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Experimental and Numerical Evaluation of Concrete Spalling during Extreme Thermal Loading

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Title: Experimental and Numerical Evaluation of Concrete Spalling during Extreme Thermal Loading
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Copyright Date: 2008

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Source Institution: University of Florida
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Permanent Link: http://ufdc.ufl.edu/UFE0006380/00001

Material Information

Title: Experimental and Numerical Evaluation of Concrete Spalling during Extreme Thermal Loading
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0006380:00001


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EXPERIMENTAL AND NUMERICAL EV ALUATION OF CONCRETE SPALLING DURING EXTREME THERMAL LOADING By WILLIAM ANDREW YANKO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

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This document is dedicated to those who lo st their lives at the World Trade Center, Pentagon, and in Somerset County, Pennsylvania on September 11, 2001.

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iii ACKNOWLEDGMENTS I thank my parents (William and Margaret Yanko), sister (Kasandra Taylor), and brother-in-law (Sean Taylor) for supporting me in my academic and personal life. I express my thanks to my doctoral faculty ad visor, Dr. Gary Consol azio, and my masters faculty advisor Dr. Ali Maher, not only for he lping me to obtain my Doctoral degree, but also for inspiring me to work hard and r eaching my full potential. I thank Drs. Kurt Gurley, Andrew Boyd, Michael McVay and Da vid Denslow for serving on my doctoral supervisory committee. My colleague Dr. Jae Chung provided much academic help and friendship during my four year s at the University of Flor ida. I also thank Scott Beresheim, John Wilkes, Ben Lehr, Jessica Hendrix, Nick Agnoli, John Bolanowski, Justin Halbert, Shaun & Niki Mackenzie, Mark Williams, Dave Schoester, and Brian Warfield for their friendship and support. I also express thanks to my friends and colleagues at DeSimone Consulting Engineers for their support during the final year of my graduate work. For financial support, I express my thanks to the University of Florida Graduate Fellowship Program a nd National Science Foundation for providing financial support for my education and research. This material is based upon work s upported by the National Science Foundation under Grant No. 9900015.

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iv TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES...........................................................................................................viii LIST OF FIGURES.............................................................................................................x ABSTRACT.....................................................................................................................xv i CHAPTER 1 INTRODUCTION...........................................................................................................1 1.1 Background of Spalling Behavior of Concrete.......................................................2 1.2 Moisture Clog Spalling Mechanism.......................................................................5 1.2.1 Stage One: Pre-Vaporiz ation of Pore Water................................................7 1.2.2 Stage Two: Vaporization of Pore Water......................................................8 1.2.3 Stage Three: Spalling Due to Pore Pressure.................................................9 1.3 Spalling Due to Differential Thermal Stress Development..................................10 1.4 Research Program.................................................................................................13 1.5 Contributions of the Research Program................................................................14 1.5.1 Contribution I: Determination of Material Parameters..............................14 1.5.1.1 Production of mixtures.....................................................................14 1.5.1.2 Permeability determination..............................................................15 1.5.1.3 Porosity determination.....................................................................17 1.5.1.4 Compressive strength determination................................................17 1.5.2 Contribution II: Transient Thermal Testing...............................................18 1.5.2.1 Furnace design..................................................................................18 1.5.2.2 Measurement of temperature profile................................................19 1.5.2.3 Measurement of pore pressure.........................................................19 1.5.2.4 Measurement of spalling..................................................................19 1.5.3 Contribution III: Development of Predictive Numerical Models...............20 1.5.3.1 Heat and mass transfer.....................................................................20 1.5.3.2 Stress analysis..................................................................................21 1.6 Summary...............................................................................................................21 2 EXPERIMENTAL DETERMINATION OF PERMEABILITY..................................23 2.1 Introduction...........................................................................................................24 2.2 Sample Production................................................................................................26

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v 2.2.1 Mixture Design...........................................................................................26 2.2.2 Sample Preparation.....................................................................................30 2.3 Experimental Testing............................................................................................36 2.3.1 Determination of Water Permeability........................................................36 2.3.2 Gas Permeability........................................................................................39 2.3.2.1 Measurement of gas permeability....................................................39 2.3.2.2 Determination of gas slip-flow parameters......................................45 2.3.3 Porosity.......................................................................................................47 2.3.4 Compressive Strength.................................................................................48 2.4 Results and Discussion.........................................................................................48 2.4.1 Water Permeability Test Results................................................................49 2.4.2 Gas Permeability Test Results....................................................................50 2.4.3 Porosity.......................................................................................................61 2.4.4 Compressive Strength.................................................................................62 2.5 Discussion and Conclusions.................................................................................63 3 EXPERIMENTAL EVALUATION OF CONCRETE PERFORMANCE DURING SEVERE THERMAL EXPOSURE...........................................................................65 3.1 Experimental Test Me thods and Equipment.........................................................66 3.1.1 Thermal Sample..........................................................................................66 3.1.2 Instrumentation...........................................................................................67 3.1.2.1 Pressure measurement......................................................................68 3.1.2.2 Spalling detection.............................................................................76 3.1.2.3 Temperature measurement...............................................................79 3.1.3 Gas Furnace................................................................................................80 3.1.3.1 Furnace geometry.............................................................................80 3.1.3.2 Thermal brick...................................................................................82 3.1.3.3 Specimen suspension........................................................................82 3.1.3.4 Heat supply.......................................................................................85 3.2 Experimental Program..........................................................................................86 3.2.1 One-Dimensional Thermal Loading, Fully Instrumented Specimens........86 3.2.2 Qualitative Thermal Testing.......................................................................88 3.3 Experimental Results............................................................................................89 3.3.1 Mortar Mixture: M25.................................................................................90 3.3.2 Mortar Mixture: M35.................................................................................97 3.3.3 Concrete Mixture: C25.............................................................................102 3.3.4 Concrete Mixture: C45.............................................................................105 3.3.5 Concrete Mixture: L35.............................................................................108 3.3.6 Qualitative Thermal Testing.....................................................................112 3.4 Discussion...........................................................................................................117 3.4.1 Furnace.....................................................................................................117 3.4.2 Instrumentation Method...........................................................................118 3.4.3 Pressure.....................................................................................................118 3.4.4 Spalling Detection....................................................................................119 3.4.5 Qualitative Testing...................................................................................119

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vi 4 MODELING HEAT AND MASS FLOW WITHIN CONCRETE DURING FIRE EXPOSURE CONDITIONS....................................................................................120 4.1 Background of the TOUGH2 Numerical Simulator...........................................120 4.2 Program Input.....................................................................................................123 4.2.1 Geometry..................................................................................................123 4.2.1.1 One-dimensional model.................................................................123 4.2.1.2 Two-dimensional model.................................................................128 4.2.2 Thermal Loading Using Boundary Super-Elements................................132 4.2.2.1 ASTM E119...................................................................................133 4.2.2.2 ASTM E1529.................................................................................135 4.2.2.3 Heat flux.........................................................................................136 4.2.3 Estimations of Material Properties...........................................................138 4.2.3.1 Permeability at High Temperatures................................................138 4.2.3.2 Relative Permeability.....................................................................145 4.2.3.3 Porosity at High Temperatures.......................................................147 4.2.3.4 Thermal conductivity, specific heat, and mass density..................148 4.3 Modeling Program..............................................................................................148 4.4 Modeling Results................................................................................................150 4.4.1 Comparisons Between Numerical M odels and Experimental Testing.....150 4.4.1.1 Thermal loading curves.........................................................................152 4.4.1.2 Comparison of results............................................................................153 4.4.2 ASTM E119 and ASTM E1529 Thermal Loading..................................165 4.4.2.1 Effects of Permeability and Porosity.....................................................166 4.4.2.2 Effects of Thermal Loading...................................................................171 4.4.2.3 Effects of Saturation Level....................................................................174 4.5 Summary and Conclusions.................................................................................175 5 STRESS DEVELOPMENT DUE TO PORE PRESSURE IN CONCRETE MATERIALS EXPOSED TO FIRE........................................................................177 5.1 Finite Element Program......................................................................................177 5.2 Input Parameters.................................................................................................178 5.2.1 Geometry of Models.................................................................................178 5.2.2 Material Models........................................................................................178 5.2.3 Loading Methods......................................................................................187 5.2.4 Boundary Conditions................................................................................189 5.3 Stress Output...............................................................................................190 5.3 Modeling Study..................................................................................................191 5.4 Modeling Results................................................................................................192 5.4.1 Effects of Permeability.............................................................................193 5.4.2 Effects of Porosity....................................................................................195 5.4.3 Effects of Thermal Loading......................................................................196 5.4.4 Effects of Initial Saturation Level............................................................198 5.5 Discussion...........................................................................................................200

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vii 6 FINDINGS AND CONCLUSIONS............................................................................204 6.1 Importance of Quality Control............................................................................204 6.2 Quantification of Permeability...........................................................................204 6.2.1 Findings....................................................................................................204 6.2.2 Recommendations....................................................................................205 6.3 Experimental Thermal Testing...........................................................................206 6.3.1 Findings....................................................................................................206 6.3.2 Recommendations....................................................................................209 6.4 Numerical Modeling...........................................................................................209 6.4.1 Findings....................................................................................................209 6.4.2 Recommendations....................................................................................211 6.5 Stress Analysis....................................................................................................212 6.5.1 Findings....................................................................................................212 6.5.2 Recommendations....................................................................................212 6.4 Concluding Remarks..........................................................................................214 APPENDIX A GAS PERMEABILITY DA TA FOR ALL MIXTURES...........................................215 B CALIBRATION GRIDS FOR PRESSURE TRANSDUCERS.................................229 C CALCULATION METHOD FOR DETERMINING INITIAL SATURATION LEVEL OF THERMALLY TESTED MIXTURES.................................................234 D FILTERED EXPERIMENTAL THERMAL LOADING CURVES FOR USE IN THE NUMERICAL MODELING PROGRAM...............................................................236 E COMPARISON PLOTS OF EXPERIMENTALLY MEASURED AND NUMERICALLY PREDICTED TEMPERATURES..............................................244 F ABSOLUTE MAXIMUM PORE PRESSU RE RESULTS FROM THE NUMERICAL MODELING PROGRAM........................................................................................254 LIST OF REFERENCES.................................................................................................259 BIOGRAPHICAL SKETCH...........................................................................................265

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viii LIST OF TABLES Table page 2-1. Proportions of the concrete and mortar mixtures produced.....................................27 2-2. Summary of experimental results for the mixtures tested........................................49 2-3. Water permeability for mixt ures in experimental program......................................50 2-4. Intrinsic gas permeability fo r mixtures in experimental program............................51 2-5. Slip flow constant for mi xtures in experimental program........................................52 2-6. Porosity values for mixt ures in experimental program............................................61 2-7. Results from compression testing.............................................................................63 3-1. Calibration grid for a typical pore pres sure transducer (grid entries is pressure transducer output in millivolts)................................................................................71 3-2. Proportions of the concrete and mortar mixtures produced.....................................88 3-3. Spalling locations and times determ ined by monitoring resistance through crackdetection circuitry in th e M25 specimen, Test #1....................................................97 3-4. Spalling locations and times determ ined by monitoring resi stance through crackdetection circuitry in th e M25 specimen, Test #2....................................................97 3-5. Spalling locations and times determin ed crack-detection circuitry in the M35 specimen.................................................................................................................102 3-6. Results from qualitative thermal testing program..................................................114 3-7. Compressive strength results from qualitative thermal testing program................117 4-1. Geometry of elements in the models for investigation into the effect of element volume size on the numerical solution...................................................................126 4-2. Properties of materials in the m odels for evaluating element geometry.................126 4-3. Properties of the materials in the two dimensional model......................................132

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ix 4-4. TOUGH2 simulations performed on the concrete and mortar mixtures................149 4-5. Calibration factors for numerical modeling............................................................155 5-1. Strength parameters for constructing st ress-strain relationships for mixtures in the experimental program............................................................................................182 5-2. Strength parameters for constructing stress-strain relationships for temperatures above 800 C (1472 F).............................................................................................186 5-3. Parameters for construc ting stress-strain relationships for temperatures above 800 C (1472 F)..................................................................................................................187 5-4. Effective stress factor s for mixtures in this study...................................................202 6-1. Parameters affecting pore pressu re and material failure of concrete......................213

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x LIST OF FIGURES Figure page 1-1. Fire induced damage of a column in the Pentagon.....................................................4 1-2. Fire induced damage of the highwa y bridge at the I-65/I-59 interchange in Birmingham, Alabama due to a tanker-truck crash ..................................................5 1-3. Stage development of mo isture clogging and pore pressure......................................6 1-4. Pore pressure and saturation surface plot s for a typical partially saturated concrete material subjected to thermal loading......................................................................11 1-5. Flowchart of research program for inve stigation of the behavi or of concrete under fire conditions...........................................................................................................14 2-1. Photo of a specimen with e poxy collar for permeability testing..............................31 2-2. Diagram of sample with epoxy collar for permeability testing................................32 2-3. Photo of the system for casting epoxy collars around the specimens for permeability testing.......................................................................................................................3 3 2-4. Schematic diagram of a ssembly for casting epoxy collars.......................................34 2-5. Schematic diagram of water permeability flow fixture............................................36 2-6. Measurement of flow rate in water permeameter.....................................................37 2-7. Schematic diagram of gas (nitrogen) permeameter..................................................40 2-8. Gas permeability flow fixture...................................................................................41 2-9. Determination of gas permeability parameters from test data..................................47 2-10. Gas permeability as a function of the reciprocal of the mean pressure..................54 2-11. Relationship between the slip flow constant and intrinsic gas permeability for the mortar mixtures........................................................................................................56 2-12. Intrinsic gas permeabil ity and slip flow data for all the mixtures in the experimental program..............................................................................................57

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xi 2-13. Variation of gas permeability with flow pressure..................................................59 2-14. Relationship between gas and water permeability for mortar mixtures.................60 3-1. Photo of a pore pressure transducer..........................................................................69 3-2. Method for installation of pore pre ssure transducer usin g a lag bolt assembly.......72 3-3. Method for installation of pore pressu re transducer by embedding the transducer..73 3-4. Crack pattern due to thermal expansi on incompatibility between lag bolt assembly and concrete sample.................................................................................................74 3-5. Response of embedded pressure transducer to an applied pressure of nitrogen gas76 3-6. Method for detecting sp alling during thermal testing..............................................77 3-7. Instrumentation layout for measurement of spalling................................................78 3-8. Photo of a series of closed-l oop wires for detection of spalling...............................79 3-9. Propane furnace for thermal testing..........................................................................81 3-10. Propane furnace for thermal testing........................................................................82 3-11. Thermal specimen suspended above the furnace...................................................83 3-12. Apparatus for the su spension of the thermal specimen on top of furnace..............84 3-13. Propane burner entering the side of the furnace.....................................................86 3-14. Schematic of system for applying h eat to the furnace from a propane source.......87 3-15. Schematic of test method for qua litative assessment of spalling at high temperatures.............................................................................................................90 3-16. M25 mortar specimen (T est #2) after thermal testing............................................91 3-17. Measured air temperature near the heated surface during th ermal testing of the M25 specimen..........................................................................................................92 3-18. Internal temperatures of the M25 speci mens measured at various depths from the heated surface...........................................................................................................93 3-19. Measured pressure at 10 and 15 mm from heated surface during testing of M25 mixture.....................................................................................................................95 3-20. M35 mortar specimen after thermal testing............................................................98

