid. ASTM C1585 [62] provides procedures for measuring sorp tivity of concrete. All but one surface of the concrete specimen is to 45 be seal ed to prevent moisture ingress and the remaining unsealed surface is kept in contact with water for penetration. The change in weight after the certain intervals should be recorded and the coefficient of sorptivity can be calculated based on the readings. Higher sorptivity indicates higher permeability and vice versa. A s imilar procedure is recommended by RILEM TC 116 - PCD [63] for measuring capillary absor ption for concrete. RILEM TC 116 - PCD [63] provides recommendations for measuring gas permeability of concrete using the Cembureau method. This method inv olves the measurement of permeability through a Cembureau permeameter with nitrogen or oxygen as the infiltrating gas. Concrete specimens are to be subjected to constant upstream pressure. Gas is to be injected at the bottom surface of the specimen. The ap plied injection pressure should be maintained till the stabilization of gas flow through the concrete specimen . The pressure and flow rate are to be recorded and t he downstream pressure will be the atmospheric pressure. The pressures at the front and back of the specimen can be measured using thermal mass flow meters. This mass flow rate can then be converted to an the isothermal flow of gas, the apparent permeab ility can be calculated. The intrinsic gas permeability of concrete can be calculated from the apparent permeability by utilizing the Klinkenberg method [64] . For measuring the porosity of concrete, test procedures are provided by ASTM C642 [65] . First, the specimen has to be dried at a temperature of 110 °C in a hot air oven until its mass is constant . Then the dry mass of the specimen is to be weighed . Followed by dry weighing, the specimen is to be immer sed in water at 21°C for 48 h and mass is to be recorded . Then , the specimen is to be boiled in hot water for 5 h, followed by cooling for 14 h to a final temperature of 25 °C. Finally , the specimen is to be suspended into water and the apparent mass in wat er is determined by 46 hydrostatic weighing. Substituting the values of mass in different conditions in a mathematical formula, the volume of voids can be determined. Porosity measurement procedure is also given by RILEM - 0 49 - TFR draft recommendations [66] , wherein the only variation from ASTM C642 is in the saturation mode. RILEM recommends subjecting to vacuum for 4 h instead of boiling. All the above - discussed standardized procedures for evaluating permeability and porosity were developed for ambient conditions. T here is absolutely no guidance for undertaking tests to character ize spalling - related transport properties of concrete at elevated temperatures. 2.2.3.3. Previous studies o n high - temperature transport properties Only one study in the literature undertaken by Li et al. [67] , measured permeabili ty of UHPC at elevated temperatures in the 20 - 300°C range. The experimental setup was developed by extending the room temperature test guidelines in RILEM - CEMBUREAU [63] , wherein the gas flow through a specimen is measured under steady air pressures . In the reported study, t he entire device was plac ed inside an electric furnace and the specimen was heated to target temperatures at a low heating rate of 1°C /min to avoid the formation of micro - cracks by thermal gradients. The 18 and 18 m 2 , which is lower than that of NSC and HSC (10 17 to 10 16 m 2 ) reported in other studies [55,56] . The general trend in permeability remained unchanged from ambient temperature to 1 05 °C, beyond which permeability increased gradually to three order s of magnitude from 1 05 to 300°C. The incre ase in permeability with temperature rise i s due to the formation of micro - cracks and the dehydration of hydrated products which makes the microstructure more porous. This study also investigated the influence of aggregate size and inclusion of PP and stee l fibers on the permeability of UHPC. Results presented in Figure 2 . 19 reveal that the inclusion of PP fibers 47 or larger aggregates increased the permeability while the addition of steel fiber did not contribute to t he enhancement of permeability of UHPC at elevated temperature. Figure 2 . 19 . Permeability of UHPCs as a function of temperature [67] . Similar to permeability, one study by Abid et al. [54] has been reported in the literature on porosity measurement of UHPC, carried out in residual state. Porosity was measured th r ough mercury intrusion porosimetry (MIP), wherein the volume of mercury that intrudes into the material with each pressure change is utilized to determine the volume of pores. The porosity of UHPC as a function of temperature is plotted in Figure 2 . 20 and compared with that of NSC and HSC as reported in the literature [68,69] . At room temperature, porosity of NSC, HSC, and UHPC is 15%, 10%, and 5% respectively. Porosity of all concretes increase s with increasing temperature primarily due to moisture evaporation, decomposition of hydration products , and micro - cra cks resulting from the thermal expansion mismatch between cement paste and aggregate . Spalling is theorized to occur primarily by the build - up of pore pressure during heating. However, till date, there is no relevant testing procedure and instrumentation i n test standards to measure pore pressure in concrete at high temperatures. Only two research groups at CSTB, France [70] 48 and Politecnico di Milano, Italy [71] have developed their own experimental set - up for measuring pore pressure in concrete specimens. The experimental set - up comprised of installing stainle ss steel pipes filled with silicon oil and connected to a pressure transducer, in the concrete specimen for measuring pore pressure. Thus, from the literature review, it is apparent that there is a serious lack of test data for temperature - dependent transp ort properties for spalling evaluation. Figure 2 . 20 . Porosity of different concrete types as a function of temperature. 2.3. Experimental Studies on UHPC Members During the last four decades, s everal researchers have conducted fire resistance experimental studies on NSC members and to a lesser extent on HSC members [72,73] . Majority of these studies were focused on RC columns, with a fewer number of fire tests on RC beams [74] . Results from past fire tests show that t he main factors which influence fire resistance of a structural member include section dimensions of RC beams and columns, concrete cover thickness, fire exposure, applied load level, concret e moisture content, concrete strength, aggregate type, concrete mix, fiber (steel, PP, jute, nylon) reinforcement, and yield strength of reinforcing steel [11,75 77] . In the 49 previous studies, minor or no spalling was reported in fire tests on NSC members. Moreover, t h is minor spalling was mostly in the form of flaking after completion of the fire tests. For the case of HSC, the occurrence of spalling was observed in a number of studies and was found to be affected by a number of factors, such as load level, fire scenario, moisture content, fiber reinforcement, type of aggregate, specimen dimensions, and lateral reinfo rcement [10,11,73] . The studies showed that the addition of polypropylene (PP) and steel fibers minimizes spalling in HSC members under fire conditions. The extent of spalling was lesser in HSC columns with bent ties at 135° and with closer tie spacing (at 0.75 times that required for NSC columns). Further, a higher rate of temperature rise and HSC members made with siliceous aggregate concrete in lieu of carbonate aggregate concrete were found to increase spalling and reduce fire resistance . While a considerable amount of literature is available on fire resistance experiments on NSC and HSC, a review of the literature ( shown in Table 2 - 5 ) indicates that there has been very limited experimental work on the evaluation of fire behavior of UHPC members. The state - of - the - art of experimental studies is discussed herein. Lee et al. [78] tested two UHPC columns under ISO - 834 standard fire exposu re for 3 h ours . The square section columns (500 × 500 mm) were 3428 mm in length. The columns were fabricated with a UHPC mix comprising of hybrid fibers; steel (0.5% by volume), nylon (0.2% by volume) , and PP fibers (0.2% by volume). Both columns experien ced only minor spalling and attained fire resistance of 3 h ours and this good performance (minor spalling) was attributed to the presence of hybrid fibers in the UHPC mix. Kahanji et al. [79] conducted fire tests on seven UHPC beams of rectangular cross - section (100 × 200 mm) with a span length of 2000 mm. Six of thes e beams were made of UHPC batch mix that had steel fibers; three beams with 2% (by volume) of steel fibers, and another three with 4% (by volume) of steel fibers. The seventh beam was made of a UHPC mix having a combination 50 of steel fibers (2% by volume) a nd PP fibers (4 kg/m 3 ). The beams were exposed to standard ISO - 834 fire exposure for 60 min, but the exposure was only on the bottom half of the beam (cross - section). All six UHPC beams, with only steel fibers (but without PP fibers), experienced severe ex plosive spalling. The seventh UHPC beam (with a high dosage of PP fibers) did not experience spalling. However, the addition of PP fibers in the seventh beam led to a significant reduction in compressive strength of the UHPC mix to 100 MPa (from 163 MPa in the case of UHPC with steel fibers only). Table 2 - 5 . Reported fire tests on UHPC members. Authors Specimen details Fiber type and dosage Compressive strength (MPa) Test parameters Main findings Lee et al. (2 012) 2 columns: 500 x 500 x 3428 mm Steel (0.5%) + PP (0.2%) + Nylon(0.2%) Steel (0.5%) + PP (0.2%) + Nylon(0.2%) 204 205 - ISO 834 standard fire exposure for 3 h. - Constant axial load of 9500 kN. - Both columns attained fire resistance of 3 h with minor sp alling. Kahanji et al. (2016) 7 beams: 100 x 200 x 2000 mm Steel (2%) Steel (2%) Steel (2%) Steel (4%) Steel (4%) Steel (4%) Steel (2%) + PP (0.4%) 157 163 178 162 166 173 100 - ISO 834 standard fire exposure to bottom half of the beams for 1 h. - Three lo ad levels: 20, 40 and 60% of ultimate capacity at room temperature. - No spalling in beam containing hybrid fibers. - Lower extent of spalling was reported under higher load level. - Beams containing 4% steel fibers spalled less than the beams with 2% steel f ibers. Hou et al. (2019) 4 beams: 200 x 400 x 4900 mm Steel (2%) + PP (0.2%) Steel (2%) + PP (0.2%) Steel (2%) + PP (0.2%) Steel (2%) + PP (0.2%) 127 127 127 127 - ISO 834 till failure of beam. - Two load levels: 30 and 50% of ultimate capacity at room temp erature. - Varying cover thickness : 25mm, 35mm . - Minor spalling in all beams. - Fire resistance increases with an increase in concrete cover thickness. 51 Hou et al. [80] tested four UHPC beams of rectangular cross - section (200 × 400 mm) with a span length of 4900 mm exposed to ISO - 834. The beams were made of a UHPC batch mix containing 2% steel fibers and 0.2% PP fibers. The test results indicated that the fire resistance of the UHPC beams increased by 40% when the cover thickness was increase Additionally, a higher load level decreased the fire resistance of the beams. Only minor spalling in the form of peeling - off was observed in the tested beams due to the presence of PP fibers. However, the strength of the UHPC mix was 127 MPa, which is lower than the characteristic strength of UHPC mix (150 MPa). The above review clearly indicates that there are only limited fire resistance studies on UHPC beams. Thus, there is a lack of data, including detailed observations and record ings of spalling, and response of UHPC beams under fire exposure. Further, i t can be seen that the previous experimental studies used a high dosage of PP fibers for the mitigation of spalling. The high PP dosage resulted in reduced compressive strength of the concrete mixes in previous studies to levels below that of optimum desired strength of 150 MPa in UHPC. Unlike previously published works, this study seeks the incorporation of a balanced dosage of PP fibers in UHPC mix to achieve spalling mitigation, without impacting on compressive strength and workability. Moreover , the reported tests in the literature were carried out by subjecting UHPC members to standard fire exposure only, without any due consideration to realistic fire scenarios; that encompass a cooling phase. In addition, the previous fire tests on UHPC members were carried out using concrete batch mixes without any coarse aggregates. Such UHPC mixes, made with fine aggregates and high superplasticizer and silica fume, incur higher costs and re quire special mixing equipment that is not commonly available in many concrete batch mix plants. 52 2.4. Numerical Studies on UHPC members Numerical studies on simulating the fire behavior of concrete structures can be undertaken at the microscopic or macroscopic level through finite - element based method. In the microscopic method, computer packages such as ABAQUS, ANSYS, and SAFIR can be utilized, wherein a structural member is discretized into a meshed model and coupled or uncoupled thermal and structural analys es are carried out to evaluate fire response. In the macroscopic method, sectional analysis is carried out at a critical cross - section , or a number of cross - sections along the length of the member to predict the fire response of the structural member. Both microscopic and macroscopic numerical studies have been undertaken for NSC and HSC structural members in previously published studies. Conversely , t here have been only a handful of numerical studies on the fire behavior of UHPC members. Mai et al. [81] analy zed a three - story two - bay UHPC frame structure subjected to standard ISO - 834 fire for 2 h using commercial software ABAQUS. The numerical simulation compared the thermal and structural response of a UHPC frame structure with that of a HSC frame structure. However, t he validation of the numerical model by comparing predicted parameters with test data was not undertaken . Hou et al. [80,82] developed a sequentially coupled thermal stress model in ABAQUS to simulate the response of the hybrid fiber reinforced UHPC beams tested by them , as discussed i n section 2.3 . Fire - induced spalling was entirely neglected in both the numerical analys es, which can be an influencing factor in tracing the fire response of UHPC structures due to the high susceptibility of UHP C to spalling . I n fire - resistance analyses of concrete structures, generally s palling is not considered , mainly due to the complexity involved in modeling the spalling phenomenon, as well as due to limited property data available to undertake analysis. Fur ther , there are conflicting theories through which spalling 53 occurs in a fire - exposed member [83] . Anyhow, t he two widely accepted mechanisms for spalling are pore - pressure build - up and thermal stress ( discussed in section 1.4 ). The proposed numerical approaches in the literature for evaluating spallin g can be broadly grouped into three categories based on the mechanism driving spalling in concrete: (i) hydro - thermal models, which assume spalling, based on pore pressure mechanism; (ii) thermo - mechanical model based on thermal stress mechanism; and (iii) hydro - thermo - mechanical model based on a combination of both the mechanisms (i) and (ii). Some of the major studies are summarized in Table 2 - 6 and discussed in the following paragraphs. In addition to the afore - me ntioned three types of models, a simplified approach was proposed by Kodur et al. [13] to account for spalling based on detailed experimental studies on high strength concrete ( HSC ) columns. This basic model was developed in order to minimize the complexity of spalling calculations and for easy usage of numerical models for fire resist ance analysis . This crude model involved the following a set of rules to determine the extent of spalling: (i) Spalling occurs when the temperatures in an element reach above (ii) In HSC column, s palling occurs only outside the reinforcement cage when the ties are bent at When ties are bent in a conventional pattern, spalling occurs throughout the cross - section. (iii) No spalling occurs inside reinfor cement core when tie spacing is 0.7 times of standard spacing. (iv) The extent of spalling is higher (100%) in the siliceous aggregate HSC than that for carbonate aggregate HSC (40%). (v) The extent of spalling in HSC columns with polypropylene fibers 0.1% to 0. 15% by volume is 0% and with steel fiber s is 50%. (vi) A higher relative humidity in HSC column (90% or higher) leads to higher spalling. 54 Table 2 - 6 . Reported numerical studies on fire - induced spalling. Authors Mo del Main findings Kodur et al. [13] Simplified - A s et of guidelines were proposed based on observations from detailed experimental studies on HSC columns for determining the extent of spalling. Bazant and Thonguthai [7] Hydro - thermal - Spalling is due to a sudden unstable release of the potential energy of thermal stresses stored in the structure and vapor pressure is not the main reason of spalling. Dwaikat and Kodur [84] Hydro - thermal - Spalling is predicted to occur when the pore pressure exceeds the tensile strength of concrete. - Fire scenario, tensile strength, and concrete permeability largely influence the extent of fire - induced spalling in concrete beams . Ichikawa and England [85] Hydro - thermal - Developed one - dimensional model to predict spalling by vapor pressure mechanism. Ulm et al. [9] Thermo - mechanical - Simulated spalling through restrained thermal expansion in "Chunnel" Tunnel. - Proposed a thermo - chemo - plastic constitutive model taking into account the hardening and softening using plastic mechanics theory and dehydration of concrete at high temperature. Msaad and Bonnet [86] Thermo - mechanical - "Chunnel" tunnel fire is modeled by a thermo - chemo - plastic constitutive model, wherein mechanical stresses and strains ne ar the heated surface (the concrete wall) are calculated. - Spalling is due to chemical decohesion (strength degradation) and not to chemical softening (rigidity reduction). Gawin et al. [87] Hydro - thermo - mechanical - The proposed model considered the multi - phase change of concrete at high temperatures and considered mass transport processes, mechanical behavior and phase changes. - Contribution of the s tored elastic energy and vapor pressure build - up to the kinetic energy of spalled concrete pieces is estimated. - An expression for permeability variation due to hydrothermal damage is proposed. Zhang and Davie [88] Hydro - ther mo - mechanical - The model utilizes an isotropic damage model formulated using a modified von Mises definition adopting strain tensors. - Concrete was modeled as a multi - phase system consisting of solid, liquid, and gas phases. - Numerical analysis of one - d imensional concrete members indicated that thermal stresses play the primary role in driving spalling. Zhao et al. [89] Hydro - thermo - mechanical - The h igh temperature behavior of HPC cubic specimens is numerically modeled and the spalling mechanism is investigated at a meso - level. - The dominant role of vapor pressure or temperature gradient - induced thermal stress on spalling is studied under two heating conditions. 55 Table 2 - 6 . Tenchev and Purnell [90] Hydro - thermo - mechanical - The model, derived based on the principles of mechanics and thermodynamics, accounts for coupling between stress analysis a nd pore pressure calculations. - Concrete permeability tensor, diffusion coefficients and material stiffness tensor are required to predict spalling. One of the preliminary hydro - thermal analysis for predicting fire - induced spalling in concrete was devel oped by Bazant and Thonguthai [5,7] . The finite element based model was developed based on coupled differential equations of heat and moisture transfer in concrete. In this model, the mass balance equations were deriv ed by assuming the different phases of water (water vapor and liquid water) as a single - phase, namely capillary water. The variation in permeability was considered to increase by two orders of magnitude beyond 100°C, which was an overestimate, causing nume rical convergence issues under rapid heating conditions. The study analyzed a concrete wall section and inferred that pore pressure is only a triggering point for spalling and the brittle fracture (spalling) of concrete is due to a sudden release of high p otential energy generated from thermal stresses. However, the authors did not evaluate mechanical stresses and strains. Another widely cited hydro - thermal model was developed by Dwaikat and Kodur [84,91,92] where spalling was assumed to occur in a concrete section when the accumulated vapor pressure exceeded the degraded tensile strength of concrete at elevated temperatures. This model incorporated the different phase changes (liquid and vapor) of moisture. Pore pressure was calculated considering the ideal gas equation and utilizing conservation equations of mass, momentum, and energy. The model was validated by comparing spalling predictions with test data in walls, beams , and columns. In this analysis, the variation in permeability due to pressure and temperature was considered using the expression developed by Gawin et al. [93] based on experimental results. Additionally, initial permeability (at room temperature) included the effects 56 of cracking and curing conditions of the concrete member through empirical relations. A s imilar hydro - thermal model was proposed by Ichikawa and England [85] to predict fire - induced spalling in concrete walls. In this study, concrete permeability and tensile strength were assumed constant with temperature. The second category of spalling models is thermo - mechanical models, which primarily incorporate plastic or damage constitutive equations to compute stresses due to thermal restraint and then resulting spalling. Ulm e t al. [9] developed a thermo - mechanical model utilizing chemo - plasticity mechanics theory to evaluate fire - using plastic strain as an indicator for evaluation of the spallin g depth. To account for the effects of elevated temperatures in concrete, a thermo - chemo - plastic constitutive model with chemo - plastic softening was proposed in this study. A similar thermo - mechanical spalling model was proposed by Msaad and Bonnet [86] , wherein spalling was evaluated using stresses developed due to restrained thermal dilatation. In the third category of spalling models, i.e. hydro - thermo - mechanical models, the coupled effect of pore pressure and restrained thermal expansion is considered. Gawin et al. [87,93] developed such a hydro - thermo - mechanical model applying the governing equations of conservation of mass, momentum , and energy principles for pore pressure calculations in heate d concrete. The model considered concrete as a multiphase porous media and accounted for the phase changes in water. One of the notable contributions by Gawin et al. [93] was the proposal of an expression for permeability variation incorporating the effect of pore pressure and temperature rise. For accounting thermal spalling, constrained elastic energy was compared against t he fracture energy in concrete, however, properties for determining fracture energy at elevated temperatures are not yet well established for concrete. Their hydro - thermo - mechanical model was utilized for 57 evaluating spalling in NSC and HSC slabs and wall s ections without any structural loading to be present [94] . Zhang and Davie [88] developed a hydro - thermo - mechanical finite element model utilizing an isotropic damage model formulated using a modified von Mises definition adopting strain tensors . It should be noted that although this study attempted to model the physical processes, the critical inputs for the model such as strain tensors are not defined at high temperature s . Concrete was modeled by the authors as a multi - phase system consisting of solid, liquid, and gas phases. The solid phase represented the concrete skeleton undergoing deforma tions . T he liquid phase comprised of free, adsorbed, and chemically bound water. The gas phase included water vapor and dry air, assumed to behave as ideal gases. T heoretical concrete wall and square column sections were analyzed with constant permeability were presented. The results showed that thermal induced stresses are the primary factor in causing spalling and the effect of stresses due to po re pressure is secondary. Zhao et al. [89] proposed a hydro - thermo - mechanical meso - level numerical model for investigating spalling mechanism in a high performance concrete (HPC) cube. Effective first principal stresses due to thermal gradients and vapor pressure were calculated, and HPC was assimilated as a two - phase material with assumed properties for each phase , that is cement paste and aggregates. The study concluded that spalling mechanisms are dependent on heating conditions. For fast heating, as under ISO standard fire, thermal stress mechanism is dominant, whereas under slower heating of 5ºC/min, pore pressure mechanism governs spalling. Tenchev and Purnell [90] proposed a hydro - thermo - mechanical finite eleme nt model to simulate fire - induced spalling in concrete wall sections without loading. Concrete was considered as a two - phase material comprising of mortar and coarse aggregate having constant volume fractions with 58 temperature. Material properties were defi ned using tensors and the effect of concrete damage due to stresses from constrained thermal expansion was included in the model. The coupling between pore pressure and stress analysis was through the application of pore pressure as a body force in the str ess analysis. Recently, Shen et al. [95] developed a three - dimensional hydro - thermal model coupled with the Lattice Discrete Particle Model (LDPM) for simulating spalling depth in fire exposed concrete. LDPM captures the concrete meso - structure by simulating the interact ion of coarse aggregate pieces. This numerical study concluded that spalling occurred due to a combined action of thermal stress and pore pressure, with thermal stress being dominant at the early stages of fire (within 25 min) and pore pressure being more pronounced with increase in heating time. The effect of load - induced stress was not considered in evaluating spalling. In the above discussed review of literature, most studies carried out spalling analysis at a section and spalling was assumed to remain u niform throughout the length of the member. Fire tests and field observations have shown that spalling in concrete members occurs in a non - uniform pattern, which implies that the spalled cross - section is not constant along the longitudinal dimension of th e member [92,96,97] . Therefore, evaluating spalling at a section (level) might not yield realistic spalling predictions in structural mem bers. In addition, the reported numerical studies in literature did not account for the effect of mechanical stress arising from structural load on the member into spalling calculations. Further, it is well known that the permeability of concrete largely influences the extent of fire - induced spalling in concrete members. Yet majority of the previous numerical studies assume concrete permeability to be uniform over the concrete cross - section (and at room temperature values), without taking into consideratio n the progression of cracking due to increasing 59 temperature, pore pressure, and load level. Moreover, among the different concrete types, UHPC and HSC are more susceptible (than conventional NSC) to fire - induced spalling, specifically UHPC due to its extre mely dense microstructure. The previously reported numerical analyses simulate spalling in structural members made of either NSC or HSC. There is a lack of validated numerical models for predicting spalling in UHPC members under fire exposure. 2.5. Provisions in Standards and Codes on Fire Resistance of Concrete Members The specifications for fire resistance ratings of concrete structural members are provided in building codes and national standards. In the USA, ACI 216.1 (20 14 ) [98] standard provides prescriptive provisions for fire design of concrete and masonry struc tures. The specifications for fire resistance ratings of concrete members provided in ACI 216.1 are derived based on results of ASTM E119 standard fire tests [99] . As per ACI 216.1 provisions , failure is considered to occur when steel reinforcement attains a critical temperature (5 93°C), without any consideration to strength or deflection failure conditions . The critical temperature is defined as the temperature at which the reinforcement loses so much of its strength that it can no longer support the applied load. ACI 216.1 specifi es minimum sectional dimensions ( width ) and concrete cover thickness requirements for achieving a required fire resistance rating in an RC beam. Additionally, separate fire ratings are specified for beams with restrained and unrestrained support conditions . ACI 216.1 provisions are applicable for conventional NSC (<83 MPa) beams only and no clear guidelines are laid down for beams made using new types of concrete such as HSC or UHPC . ACI 216.1 also provides minimum sectional dimensions for RC columns made w ith NSC to attain the required fire resistance rating, giving consideration to three aggregate types: carbonate, silicate, and semi - lightweight. For HSC columns, ACI 216.1 provides additional guidance for preventing fire - 60 induced spalling by the provision o f rectangular ties with 135° bends, and circular ties with 90° bends. In Europe , Eurocode 2 , Part 1 - 2: Structural fire design [16] provides a choice of tabul ated data , simplified, or advanced methods for determining the fire resistance of concrete members. The data in tabulated format provides minimum dimensions and cover thickness to attain desired fire ratings for concrete members based on fire tests carried out as per ISO 834 [100] standard. For RC beams, the tabulated data is applicable to NSC made with siliceous aggregates. The same tabular data can be applied for carbonate aggregate concrete and high strength concrete through alteration of the required minimum sectional dimensions by modification factors. For RC columns , Eurocode 2 specifies two tabulated methods: Method A and Method B. Method A utilizes an empirical equation, whereas Method B is based on tabulated valu es. B oth the methods provide minimum dimensions and axis distance to the main reinforcement to achieve the specified fire rating in the column . The simplified method in Eurocode 2 is based on evaluating reduced sectional capacity at a critical section, co nsidering reduced strength of constituent materials due to temperature. The simplified calculation method is applicable only to concrete members subjected to standard fire exposure. The advanced method in Eurocode 2 involves detailed thermal and structural analysis and require s the use of sophisticated numerical models. Even by following advanced fire resistance calculations, fire - induced spalling cannot be easily accounted for due to complexities in the analysis. For addressing spalling, Eurocode 2 state s that spalling is unlikely to occur when the moisture content in concrete is lower than 3%. Some general provisions in Eurocode 2 for mitigating spalling in concrete elements are: (i) use of secondary reinforcement mesh with a nominal cover 61 of 15 mm; (ii) u se of concrete that does not have a tendency to spall; (iii) limit the maximum content of silica fume to less than 6% by weight of cement; (iv) use protective thermal layers; and (v) addition of at least 2kg/m 3 polypropylene fibers in the concrete batch mi x. The guidelines in Eurocode 2 are qualitative and without due consideration to critical factors that influence the phenomenon, such as permeability and tensile strength of concrete, heating conditions , and level of loading. Based on the above review, it can be summarized that the fire resistance provisions in current codes and standards do not fully account for realistic fire and loading conditions, as well as spalling, encountered by structural members under fire conditions. Additionally, the fire perfor mance of structural members made using new concrete types such as UHPC can be significantly different and lower than that of conventional concrete members. Therefore, c urrent prescriptive methods specified for conventional NSC members cannot be directly ap plied for the advanced concretes . Currently, there are limited guidelines and design recommendations for the structural design of UHPC members at room temperature only , including FHWA [101] , AFGC - SETRA [40] , JSCE [1] , and KCI [102] developed by the US, France, Japan, and South Ko rea respectively . Although there is limited guidance on structural design at ambient temperature conditions, as the literature review indicates there are absolutely no design provisions for UHPC members under fire conditions. This is primarily due to a lac k of fire - related research on UHPC members . Further research , including detailed experimental and numerical studies , is needed to quantify the fire performance of UHPC members for the development of fire resistance design guidelines. 