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xii 3-21. Measured air temperature near the heated surface during th ermal testing of the M35 specimen..........................................................................................................98 3-22. Internal temperatures of the M35 speci mens measured at various depths from the heated surface.........................................................................................................100 3-23. Internal temperatures measured at 20 mm (0.787 in.) during thermal testing of each of the mortar specimens.................................................................................100 3-24. Measured pressure at 10 and 15 mm from heated surface during testing of M35 specimen.................................................................................................................101 3-25. C25 concrete specimen after thermal testing........................................................103 3-26. Measured air temperature near the heated surface during th ermal testing of the C25 specimen.........................................................................................................103 3-27. Internal temperatures of the C25 speci mens measured at various depths from the heated surface.........................................................................................................104 3-28. Measured pore pressure at 10 and 15 mm from heated surface during testing of C25 specimen.........................................................................................................105 3-29. C45 concrete mixture after thermal testing..........................................................106 3-30. Measured air temperature near the heated surface during th ermal testing of the C45 specimen.........................................................................................................106 3-31. Internal temperatures of the C45 speci mens measured at various depths from the heated surface.........................................................................................................107 3-32. Measured pressure at 10 and 15 mm from heated surface during testing of C45 specimen.................................................................................................................108 3-33. L35 concrete mixture after thermal testing...........................................................109 3-34. Top of the L35 concrete specimen during thermal testing...................................110 3-35. Measured air temperature near the heated surface during th ermal testing of the L35 specimen.........................................................................................................111 3-36. Internal temperatures of the L35 speci mens measured at various depths from the heated surface.........................................................................................................112 3-37. Measured pressure at 10 and 15 mm from heated surface during testing of L35 specimen.................................................................................................................113 3-38. Specimens tested in qualitative thermal testing....................................................115

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xiii 4-1. One-dimensional model us ed for numerical simulations........................................124 4-2. Profiles of pore pressure at 1200 s econds for the one-dimensional models with different element heights (or volumes)..................................................................127 4-3. Profiles of temperature at 1200 sec onds across the depth of the one-dimensional models with different element heights (or volumes)..............................................128 4-4. Profiles of saturation le vel at 1200 seconds across the depth of the one-dimensional models with different element heights (or volumes)..............................................129 4-5. Initial two-dimensional (axisymmetr ic) model used for numerical simulations....130 4-6. Final two-dimensional (axisymmetric ) model used for numerical simulations.....131 4-7. ASTM E119 time-temperature curve......................................................................133 4-8. ASTM E119 time-temperature cu rve fitted for the first 40 minutes......................134 4-9. ASTM E1529 time-temperature curve....................................................................136 4-10. Flowchart of modifications to intrin sic permeability and slip flow factor based on a change in temperature..........................................................................................139 4-11. Relative permeability functions............................................................................146 4-12. Flowchart detailing numerical modeling process.................................................151 4-13. Filtering of the experimental air temp erature for Test #1 of the M25 specimen for the TOUGH2 boundary super-element..................................................................153 4-14. Pore pressures predicted by numerical models using the experimental furnace time-temperature loading curves............................................................................154 4-15. Comparison between pressure measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M25 specimen (Test #1).................................................................................................157 4-16. Comparison between pressure measured experimentally and predicted numerically at 15 mm (0.591 in.) from the heated surface for the thermal testing of the M25 specimen (Test #2).................................................................................................158 4-17. Comparison between pressure measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M35 specimen.................................................................................................................159 4-18. Comparison between pressure measured experimentally and predicted numerically for the thermal testing of the C25 specimen...........................................................160

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xiv 4-19. Pore pressure output from one-dimensional numeri cal modeling of C25 specimen161 4-20. Comparison between pressure measured experimentally and predicted numerically for the thermal testing of the C45 specimen...........................................................162 4-21. Comparison between pressure of air vo id in 2D model and pore pressure from 1D model for the numerical modeling of the C45 specimen.......................................163 4-22. Comparison between pore pressure measured experimentally and predicted numerically for the thermal te sting of the L35 specimen.......................................164 4-23. Comparison between pressure of air vo id in 2D model and pore pressure from 1D model for the numerical modeling of the L35 specimen.......................................165 4-24. Data filtering procedure for dete rmining absolute maximum pore pressure........167 4-25. Variation of absolute maximum pore pressure with intrinsic gas permeability (90% initial saturation level)..................................................................................168 4-26. Variation of absolute maximum pore pressure with intrin sic water permeability (90% initial saturation level)..................................................................................169 4-27. Variation of absolute maximum pore pr essure with porosity (90% initial saturation level).......................................................................................................................17 1 4-28. Variation of absolute maximum pore pressure with compressive strength (90% initial saturation level)............................................................................................172 4-29. Variation of absolute maximum pore pressure with thermal loading and initial saturation level for the C45 mixture.......................................................................173 4-30. Variation of absolute maximum pore pressure with saturation level for ASTM E119 thermal loading.............................................................................................174 4-31. Variation of absolute maximum pore pressure with saturation level for ASTM E1529 thermal loading...........................................................................................175 5-1. Locating nodes in the finite element m odel based on the geometry of the numerical model......................................................................................................................179 5-2. Derivations of the stre ss-strain curve for concrete using the Collins and Mitchell formulation.............................................................................................................181 5-3. Stress-strain curves for the Collin s and Mitchell, ADINA concrete model, and linear elastic formulations for the C20 concrete mixture.......................................184 5-4. Variation of compressive stress with temperature..................................................184 5-5. Variation of strength parameters with temperature for the C20 mixture...............185

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xv 5-6. Mapping of pore pressure and temperature results from numerical models into finite element models.......................................................................................................188 5-7. Free body diagram for calculating hydros tatic tensile stress from pore pressure..189 5-8. Boundary conditions for the finite el ement models (full restrain in x and y directions)...............................................................................................................191 5-9. First principal stress as a percentage of tensile strength versus distance from the heated surface for E119 thermal loading w ith an initial satu ration level of 90%..193 5-10. First principal stress as a percentage of tensile strength versus intrinsic gas permeability for E1529 thermal loading with an initial saturation level of 90%...194 5-11. First principal stress as a percentage of tensile strength versus porosity for E1529 thermal loading with an initi al saturation level of 90%.........................................195 5-12. Second principal stress as a percentage of compressive streng th versus porosity for E1529 and E119 thermal loadings with an initial saturatio n level of 90%............197 5-13. Temperature versus depth for E1529 and E119 thermal loadings of the graniteaggregate concrete mixtures with an initial satura tion level of 90%.....................198 5-14. Second principal stress as a percentage of compressive strength versus depth for E1529 and E119 thermal loadings of the gran ite-aggregate concrete mixtures with an initial saturation level of 90%............................................................................199 5-15. First principal stress as a percentage of tensile strength versus porosity for E119 thermal loading with initial sa turation levels of 25 and 90%.................................200 5-16. Second principal stress as a percentage of compressive streng th versus porosity for E119 thermal loading with initial saturation levels of 25 and 90%.......................201

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xvi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EXPERIMENTAL AND NUMERICAL EV ALUATION OF CONCRETE SPALLING DURING EXTREME THERMAL LOADING By William Andrew Yanko December 2004 Chair: Gary R. Consolazio Major Department: Civil and Coastal Engineering To better understand how concrete behave s under fire conditions, an experimental program coupled with numerical modeling (usi ng theories of heat and mass transfer) is implemented to measure and predict por e pressures in concrete under extreme temperatures. In intense fire conditions, the low permeability of concrete inhibits internal flow of steam (generated by the heating) and th us causes an increase in pore pressure that may then lead to spalling. Spalling of concrete under thermal loading due to pore pressure buildup is highly dependent upon the intensity and duration of heat input. Therefore, pore pressures measured experi mentally or predicted from heat and mass transfer numerical models produce varied re sults depending on the characteristics of thermal loading. Many individuals regard th e ASTM E119 thermal loading profile as the standard for determining the dur ability of structural members in fire conditions, however, this standard may not represent the worst-case scenario for the structure.

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xvii In this study, pore pressure and temperatur e are experimentally measured in various concrete mixtures under extreme thermal lo ading conditions (more severe than those specified in ASTM E119). A numerical m odel is then implemented for each of the mixtures to predict pore pressure and temper ature distributions over time. Because the numerical model accounts for mass transport, th e ability of gases a nd liquids to migrate through concrete is first quantified through e xperimental measurement of gas and water permeability to generate input data for the num erical model. The behavior of concrete subjected to severe thermal loading c onditions is then be tter understood through experimental measurement and numerical predic tion of internal temperature and pressure data.

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1 CHAPTER 1 INTRODUCTION Recent increases in concrete strength and durability have been accompanied by an increased tendency for explosive spalling under extreme thermal conditions such as fires. This is mainly due to significantly lower material permeability which thus produces higher thermally induced pore pressures. Comb ining the effective stresses due to pore pressure and thermal stresses caused by mate rial expansion, thermally induced spalling has become more likely for higher performance concrete. It will be demonstrated that a combination of differential thermal stress a nd pore pressure buil dup contributes to the spalling of concrete under rapid thermal loading. Mechanisms were investigated through e xperimentation and numerical modeling to quantify pore pressure buildup due to moistu re clogging and the development of high differential thermal stresses during heat tran sfer. Past research has shown promising results to support the idea that the combination of these two mechanisms causes spalling under high heat flux conditions (Consolazio et al.1998, Kalifa et al. 2000, Kalifa et al. 2001, Tenchev et al. 2001, Li et al. 2001, Yanko and Consolazio 2004). The primary goals of the investigation pr esented herein involved experi mental characterization of concrete failure under severe thermal loadi ng and methods of modeling such behavior using numerical and finite element s imulation computer codes (Pruess 1987, 1991, ADINA R&D 1997). Understanding the behavior of concrete ma terial subjected to rapid heating rates will permit engineers to better assess the serv iceability and strength of civil engineering

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2 facilities during fires. Results from this res earch will help in the development of methods to predict the coupled effects of moisture clog spalling with differential thermal stress in concrete structural systems exposed to fire. 1.1 Background of Spalling Behavior of Concrete Spalling that occurs in conc rete during the exposure to ra pidly rising temperature is difficult to predict and analytically characteri ze. Two theories have evolved to explain the causes of spalling in concrete under severe thermal loading. One theory assumes that thermal gradients in the concrete cause di fferential expansion and thus differential thermal stresses that exceed the strength limits of the material (Bazant 1997). When solid materials are subjected to a heat flux, te mperatures decrease nonlinearly as one moves away from the heat source. This temperature distribution follows established laws of heat conduction. The temperature gradient that is induced from the heat input will cause the solid material to expand from its original unheated condition. For typical situations involving the surface of a concrete member being heated, compressive thermal stresses develop parallel to the surface. Depending on the steepness of the temperature gradient, the principal stresses arising from differentia l thermal expansion can exceed the material strength and initiate cracking. Other studies (Hamarthy 1965, Consolazio et al.1998, Kalifa et al. 2000, Kalifa et al. 2001, Tenchev et al. 2001, Li et al. 2001) have strengthen ed the theory that pore pressure buildup associated with moisture cl ogging may also play an important role in initiating the spalling of concrete. Essentially, this theory states that in low permeability porous materials, the flow of water and steam that occurs during hea ting is restricted and consequently vapor pressures increase in the pore structure to a point that the resulting skeleton stresses exceed the material strength. High strength concrete is especially prone

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3 to this type of failure because it has very low permeability and yet often has a high degree of liquid saturation. Although the moisture clog spalling theory has been summarized only briefly here, the failure mechanism i nvolved is both complex and dependent on a number of material properties. In terms of mass transfer, parameters such as water permeability, gas permeability, phase interference, porosity, and slip-flow constant are needed in order to conduct analyses capable of modeling clog formation. Both theories outlined above are well supported by principles of mechanics and material science and have been studied usi ng experimental and anal ytical techniques. However, the coupling of these two failure m echanisms requires further experimental and analytical exploration, thus giving rise to the investigation presented in this dissertation. A unified theory of thermally induced spal ling must include a combination of stress induced by pore pressure and differential therma l stress. Moisture clog spalling plays an important role in failure when the thermal gr adients are not as steep (lower heat flux). However, if temperature gradients are very steep (high heat flux), ther mal stresses tend to dominate the material response. A key focal point of this investig ation was to quantify the degree to which each of these stress sources contributes to the in itiation of explosive spalling under typical structur al fire conditions. Quantifyi ng the roles of each stress source was accomplished through a combination of experimental and analytical modeling activities. Due to the complex microstructure of concrete, the necessity for coupled heat and mass flow analysis, and the diffi cultly of laboratory testing at high temperature, the topic of thermal spalling of concrete has been spar ingly explored in recent years. Therefore,

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4 new experimental and analytical information related to performance of concrete during a fire is of significant interest to the structural engineering community. Modeling the mechanical behavior of concre te under extreme thermal loading is of considerable interest in the evaluation of se rvice performance of bu ildings, bridges, and tunnels. In particular, there is a need for methods that ca n predict the performance of concrete materials when subjected to varied fire conditions. Structural failures of concrete elements at the Pentagon (Figure 11) and an I-65 highway bridge in Alabama (Figure 1-2) under fire conditions have defini tively shown a need for further exploration of this topic. Columns in both of these st ructures were constructed of concrete and spalling occurred under intense thermal conditions. Figure 1-1. Fire induced damage of a colu mn in the Pentagon (Mlakar et al. 2003)

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5 Figure 1-2. Fire induced damage of the highw ay bridge at the I-65/I-59 interchange in Birmingham, Alabama due to a tanker-truck crash (Photo courtesy of Alabama Department of Transportation) 1.2 Moisture Clog Spalling Mechanism There are multiple steps in the formation of the moisture clog spalling mechanism in partially and fully saturated concrete mate rials. Since concrete is unlikely to be initially saturated under typi cal environmental conditions (Jacobs 1998), the stages of moisture clog development discussed here fo cus on partially satura ted initial conditions (saturation levels, 0 < L S< 1.0). The key stages describe d below and shown in Figure 13 will assist in understanding this failure mechanism and reveal the significance of certain material properties that are requi red for the study of this phenomenon. Three stages are detailed based on the three differe nt magnitudes of pore pressures. Stage one describes the condition in which water has not vaporized within the concrete and thus pore pressures are relatively low. Stage two is entered when water begins to vaporize and

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6 pore pressure increase dramatically. Stage th ree is reached when the pore pressures reach a level that causes the stresses in the conc rete skeleton to reach the failure point and failure occurs. Temperature Pore pressure Stage 1Prevaporization of pore water Stage 2Vaporization of pore water Stage 3Continued vaporization Pore pressure high enough to cause spalling Pore pressure not yet high enough to cause spalling Not significant pore pressure increase while below water vaporization point H eat source Moist concrete Figure 1-3. Stage development of mo isture clogging and pore pressure

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7 1.2.1 Stage One: Pre-Vaporization of Pore Water The first stage in the development of the moisture clog spalling mechanism involves a condition in which for internal pore water has not reached the vaporization point during heating. This is considered an important stage because even though pore pressures do not increase signi ficantly (prior to water vapor ization), there is heat and mass flow during this stage. The heat and mass flow will thus cause the saturation level and temperatures to be different fr om the initially cooled condition. Consider an initially cool semi-infinite conc rete slab that is subjected to a heat flux on one surface where no internal pore water ha s reached the point of vaporization. The internal pore fluids are th erefore liquid water and air (proportions dependent upon the initial liquid saturation level). It is important to note that vaporization is dependent upon temperature and pressure (Colli er 1972). As pressure increas es, the temperature required to cause a phase change also increases (Hal liday and Resnick 1988). This fact will be important in later stages of the moisture clog formation. At the initial application of heat flux, the fluid constituents within the pores (air and liquid water) near the surface will experience a pressure increase due to a temperature increase. Any water or air near the heat ed surface will migrate out of the specimen because the surface of the concrete will be at atmospheric pressure and thus less than the internal pore pressure. This pore pressure increase is now the driving mechanism for mass flow of fluid constituents within the specimen. Depending on the direction of the pressure gradient, the constituents will either flow toward the heated surface or away from the heated surface. For positions betw een the heated surface and the location of the maximum pore pressure, the pressure gradient will drive flow in a direction toward the

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8 heated surface. The rate of mass flow will be dependent upon the ability of the concrete skeleton to transport water and air through th e capillary network, which can be quantified by gas and water permeability values. Therefor e, the pore pressure values in this stage are dependent upon the concrete specimen’s transient temperatur e profile across the depth; the ability to transport liquid wate r (water permeability); and the ability to transport air (gas permeability). The por e pressure increase caused by air or water expansion at this stage of heating is no t significant enough to cause spalling of the concrete. 1.2.2 Stage Two: Vaporization of Pore Water Stage two involves phase change of liquid water into steam at locations in the system where the boiling point of water has been reached. For concrete to be in this stage of the moisture clog formation, the boiling point based on both the pore pressure and temperature must have been reached. The first location where phase change of liquid water will occur is at the heated surface of the specimen because the temperature is highest and the pressure is cl ose to standard atmospheric pressure. Water vapor that has undergone a phase change in the pores clos e to the surface will es cape from the system based on the ability of the pore structure to transport steam. At the same time, all other locations in the specimen w ill still exhibit mass movement through liquid flow. Moving away from the heated surface and deeper in to the specimen, the temperature decreases and the pore pressure increases. As heat flux continues, pore water at locations near the heated surface will start to undergo a phase chan ge. Phase changes will continue to occur at locations progressively farther from th e heated surface as the pore water reaches temperatures and pressure s that cause vaporization.

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9 Numerical simulations conducted using a heat and mass flow program (Pruess 1987, 1989) have demonstrated that desaturati on zones exist at locations between the heated surface and the point of maximum pore pr essure. This qualitatively indicates that the peak of the pore pressure profile is also at or near the vaporizati on point. Therefore, locations between the heated surface and the point of pe ak pore pressure contain a mixture of water vapor and air while regions further from the heated surface consist of liquid water and an air-water vapor mixture. When liquid water at the point of peak pore pressure undergoes a phase change, flow of the vapor will occur in two directions It will flow in the direction towards the heated surface and towards the deeper and cooler regions of the specimen. This fact is due to the pressure gradients that arise in both directions at the location of the maximum pore pressure. As vapor migrates towards th e deeper and cooler regions, it will condense because the pressure and temperature conditions required to maintain a steam state are no longer met. Any vapor that condenses will be added to the existing pore liquid water in these regions and the liquid satu ration level will increase. It should be noted that the location of the p eak pressure is not stationary with time. With continued heating, it will move deep er into the specimen due to the changing moisture distribution within the concrete. Liqui d water at the very edge of the “saturated front” will continually turn to vapor as th e temperature increases. Therefore, the saturation front will move deeper into the specim en as heat input continues at the surface. 1.2.3 Stage Three: Spalling Due to Pore Pressure The third and final stage of the failure mechanism involves the actual spalling of the concrete. At this point, pores at depths beyond the location of the peak pressure are filled with liquid water migrating deeper into the specimen according to the water

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10 permeability of the material. In contrast, pores located between the heated surface and the location of the peak pressure are in a desaturated condition. In this region, vapor and/or air migrates toward the heated surface according to the material gas permeability. Since the water permeability of concrete is far less than gas permeability, gas escapes from the surface at a rate that is quicker than liquid water migrates deeper into the material. As the cycle of vaporization-migr ation-condensation con tinues, the saturation levels of the pores near the vapor-liquid interface will increase. A highly saturated front will then form that will impede any more wa ter vapor from condensing and entering the liquid filled pores. Figure 1-4 demonstrates the evolution of pore pressure and liquid saturation distribution through a concrete specimen over time (Consolazio and Chung 2004). The edge of the liquid saturated zone (SL=1) indicates the edge of the developed moisture clog. The edge of the saturated zone also corresponds to the location of the peak pore pressure. As the steam attempts to migrate from the front to the surface, the flow rate will be governed by the gas permeab ility of the concrete (Kalif a et al. 2000). Steam that cannot migrate rapidly enough toward the heat ed surface will cause a pore pressure increase due to continued temperature increas e. Spalling occurs when the pore pressure at (or near) the edge of the saturated zone reaches a point that causes stresses in the porous solid skeleton to exceed the strength of the material (Kalifa et al. 2000). 1.3 Spalling Due to Differential Thermal Stress Development Thermal stresses occur in conc rete due to both the expans ive nature of cementitious materials during temperature increases and the mechanical boundary conditions that restrict expansion. For the one-dimensiona l heating investigated in this study, the

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11 10 20 30 40 50 60 70 80D i s t a n c e f r o m h e a t e d s u r f a c e ( m m ) ( N o t e : W a l l i s 1 5 0 m m t h i c k h o w e v e r o n l y 8 0 m m o f t h i c k n e s s a r e s h o wn ) 500 1000 1500 2000 2500 3000T i m e ( s e c ) 0 0.2 0.4 0.6 0.8 1 10 20 30 40 50 60 70 80 500 1000 1500 2000 2500 3000T im e ( s e c ) 0 10 20 30 40 50Pressure (atm)0 00 0Liquid Saturation (S ) S initial N o n h e a te d S u r f a c eH e a te d S u r f a c eDesaturated zone Clog width Saturated zone S initial Peak pressure at face of clog Saturated pressure gradient Desaturated pressure gradient I n i t i a l c o n d i t i o n o f w a l l a t t = 0 s e c I n i t i a l c o n d i t i o n o f w a l l a t t = 0 s e c .D i s t a n c e f r o m h e a t e d s u r f a c e ( m m ) ( N o t e : W a l l i s 1 5 0 m m t h i c k h o w e v e r o n l y 8 0 m m o f t h i c k n e s s a r e s h o wn ) Figure 1-4. Pore pressure and saturation su rface plots for a typical partially saturated concrete material subjected to th ermal loading (Consolazio and Chung 2004)

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12 boundary condition that is critical for ther mal stress quantifica tion is the lateral confinement of the concrete. If the material is restricted from expanding in this direction, which is parallel to the heat ed surface, high compressive stresses may develop. Such stresses may approach or exceed the compressive strength of the concrete and thus cause material failure. In addition, because cementitious materials tend to decrease in strength with an increase in temperature (Phan and Carino 1998), the limits on compressive stress are lower. In practical applications, the lateral confin ement is most likely partially restricted from expanding, which means that the compre ssive thermal stresses are less severe compared to the fully restricted case. Wh en approaching situations of two and threedimensional geometry, the thermal stresses becomes more complex and thus more difficult to quantify. Because a goal of this study was to isolate the effects of thermal stress and pore pressure on ma terial failure, the thermal analysis performed in this study is restricted to the simplest cases of hea ting and geometry (one-dimensional heating and semi-infinite geometry) with the extreme cas es of fully restricted and unrestricted expansion in the lateral direction. Tensile stresses perpendicular to the h eated surface generally do not occur during one-dimensional heating. Stresses in this direction are generally a result of the effective stresses caused by pore pressure. However, because an increased temperature causes a decreased tensile strength in cementitious materials, the effective stresses caused by pore pressure will be a greater proportion of the te nsile strength. Theref ore, temperature is needed to quantify both the confining thermal stresses and the decrease in strength.

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13 1.4 Research Program The goal of quantifying the effects of por e pressure development and differential thermal stress on spalling of cementitious materials requires the completion of several tasks. Broadly, these tasks can be separa ted into two distinct categories: direct experimental evaluation, and numerical analys is. Experimental thermal testing of the concrete includes the measurement of pore pressure, temperature, and detection of cracking. Time-histories of such measured parameters provide quantitative and qualitative data for gaining a better understanding of spalling behavior. Figure 1-5 shows a flow-chart of the research program that was carried out in this study in order to quantify the effects of pore pressure and differential thermal stress. Numerical models that quan tify heat and mass flow require material parameters such as permeability and porosity to quantify concrete’s ability to transport liquid and gas. Rather than estimating these critic al values for simulation purposes, direct experimental determination was carried out to enable development of accurate predictive numerical models. From input of these para meters into predictive numerical models, the results of experimental thermal testing a nd predictive modeling were compared. The results (e.g., pore pressure, temperature) fr om the modeling are shown later in this dissertation to compare well with data meas ured during scaled experimental tests, resulting in a valid predictive model that can be applied to larger scale systems. Listed below are the top-level tasks that constitute the research program.

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14 Experimental thermal testing Heat and mass flow modeling of experimental testsGas permeability Water permeability Porosity Auxiliary Experimentation model input Heat and mass flow modeling of "standard" fires: ASTM E119, E1529 Finite element modeling of "standard" fires (stress analysis) Pore pressure, temperature, and spalling Pore pressure, temperature compare Trends with mixture properties Gas permeability Water permeability Porosity model input Compressive strength model input Top-level Tasks Key Output Figure 1-5. Flowchart of research program for investigation of the be havior of concrete under fire conditions 1.5 Contributions of the Research Program 1.5.1 Contribution I: Determination of Material Parameters 1.5.1.1 Production of mixtures Three sets of mixtures have been pro duced in the laboratory for permeability, porosity, compressive strength, and thermal testing. The first se t consisted of four mortar mixtures with varying water-binder (cemen t plus silica fume) ratios (w/b = 0.20, 0.25, 0.30, 0.35). For these mixtures, variables such as binder-aggregate ratio and silicacement ratio were kept constant with the in tention of creating a si ngle factorial (waterbinder ratio) set of mixtures. Coarse a ggregate was eliminated to create more

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15 homogenous materials. A sec ond set of mixtures included th e addition of coarse granite aggregate as an ingredient. The binder-aggregate and silica -cement ratios were also held constant for each of these mixtures, as the water-binder ratio was the sole parameter that varied across the mixtures (w/b = 0. 20, 0.25, 0.30, 0.35, 0.40, 0.45). The third set of mixtures was similar to the second set except th at the granite aggregat e was replaced with lime rock aggregate. Water-binder ratios for this set of mixtures were also varied (w/b = 0.30, 0.35, 0.40). Not all of the mixtures could be thermally tested due to limits on the scope and time constraints of this study. Two mortar mi xtures, two concrete mixtures with granite aggregate, and one mixture with limerock ag gregate were chosen as the materials to undergo thermal testing. Mortar and concre te were both tested to demonstrate the influence of aggregate on mixture properties and thus pore pressure development. The two types of concrete mixtures were tested to demonstrate the diffe rence in performance based on aggregate selection. The key parame ters that were kept constant between mixtures were the super plasticizer-binde r ratio (0.1), binder-aggregate ratio (0.5 for mortar and 0.4 for concrete), and coarse-f ine aggregate ratio (0.625 for concrete). 1.5.1.2 Permeability determination Permeability is an important parameter in characterizing moisture flow through cementitious materials and therefore in studying the formation of moisture clogs. Pore pressure buildup during thermal loading is di rectly related to water and steam being unable to migrate through concre te at high rates. The permeab ility of porous materials is dependent upon the permeant used during flow rate quantification. Permeability values calculated by flow rates of water and gas thr ough concrete or mortar will be inherently different due to physiochemical processes in th e solid skeleton and due to gas slip-flow.

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16 In particular, the primary physiochemical pro cess at hand is the sw elling of the skeleton when exposed to water. In contrast, when c oncrete is subjected to elevated temperatures, micro cracking will occur in the solid skelet on and the permeability to fluid flow will increase. This physical change of the por ous structure of concrete based on water exposure will therefore also have an in fluence on permeability, and thus should be quantified for both saturated a nd de-saturated conditions. Furthermore, slip-flow theory states that as gas flows adjacent to a surface, the velocities of the gas molecules closest to the wall are not zero. This differs from the laminar flow regime assumed by Darcy’s la w and has been proven to be true by many researchers (Klinkenberg 1941, Whiting 1988, Bamforth 1991, Klieger and Lamond 1994, Dhir et al. 1995, McVay 1995) as well as the author. Due to slip-flow, the apparent gas permeability (from flow rate measurement) will vary based on variations in test pressure. For different upstream and downstr eam pressures applied to the same porous material, the calculated gas permeability will be different. Due to this difference, the gas permeability value at a particular test pressure shall be referred to as the apparent gas permeability ( g aK). From a set of apparent gas pe rmeability tests conducted at various test pressures, the intrinsic gas permeability can be calculated. The intrinsic gas permeability ( g K) is a singular value that has the pre ssure dependency (slip-flow effects) removed. Past research (Klinkenberg 1941, Am erican Petroleum Institute [API] 1956) has also shown that the intrinsic gas permeability is constant for a material regardless of the gas permeant used (nitrogen, oxygen, etc.) for non-reactive test gases. Slip-flow can thus be quan tified for a material based on a locus of apparent gas permeability data points. It was also disc overed (API 1956) through analytical derivation

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17 and experimentation that the apparent gas pe rmeability has a linear relationship with the reciprocal of the mean test pressures. This relation varies from one material to another based on differences in pore structure and is described by a single parameter known as the slip flow-constant. Some researchers (Whiting 1988, Dhir et al. 1989, Bamforth 1991) have assumed that water permeability (wK or K) and intrinsic permeability are identical. Although this assumption may be valid when physiochemical reactions of the material to water are absent, such an assumpti on is not true for cement-based materials. Thus, a significant contribution of the present study has involved independent determination of the relationships between water and gas permeability. As will be later discussed in detail, this has been achieved through independent te sting of identically prepared cementitious specimens in which both water and nitrogen gas permeability tests have been conducted. 1.5.1.3 Porosity determination Porosity is a parameter that quantifies the volumetric percentage of a material that is occupied by voids. Determination of porosity is a critical step for proper numerical simulation of moisture clogging because por e volume quantifies the volume of pore constituents (water, steam, air) that have the potential to flow through the capillary structure during thermal loading. Porosity m easurements were thus performed for all of the concrete and mortar mixtures in this st udy so that they could be used as input to numerical models. 1.5.1.4 Compressive strength determination Analyzing the coupled effects of differen tial thermal expansion and moisture clog formation requires knowledge of material mechan ical behavior. Such information is also

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18 required as input into stress an alysis models. Mechanical be havior parameters such as elastic modulus and tensile capacity can be estimated for concrete materials by ultimate compressive strength values (MacGregor 1997). Compressive strength tests were thus performed for the mortar and concrete mixes in this experimental program according to the ASTM C39 specification. 1.5.2 Contribution II: Transient Thermal Testing The goal of the experimental thermal tes ting was to devise methods to detect spalling failure in concrete due to the co mbined effects of moisture clogging and differential thermal stresses. A test confi guration was devised to measure pore pressure, temperature and cracking so that the failure mechanism can be properly characterized. Additionally, these three measurements were used to validate numerical models of concrete exposed to fire. 1.5.2.1 Furnace design Furnace designs were developed that could properly deliver transient temperatures typical of those found in building fires and fuel fires. Of primary importance was ensuring that the furnace could be adjusted to deliver heating ra tes capable of causing both thermal stress dominated spalling as we ll as moisture clog do minated spalling. To facilitate comparisons to research resu lts already published (Consolazio et al. 1998, Kalifa et al. 2000, Kalifa et al 2001, Li et al. 2001, Tenche v et al. 2001) the use of “standard” test fires was desira ble. Common test fires such as those provided in the ASTM E119 and ASTM E1529 specifications are often used to evaluate concrete durability during fire exposure. The furnace de veloped in this study was thus designed to produce heating rates similar to the ASTM standards.