62 2.6. Cost of UHPC UHPC exh ibits enhanced mechanical and durability properties as compared to conventional concrete. However, one of the limitations to the widespread use of UHPC in construction projects is its high initial cost due to the incorporation of high volumes of fineness m aterials and steel fibers. In North America, t he cost of UHPC is around $2000 per cubic yard, whereas the cost of conventional NSC is $100 per cubic yard [103] . For wide r adoption of UHPC by the infrastructure market, ongoing research studies are aimed at developing economic UHPC mixes by optimizing raw materials and production techniques while retaining the same level of mechanical performance [104,105] . Such studies have led to the development of cost - effective UHPC mixes in comparison to the cost of typical UHPC mixes formulated decades ago. Moreover, despite the initial cost of UHPC being higher than that of conventi onal concrete, UHPC structures can be cost - effective in terms of other performance factors . Due to the superior mechanical properties of UHPC, members with smaller cross - sections and lower reinforcement can be designed for carrying the same level of load a s compared to conventional concrete members. This leads to lower costs owing to a reduction in quantities of concrete, reinforcement, formwork, and associated labor and transport costs required for fabrication. In addition , due to high durability propertie s, UHPC exhibits high permeability resistance to water and chemicals, resulting in lower susceptibility to corrosion in rebars, which in turn lowers maintenance and repair costs in the long run. Consequently , lower life - cycle costs for UHPC structures have been assessed by studies in the literature in terms of costs incurred during production, repair, maintenance, and demolition [104,106,107] . 2.7. Knowledge Gaps The state - of - the - art review presented in this chapter clearly shows that there is a lack of data on the behavior of UHPC at high temperature s . Very l imited data is available on the material 63 properties of UHPC at elevated temperature s . Likewise , limited fire tests and numerical studies have been carried out to evaluat e the fire resistance of the UHPC members. M ost of the reported numerical studies on RC members did not incorporate the effect of fire - induced spalling. Further, there is a lack of validated numerical models that can evaluate spalling in concrete members. In addition, the available codes and standards do not provide any guidelines for the fire resistance design of UHPC members. The current provisions in design codes for evaluating fire resistance of concrete structural members are only for NSC members, and to a limited extent for HSC members . Moreover, t he fire resistance ratings in the design codes are based on prescriptive approaches without specifically accounting for spalling , which is a serious concern for UHPC . The following are major knowledge gaps on the behavior of UHPC at the material level and structural level: T here is a lack of high - temperature property relations of UHPC for fire resistance modeling of UHPC structural members. Further, there are no standardized testing procedures for measuring hi gh - temperature material properties of UHPC. There is absolutely no guidance for undertaking tests to characterize special properties in new concretes, such as temperature - induced spalling, permeability , and pore pressure variations at elevated temperatures . There is a lack of experimental data on the fire response of UHPC members. Such data from fire experiments is critical for validating numerical model s to trace the response of structural members under fire conditions. Most of the available numerical mode ls for fire resistance analysis of RC members are for NSC and HSC , and do not account for fire - induced spalling. In particular, there are no numerical models for evaluating the fire response of UHPC beams. 64 The current spalling models do not fully account f or the effects of structural loading and assume the same spalling level as in the analyzed critical cross - section, instead of member level. There are no numerical studies on the prediction of spalling in UHPC members. There are no design approach es and gui d ance in codes and standards on fire resistance design of UHPC members. 65 CHAPTER 3 3. Experimental studies 3.1. General As summarized in the literature review in Chapter 2, there have been a number of experimental studies on the fire performance of NSC beams, and to a lesser extent on HSC beams. These studies investigated the effect of various parameters, such as fire scenario, the extent of spalling , cross - sectional size, concrete strength, load intensity, reinforcement ratio, etc., on the fire response of RC bea ms. However, the review shows that there has been only very limited research on large - scale UHPC beams under fire exposure. Thus, there is a lack of data, including detailed observations and recordings of spalling, and response of UHPC beams under fire exp osure. Moreover, there is very limited information on the fire response of beams made of UHPC with polypropylene fiber reinforce ment . Additionally, it is remarkable to note that the previous experimental studies used a high dosage of polypropylene ( PP ) fib ers (4 kg/m 3 ) for mitigation of spalling , which resulted in reduced compressive strength of the concrete mixes to levels below that of optimum desired strength of 150 MPa in UHPC. Unlike previously published works, this study seeks the incorporation of a b alanced dosage of PP fibers in the UHPC mix to achieve spalling mitigation, without impacting on compressive strength and workability. Furthermore, the reported tests in the literature were carried out by subjecting UHPC members to standard fire exposure o nly, without any due consideration to realistic fire scenarios that encompass a cooling phase. For evaluating the fire response of UHPC members, high temperature - dependent material properties of UHPC are required. However, there is a lack of data on the pr operties of UHPC and polypropylene fiber reinforced UHPC at elevated temperatures. Even in these limited studies, there is substantial variance associated with the experimental setup and test procedures including 66 varying specimen size, heating rate, moistu re content, concrete mix proportions adopted in the reported studies. This wide disparity is owing to the lack of standardized testing procedures and limitation in testing equipment for measuring material properties of concrete at high temperatures . Furthe rmore, UHPC is highly prone to fire - induced spalling at lower heating rates due to its dense microstructure and low permeability, which further adds to the complexities in characterizing its high - temperature property variation. To address the aforementione d knowledge gaps , a detailed experimental program was designed as a part of this study. The experimental program consisted of undertaking a set of thermal and mechanical property tests on UHPC specimens in the temperature range of 20 - 800°C. In addition, fi re resistance tests on four ultra - high performance concrete (UHPC) beams were carried out under simultaneous application of structural loading and fire exposure. Full details on the fabrication of test specimens , instrumentation, test procedures together w ith measured properties and response parameters are presented in this chapter. 3.2. Mix Design of UHPC The batch mix proportions in conventional UHPC mixes mainly comprise of specially graded fine aggregates, high volume of silica fume, and superplasticizers, and do not usually contain coarse aggregates. Such conventional UHPC mixes require considerably high mixing energy and the use of specialized mixing equipment. The mixing procedure is complex, and the specialized equipment is not readily available in most concrete production plants at the current time [105] . Th erefore, in the present study, a relatively new mix design for UHPC was adopted in which a controlled amount of coarse aggregates (as in conventional concrete mixes) were also included in the batch mix in order to facilitate ease of preparation and to redu ce the dosage of cementitious material and thus 67 the cost of UHPC. The specialized UHPC mix design was developed by Metna Co. (Prof. Soroushian) as part of a larger ongoing project on Ultra - High Performance Concrete [108] . Four batch mixes, namely UHPC plain (without any fibers), UHPC - S1 (steel fibers), UHPC - S2 (steel fibers), and UHPC - H (with hybrid i.e. steel and polypropylen e fibers) were prepared . The batch mix proportions are given in Table 3 - 1 . All the batches comprised of binder (including cement - type I, silica fume, slag, and limestone powder) and calcareous (carbonate based) coar se aggregates with a maximum size of 12.7 mm, and fine aggregates (natural sand and silica sand). The desired workability of UHPC was obtained by adding a high - range water reducer (HRWR), which is a polycarboxylate - based superplasticizer (Chryso 150) [109] . Table 3 - 1 . Mix proportions in UHPC batch m ixes. Ingredient UHPC plain (Kg/m 3 ) UHPC - S1 (Kg/m 3 ) UHPC - S2 (Kg/m 3 ) UHPC - H (Kg/m 3 ) Coarse Aggregate 517 478 517 517 Natural sand 544 504 544 544 Silica sand 299 277 299 299 Cement 510 472 510 510 Silica fume 224 208 224 224 Slag 102 94 102 102 L imestone powder 184 170 184 184 Water 121 136 121 121 Superplasticizer 48 43 48 48 Steel fibers (1.5% vol.) - 118 127 127 PP fibers (0.11% vol.) - - - 1.6 Water to binder ratio 0.14 0.15 0.14 0.14 Beams casted - U - B1, U - B2 - U - B10, U - B11 High temper ature property test specimens Thermal - Thermal, mechanical Thermal, mechanical Comp . strength - 28 th day 151 145 168 160 Comp . strength - 90 th day 164 167 178 173 Split tensile strength - 28 th day 6 14 15 14 Split tensile strength - 90 th day 7 15 16.5 15 Casting date April 2018 July 2015 April 2018 April 2018 68 The batch mixes were prepared by a local ready - mix concrete plant and were supplied to the site for fabrication of beams, prisms, and cylinders. Batch UHPC - S1 was cast at a field site o n Michigan St ate University campus in July 2015. Batches UHPC plain, UHPC - S2, and UHPC - H were poured at the Civil Infrastructure Laboratory of Michigan State University in April 2018. The UHPC mixing sequence is crucial for attaining a uniform and workable mix without fiber balling. For the batch poured earlier in July 2015, cement and coarse aggregate were added using the automated system in the plant. Then, 80% of total water was added to the mix truck followed by the addition of superplasticizer. After that, silica s and, silica fume, slag , and limestone powder were loaded into the truck. Then, the rest of the water and steel fibers were added. All the ingredients were mixed at a rate of 70 revolutions within 5 7 min and transported to the field site approximately 10 m iles away. However, cement balling and fiber balling were observed in this batch (UHPC - S1). Therefore, a new mixing procedure was adopted for the next batch. The mix UHPC - S1 was poured into two beams (U - B1 and U - B2) and specimens for strength tests. For th e concrete batches cast in April 2018, the coarse and fine aggregates were first dry mixed, followed by dry mixing of the binders in the following order: silica fume, slag, limestone powder, and cement. Then, one - third amount of the total water was added t o the mix in the form of ice, for slowing down the reaction time. Pre - mixed remaining water (two - third of total) and superplasticizer were added and mixed at high speed (1 revolution per 4 seconds) for 5 minutes, followed by reversing the mixing bowl of th e truck in order to bring the settled ingredients from the bottom to the top, to ensure uniformity in the mix. At this point, the plain UHPC mix was poured into specimens for thermal property and strength tests. Following this, the remaining mix was used f or batches UHPC - S2 and UHPC - H, wherein steel fibers were added and mixed for another 5 min with bowl reversal to attain a homogenous mixture. Polypropylene fibers are added 69 in UHPC - H and mixed for another 5 min. UHPC - H was poured into two beams (U - B10 and U - B11), and both UHPC - S2 and UHPC - H were poured into specimens for thermal and mechanical property tests. Steel fibers, 1.5% by volume fraction was added to all batch mixes, except batch UHPC plain. Based on the literature review, steel fibers with an aspe ct ratio higher than 65 did not significantly improve the strength and ductility properties and also instituted problems of poor flowability, fiber balling, and uneven distribution of fibers in UHPC [110,111] . Thus, the steel fibers with an aspect ratio of 65 (0.2 mm diameter and 13 mm length) were incorporated. The steel fibers were of straight type (without hooks) and had tensile strength in the range of 690 to 1000 MPa. In additio n to steel fibers, polypropylene (PP) fibers, 0.11% by volume fraction, were added to UHPC - H mix. The optimal amount of polypropylene fibers recommended to mitigate spalling ranges from 1 to 3 kg/m 3 and this is mostly based on studies for HSC members [112] . The dosage of PP fibers was selected prudently as 1.6 kg/m 3 , to attain the desi red high strength and workability of the UHPC mix. Monofilament PP fibers with a length of 13 mm and a melting point of 160°C were used. The tensile strength of the PP fibers is in the range of 570 660 MPa. The steel and polypropylene fibers utilized in th is study are shown in Figure 3 . 1 and their property details are presented in Table 3 - 2 . Table 3 - 2 . Properties of steel and poly propylene fibers used in UHPC batch mix. Type of fiber Diameter d f (mm) Length l f (mm) Aspect ratio (l f /d f ) Tensile strength (MPa) Density (kg/m 3 ) Melting temperature (°C) Steel 0.2 13 65 960 7850 - Polypropylene 0.018 13 722 570 - 660 910 170 70 a) b) Figure 3 . 1 . F ibers: (a) Steel (b) Polypropylene (PP). 3.3. Design and Fabrication of UHPC Specimens and Beams The UHPC beams were designed based on the available best practice recommendations as no specific design provisions for UHPC members are currently available [110,113 115] . Four UHPC beams, designated as U - B1, U - B2, U - B10 , and U - B11, were designed and fabricated. Beams U - B1 and U - B2 were fabricated from UHPC mix reinforced with steel fibers only (UHP C - S1), while beams U - B10 and U - B11 were fabricated from UHPC mix with steel and polypropylene fibers (UHPC - H). All t he UHPC beams were of rectangular cross section with dimensions of 180 mm in width and 270 mm in depth . The length of the beams was 4000 mm and dictated by the size of the furnace and loading equipment at MSU civil infrastructure laboratory. This experimental study is a part of an ongoing larger research project to develop information on the performance of UHPC beams at ambient and elevated t emperatures. As a part of this larger research project, the effect of removing compression and shear reinforcement (stirrups) in beams, to take advantage of high compressive and high tensile strength offered by UHPC, is being explored. Hence, beams U - B1, U - B2, and U - B10 had only three reinforcing bars (no compression rebars or stirrups) of 13 mm diameter as tensile reinforcement t ), whereas beam U - B11, in v ). 71 The shear reinforcement in beam U - B11 is comprised of close looped stirrups spaced at 100 mm and made from 10 mm diameter steel rebar. All beams are provided wit h a nominal concrete cover of 35 mm to tensile reinforcing bars. The rebars spacing, arrangement , and shear reinforcement were designed as per ACI - 318 requirements for NSC beams [116] . Geometric characteristics of the tested UHPC beams are tab ulated in Table 3 - 3 and their detailed cross - sectional configuration s are shown in Figure 3 . 2 . Table 3 - 3 . Sectional dimensions and reinforcement details in UHPC beams. Beam Designation Width (mm) Depth (mm) Span l ength (mm) Fiber Tensile Reinforcement t (%) v (%) U - B1 180 270 3658 Steel 3 - Ø13mm 0. 90 - U - B2 180 270 3658 Steel 3 - Ø13mm 0. 90 - U - B10 180 270 3658 PP*+Steel 3 - Ø13mm 0. 90 - U - B11 180 270 3658 PP*+Steel 3 - Ø13mm 0. 90 0.79 PP*: Polypropylene fibers, : Tensile reinforcement rati o, : Shear reinforcement ratio Figure 3 . 2 . Layout and cross section of UHPC beams (All units are in mm). 72 In addition to beams, for measuring high - temperature material properties, small specimens includin g 75 x 150 mm cylinders, 100 x 100 mm cubes, and 100 x 100 x 300 mm prisms were prepared. Thermal property tests were undertaken on specimens fabricated using UHPC plain, UHPC - S2, and UHPC - H, whereas mechanical property tests were carried out on specimens made using UHPC - S2 and UHPC - H. Details of specimens utilized for high - temperature property tests are shown in Table 3 - 4 . Mechanical property tests were carried out on 75 x 150 mm cylinders. For thermal property test s, specimens were cut from cured concrete prisms and the size of the test specimens was different for different thermal property tests. Table 3 - 4 . Test matrix of specimens utilized for high temperature materia l property tests. Property Concrete type Specimen shape Specimen dimensions Test temperature (°C) Heating rate (°C/min) Number of specimens (property x concrete type x temperature x heating rate x repetitions) Thermal conductivity Specific heat UHPC plain UHPC - S2 UHPC - H Prism 50x50x25 mm 20 - 700 N/A 2x3x1x1x3=18 Thermal expansion UHPC plain UHPC - S2 UHPC - H Prism 10x10x18 mm 20 - 900 3 1x3x1x1x3=9 Mass loss UHPC plain UHPC - S2 UHPC - H Prism 50x50x25 mm 20 N/A 1x3x5x1x2=30 200 400 500 600 750 0.5 Compress ion Tension UHPC - S2 UHPC - H Cylinder 75x150 mm 20 N/A 2x2x1x1x3=12 200 400 600 750 0.5 2 2x2x4x2x1=32 As part of the fabrication of the beams, plywood forms were assembled to achieve the required internal dimensions in the beams. Thermal curing is es sential for the development of a denser microstructure of UHPC with the completion of pozzolanic reactions for increased formation of 73 calcium silica hydrate (C - S - H) [117] . To attain in - situ high - temperature curing, from the heat of hydration of high cementitious binder contents in UHPC, adequate insulation was provided in the formwork of the beams using rigid Styrofoam. Rigid Styrofoam insulation of 50 mm thickness was installed on two interior sides of the framework and the bottom side of the framework was provided with rigid Styrofoam of 100 mm thickness ( Figure 3 . 3 (a)). In the fabrication of UHPC structures, the heat of hydration with surface cooling effects can generate high tempera ture gradients with higher temperatures developing in the concrete core (due to heat of hydration of cementitious components) as compared to regions closer to the external surface of the beams. Such non - uniform temperature distribution can disrupt the hydr ation process and cause cracking in concrete from thermal stresses. Besides assisting in thermal curing, the insulation provided in the formwork also helps to prevent such early age cracking by maintaining relatively uniform temperatures within the casted beams. The beams were fabricated using a UHPC mix supplied in a ready - mix truck ( Figure 3 . 3 (b)). Following casting, insulating blankets were used to cover the casted beams ( Figure 3 . 3 (c)), and a wet muslin cloth to cover the small specimens for preventing heat loss, generated during hydration of the binder in UHPC. The temperatures developed while curing of UHPC beams , from the heat of hydration of the cementitious matrix , wer e monitored. A sustained rise in temperature was observed in the first 25 h of curing time with peak temperatures reaching about 75°C. During the fabrication of UHPC beams, cylinders and prisms were also cast , as mentioned above. The cylinders and prisms w ere steam cured for 48 h and subsequently stored in controlled conditions of air maintained at 25°C temperature and 60% relative humidity. Compression and splitting tensile strength tests were carried out on three specimens of each UHPC mix for repeatabili ty and reliability. The average compressive and tensile strength of concrete cylinders measured at 28 and 74 90 days are plotted in Figure 3 . 4 and Figure 3 . 5 respectively with t he standard deviation in measurements as error bars, as well as tabulated in Table 3 - 1 . Figure 3 . 3 . (a) Formwork for UHPC beams, (b) Casting of beams, (c) Curing of beams using insulation blankets and lining. (a) (b) (c) 75 Figure 3 . 4 . Compression strength test results for each UHPC mix. Figure 3 . 5 . Tension strength test resu lts for each UHPC mix. 3.4. Instrumentation For mechanical property tests, cylinders were instrumented with three type K chromelalumel thermocouples, 0.91 mm thick, to measure temperature in the furnace, at the surface , and mid - 76 depth of the specimen. The inst rumentation mounted in the beams included thermocouples, displacement transducers , and strain gauges. Type - K chromelalumel thermocouples, 0.91 mm thick, were installed at two different cross sections (mid - span and quarter span) in each beam for measuring c oncrete and rebar temperatures. The deflection of each beam is measured at mid - span as well as at the location of the two - point loads using linear variable differential transformers (LVDTs). These LVDTs were placed outside the furnace (on the top of the be am) since they cannot survive high - temperature exposure within the furnace. LVDTs are connected to a well - insulated stiff threaded steel rod attached to mid span and two load points in the beam. The steel rod extends vertically to pass through a special op ening in the furnace lid. The strain gauges were mounted on two main longitudinal reinforcements and one compression reinforcement for beam U - B11 with an adhesive (glue) application. These strain gauges were of the high - temperature foil strain gauge type, which usually is able to provide reliable strain readings in the temperature range of 20 - 350 °C. These high - temperature strain gauges were used to obtain strain data at rebar level to supplement the data obtained externally th r ough LVDTs. The location and n umbering of the thermocouples and strain gauges are shown in Figure 3 . 6 . 77 Figure 3 . 6 . Location of strain gauges and thermocouples at various cross - sections in (a) beams U - B1, U - B2, and U - B10, (b) beam B - 11 (All units are in mm). 3.5. High Temperature Propert y Tests on UHPC To develop high temperature thermal and mechanical properties for UHPC, a comprehensive test program was undertaken on different types of UHPC namely, UH PC plain ( no fibers ), UHPC with steel (UHPC - S 2 ), and hybrid fibers (UHPC - H). 78 3.5.1. Thermal Prop erties 3.5.1.1. Test Specimens For thermal property tests, specimens were cut from concrete prisms using a power saw and perfectly ground at the ends for accurate measurements . For thermal conductivity, specific heat, and mass loss measurements, specimens had dimensions 50 × 50 × 25 mm ( Figure 3 . 7 (a)) , whereas for thermal expansion measurements, specimens of size 10 × 10 × 18 mm were cut from the prisms ( Figure 3 . 7 (b) ) . The thermal properties of UHPC s were measured using relevant test procedures and equipment [25] . Figure 3 . 7 . Specimens for thermal property tests: (a) 50×50×25 mm; (b) 10×10×18 mm. 3.5.1.2. Test Procedure Thermal expansion measurements were carried out as per the procedure laid out in ASTM E831 [32] . A thermomechanical analyzer (TMA) was used for thermal expansion measurements in the temperature range of 20 900°C. The TMA utilized a movable LVDT, which generates an output signal corresponding to the dimensional change of the test specimen. A flat - tipped expansion probe was placed on the concrete specimen and a small static force was applied to the probe, so that the probe remained in contact with the specimen throughout the test. The heating rate in the TMA was 79 set to 3°C/min and the linear dimension changes (expansion or contraction) of the specimen w ere recorded at various target temperatures. During the thermal expansion test, one of the UHPC - S 2 specimens spalled at around 200°C as shown in Figure 3 . 8 (a) , which severely damaged the TMA ( Figure 3 . 8 (b)) . The thermal expansion tests were repeated on thr ee specimens from each concrete batch and the variability was within 5%, indicating good reliability of the measurements as shown in Fi gure 3 . 9 . The error bars could not be plotted for thermal expansion curves as th ey are measured as a continuous function of temperature through TMA. Figure 3 . 8 . Exploded specimen during (a) TMA test; and (b) damaged glass specimen holder from TMA test; and (c) mass loss test. 80 Fi gure 3 . 9 . Measured thermal expansion for each UHPC mix. Thermal conductivity and specific heat measurements were carried out using the Hot Disk TPS 2500S thermal constant analyzer, as per the procedure laid out in ISO 22007 - 2 [29] . The specimens were exposed to elevated temperatur es in a furnace connected to the Hot Disk apparatus. Hot Disk utilizes a transient plane source (TPS) technique to measure thermal conductivity and specific heat. A flat sensor, which is a spiral nickel wire probe insulated between layers of mica was place d between two specimens. The Hot Disk test regime was set up to record thermal property measurements at eight different target temperatures of 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, 81 600°C, and 700°C. At each target temperature, upon attainment of equilib rium conditions in the specimen, the sensor simultaneously measured thermal conductivity and thermal diffusivity, and then specific heat was computed internally. Mass loss measurements were carried out by recording the mass of the test specimen before and after exposure to a target elevated temperature in an enclosed electric furnace. Mass loss of the test specimen s at different target temperatures of 20°C, 200°C, 400°C, 500°C, 600°C, and 750°C was measured. Test specimens from the plain UHPC and UHPC - S 2 (w ithout PP fibers) batch mix suffered explosive spalling at around 200°C when subjected to heating rates of more than 0.5°C / min as shown in Figure 3 . 8 (c) . Therefore, all mass loss test specimens were heated at a con sistent low heating rate of 0.5°C / min to target temperatures. To ensure the reliability of the measurements, thermal conductivity, specific heat, and mass loss measurements were conducted on two repeat specimens at each target temperature and the measured values were within 5% as plotted in Figure 3 . 10 with standard deviations of the measurements as error bars . Figure 3 . 10 . Measured thermal properties for each UHPC mix : (a) Thermal conductivity; (b) Specific heat; and (c) Mass loss. (a) 82 Figure 3.10 . 3.5.1.3. Results The variation of thermal conductivity, specific heat, mass loss, and thermal expansion of UHPC (plain), UHPC - S 2 , and UHPC - H as a function of temperatur e is plotted in Figure 3 . 11 . These variations with temperature follow a similar trend in all three UHPCs and can be grouped into four stages. The variation of thermal properties in concrete with temperature is mainl y governed by the change in moisture levels occurring with temperature increase. Moisture is present in concrete in (b) (c) 83 different forms and the variation in the moisture level is influenced by microstructural changes that take place in concrete under high - temp erature exposure as summarized in Table 3 - 5 . At temperatures above 100°C, the free water starts to evaporate, and when the concrete temperature reaches about 300°C, adsorbed water, interlayer water from calcium sili cate hydrate (C - S - H) gel and a portion of the chemically bonded water start to evaporate. Further increase in concrete temperature to 400°C causes decomposition of calcium hydroxide, Ca(OH) 2 into CaO and H 2 O, leading to more evaporation of moisture. Furthe r temperature rise beyond 500°C leads to decomposition of C - S - H and further deterioration of concrete and aggregate. Figure 3 . 11 . Measured thermal properties as a function of temperature for three U HPC types: (a) Thermal conductivity; (b) Specific heat; (c) Mass loss; and (d) Thermal expansion. 84 Figure 3.11 85 Figure 3.11 Table 3 - 5 . with rise in temperature. Temperature (°C) Changes in microstructure 100 Evaporation of free water out of concrete 200 Meltdown of polypropylene fibers (if present) 300 Loss of adsorbed, interlayer C - S - H water and chemically bounded water 400 Dissociat ion of Ca(OH) 2 into CaO and H 2 O 500 Decomposition of C - S - H 600 700 Quartz phase transformation in some aggregate ( siliceous ) types Dissociation of dolomite in some aggregate (carbonate) types (endothermic reaction) 900 Complete decomposition of C - S - H Thermal Conductivity The variation of thermal conductivity of plain UHPC, UHPC - S2 , and UHPC - H with temperature is plotted in Figure 3 . 11 (a) . The thermal conductivity of these three types of UHPC at room temperature is in the range of 2.9 and 3.8 W/m°C. In general, the variation of thermal conductivity 86 with temperature follow s a similar trend for all three UHPCs and can be grouped into four stages. For all three types of UHPC, thermal conductivity sharply decreases i nitially up to a temperature of 100°C in stage 1. This can be attributed to moisture loss resulting from the evaporation of free water present in concrete. In stage 2, i.e. 100 - 300°C, the remaining free water, together with the adsorbed water, as well as i nterlayer water from calcium silicate hydrate (C - S - H) gel and a portion of the chemically bonded water evaporate resulting in a steady decrease of thermal conductivity. Thermal conductivity for all UHPCs varies marginally from 300 to 500°C in stage 3, owin g mainly to the decomposition of Ca(OH) 2 into CaO and H 2 O, moisture increases, resulting in a small increase in thermal conductivity. This is followed by stage 4, beyond 500°C and up to 700°C, where a slight decrease in thermal conductivity occurs due to t he second phase of C - S - H decomposition involving release of a small amount of strongly held moisture left within calcium silicate hydrate (C - S - H) layers. Figure 3 . 11 (a) also shows the effect of fibers on the therma l conductivity of UHPC as a function of temperature. At room temperature, the fiber - reinforced UHPC mixes (UHPC - S 2 and UHPC - H) exhibit slightly higher thermal conductivity than plain UHPC (without any fibers) and this can be attributed to the presence of s teel fibers which have high thermal conductivity in the range of 50 W/m°C. Upon heating beyond 100°C, thermal conductivity of UHPC - H is lower than UHPC - S 2 and follows closely to that of UHPC, due to the presence of polypropylene (PP) fibers. PP fibers have inherent low thermal conductivity values (0.1 - 0.2 W/m°C) and melting point of around 160°C, which create pores in concrete matrix upon melting and lower the thermal conductivity further. However, upon complete melting of all the PP fibers at high temperat ures beyond 400°C, the thermal conductivity values of UHPC - S 2 and UHPC - H are close to each other, and slightly 87 higher than UHPC without any fibers. Overall, the trends indicate that there is no significant effect of fibers in thermal conductivity values of UHPC throughout the temperature (20 - 700°C) range. Specific Heat The measured specific heat of three types of UHPC is plotted in Figure 3 . 