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19 1.5.2.2 Measurement of temperature profile Determining the temperature profile acro ss a sample during a thermal test was useful for quantification of thermal conduc tivity, heat flux input, verification of numerical models, and for the quantification of thermal stresses. Differential thermal stresses were quantified from the variati on of temperature across each sample. This helped in isolating failure mechanisms and determining which failure mechanism was dominant. 1.5.2.3 Measurement of pore pressure Pore pressures were measured within mortar a nd concrete samples at distances of 10 and 15 mm from the heated surface. Pore pressure profiles followed suit with the previous mechanisms described for moisture cl og spalling and differential thermal stress. Spalling occurred when the pore pressure coupled with the effects of a thermal gradient caused stresses in excess of the material st rength. Measurement of pore pressure coupled with measurement of cracking helped in identifying the dominant mechanisms responsible for causing spalling. 1.5.2.4 Measurement of spalling Few previous studies have been conducte d to develop methods to experimentally detect and locate spalling in concrete during thermal load ing. Strain gages cannot not readily be applied internally in concrete specimens and the epoxy needed to secure a strain gage will melt at the test temperatures of interest here. A method was thus devised in this study to identify cracking parallel to th e heated surface (i.e. spalling) by using fine gage wire embedded in the concrete. Conc rete failure was detected during thermal testing by looping the embedded fine gage wire at a particular distance from the heated surface and measuring resistance at the ends of the wire. When cracking across the wire

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20 occurs during a thermal test, the wire will break and the circuit will no longer be closed. An infinite measured resistance will then be measured across the ends of the crack detection circuit. 1.5.3 Contribution III: Development of Predictive Numerical Models 1.5.3.1 Heat and mass transfer Coupled heat and mass flow modeling in th is study was performed using a finite difference program known as TOUGH2 (Pruess 1991). TOUGH2 is a numerical simulation program for transient coupled heat and mass flow of multiphase multicomponent fluid mixtures in porous media. Data predicted by the program include pore pressure, temperature, and sa turation level. TOUGH2 input models were created to geometrically and physically represent the co ncrete and mortar mixtures that were prepared and thermally tested in the labor atory. Values of intrinsic gas permeability, water permeability, porosity a nd slip-flow constant experime ntally determined during the course of this study were used to model each of the mixtures. Other parameters needed to build the models were obt ained by reviewing past rese arch (Klieger and Lamond 1994, Consolazio et al. 1998, Gieck 1997, Li et al. 2001, Tenchev et al. 2001). A number of different thermal loading conditions were appl ied to each of the models. The heat flux histories applied to the mort ar models included those spec ified in the ASTM E119 and ASTM E1529 specifications, as well as wh at was applied using the furnace. A limitation of TOUGH2 is that the stre sses in the material skeleton are not included in the numerical solution. Therefore, any skeleton cracking due to pore pressure buildup is not included in the pressure, temper ature, and saturation predictions. For this reason, a separate finite element program wa s used for calculating stresses induced by temperature gradients and pore pre ssure as predicted by TOUGH2.

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21 1.5.3.2 Stress analysis In an attempt to incorporate material stre sses into a thermal analysis, steps were taken to use a finite element program (ADI NA) with results from experimental testing and heat and mass flow (TOUGH2) simulations To assess the extent of differential thermal stresses developed during a one-dimen sional thermal test, temperature profiles from both TOUGH2 and experimental simula tions were applied to thermo-elastic material models. An important element of this study involve d verification of laboratory results with numerical analysis. Creation a nd calibration of numerical mode ls will aid in predicting spalling in a broad range of cementitious materials subjected to thermal loading. Development of predictive spalling models based on mate rial parameters such as porosity, permeability, and strength will help in the evaluation of other concrete mixes. From the solution of the mechanical stresses the effects of thermal stresses and pore pressures were quantified and the mechanisms separated. 1.6 Summary A unique and significant outcome of this study is the demonstration that a link exists between permeability and the formation of moisture clogging during thermal loading of cementitious materials. Because of this link, it will be shown that it is necessary to experimentally measure permeability to obtain more accurate values, and thus a better assessment of thermal behavi or. To demonstrate this link, a coupled experimental and numerical program was in itiated that quantified pore pressure and temperature within thermally loaded conc rete and mortar mixtures with varying permeability, porosity, and strength.

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22 During the course of this study, methods to experimentally measure water and gas permeability (with slip-flow effects) were de veloped. For experimental thermal loading, methods were developed to deliver fire-equiv alent heating rates to concrete specimens with simultaneous measurement of internal pore pressure, temperat ure, and spalling. Finally, comparisons were made between the experimental thermal testing data and the results from numerical modeling.

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23 CHAPTER 2 EXPERIMENTAL DETERMINATION OF PERMEABILITY The magnitude of pore pressure in concrete during fire conditions is directly related to the migration rate of steam and water th rough the material. Prope r characterization of fluid flow in high strength, low permeability cementitious materials requires that both liquid and gas permeability testing be conducted, even when intrinsic (theoretically fluidindependent) flow properties are being determined. When a cementitious material comes into contact with water, reactions take pl ace that result in measured water (liquid) permeability parameters being significantly different than equivalent parameters determined using non-reactive gas permeants (Cabrera and Lynsdale 1988, Dhir et al. 1995). This disparity remains even after diffe rences in the viscosity and density of the test permeant, as well as pressure-dependent effects such as gas slip-flow, have been accounted for and intrinsic parame ters have been computed. This chapter focuses on the development of accurate and reliable test methods for determining water permeability, gas permeability, and gas slip-flow parameters for highstrength, low-permeability cementitious materials. Results from independent liquid and gas permeability tests conducted on identically cast concrete and mortar specimens are presented and expressions relating key fl ow properties are developed. Quantifying permeability parameters for cementitious materials such as concrete and mortar provides important information regarding mass flow th rough the cementitious skeletal structure. This has a direct affect on the developmen t of the moisture clog spalling mechanism (Hamarthy 1965).

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24 2.1 Introduction When using experimental methods to measure the permeability of a porous medium for use in flow calculations, it is often desira ble to determine the intrinsic permeability of the material (also called absolute permeability ) rather than the coefficient of permeability (also called hydraulic conductivity). Under ideal conditions, intrinsic permeability is a function only of the characteristics of the porous solid skeleton, not of the specific fluid permeant used in the test procedure. Thus, theoretically at least, intrinsic permeabilities determined using either liquid water or gases su ch as nitrogen, etc. should be equal. This is in contrast to the coefficient of permeab ility, in which characteristics of both the solid skeleton and the fluid permeant properties (t emperature, viscosit y, density, etc.) are lumped together into a single parameter. However, due to the reactive nature of hardened cement paste when exposed to water, i.e. swelling (Kosmatka and Panare se 1988, Klieger and Lamond 1994), intrinsic permeability to water flow and intrinsic permeability to gas flow represent two independent properties and mu st therefore be independently determined. This is especially important in applications i nvolving partially satura ted flow in which simultaneous transport of both liquid and gas phases must be considered. Liquid water flow through a saturated, and thus swelle d, porous material is quantified by water permeability, whereas gas (air, vapor) flow through a partially saturated or desaturated porous material is governed by gas permeability parameters. Independent measurements of both liquid and gas permeabilities are needed to accurately model mass transport under varied saturation conditions. While a great deal of experimental pe rmeability data has been published in the literature, few studies have measured and re ported the quantity of da ta needed to fully

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25 characterize not only liquid flow but also gas flow. As will be discussed in this paper, slip-flow effects (Klinkenberg 1941, American Petroleum Institute (API) 1956) are often significant in gas flow situations, therefor e accurate determination of gas permeability parameters requires the use of multiple tests conducted at varied flow pressures. In the literature, gas permeability data is often dete rmined from tests conducted at only a single flow pressure. Data determined in this ma nner can only be used to predict flow rates occurring at the same pressure as that used in the test and thus are limited in application. Equally important, a wide variety of drying tech niques has been used in the literature to prepare specimens for gas permeability testing. Given that gas flow can be affected by even small amounts of pore moisture (Jacobs 1998), the variability in drying procedures used by different researchers makes it very difficult to draw conclusions based on reviewing permeability data published by different authors. Thus, a primary goal of this study was to perform parallel liquid and gas permeability tests on identically prepared (mixed, cast, cured, and cut) cementitious specimens. All gas permeability testing was performed on identically dried specimens and at multiple pressure levels so that pr essure-dependent gas permeability constants could be computed and reported. Focus wa s also placed on developing experimental apparatuses and procedures capable of pr oducing accurate and repeatable permeability data even when applied to low permeability mate rials. In order to evaluate the proposed apparatuses and procedures, permeability para meters were initially measured for four different high strength, low permeability cem entitious mixtures—each having a different water-binder ratio. The data collected provided useful insi ghts into the relationships between water permeability, gas permeability, and slip-flow parameters.

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26 Flow rates arising during the permeability tests were measured using multiple, redundant methods so that the accuracy of th e test apparatuses could be confirmed. Evaluating the repeatability of test results was addressed by using multiple test specimens cut from multiple cylinders. To establish test procedures and verify that the experimental apparatus was adequate, mortar mixtures were initially produced in this study to exclude the variables associated with coarse aggregat e. Permeability variations attributable to large aggregate effects—such as the dist ribution of aggregate particles within a permeability specimen cut from a full size cy linder, cement-aggregate interaction, and variability in aggregate grading—were elimin ated while keeping the pore structure and capillary system typical of a cement-based mate rial. In this way, the repeatability of the test procedures could be evaluated while still working with specimens that were cementitious in nature. Once these procedures for measuring permeability were established using the mortar mixtures, concrete that included coarse aggregate was tested. 2.2 Sample Production 2.2.1 Mixture Design Each of the mortar mixtures tested in this study consisted of Type I Portland cement, masonry sand, silica fume in the form of slurry, and a commercial super plasticizer. The concrete mixt ures contained the same ingred ients, but a portion of the sand was replaced by ASTM Type 57 limeroc k aggregate or ASTM Type 67 granite aggregate. The primary variables that diffe red between mixtures were the water-binder ratio and the super plasticizer content. Propor tions and ratios for each of the mixtures are shown in Table 2-1. All material batchi ng was conducted in a laboratory setting to ensure a high degree of consistency and quali ty. Rigorous quality control was used to ensure that the ingredients were precisely what the mixture designs prescribed. The

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27 Portland cement used in each mixture was produced by the same supplier to ensure—as much as possible—that the cement chemistry was the same for each mixture. In addition, the cement was acquired one day before each ba tching date to limit moisture infiltration and premature hydration. The fine aggregate used was masonry sand obtained locally from an aggregate and concrete producer. All of the sand used fo r all mixtures prepared in this study was delivered at one time to ensure identical pr operties. Subsequently, the sand was dried Table 2-1. Proportions of the concre te and mortar mixtures produced Mixture type Mixture ID Waterbinder ratio, w/b Watercement ratio, w/c Cementaggregate ratio, c/a Finecoarse aggregate ratio, fa/ca Silicabinder ratio, s/b (%) Super plasticizerbinder ratio, SP/b (%) 0.097 0.049 M20 0.198 0.219 0.499 (9.7 %) (4.9 %) 0.098 0.029 M25 0.248 0.275 0.499 (9.8 %) (2.9 %) 0.097 0.024 M30 0.298 0.330 0.498 (9.7 %) (2.4 %) 0.098 0.009 Mortarwithout coarse aggregate M35 0.348 0.386 0.499 (9.8 %) (0.9 %) 0.095 0.039 C20 0.196 0.217 0.398 (9.5 %) (3.9 %) 0.097 0.020 C25 0.248 0.274 0.399 (9.8 %) (2.0 %) 0.096 0.010 C30 0.297 0.328 0.398 (9.6 %) (1.0 %) 0.096 0.010 C35 0.347 0.384 0.398 (9.6 %) (1.0 %) 0.097 0.004 C40 0.398 0.440 0.398 (9.7 %) (0.4 %) 0.097 0.004 Concretewith granite aggregate C45 0.448 0.496 0.399 0.625 (9.7 %) (0.4 %) 0.097 0.019 L30 0.298 0.330 0.399 (9.7 %) (1.9 %) 0.096 0.012 L35 0.347 0.384 0.398 (9.6 %) (1.2 %) 0.095 0.006 Concretewith limerock aggregate L40 0.397 0.439 0.398 0.625 (9.5 %) (0.6 %)

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28 Table 2-1. Continued kg/m3 (lb/yd3) L/m3 (floz/yd3) Mixture ID Portland cement (Type I) Silica fume Water Fine aggregate Coarse aggregate Super plasticizer Super plasticizer 648 70 142 1439 35.2 32.6 M20 (1091) (118) (239) (2425) (59.3) (843) 642 69 176 1426 20.5 18.9 M25 (1081) (117) (297) (2403) (34.5) (490) 633 68 209 1408 16.6 15.4 M30 (1068) (115) (352) (2372) (28.0) (398) 627 68 242 1392 6.5 6.1 M35 (1056) (114) (408) (2346) (11.0) (157) 566 60 123 604 967 24.6 22.8 C20 (953) (101) (207) (1018) (1629) (41.4) (588) 560 60 154 599 958 12.2 11.3 C25 (944) (102) (259) (1009) (1614) (20.5) (292) 555 59 182 593 949 6.0 5.5 C30 (936) (99) (307) (1000) (1560) (10.1) (143) 548 58 211 585 937 5.8 5.36 C35 (924) (98) (355) (987) (1579) (9.7) (139) 542 58 239 579 926 2.5 2.33 C40 (913) (98) (402) (975) (1560) (4.2) (60) 535 57 265 572 914 2.3 2.16 C45 (902) (97) (447) (963) (1541) (3.9) (55) 553 59 182 591 946 11.6 10.75 L30 (933) (100) (307) (996) (1594) (19.6) (278) 547.8 58.1 210 585 936 7.0 6.48 L35 (923) (98) (355) (986) (1578) (11.8) (168) 542 57 238 579 927 3.7 3.45 L40 (914) (96) (401) (976) (1562) (6.3) (89) before mixture batching to ensure that la tent water had been expelled. Because the water-binder ratios for the mixtures tested in this study were small (low water content), it was important that very little water accomp any the sand when used in mixing to avoid unintentional inflation of the wa ter-binder ratio above the targ et value. For example, a moisture content of five percent in the sa nd would add 5 kg (11 lbs) of water per 100 kg (220 lbs) of aggregate. Consid ering that the mixture designs ca lled very little water to be added, five percent moisture would inflate th e water-binder ratio well above the target.