11 (b) as a function of temperature. The room temperature specific heat of th e three types of UHPC lies around 1.4 - 2 MJ/m 3 °C. Similar to thermal conductivity, the specific heat variation in all three types of UHPC is influenced by microstructural changes due to variation of moisture and can be broadly grouped into four stages. Spec ific heat is also governed by the physicochemical changes that occur in the cement paste and the aggregates at temperatures exceeding 600°C. Specific heat around 100°C (in stage 1), increases due to evaporation of moisture present in the form of free water . In stage 2, i.e. 100 - 300°C range, specific heat increases further due to evaporation of moisture present in the remaining free water, along with adsorbed and bonded water. Specific heat in stage 3, i.e. 300 - 500°C range, remains almost constant due to cou nteracting effects of decrease in moisture owing to complete evaporation of all the water present in concrete and increase in moisture due to the release of chemically bound water in concrete from the decomposition of Ca(OH) 2 . Finally, specific heat increa ses followed by stabilization in stage 4, i.e. 500 - 700°C range, due to release of moisture from C - S - H gel decomposition and significant deterioration of microstructure within concrete. The micro and macro crack development beyond 600°C increases the porosi ty of UHPC resulting in lower specific heat at elevated temperature. All three types of UHPC (plain, with steel fiber, steel , and with hybrid fibers) exhibit similar variation in specific heat with increasing temperature. Overall, the specific heat of UHPC - H and UHPC - S 2 are lower than UHPC throughout the temperature range. The lower specific heat of fiber - reinforced UHPC can be attributed to the increase in porosity due to the addition of fibers. 88 Moreover, the specific heat of UHPC - H (with steel and PP fibe rs) is slightly lower than that of UHPC - S 2 (with steel fibers only) in 200 - 700°C range. I n the case of UHPC - H , polypropylene fibers decompose (after burning), leading to an increase in the porosity of concrete. As a result, UHPC - H becomes more pervious , an d less amount of heat is required to raise its temperature . Mass Loss The mass of concrete decreases with temperature rise due to loss of moisture. In addition, mass loss in carbonate aggregate concrete is higher due to the dissociation of dolomite in carb onate aggregate at around 600°C. The mass loss in UHPC (plain), UHPC - S 2 , and UHPC - H , is plotted in Figure 3 . 11 (c) and can be grouped into four stages based on the observed trends. In stage 1, i.e. 20 - 100°C range, i nitial mass loss in all the three types of UHPC is very small, and this loss is attributed to evaporation of free water present in concrete. Since, UHPC has a very dense microstructure due to low water - cement ratio, the free water in UHPC is considerably l ess. Hence, the rate of mass loss due to the evaporation of free water is marginal. In comparison with stage 1, mass loss is slightly higher in stage 2, i.e. 100 - 300°C range and this can be attributed to the evaporation of the left - over free water, as wel l as adsorbed and bounded water. In stage 3, i.e. 300 - 500°C range, rapid mass loss takes place due to increase in available water in the concrete microstructure from the decomposition of Ca(OH) 2 into CaO and H 2 O. Finally, in stage 4, between 500 - 750 °C rang e, mass loss stabilizes owing to complete evaporation of the water present in concrete. Only a slight increase in the extent of mass loss can be observed in this stage due to dissociation of dolomite in carbonate aggregate present in concrete. Overall, the mass loss in all types of UHPCs is within 8% in 200 - 750°C temperatures owing to less amount of available moisture in UHPC. Further, the effect of fibers on mass loss of UHPC is minimal due to very small amount of fibers (1.5% for steel and 0.11% for PP fi bers) present in UHPC. 89 Thermal Expansion The variation of measured thermal expansion of UHPC, UHPC - S2 , and UHPC - H , is presented as a function of temperature in Figure 3 . 11 (d) . For all UHPC types, thermal expansion is taken to be zero at room temperature. The thermal expansion increases steadily in 20 - 600°C range, becomes invariant between 600 - 700°C, decreases in 700 - 800°C and then, increases sharply in 800 - 900°C range. The variation of thermal strain of concrete wit h temperature is linked to changes in moisture content, cement paste , and aggregates and can be grouped under four stages as in the case of other thermal properties. In stage 1, i.e. 20 - 100°C range, thermal expansion increases at a substantial rate due to high thermal expansion of cement paste and constituent aggregates of concrete. The thermal expansion increases at a slightly lower rate in stage 2, i.e. 100 - 300°C range , and this is attributed to the evaporation of free, adsorbed , and combined water from t he cement matrix. Loss of water due to heating contributes to thermal shrinkage rather than expansion of concrete. Thermal expansion of UHPC continues to increase with temperature in stage 3 comprising of 300 - 600°C range. The rate of increase is slower bet ween 400 - 500°C due to evaporation of remaining water in C - S - H layers and water liberated from the dissociation of Ca(OH) 2 . Above 500°C, thermal expansion increases steeply due to the quartz transformation in natural sand present in UHPC, along with an expa nsion of the cement paste. The expansion rate initially subsides but is followed by an increasing trend in stage 4, between 600 and 900°C for UHPC. The initial decrease in thermal change indicates negative volume change or shrinkage, and can be attributed to the release of chemically bound water in hydrates present in the concrete. Beyond 800°C, in stage 4, thermal expansion increases again, along with softening of concrete and development of macro - crack in the specimen. This substantial increase in expansi on is due to decarbonation of limestone - based 90 (carbonate) aggregate. Severe cracking was observed in all the three UHPC types (plain UHPC, UHPC - S 2 , and UHPC - H) beyond 800°C. As can be seen in Figure 3 . 11 (d) , the pr esence of fiber has only a moderate influence on thermal expansion between 20 - 160°C. It can be seen that the hybrid - fiber (steel and PP) reinforced UHPC has a slightly lower thermal expansion than that of plain UHPC and UHPC - S 2 types beyond 160°C. The decr ease in the rate of thermal expansion beyond 160°C can be attributed to the ease of dehydration of comparatively porous UHPC - H specimen, resulting from empty channels formed after melting of polypropylene fibers. However, beyond 750°C, the effect of burnin g of polypropylene fibers in UHPC - H diminishes, and the rise in thermal expansion is similar to that of UHPC - S 2 . The addition of steel fibers does not have a pronounced effect o n thermal expansion, due to counteracting effects of steel expansion and crack control effect facilitated by steel fibers. Above 800°C, the thermal expansion of steel fiber reinforced concrete increases slightly more, with temperature as compared to plain UHPC. This slight increase with temperature can be attributed to the presence o f steel fibers in UHPC - S 2 , which continue to expand at elevated temperatures. From the measured data, it can be clearly seen that the addition of fibers does not significantly influence the thermal properties of UHPC. However, the effect of addition of fi bers is in the form of minimizing spalling in fiber - reinforced specimens as compared to plain UHPC specimens. Specimens fabricated with plain UHPC and steel - reinforced UHPC experienced spalling during thermal property tests. On the other hand, UHPC - H speci mens, fabricated with a combination of steel and polypropylene (PP) fibers, did not experience any spalling in the entire 20 - 800°C temperature range. This can be attributed to the fact that the polypropylene fibers present in UHPC - H melt at about 160ºC cre ating pores and microcracks in concrete that are sufficient for relieving 91 vapor pressure developed in the concrete. The presence of steel fibers in UHPC - H has also some influence in minimizing spalling since steel fibers enhance the tensile strength of UHP C - H, which in turn helps in withstanding tensile stresses exerted by high pore pressure generated in concrete. However, it is evident from the undertaken tests that the sole incorporation of steel fibers is less efficient than hybrid fibers (steel and PP) in UHPC for mitigating fire - induced spalling. 3.5.1.4. Property Relations Data generated from the thermal property measurements were utilized to develop property relations for different UHPC types as a function of temperature [118] . The correlations were developed using linear and polynomial regression analysis. Because the test data indicate that fibers have no significant effect on the thermal properties of UHPC, the developed relations are applicable for pl ain and fiber - reinforced UHPC (UHPC - S 2 and UHPC - H). The developed empirical relations are shown in Table 3 - 6 over temperature ranges of 20 700°C for thermal conductivity and specific heat, 20 750°C for mass loss, an d 20 900°C for thermal expansion. Table 3 - 6 . Thermal property relations of UHPCs generated utilizing data from tests. Thermal property UHPC property relation Temperature range Thermal conductivity (W/m °C) k t = - 0.0092T+3.1136, 20 °C 100 °C k t = - 0.0035T+2.5802, 100 °C 400 °C k t = 0.0021T+0.3481, 400 °C 500 °C k t = - 10 - 5 T 2 +0.0111T - 1.6565, 500 °C 700 °C. Specific heat (MJ/m 3 °C) c= 2x10 - 6 T 2 +0.0013T+1.6918, 20 °C 300 °C c= - 0.0046T+3.6677, 300 °C 400 °C c= 0.0054T - 0.3217, 400 °C 600 °C c= 0.0006T+2.5588, 600 °C 700 °C. Thermal expansion (%) th = 2x10 - 6 T 2 +0.0002T +0.0014, 20 °C 600 °C th = - 1.443x10 - 5 T 2 +0.0188T - 5.2031, 600 °C 800 °C th = 0.0037T - 2.342, 800 °C 900 °C. Mass loss (%) M/Mo= 1.0005 - 3x10 - 5 T, 20 °C 200 °C M/Mo= 1.0451 +2x10 - 7 T 2 - 0.0003T, 200 °C 750 °C. 92 The thermal property relations were developed using the least squares method of regression analysis for a set of data point s corresponding to the high temperature experimental trends. This was carried out using the analysis package available in Microsoft Excel. Microsoft Excel is selected due to the unified ease of performing regression analysis and plotting fitted data with t he trends generated in thermal property tests. The regression analysis is carried out with specific thermal property as a response parameter (dependent variable) and temperature as their predictor parameter (independent variable). The accuracy of the regre ssion analysis or the curve fitting of the relation is represented by the coefficient of determination, R 2 . The value of R 2 always lies between 0 and 1, and the closer its value is to 1, the more accurate is the data fit . The relations obtained through reg ression analysis show R 2 values ranging from 0.97 to 1, which represents a reasonably high confidence level in fitting the equations with the measured thermal property of UHPC. 3.5.1.5. Comparison between thermal properties of UHPC and conventional concrete The te mperature - dependent thermal conductivity variation of UHPC is compared in Figure 3 . 12 (a) with that of conventional NSC and HSC, taken from published literature [21,11 9,120] . There exists notable variation in the available reported data on thermal conductivity of NSC and HSC, which can be mainly attributed to varying moisture content, test conditions, and measurement techniques used in previous set of experiments. The thermal conductivity for all concrete types decreases with temperature, and this decrease is dependent on the concrete mix properties, specifically moisture content and permeability. At ambient temperature, the thermal conductivity of NSC and HSC, ranges b etween 1.3 to 2.5 W/m°C (with HSC being on the higher side of this range). The thermal conductivity of UHPC is relatively higher than the thermal conductivity of conventional NSC and HSC at elevated temperatures. The higher thermal conductivity of UHPC 93 can be attributed to the inherent less amount of water present in UHPC. Moreover, the dense microstructure of UHPC with less porosity as compared to other types of concrete, further limits dehydration in concrete and thus maintains higher thermal conductivity than that of NSC and HSC . The specific heat of UHPC is compared in Figure 3 . 12 (b) with that of conventional NSC and HSC made of carbonate aggregate as reported from various studies [21,119,121] . UHPC exhibits similar values of specific heat as that of NSC a nd HSC in 20 - 400°C range. Specific heat of UHPC is relatively higher than that of NSC and HSC in 400 - 600°C range, which can be attributed to the lower permeability and dense microstructure of UHPC that requires more heat for evaporation of water. In the te mperature range of 600 - 800°C, the specific heat of NSC and HSC, made of carbonate aggregates is very high due to the substantial amount of heat utilized (i.e. endothermic reaction) for dissociation of dolomite in carbonate aggregate. However, this high ran ge of specific heat at temperatures above 600°C is not that apparent in UHPC due to the controlled (lower) amount of coarse aggregates present in the UHPC mix, so as to obtain a dense microstructure using fine constituent materials. The measured mass loss for UHPC is compared with mass loss in NSC and HSC [20,120,122] in Figure 3 . 12 (c). The mass loss is not significant until 600°C in all concrete typ es. In the temperature range of 600 - 800°C, extent of mass loss in UHPC is significantly less compared with that in NSC and HSC. Mass loss in the temperature range of 600 - 800°C occurs in carbonate aggregate concrete mainly due to the dissociation of dolomit e which results in evaporation of hidden moisture present in the carbonate aggregate [17] . The lower mass loss in UHPC than in NSC an d HSC can be attributed to the lower (or none) amount of coarse aggregate present in UHPC, as opposed to a larger proportion of coarse (carbonate) aggregate present in conventional concrete mixes (NSC and HSC). 94 The measured thermal expansion for UHPC, alon g with compiled data for NSC and HSC from published test results [20,21,120] is plotted in Figure 3 . 12 (d) as a function of temperature. The thermal expansion of all concretes (including UHP C) var ies in a similar manner in 20 - 500°C range. UHPC exhibits higher thermal expansion in the 500 - 700°C range as compared to conventional NSC and HSC. The expansion rate for concretes in this temperature range is due to the expansion of cement paste. UHPC has a higher proportion of cement paste (and a lower proportion of coarse aggregates) for a dense impermeable microstructure, which results in higher thermal expansion. The rate of thermal expansion for all concrete types slows down between 700 - 800°C rang e. The subsiding trend in thermal expansion of concrete in 700 - 800°C range is attributed to the loss of water present in hydrates. To achieve the desired concrete strength properties, a higher dosage of mineral admixtures, such as silica fume and slag is p resent in the mix for UHPC as compared to the other two concrete types (NSC and HSC). These mineral admixtures present in UHPC, react with the hydration products to form additional C - S - H gel (hydrate), the part of cement paste responsible for strength in c oncrete. Thus, shrinkage is observed in UHPC between 700 and 800°C, as opposed to a slower increase in thermal expansion in NSC and HSC because of loss of water from higher volume of hydrates in UHPC. Beyond 800°C, the increase in thermal expansion is owin g to microstructural changes in coarse aggregate present in concrete. UHPC has relatively lower thermal expansion values than other concretes beyond 800°C, which is attributable to the limited proportion of coarse aggregates in UHPC as opposed to a substan tial amount of coarse aggregate in NSC and HSC. 95 Figure 3 . 12 . Comparison between thermal properties of UHPC with NSC and HSC. 96 Figure 3.12. 97 3.5.2. Mechanical Properties 3.5.2.1. Test Specimens Mechanical pr operty tests were carried out on two types of UHPC, namely UHPC reinforced with steel fibers (UHPC - S 2 ) and UHPC reinforced with hybrid (steel and polypropylene) fibers (UHPC - H). From each batch, 75 x 150 mm cylindrical specimens were utilized for undertaki ng mechanical property tests on each type of concrete. 3.5.2.2. Test Procedure Unstressed testing regime was followed, wherein the test specimen is heated to a certain temperature without any loading, and following the attainment of the target temperature, the spe cimen is loaded in increments until failure. The test equipment for evaluating temperature - dependent mechanical properties of UHPC consisted of a heating device and a loading device. The heating device used to heat the concrete specimens is an electric fur nace (shown in Figure 3 . 13 (a)). The electric furnace has internal dimensions of 100 x 200 mm and can simulate a maximum temperature of 750°C. It is internally fitted with electric heating elements, and is capable of implementing various heating rates, and can maintain a target temperature for a specified duration. The loading device utilized to undertake the strength tests is Forney strength test machine; displayed in Figure 3 . 13 (b) . This Forney strength test equipment is a 2670 kN load - controlled compressive test machine, with a digital interface for controlling the test parameters such as loading rate, failure point, etc. and is capable of capturing the stress - strain respons e of test specimens. 98 Figure 3 . 13 . Test equipment for evaluating high - temperature mechanical properties: (a) Electric furnace; (b) Forney strength test machine. For mechanical property measurements at room t emperature, specific test procedures are given in test standards [43,44] . However, test standards do not provide any guidance for evaluating the mechanical properties of concrete at elevated temperatures. Only RILEM recommendations provide procedures for evaluating the mechanical properties of concrete at high temperatures in the range of 20 750°C [45] . However, these high - temperature test procedures spe cified in RILEM are developed based on property tests on conventional concretes , and hence, they may not be practicable and fully applicable for higher strength concretes, such as UHPC. For instance, RILEM recommends a heating rate of 2°C/min for a concret e cylinder of 75 mm in diameter, as utilized in this study. When UHPC - S cylinders (without PP fibers) were subjected to any heating rate greater than 0.5°C/min, the specimens suffered explosive spalling as shown in Figure 3 . 14 , at temperatures around 200°C. It is worth noting that the UHPC - H cylinders did not encounter major spalling during heating at a rate of 2°C/min as in the case of UHPC - S, due to the decrease of pore pressure by melting of PP fibers present in t he UHPC - H mix. 99 Currently, there is no guidance on a critical limit of moisture content for limiting fire - induced spalling in UHPC. For conventional concretes (below the strength of 80 MPa), Eurocode2 [16] states that spalling is unlikely to occur, when the moisture content (by weight) is less than 3%. Such explosive spalling at low he ating rates was reported i n studies by other researchers. The literature review in Chapter 2 revealed that previous high - temperature studies on UHPC dried the test specimens in the oven, prior to heating them in the furnace. Oven drying the specimens elimi nates moisture and reduces the risk of spalling. However, pre - oven - drying is not a standardized test procedure and more importantly, it is not reflective of realistic situations in - built infrastructure. Therefore, to generate test data on UHPC while invest igating the influence of heating rates and oven drying on the mechanical properties of UHPC, two heating regimes were adopted in this study: (i) heating the cylinder at a low heating rate of 0.5°C/min; (ii) oven - drying followed by heating the cylinder at a rate of 2°C/min, as shown schematically in Figure 3 . 15 . As part of the drying treatment, the specimens were exposed to 105°C temperature in the oven ( Figure 3 . 16 ) for 7 days . Following oven drying, the dried specimens were kept in sealed bags to prevent moisture absorption until the day of testing. Figure 3 . 14 . Spalled UHPC - S 2 specimen during heating for mechanical property tes t . 100 Figure 3 . 15 . Schematic of testing procedure followed for mechanical property evaluation of UHPC at elevated temperature. Figure 3 . 16 . Oven drying of UH PC specimens. To evaluate the high - temperature mechanical properties of UHPC, the test specimens were heated to target test temperatures of 200, 400, 600, and 750°C according to the selected heating regime in the electric furnace ( Figure 3 . 13 (a)). For monitoring temperatures, two Type K thermocouples were installed at the surface and center at mid - height of the cylinder, and another one was placed Oven rack Oven Concrete cylinder Thermo couple 101 inside the electric furnace for measuring the increase in temperature with time. The temperature development inside the furnace, on the surface , and at the center of UHPC - S 2 cylinder heated at two different rates for attaining 750°C target temperature is shown in Figure 3 . 17 . It can be observed that lower thermal gradients developed in the specimen upon heating at 0.5°C/min, which could lead to uniform drying and lower build - up of pore pressure. When heated at 2°C/min, larger thermal gradients developed resulting in larger pressure gr adients and higher accumulation of pore pressure, along with higher thermal stresses due to differential thermal gradients. The combined stresses imposed by pore pressure and thermal stresses could accelerate spalling phenomenon in UHPC specimens. When the temperature in the furnace reached the aimed temperature, the cylinder continued to remain in the furnace at this temperature for 2 hours to attain thermal equilibrium (steady state) conditions. After steady state conditions are reached throughout the cyl inder specimen, the hot cylinder was taken out and moved to the strength testing machine. For minimizing heat loss while transferring the heated specimen to the loading device, a thermal insulating cover was utilized for compressive strength test, and a st eel bracket frame was used for splitting tensile strength test [25] . the time of the end of heating to the end of the strength test [123] . 102 (a) (b) Figure 3 . 17 . Temperature progression in UHPC - S2 speci men for target temperature of 750 °C at a heating rate of : (a) 0.5 °C/min ; (b) 2 °C/min . For the compression test, the specimen was loaded axially ( Figure 3 . 18 (a)) at a uniform rate of 0.25 MPa/sec till failure, as per ASTM C39 [43] . The load - displacement values measured at each load increment were utilized to generate the stress - strain curves, from which the p eak failure load 103 was obtained. The load and displacement were recorded through the built - in load cell and linear variable displacement transducers (LVDTs) connected to the embedded data acquisition system in Forney strength test equipment. Prior to the tes t, exact dimensions of the test specimen were measured using a Vernier caliper and inputted in the strength test machine through its digital interface. The load and displacement were recorded at a frequency of 32 readings per second. At each time step, str ess is computed internally by dividing the load by cross - sectional area of the test specimen. Figure 3 . 18 . Testing of the heated specimen: (a) Compression; (b) Tension. For measuring displacement, two LVDT s pre - attached to the top and bottom plates of the compression loading device were utilized as it is extremely difficult to connect LVDTs to hot cylinders. The strain is calculated by taking the average of the measured change in displacements at each time increment. The accuracy of displacement measurement is + 3%. Modulus of elasticity was computed utilizing the compression stress - strain curves, following ASTM C469 test standard [46] . The high - temperature splitting tensile strength test was conducted by applying a diametrical load at a rate of 0.013 MPa/sec as specified in ASTM C496 test standard [44] , till the splitting failure occurred in concrete cylinder ( Figure 3 . 18 (b)). The time taken for moving out the hot 104 spe cimen from the furnace to application of the ultimate load took around 10 minutes, depending upon the temperature - degraded strength. 3.5.2.3. Results Compressive Strength The peak loading point at which the heated cylinder attained failure in compression was taken as the ultimate failure load. This peak load is divided by the cross - sectional area of the cylinder to obtain the compressive strength of concrete at that particular temperature. At room temperature, UHPC - H has a slightly (4%) lower compressive strength of 171 MPa, as compared to that of UHPC - S 2 (177 MPa), which can be attributed to the slight reduction in its density due to the addition of PP fibers in UHPC - H. The inclusion of polypropylene fibers leads to a reduction in density because of the lower bond s trength of PP fibers, which forms a relatively weaker bond with the cement matrix and initiates micro - cracking [124] cT ) and the room temperature, f cT /f c ) are plotted in Figure 3 . 19 (a) and Figure 3 . 19 (b) respectively as a function of temperature for both types of UHPC. Both types of UHPCs experienced a steady loss in compressive strength with temperature rise throughou t 20 - 750°C and this is due to microstructural changes that take place in concrete when exposed to elevated temperatures. 105 Figure 3 . 19 . Variation in compressive strength as a function of temperature: (a) Abs olute; (b) Relative. During heating from room temperature to 200°C, the reduction in compressive strength is owing to the evaporation of most of the free water present in capillary pores and to some extent, adsorbed water between layers of cement paste in concrete. The compressive strength of UHPC - S2 remained 106 to be slightly higher than UHPC - H until 200°C. Upon further increase in temperature, UHPC - H retains higher strength as compared to UHPC - S2 in 200 - 400°C. This improved strength retention in UHPC - H can b e attributed to the dissipation of pore pressure facilitated by the melting of PP fibers at about 170°C, resulting in lower degradation of the microstructure. Beyond 400°C, compressive strength values of both the UHPCs continued to degrade and follow a sim ilar trend up to 750°C. At temperatures higher than 400°C, chemically bound water gets released from concrete through the disintegration of calcium hydroxide (Ca(OH) 2 ) and calcium silicate hydrate (C S H) gel resulting in further reduction in strength. Mor eover, when the temperature is above 600°C, decarbonation of calcium carbonate present in limestone (calcareous) aggregates, also reduces compressive strength. At about 750°C, excessive micro - cracking and deterioration in concrete microstructure led to sig nificant strength loss, and only about 23% of the original compressive strength is retained in both UHPCs. There is no variation in the reduction in compressive strength under two heating rates. Elastic Modulus The elastic modulus was evaluated as the seca nt modulus at 40% of the peak stress from the respective compressive stress - strain curve at each target temperature. The elastic modulus at room temperature for both UHPC - S2 and UHPC - H is 43 GPa. Figure 3 . 20 (a) pre sents the variation in elastic modulus for specimens from either of the UHPC mixes at both heating rates. The variation in relative elastic modulus, defined as the proportion of the elastic modulus at a target temperature to that at ambient temperature (E c T /E c ) is shown in Figure 3 . 20 (b). The plotted trends reveal that the effect of exposure to high temperatures on the loss of modulus of elasticity is nearly identical for the two types of UHPC measured at different heating rates, with less than 10% deviation. 107 Figure 3 . 20 . Variation in elastic modulus as a function of temperature: (a) Absolute; (b) Relative. The deterioration in elastic modulus with temperatur e is mainly associated with the moisture content and the microstructure of hydrated cement products within concrete. The average values of elastic modulus at 200, 400, 600, and 750°C are 58%, 32%, 8%, and 4% to that of room temperature respectively. The de gradation of modulus up to 400°C is due to micro - cracking and microstructural alterations in concrete resulting from moisture loss and shrinkage of cement paste. 108 In the 400 to 750°C temperature range, the deterioration of aggregate - paste bond because of th ermal mismatch and onset of disintegration of Ca(OH) 2 and C - S - H causes degradation of elastic modulus [17,39] . Comparison of loss in elastic modulus shows that there is no significant difference in the behavior of UHPC - S and UHPC - H at el evated temperatures. Tensile Strength Tensile strength of conventional normal strength concrete is considerably lower than compressive strength and thus, is often neglected in strength calculations at room temperature. Conversely, the tensile strength of U HPC is much higher (in comparison to NSC) and can be efficiently utilized in achieving higher capacity in concrete in different ways. Further, under fire conditions, tensile strength is an important property because tensile strength resists crack propagati on in concrete. Moreover, in higher strength concretes, tensile strength is a critical property as it helps to overcome fire - induced spalling to some extent [42,125] . Tensile st rength is mostly measured as the splitting tensile strength due to its ease of execution and comparatively lower scattering in test results [126] . At each temperature, t he failure load at which the heated cylinder diametrically s plits in tension is used to evaluate splitting tensile strength. The trends of absolute and relative strength degradation for UHPC - S2 and UHPC - H at each heating rate (0.5 °C/min and 2 °C/min ) are shown as a function of temperature in Figure 3 . 21 . The inclusion of steel fibers in UHPC helps in slowing down the strength loss with increasing temperature [120] . At room temperature, the tensile strength of UHPC - H is 15 MPa, which is marginally lower than that of UHPC - S2, 16.5 MPa. This significantly high tensile strength in both UHPCs is attributed to the presence of steel fibers in UHPC. It should be pointed out that NSC possesses tensile strength in the range o f 2 - 3 MPa. The results show that with respect to the adopted heating rates, there are no considerable differences in the individual trends of loss in tensile strength for both UHPCs in 109 the entire 20 to 750°C temperature range. The reduction in tensile stre ngth of UHPC is associated with the coalescence of internal cracks formed by moisture evaporation and aggregate - paste debonding [127] . Figure 3 . 21 . Variation in splitting tensile strength as a function of temperature: (a) A bsolute; (b) Relative. The test data indicates the average splitting tensile strength retention in UHPCs at 200, 400, 600, and 750°C to be 70%, 55%, 40%, and 20% respectively, of that at room temperature. In 20 to 110 600°C temperature range, the relative tens ile strength retention of UHPC - H is better than that of UHPC - S2 as the melting of polypropylene fibers in UHPC - H helps to reduce the crack growth by lowering the internal pressure developed in the concrete matrix. Beyond 600°C, the trend of strength degrad ation in UHPC - S2 and UHPC - H is similar and both the UHPCs suffered a major loss in tensile strength. The higher decrease in tensile strength in 600 - 750°C was accompanied by severe cracking resulting from physical and chemical deterioration of their microst ructure, and thermal incompatibility between fibers, aggregates, and cement paste [123] . Stress - strain Response The compressive stress - strain response of UHPC - S2 and UHPC - H in the temperature range of 20 - 750°C was recorded at each target temperature and plotted in Figure 3 . 22 . The stress - strain curves at each temperature comprises an elastic region followed by a parabolic section leading to peak stress and finally a descending section until the concrete specimen attains failure. The stress - strain curve can be characterized through three major parameters: (i) peak compressive stress (or strength); (ii) corresponding strain at peak stress; and (iii) modulus of elasticity. In order to compare the effect of varying heating rates, the stress - strain response recorded by following both the heating rates, 0.5°C/min and 2°C/min, are plotted concurrently in Figure 3 . 22 for each UHPC type. It can be seen from Figure 3 . 22 that the stress - strain curves obtained by complying with the two different heating rates follow closely, with less than 10% variation in the three main parameters, at all the target test temperatures for both the UHPCs. 111 Figure 3 . 22 . High temperature stress - strain response of: (a) UHPC - S2; (b) UHPC - H. The main purpose of Figure 3 . 23 is to compare the influence of polypropylene fibers on temperature - dependent stress - - H retains slightly lower stress (strength) t han UHPC - S2, 112 and this can be attributed to the slight reduction in density and formation of weaker zones due to addition of PP fibers in UHPC - H [130] . - H as compared to UHPC - S2, since melting of PP fibers increases permeability and reduces deterioration in concrete microstructure. Additionally, above 400°C, the stress - strain response becomes increasingly flatte r with the increasing temperatures in both the UHPCs. The enhanced ductility is a consequence of the presence of steel fibers, as well as softening that occur s at elevated - H retains slightly lower stress and higher ductility due to increased micro cracking by complete melting of PP fibers. The average strains corresponding to peak stress in UHPC - S2 at 200, 400, 600, and 750°C are 1.7, 2.4, 4.1, and 5 times the strains at room temperature. Likewise, for UHPC - H, at 200, 400, 600, and 750°C, the peak strains are 2.4, 5, 7.6, and 8.6 times the strains at room temperature. The peak strains show that the a ddition of PP fibers slightly increased the ductility in UHPC - H through micro - cracking and additional strain during micro diffusion of pore water [18] . Based on the obtained test results, it can be concluded that there is no significant influence of the rate of heating on mechanical property degradation in UHPC for the two heating rates adopted in this study. This implies that an alternative testing procedure utilizing a lower heating rate of 0.5°C/min can be adopted for the measurement of mechanical properties, omitting the step of pre - drying in the oven. Further, it can be inferred that the addition of 0.11% polypropylene fibers did not deteriorate the high - temperature mechanical properties of UHPC and assisted in preventing fire - induced spalling in UHPC - H specimens as compared to UHPC - S2 specimens. 113 Figure 3 . 23 . Comparison of stress - strain response of UHPC - S2 and UHPC - H following heating rates: (a) 0.5°C/min; (b) 2°C/min. 3.5.2.4. Property Relations Da ta obtained from the aforementioned mechanical property measurements are applied to develop high - temperature property relations which can be used for fire resistance analysis on structural 114 members made of UHPC. Each property is expressed as an empirical re lation over the temperature range of 20 - 750°C for tensile strength, compressive strength, elastic modulus, and stress - strain response. Since the test data revealed that PP fibers do not exhibit significant influence on mechanical properties of UHPC, a sing le set of developed relations is applicable for both types of UHPC (UHPC - S 2 and UHPC - H). These empirical relations are derived through least squares regression analysis in MATLAB on mechanical properties data obtained from test results in this study. For r egression analysis, the line of best fit was calculated considering temperature as an independent variable and the measured material properties as dependent variables. The coefficient of determination, R 2 is the ratio of the sum of the square of error abou t their independent variable and denotes the accuracy of an empirical mathematical relation developed through regression analysis. The evaluated values of R 2 for the developed high - temperature mechanical property equations for UHPC lie between 0.97 and 1, indicating that the proposed equations effectively cT tT ), and elastic modulus (E cT T representing the ratio of measured c t, and E c ). The values of T derived for respective mechanical properties at elevated temperatures are given in the form of equations in Table 3 - 7 fo r UHPC. Table 3 - 7 . Mechanical property relations of UHPC generated utilizing data from tests. Property Relation Temperature range Compressive strength T,compression = - 1.02*10 - 3 *T + 1.02 20°C < T < 750°C Split ting tensile strength T,tensile = - 1.8*10 - 3 *T+1.04 = - 7*10 - 4 *T+0.82 = - 1.4*10 - 3 *T+1.26 20°C < T < 200°C 200°C40%) , whereas , on the other hand, increasing load ratio causes a faster rise in deflections. Further, a higher load ratio also generates load - induced mechanical stresses which accelerate spalling. 220 Figure 5 . 5 . Effect of load ratio on deflection of UHPC beams. 5.3.4.2. Effect of fire scenario UHPC beams subjected to 50% load ratio were analyzed under v arying fire exposure scenarios to study the effect of fire scenario on the ir fire resistance . The investigated fire scenarios are shown in Figure 5 . 2 , and include two standard fire scenarios, namely, ASTM E119 [99] and ASTM E1529 [190] hydrocarbon fire, and three design fire scenarios ; name ly, Design Fire 1 (DF1) , Design Fire 2 (DF2) , and Design Fire 3 (DF3) . The design fires represent fire exposures typically encountered in buildings with varying fuel load and their respective time - temperature curves are calculated as per Eurocode 1 [143] provisions. The cooling phase of the design fires are calculated assuming ventilation - controlled conditions and the cool ing rate is dependent on the duration of the heating phase [181] : ( 5 - 1 ) 221 where T c =temperature ( of fire curve in c ooling phase ; T f,max = peak fire temperature ( attained during heating phase ; t = time in hours ; and DHP = the duration of the heating phase in hours. The thermal response of the analyzed UHPC beams is illustrated by plotting the temperatures at corner re bar and mid - depth in Figure 5 . 6 . In all the analyzed beams, t he temperatures at mid - depth follow a similar trend to that at rebar locations , and temperatures at mid - depth are lower than at corner rebar due to their corresponding distance from fire exposure. The temperature rise in the beam subjected to ASTM E119 was similar to the beam exposed to DF2, as well as the beam subjected to ASTM E1529 was similar to the beam exposed to DF 3. This is because the time - temper ature curves during the heating phase of DF2 and DF3 are the same as the ASTM E119 and ASTM E1529 standard fire exposures, respectively. It can be seen from Figure 5 . 6 that the rate of increase in sectional temperat ures of all the analyzed UHPC beams depends on the temperature rise in time - temperature curves of respective fire exposure scenarios. The beams subjected to ASTM E1529 (hydrocarbon fire) and DF3 have the fastest temperature progression, followed by ASTM E1 19 and DF2, and lastly followed by DF1. D esign fire DF2 has a shorter duration of heating phase than DF1 and lower fire severity than DF3 . T he heat propagation within the beam subjected to DF2 stops when the decay phase starts, and gradually, the rise in s ectional temperatures ceases and starts to decrease. The rebar temperatures in the beam subjected to DF2 remain below the critical temperature limit of 593 [99] . T he critical temperature is defined as the temperature at which the reinforcement loses so much of its strength that it can no longer support the applied load. However, the rebar temperatures in the beams exposed to the standard fire exposures (ASTM E119 an d ASTM E1529) and the other design fires, DF1 and DF 3 reach critical temperature limit of 59 3 , resulting in faster degradation of stiffness and early failure of the beam prior to entering the cooling phase. 222 Figure 5 . 6 . Effect of fire scenario on temperature rise at corner rebar and mid - depth of U HPC beams. In addition, Figure 5 . 6 shows that despite being subjected to the fire exposure of lowest severity i.e. DF1, the corner rebar in this UHPC beam attained the critical temperature limit of 593 can b e attributed to the longer duration of 90 minutes in the heating phase of DF1 followed by a 223 slower cooling rate as compared to the other design fire exposure scenarios which although had higher fire severity, but comprised of shorter heating phase, followe d by faster cooling rate. Therefore, along with the fire severity, the durations of heating phase and subsequent cooling rate are critical for inferring sectional temperatures in UHPC beams. The extent of spalling in the analyzed UHPC beams is shown in Figure 5 . 7 as a function of fire exposure time. The amount of s palling is the lowest (5.35%) for the beam under DF1, due to the lower fire intensity and lower rate of heating in DF1 , which in turn result ed in lower th ermal gradients and slower drying of concrete conducing lower hydro - thermal stresse s in the beam . ASTM E1529 and DF 3 encompass high heating rate s , resulting in the generation of high pore pressure and thermal stresses, leading to higher spalling ( 6.17% ) in the UHPC beams , as compared to the beam subjected to DF1 . However, the fast heating in ASTM E1529 and DF3 leads to excessive microcracking in concrete and releases pore pressure, slightly lowering the extent of spalling in the exposed beams than those exp osed to intermediate fire scenarios of ASTM E119 and DF2 (6.58%) . ASTM E119 and DF 2 comprise a moderate heating rate which is sufficiently high to result in buildup of pore pressure and also, adequately low to hinder the escape of pore pressure by limiting cracking. Therefore, it can be deduced that fire exposure scenarios with intermediate heating rates cause a higher extent of spalling as compared to slow or fast heating . 224 Figure 5 . 7 . Effect of fire scenario on extent of spalling in UHPC beams. To illustrate the comparative structural response of the analyzed UHPC beams under varying fire scenarios, their progression of mid - span deflection with fire exposure time is plotted in Figure 5 . 8 . The beams subjected to fire scenarios with high severity, ASTM E1529 and DF 3 , have the lowest fire resistance (50 min) due to early rebar yielding as a result of rapid rise in rebar temperatures . The beam subjected to ASTM E119 standa rd fire without a cooling phase, failed at 63 min with Although, the amount of spalling under ASTM E119 was slightly higher (6.58%) than that under ASTM E1529 and DF3 (6.17%), the lower fire severity of ASTM E119 in comparison to hydrocarbon fire curves led to higher fire resistance. The rebar in UHPC beam under DF2 also experienced elevated partial recovery of deflection (50%) without failure occurred in this beam . This can be attributed to the presence of cooling phase which lower ed the sectional temperatures and facilitate d partial recovery of strength and stiffness properties . The residual deflection in this beam can be attributed to the unrecoverable residual plastic strain s in concrete and rebars, and transient creep strains in concrete. In addition, loss of cross - section due to spalling (of 6.58%) contributed to irrecoverable 225 deflections in the beam. Under fire scenario DF1, the beam attains high rebar temperature s above 5 because of the prolonged heating phase of 90 min, and fails at 107 min before temperatures start to decrease in the cooling phase. However , the beam experienced lowest spalling (5.35%) under DF1 , which contributed to attainment of the highest fire resi stance among the beams that failed. Therefore, these results infer that fire scenario has significant influence on the fire response of the UHPC beams , wherein the rate of increase in deflection is dependent on the severity and the rate of rise in fire tem peratures. Figure 5 . 8 . Effect of fire scenario on deflection of UHPC beams. 5.3.4.3. Effect of tensile reinforcement ratio To study the effect of tensile reinforcement ratio , which is the ratio of the area of tensio n steel to the effective area of the beam cross - section, on fire resistance of UHPC beams , four different ratios were considered in the range of 0.9% - 1.65%. The sectional dimensions and cover thickness were same across the analyzed beams, and only the numb er and diameter of tensile steel reinforcement 226 was varied as shown in Table 5 - 2 . With the increase in longitudinal reinforcement, the room temperature bending moment capacity of the UHPC beams increase d significantl y, resulting in a 60% increase in capacity over an increase of 0.85% in reinforcement. For exclusively investigating the effect of tensile reinforcement ratio, the load ratio was maintained constant as 50% of the corresponding load carrying capacity at roo m temperature for each beam ( shown in Table 5 - 2 ) . All the analyzed UHPC beams were subjected to ASTM E119 fire exposure. The progression of the mid - span deflection of the studied beams is plotted in Figure 5 . 9 as a function of fire exposure time. From the analysis results, it was found that the effect of tensile reinforcement ratio on fire resistance of UHPC beams was insignificant with negligible variations in thermal, spalli ng, and structural response of the beams. This unaltered response for different ratios of tensile reinforcement is because of the equivalent rate of reduction in capacity due to similar temperature rise in rebars provided with same cover in all the beams. Further, due to the equivalent thermal distribution and load ratio, the level of spalling was uniform across the analyzed beams. 227 Figure 5 . 9 . Effect of tensile reinforcement ratio on deflection of UHPC beams. 5.3.4.4. Effect of cover thickness The effect of concrete clear cover thickness on fire resistance of UHPC beams is investigated by analyzing six beams subjected to ASTM E119 fire exposure and 50% load ratio . For the analysis, t he bottom clear cover thickness to tensile rebar and side (lateral) clear cover thickness to corner rebar is varied in the range of 28 to 4 4 mm as shown in Table 5 - 2 . T he total depth of the beam remain ed unchanged at 270 mm and only the cover thickne ss is varied in this investigation . V arying the bottom cover thickness alters the flexural capacity of the beam due to variation in the moment lever arm. However, th e variation in moment capacity for the analyzed beams with different cover thickness es was within 4%. Thus, all the analyzed beams are subjected to 50% load ratio computed for the reference beam U - B0. Figure 5 . 10 shows the effect of concrete cover thickness on temperature rise in corner rebar of UHPC beam s. It can be clearly seen that with higher concrete cover thickness, either from bottom surface or lateral surface, progression of rebar temperatures is slower . The slower rise in rebar 228 temperatures is due to the resulting increase in distance between the fire exposed surface and tensile rebar , which lowers the ingress of heat to the steel reinforcement. T his variation in temperature propagation minimized with increase in distance from the exposed layers due to low thermal conductivity of concrete. T he temp eratures at concrete mid - depth for the analyzed beams were similar and hence, they are not plotted here. In the analyzed beams, the extent of spalling did not vary with cover thickness as shown in Table 5 - 5 . Fire - in duced spalling of concrete is a local phenomenon and as observed in the fire tests, majority of the spalling occurs in upper compressive zone of the beam, with lower spalling in bottom portion due to cracking in the tensile zone. Therefore, the variation i n cover thickness to tensile reinforcement in the bottom portion of the beam did not alter the extent of spalling. Figure 5 . 10 . Effect of cover thickness on temperature rise at corner rebar in UHPC beams. Fi gure 5 . 11 shows the progression in mid - span deflections of UHPC beams of varying concrete cover thickness . It can be seen from Fi gure 5 . 11 that the increase in deflection is s lower and fire resistance is higher with increasing cover thickness. For instance, the fire resistance increased by 229 20% upon increasing bottom cover thickness from 28 mm to 44 mm and lateral cover thickness from 28 mm to 38 mm. Higher cover thickness redu ces temperature propagation in steel rebars and slows down strength and modulus degradation of reinforcing bars , in turn retarding the reduction in moment capacity and further, slowing down the increase in deflection. Therefore, the analysis results indica te that fire resistance of UHPC beams can be increased by rationally increasing the concrete cover thickness. The variation in bottom cover thickness and side (or lateral) cover thickness had a similar level of impact on fire resistance of UHPC beams. Fi gure 5 . 11 . Effect of cover thickness on deflection of UHPC beams. 5.3.4.5. Effect of concrete type To investigate the effect of concrete type, four RC beams made of NSC, HSC, conventional UHPC with only steel fibers ( UHPC - St), and UHPC with both steel and polypropylene fibers (UHPC - StPP) were analyzed. UHPC - St comprised of 1.5% by volume of steel fibers and UHPC - StPP contained 1.5% by volume of steel fibers and 0.11% by volume of polypropylene fibers. All t he 230 beams we re subjected to the same fire exposure of ASTM E119 and same loading conditions under 50% load ratio . The NSC and HSC beams were designed as per ACI 318 specifications [116] , whereas t he UHPC beams were designed based on the available best practice recommenda tions since no design provisions for UHPC members are currently available in codes and standards [188] . The UHPC beams were provided only tensile reinforcement (no shear and compression reinforcements) to take advantage of its high compressive and high tensile strength . All the beams were designed to have the same bottom and lateral concrete cover thickness and same moment capacity of 70 kN - m . The cross - sectional details of the NSC, HSC, UHPC - StPP, and UHPC - St beams are shown in Figure 5 . 12 . Figure 5 . 12 . Cross - section of the analyzed beams with varying concrete type. Thermal , mechanical , and permeability properties specific to NSC, HSC, UHPC - St , and UHPC - StPP were inputted in the pro gram for the analysis to trace the fire response of beams . Details on material properties corresponding to concrete type can be found in section 4.4.2 . The thermal response of the analyzed beams is compared by pl otting the temperature progression in corner rebar and concrete (at mid - depth) with fire exposure time in Figure 5 . 13 . In all four beams, the temperatures in concrete (at mid - depth) increase d less rapidly than that in corner rebar. This can 231 be attributed to low thermal conductivity and high specific heat of concrete that delays heat penetration to the inner concrete layers. From the comparison of thermal response trends in Figure 5 . 13 , it can be seen that the sectional temperatures in both UHPC - St and UHPC - StPP beams increase at a faster pace as compared to HSC and NSC beams. As shown in Figure 5 . 12 , UHPC - St and UHPC - StPP beams were desi gned to have reduced cross - sectional area to utilize high compressive strength of UHPC [191] . These smaller sectional dimensions contributed to the reduction in thermal mass and utilization of more heat for temperature rise in both UHPC - St and UHPC - StPP beams as compared to beams made of NSC and HSC. Moreover, severe spalling occurred in UHPC and UHPC - StPP beams (see Table 5 - 5 and Figure 5 . 14 ), which led to a loss of concrete section and in tur n resulted in rapid temperature rise. In addition, UHPC has slightly higher thermal conductivity as compared to NSC and HSC, which further resulted in faster progression of sectional temperatures in the UHPC - St and UHPC - StPP beams [118] . Figure 5 . 13 . Effect of concrete type on temperature rise at corner rebar and mid - depth in beams. 232 Figure 5 . 14 sho ws the predicted extent of spalling in the analyzed beams and Figure 5 . 15 shows the pore pressure trends in the beams at 30 mm from the exposed right surface and 60 mm depth from the top surface. Because of high per meability in NSC, much of the vapor is released and only low levels of (pore) pressure build up in the NSC beam . A peak pressure of around 0.7 MPa and no spalling was predicted for NSC beam . Much higher pore pressure develop ed in the HSC and UHPC beams, an d this is attributed to their dense microstructure and lower permeability that hinder the vapor pressure to escape. A peak pore pressure of about 2.2 MPa develop ed in the HSC beam and higher peak pore pressure s of 4.2 MPa and 5.8 MPa develop ed in UHPC - StPP and UHPC - St beams respectively. The extent of spalling in UHPC - StPP beam was lower (5.29%) than that in the UHPC - St beam without polypropylene fibers (6.58%), due to the enhanced permeability and partial dissipation of pore pressure through melting of PP fibers at about 160 °C. The extent of spalling in HSC beam (4.17%) was lower than UHPC beams due to relatively lower permeability, but was much higher than the null amount of spalling in the NSC beam. Figure 5 . 14 . Effect of concrete type on extent of spalling in beams. 233 Figure 5 . 15 . Effect of concrete type on pore pressure in beams. The progression of mid - span deflection in the analyzed beams made of different c oncrete types is plotted in Figure 5 . 16 . UHPC - St and UHPC - StPP beams experienced rapid rise in deflections as compared to a gradual increase in deflection in NSC and HSC beams. This trend can be attributed to the hi gher rebar (and concrete) temperatures in UHPC - St and UHPC - StPP beams and also due to faster degradation of strength and stiffness properties of UHPC at elevated temperatures, as compared to NSC and HSC . Among the two UHPC beams, the UHPC - St beam experienc ed a more rapid increase in deflections due to higher capacity degradation that resulted from the removal of concrete due to severe spalling. In comparison, the rate of deflection increase in UHPC - StPP beam was at a moderate pace as compared to the case of UHPC - St beam without polypropylene fibers . This can be attributed to slower deterioration of stiffness owing to reduced loss of cross - section through spalling mitigation facilitated by the melting of polypropylene fibers present in UHPC - StPP. 234 Furthermore , the deflection - time curves in Figure 5 . 16 show that the mid - span deflection of NSC beam is lower than that of HSC beam throughout the entire duration of fire exposure. The slower progression in deflections in NSC beam than other beams can be attributed to slower degradation of strength and stiffness properties of NSC and negligible extent of spalling, which in turn resulted in lower rebar temperatures. The UHPC - St beam failed in 63 min, while UHPC - StPP beam failed in 74 min. This shows that fire resistance of UHPC beams can be increased by lowering the extent of spalling through the addition of polypropylene fibers to UHPC mix. The UHPC beams (UHPC - St and UHPC - StPP) failed earlier than the NSC and HSC beams due to s evere spalling, thinner cross - sections, and faster deterioration in mechanical properties. The HSC beam failed in 120 min, which is much higher than that of the UHPC beams but less than the NSC beam. The NSC beam had the highest fire resistance (125 min) a mong the four analyzed beams and this can be mainly attributed to minimal spalling and slower degradation of strength properties of NSC . Figure 5 . 16 . Effect of concrete type on deflection in beams. 235 5.3.4.6. Effect o f cross - sectional shape Using beams of thinner sectional shapes other than rectangular is becoming prevalent in structural applications , especially in high rise buildings, due to lower dead load, construction time, material and fabrication costs. At presen t, there is no experimental data on fire response of UHPC beams of different cross - sectional shapes such as I - section and T - section , with leaner web portion . Moreover, majority of the previous tests at room temperature conditions were carried out on rectan gular sections and very few tests have been reported on beams with non - rectangular sections . The efficacy of the developed numerical model for analyzing UHPC beams of different sectional shapes was gauged by comparing model predictions for an I - section be am against test results reported by Hasgul et al. [192] at ambient conditions. The cross - sectional details and loading set - up are shown in Figure 5 . 17 . The s elected test beam was made of UHPC with 1.5% steel fibers by volume and had a compressive strength of 154 MPa and tensile strength of 8.8 MPa. The predicted and measured load - deflection response s of the I - shape beam are compared in Figure 5 . 18 . The figure shows that the predicted load - deflection response follows closely with the measured data and captures the salient points of rebar yielding, strain hardening, peak load, and ultimate load (discussed in 4.4.3 ). Despite the absence of shear and compression reinforcement, the I - beam exhibited strain hardening and ductile response due to the presence of steel fibers. By means of good agreement in the predicted and measured resp onse s , the model is deemed acceptable for evaluating the performance of UHPC beams of different sectional shapes. 236 Figure 5 . 17 .Details of I - shape UHPC beam tested by Hasgul et al. [192] . Figure 5 . 18 . Predicted and measured load - deflection response for I beam. To study the effect of different cross - sectional shapes on fire resistance of UHPC beams, a set of analys e s was carried out on UHPC beams of rectangular, I, and T sectional shapes. The three UHPC beams of different sectional shapes were designed to have the same moment capacity of 136 kN - m. This moment capacity is higher than that of the reference be am UHPC - B0 utilized in other parametric analysis in order to conduct a reasonable comparison with the I - section and T - section beams which were designed following ACI 318 [116] provisions . S imilar to the reference 237 beam UHPC - B0 , the rectangular beam is not provided with any compression or shear reinforcement to fully utilize the strength of UHPC . While there have been a few fire tests on UHPC beams without stirrups having rectangular sections , there have been none on UHPC beams without stirrups h aving non - rectangular sections with thinner stems. Therefore, for evaluating the effect of sectional shape of fire performance of UHPC beams, t he beams with I - section and T - section are reinforced in compression and shear, similar to traditional RC beams. T he cross - sectional details of the analyzed UHPC beams of different shapes are shown in Figure 5 . 19 . The beams were provided with same bottom and lateral cover thickness. Height to width ratio of 1.5 was maintained a cross all beams. All the beams were analyzed under ASTM E 119 standard fire exposure and 50% load ratio. Figure 5 . 19 . Cross - sectional details of UHPC beams of different shapes. 238 Figure 5.19. 239 To assess the influence of specimen shape on the thermal response of UHPC beams of different sectional shapes , the temperatures at corner rebar and concrete mid - depth are plotted in Figure 5 . 20 . In all the beams, the progression in temperatures at corner rebar is faster than temperatures at concrete mid - depth due to the closeness of corner reinforcement to the bottom and side fire exposed surface s . The temperature progression in cor ner rebars is similar in all the beams due to the provision of same cover thickness to tensile reinforcement. However, the temperatures at concrete mid - depth are significantly higher in I - section and T - section beams as compared to rectangular beam. This ca n be attributed to the lower thermal mass resulting from smaller width (135 mm) in I - section and T - section beams, which causes more heat propagation as compared to the width of rectangular beam (190 mm). Figure 5 . 20 . Effect of specimen shape on temperatures at rebar and mid - depth of UHPC beams. All the UHPC beams experienced spalling and the extent of spalling in the analyzed beams is plotted in Figure 5 . 21 as a funct ion of fire exposure time . The amount of spalling was lower in I - section (2%) and T - section beams (3.3%), which was lower than that in rectangular beam, 5.9%. 240 The lower spalling in I and T beams is due to the lower thermal gradients in the slender portion of the beams, wherein moisture migration can readily occur as compared to the wide cross - section of rectangular beam which hinders moisture movement within the beam due to the dense microstructure of UHPC . The rise in mid - span deflections in the analyzed b eams of different sectional shapes is plotted in Figure 5 . 22 . All the beams failed through strength criteria prior to reaching the deflection limit due to rapid degradation of mechanical properties owing to high reb ar temperatures of above 500 the first 45 min of fire exposure. Despite lower extent of spalling, its impact on fire resistance of the slender beams was detrimental . The T - section and I - section UHPC beams under went higher deflections and had lower fire resistance of 55 min and 60 min respectively, as compared to the rectangular UHPC beam which failed later at 66 min. The thinner cross - sections in non - rectangular members specifically in stem region lead to higher heat transmission (as shown in Figure 5 . 20 ) which in turn leads to faster degradation of strength and stiffness properties of concrete and steel , resulting in early failure in contrast to conventional rectangular beam. Figure 5 . 21 . Effect of specimen shape on extent of spalling in UHPC beams. 241 Figure 5 . 22 . Effect of specimen shape on deflections in UHPC beams. 5.3.4.7. Effect of sectional dimensions The influence of sectional dimensions on the fire resistance of UHPC beams is studied by analyzing five UHPC beams of different cross - sectio nal sizes as summarized in Table 5 - 2 , subjected to ASTM E119 fire exposure and 50% of their respective load ratio. The clear cover thickness to tensile reinforcement and reinforcement ratio were maintained constant as 28 mm and 0.09 % respectively, in all the beams in the analysis . A dditionally, every beam was designed to have the same width to depth ratio of 1.5. T he progression of temperatures at corner rebar and mid - depth as a function of fire exposure time is plotted in Figure 5 . 23 . The reb ar temperatures rise at a similar rate in all the beams , which is on expected lines due to the same cover thickness to tensile reinforcement in the analyzed beams. The influence of sectional dimensions can be clearly seen in the trends of temperature rise at mid - span. As the sectional size of the beam increases, heat transmission in the cross - section reduces , due to higher thermal mass provided by larger sections and thus , resulting in significantly lower temperatures at mid - depth . 242 Figure 5 . 23 . Effect of specimen dimensions on temperature rise at corner rebar and mid - depth of UHPC beams. Figure 5 . 24 shows the effect of sectional size on spalling response as a function of fire exposure time. The results indicate that extent of spalling reduces with increasing cross - section of UHPC beam. This can be attributed to the considerably lower temperatures in the concrete layers of the larger sections impeding moisture evaporatio n, migration, and build up of pressure for inducing spalling. Also, degradation of strength properties for resisting spalling - inducing stresses is slower due to lower sectional temperatures in beams with higher sectional size. Figure 5 . 