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29 Tests indicated that, after drying, the moistu re content of the sand was less than one percent when mixing was performed. Silica fume was obtained from W.R. Grace (F orce 10,000) in the form of slurry (to facilitate high quality, consistent mixing). The water content of th e slurry—specified by the producer and verified by laboratory testi ng—was included in the total mixture water when targeting a particular water-binder ratio. Due to the low water-binder ratios used for all of the mixtures, super-plasticizer wa s required to achieve the desired level of workability (Kosmatka and Panarese 1988, Kh an and Lynsdale 2002). An ASTM C494 Type F high range water-reducer provided by W.R. Grace (ADVA Flow) was used for each mixture in quantities indicated in Table 2-1. Test specimens were cast in 102 mm di ameter by 203 mm tall (4 in. by 8 in.) cylindrical plastic molds. After hardening for two days, the specimens were demolded and submerged in water—containing dissolved lime—for at least three months to cure. After curing was complete, multiple cylindrical slices were cut from the interior of each full size cylinder (excluding material at the extreme top and bottom) for testing in the water and gas permeability apparatuses. Af ter wet sawing, water permeability specimens were re-submerged in water to maintain their saturated condition until testing. Specimens to be used for gas permeability testing were oven dried, starting at low temperature and gradually ramping up to 105 C (221 F). Although drying the specimens at 105 C (221 F) may have caused micro-cr acking in the specimens (Hewlett 1988), it was important to eliminate al l water because even small am ounts of pore water have a large influence on gas permeability measuremen ts (Cabrera and Lynsdale 1988, Dhir et al. 1989, Dhir et al. 1995). Once the specimen weights, which were measured regularly

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30 during oven drying, stopped changing the sp ecimens were considered to be fully desaturated and were then cooled and placed in moisture proof bags to prevent reabsorption of moisture. Because of limitations on the scope and dur ation of the project, the permeability of partially saturated specimens was not measur ed. Based on the results of a literature search, it was found that a device to measure relative permeability wa s available (Martin 1986, Jacobs 1998). However, such testing was not feasible in this study. Therefore, a previous relative permeability relationship wa s used for the numerical modeling and is discussed in Chapter 4. 2.2.2 Sample Preparation Specimens used for determining intrinsic water permeability (wK ) consisted of saturated 102 mm (4 in.) diameter, 51 mm (2 in.) thick slices cut from 102 mm diameter by 203 mm tall (4 in. by 8 in.) cylinders. Gas permeability test specimens were 102 mm (4.0 in.) in diameter and between 38 mm (1.5 in.) and 51 mm (2.0 in.) in thickness. Around each specimen, an impermeable epoxy collar (Sikadur Hi-Mod) was cast and allowed to cure for at least 24 hours. Us e of an impermeable collar prevented flow through and along the outer circumferential boundary during testing and thus ensured conservation of mass and one-dimensional vert ical flow through each porous specimen. In addition, the epoxy had higher strength and a similar coefficient of thermal expansion compared to the mixtures in this study. This meant that the epoxy collar would both outlast the concrete specimen under any lo ading conditions and would expand at the same rate as the concrete specimen under a uniform thermal loading. A photo of a

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31 specimen is shown in Figure 2-1 and a diagra m of a sample with an epoxy collar is shown in Figure 2-2. Figure 2-1. Photo of a specimen with epoxy collar for permeability testing An assembly with a design based on prev ious research (Soonswang et al., 1989) was constructed to cast epoxy collars around the specimens. Figures and 2-3 and 2-4 show a photo and the schematic of the syst em constructed for simultaneously casting epoxy collars around four mortar or concrete specimens. Before epoxy casting, the side surface of the specimens was sanded to remove paste and thus crea te a better bond with the epoxy. To avoid any epoxy being spilled on the surface of the samples, adhesive tape was affixed to the surface. After the epoxy was placed and cured, the tape was removed

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32 Epoxy collar Mortar or concrete sample (a) Mortar or concrete sample 38.4 mm (1.5 in.) 101.6 mm (4.0 in.) 25.4 mm (1.0 in.) 25.4 mm (1.0 in.) Epoxy collar Epoxy collar (b) Mortar or concrete sample 50.8 mm (2.0 in.) 101.6 mm (4.0 in.) 25.4 mm (1.0 in.) 25.4 mm (1.0 in.) Epoxy collar Epoxy collar Epoxy coating (c) Figure 2-2. Diagram of sample with epoxy coll ar for permeability te sting: (a) Top view, (b) Plan view of specimen (for gas pe rmeability testing), (c) Plan view of specimen (for water permeability testing)

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33 Figure 2-3. Photo of the system for casti ng epoxy collars around the specimens for permeability testing

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34 Steel angles 1.25 x 1.25 x 0.125", 18" long (31.8 x 31.8 x 3.2 mm, 457.1 mm long) Concrete specimen 4.0" diam., 1.5-2.0" ht. (101.6 mm diam., 38.1-50.8 mm ht.) PVC ring (from pipe) 6.0" inside diam.,2.0" ht. (304.8 mm diam., 50.8 mm ht.) Aluminum angles 1.0 x 1.0 x 0.125", 18" long (25.4 x 25.4 x 3.2 mm, 457.1 mm long) Location of epoxy placement View B View A (a) Figure 2-4. Schematic diagram of assembly for casting epoxy colla rs: (a) Top view, (b) View A, (c) View B

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35 Bolts 0.25" diam., 2.5" length (6.4 mm diam., 63.5 mm length) Bolts 0.25" diam., 3.5" length (6.4 mm diam., 88.9 mm length) (b) Eye bolts 0.375" diam. (9.5 mm diam.) Threaded holes 0.375" diam. (9.5 mm diam.) (c) Figure 2-4. Continued

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36 with any spilled epoxy. The final sample pr eparation step before epoxy casting involved the spreading of a thin coat of wax over th e surface of the PVC ri ngs and the aluminum plate. With this step, the samples with the cured epoxy collars were easily removed from the plate and the rings. 2.3 Experimental Testing 2.3.1 Determination of Water Permeability A specimen flow fixture th at produces one dimensional water flow from one cylindrical face to the other, previously developed by Soongswang et al. (1988), was used to secure each specimen for testing (see Figur e 2-5). The Plexiglas ring above the sample is essentially a chamber filled with pressurized water. The opposite side of the sample is exposed to ambient pressure conditions. Theref ore, a pressure gradient is formed across the sample and water is forced to flow through it. Mortar or concrete sample 25.4 mm (1.0 in) 19.1 mm (0.75 in) 19.1 mm (0.75 in) Plexiglas Plate Plexiglas Plate Plexiglas Ring Water Inflow Water Outflow Steel Bolts Gasket Rings 50.8 mm (2.0 in) Epoxy Coating (to seal side of sample) Epoxy collar Epoxy collar Figure 2-5. Schematic diagram of water permeability flow fixture

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37 During each test, water was driven thr ough a specimen by applying an upstream absolute pressure of 584 kPa (84.7 psi) to a continuous water column residing above the specimen. The downstream side of the sample was exposed to atmospheric conditions and thus was maintained at an absolute pressure of 101.3 kPa (14.7 psi). By measuring the change in position of the top of the wate r column inside a metering tube through time (see Figure 2-6), and by knowing the interior cross-sectiona l area of the tubing (which was experimentally determined at the test pr essure used), the volum etric flow rate of water through each specimen could be determined to within a resolution of 10 mm3 (0.0006 in3)—small enough to quantify daily flow even for the lowest permeability Air Pressure Source Initial Water Level (@ time = 0) Final Water Level (@ time = t) Change in height over time Ambient conditions Water permeability fixture Tube with known inside diamter Figure 2-6. Measurement of flow rate in water permeameter

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38 materials tested. Flow measurements continue d until a steady state fl ow rate through each specimen was achieved. Due to the very low water permeability of the concrete and mortar mixtures tested in this study, the ti me required to achieve a steady state condition exceeded four weeks in some cases. In order to compute the intrinsic water permeability (wK ) for each specimen, the steady state mass flow rate (mQ ) was computed from the volum etric flow rate measured in the metering tube as: tube mvhA QQ t (2-1) where mQ is the mass flow rate th rough the specimen (kg/sec), is the water permeant density (kg/m3), vQ is the volumetric flow rate (m3/sec), h is the change of permeant liquid level in the metering tube (m), tubeA is the inner cross-sectional area of the metering tube (m2), and t is the duration of time—unde r steady state conditions—over which the change of liquid height h occurred. Darcy’s law for one-dimensional viscous, incompressible fluid fl ow through a porous medium was then used to determine the intrinsic water permeability (wK ): ()m w hQH K APP (2-2) where is the absolute viscosity of water (Pa-s), H is the height (thickness) of mortar specimen (m), A is the cross-sectional area of the specimen (m2), hP is the high-pressure upstream pressure (Pa), and P is the low-pressure dow nstream pressure (Pa).

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39 2.3.2 Gas Permeability 2.3.2.1 Measurement of gas permeability A key element of this study involved the development of a new nitrogen gas permeameter capable not only of measuring apparent gas permeability but also of controlling pressures on both faces of the test specimen. Thus, both the pressure gradient across the specimen and the mean pressure in the specimen can be controlled during testing. A schematic diagram of the overall te st apparatus is shown in Figure 2-7. Main components include a regulated high pressu re nitrogen source, a compression-sealed fixture for generating one-dimensional flow th rough cylindrical test specimens, flow rate metering devices (a metering tank and volumetri c flow meters), and downstream pressure regulation. During a permeability test, gas is forced to flow through the specimen being tested along an imposed pressure gradient. By meas uring the steady-state gas flow rate through the specimen, permeability can be computed as described later. When a specimen was scheduled for testing, it would be installed in the one-dimen sional flow fixture that was developed as part of this study (shown in Fi gure 2-8). Two hollow cylindrical aluminum rings extend between the surfaces of the e poxy collar and the surfaces of 25.4 mm (1.0 in.) thick aluminum end plates thus formi ng upstream and downstream pressure chambers on either side of the specimen. Deformab le O-ring gaskets were installed in groves machined into each side of the pressure ch amber rings and then compressed by tightening eight high-strength bolts that spanned between the rigid end plates. Submerging the apparatus under water while pressurizing both chambers verified that the system was sealed and that no leaks occurred.

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40 Over-pressure relief valve Discharge valve Venturi vacuum Pressure transducer 0-3.4 atm (0-50 psia)N 2 supplyNitrogen regulator 1-137.1 atm (0-2000 psig) PVC metering tanks, rated for 10.5 atm (140 psig) J-type thermocouple Over-pressure relief valve Discharge valve J-type thermocouple Back pressure regulator, 1-5.08 atm (0-60 psig) Pressure transducer 1-35.0 atm (0-500 psig) Compressed air supply J-type thermocouple J-type thermocouple Air filter J-type thermocouple Pressure transducer 0-6.80 atm (0-100 psia) Pressure transducer 0-6.80 atm (0-100 psia) Back pressure regulator, 1-5.08 atm (0-60 psig) Pressure transducer 0-3.4 atm (0-50 psia) Figure 2-7. Schematic diagram of gas (nitrogen) permeameter Pressure in the upstream chamber of th e flow fixture was controlled by a highpressure regulator on the nitrogen supply. Pressure in the downstream chamber was controlled by using a backpressure regulator in the line connecting the flow fixture to the metering tank. A backpressure regulator main tains a fixed magnitude of pressure at its upstream side by permitting gas to bleed through whenever the upstream pressure attempts to exceed the set regulation value. In the type of backpressure regulator used in

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41 Mortar or concrete sample 38.1 mm (1.5 in) 25.4 mm (1.0 in) 25.4 mm (1.0 in) 19.1 mm (0.75 in) 19.1 mm (0.75 in) Aluminum Plate Aluminum Plate Aluminum Ring Aluminum Ring Gas Inflow Gas Outflow High Strength Steel Bolts Gasket Rings Epoxy collar Epoxy collar (a) (b) Figure 2-8. Gas permeability fl ow fixture: (a) Schematic of the gas permeability fixture, (b) Photo of the assembly with a sample installed

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42 this study, all bleed-through gas exits the regulator through a th readed port (some regulators simply bleed into the atmosphere through non-threaded vent s holes). Pressures in the upstream pressure chamber, downstream chamber (before the back-pressure regulator), and in the metering tank were reco rded electronically throughout the duration of each test using pressure transducers. Pr essure gages were also installed on the flow fixture plates and on the metering tank to allo w manual verification of the pressure in the upstream and downstream chambers. By permitting the pressure on both the upstream and downstream sides of the specimen to be controlled (via the nitrogen regulator and backpressure regulator), the permeameter allows both the pressure differen tial across the sample as well as the mean (average) pressure in the sample to be varied from one test to another. As will be demonstrated in the following section, being able to run multiple tests at different mean pressure levels is an essential part of the pr ocess of determining gas slip flow parameters. Each permeability test conducted in this study proceeded as follows. First, the target upstream, high-pressure (hP) and downstream, low-pressure (P) values were chosen to achieve the desired mean pressure 1 2 mhPPP in the specimen. The backpressure regulator was adjusted to produce the desired pressure (P) at the downstream side of the flow fi xture. After installing an e poxy collared specimen into the flow fixture and compressing the O-ring seals, th e fixture was attached to the rest of the system and all flow tube connections were secured. A venturi vacuum device was then used to vacuum the entire system (pressu re chambers, tubes, and metering tank) to remove all air from the system. Since the pressure in the meteri ng tank would later be correlated to nitrogen density for mass flow calculations, it was important that all gases

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43 other than nitrogen be present in only neglig ibly small amounts. Vacuuming the system before each test ensured that only nitr ogen was present in significant amounts. Next, gas flow through the system was initia ted by allowing nitrogen to flow into the upstream pressure chamber at pressure hP. Once gas flowed through the specimen, pressure would build at the ups tream side of the backpressure regulator and thus also in the downstream chamber of the flow fixtur e. When the target pressure for the backpressure regulator was reached, gas woul d start to bleed through to the metering tank. Steady state flow conditions were know n to have been reached when the upstream and downstream chamber pressures stabilized and the rate of increase of pressure in the metering tank reached a constant value. In a ddition, the stabilization of gas flow rate was verified by monitoring a set of flow meters in the line of ga s flow just downstream of the test specimen. Throughout each test, a data acquisition syst em was used to monitor temperatures (measured with thermocouples) in the flow path as well as in the metering tank. In all tests run, the temperature vari ations from location to locati on and from one point in time to another during the test were found to be negligible. Thus, flow assumed to be was isothermal. In order to compute the apparent gas permeability for each specimen at each mean pressure tested, the mass flow rate under st eady state flow conditions first had to be computed using the relationship: tank mV m Q tt (2-3) where mQ is the mass flow rate th rough the specimen (kg/sec), m (kg) is the change of nitrogen mass in the metering tank, t is the duration of time over which the mass

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44 change occurred (sec.), tankV is the tank volume (m3), and is the change of nitrogen density (kg/m3) over time increment t Treating nitrogen as an ideal gas, then we have the density relationship PRT where P is the gas pressure (Pa), R is the engineering gas constant fo r nitrogen (297 J/kgK), and T is the gas temperature (K). Under isothermal conditions (T=constant), PRT thus the steady state mass flow rate can be computed as: tank mVP Q R Tt (2-4) In order to make use of Equation 2-4, pr essure transducer data collected during each test was used to compute P for a selected duration of time t The validity of Equation 2-4 relies on the assumption that nitrogen is an ideal gas. To validate this assumption, and thus the accuracy of using m easured pressure changes to compute mass flow, direct measurements of ga s flow rate were also made using flow meters (see Figure 2-3). These devices measure total volumetric flow rate at a particular location (and pressure) in the flow path. Mass flow ra te data computed using Equation 2-4 was converted into volumetric flow ra te data using the relationship, vmQQ Using the ideal gas relationship PRT the volumetric flow rate vQ (m3/sec) at the location of the flow meters was then computed as: mm vQQRT Q P (2-5) where the pressure P and temperature T were both experimentally measured at the location of the volumetric flow meters (dow nstream of the specimen). Mass flow rates computed using tank pressure data and Equati on 2-4 were then convert ed into equivalent volumetric flow rates effective at the location of the flow meters using Equation 2-5.