25 shows the deflections of the analyzed beams and it can be seen that the deflections rise at a faster rate for beams with smaller dimensions. While the fire resistance of the beam of size 150 mm x 230 mm is 53 min, the fire resistanc e of the beam of size 360 mm x 540 mm is 96 min. Thus, increasing member size increases the fire resistance of the member (see Table 5 - 5 ) . This is 243 due to slower capacity degradation of the beam owing to lower temper atures within the cross section and lower extent of spalling. Figure 5 . 24 . Effect of specimen dimensions on extent of spalling in UHPC beams. Figure 5 . 25 . Effe ct of specimen dimensions on deflection of UHPC beams. 244 As per ACI 216, the minimum width of RC beam for 1 hour fire rating is specified as 127 mm with minimum cover thickness of 19 mm. However, the fire resistance of the analyzed UHPC beam having dimension s of 150 mm x 230 mm and cover thickness of 28 mm is lower than 1 hour. For comparison, NSC and HSC beams with same sectional dimension s of 150 mm x 230 mm , cover thickness of 28 mm , and same moment capacity of 41 kNm as the UHPC beam were analyzed , and th e progression in deflections with fire exposure time is plotted in Figure 5 . 26 . According to the analysis, the fire resistance of the NSC beam is 97 min and that of HSC beam is 87 min. Unlike the UHPC beam, both NSC and HSC beams can attain fire resistance of greater than 1 hour. Thus, utilizing ACI 216 for the prediction of fire resistance of UHPC beams is not practical and provides unrealistic and unreliable fire ratings. Figure 5 . 26 . D eflection s of beam with dimensions 150 mm x 230 mm made using different concrete types . To determine the optimum minimum cover thickness for UHPC beams with different sectional sizes in order to attain fir e resistance ratings of 1 - 3 hou rs, additional cases are run. Since the fire 245 resistance of UHPC beam with width of 150 mm was lower than 1 hour, the iterations were carried out on the other four beams in Table 5 - 2 having larger sectional sizes. Fr om the analysis, the minimum width and cover thickness for 1 hour rating were found to be 180 mm and 28 mm respectively. The variation of deflection in the typical UHPC beams made using steel fibers (UHPC - St) and also UHPC beams made with both steel and po lypropylene fibers (UHPC - StPP) of varying sectional sizes are plotted in Figure 5 . 27 . The cover thickness was increased from 28 mm to 76 mm with reasonable size increments and the minimum cover thickness was determi ned for the different fire ratings of 1 hour, 1.5 hours, 2 hours, and 3 hours, similar to the ratings provided in ACI 216 for conventional concrete. For minimum width of 180 mm, UHPC - St beam can attain fire rating of 1 hour with cover of 28 mm and UHPC - St PP beam can attain fire rating of 1.5 hours with cover of 44 mm . For minimum width of 240 mm, UHPC - St beam can attain fire rating of 2 hours with concrete cover of 64 mm and UHPC - StPP beam can attain fire rating of 2 hours with a lower cover thickness of 5 1 mm. For minimum width of 270 mm, UHPC - St beam can attain fire rating of 2 hours with concrete cover of 44 mm and UHPC - StPP beam can attain fire rating of 3 hours with a cover thickness of 76 mm. For minimum width of 360 mm, UHPC - St beam can attain fire r ating of 3 hours with concrete cover of 64 mm and UHPC - StPP beam can attain fire rating of 3 hours with a lower cover thickness of 57 mm. As shown in Figure 5 . 27 , UHPC beams with polypropylene fibers could attain hi gher fire resistance than the UHPC beam without polypropylene fibers, due to lower spalling and slower rise in sectional temperatures. Further, as sectional size is increased, higher fire ratings can be attained with a lower increase in cover thickness. 246 Figure 5 . 27 . Deflections of UHPC beams with varying sectional sizes and cover thicknesses. 247 Figure 5.27. 248 5.3.4.8. Effect of span length To study t he effect of varying span length s on the fire respo nse of UHPC beams, four beams with different span lengths of 3.66 m, 5 m, 6.5 m, and 8 m were analyzed under standard ASTM E119 fire exposure and 50% load level. The sectional temperatures and level of spalling at mid - span were similar in all the analyzed beams owing to the same fire exposure and same moment due to structural loading at mid - span. However, rebar temperatures in the portion of the beam between the end support and point load , for the beam with span length of 3.66 m were higher than the other b eams with a greater span length , as shown in Fi gure 5 . 28 . This can be attributed to the fluctuations in level of spalling along the beam length due to varying applied moment associated with varying span length . The predicted spalling at the end of fire exposure along with the lengthwise beam segments together with the applied bending moment is plotted in Figure 5 . 29 for two beams with span lengths of 3.66 m and 8 m. The segme nts close to mid - span of the beam are subjected to higher mechanical stresses due to higher bending moment, which in turn enhances cracking and also increases permeability. The increased permeability results in lower pore pressure and a relatively lower ex tent of spalling. Since the applied moment is same for the analysis, the level of spalling is same for the beams in the mid - portion between the two load - points. The applied moment decreases in the segments away from the mid - span, which in turn results in l ower cracking and lower permeability leading to a higher extent of spalling in these segments. The differences in spalling along the beam length result in differences in the total extent of spalling in the analyzed beams as summarized in Table 5 - 5 . The extent of spalling in the beam with span length of 3.66 m is 6.58%, whereas spalling in the beam with span length of 8 m is 3.92%. Overall, t he extent of spalling is lower in UHPC beams with higher span length. 249 Fi gure 5 . 28 . Effect of span length on corner rebar temperatures at L/5 from support in UHPC beams. Figure 5 . 29 . Effect of span length on extent of spalling in UHPC beams. Figure 5 . 30 shows the mid - span deflections of the analyzed beams with varying span length. It can be seen from the figure that the deflection of all the UHPC beams increases with fire exposure 250 time. However, mid - span deflection increases with an increasing span length of the beams . Deflections are computed in the analysis by integrating curvature which accounts for changes in stiffness along the beam length . With increasing span length, the flexural stiffness reduces (due to higher span to depth ratio) resulting in higher deflections. Further, the fire resistance of UHPC beams as computed based on deflection failure criteria slightly decreases with increasing span length. For instance, fire resistance decrease s from 63 to 61 minutes upon an increas e in span length from 3.66 m to 8 m. Figure 5 . 30 . Effect of span length on deflection of UHPC beams. 5.3.4.9. Effect of loading type To assess the influence of loading type on fire resistance of UHPC beams, the simply supported reference UHPC beam B0 is analyzed under two different loads . The first loading pattern is uniformly distributed load (UDL) of 21 kN/m and the second loading type is two point load s of 25 kN each . Both t he beams were subjected to ASTM E119 standard fire exposure under equal load 251 ratio of 50% of the flexural capacity at room temperature (70 kNm) . S hear force and bending moment diagram s along the span of the beam under both the loading configurations are pl otted in Figure 5 . 31 and Figure 5 . 32 . Pursuant to t he loading type in these two beams , the magnitude of peak bending moment is the same at the critical mid - span section, mean while , the resulting shear force distribution along the length of the beams is different as illustrated in Figure 5 . 31 and Figure 5 . 32 . For the two point loading scenario, a pure bending without any shear is generated between the two loading points, while shear force is non - zero along the entire span length under UDL. However, the level of bending moment is 50% of the moment capacity of the beam s , whereas shear force is much l ower less than 1 5 % of the shear capacity (257 kN) . Hence, in this set of analysis , shear effects are minor and flexure dominates the fire behavior and failure of the analyzed beams. 252 Figure 5 . 31 . Uniformly di stributed loading on UHPC beam. 253 Figure 5 . 32 . Two p oint loading on UHPC beam. As a result of the same fire exposure, beam dimensions, load ratio, and flexure - dominant loading in the two beams, the temperatu re gradient, pore pressure, and stresses were similar. Consequently, the thermal response, extent of spalling, deflections, and fire resistance were similar in the analyzed beams. The progression of mid - span deflection of the beams is shown in Figure 5 . 33 . The deflection response of the beam is computed along the length of the beam and is governed by 254 the level of stresses due to the bending moment in the particular section. For the UHPC beam subjected to UDL, the max imum moment occurs at the mid - span while for the UHPC beam subjected to two point loading, the region between the two point loads experiences maximum levels of bending moment. However, as shown in Figure 5 . 34 , the r esulting bending moment from both the loading patterns are similar with minimal differences. This leads to similar mid - span deflections and fire resistance in the analyzed UHPC beams. The response of UHPC beams under shear dominant loading might be differe nt due to variations in developed stresses in the beam, and further studies are required in the future to characterize this behavior. Figure 5 . 33 . Effect of loading type on deflection of UHPC beams. 255 Figure 5 . 34 . Bending moment along span length of UHPC beams under different loading type. 5.3.4.10. Effect of varying dosage of steel fibers To study the influence of the amount of steel fibers on the fire response of UHPC be ams, UHPC with varying dosage of steel fiber s of 0.75% , 1.5%, 2.25%, and 3% by volume were utilized. Initial strength properties for UHPC with different volume fractions of steel fibers were incorporated as summarized in Table 5 - 3 , based on room temperature material property tests conducted by Wu et al. [168] which implied that t he compressive and tensile strength of UHPC increased with increasing steel fiber dosage. As an illustration, the compressive and tensile strength of UHPC with 0.75% steel fibers are 157 MPa and 5 MPa respectively, whereas for UHPC with 3% steel fibers, compressive strength is 182 MPa and tensile strength is 9.5 MPa. Prelimi nary studies on high - temperature mechanical properties by Zheng et al. [52] have shown that the rate of relative strength degradation with temperature is not inf luenced by the dosage of steel fibers. Therefore, the room temperature mechanical properties were extended to high temperature utilizing the empirical relations developed in section 3.5 of this thesis. It should be noted that there is a lack of 256 data on high - temperature material property variation of UHPC with different amounts of steel fiber. Table 5 - 3 . Effect of varying content of steel fibers on strength of UHPC. Ca se Beam Steel fibers content (% by volume) Room temp. compressive strength f'c (MPa) Room temp. direct tensile strength f't (MPa) 1 UHPC - B29 0.75 157 5 2 UHPC - B0 1.5 175 6 3 UHPC - B30 2.25 178 7.5 4 UHPC - B31 3 182 9.5 All the UHPC beams were subjecte d to ASTM E119 standard fire exposure and 5 0% load ratio of capacity at room temperature. The thermal response of UHPC beams with 0.75%, 1.5%, 2.25%, and 3% of steel fibers by volume , is illustrated in Figure 5 . 35 b y plotting comparative the temperature progression in corner rebar and concrete mid - depth as a function of fire exposure time. The rise in temperatures at mid - depth and rebar occurs at different rates with increasing fire temperatures , with lower temperatu res at concrete mid - depth in all the beams than that in the rebar. This is attributed to the lower thermal conductivity of concrete and location of the rebar being closer to the periphery of the fire exposed surface. It can be observed from Figure 5 . 35 that the rate of rise in temperatures at rebar and mid - depth is slower in the UHPC beam with 3% steel fibers than the other UHPC beams with lower dosage of steel fibers. This can be attributed to the much lower extent of spalling (2.8%) in the UHPC beam with 3% steel fibers as compared to higher amount of spalling (in the range of 5.7 - 7.8%) in the other UHPC beams. The higher temperatures in other beams with lower dosage of steel fiber resulted from loss of concrete du e to fire - induced spalling. Figure 5 . 36 shows the comparative extent of spalling in the analyzed UHPC beams as a function of fire exposure time. It can be seen from the figure that extent of spalling decreases with increase in volume of steel fibers, and this can be attributed to the improved tensile 257 strength of UHPC facilitated by the steel fibers. Due to t he enhanced tensile strength in UHPC with increasing content of steel fiber, the resistance to t he internal ten sile stresses developed from pore pressure, thermal gradients, and mechanical loading is improved and in turn , the extent of spalling is minimized . Figure 5 . 35 . Effect of steel fibers on temperature rise at corner rebar and mid - depth of UHPC beams. Figure 5 . 36 . Effect of steel fibers on extent of spalling in UHPC beams. 258 Figure 5 . 37 shows the comparative variation of mid - span deflection as a function of fire exposure time. In the early stages of fire exposure till 4 0 min , the response of all the UHPC beams with different dosage of steel fibers is similar due to adequate strength and stiffness in the beams for resisting the applied load level of 50% of their capacity at room temperature . Beyond 45 min into fire exposure, the rate of deflection increase in fire - exposed UHPC beams becomes gradual and s lower with increase in steel fiber content. The UHPC beams with higher steel fiber content have higher initial strength than the UHPC beams with lower steel fiber content. Higher initial strength leads to slower degradation of material properties and reduced loss of concrete cross section (due to the lower fire - induced spalling) i n the se beams with higher amount of steel fibers . Thus, relatively lower deflections and higher fire resistance is experienced by UHPC beams with higher steel fiber content. According to the results of this analysis, the fire resistance of UHPC beams can b e increased to 74 min by incorporating 3% by volume steel fibers as compared to fire resistance of 60 min by including 0.75% steel fibers . Figure 5 . 37 . Effect of steel fibers on deflection of UHPC beams. 259 5.3.4.11. Eff ect of varying dosage of polypropylene (PP) fibers To evaluate the influence of varying dosage of polypropylene (PP) fiber s on the fire response of UHPC beams , four UHPC beams with 0%, 0.1%, 0.2%, and 0.3% by volume PP fiber content were analyzed. All the beams were assumed to contain 1.5% by volume of steel fibers. All four beams were loaded with 50% of their room temperature capacity and exposed to ASTM E119 standard fire exposure. The relative increase in permeability due to the melting of PP fiber s at 1 60 is dependent on the fiber dosage amount and is computed in the program according to the fiber percolation theory discussed in section 4.4.2 . Additionally, increasing PP fiber dosage results in lower strength (s ummarized in Table 5 - 2 ) due to lower density and introduction of weaker zones in the concrete matrix. The compressive strength of beams with 0%, 0.1%, 0.2%, and 0.3% PP fibers is 175, 162, 151, and 143 MPa. The effe ct of PP fibers on tensile strength is not significant and ranges from 6 to 5.2 MPa for the considered amounts of PP fiber. Table 5 - 4 . Effect of varying content of polypropylene fibers on strength of UHPC. Cas e Beam Polypropylene fibers content (% by volume) Room temp. compressive strength f'c (MPa) Room temp. direct tensile strength f't (MPa) 1 UHPC - B0 0 175 6 2 UHPC - B32 0.1 162 5.8 3 UHPC - B33 0.2 151 5.5 4 UHPC - B34 0.3 143 5.2 The thermal response of t he four UHPC is compared in Figure 5 . 38 by plotting corner rebar and concrete mid - depth temperatures as a function of fire exposure time. The temperatures of the beam without any PP fibers increased at a faster rate compared to the other beams and this can be attributed to the highest extent of spalling (6.58%) in this beam , as shown in Figure 5 . 39 . Spalling results in loss of concrete cross - section and higher transmission of heat, resulting in higher temperatures. It can be seen that the steel rebar temperatures in the beams with PP fiber are 260 identical since spalling was concentrated at upper portions of the beam due to the release of pore pressure through tensile cracking in the region near tensile reinforcement. The effect of varying PP dosage and corresponding spalling on temperatures can be seen at mid - depth wherein the beam with the lowest amount of PP fiber (0.1%) has a higher temperature rise as compared to beams with 0. 2% and 0.3% of PP fibers. The temperature rise at mid - depth is similar in beams with 0.2% and 0.3% PP fibers due to a similar extent of spalling (below 1%). Figure 5 . 38 . Effect of polypropylene fibers on temp erature rise at corner rebar and mid - depth of UHPC beams. The progression of extent of spalling with fire exposure time is plotted in Figure 5 . 39 . It can be seen that the extent of spalling decreases with increase in PP dosage, and even spalling is completely suppressed upon addition of 0.3% PP fiber. The reduction in extent of spalling with increase in amount of PP fibers can be attributed to higher increase in permeability due to well - connected formation of micro - channels upon melting of PP fiber facilitating dissipation of high 261 pore pressure generated within a concrete member. The variation of pore pressure with fire exposure time for the analyzed beams at 30 mm from the exposed right surface and 60 mm depth from the top surface is plotted in Figure 5 . 40 . It can be observed from Figure 5 . 40 that a peak pore pressure of 5.8 MPa, 4.2 MPa, 3.4 MPa, and 2.6 MPa develops in UHPC beams with 0%, 0.1%, 0.2%, and 0.3% PP fiber respectively. The peak pore pressure decreases gradually with an increase in the amount of PP fibers in the concrete mix due to the resultant increase in permeability. Figure 5 . 39 . Effect of polypropylene fibers on extent of spalling in UHPC beams. 262 Figure 5 . 40 . Effect of polypropylene fibers on pore pressure in UHPC beams. The structural response of the four UHPC beams, with va rying amount of PP fibers, is compared in Figure 5 . 41 , by plotting the variation in mid - span deflection as a function of fire exposure time. Overall, it can be seen that the beam without PP fibers experienced much l arger deflections and failed earlier (at 63 min), than the beams with PP fibers throughout the fire exposure. This can be attributed to faster capacity degradation that resulted from the loss of concrete cross section due to severe spalling in the beam wit hout any PP fibers. The rise in deflections was slower in the beams with PP fibers due to slower degradation of strength and stiffness properties owing to spalling mitigation facilitated by melting of PP fibers. The overall progression of the beams with PP fibers was similar and with the inclusion of 0.1%, 0.2%, and 0.3% of PP fibers, the fire resistance was 73 min, 74 min, and 76 min respectively. The improvement in fire resistance with an increase in fiber dosage was lower in proportion due to a reduction in strength by adding a higher volume of PP fibers. 263 Figure 5 . 41 . Effect of polypropylene fibers on deflection of UHPC beams. 5.3.4.12. Effect of shear reinforcement (and compression bars) UHPC possesses high compress ive and tensile strength, as well as high ultimate tensile strain and ductility, and this can be utilized to realize high shear capacity in UHPC beams. Room temperature studies in the literature have shown that , unlike conventional concrete beams, UHPC bea ms without shear and compression reinforcement exhibit a similar response as beams with stirrups, without reduction in load carrying capacity and ductility [193 195] . However, the removal of stirrups from beams is not recognized by building design codes (ACI 318 [116] ). Moreover, no stud ies have been undertaken at elevated temperatures to gauge the feasibility of removing stirrups from UHPC members. Under shear dominant loading (a s discussed in section 5.3.4.9 ) , the contribution of stirrups and steel fibers in resisting shear forces is critical for determining shear capacity and failure mechanism of UHPC beams. 264 Due to the lack of fire tests on UHPC beams under shear for model validation, the effect of shear reinforcement cannot be investigated i n the current study. In addition, the confinement effect and shear strength provided by stirrups in the beams are not explicitly considered in the developed numerical model. This is because the focus of the thesis is primarily on flexure - dominant loading w ith no shear between the two point loads utilized in the experimental part of the study. Further studies are needed in the future to specifically study the feasibility of removing shear reinforcement in UHPC beams under fire conditions. Table 5 - 5 . Summary of varied parameters and results from parametric study. Varied Parameter Beam Designation Parameter Value Fire Resistance (min) Extent of spalling Load level UHPC - B1 Load level - 30% of room temperature capacit y 87 13.17% UHPC - B2 Load level - 40% of room temperature capacity 76 8.64% UHPC - B0 Load level - 50% of room temperature capacity 63 6.58% UHPC - B3 Load level - 60% of room temperature capacity 55 5.76% UHPC - B4 Load level - 70% of room temperature capacity 4 6 5.76% Fire scenario UHPC - B0 ASTM E119 63 6.58% UHPC - B5 ASTM E1529 (Hydrocarbon) 50 6.17% UHPC - B6 Design Fire 1 107 5.35% UHPC - B7 Design Fire 2 NF 6.58% UHPC - B8 Design Fire 3 50 6.17% Tensile reinforcement ratio UHPC - B0 3 - 63 6.58% Moment capacity - 70 kNm UHPC - B9 3 - 64 6.58% Moment capacity - 91 kNm UHPC - B10 4 - 62 6.58% Moment capacity - 84 kNm UHPC - B11 4 - 63 6.58% Moment capacity - 112 kNm 265 Table 5 - Clear co ver thickness UHPC - B12 Bottom - 28 mm, Side - 28 mm 61 6.58% UHPC - B13 Bottom - 34 mm, Side - 28 mm 63 6.58% UHPC - B14 Bottom - 44 mm, Side - 28 mm 67 6.58% UHPC - B0 Bottom - 28 mm, Side - 38 mm 63 6.58% UHPC - B15 Bottom - 34 mm, Side - 38 mm 67 6.58% UHPC - B16 Bott om - 44 mm, Side - 38 mm 73 6.58% Concrete type UHPC - St - B0 f'c=175 MPa, f't=6 MPa, 63 6.58% k0=1.2x10^ - 18m 2 , 1.5% Steel fibers UHPC - StPP - B17 f'c=161 MPa, f't=5.8 MPa, 74 5.29% k0=1.2x10^ - 18m 2 , 1.5% Steel and 0.11 %PP fibers NSC - B1 f'c=35 MPa, f't=2.7 MPa, 125 0% k0=6.5x10^ - 16m 2 , Plain/ no fibers HSC - B1 f'c=105 MPa, f't=3.6 MPa, 120 4.17% k0=2.0x10^ - 17m 2 , Plain/ no fibers Specimen shape UHPC - B18 Rectangular shape 66 5.96% UHPC - B19 T shape 55 3.29% UHPC - B20 I shape 60 1.88% Sectional dimensions UHPC - B21 150mm x 230mm, 53 7.53% Moment capacity - 41 kNm UHPC - B0 180mm x 270mm, 63 6.58% Moment capacity - 70 kNm UHPC - B22 240mm x 360mm, 74 5.09% Moment capacity - 129 kNm UHPC - B23 270mm x 4 10mm, 80 4.15% Moment capacity - 165 kNm UHPC - B24 360mm x 540mm, 96 3.29% Moment capacity - 379 kNm Span length UHPC - B25 3.66 m 63 6.58% UHPC - B26 5 m 62.5 4.31% UHPC - B0 6.5 m 62 4.04% UHPC - B27 8 m 61 3.92% 266 Table 5 - Loading ty pe UHPC - B28 Uniformly distributed load; Load level - 50% 63 6.58% UHPC - B0 Two - point load; Load level - 50% 63 6.58% Steel vol. fraction UHPC - B29 0.75% vol., f'c=157 MPa, f't=5 MPa 60 7.82% UHPC - B0 1.5% vol., f'c=175 MPa, f't=6 MPa 63 6.58% UHPC - B30 2. 25% vol., f'c=178 MPa, f't=7.5 MPa 71 5.76% UHPC - B31 3% vol., f'c=182 MPa, f't=9.5 MPa 74 2.88% Polypropylene fiber dosage UHPC - B0 0 % vol. PP fiber, f'c=175 MPa, f't= 6 MPa 63 6.58% UHPC - B32 0.1 % vol. PP fiber, f'c=162 MPa,f't=5.8 MPa 73 5.29% UHP C - B33 0.2% vol. PP fiber, f'c=151 MPa,f't=5.5 MPa 74 0.82% UHPC - B34 0.3% vol. PP fiber, f'c=143 MPa,f't=5.2 MPa 76 0% 5.3.5. Summary A macroscopic finite element analysis is applied to quantify the influence of critical factors on the fire response of UHPC be am s . Based on the results presented in this c hapter , the following observations can be drawn on the performance of fire exposed UHPC beams: Fire intensity, load level, cross - sectional dimensions, cover thickness, specimen shape, presence , and dosage of ste el and polypropylene fibers have a significant influence on the fire performance of the UHPC beams , whereas the tensile reinforcement ratio, span length, and type of flexural loading have a minor or no impact on the fire performance of the UHPC beams. Load level has a significant effect on the response of UHPC beams under fire conditions. The fire resistance of UHPC beams can double by reducing the load ratio from 70% to 30% of the room temperature capacity of the beam. However, the extent of spalling in UH PC 267 beams under higher load levels is lower due to the escape of pore pressure resulting from higher cracking in the tensi le zone of the beam . Fire severity has a significant effect on the fire behavior of UHPC beams , wherein a higher intensity fire results in lower fire resistance . Extent of spalling is maximum under moderate fire intensity as lower heating results in slow drying of concrete and higher heating results in the release of pore pressure through thermal cracking. Cross - sectional dimensions have a significant influence on the response of fire exposed UHPC beams ; with larger beam cross - section (higher thermal mass) leading to higher fire resistance and lower extent of spalling. Increasing c over to tensile reinforcement has a beneficial effect on th e fire resistance of UHPC beams. The fire resistance of a UHPC beam can improve by 20% upon increasing bottom cover thickness from 28 mm to 44 mm and lateral cover thickness from 28 mm to 38 mm. The sectional shape has a significant effect on the response of UHPC beams under fire conditions, wherein the sections with thinner web (I - section, T - section) exhibit lower fire resistance than rectangular section s . The addition of 1.5 - 3 % by volume of steel fibers enhances fire resistance of UHPC beams and mitigate s fire - induced spalling through slower degradation of tensile strength in UHPC . Incorporating polypropylene fibers using a dosage in the range of 0.1 - 0.3% by volume to UHPC significantly reduces the extent of fire - induced spalling in UHPC beams and thereby , enhances fire resistance of the beam. 268 CHAPTER 6 6. Design Recommendations 6.1. General Ultra - high performance concrete (UHPC) is designed to outperform conventional normal strength concrete (NSC) and high strength concrete (HSC) , and is therefore optimized to achieve high er strength (dense and compact microstructure) and enhanced durability (i.e. low permeability to decrease corrosion of steel reinforcement) characteristics . Despite outstanding performance at room temperature , studies clearly indicate that UHPC exhibits lower performance under fire conditions , as compared to NSC and HSC. To attain the dense microstructure of UHPC, admixtures , fillers, and additives are added , which contribute to rapid degradation of strength properties at elevated temperatures . In addition , UHPC is highly prone to fire - induced spalling , which leads to the reduction of concrete cross - section, further accelerating the rate of strength and modulus degradation and causing a loss in load bearing capacity. Spalling not only reduces the fire resistance of concrete members, but also complicates fire resistance assessment, making the prediction of thermal response, structural response, and fire resistance of UHPC difficult. Furthermore, fire - induced spalling is affected by several factors and is interdependent on a number of parameters . Despite the adverse effects of fire - induced spalling on the fire response of concrete members , very limited guidelines and recommendations are available on the treatment of spalling in evaluating fire resist ance of concrete members. The current provisions in codes and standards typically assign fire resistance ratings to concrete members as a function of minimum required dimension (width) and concrete cover thickness to steel reinforcement. Moreover , there ar e no specific guidelines in codes and standard s for the fire resistance design of UHPC structural members. This is mainly owing to the lack of information 269 on fire resistance of UHPC members due to only limited data from few fire tests and numerical studies on UHPC members. Likewise, it is not reasonable to develop simplified design methodologies or expressions for evaluating the fire resistance of UHPC members based on the limited amount of available experimental data. Nonetheless, based on the available in formation from the undertaken research, broad guidelines are recommended in this study for minimizing spalling and increasing the fire resistance of UHPC beams . 6.2. Critical factors governing fire performance of UHPC beams T he fire performance of reinforced c oncrete (RC) members is broadly influenced by concrete cover thickness , specimen dimensions, applied load level, fire scenario compressive strength of concrete , transverse reinforcement, presence of fibers , and aggregate type. These factors were identified and widely studied through fire tests and numerical studies in the literature , extensively carried out on beams and columns made of normal strength concrete (NSC) and high strength concrete (HSC). Contrarily , ultra - high performance concrete (UHPC) being a new class of cementitious material, there have been no studies on the quantification of the critical factors influencing the fire performance of UHPC members . Moreover, the fire behavior of UHPC members is different from that of NSC and HSC members due to the following reasons: (i) slender sections are possible for UHPC members due to high tensile strength of UHPC, which results in reduced thermal mass; (ii) lower cover thickness is needed for prevention against corrosion in UHPC members due to high durabi lity characteristics of UHPC, resulting in lower insulation from fire; ( iii ) densely packed microstructure of UHPC increases the tendency of UHPC members to spall; ( iv) faster degradation of mechanical properties with temperature in UHPC as compared to NSC and HSC . These unique characteristics of UHPC members have not been accounted for in previous studies and therefore, the same level of quantification of the influenc ing parameters on the fire performance of RC 270 members made of NSC and HSC cannot be directl y applied for UHPC members. H ence, detailed experimental and analytical studies were undertaken in this thesis . Data from the fire tests, numerical model, and parametric studies presented in this thesis show that the fire performance of UHPC , in general, a nd spalling , in particular, is complex and is dependent on a number of factors. The key factors that influence the occurrence of spalling and eventually fire resistance of UHPC beams are discussed here. Fire scenario Fire severity measured in terms of heat ing rate, intensity ( peak temperatures ) , and duration of fire , significantly influences the fire resistance of RC beams [3,72,73] . A severe fire scenario leads to higher peak temperatures in the member cross - sect ion, resulting in higher degradation of strength in concrete and steel rebars, which in turn decreases fire resistance of the member . UHPC beams are designed to have smaller cross - sections than NSC and HSC beams due to their high strength. As a result of t he smaller size of UHPC beams, rise in sectional temperatures are faster, resulting in poorer fire resistance than conventional NSC and HSC beams. In addition, fire scenarios with faster heating rate can induce spalling in concrete members due to the devel opment of high sectional temperature gradients, that generate high thermal stresses and pore pressure in concrete , which can lead to spalling and consequently, reduce fire resistance in concrete members. This effect is more pronounced in beams made of UHPC due to its high susceptibility to spalling as a result of low permeability and dense microstructure of UHPC , as compared to NSC and HSC. The existing fire provisions in codes and standards are based on standard fire scenarios, which reflect typical build ing fires. Currently, UHPC finds increasing applications in parking structures and bridges, wherein fires tend to be much more rapid, than building fires . Fires in parking structures and bridges are characterized by fast heating rates or high fire intensit ies and such fire exposures can lead to higher spalling and consequently, lower fire resistance of UHPC beams. 271 Therefore, the fire resistance of UHPC beams, based on standard fire exposure, may not be a realistic indication of fire performance. Specimen d imensions Published literature shows that fire resistance of RC beam s increases by enlarging the cross - sectional dimensions. This is because members with larger sectional size experience slower temperature rise owing to larger thermal mass , which slows dow n the rise in sectional temperatures result ing in slower degradation in sectional capacity [73,83,196] . As compare d to NSC and HSC beams, UHPC beams are typically leaner due to their higher load carrying capacity , as a result of high compressive and tensile strength of UHPC . Thus, due to smaller size and lower thermal mass of UHPC beams, higher temperatures develop ac ross the cross - section, resulting in lower fire resistance of UHPC beams as compared to conventional NSC and HSC beams. Increasing the cross - section of UHPC beam decreases the extent of spalling and improves the fire resistance of that beam, due to lower s ectional temperatures through greater mass of concrete. Previous studies have indicated that increasing the sectional dimensions, specifically of HSC members, might increase the risk of spalling as the specimen size is directly related to the amount of mo isture it can contain [73,138,197] . Since the size of UHPC members are smaller than HSC and NSC members, the concern of increase in spalling with increase in size of the member is not envisaged. Further, u pon incorporation of appropriate spalling mitigation measures, the risk of spalling lowers and the fire resistance improves with the increasing size of the RC members. Cover thickness Current fire design codes and standards assign fire resistance ratings to concrete beams (mainly made of NSC) by prescribing a minimum cover thickness to steel reinforcement and a minimum required width [16,134] . The cover thickness specifications for fire resistance are primarily determined based on corrosi on control requirements. Although the design codes do not provide 272 specific concrete cover thickness requirements for fire ratings of HSC beams, previous studies recommend specifying similar cover thickness to reinforcement for HSC beams, as in the case of NSC beams based on corrosion control requirements [73] . In comparison to NSC and HSC, UHPC has significantly improved durability and crack - control properti es which provide higher resistance to corrosion . Therefore, the minimum concrete cover thickness required for corrosion control in UHPC beams may be much lower than NSC and HSC beams, and can be inadequate for satisfying fire resistance requirements in UHP C beams. T he fire resistance of RC beams can be improved by increasing the concrete cover thickness to the tensile steel reinforcement [189] . This is because the temperature rise in steel rebars slows down as the concrete cover thickness increases, which delays the temperature - induced strength deterioration in reinforcement and improves fire resistance of the beam. However, as the thickness of the concrete cover increases, its effect on the rise in rebar temperatures and improvement in fire resistance is somewhat limited. The moment capacity of a n RC beam at room temperature depends on the effective depth which is a function of bott om concrete cover thickness. As a result, increasing the bottom concrete cover thickness reduces the flexural capacity of the beam. Further, increasing bottom cover thickness can also widen the tensile cracks in concrete, which can lead to an increase in h eat propagation to rebars and decrease fire resistance. Consequently, it is not practical to excessively increase the concrete cover thickness without limitation to improve the fire resistance of RC beams [198] . Load level Load level has a significant influence on fire - induced spalling and the resulting fire resistance of RC beams [73,75] . Higher load leve ls reduce the fire resistance of RC beams by inducing early weakening and softening of the constituent materials , resulting in a faster decrease of strength and stiffness of the beam. Th is effect is more pronounced in UHPC beams since the temperature - 273 induced strength degradation is greater in UHPC as compared to that in NSC and HSC. Further , previous studies on NSC and HSC beams show that higher applied loading generates higher mechanical stresses, in addition to stresses arising from thermal gradients and pore pressure, and can exacerbate the extent of spalling in the beam [11,91,197] . However, unlike N SC and HSC beams, the extent of spalling in UHPC beams is mostly lower under higher load levels . This is mainly due to the alleviation of pore pressure resulting from increased concrete permeability and cracking in the tension zone of the beam under higher loads [79,96] . Sectional shape The different cross - sectional shape s , namely, rectangular, T - shape, I - shape , etc. can influence the fire resistance of RC beams . Typically, the beams with non - rectang ular sectional shapes experience faster transmission of heat in the thinner portion s due to reduced thermal mass , which leads to faster degradation in mechanical properties of the constituent materials and consequently, decreases fire resistance of the bea m [199] . Further, the occurrence of even low levels of spalling in a beam section with slender stem s can have a detrimental impact on the fire resistance of that member [3] . The negative impact on fire resistance is even more severe for UHPC beams with thinner stems due to further reduction in sectional size (lower thermal mass) of the beam as c ompared to non - rectangular shape beams made using NSC or HSC. Fiber reinforcement The addition of polypropylene or steel fibers minimizes fire - induced spalling and increases the fire resistance of RC members. The polypropylene fibers present in a concrete member melt around 160°C leading to increased permeability in a concrete section, which in turn facilitates the dissipation of fire - induced vapor pressure [10,69,83] . Th e release of pore pressure helps mitigate fire - induced spalling in concrete members. Addition of st eel fibers to concrete mix helps minimize the extent of spalling by improving tensile strength of concrete, as well as slowing down the rate 274 of degradation in tensile strength with temperature [10,73,75] . Since spalling is not a concern in NSC members, majority of previous studies on strategies for mitigation of spalling were mainly focused on HSC members. Previous research also s uggests the incorporation of hybrid fibers , comprising of both steel and steel fibers, for mitigation of fire - induced spalling in HSC member s [125,200] . The increased tensile strength, together with higher permeability , resulting from the presence of hybrid fibers reduces fire - induced spalling in an HSC member. It is critical to incorporate an optimal amount of steel and polypropylene fibers in the concrete mix to favorably minimize spalling and enhance fire resistance of the memb er. For instance, a ddition of a lesser amount of steel fibers results in lower tensile strength, which could be inadequate to resist tensile stresses for minimizing spalling. On the other hand, overly i ncreasing the amount of steel fibers does not exhibit any considerable increase in tensile strength and can result in fiber balling and non - uniformity in the concrete mix. Similarly, l ower content of polypropylene fiber limits the connectivity of micro - channels after melting of polypropylene fibers, in turn l owering the increase in permeability, and restricting the release of pore pressure for mitigating spalling. Conversely, the a ddition of higher volumes of polypropylene fibers to the concrete mix leads to a substantial reduction in the strength and workabil ity of the mix. In contrast to NSC and HSC, UHPC mixes are typically designed to contain steel fibers for attaining their high tensile strength and ductility. Based on past studies , the recommended fiber content for minimizing spalling in HSC members is 0. 15% of mix volume in the case of polypropylene fibers, and 0.5% of mix volume in the case of steel fibers , [3,73,125] . Based o n the results presented in this thesis, t he optimum fiber content for minimizing spalling in UHPC beams is proposed as 0. 2 % to 0.3% in the case of polypropylene fibers, and about 1.5% to 3% in the case of steel fibers. The optimum dosage of steel and polyp ropylene fibers for UHPC was found to be 275 much different and higher than that for HSC owing to differences in their respective microstructure and characteristic properties. Shear reinforcement Previous high temperature studies on NSC and HSC members, especi ally columns, have shown a positive influence on fire resistance by reducing spacing in lateral reinforcement and modifying tie configuration in columns. Further, a reduction in the extent of late - stage spalling has been reported through improved lateral r einforcement configuration in columns due to the contribution of ties holding the longitudinal rebar in place under fire conditions [201 203] . However, t here is a lack of such comparative data on the fire response of UHPC members with and without lateral reinforcement. Typically, the shear capacity of UHPC beams is high owing to the higher tensile strength of UHPC due to the presence of steel fibers. Recent studies at room temperature have indicated the feasibility of removing shear reinforcement from UHPC beams [113,193,194] . However, the reduced shear capacity by removing stirrups can adversely impact the fire resistance of UHPC beams under certain loading conditions , such as shear - dominant loading. Fur ther studies are needed for quantifying the contribution of shear reinforcement in influencing the fire resistance of fire - exposed UHPC beams. In the meantime, it is conservatively recommended to incorporate shear reinforcement in UHPC beams for applicatio ns in built infrastructure. Batch m ix proportions Two types of aggregates are commonly utilized in conventional concrete batch mixes; carbonate aggregate (predominantly consisting of limestone) and siliceous aggregate (largely comprising quartz). Among the se two aggregate types, carbonate aggregate provides higher fire resistance and better spalling resistance than siliceous aggregate in concrete members . This can be attributed to an endothermic reaction occurring at around 700°C which lowers the rate of he at increase and 276 delays the deterioration of strength in concrete. In general, the fire resistance of HSC columns made with carbonate aggregate concrete is about 10% higher than HSC columns made with siliceous aggregate concrete [10,201] . Usually, to attain its dense microstructure, UHPC batch mixes comprise of only fine aggrega tes (no coarse aggregates) or a controlled amount of coarse aggregates. However, when coarse aggregates are incorporated, it is advantageous to use carbonate aggregate instead of siliceous aggregate based on previous studies. Concrete type ( strength and pe rmeability) The type of concrete, in terms of the magnitude of its compressive strength and permeability, can significantly influence fire - induced spalling and consequently, fire resistance of reinforced concrete ( RC ) structural member s . The concretes util ized currently for construction can be broadly grouped under normal strength concrete (NSC), high strength concrete (HSC), and ultra - high performance concrete (UHPC) based on compressive strength range. Generally, concrete below a compressive strength of 7 0 MPa is referred to as NSC, concrete with compressive strength in the range of 70 to 150 MPa is classified as HSC, while concrete with compressive strength above 150 MPa is designated as UHPC [3,17] . Ho wever, the definitions for classifying concrete into different categories vary in different codes and standards, such as ACI 216.1 classifies concrete as HSC when the compressive strength is above 83 MPa [134] . Higher strength in concretes ( above 70 MPa) is attained through the addition of supplementary cementitious materials and fillers such as silica fume and fly ash to the batch mix. The addition of such fillers reduce s interstitial voids and lowers the permeability of concrete . The permeability of UHPC, HSC, and NSC is in the order of 10 - 18 , 10 - 17 , and 10 - 16 m 2 respectively [67,175] . The low permeability in concrete hinders the release of pore pressure and leads to fire - induced sp alling. The higher the strength, or the associated lower permeability, the higher is the probability of spalling [203] . Further, the loss of strength with temperature is higher for UHPC as compared to 277 NSC and HSC. Results from this thesis have shown that UHPC beams exhibit higher spalling levels and significantly lower fire resistance , than NSC and HSC beams [186] . 6.3. Current provisions for fire design of NSC and HSC beams Provisions for evaluating the fire resistance of reinforced concrete ( RC ) beams are specified in design codes and standards , namely, ACI 216 .1 [98] and Eurocode 2 [16] . The design codes and standards follow a prescriptive approach by specifying the minimum sectional dim ensions and concrete cover thickness for a concrete member to attain a required fire rating. In some cases , limited consideration is given to aggregate type, density , and support (restraint) conditions of a member. The prescriptive provisions are based on standard fire tests, without taking into account critical parameters such as realistic fire scenarios, loading level , and extent of spalling. Moreover, failure is determined based on the temperature attained in the steel reinforcement, without any consider ation to realistic failure criteria based on strength or deflection limits. For instance, ACI 216.1 provides tables for evaluating fire resistance rating for RC beams and columns made of normal strength concrete (NSC) with a compressive strength lower than 83 MPa. Fire rating listings tabulated in ACI 216.1 for NSC beams are shown in Table 6 - 1 . However, ACI 216.1 does not specify any guidelines for beams made using new types of concrete such as HSC or UHPC. Current p rescriptive methods cannot be directly applied for these newer concrete types due to problems such as fire - induced spalling and difference in microstructures. ACI 216.1 only provides some guidelines for mitigating spalling in HSC columns (with compressive strength greater than 83 MPa) , through the provision of ties ( lateral reinforcement) with 135° bends back into the core of the column , instead of the regular 90° bends in columns . 278 Table 6 - 1 . Minimum width an d cover thickness requirements of unrestrained RC beam for achieving fire resistance adopted from ACI 216.1 [98] Minimum width (mm) Minimum cover (mm) 1 hour 1.5 hours 2 hours 3 hours 4 hours 127 19 25 32 - - 178 19 19 19 44 76 254 19 19 19 25 44 Eurocode 2 [16] provides a choice of tabulated data, simplified, or advanced methods for determining the fire resistance of concrete beams . The data in tabulated format provides minimum dimensions and cover thickness to attain desired fire ratings for concrete members based on standard fire tests. For RC beams, the tabulated data is applicable to NSC made with siliceous aggregates. The same tabular data can be used for carbonate aggregate concrete and HSC by altering the required minimum sectional dimensions through specified modification factors. The prescriptive tabulated data only accounts for a limited number of factors influencing fire performance, without any consideration to a number of critical factors such as realistic fire scenarios, loading, spalling, and restraint. The simplified method in E urocode 2 is based on evaluating reduced sectional capacity at a critical section, considering temperature - induced strength reduction factors to evaluate the reduction in capacity of a structural member at a given fire exposure time. When the decreasing se ctional moment capacity reaches below the moment due to applied loading, failure is said to occur. However, the simplified rational design approaches do not fully account for spalling and various failure modes, encountered by structural members under fire conditions . The advanced method in Eurocode 2 involves comprehensive thermal and structural analys es and requires the use of specialized numerical models. Even through advanced methods for evaluating fire resistance, Eurocode 2 does not provide specific gu idelines for accounting fire - induced spalling in the analysis. 279 For addressing spalling, Eurocode 2 states that spalling is unlikely to occur when the moisture content in concrete is lower than 3%. In addition, Eurocode 2 provides some general provisions fo r mitigating spalling in concrete: (i) use of secondary reinforcement mesh with a nominal cover of 15 mm; (ii) use of concrete that does not tend to spall; (iii) limit the maximum content of silica fume to less than 6% by weight of cement; (iv) use protect ive thermal layers; and (v) addition of at least 2kg/m 3 polypropylene fibers in the concrete batch mix. The guidelines in Eurocode 2 are qualitative and do not take into account the critical factors that influence spalling phenomenon, such as permeability and tensile strength of concrete, heating conditions, and level of loading. While fire - induced spalling might occur in all concrete types, UHPC is more susceptible than NSC or HSC, due to its extremely low permeability. T he current fire design codes do not provide any design recommendations for UHPC beams under fire conditions. Further, t he current fire design provisions in codes of practice for NSC and HSC beams cannot be directly used for UHPC beams as they do not rationally account for fire - induced spall ing and temperature - induced strength degradation specific to UHPC. Moreover , these provisions are not applicable for estimating fire resistance under realistic fire scenarios and load conditions. For realistic fire resistance evaluation of UHPC beams, fire tests and numerical studies were undertaken in this thesis. Based on the test data and results from numerical analyses, along with the literature review conducted in Chapter 2, a set of preliminary design guidelines are proposed for mitigating spalling an d enhancing the fire performance of UHPC beams. 6.4. Design r ecommendations for UHPC beams UHPC is highly susceptible to fire - induced spalling due to its lower permeability and dense microstructure. S palling reduces the overall concrete cross - sectional area an d increases heat transmission from fire to steel reinforcement and inner concrete layers, thereby accelerating the 280 rate of strength and modulus deterioration causing additional losses in member capacity. The degradation in mechanical properties in concrete and steel reinforcement, combined with loss of concrete cross section due to spalling, can considerably lower the fire resistance of UHPC beam. Based on experimental and numerical studies carried out in this thesis, as well as reported studies in the lite rature, the following preliminary guidelines and recommendations for enhancing fire resistance and minimizing spalling are proposed . 6.4.1. Guidelines for enhancing the fire resistance of UHPC beams UHPC is a high - performing construction material that offers a nu mber of advantages. However, there are no specific guidelines in codes and standards for the fire resistance design of the UHPC beams. Based on the detailed studies undertaken in this thesis and in the literature , the following are some of the preliminary guidelines that can be implemented for enhancing fire performance of UHPC beams: Although there have been recent studies exploring the feasibility of UHPC beams without stirrups, no data on their fire performance is currently available. Therefore, s tirrups must be provided to improve the fire resistance of UHPC beams through increased levels of confinement , and the spacing of the stirrups should not be lower than those for the conventional reinforced concrete beams . S palling in UHPC beams tends to be more severe in fire scenarios characterized by rapid heating rates or high fire intensities. When UHPC is to be used in structural applications where severe fire conditions (e.g. hydrocarbon fire ) is likely to occur, such as parking garages, bridges , etc. , the fire resistance of UHPC beams should be evaluated by taking into consideration the loss of cross - section due to spalling through advanced analysis approaches . 281 The minimum cross - sectional width and cover thickness for attaining the fire resistance ratings ( under standard fire exposure) in UHPC beams , with and without polypropylene (PP) fibers are listed in Table 6 - 2 . The recommended cover thickness for UHPC beam is higher than the currently required cover thickness f or NSC beam , as per ACI 216.1 . There is no guidance for fire ratings of HSC beams in ACI 216.1. As an illustration, to attain a fire rating of 1.5 hours , the minimum width required for UHPC beam without polypropylene fibers is 240 mm with a cover of 44 mm, and for UHPC beam with polypropylene fibers is 180 mm with a cover of 44 mm , whereas the minimum width required for NSC beams is 127 mm with a 25 mm cover. Table 6 - 2 . Minimum width and cover thickness of UHPC beam for achieving fire resistance . Minimum width (mm) Minimum clear cover (mm) 1 hour 1.5 hours 2 hours 3 hours Steel fibers Steel and PP fiber Steel fibers Steel and PP fiber Steel fibers Steel and PP fiber Steel fibers Steel and PP fiber 180 30 3 0 - 45 - - - - 240 30 30 45 40 65 50 - - 270 30 30 40 30 45 45 - 75 360 30 30 30 30 40 30 65 55 Incorporation of alternate solutions such as the application of available commercial insulations will enhance the fire resistance of UHPC beams by providin g thermal insulation and delaying the rise in sectional temperatures. 6.4.2. Guidelines for minimizing spalling UHPC is highly susceptible to fire - induced spalling because of its very low permeability and extremely dense microstructure. By adopting the following broad design guidelines from research carried out in this thesis and past studies , spalling in UHPC beams can be minimized to a significant extent: 282 Addition of polypropylene fibers, about 0.2% to 0.3% by volume, to UHPC batch mix will reduce spalling in UH PC beams . Steel fibers are typically present in UHPC , and the recommended content of steel fibers by volume for reducing the level of spalling in UHPC beams is 1.5% to 3% . The u se of carbonate aggregate , instead of siliceous aggregate in UHPC batch mix wil l reduce the extent of spalling in UHPC beams . 6.4.3. Guidance for a dvanced analysis The design recommendations are given for the analyzed beam sizes subjected to 50% load level and ASTM E119 standard fire exposure. However, UHPC beams are prone to spalling which is a complex phenomenon and is influenced by numerous parameters. Hence, it is not possible to account for all the influencing parameters through guidelines or simplified approaches . To account for different critical parameters in evaluating fire resistan ce, advanced analysis approaches can be applied . Advanced analysis procedures require significant experience, and results are highly contingent on the level of complexity adopted in the analysis. A dvanced analysis can be carried out using a macroscopic fin ite element approach at incrementing time steps as discussed in Chapter 4 or through the use of commercial finite element (FE) programs such as ANSYS, ABAQUS, etc . The analysis involves the idealization of a UHPC beam into segments and further discretizati on of the mid - section of each segment into a number of elements. Cross - sectional temperature rise in each segment is calculated through heat balance equations. Temperature - dependent thermal properties of concrete, as discussed in section 4.4.2. form the in put of this analysis. Following temperature calculations, pore pressure is calculated in each element by utilizing principles of mechanics and thermodynamics, including the conservation of the mass of liquid 283 water and water vapor. Utilizing the sectional t emperatures, thermal stress is evaluated based on the temperature - dependent thermal expansion coefficient of concrete and thermal gradients . Also, load - induced (mechanical) stress arising from the applied load present on the beam is evaluated through stres s - strain relationships as discussed in section 4.4.2. At each time step, the extent of fire - induced spalling is calculated by taking into consideration the hydro - thermo - mechanical stresses generated due to pore pressure, thermal strains, and structural loa ding. Spalling in concrete elements is evaluated based on a two - step mechanism. As per the first step, the spalling of concrete boundary elements (the first layer of a discretized concrete section close to the fire - exposed surface) will occur if the resul ting tensile stress due to pore pressure build - up exceeds the decreasing tensile strength due to the increase in sectional temperature. As per the second step, when tensile strength is exceeded by pore pressure in any interior element (elements located in layers beneath the first fire - exposed layer i.e. in second, third, fourth layer , and so on), and the resultant tensile stress due to thermal gradient, load and pore pressure in the elements in front of the interior element is higher than the thermally degr aded tensile strength, spalling occurs in those interior and boundary elements. Once spalling occurs in an element, that element is removed from the cross - section , and the reduced cross - section with updated boundary conditions is considered for the subsequ ent time - step . The cross - sectional temperatures from the thermal analysis, together with the updated geometry of the beam from the spalling analysis, are used to evaluate the structural response of the UHPC beams. Time - dependent sectional moment - curvature relations are generated at each beam segment utilizing the temperature - dependent degradation in mechanical properties of concrete and reinforcement. These moment - curvature relations form the basis to trace the response of the UHPC beam in the entire range of loading till collapse under fire conditions. A flowchart showing the 284 steps associated with the fire resistance evaluation of UHPC beam through advanced analysis is presented in Figure 4 . 1 . The analysis is carried out in incrementing time steps until the failure of the beam. A number of response parameters, namely, temperatures, pore pressure, strains, stresses, deflections, and moment capacities, can be generated at each fire exposure time. At each time step, the computed capacity at each segment and deflection in the beam are used to check for failure against predetermined strength and deflection failure limits. The duration to reach the time - step preceding failure is taken as the fire resistance of the beam. The application of an advanced analysis approach for evaluating the fire performance of a typical UHPC beam is illustrated in Appendix C. 6.5. Limitations Although the presented approach can be applied to evaluate the fire resistance of a range of UHPC beams, ther e are certain inherent limitations of the approach, as listed below: The proposed guidelines are for UHPC beams subjected to flexure dominant loading and may not be applicable for beams under shear dominant loading. The proposed guidelines for mitigating s palling and improving fire resistance of UHPC beams is only applicable over a certain range of parameters , shown in Table 6 - 3 . Table 6 - 3 . Range of limits for applicabil ity of proposed guidelines. Parameter Range Load ratio 0.5 Fire scenario ASTM E119 standard Beam width (mm) 180 - 360 Beam width to depth ratio 1.5 Concrete cover thickness (mm) 28 - 76 Concrete aggregate type Limestone/c arbonate The proposed guidelin es are applicable to simply supported UHPC beams only, since the re is not sufficient data on the effect of fire - induced restraint resulting on fire performance . 285 6.6. Summary This c hapter presents guidelines for the fire design of UHPC beams based on results f rom the parametric studies. The following conclusions can be drawn based on the information presented in this c hapter : The fire severity , load level, cover thickness, specimen shape, sectional dimensions, and dosage of steel and polypropylene fibers have a major influence on the fire performance (both spalling and fire resistance) of UHPC beams , while the tensile reinforcement ratio, span length, and type of flexural loading have a marginal impact on the fire performance of UHPC beams. Design recommendation s are proposed to attain practical fire resistance ratings in UHPC beams , upto 3 hours under standard fire exposure . By incorporating proper measures , both at material and structural levels, spalling in UHPC beams can be minimized to a significant extent a nd fire resistance can be enhanced. Advanced analysis procedure is recommended for evaluating fire resistance of UHPC beams, specifically in case of non - conventional slender UHPC sections such as I - beam, T - beam, etc . Through advanced analysis, the behavior of UHPC beams can be simulated with higher accuracy by incorporating influencing factors, such as fire - induced spalling, specific high - temperature properties of concrete and rebars. 286 CHAPTER 7 7. Conclusions 7.1. General Ultra - high performance concrete (UHPC) i s an advanced cementitious material possessing high compressive and tensile strength, improved ductility, and excellent durability characteristics [101,114,204] . These enhanced properties of UHPC result through optimiz ation of the granular mixture with a low water - to binder ratio, hi gh fineness admixtures , and steel fibers [111] . As a result of these improved properties, UHP C can be attractive for building more economic, aesthetic, and long - lasting structures than conven tional concrete structures . Th us, UHPC is finding increasing applications in high - rise buildings, large - span bridges, and special structures. Although , UHPC possesses superior mechanical properties than normal strength concrete (NSC) and high strength conc rete (HSC), UHPC may not exhibit the same level of performance as NSC under fire conditions. Limited studies exist on the response of UHPC members under fire conditions. In addition, there is a lack of data on high - temperature properties specific to differ ent types of UHPC (with and without polypropylene fibers). Also, there is no numerical methodology to predict fire - induced spalling in UHPC members. To overcome these knowledge gaps, t his dissertation presents a comprehensive study on the behavior of UHPC beams under fire conditions. Both experimental and numerical studies were carried out to evaluate the fire resistance of UHPC beams and to quantify the influence of critical factors influencing the fire response . As part of experimental studies, a series o f property tests were carried out to generate data on the variation of thermal and mechanical properties of UHPC as a function of temperature. Data from these tests were utilized to formulate empirical property relations for UHPC over 20 - temperature range. In addition , 287 full - scale fire resistance tests were carried out on four UHPC beams. Data from fire tests w ere utilized to gauge the effect of load level, fire scenario, and presence of polypropylene fibers on the extent of spallin g and fire resistance of UHPC beams. As part of numerical studies, a numerical model, previously developed for normal strength concrete (NSC) and high strength concrete (HSC) beams, was extended to model the response of UHPC beams under realistic fire and loading conditions. This model is based on a macroscopic finite element approach and utilizes time - dependent moment - curvature relationships to trace the response of UHPC beam from pre - loading to failure under fire conditions. The model accounts for high - te mperature properties of constituent materials, various strain components, and fire - induced spalling . Spalling was evaluated by taking into account the stresses generated due to pore pressure, thermal gradients, and structural loading under fire conditions. The validity of the mod e l was established by comparing predicted response parameters with measured data from fire resistance tests carried out as part of the experimental program . The validated numerical model was further applied to conduct a set of param etric studies to quantify the influence of critical factors on the fire response of UHPC beams. Results generated from parametric studies were utilized to develop general design guidelines for mitigating spalling and increasing fire resistance in UHPC beam s. 7.2. Key Findings The following key conclusions can be drawn based on information generated as part of this thesis: 1) Mechanical and spalling - related properties of UHPC at elevated temperatures vary quite different ly from that of normal and high strength con crete . Therefore, prescriptive - based specifications for normal strength concrete (NSC) and high strength concrete (HSC) beams cannot be directly applied to UHPC beams. 