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45 Volumetric flow rates computed in this manner were found to be in very close agreement with direct readings (measurements) taken fr om the flow meters. Thus, the assumption that nitrogen behaves as an ideal gas under the flow conditions present in the permeameter was confirmed and the use of tank pressure data to compute mass flow rates mQ using Equation 2-4 was validated. With the mass flow rate known, the apparent gas permeability ( g aK) of each specimen (at each mean test pressure) was then computed using the relationship (see API 1956 for a full derivation): 222m ga hQHRT K APP (2-6) where is the absolute viscosity of nitrogen (Pa-s) and all other terms have been previously defined. 2.3.2.2 Determination of gas slip-flow parameters Apparent gas permeability values, g aK, determined experimentally as described above, are sufficient only to characterize gas flow permeability at the same pressure as that utilized during the test. For example, a g aK value determined using a mean specimen pressure of mP= 10 atm (147 psi) will not, in general, provide useful information for predicting gas flow rates if the flow pressure of interest differs significantly from 10 atm. Particularly in low permeability materials such as high strength mortar and concrete, th ere is significan t variation of g aKwith respect to changes of flow pressure (Kundt and Warbur g 1876, Klinkenberg 1941, API 1956).

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46 In this study, gas permeability was assu med to conform to Klinkenberg’s model (1941) of gas slip flow through porous medi a in which apparent gas permeability is pressure dependent as follows: m sf g gaP b K K 1 (2-7) where g K and s fb are characteristics of the por ous medium (the intrinsic gas permeability and the slip flow constant respectively), P is the flow pressure, and g aK is the apparent (or effective) pe rmeability at flow pressure P. Determination of the underlying material constants g K and s fb is accomplished by experimentally measuring multiple g aK values over a variety of different test pressures. Rewriting Equation 2-7 in an alternate form: m slope sf g ntercept i g gaP b K K K 1 (2-8) It becomes clear that apparent gas pe rmeability is linear with respect to the reciprocal of pressure ( 1P) and has an offset (intercept ) equal to the intrinsic gas permeability ( g K) at the infinite pressure condition (P or 10P). These characteristics are illustrated graphically in Figure 2-9. In order to determine g K and s fb, multiple gas permeability tests are conducte d in which the mean pressure in the specimen, 1 2 mhPPP is varied over a range of values. From each test, the measured g aK is plotted against the reciprocal of the mean specimen pressure 1mP. With several such experimentally determined data points, linear regr ession can be applied

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47 to the data (as illustrated in Figure 2-9) to extract the intrinsic gas permeability g K and slip flow constant s fb for the material. Once these have been determined, either Equation 2-7 or 2-8 can be used to quantify the apparent gas permeability of a porous medium at any desired pressure level. Using the nitrogen gas permeameter deve loped in this st udy, apparent gas permeabilities were computed for at least three specimens from each mortar mix. For each specimen, multiple gas permeability tests (a t different mean specimen test pressures) were conducted so that gas slip flow cons tants for each specimen could be computed. Gas permeabilityReciprocal of mean pressure, Typical apparent gas peremeability test data (Kga) at various mean pressures Intercept : intrinsic gas p ermeability (Kg) slope = bsfKgBest fit linear regression line m1/PK = K + K b (1/P )ga ggsfm Figure 2-9. Determination of gas permeability parameters from test data 2.3.3 Porosity The porosity of each mortar mixture te sted in this study was determined experimentally by measuring th e saturated-surface weight ( s W), buoyant weight (bW),

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48 and dry weight (dW) of each specimen and then using the following relationship (Klieger and Lamond 1994) to compute the porosity : s d s bWW WW (2-9) Porosity was computed in this manner fo r at least fifteen specimens from each batch and then averaged to ensure that a representative value was obtained. Buoyant weights and saturated surface dry weights we re measured shortly after cutting (wetsawing) each sample. Dry weights were de termined by drying each specimen in an oven where the temperature was ramped up to 105 C (221 F) until a consta nt specimen weight was achieved (indicating that all la tent water had been expelled). 2.3.4 Compressive Strength For each mixture, compression testing was carried out—in accordance with the ASTM C39 specifications (ASTM 1997)—for three 100 mm diameter, 200 mm tall (4 in. by 8 in.) cylinders. Tests were conducted after approximately 90 days of submerged water curing. 2.4 Results and Discussion Compressive strength, porosity, and permeability results for the mortar and concrete mixtures tested in this study are summarized in Table 2-2. As expected, compressive strength (c f ) was higher for mixtures with lower water-binder ratios whereas porosity ( ), intrinsic water permeability (wK), and intrinsic gas permeability ( g K) all decreased with decreasing water content. Slip flow constants ( s fb) were found to grow larger as the water-binder ratios decreased for mortar, but were smaller as the

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49 water-binder ratios decreased for the granite-aggregate conc rete (further discussion is below). Table 2-2. Summary of experimental results for the mixtures tested Mixture type Mix I.D. w/b % f`c, MPa (ksi) Kwx10-21, m2 (ft2) Kgx10-17, m2 (ft2) bsf, atm (psia) Kw/Kg 127.1 2.77 0.007 7.75 M20 0.198 11.2 (18.4) (29.78) (0.073) (113.9) 0.0405 127.0 2.85 0.008 6.63 M25 0.248 11.9 (18.4) (30.64) (0.085) (97.4) 0.0356 96.9 3.32 0.045 5.26 M30 0.298 13.0 (14.1) (35.76) (0.485) (77.3) 0.00737 85.9 4.12 0.10 4.49 Mortar M35 0.348 14.9 (12.5) (44.40) (1.086) (66.1) 0.00409 143.1 3.83 0.21 0.92 C20 0.196 7.9 (20.8) (41.21) (2.31) (13.5) 0.00179 122.8 4.61 0.81 0.99 C25 0.248 10.2 (17.8) (63.63) (8.72) (14.6) 0.00057 109.3 3.93 1.37 1.65 C30 0.297 13.1 (15.9) (42.32) (14.73) (24.2) 0.00029 106.4 4.75 1.90 0.90 C35 0.347 14.8 (15.4) (51.15) (20.49) (13.2) 0.00025 91.1 4.61 3.00 1.24 C40 0.398 16.0 (13.2) (49.61) (32.29) (18.2) 0.00015 79.7 5.00 4.21 1.86 Concrete with granite aggregate C45 0.448 19.3 (11.6) (53.83) (45.37) (27.4) 0.00012 104.1 7.17 2.68 1.56 L30 0.298 13.7 (15.1) (77.2) (28.9) (16.8) 0.000268 88.2 8.63 6.95 1.82 L35 0.347 15.0 (12.8) (92.9) (74.8) (19.6) 0.000124 78.7 11.66 72.77 1.22 Concrete with limerock aggregate L40 0.397 16.6 (11.4) (125.5) (783.3) (13.2) 0.000016 2.4.1 Water Permeability Test Results For each mortar mixture tested, flow rates were measured using the water permeameter described earlier for a period of time sufficient to achieve a steady state flow condition. In the lowest permeability mixtures, approximately five weeks were required to achieve steady state flow. Once steady state conditions were achieved, flow rate data were collected for an additional two weeks and then used in conjunction with Equations 2-1 and 2-2 to determine the intrinsic water permeability (wK) of the specimen

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50 being tested. wK values were computed in this way for at least three different specimens from each mixture and then averaged to give a single representative value (see Table 23). Table 2-3. Water permeability for mi xtures in experimental program Water Permeability Kw, x10-21 m2 (x10-21 ft2) Mix ID Sample 1 Sample 2 Sample 3 Sample 4 Mean Std. dev. 2.50 2.83 2.97 2.77 0.24 M20 (27.0) (30.5) (31.9) (29.8) (2.5) 3.13 3.21 2.20 2.85 0.56 M25 (33.7) (34.6) (23.7) (30.6) (6.1) 3.50 3.01 3.45 3.32 0.27 M30 (37.7) (32.4) (37.2) (35.8) (2.9) 4.42 3.79 4.16 4.12 0.32 M35 (47.6) (40.8) (44.7) (44.4) (3.4) 3.93 4.04 3.51 3.83 0.28 C20 (42.3) (43.5) (37.8) (41.2) (3.0) 4.85 4.88 4.11 4.61 0.44 C25 (52.2) (52.5) (44.2) (49.6) (4.7) 4.42 3.06 3.81 4.44 3.93 0.65 C30 (47.6) (32.9) (41.0) (47.8) (42.3) (7.0) 4.46 4.85 4.98 4.72 4.75 0.22 C35 (48.0) (52.2) (53.6) (51.3) (2.9) 4.51 3.45 5.86 4.61 1.21 C40 (48.6) (37.2) (63.1) (49.6) (13.0) 4.93 5.73 4.34 5.00 0.70 C45 (53.0) (61.7) (46.7) (53.8) (7.5) 7.09 4.62 9.65 7.33 7.17 2.06 L30 (76.3) (49.7) (103.9) (78.9) (77.2) (22.1) 8.66 9.38 9.67 6.81 8.63 1.28 L35 (93.2) (100.9) (104.0) (73.3) (92.9) (13.8) 11.08 12.29 13.49 9.78 11.66 1.59 L40 (119.3) (132.2) (145.2) (105.3) (125.5) (17.1) 2.4.2 Gas Permeability Test Results To determine the intrinsic gas perm eability and slip-flow (Klinkenberg’s) constant, each mortar specimen was tested in the gas permeameter using multiple upstream gas pressures. Pressure transducers were used to obtain accurate measurement of gas pressure during each te st. Intrinsic permeability and the slip flow constant were

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51 computed from each sample tested and are presented in Tables 2-4 and 2-5 and are graphically illustrated in Figur e 2-11. Apparent gas permeabil ity data for each specimen from each mixture tested are plotted in Appendix A. For each test specimen, linear regression was performed on the apparent gas permeability data ( g aK) using the reciprocal mean test pressures ( 1mP) as the independent variables. The sl ope and intercept from the re gression were then used to determine the intrinsic gas permeability and slip flow constant. Table 2-4. Intrinsic gas permeability for mixtures in experimental program Intrinsic Gas Permeability Kg, x10-17 m2 (x10-17 ft2) Mix ID Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Mean Std. dev. 0.0061 0.0081 0.0063 0.0068 0.0011 M20 (0.065) (0.087) (0.068) (0.073) (0.012) 0.0074 0.0083 0.0070 0.0093 0.0074 0.0080 0.0010 M25 (0.079) (0.089) (0.076) (0.100) (0.080) (0.086) (0.011) 0.0478 0.0472 0.0402 0.0451 0.0042 M30 (0.515) (0.508) (0.432) (0.485) (0.046) 0.0943 0.1174 0.0908 0.1009 0.0144 M35 (1.015) (1.264) (0.978) (1.086) (0.155) 0.21 0.17 0.25 0.23 0.21 0.03 C20 (2.2) (1.9) (2.6) (2.5) (2.3) (0.3) 0.97 0.70 0.76 0.81 0.14 C25 (10.5) (7.5) (8.1) (8.7) (1.6) 1.80 1.16 1.14 1.37 0.38 C30 (19.4) (12.5) (12.3) (14.7) (4.0) 1.79 1.73 2.00 2.11 1.90 0.18 C35 (19.2) (18.6) (21.5) (22.7) (20.5) (1.9) 2.32 3.11 3.57 3.00 0.63 C40 (25.0) (33.4) (38.4) (32.3) (6.8) 3.53 4.71 4.27 4.35 4.21 0.50 C45 (38.0) (50.7) (45.9) (46.8) (45.4) (5.3) 2.45 3.09 2.36 2.84 2.68 0.34 L30 (26.4) (33.3) (25.4) (30.5) (28.9) (3.7) 7.09 7.91 5.86 6.95 1.03 L35 (76.3) (85.1) (63.1) (74.8) (11.1) 90.00 61.62 64.61 74.86 72.77 12.81 L40 (968.8) (663.3) (695.5) (805.8) (783.3) (137.9)

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52 Table 2-5. Slip flow constant fo r mixtures in experimental program Slip flow constant bsf, atm (psia) Mix ID Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Mean Std. dev. 8.68 6.69 7.88 7.75 1.00 M20 (93.4) (72.0) (84.8) (83.4) (10.8) 8.32 6.02 6.27 5.39 7.12 6.50 1.27 M25 (89.6) (64.9) (67.5) (58.1) (76.6) (70.0) (13.6) 4.35 6.02 5.40 5.26 0.84 M30 (46.9) (64.8) (58.1) (56.6) (9.0) 4.65 4.57 4.26 4.49 0.21 M35 (50.0) (49.2) (45.8) (48.4) (2.2) 0.67 0.98 0.74 1.28 0.92 0.28 C20 (7.2) (10.5) (7.9) (13.8) (9.8) (3.0) 0.78 1.10 1.10 0.99 0.19 C25 (8.4) (11.8) (11.9) (10.7) (2.0) 0.92 1.57 2.45 1.65 0.77 C30 (9.9) (16.9) (26.4) (17.8) (8.3) 1.13 0.95 0.77 0.75 0.90 0.18 C35 (12.1) (10.2) (8.3) (8.1) (9.7) (1.9) 1.39 1.24 1.09 1.24 0.15 C40 (14.9) (13.4) (11.7) (13.4) (1.6) 2.07 2.07 1.85 1.47 1.86 0.29 C45 (22.3) (22.3) (19.9) (15.8) (20.1) (3.1) 1.59 1.35 1.33 1.96 1.56 0.29 L30 (17.1) (14.6) (14.3) (21.1) (16.8) (3.2) 2.19 1.75 1.51 1.82 0.35 L35 (23.6) (18.8) (16.3) (19.6) (3.7) 1.01 1.72 1.50 0.67 1.22 0.47 L40 (10.9) (18.5) (16.1) (7.2) (13.2) (5.1)

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53 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Mixture identification M35 M30 M25 M20 (a) 0 2 4 6 8 10 0.0 0.1 0.2 0.3 0.4 0.5 0 20 40 60 80 100 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Mixture identification C45 C40 C35 C30 C25 C20 (b) Figure 2-10. Gas permeability as a function of the reciprocal of the mean pressure: (a) mortar (b) Concrete with granite a ggregate, (c) Concrete with limerock aggregate