288 2) The variation of thermal propert ies with temperature , for plain UHPC , UHPC with only st eel fibers, and UHPC with both steel and polypropylene fibers are very much in the same pattern . The thermal conductivity of UHPC decreases in the 20°C - 400°C range and increases in the 400°C - 7 5 0°C range. The specific heat of UHPC remains almost constant up to about 400°C, and then increases up to 600°C followed by a constant trend in the 600°C - 75 0°C range. UHPC experiences an overall mass loss of about 7% in the 20°C - 750°C range. The thermal expansion of UHPC increases in the 20°C - 900°C range, with the exce ption of thermal shrinkage taking place in the 700°C - 800°C range. T hermal conductivity and thermal expansion are slightly higher in UHPC , whereas specific heat and mass loss are moderately lower in UHPC at elevated temperature s as compared to those in NSC and HSC. 3) The mechanical properties of the two types of UHPC, i.e. UHPC with only steel fibers , and UHPC with both steel and polypropylene fibers exhibit the same trend in mechanical properties throughout the 20°C - 750°C temperature range. The compressive st rength and tensile strength of UHPC degrade at a gradual rate with temperature , retaining about 2 0 % of room temperature compressive and tensile strength s at 750°C. The elastic modulus of UHPC rapidly degrades till 600°C and then, the rate of loss in elasti c modulus slows down in 600 - 750°C, retaining only 5% of the room temperature elastic modulus at 750°C. The degradation of relative strength and modulus properties with temperature is higher in UHPC and HSC , as compared to NSC, due to the higher cement to a ggregate ratio in higher strength concretes, resulting in thermal incompatibilities. Lastly, t here is no significant influence of heating rate on mechanical property degradation in UHPC according to the two heating rates adopted in th e study i.e. 0.5°C/min and 2°C/min. 289 4) UHPC beams with only steel fibers (no polypropylene fibers) are highly susceptible to fire - induced spalling due to their dense microstructure, and lower permeability and exhibits lower fire resistance. Fire - induced spalling in UHPC beams main ly occurs in the upper portion (compression zone) resulting in faster temperature rise in the inner compressive layers of concrete. Addition of polypropylene fibers (along with steel fibers) in UHPC significantly reduces the extent of fire - induced spalling in these beams and this , in turn , enhances the fire resistance of the beam. The extent of spalling is less severe in UHPC beams (with only steel fibers , and with both steel and polypropylene fibers) under higher load levels due to alleviation of pore pres sure resulting from increased cracking in the tension zone of the beam. 5) The proposed macroscopic finite element based model is capable of tracing the response of UHPC beams from pre - cracking stage to collapse under ambient and fire conditions. The model ca n account for fire - induced spalling, concrete permeability variations with temperature , different strain components, high - temperature material properties of concrete and steel reinforcement, and realistic failure criteria. Spalling is modeled through the s tresses arising due to combined effects of thermal gradients, structural loading , and pore pressure generated in concrete section. In the boundary elements, stresses arising from pore pressure can cause spalling , individually . However, in the interior elem ents, stresses due to pore pressure , together with tensile stresses induced in the transverse direction by thermal and mechanical loading , cause spalling. T he level of spalling significantly influences the fire resistance of UHPC beams, and neglecting spal ling can lead to un - conservative fire resistance predictions in certain scenarios. 290 6) The critical factors that have an influence on the fire performance of UHPC beams are load level, fire scenario, cover thickness, specimen shape, sectional dimensions, and d osage of steel and polypropylene fibers. Other factors such as tensile reinforcement ratio, span length, and type of flexural loading have a moderate influence on the fire resistance of UHPC beams. Further, among beams of different concrete types, the fire resistance of UHPC beams was significantly lower due to higher spalling levels resulting from their lower permeability, than NSC and HSC beams, where permeability is relatively higher. 7) T he proposed preliminary guidelines , which include, the addition of p olypropylene fibers and increasing cover thickness and sectional dimensions, are effective in minimizing spalling and improving fire resistance of UHPC beams, in lieu of specific guidelines in codes and standard s for fire design of UHPC beams. 7.3. Research im pact Ultra - high performance concrete is an emerging construction material and exhibits excellent strength and durability characteristics, over conventional concrete. The information developed as part of this research will have a significant impact on the u se of UHPC in building applications. For use in building applications, UHPC members need to satisfy required fire ratings to adhere to building codes. Limited research has shown that UHPC exhibits poor fire performance with faster degradation of properties at elevated temperatures and is highly prone to fire - induced spalling. At present, the required fire resistance ratings of members specified in building codes are assessed through prescriptive rules wherein, fire resistance is determined based on member t hickness and concrete cover thickness to reinforcement. These prescriptive rules were developed based on data from standard fire tests on mostly NSC members and do not account for loading, fire, and spalling 291 effects. Thus, the current design guidelines may not yield realistic fire performance of UHPC members. The studies presented in this thesis ha ve contributed to the fundamental understanding of the behavior of UHPC beams under fire conditions. The effects of critical influencing factors, such as load lev el, fire scenario, presence of polypropylene fibers, and influence of spalling are quantified through experimental and numerical studies. Moreover , the numerical model presented in this study provides an effective alternative to fire resistance tests for e valuating the fire response of UHPC beams. This model can predict spalling at a member level incorporating hydro - thermo - mechanical stresses, and accounts for all critical factors that affect the behavior of UHPC beams under fire conditions, namely , tempera ture - induced property degradation of specific to concrete type , permeability variations due to cracking in concrete, and different failure limit states. T he numerical model is used for undertaking parametric studies to quantify the effects of critical infl uencing factors on the fire resistance of UHPC beams . Further , data from the numerical studies was utilized to develop general design recommendations for improving fire resistance and mitigating fire - induced spalling in UHPC beams . The information develope d as part of this research can promote the use of UHPC in structural applications. 7.4. Recommendations for Future Research This thesis has advanced the state - of - the - art with respect to the fire response of UHPC beams by generating comprehensive data from expe riments as well as results from numerical modeling on the behavior of UHPC beams. However, there is additional scope for further research in this area , and the following are a few of the key recommendations for future research: 292 Further experimental and num erical studies are needed to develop data on fire response of UHPC beams with different configurations , including cross - sectional shape, shear reinforcement ratio, volume fraction and types of fibers , and loading configurations . S palling - related propertie s of UHPC can be refined by measuring permeability, pore pressure, porosity, etc. as a function of temperature in UHPC specimens under different heating, loading, and specimen conditions. Such information on spalling - related properties will help to enhance the capability and confidence level in model predictions. The numerical approach developed in this study for evaluating the fire response of UHPC beams was through macroscopic finite element method . For ease of use in design practice, future studies demo nstrating the implementation of the numerical model using commercial software packages such as ABAQUS, ANSYS, etc. are needed. The proposed fire design guidelines, for UHPC beams in this study, are preliminary and formulated mainly by undertaking parametri c studies. Additional fire tests on a variety of parameters are needed to validate the numerical studies and establish codal provisions for UHPC beams. 293 APPENDI CES 294 APPENDIX A . D esign calculations for UHPC test beams This appendix summarizes the room temp erature design calculations carried out for the UHPC beams tested in this study [205] . ACI 544 [206] p rovisions for fiber - reinforced concrete members were followed for the design calculations . The cross - sectional details and loading configurations of t he UHPC beams are shown in Figure A. 1. The shear force and bending moment diagrams for the beams tested under two - point flexural loading are shown schematically in Figure A. 2. Figure A. 1 . Cross section and loading set up o f UHPC beams (All dimensions are in mm). 295 Figure A. 2 . Schematic of shear force and bending moment diagram for tested UHPC beams. Compressive strength ( ) and elastic modulus ( ) of UHPC were considered to be 160 MPa a nd 41 GPa , respectively, and yield strength ( ) and elastic modulus ( ) of steel reinforcement were considered to be 400 MPa, and 200,000 MPa, respectively. The UHPC mix used in this study comprises 1.5% (by volume) steel fibers with length ( ) o f 13 mm and diameter ( ) of 0.2 mm. The nominal concrete cover to the center of the steel rebar is 35 mm in all the beams. 296 According to ACI 544 , the flexural capacity of a steel fiber reinforced concrete (FRC) section is calculated by design assumptions for equivalent stress block diagrams as shown in Figure A. 3 . Utilizing the equivalent stress blocks for the compressive and tensile regions, the flexural capacity (M n ) of a steel fiber reinforced concrete section with a rectangular cross - section is calcul ated by the following equation: where A s = cross - sectional area of tensile reinforcement; f y = yield strength of steel reinforcement; d=effective depth; h= height of the beam ; b= width of the beam ; a= depth of equival ent compressive stress block ; c = neutral axis depth ; e = distance between the extreme concrete compression fiber to the top of the tensile stress block of fibrous concrete ; and t = the tensile strength of fibrous concrete . Figure A. 3 . Design assumptions for analysis of reinforced concrete beams with steel f ibers . Although, the tensile stress (strength) of concrete is neglected in plain normal strength concrete (NSC), the tensile stress of the concrete of UHPC members (with s teel fibers) is accounted for in the design calculation. The tensile stress of fibrous concrete, t (MPa) is calculated by : 297 where = length of steel fiber ; = diameter of steel fiber ; V = percent by volume of steel fiber ; and be = bond efficiency fact or which varies from 1.0 to 1.2 depending upon fiber characteristics. be of 1. 2 was used in the present study. The tensile stress of fibrous concrete, t dictates the tensile stress block which is located at distance e from the extreme compression fiber and can be calculated as: where s (fibers) = the maximum tensile strain in the fibers and c = the depth of the neutral axis. c ) is 0 .003 5 as per design code ACI 544 [206] . The tensile stress in steel fibers, sf (MPa) is given by: where = the average bond strength of fibers, for 1.5% volume fraction of fibers is considered to be 10.26 according to test results from Yoo et al. [111] . The s (fibers) is calculated as: where E s f = elastic modulus of the steel fibers. The depth of the neutral axis (c) is calculated by tensile and compressive force equilibrium equation of the se ction , which can be written as: where C= 0.85f c ab , wherein f c =compressive strength of UHPC; a=effective depth of the compress ion stress block; and b= width of the beam. The tensile force is computed by accounting for tensile stres ses in steel rebar ( T rb ) and in steel fiber reinforced UHPC (T fc ) : 298 C= 0.85 = 0.85 160 0.65 180 = + ( ) = + ( ) ) = 3 ( 12.7 2 ) 400 + 7.6 180 (270 ) Solving = ; we get = 26.23 Strain in tensile steel can be calculated by interpolation as follows: = ( )× 0.0035 = ( )× 0.0035 = 0.028 > ( i.e. 0.005) Therefore, the assumption of rebar yielding is valid. = 26.23 = 76.22 The longitudinal steel reinforcement spacing, arrangement, and cover were designed as per ACI - 318 requirements for conventional beams [116] . Minimum clear spacing between longitudinal bars is times the maximum diameter of aggregate . UHPC b eam U - B11 was provided with minimum shear reinforcement as per ACI - 318 requirement. = 33.17 kN > 0.3 44 299 Using # 3 stirrups, for providing minimum shear reinforcement: Also, spacing of stirrups, ; = 117.5 mm Therefore, stirrups spacing of 100 mm was selected for beam U - B11. AFGC [2] recommends expressions for calculating shear capacity of UHPC beams, which consider the shear resistance provided by concrete ( conc ) , fibers ( ) , and shear reinforcement ( ) . Since i n the designed beams, either stirrups were not provided or the contribution of stirrups to shear capacity was not accounted for in the design, only the contribution of concrete ( + ) is calculated. = conc + conc = = where b = the width of the beam, d = the effective depth of the beam, f c =compressive strength of UHPC, is the strength reduction factor = 1.5 (for reinforced beams). f = = where is the inclination angle between a diagonal crack and longitudinal direction of the beam (a minimum value of 30º is recomm ended), is the orientation coefficient for general effects, 300 ( ) is the experimental characteristic post - cracking stress for a crack width of , is ultimate crack width. is adopted from tests conducted by Yoo et al. [111] . = f = = 186.2 KN = 74.9 + 186.2= 257.5 kN 301 APPENDIX B . Illustration of condition of beams during fire tests A s ignificant amount of data and a series of pictures and videos were recorded during the fire tests of the UHPC beams. Few a dditional images of the tested beams taken through the furnace viewport at key time intervals are provided in this appendix . Figure B. 1 . Typical UHPC beam just prior to fire exposure. Figure B. 2 . UHPC beam U - B1 with only steel fibers (no polypropylene fibers) after 40 minutes into fire exposure. 302 Figure B. 3 . UHPC beam U - B11 with both s teel and polypropylene fibers after 40 minutes into fire exposure. 303 APPENDIX C. Evaluation of fire performance of a UHPC beam through advanced analysis numerical example This appendix provides a worked example illustrating the application of advanced an alysis for evaluating the fire response of a typical UHPC beam. Th e UHPC beam in this example, has a width of 180 mm , depth of 27 0 m m , and span length of 6 000 mm . The cross - section and elevation of the UHPC beam are shown in Figure C. 1. The compressive str ength , direct tensile strength , elastic modulus, and permeability of UHPC are 175 MPa , 6 MPa , 43 000 M Pa, and 1.2x10 - 18 m 2 , respectively. The tensile reinforcement had a yield strength of 436 MPa, consisting of 3 rebars of 1 6 mm diameter providing a reinforc ement ratio ( t ) of 1.24 % . The nominal concrete cover to the middle of steel reinforcement is 35 mm. The beam is loaded with a uniformly distributed load of 10 kN/m and subjected to ASTM E119 standard fire scenario. Figure C. 1 . Cross - se ction and elevation of UHPC beam used in the illustration for advanced analysis (All dimensions are in mm). 304 Step 1: Discretization of the beam The beam is divided into a number of segments along the length and the mid - section of each beam segment is furth er discretized into a mesh of two - dimensional rectangular elements as shown in Figure C. 2 . Figure C. 2 . Discretization of beam into segments along length and discretization of cross - section into elements. Step 2: Evaluation o f fire temperatures At each time - step , the temperatures due to fire exposure are established from the ASTM E119 standard fire time - temperature relationship, which is plotted in Figure C. 3. Figure C. 3 . Time - temperature curve f or s tandard fire scenario used in the analysis. 305 Step 3: Evaluation of sectional temperatures The three sides of the beam (bottom surface and two sides) are assumed to be exposed to fire temperatures as determined from the previous step, while ambient condi tions prevail on the top surface to simulate the presence of a slab. Cross - sectional temperatures are evaluated through thermal analysis by establishing heat balance for each element in mid - section of each segment along the beam. The predicted temperatures at corner rebar, middle rebar, and mid - depth as a function of time are shown in Figure C. 4. The calculated sectional temperature contours at mid - span after 10 minutes into fire exposure are shown in Figure C. 5. Figure C. 4 . C ross - sectional temperatures as a function of time in the analyzed UHPC beam. 306 Figure C. 5 . Cross - sectional temperature contours at mid - span in the analyzed UHPC beam a fter 10 minutes into fire exposure. Step 4: Evaluation of fi re - induced spalling The evaluation of f ire - induced spalling is based on two - step mechanism and involves calculation of p th ) , me ). The pore pressure in each element is evaluated by applying mass balance equations , along with the principles of thermodynamics, including the conservation of mass of liquid wate r and water vapor. The pore pressure distribution at mid - span after 10 minutes into fire exposure is shown in Figure C. 6. The thermal stress is evaluated utilizing the thermal gradients developed within the cross - section and temperature - dependent thermal e xpansion coefficient of concrete. The thermal gradients induced transverse thermal stress distribution at mid - span after 10 minutes into fire exposure is shown in Figure C. 7. The mechanical stresses in each element are obtained by utilizing the temperatur e - dependent stress - strain relations of concrete corresponding to the mechanical strain computed from the moment - curvature analysis. The mechanical stress distribution in the transverse direction at mid - span after 10 minutes into fire exposure is shown in F igure C. 8. 307 Figure C. 6 . Pore pressure distribution at mid - span in the analyzed UHPC beam after 10 minutes into fire exposure. Figure C. 7 . Cross - sectional thermal stress contours at mid - span in th e analyzed UHPC beam after 10 minutes into fire exposure. 308 Figure C. 8 . Cross - sectional mechanical stress contours at mid - span in the analyzed UHPC beam after 10 minutes into fire exposure. As per the first step of the spalling mechanism, the concrete boundary elements (located in the first layer of a discretized concrete section close to the fire - exposed surface) will spall if the resulting tensile stress due to pore pressure build - up exceeds the decreasing tensile strength due to the rise in sectional temperature. As per the second step of the mechanism, when tensile strength is exceeded by pore pressure in any interior element (located in layers beneath the first layer closest to the fire i.e. second, third, fourth layer , and so on) , and the resultant tensile stress due to thermal gradient, load and pore pressure in the elements in front of the interior element is higher than the thermally degraded tensile strength, spalling occurs in those interior and boundary elements. At ea ch time increment, based on the spalling mechanism, the spalled elements (area) are removed from the cross - section, and the remaining cross - section. The evaluated extent of spalling as a function of fire exposure time for the analyzed UHPC beams is shown i n Figure C. 9. 309 Figure C. 9 . Extent of spalling as a function of time in the analyzed UHPC beam. Step 5: Calculation of moment - curvature relations Using the temperature - dependent mechanical properties of constituent materials, namely, concrete and steel reinforcement, a moment - curvature relation is generated , through an iterative process, for each segment at various time steps. The calculated moment - curvature curves for the mid - span of the analyzed UHPC beam are shown in Figure C. 10 at various time steps. Figure C. 10 . Moment curvature curves at various fire exposure times for the analyzed UHPC beam. 310 Step 6: Calculation of moment capacity and deflection of the beam The maximum value of the moment in the moment - curvature relations determines the moment capacity of each segment of the beam at each time step , as shown in Figure C. 11 . The mid - span deflection of the beam is calculated using the moment - area method and is plotted in Figure C. 12 as a functio n of fire exposure time. Figure C. 11 . Variation of moment capacity for the analyzed UHPC beam as a function of fire exposure time. 311 Figure C. 12 . Variation of deflection for the analyzed UHPC bea m as a function of fire exposure time. Step 7: Calculation of fire resistance of the beam The moment capacity and deflection of the UHPC beam computed in the previous step are utilized to check the failure of the beam. At each time increment, each segmen t of the beam is checked to see if the moment capacity or deflection has exceeded the limiting criterion. The analyzed UHPC beam failed at 65 minutes according to both the strength and deflection criteria. 312 APPENDIX D. Material properties at elevat ed temperatures This appendix provides a summary of high temperature material property relationships used in the numerical model and parametric studies for concrete (normal strength concrete (NSC), high strength concrete (HSC), and ultra - high performance concrete (UHPC)) and steel reinforcement. D.1. Normal Strength Concrete The equations presented in this section have been reproduced from ASCE manual [22] . D.1.1. Thermal Capacity For carbonate aggregate concrete , c T = 2.566 x 10 6 20 (0.1765T 68.034) x 10 6 400 ( - 0.05043T + 25.00671) x 10 6 410 2.566 x 10 6 445 (0.01603T 5.44881) x 10 6 500 (0.005T 100.90225) x 10 6 635 ( - 0.22103T 176.07343) x 10 6 715 2.566 x 10 6 785 D.1.2. Thermal Conductivity For carbonate aggregate concrete , k cT = 1.355 20 - 0.001241T + 1.7162 293 D.1.3. Thermal Strain th = [ 0.004 (T 2 - 400) +6 (T - 20) ] x 10 - 6 313 D.1.4. Stress - strain Relationships D.2. High Strength Concrete The equations presented in this section have been reproduced from Kodur et al. [41] . D. 2 .1. Thermal Capacity For carbonate aggregate concrete, cT = 2.45 x 10 6 20 (0.026T 12.85) x 10 6 400 (0.0143T - 6.295) x 10 6 475 (0.1894T 120.11) x 10 6 650 ( - 0.263 212.4) x 10 6 735 2x 10 6 800 D. 2 .2. Thermal Conductivity For carbonate aggregate concrete, k cT = 0.85(2 - 0.0013T) 20 300 0.85(2.21 - 0.002T) 300 D. 2 .3. Thermal Strain th = [ 0.004 (T 2 - 400) +6 (T - 20) ] x 10 - 6 314 D. 2 .4. Stress - strain Relationships D.3. Ultra High Performance Concrete The equations presented in this section are based on experiments carried out in this thesis. The therm al properties are proposed by Kodur et al. [118] and the mechanical properties are proposed by Banerji and Kodur [165] . D.3.1. Specific Heat cT = 2x10 - 6 T 2 +0.0013T+1.6918 20 °C 300 °C - 0.0046T+3.6677 300 °C 400 °C 0.0054T - 0.3217 400 °C 600 °C 0.0006T+2.5588 600 °C 700 °C D.3.2. Thermal Conductivity k cT = - 0.0092T+3.1136 20 °C 100 °C - 0.0035T+2.5802 100 °C 400 °C 0.0021T+0.3481 400 °C 500 °C - 10 - 5 T 2 +0.0111T - 1.6565 500 °C 700 °C 315 D. 3 .3. Thermal Strain th = 2x10 - 6 T 2 +0.0002T +0.0014 20 °C 600 °C - 1.443x10 - 5 T 2 +0.0188T - 5.2031 600 °C 800 °C 0.0037T - 2.342 800 °C 900 °C D. 3 .4. Strength Degradation The following equations provide reduction factors of compressive strength, elastic modulus, tensile strength and peak strain at elevated temperatures. T,compression = - 1.02*10 - 3 *T + 1.02 T,modulus = 1.42*10 - 6 *T 2 - 2.4*10 - 3 *T+1 .05 max,T = 2.7*10 - 8 *T 3 - 2*10 - 5 *T 2 +8.1*10 - 3 *T+ 0.85 T,tensile = 2x10 - 6 T 2 +0.0002T +0.0014 20 °C 600 °C - 1.443x10 - 5 T 2 +0.0188T - 5.2031 600 °C 800 °C 0.0037T - 2.342 800 °C 900 °C D.3.5. Stress - strain Relationships 316 D.4. Reinforcing Steel D.4.1. Thermal strain The equations presented in this section have been reproduced from Eurocode 2 [16] . ths = 1.2x10 - 5 T + 0.4x10 - 8 T 2 - 2.416x10 - 4 20 1.1 x 10 - 2 750 2x10 - 5 T 6.2x10 - 3 860 D.4.2. Stress - strain relationship The stress - strain relationships have been adopted from Shakya and Kodur [162] . The strength and modulus degradation have been reproduced from Eurocode 2 [16] . 317 Table D - 1 . Values for the Main Parameters of the Stress - strain Relationships of Reinforcing Steel at Elevated Temperatures (Eurocode 2). Steel Temperature T f yT / f y E sT / E s 20 1 1 1 00 1 1 200 1 0.9 300 1 0.8 400 1 0.7 500 0.78 0.6 600 0.47 0.31 700 0.23 0.13 800 0.11 0.09 900 0.06 0.0675 1000 0.04 0.045 1100 0.02 0.0225 1200 0 0 fy and Es are yield strength and modulus of elasticity at room temperature 318 REFERENCES 319 REFERE NCES [1] JSCE. Recommendations for design and construction of ultra - high strength fiber reinforced concrete structures 2004. [2] AFGC/SETRA. Ultra high performance fibre - reinfo rced concretes. French Civil Engineering Association, Bagneux, France n.d.;2002. [3] Kodur V, Naser M. Structural fire engineering. McGraw Hill Professional London; 2020. [4] Harmathy TZ. Fire safety design and concrete. Harlow, U.K.: Longman; 1993. [5] Ba zant ZP, Thonguthai W. Pore pressure and drying of concrete at high temperature. ASCE J Eng Mech Div 1978;104:1059 79. [6] Peng SW, Qin QH, Cheng SM, Chen GQ. Exact solution of coupled heat and mass transfer w the fick and darcy laws. International Journal of Energy Research 1992;16:401 11. https://doi.org/10.1002/er.4440160507. [7] Bazant ZP. Analysis of Pore Pressure, Ther mal Stress and Fracture in Rapidly Heated Concrete. International Workshop on Fire Performance of High - Strength Concrete. Proceedings. Appendix B: Workshop Papers. B10, Gaithersburg, MD: NIST; 1997, p. 155 64. [8] Anderberg Y. Spalling phenomenon of HPC an d OC. NIST SP 919, Gaithersburg, MD: NIST; 1997, p. 69 75. [9] Ulm F - heated concrete. Journal of Engineering Mechanics 1999;125:272 82. https://doi.org/10.1061/(ASCE)0733 - 9399(1999)125:3(272). [10] Kodur V. K. R., Cheng Fu - Ping, Wang Tien - Chih, Sultan M. A. Effect of Strength and Fiber Reinforcement on Fire Resistance of High - Strength Concrete Columns. Journal of Structural Engineering 2003;129:253 9. https://doi.org/10.1061/(ASCE)0733 - 9445(2003)129:2(253). [11] Dwaikat MB, Kodur VKR. Response of restrained concrete beams under design fire exposure. Journal of Structural Engineering 2009;135:1408 17. https://doi.org/10.1061/(ASCE)ST.1943 - 541X.0000058. [12] Phan LT, Carino NJ. Fire performance of high strength concrete: research needs. A dvanced Technology in Structural Engineering, 2000, p. 1 8. 320 [13] Kodur VKR, Wang TC, Cheng FP. Predicting the fire resistance behaviour of high strength concrete columns. Cement and Concrete Composites 2004;26:141 53. https://doi.org/10.1016/S0958 - 9465(03) 00089 - 1. [14] Felicetti R, Gambarova PG, Meda A. Residual behavior of steel rebars and R/C sections after a fire. Construction and Building Materials 2009;23:3546 55. https://doi.org/10.1016/j.conbuildmat.2009.06.050. [15] LaMalva KJ. Structural fire engin eering, American Society of Civil Engineers; 2018. [16] EN 1992 - 1 - 2. Eurocode 2: Design of concrete structures - Part 1 - 2: General rules - structural fire design. CEN, Brussels: 2004. [17] Kodur V. Properties of Concrete at Elevated Temperatures. ISRN Civil En gineering 2014. https://doi.org/10.1155/2014/468510. [18] Khaliq W, Kodur V. High Temperature Mechanical Properties of High - Strength Fly Ash Concrete with and without Fibers. ACI Materials Journal 2012;109. [19] Shin K - Y, Kim S - B, Kim J - H, Chung M, Jung P - S. Thermo - physical properties and transient heat transfer of concrete at elevated temperatures. Nuclear Engineering and Design 2002;212:233 41. [20] Kodur VKR, Sultan MA. Effect of temperature on thermal properties of high - strength concrete. Journal of Mat erials in Civil Engineering 2003;15:101 7. [21] Kodur V, Khaliq W. Effect of temperature on thermal properties of different types of high - strength concrete. Journal of Materials in Civil Engineering 2011;23:793 801. [22] Lie TT. Structural fire protection, American Society of Civil Engineers; 1992. [23] Kodur VKR, Harmathy TZ. SFPE Handbook of Fire Protection Engineering. Properties of Building Materials, Section 1 2002. [24] eight concrete exposed to high temperature. Fire and Materials 2013;37:200 16. [25] Kodur VK, Banerji S, Solhmirzaei R. Test methods for characterizing concrete properties at elevated temperature. Fire and Materials 2020;44:381 95. [26] ASTM C177 - 19: Stand ard test method for steady - state heat flux measurements and thermal transmission properties by means of the guarded - hot - plate apparatus. ASTM International, West Conshohocken, PA n.d.;2019. 321 [27] ASTM C1363 - 19: Standard test method for thermal performance o f building materials and envelope assemblies by means of a hot box apparatus. ASTM International, West Conshohocken, PA n.d.;2019. [28] ISO 8302: 1991 - Thermal insulation Determination of steady - state thermal resistance and related properties Guarded ho t plate apparatus. Switzerland, Geneva 1991. [29] ISO - ISO 22007 - 2:2015 - Plastics Determination of thermal conductivity and thermal diffusivity Part 2: Transient plane heat source (hot disc) method n.d. https://www.iso.org/standard/61190.html (access ed June 15, 2020). [30] ASTM E1269 - 11(2018): Standard test method for determining specific heat capacity by differential scanning calorimetry. ASTM International, West Conshohocken, PA n.d.;2018. [31] ISO 11357 - 4:2014 - Plastics Differential scanning ca lorimetry (DSC) Part 4: Determination of specific heat capacity. Switzerland, Geneva n.d.;2014. [32] ASTM E831. Standard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis. West Conshohocken, PA: ASTM International; 2014. https://doi.org/10.1520/E0831 - 14. [33] ISO 11359 - 2:1999 - Plastics Thermomechanical analysis (TMA) Part 2: Determination of coefficient of linear thermal expansion and glass transition temperature. Switzerland, Geneva n.d.;1999. [34] ASTM E1131 - 20, Standard test method for compositional analysis by thermogravimetry. ASTM International, West Conshohocken, PA n.d.;2020. [35] ISO 11358 - 1:2014 - Plastics Thermogravimetry (TG) of polymers Part 1: General principles. Switzerland, Geneva n.d.;2014. [36] Kodur VKR, Dwaikat MMS, Dwaikat MB. High - Temperature Properties of Concrete for Fire Resistance Modeling of Structures. MJ 2008;105:517 27. https://doi.org/10.14359/19982. [37] Ju Y, Liu H, Liu J, Tian K, Wei S, Hao S. Investigation on thermophysical prope rties of reactive powder concrete. Science China Technological Sciences 2011;54:3382 403. [38] Zheng W, Luo B, Wang Y. Stress strain relationship of steel - fibre reinforced reactive powder concrete at elevated temperatures. Mater Struct 2015;48:2299 314. ht tps://doi.org/10.1617/s11527 - 014 - 0312 - 9. [39] Sanchayan S, Foster SJ. High temperature behaviour of hybrid steel PVA fibre reinforced reactive powder concrete. Mater Struct 2016;49:769 82. https://doi.org/10.1617/s11527 - 015 - 0537 - 2. 322 [40] AFGC/SETRA. Ultra h igh performance fibre - reinforced concretes 2002. [41] Cheng F - P, Kodur VKR, Wang T - C. Stress - Strain Curves for High Strength Concrete at Elevated Temperatures. J Mater Civ Eng 2004;16:84 90. https://doi.org/10.1061/(ASCE)0899 - 1561(2004)16:1(84). [42] Khali q W, Kodur VKR. Effect of High Temperature on Tensile Strength of Different Types of High - Strength Concrete. ACI Materials Journal 2011;108. [43] ASTM C39/C39M - 18: Standard test method for compressive strength of cylindrical concrete specimens. ASTM Intern ational, West Conshohocken, PA n.d.;2018. [44] ASTM C496/C496M - 17: Standard test method for splitting tensile strength of cylindrical concrete specimens. ASTM International, West Conshohocken, PA n.d.;2017. [45] RILEM TC 129 MHT. Test methods for mechanica l properties of concrete at high temperatures n.d.;1995. [46] concrete in compression. ASTM International, West Conshohocken, PA n.d.;2014. [47] ASTM C78 / C78M - 18: S tandard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third - Point Loading). ASTM International, West Conshohocken, PA n.d.;2018. [48] ASTM C1583 / C1583M - 20: Standard Test Method for Tensile Strength of Concrete Surfaces and the B ond Strength or Tensile Strength of Concrete Repair and Overlay Materials by Direct Tension (Pull - off Method). ASTM International, West Conshohocken, PA n.d.;2020. [49] Tai Y - S, Pan H - H, Kung Y - N. Mechanical properties of steel fiber reinforced reactive po wder concrete following exposure to high temperature reaching 800 C. Nuclear Engineering and Design 2011;241:2416 24. [50] Zheng W, Luo B, Wang Y. Compressive and tensile properties of reactive powder concrete with steel fibres at elevated temperatures. Co nstruction and Building Materials 2013;41:844 51. https://doi.org/10.1016/j.conbuildmat.2012.12.066. [51] Zheng W, Li H, Wang Y. Compressive behaviour of hybrid fiber - reinforced reactive powder concrete after high temperature. Materials & Design 2012;41:40 3 9. https://doi.org/10.1016/j.matdes.2012.05.026. [52] Zheng W, Li H, Wang Y. Compressive stress strain relationship of steel fiber - reinforced reactive powder concrete after exposure to elevated temperatures. Construction and Building Materials 2012;35:93 1 40. https://doi.org/10.1016/j.conbuildmat.2012.05.031. 323 [53] Li H, Liu G. Tensile Properties of Hybrid Fiber - Reinforced Reactive Powder Concrete After Exposure to Elevated Temperatures. Int J Concr Struct Mater 2016;10:29 37. https://doi.org/10.1007/s4006 9 - 016 - 0125 - z. [54] Abid M, Hou X, Zheng W, Hussain RR. Effect of Fibers on High - Temperature Mechanical Behavior and Microstructure of Reactive Powder Concrete. Materials 2019;12:329. https://doi.org/10.3390/ma12020329. [55] Zeiml M, Lackner R, Leithner D, Eberhardsteiner J. Identification of residual gas - transport properties of concrete subjected to high temperatures. Cement and Concrete Research 2008;38:699 716. https://doi.org/10.1016/j.cemconres.2008.01.005. [56] Noumowe AN, Siddique R, Debicki G. Permea bility of high - performance concrete subjected to elevated temperature (600°C). Construction and Building Materials 2009;23:1855 61. https://doi.org/10.1016/j.conbuildmat.2008.09.023. [57] Kalifa P, Chene G, Galle C. High - temperature behaviour of HPC with p olypropylene fibres From spalling to microstructure. Cement and Concrete Research 2001:13. [58] Liu X, Ye G, De Schutter G, Yuan Y, Taerwe L. On the mechanism of polypropylene fibres in preventing fire spalling in self - compacting and high - performance cemen t paste. Cement and Concrete Research 2008;38:487 99. https://doi.org/10.1016/j.cemconres.2007.11.010. [59] and with polypropylene fibers at elevated temperatures using a new test setup. Cement and Concrete Research 2013;53:104 11. https://doi.org/10.1016/j.cemconres.2013.06.005. [60] ASTM C1202 - Resist Chloride Ion Penetration. ASTM Internation al, West Conshohocken, PA n.d.;2019. [61] Kim H, Lee C - J, Shon C - S, Moon H, Chung C - W. Mechanical performance and chloride ion penetration of polyolefin fiber reinforced concrete designed for shotcreting at marine environment. Journal of Structural Integri ty and Maintenance 2020;5:8 17. https://doi.org/10.1080/24705314.2019.1692164. [62] ASTM C1585 - 20: Standard Test Method for Measurement of Rate of Absorption of Water by Hydraulic - Cement Concretes. ASTM International, West Conshohocken, PA n.d.;2020. [63 ] RILEM TC 116 - PCD. Permeability of Concrete as a Criterion of its Durability. Recommendations 2009. [64] Klinkenberg LJ. The permeability of porous media to liquids and gases. Drilling and production practice, American Petroleum Institute; 1941. 324 [65] ASTM C642 - 13: Standard Test Method for Density, Absorption, and Voids in Hardened Concrete. ASTM International, West Conshohocken, PA n.d.;2013. [66] RILEM 049 - TFR. Testing methods for fibre reinforced cement - based composites 1984. [67] Li Y, Tan KH, Yang E - H. Influence of aggregate size and inclusion of polypropylene and steel fibers on the hot permeability of ultra - high performance concrete (UHPC) at elevated temperature. Construction and Building Materials 2018;169:629 37. https://doi.org/10.1016/j.conbuil dmat.2018.01.105. [68] Poon C - S, Azhar S, Anson M, Wong Y - L. Comparison of the strength and durability performance of normal - and high - strength pozzolanic concretes at elevated temperatures. Cement and Concrete Research 2001;31:1291 300. https://doi.org/10 .1016/S0008 - 8846(01)00580 - 4. [69] Yermak N, Pliya P, Beaucour A - L, Simon A, Noumowé A. Influence of steel and/or polypropylene fibres on the behaviour of concrete at high temperature: Spalling, transfer and mechanical properties. Construction and Building Materials 2017;132:240 50. https://doi.org/10.1016/j.conbuildmat.2016.11.120. [70] Li Y, Pimienta P, Pinoteau N, Tan KH. Effect of aggregate size and inclusion of polypropylene and steel fibers on explosive spalling and pore pressure in ultra - high - performa nce concrete (UHPC) at elevated temperature. Cement and Concrete Composites 2019;99:62 71. https://doi.org/10.1016/j.cemconcomp.2019.02.016. [71] Felicetti R, Lo Monte F, Pimienta P. A new test method to study the influence of pore pressure on fracture beh aviour of concrete during heating. Cement and Concrete Research 2017;94:13 23. https://doi.org/10.1016/j.cemconres.2017.01.002. [72] Kodur VKR. Guidelines for fire resistance design of high - strength concrete columns. Journal of Fire Protection Engineering 2005;15:93 106. https://doi.org/10.1177/1042391505047740. [73] Kodur VK. Innovative strategies for enhancing fire performance of high - strength concrete structures. Advances in Structural Engineering 2018;21:1723 32. https://doi.org/10.1177/1369433218754335 . [74] Shah AH, Sharma UK. Fire resistance and spalling performance of confined concrete columns. Construction and Building Materials 2017;156:161 74. https://doi.org/10.1016/j.conbuildmat.2017.08.167. [75] Ali F, Nadjai A, Silcock G, Abu - Tair A. Outcomes of a major research on fire resistance of concrete columns. Fire Safety Journal 2004;39:433 45. [76] Franssen J - M, Dotreppe J - C. Fire Tests and Calculation Methods for Circular Concrete Columns. Fire Technology 2003;39:89 97. https://doi.org/10.1023/A:1021 783311892. 325 [77] Choi EG, Shin YS. The structural behavior and simplified thermal analysis of normal - strength and high - strength concrete beams under fire. Engineering Structures 2011;33:1123 32. [78] Lee J - H, Sohn Y - S, Lee S - H. Fire resistance of hybrid fib re - reinforced, ultra - high - strength concrete columns with compressive strength from 120 to 200 MPa. Magazine of Concrete Research 2012;64:539 50. [79] Kahanji C, Ali F, Nadjai A. Explosive spalling of ultra - high performance fibre reinforced concrete beams u nder fire. Journal of Structural Fire Engineering 2016;7:328 48. [80] Hou X, Ren P, Rong Q, Zheng W, Zhan Y. Effect of fire insulation on fire resistance of hybrid - fiber reinforced reactive powder concrete beams. Composite Structures 2019;209:219 32. https ://doi.org/10.1016/j.compstruct.2018.10.073. [81] Mai V - C, Nguyen T - C, Dao C - B. Numerical simulation of ultra - high - performance fiber - reinforced concrete frame structure under fire action. Asian J Civ Eng 2020;21:797 804. https://doi.org/10.1007/s42107 - 020 - 00240 - 4. [82] Ren P, Hou X, Rong Q, Zheng W. Quantifying Fire Insulation Effects on the Fire Response of Hybrid - Fiber Reinforced Reactive Powder Concrete Beams. Fire Technol 2019. https://doi.org/10.1007/s10694 - 019 - 00937 - 2. [83] Kodur VKR. Spalling in high strength concrete exposed to fire: concerns, causes, critical parameters and cures. Advanced Technology in Structural Engineering, Philadelphia, Pennsylvania, United States: ASCE; 2000, p. 1 9. https://doi.org/10.1061/40492(2000)180. [84] Dwaikat MB, Kodu r VKR. Hydrothermal model for predicting fire - induced spalling in concrete structural systems. Fire Safety Journal 2009;44:425 34. https://doi.org/10.1016/j.firesaf.2008.09.001. [85] Ichikawa Y, England GL. Prediction of moisture migration and pore pressur e build - up in concrete at high temperatures. Nuclear Engineering and Design 2004;228:245 59. https://doi.org/10.1016/j.nucengdes.2003.06.011. [86] Msaad Y, Bonnet G. Analyses of heated concrete spalling due to restrained thermal dilation: Application to th 32. https://doi.org/10.1061/(ASCE)0733 - 9399(2006)132:10(1124). [87] Gawin D, Pesavento F, Schrefler BA. Towards prediction of the thermal spalling risk through a multi - phase porous media mode l of concrete. Computer Methods in Applied Mechanics and Engineering 2006;195:5707 29. https://doi.org/10.1016/j.cma.2005.10.021. 326 [88] Zhang HL, Davie CT. A numerical investigation of the influence of pore pressures and thermally induced stresses for spall ing of concrete exposed to elevated temperatures. Fire Safety Journal 2013;59:102 10. [89] Zhao J, Zheng J, Peng G, van Breugel K. A meso - level investigation into the explosive spalling mechanism of high - performance concrete under fire exposure. Cement and Concrete Research 2014;65:64 75. [90] Tenchev R, Purnell P. An application of a damage constitutive model to concrete at high temperature and prediction of spalling. International Journal of Solids and Structures 2005;42:6550 65. https://doi.org/10.1016/j .ijsolstr.2005.06.016. [91] Dwaikat MB, Kodur VKR. Fire induced spalling in high strength concrete beams. Fire Technology 2010;46:251. https://doi.org/10.1007/s10694 - 009 - 0088 - 6. [92] Kodur V, Dwaikat M. Fire - induced spalling in reinforced concrete beams. P roceedings of the Institution of Civil Engineers - Structures and Buildings 2012;165:347 59. https://doi.org/10.1680/stbu.11.00013. [93] Gawin D, Pesavento F, Schrefler BA. Modelling of hygro - thermal behaviour of concrete at high temperature with thermo - ch emical and mechanical material degradation. Computer Methods in Applied Mechanics and Engineering 2003;192:1731 71. https://doi.org/10.1016/S0045 - 7825(03)00200 - 7. [94] Gawin D, Pesavento F, Castells AG. On reliable predicting risk and nature of thermal spa lling in heated concrete. Archives of Civil and Mechanical Engineering 2018;18:1219 27. https://doi.org/10.1016/j.acme.2018.01.013. [95] Shen L, Li W, Zhou X, Feng J, Di Luzio G, Ren Q, et al. Multiphysics Lattice Discrete Particle Model for the simulation of concrete thermal spalling. Cement and Concrete Composites 2020;106:103457. https://doi.org/10.1016/j.cemconcomp.2019.103457. [96] Banerji S, Kodur V, Solhmirzaei R. Experimental behavior of ultra high performance fiber reinforced concrete beams under f ire conditions. Engineering Structures 2020;208:110316. https://doi.org/10.1016/j.engstruct.2020.110316. [97] Zeiml M, Lackner R, Mang HA. Experimental insight into spalling behavior of concrete tunnel linings under fire loading. Acta Geotechnica 2008;3:29 5 308. https://doi.org/10.1007/s11440 - 008 - 0069 - 9. [98] ACI A. 216.1 M - 07: Standard Method for Determining Fire Resistance of Concrete and Masonry Construction Assemblies. Detroit, USA: American Concrete Institute 2007. [99] ASTM E119 - 19. Standard Test Meth ods for Fire Tests of Building Construction and Materials. West Conshohocken, PA: American Society of Testing Materials; 2019. 327 [100] ISO 834 - 1:1999. Fire Resistance Tests Elements of Building Construction - Part 1: General Requirements. Switzerland, Geneva : 1999. [101] Russell HG, Graybeal BA, Russell HG. Ultra - high performance concrete: A state - of - the - art report for the bridge community. United States. Federal Highway Administration. Office of Infrastructure; 2013. [102] KCI. Design recommendations for ult ra - high performance concrete K - UHPC 2012. [103] Wille K, Boisvert - Cotulio C. Material efficiency in the design of ultra - high performance concrete. Construction and Building Materials 2015;86:33 43. https://doi.org/10.1016/j.conbuildmat.2015.03.087. [104] W ang J, Liu J, Wang Z, Liu T, Liu J, Zhang J. Cost - Effective UHPC for Accelerated Bridge Construction: Material Properties, Structural Elements, and Structural Applications. Journal of Bridge Engineering 2021;26. https://doi.org/10.1061/(ASCE)BE.1943 - 5592.0 001660. [105] Sbia LA, Peyvandi A, Lu J, Abideen S, Weerasiri RR, Balachandra AM, et al. Production methods for reliable construction of ultra - high - performance concrete (UHPC) structures. Materials and Structures 2017;50:7. [106] Dong Y. Performance assess ment and design of ultra - high performance concrete (UHPC) structures incorporating life - cycle cost and environmental impacts. Construction and Building Materials 2018;167:414 25. [107] Racky P. Cost - effectiveness and sustainability of UHPC. Proceedings of the International Symposium on Ultra High Performance Concrete, Kassel, Germany, 2004, p. 797 805. [108] Kodur V, Solhmirzaei R, Agrawal A, Aziz EM, Soroushian P. Analysis of flexural and shear resistance of ultra high performance fiber reinforced concrete beams without stirrups. Engineering Structures 2018;174:873 84. [109] Chen Y, Matalkah F, Yu Y, Rankothge W, Balachandra A, Soroushian P. Experimental Investigations of the Dimensional Stability and Durability of Ultra - High - Performance Concrete. Advances in Materials Science 2017;6:1 8. [110] Yoo D - Y, Yoon Y - S. Structural performance of ultra - high - performance concrete beams with different steel fibers. Engineering Structures 2015;102:409 23. [111] Yoo D - Y, Lee J - H, Yoon Y - S. Effect of fiber content on mech anical and fracture properties of ultra high performance fiber reinforced cementitious composites. Composite Structures 2013;106:742 53. [112] Khoury GA. Effect of fire on concrete and concrete structures. Progress in Structural Engineering and Materials 2 000;2:429 47. https://doi.org/10.1002/pse.51. 328 [113] Yang IH, Joh C, Kim B - S. Structural behavior of ultra high performance concrete beams subjected to bending. Engineering Structures 2010;32:3478 87. [114] Yoo D - Y, Banthia N, Yoon Y - S. Experimental and num erical study on flexural behavior of ultra - high - performance fiber - reinforced concrete beams with low reinforcement ratios. Canadian Journal of Civil Engineering 2017;44:18 28. [115] Yoo D - Y, Yoon Y - S. A review on structural behavior, design, and applicatio n of ultra - high - performance fiber - reinforced concrete. International Journal of Concrete Structures and Materials 2016;10:125 42. [116] Committee ACI. Building code requirements for structural c oncrete (ACI 318 - 19) and commentary (ACI 318R - 19), Farmington Hills, MI: American Concrete Institute; 2019. [117] Chen T, Gao X, Ren M. Effects of autoclave curing and fly ash on mechanical properties of ultra - high performance concrete. Construction and Bu ilding Materials 2018;158:864 72. [118] Kodur V, Banerji S, Solhmirzaei R. Effect of Temperature on Thermal Properties of Ultrahigh - Performance Concrete. J Mater Civ Eng 2020;32:04020210. https://doi.org/10.1061/(ASCE)MT.1943 - 5533.0003286. [119] Shin K - Y, Kim S - B, Kim J - H, Chung M, Jung P - S. Thermo - physical properties and transient heat transfer of concrete at elevated temperatures. Nuclear Engineering and Design 2002;212:233 41. https://doi.org/10.1016/S0029 - 5493(01)00487 - 3. [120] Lie TT, Kodur VKR. Therma l and mechanical properties of steel - fibre - reinforced concrete at elevated temperatures. Canadian Journal of Civil Engineering 1996;23:511 7. [121] Kodur VKR, Sultan MA. Structural behaviour of high strength concrete columns exposed to fire 1998. [122] Abd allah S, Fan M, Rees DWA. Effect of elevated temperature on pull - out behaviour of 4DH/5DH hooked end steel fibres. Composite Structures 2017;165:180 91. https://doi.org/10.1016/j.compstruct.2017.01.005. [123] Khaliq W, Kodur V. Thermal and mechanical prope rties of fiber reinforced high performance self - consolidating concrete at elevated temperatures. Cement and Concrete Research 2011;41:1112 22. [124] Richardson AE. Compressive strength of concrete with polypropylene fibre additions. Structural Survey n.d.; 2006. [125] Khaliq W, Kodur V. Effectiveness of polypropylene and steel fibers in enhancing fire resistance of high - strength concrete columns. Journal of Structural Engineering 2018;144:04017224. https://doi.org/10.1061/(ASCE)ST.1943 - 541X.0001981. 329 [126] Ka general relation. Materials and Structures 2002;35:28. [127] Khaliq W, Taimur. Mechanical and physical response of recycled aggregates high - strength concrete at ele vated temperatures. Fire Safety Journal 2018;96:203 14. https://doi.org/10.1016/j.firesaf.2018.01.009. [128] Peng G - F, Huang Z - S. Change in microstructure of hardened cement paste subjected to elevated temperatures. Construction and Building Materials 2008 ;22:593 9. [129] Giaccio GM. Mechanical behaviour of thermally damaged high - strength steel fibre reinforced concrete. Mater Struct 2005;38:335 42. https://doi.org/10.1617/14175. [130] Li Y, Zhang Y, Yang E - H, Tan KH. Effects of geometry and fraction of pol ypropylene fibers on permeability of ultra - high performance concrete after heat exposure. Cement and Concrete Research 2019;116:168 78. https://doi.org/10.1016/j.cemconres.2018.11.009. [131] Carreira DJ, Chu K - H. Stress - Strain Relationship for Plain Concre te in Compression. ACI Journal n.d.;1985:797 804. [132] Wu Z, Shi C, He W, Wang D. Uniaxial compression behavior of ultra - high performance concrete with hybrid steel fiber. Journal of Materials in Civil Engineering 2016;28:06016017. [133] Hurley MJ, Gottuk DT, Hall Jr JR, Harada K, Kuligowski ED, Puchovsky M, et al. SFPE handbook of fire protection engineering. Springer; 2015. [134] ACI 216.1. Code requirements for determing fire resistance of concrete and masonry construction assemblies. Farmington Hills, MI, USA.: American Concrete Inst; 2014. [135] Castillo C. Effect of transient high temperature on high - strength concrete. PhD Thesis, Rice University n.d.;1987. [136] Williams B, Kodur V, Green MF, Bisby L. Fire endurance of fiber - reinforced polymer streng thened concrete T - beams. ACI Structural Journal 2008;105:60. [137] and Materials 2019;43:310 22. [138] Hertz KD. Limits of spalling of fire - exposed concrete. Fire Safe ty Journal 2003;38:103 16. [139] Yoo D - Y, Banthia N, Yoon Y - S. Flexural behavior of ultra - high - performance fiber - reinforced concrete beams reinforced with GFRP and steel rebars. Engineering Structures 2016;111:246 62. 330 [140] Gao WY, Dai J - G, Teng JG, Chen G M. Finite element modeling of reinforced concrete beams exposed to fire. Engineering Structures 2013;52:488 501. https://doi.org/10.1016/j.engstruct.2013.03.017. [141] of high performance concrete at high temperatures. Engineering Computations 2002. https://doi.org/10.1108/02644400210444320. [142] y generalised, coupled, multi - phase, hygro - thermo - mechanical model for concrete. Materials and Structures 2010;43:13 33. https://doi.org/10.1617/s11527 - 010 - 9591 - y. [143] EN 1991 - 1 - 2. Eurocode 1 Actions on Structures. Part 1 2: General Actions Actions o n Structures Exposed to Fire. CEN, Brussels 2002. [144] Lie TT, Erwin RJ. Method to calculate the fire resistance of reinforced concrete columns with rectangular cross section. ACI Structural Journal 1993;90:52 60. [145] Kalifa P, Menneteau F - D, Quenard D. Spalling and pore pressure in HPC at high temperatures. Cement and Concrete Research 2000;30:1915 27. https://doi.org/10.1016/S0008 - 8846(00)00384 - 7. [146] Ortiz M. A constitutive theory for the inelastic behavior of concrete. Mechanics of Materials 1985;4 :67 93. https://doi.org/10.1016/0167 - 6636(85)90007 - 9. [147] Kodur VKR, Dwaikat M. A numerical model for predicting the fire resistance of reinforced concrete beams. Cement and Concrete Composites 2008;30:431 43. https://doi.org/10.1016/j.cemconcomp.2007.08 .012. [148] Anderberg Y, Thelandersson S. Stress and deformation characteristics of concrete at high temperatures: experimental investigation and material behaviour model. Lund Institute of Technology Lund, Sweden; 1976. [149] Harmathy TZ. A comprehensive creep model 1967. [150] Hibbeler RC. Structural analysis. 8th ed. Upper Saddle River, NJ: Pearson Education Inc.; 2014. [151] Yazdani S, Schreyer HL. An anisotropic damage model with dilatation for concrete. Mechanics of Materials 1988;7:231 44. https://do i.org/10.1016/0167 - 6636(88)90022 - 1. [152] Concept. Journal of Engineering Mechanics 1993;119:1865 85. https://doi.org/10.1061/(ASCE)0733 - 9399(1993)119:9(1865). 331 [153] Kodur V, Banerji S. Modeling the fire - induced sp alling in concrete structures incorporating hydro - thermo - mechanical stresses. Cement and Concrete Composites 2021;117:103902. https://doi.org/10.1016/j.cemconcomp.2020.103902. [154] Gernay T, Millard A, Franssen J - M. A multiaxial constitutive model for con crete in the fire situation: Theoretical formulation. International Journal of Solids and Structures 2013;50:3659 73. https://doi.org/10.1016/j.ijsolstr.2013.07.013. [155] Tenchev RT, Li LY, Purkiss JA. Finite element analysis of coupled heat and moisture transfer in concrete subjected to fire. Numerical Heat Transfer: Part A: Applications 2001;39:685 710. https://doi.org/10.1080/10407780119853. [156] Shi H, Xu B, Zhou X. Influence of mineral admixtures on compressive strength, gas permeability and carbonat ion of high performance concrete. Construction and Building Materials 2009;23:1980 5. https://doi.org/10.1016/j.conbuildmat.2008.08.021. [157] Boel V, Audenaert K, De Schutter G. Gas permeability and capillary porosity of self - compacting concrete. Material s and Structures 2008;41:1283 90. https://doi.org/10.1617/s11527 - 007 - 9326 - x. [158] Kollek JJ. The determination of the permeability of concrete to oxygen by the Cembureau method a recommendation. Materials and Structures 1989;22:225 30. [159] Pijaudier - Cab ot G, Dufour F, Choinska M. Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions. J Eng Mech 2009;135:1022 8. https://doi.org/10.1061/(ASCE)EM.1943 - 7889.0000016. [160] Nguyen D - L, Thai D - K, Kim D - J. Direct tension - dependent flexural behavior of ultra - high - performance fiber - reinforced concretes. The Journal of Strain Analysis for Engineering Design 2017;52:121 34. https://doi.org/10.1177/0309324716689625. [161] ffening Model for Planar Reinforced Concrete Members. Journal of Structural Engineering 1990;116:3039 58. https://doi.org/10.1061/(ASCE)0733 - 9445(1990)116:11(3039). [162] Shakya AM, Kodur VKR. Effect of temperature on the mechanical properties of low relax ation seven - wire prestressing strand. Construction and Building Materials 2016;124:74 84. https://doi.org/10.1016/j.conbuildmat.2016.07.080. [163] Tao Z, Wang X - Q, Uy B. Stress - Strain Curves of Structural and Reinforcing Steels after Exposure to Elevated T emperatures. J Mater Civ Eng 2013;25:1306 16. https://doi.org/10.1061/(ASCE)MT.1943 - 5533.0000676. [164] Garcia MA. Sedimentation Engineering: ASCE Manuals and Reports on Engineering Practice No. 110. American Society of Civil Engineers, New York 2008. 332 [165 ] Banerji S, Kodur V. Effect of Temperature on Mechanical Properties of Ultra - High Performance Concrete. Fire and Materials 2021. [166] Youssef MA, Moftah M. General stress strain relationship for concrete at elevated temperatures. Engineering Structures 2 007;29:2618 34. https://doi.org/10.1016/j.engstruct.2007.01.002. [167] Felicetti R, Gambarova PG, Sora MN, Khoury GA. Mechanical behaviour of HPC and UHPC in direct tension at high temperature and after cooling. Fifth RILEM symposium on fibre - reinforced co ncretes, Lyon, France: 2000, p. 749 58. [168] Wu Z, Shi C, He W, Wu L. Effects of steel fiber content and shape on mechanical properties of ultra high performance concrete. Construction and Building Materials 2016;103:8 14. [169] Rasul M, Ahmad S, Adekunle SK, Al - Dulaijan SU, Maslehuddin M, Ali SI. Evaluation of the Effect of Exposure Duration and Fiber Content on the Mechanical Properties of Polypropylene Fiber - Reinforced UHPC Exposed to Sustained Elevated Temperature. JTE 2019;48:4355 69. https://doi.org/ 10.1520/JTE20180687. [170] Bentz DP. Fibers, percolation, and spalling of high - performance concrete. Materials Journal 2000;97:351 9. [171] Shi C, Wu Z, Xiao J, Wang D, Huang Z, Fang Z. A review on ultra high performance concrete: Part I. Raw materials and mixture design. Construction and Building Materials 2015;101:741 51. [172] Wang C, Yang C, Liu F, Wan C, Pu X. Preparation of ultra - high performance concrete with common technology and materials. Cement and Concrete Composites 2012;34:538 44. [173] Liu X, Ye G, De Schutter G, Yuan Y, Taerwe L. On the mechanism of polypropylene fibres in preventing fire spalling in self - compacting and high - performance cement paste. Cement and Concrete Research 2008;38:487 99. [174] Wu Z, Wong HS, Buenfeld NR. Influence of d rying - induced microcracking and related size effects on mass transport properties of concrete. Cement and Concrete Research 2015;68:35 48. [175] and with polypropylene fibers at elevated temperatures using a new test setup. Cement and Concrete Research 2013;53:104 11. [176] Tran VH, Meftah F, Izoret L, Beh loul M. On explicit modeling of polypropylene fiber effects on hydro - thermal behavior of heated concrete. MATEC Web of Conferences 2013;6:05007. https://doi.org/10.1051/matecconf/20130605007. 333 [177] Progelhof RC, Throne JL, Ruetsch RR. Methods for predictin g the thermal conductivity of composite systems: a review. Polymer Engineering & Science 1976;16:615 25. [178] composite materials. Composites Science and Technology 2003;63:113 7. [179] Kaviany M. Principles of heat transfer in porous media. Springer Science & Business Medi a; 2012. [180] Hill AA, Straughan B. Poiseuille flow in a fluid overlying a porous medium. Journal of Fluid Mechanics 2008;603:137 49. [181] Gernay T. Fire resistance and burnout resistance of reinforced concrete columns. Fire Safety Journal 2019;104:67 78 . https://doi.org/10.1016/j.firesaf.2019.01.007. [182] Neves IC, Rodrigues JPC, Loureiro A de P. Mechanical Properties of Reinforcing and Prestressing Steels after Heating. Journal of Materials in Civil Engineering 1996;8:189 94. https://doi.org/10.1061/(A SCE)0899 - 1561(1996)8:4(189). [183] EN 1994 - 1 - 2. Eurocode 4 Design of Composite Steel and Concrete Structures. Part 1 2: General Rules Structural Fire Design. Brussels 2005;Commission of European Communities. [184] Franssen JM. Thermal elongation of con crete during heating up to 700 C and cooling. University of Liege, Available at: Http://Hdl Handle Net/2268/531 1993. [185] Schneider U. Concrete at high temperatures a general review. Fire Safety Journal 1988;13:55 68. [186] Kodur V, Banerji S. Comparativ e fire behavior of reinforced concrete beams made of different concrete strengths. 2020. https://doi.org/10.14264/bd10594. [187] Connolly RJ. The spalling of concrete in fires. Ph.D. Thesis. Aston University, United Kingdom, 1998. [188] Banerji S, Kodur VK R, Solhmirzaei R. Fire response of ultra high performance concrete beams. International Interactive Symposium on Ultra - High Performance Concrete, vol. 2(1), Albany, New York, USA: Iowa State University Digital Press; 2019. [189] Kodur VKR, Dwaikat M. Perfo rmance - based Fire Safety Design of Reinforced Concrete Beams. Journal of Fire Protection Engineering 2007;17:293 320. https://doi.org/10.1177/1042391507077198. [190] ASTM. ASTM E1529 - 14a: . Standard test methods for determining effects of large hydrocarbon pool fires on structural members and assemblies. West Conshohocken, PA, USA 2014. 334 [191] Sritharan S. Design of uhpc structural members: Lessons learned and astm test requirements. Advances in Civil Engineering Materials 2015;4:113 31. [192] Hasgul U, Yavas A, Birol T, Turker K. Steel fiber use as shear reinforcement on I - shaped UHP - FRC beams. Applied Sciences 2019;9:5526. [193] Solhmirzaei R, Kodur VKR, Banerji S. Shear Behavior of Ultra High Performance Concrete Beams without Stirrups. International Interactive Symposium on Ultra - High Performance Concrete, vol. 2, Iowa State University Digital Press; 2019. [194] Voo YL, Poon WK, Foster SJ. Shear Strength of Steel Fiber - Reinforced Ultrahigh - Performance Concrete Beams without Stirrups. J ournal of Structural Engineering 2010;136:1393 400. https://doi.org/10.1061/(ASCE)ST.1943 - 541X.0000234. [195] Lantsoght EO. How do steel fibers improve the shear capacity of reinforced concrete beams without stirrups? Composites Part B: Engineering 2019;17 5:107079. [196] Majorana CE, Salomoni VA, Mazzucco G, Khoury GA. An approach for modelling concrete spalling in finite strains. Mathematics and Computers in Simulation 2010;80:1694 712. [197] Naser MZ. Heuristic machine cognition to predict fire - induced sp alling and fire resistance of concrete structures. Automation in Construction 2019;106:102916. https://doi.org/10.1016/j.autcon.2019.102916. [198] Shi X, Tan T - H, Tan K - H, Guo Z. Influence of concrete cover on fire resistance of reinforced concrete flexura l members. Journal of Structural Engineering 2004;130:1225 32. [199] Khoury GA. Effect of fire on concrete and concrete structures. Progress in Structural Engineering and Materials 2000;2:429 47. https://doi.org/10.1002/pse.51. [200] Ali F, Nadjai A. Fire resistance of concrete columns containing polypropylene and steel fibers. Special Publication 2008;255:199 216. [201] Kodur V, Mcgrath R. Fire endurance of high strength concrete columns. Fire Technology 2003;39:73 87. [202] Kodur VK, McGrath R. Effect of silica fume and lateral confinement on fire endurance of high strength concrete columns. Canadian Journal of Civil Engineering 2006;33:93 102. [203] Kodur VKR, Phan L. Critical factors governing the fire performance of high strength concrete systems. Fire Safety Journal 2007;42:482 8. https://doi.org/10.1016/j.firesaf.2006.10.006. 335 [204] Shafieifar M, Farzad M, Azizinamini A. Experimental and numerical study on mechanical properties of Ultra High Performance Concrete (UHPC). Construction and Building Materia ls 2017;156:402 11. https://doi.org/10.1016/j.conbuildmat.2017.08.170. [205] Solhmirzaei R. Response of Ultra High Performance Fiber Reinforced Concrete Beams under Flexure and Shear. vol. Ph.D. Thesis. Michigan State University; 2021. [206] Committee 544 ACI. Design considerations for steel fiber reinforced concrete, American Concrete Institute; 2009.