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54 0 20 40 60 80 100 120 140 0.0 0.1 0.2 0.3 0.4 0.5 0 200 400 600 800 1000 1200 1400 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Mixture identification L40 L35 L30 (c) Figure 2-11. Continued The gas permeability data summarized in Table 2-2 and detailed in Table 2-3 indicate a trend consistent with observations made by othe r researchers (Bamforth 1987, API 1956) in that the slip flow constants ( s fb) were found to grow larger as the waterbinder ratios decreased. In addition, the observed s fb values indicate that the apparent gas permeability of high strength, low permeab ility mixtures can vary significantly with pressure changes. To demonstrate this c oncept, consider the M20 mixture (see Table 22) with s fb= 7.748 atm (0.785 MPa, 114 psi). Recalling Equation 2-7, the apparent gas permeability for a particular flow pressure is given by 1gagsfKKbP Consider two different gas flow situations involving the M20 material each at a different pressure, 1P = 5 atm (0.51 MPa, 73.5 psi) and 2P = 50 atm (5.1 MPa, 735 psi). The difference in

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55 permeability for these two flow conditions can be quantified by taking the ratio of their apparent gas permeabilities at each flow pressure: ,1 ,2 21 17.748atm5atm 2.550 2.208 17.748atm50atm1.155 1gsf ga 1 ga gsfK KbP K KbP Note that the apparent (or effective) permeability of the material ,1 g aK at pressure 1P is more than double the permeability ,2 g aK of the same material carrying gas flow at pressure 2P. Proper prediction of gas flow th rough low permeability materials—e.g., high strength mortar and concre te—thus requires both considerat ion of slip flow effects and appropriate determination of the slip flow constant ( s fb). Curve fitting in the form of logarithmic regression was also used to establish a relationship between s fb and g K for the materials tested. Based on fitting the data in Table 2-2, the following re lationship was found for the mortar mixtures tested: 0.1725 33.51710sfgbK (2-10) where s fb is measured in atm and g K is measured in m2 (the coefficient of correlation, 2 R for this relationship was 0.714). In Fi gure 2-12, Equation 2-10 is compared to a relationship proposed by the AP I (1956). The API relationship was developed for porous materials having higher permeability than the mortar materials tested in the present study. Thus, in order to compare it to Equation 2-10, it had to be extended beyond its originally intended range of applicability. Despite this fact, both relationships exhibit similar trends in that s fb varies logarithmically with intrinsic permeability g K.

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56 1 10 100 1000 1 10 100 1000 Slip flow constant, bsf (atm)Intrinsic gas permeability, Kg (x10-20 m2) Relationship proposed by API (1956) Equation fitted to mortar mixture data Mortar mixture data 0.1725 33.51710sfgbK 0.390 61.09210sfgbK Figure 2-12. Relationship between the slip flow constant and intrinsic gas permeability for the mortar mixtures A similar logarithmic relationship between s fb and g K was not found to exist for the concrete mixtures. In fact, there was a tendency for the slip flow constant to decrease for the granite-aggregate concrete mixtures rather than increas e with an increasing intrinsic permeability. Between the most and least permeable granite aggregate concrete mixtures, s fbdecreased by a factor of two even though the permeability decreased by a factor twenty, which indicates that there is not a strong relations hip between these two values. Figure 2-13 shows the data from a ll of the mixtures and how the data for the concrete tends to deviate from th e relationship given by Equation 2-10.

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57 Figure 2-13. Intrinsic gas perm eability and slip flow data for all the mixtures in the experimental program It is believed that there is channeling due to the CaOH structure at the interface between the granite and the su rrounding mortar. This would explain the increase of the slip flow constant with an increase in intrinsic permeability. B ecause the gas flowing through the mixture will attempt to find the path of least resistance, flow will occur at the aggregate-mortar interface. This holds true if porous permeability of the mortar material surrounding the aggregate is lo wer than the flow capacity at the aggregate-mortar interface. There will be flow through the porous material, but it may be insignificant compared to the interface fl ow. Comparing two mixtures one with a high permeability and one with a low permeability a greater proportion of flow will occur at the interface rather than through the mortar material for the mixture with lower permeability. This 0.01 0.1 1 10 100 0.001 0.01 0.1 1 10 100 1000 Slip flow constant, bsf (atm)Intrinsic gas permeability, Kg (x10-17 m2) Mixture identification Mortar, M20-M25 Concrete, C20-C45 Concrete, L30-L40 Equation 2-10

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58 may explain why the slip flow constant ac tually increases with permeability for the granite-aggregate concrete. To better understand the relationship between pre ssure and apparent gas permeability, a formula directly relating the two can provide additional insight. If Equation 2-10 is substituted into Equation 2-7, we obtain a formula that predicts apparent gas permeability ( g aK) directly as a function of intr insic gas permeab ility and flow pressure: 0.8275 31 3.51710gaggKKK P (2-11) Figure 2-14 graphically illu strates Equation 2-11 evalua ted for materials having several different intrinsic gas permeabilities. This figure can be used to rapidly determine the apparent gas permeability for a particular combination of material and flow pressure and can be used to qualitatively determine the sensitivity of apparent permeability to changes in flow pressure. For example, at pressures exceeding approximately P = 50 atm (5.1 MPa, 735 psi), there is almost no variation of g aK for moderate changes in pressure. However, for pressures less than P = 10 atm (1.01 MPa, 147 psi), g aK can change significantly with changes in pressure.

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59 1E-19 1E-18 1E-17 1E-16 0.11101001000 Flow pressure, P (atm)Apparent gas permeability K (m 2 ) Kg = 1 x 10-19 m2At high pressure, the apparent gas permeability converges to the intrinsic gas permeabilty. At low pressure, the apparent gas permeability is well above the intrinsic gas permeabilty. Mean pressure < 1 atm requires a below-atmospheric condition. ga Kg = 10 x 10-19 m2Kg = 2 x 10-19 m2Kg = 3 x 10-19 m2Lines of equal intrinsic gas permeability, Kg Figure 2-14. Variation of gas pe rmeability with flow pressure If neither the water nor nitrogen permeants used in this study reacted with the cementitious materials tested, then upon co mputing the intrinsic water permeability wK and intrinsic gas permeability g K from measured flow data, one should find that wgKK for each specimen. When plot ted graphically, the relationship wgKK is called a “line of equality.” In Figure 2-15 the line of equality is compared to the permeability data (values of wK and g K) experimentally measured in this study. The trend of the experimental data indicates that wgKK for all cases. When water passes through a cementitious material—whether in a permeability test or in a structural

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60 application—the effect of microstructure sw elling due to contact wi th water reduces the permeability and the material exhibits a fundame ntally different resistance to flow than that which would be determined using non-re active permeants (e.g., nitrogen, dry air, etc.). In addition, because water molecules ar e much larger than gas molecules, the water molecules have a more difficult time migrati ng through the capillary system. Rather than having a single intrinsic permeability that fu lly characterizes flow through the material (i.e. wgKKK as the line of equality implies), there are two material parameters, wK and g K, that must each be experimentally de termined by separate procedures. The difference between the trend of experimental data and the line of equality shown in Figure 2-15 graphically i llustrates this point. 0.001 0.01 0.1 1 10 100 0.001 0.01 0.1 1 10 100 Intrinsic gas permeability, Kg (x10-17 m2)Intrinsic water permeability, Kw (x10-17 m2) Mixture identification Mortar, M20-M25 Concrete, C20-C45 Concrete, L30-L40 Line of equality Figure 2-15. Relationship between gas and water permeability for mortar mixtures

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61 2.4.3 Porosity Porosity calculations based on buoyant, sa turate-surface-dry, and dry weights are presented in Table 2-6 for the mixtures in the experimental program. There was very little variation in porosity between specime ns of each mixture, except for the L30 mixture. It is believed that this mixt ure may have been over-vibrated during casting Table 2-6. Porosity values for mixtures in experimental program Mix ID Spec. Num. M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 1 11.38 11.83 12.88 14.737.92 10.1613.3114.3715.9120.32 16.59 15.1417.37 2 11.57 11.88 12.49 14.887.48 10.2713.9215.6916.0320.45 15.39 15.4817.47 3 11.83 12.06 13.00 14.968.05 9.47 13.2215.3714.9018.17 14.04 15.1816.73 4 10.85 11.99 13.30 15.187.90 11.2912.5814.3815.6820.12 13.01 14.1916.76 5 11.10 11.87 13.16 15.157.79 10.7313.0216.5616.2820.14 16.60 15.2616.72 6 11.08 12.05 13.35 15.177.37 9.62 11.2216.4815.0018.99 13.63 15.0016.68 7 11.59 12.20 12.61 15.208.31 9.90 11.9815.1015.6219.98 12.62 15.7016.56 8 11.12 12.05 13.19 15.038.19 9.45 13.1316.1615.6919.31 11.65 14.6216.13 9 11.40 11.94 12.96 14.947.64 9.40 12.6515.4414.9617.47 16.95 14.8615.96 10 11.13 11.86 13.50 15.148.06 10.7713.4214.7916.2620.93 14.80 15.2016.78 11 11.33 12.05 12.65 15.028.08 10.3013.8814.4217.2719.58 12.30 15.2216.26 12 11.31 12.08 13.25 15.117.58 9.86 12.7913.3116.9818.02 11.57 13.8616.61 13 10.78 11.98 12.88 14.788.12 9.79 14.0814.3016.4319.01 11.64 14.6816.11 14 10.70 11.92 12.82 14.677.74 10.7313.8115.7916.4919.32 11.07 15.5415.55 15 10.63 11.93 14.677.63 10.4812.7114.3015.5717.57 16 12.21 8.09 14.0216.4819.18 17 11.58 7.99 13.7316.1620.48 18 11.70 7.79 12.8915.2918.78 19 11.91 8.02 14.1515.8520.56 20 11.54 8.04 15.0616.6718.92 21 11.59 7.47 15.0316.4218.30 22 11.77 23 11.57 24 11.63 25 11.86 Mean 11.19 11.88 13.00 14.977.87 10.1513.0514.8216.0019.32 13.71 15.0016.55 Std. dev. 0.35 0.19 0.30 0.19 0.26 0.57 0.77 0.99 0.65 1.02 2.06 0.51 0.52

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62 resulting in much of the aggregate settling to the bottom of the mold s. Therefore, the specimens used for gas permeability testing of that mixture were selected based on the closeness of the specimen poros ity to the mean of the mixt ure porosity. The porosity of the water permeability specimens could not be targeted for this mixture because these were not tested for porosity. Therefore water permeability specimens were cut from the middle of the 101.6x304.8 mm (4.0x8.0 in.) samp les in attempt to obt ain material that was not overor under-compacted. 2.4.4 Compressive Strength The compressive strength was calculated based on testing of two to four 102x203 mm (4.0x8.0 in.) cylindrical specimens from each mixture. Despite the fact that the ASTM specification calls for at least three speci mens to be tested from each mixture, the batch size of some of the mixtures limited th e number of specimens to two in some cases. All specimens were tested with a constant st ress rate of 0.165 MPa/ s (23.9 psi/s), which corresponds to a load rate of approximately 1321 N/s (297 lb/s) for the 102 mm (4.0 in.) diameter cylinders tested. Resu lts are presented in Table 2-7. The results show that the compressive stre ngths for these mixtures were very high, which should be expected given the proportions and ingredients in the mixtures. The mixtures with limerock aggregate had lower co mpressive strength than the mixtures with granite aggregate, even though the proportions were the same. This is mainly due the quality and strength of limerock versus gr anite. The compressive strength of the limerock mixtures was actually higher than what was anticipated based on previous research (Klieger and Lamond 1994). The comp ressive strengths of the mortar mixtures were also similar to those previously obt ained in other research endeavors.

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63 Table 2-7. Results fr om compression testing Maximum compressive stress, MPa (ksi) Mix ID Sample 1 Sample 2 Sample 3 Sample 4 Mean Std. dev. 122.9 131.2 125.7 128.9 127.2 3.64 M20 (17.8) (19.0) (18.2) (18.7) (18.4) (0.53) 135.3 123.4 122.2 127.0 7.25 M25 (19.6) (17.9) (17.7) (18.4) (1.05) 92.2 91.3 100.3 104.0 96.9 6.20 M30 (13.4) (13.2) (14.5) (15.1) (14.1) (0.90) 88.4 83.4 85.9 3.55 M35 (12.8) (12.1) (12.5) (0.52) 140.8 140.1 136.0 139.0 2.59 C20 (20.4) (20.3) (19.7) (20.2) (0.38) 124.1 121.5 122.8 1.84 C25 (18.0) (17.6) (17.8) (0.27) 109.7 108.9 109.3 0.57 C30 (15.9) (15.8) (15.9) (0.08) 107.2 107.6 104.4 106.4 1.73 C35 (15.5) (15.6) (15.1) (15.4) (0.25) 91.7 90.7 90.8 91.1 0.58 C40 (13.3) (13.2) (13.2) (13.2) (0.08) 79.8 79.4 79.9 79.7 0.27 C45 (11.6) (11.5) (11.6) (11.6) (0.04) 101.3 107.6 103.3 104.1 3.22 L30 (14.7) (15.6) (15.0) (15.1) (0.47) 86.2 95.9 82.5 88.2 6.96 L35 (12.5) (13.9) (12.0) (12.8) (1.01) 85.5 77.1 73.5 78.7 6.17 L40 (12.4) (11.2) (10.7) (11.4) (0.90) 2.5 Discussion and Conclusions Experimental test apparatuses capab le of quantifying both water and gas permeability parameters for cementitious materials have been developed and presented in this chapter. Based on resu lts obtained from tests conduc ted on different high strength, low permeability mortar and concrete mixtur es, the following conclusions can be made. Accurate and repeatable measurement of gas permeability parameters can be achieved using the gas permeability test apparatus described herein. Redundant measurement of gas flow rates made usi ng both pressure change measurements and direct volumetric flow measurement, confirmed the accuracy of the gas permeability data collected.

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64 Slip flow constants for low permeability cementitious materials are sufficiently large for most practical flow problems, e.g., flows driven by pressures between 1 atm and 50 atm, that slip flow effects mu st be considered in order to accurately predict flow rates. In addition, Klinke nberg’s model of slip flow was found to represent the gas flow data measured in this study to a satisfactory level of accuracy. A relationship between slip flow constant and intrinsic gas permeability has been proposed for mortar mixtures. The trend represented by this relationship, namely that slip flow constants decrease (become less influential on flow rate) with increasing gas permeability (related to incr easing water-binder rati o) is consistent with results obtained by other researchers for non-cementitious porous materials. This particular relationship did not hold true for the concrete mixtures tested.

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65 CHAPTER 3 EXPERIMENTAL EVALUATION OF CONCRETE PERFORMANCE DURING SEVERE THERMAL EXPOSURE Direct measurement of pore pressure, te mperature, and spalling within concrete during extreme thermal loading provides valu able information rega rding the heat and mass flow that occur. The experimental progr am presented in this chapter includes direct measurements within various concrete a nd mortar mixtures during experimentally generated heating conditions th at are representative of fires. Methods to measure pore pressure, temperature, and sp alling have been developed an d an apparatus for providing heating conditions similar fires was constructed. A key goal of this study was to quantify pore pressure in concrete and mortar mixtures for which the permeability and porosity are also measured, which are key inputs to heat and mass flow numerical models. Research to evaluate heat and mass flow in concrete during fire has prev iously been conducted through numerical means (Bazant 1997, Gawi n et al. 1999, Tenchev et al. 2001) and through experimental means to a more lim ited extent (Kodur and Sultan 1997, Kutzing 2000 Phan et al. 2000, Phan et al. 2001). On ly a limited number of endeavors, however, have attempted to couple an experimental program involving measurement of internal pore pressure together with the implementa tion of a numerical c ode (Consolazio et al. 1998, Khalifa et al. 2000). This chapter deve lops the link to the num erical part of the study (presented in Chapters 4 and 5) via an experimental program. The goals of this chapter are to present: Apparatus developed for generating heating conditions similar to those of a fire,

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66 Instrumentation methods for measurement of internal pore pressure, temperature, and spalling within concrete materials, Detailed experimental data from se lect concrete and mortar mixtures. 3.1 Experimental Test Methods and Equipment 3.1.1 Thermal Sample There is limited research in the literat ure regarding quantifying pore pressure within concrete during fire conditions, thus li ttle basis was available for choosing sample geometry. More complex geometries and sy stems (e.g., structural members such as beams and columns) have more complex stress states and thus the isolation of the stress caused pore pressure is more difficult. C hoosing the specimen si ze and shape hinged on the goal of producing a one-dimensional conditio n of heat and moistu re flow with the minimum amount of thermo-m echanical stresses. The thermal specimens used in this study we re cylindrically shap ed with diameters of 305 mm (12 in.) and thicknesse s of 76 mm (3 in.) and were heated on one of the round faces while keeping the other face exposed to ambient conditions. This specimen shape was chosen to eliminate any unusual stress development or mass flow. The thickness was chosen based on results from previous rese arch (Consolazio et al. 1998, Khalifa et al. 2000) and because the majority of spalling in preliminary experimentation was found to be very close to the heated surface. Ther mal specimens initially had diameters of 152 mm (6 in.), but it was found that measured por e pressures in such samples were erratic during heating. After the test specimens were cured for 28 days submerged in water, extensive preparation was required before thermal testing. Four holes were dr illed to a depth of 12.7 mm (0.5 in.) and a diam eter of 12.7 mm (0.5 in.) on what would be the unheated

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67 side (or top) of each specimen. The holes were located at a distance of 25.4 mm (1.0 in.) from the outside edge of the specimen a nd were approximately equal circumferential distances apart. Bolts were then grouted into these holes (with cement paste) to provide a means of suspending the specimen above the furn ace (discussed later). Next, the sides of the specimens were coated with three to four layers of thermal ceramic mortar. These were applied at 24 hour increments to let each layer cure independent ly. The intention of this step was to limit the amount of heat es caping in the radial di rection during thermal testing. Specimens were then ready for th e embedded (cast-in) instrumentation to be connected the data acquisition system. 3.1.2 Instrumentation The experimental tests conducted in th is study required care in choosing the appropriate instrumentation a nd installation methods due to the very high temperatures involved. The installation procedure that wa s adopted involved s ecuring each piece of instrumentation in its proper location (i.e., distance from the heated surface) in the specimen formwork before casti ng. The goal was to ensure as much as possible that each sensor was well integrated into the concrete/mortar matrix. An alternative to casting th e concrete around the instru mentation involves grouting the instrumentation into drille d holes in the specimen after it has cured. However, this method can result in material discontinuity between the grout and the specimen which would affect the flow of pore constituents and heat near th e instrumentation. Such a method was used for a portion of this expe rimental program, but was abandoned after it was observed that significant moisture escap ed through the cool surface of the sample

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68 holes that were used to post-install the sensor s. The results presen ted therefore represent data collected from sensors which were placed prior to casting. To limit the effect of radial heat and mass flow on the measurement of internal pressure and temperature, the instrumentati on was placed at a comm on radial distance of 63.5 mm (2.5 in.) from the center of each specimen. The distance between the instrumentation and the outside edge was then 88.9 mm (3.5 in.), which was considered sufficient enough to elim inate edge effects. 3.1.2.1 Pressure measurement Direct measurement of internal pressure in concrete during fire can be useful for comparison to the results of a heat and ma ss flow modeling program A difficulty with direct measurement of internal pore pressure during fire, however, is that the temperature at the point of measurement typically far exceeds the phys ical limitations of most available pressure transducers. However, recent technological advances in sensor manufacturing have resulted in pore pressu re transducers that can withstand higher temperatures than those previously available. 3.1.2.1.1 Transducer size. Size was a major consideration for choosing the pressure transducer. The size of the pressu re transducer selected was relatively small compared to typical transducers (See Figure 3-1). The casing was cylindrical in shape and had a height of 9.53 mm (0.375 in.) and a di ameter of 2.54 mm (0.100 in.). This was the smallest transducer available from the selected manufacturer (Kulite Semiconductors) and was chosen to have a limited effect on he at and mass flow with in the concrete or mortar. In addition, this tr ansducer had the smallest ai r void volume at the point of pressure measurement (discussed in Chapter 4).

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69 3.1.2.1.2 Transducer specifications. The transducers had a maximum pressure capacity of 34.0 atm (500 psia) and were th ermally compensated up to 260 C (500 F). The temperature range on the transducer was the maximum available at the time of purchase. Transducers were available fr om the manufacturer that had maximum pressures far above 34.0 atm (500 psia), but previous research (C onsolazio et al. 1998, Khalfa et al. 2000, Khalifa et al. 2001) indicated that the test pore pressures would not exceed this value. In addition, as the ma ximum pressure range increases, the resolution of the pressure measurement decreases. Fo r instance, a transducer with a maximum pressure of 340.0 atm (5000 psia) had a resolu tion of 0.34 atm (5 ps ia) whereas one with a 34.0 atm (500 psia) maximum pressure had a resolution of 0.034 atm (0.5 psia). Figure 3-1. Photo of a por e pressure transducer

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70 Transducers were purchased from the manu facturer at two different times during the experimental program, resu lting in calibrations that we re slightly different, but similiar. The transducers in the first shipment were pressure-calibrated (by the manufacturer) at five differe nt temperatures: 23.9, 93.3, 148.9, 204.4, and 260.0 C (75, 200, 300, 400, and 500 F). The second shipment of transducers had an additional calibration at 37.8 C (100 F). When meas urement of pressure commenced during a thermal test, if the temperature at the tran sducer location was not within the calibration range (23.9 to 260.0 C), the voltage was extr apolated based on eith er the low or high temperature limits. For example, if th e temperature exceeded 260.0 C (500 F), the voltage was converted into pressure base d on the calibration at 260.0 C (500 F). At each temperature, each of the transducer s in the first shipment were subjected to five different pressures and the resulting voltage output was meas ured. The calibration pressures were 0.0, 8.5, 17.0, 25.5, and 34. 0 atm (0, 125, 250, 375, and 500 psia). In the second shipment, improvements were made to the instrumentation by the manufacturer to make the voltage-pressure relati onship more linear. Therefore, the second set of pressure transducers were only calibrated at 0.0, 17.0, and 34.0 atm (0, 250, and 500 psia). Thus for each pressure transducer, there was a calibration grid as shown in Table 3-1 (Appendix B contains the calibratio n grids for all of the pressure transducers used in this study). The output voltages measured during the thermal tests we re converted into pressures according to the calibration grids. 3.1.2.1.3 Installation method. Two different methods of embedding pore pressure transducers within the concrete samples were evaluated. In the first method (See Figure 3-2), each pressure transducer was embedde d into a lag bolt using a high melting point

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71 epoxy with the intention of being able to rec over the transducer afte r each thermal test. However, it was found that the temperatures experienced by the tr ansducers exceeded sensor limitations and thereby eliminate any ch ance of recovery. In addition, the thermal incompatibilities between the lag bolt (made of steel) and the concrete or mortar has the potential to cause significant cracking in the vicinity of th e pore pressure measurement. The second installation method (See Figure 33) involved embedding each pore pressure transducer directly into the concrete sp ecimen during casting. The effects of microcracking generated by drilling, inconsistencies in thermal expansion coefficients, etc. were thus eliminated. During experimental thermal tests involvi ng the use of the lag bolts, the entire sample would often split along th e location of the lag bolts (S ee Figure 3-4) as a result of thermal expansion differences. This type of failure adversely affects measurement of pressure because it may occur prior to pore pressure induced surface spalling thus altering internal moisture flow It was found that this type of specimen failure did not occur when the pressure trans ducers were directly embedded into the samples without the use of drilling lag bolts, and grout. Table 3-1. Calibration grid for a typical pore pressure transdu cer (grid entries is pressure transducer output in millivolts) Temp. Pressure 23.9 C (75 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) -0.43 -0.11 0.44 1.19 2.35 8.5 atm (125 psia) 21.17 21.79 22.38 23.03 23.92 17.0 atm (250 psia) 42.79 43.73 44.31 44.83 45.42 25.5 atm (375 psia) 64.4 65.65 66.23 66.61 66.69 34.0 atm (500 psia) 85.94 87.52 88.11 88.34 88.37

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72 Heated surface Drilled hole: 12.7 mm diam. (0.5 in.), grouted with mortar Lag bolt: 9.5 mm diam. (0.375 in.) High performance epoxy: melting point = 260 C (500 F) Pore pressure transducer: 2.54 mm diam., 9.5 mm length (0.100 in. diam., 0.375 in. length) Concrete/mortar test specimen Figure 3-2. Method for installa tion of pore pressure transduc er using a lag bolt assembly

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73 Concrete/mortar test specimen Unsheathed fine gage wired: 0.0762 mm (0.003 in.) diam. Transducer wire leads kept taut by securing above sample during casting Heated surface Pore pressure transducer: 2.54 mm diam., 9.5 mm length (0.100 in. diam., 0.375 in. length) Figure 3-3. Method for inst allation of pore pressure transducer by embedding the transducer.

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74 Concrete sample for thermal testing Lag bolts with embedded pore pressure transducers Typical crack pattern observed during thermal testing Heated surface Top view Side view (a) (b) Figure 3-4. Crack pattern due to thermal expansion incompatibility between lag bolt assembly and concrete sample: (a) Typi cal pattern of crack ing, (b) Photo of mortar sample after thermal cracking

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75 3.1.2.1.4 Verification of pressure measurement. To verify that the in-situ pressure that was measured during thermal tes ting was reliable, a pressure transducer was embedded into a small sample of mortar ma terial and pressurized for a variety of different conditions. The samp le of mortar was cylindrical with a diameter of 25.4 mm (1.0 in.) and a height of 12.7 mm (0.5 in.) and was approximately the mixture proportions of the M35 mortar mixture (without silica fume or super plasticizer). The specimen was pressurized with nitrogen gas, which was monitored by an additional pressure transducer attached to the source. The size of specimen wa s chosen so that it c ould be inserted into the gas permeameter (inside the upstream pressure chamber) where the gas pressure applied can be controlled with a high degree of accuracy. The pore pressure transducer was fully embedded into the mortar speci men to mimic the conditions used for installation in a typical thermal specimen. The pressures applied to the specimen a nd those measured from the pore pressure transducer are presented in Figure 3-5. A number of different transient pressure conditions were applied to the specimen to evaluate the re sponse time of the transducer and its long-term stability. The magnitude of pressures applied was based on values that were anticipated during thermal testing. The embedded transducer produced accurate pressures, in comparison to the pressure tran sducer attached to the nitrogen source, and showed accurate responses to bot h abrupt and gradual increases in pressure. In addition, the embedded transducer performed well in the tests of long term-stability and to a decrease in pressure. Based on these result s, the pressure transducers and embedment methods were deemed to be reliable for m easurement of pore pressure within concrete specimens.

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76 Figure 3-5. Response of embedded pressure tran sducer to an applied pressure of nitrogen gas 3.1.2.2 Spalling detection A new type of instrumentation was devel oped to quantify the location and time at which spalling occurred during thermal testing. The instrumentation consisted of fine gage wire (diameter of 0.0762 mm (0.003 in. )) embedded within the concrete and looped at a prescribed distance from the heated surf ace (see Figure 3-6). Similar to the pressure transducers, concrete was cas t around the wires which were kept taut by securing them above and below the sample. Spalling was detected by supplying a current through the ends of one of the looping wires while measur ing resistance. When a wire is unbroken, a closed circuit exists and the el ectrical resistance is nearly zero. When a wire is broken, the circuit is no longer closed and the re sistance becomes nearly infinite. 0 3 6 9 12 15 0 1800 3600 5400 7200 9000 10800 0 30 60 90 120 150 180 210 0 30 60 90 120 150 180 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Transducer Pressure supply Embedded Evaluation of abrupt increase in pressure Evaluation of long term stability Evaluation of gradual increase in pressure Evaluation of decrease in pressure

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77 time = 0 time >> 0 Heat Input Heat Input resistance = 0 (no spalling detected) resistance = infinite (spalling detected) Fine gage wire Concrete or mortarWire breaks during spalling Figure 3-6. Method for detecti ng spalling during thermal testing Through a series of wires l ooping at different depths fr om the heated surface and continuous measurement of resistance thr oughout the duration of a thermal test, the location and time of spalling may be quantified. For example, if concrete spalls off at a depth of 13 mm (0.512 in.) from the initial loca tion of the heated surf ace, a wire loop that ends at a distance of 10 mm (0.394 in.) from the heated surface will break and one that ends at 15 mm (0.591 in.) will not. Becau se the resistance is continually measured through both wires, it is then known that sp alling occurred between 10 and 15 mm (0.394 and 0.591 in) at a particular time. The locati ons of the spalling detection instrumentation for this experimental program were 0, 5, 10, 15, and 20 mm (0, 0.197, 0.394, 0.591, 0.787 in.) from the heated surface. For redundancy, two additional wire l oops were used at 5 and 10 mm (0.197 and 0.394 in.) from the heated surface. Figure 3-7 shows the

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78 instrumentation layout of a typical th ermal sample and Figure 3-8 shows the instrumentation before placement of the M25 mortar mixture. To data acquisition system, Supplying current, measuring resistance Acrylic ring for securing sheathed wire Fine gage wire Teflon sheathing Diameter = 0.0762 mm (0.003 in.) Fine gage wire Unsheathed Diameter = 0.0762 mm (0.003 in.) Concrete/mortar test specimen Diameter = 304.8 mm (12 in.) Thickness = 76.2 mm (3 in.) Plywood formwork Thickness = 12.7 mm (0.5 in.) Unsheathed wire secured to plywood Sheathed wire secured to ring Radius =152.4 mm (6.0 in.) Radius = 63.5 mm (2.5 in.) Center-to-center spacing between instrumentation Arc length = 12.7 mm (0.5 in.) Figure 3-7. Instrumentation la yout for measurement of spalling Two gas permeability tests were preformed to evaluate the effects of channeling of gas around the fine gage wire. Two identical specimens, one with a fine gage wire running through it and one without, were tested and it was found that the gas permeability

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79 was not affected by the wire. However, local channeling around the wire should be further explored in the future. 3.1.2.3 Temperature measurement Temperature was measured at multiple dist ances from the heated surface to obtain transient temperature profiles across each sp ecimen. Measurements were taken using thermocouples at five different distances fr om the heated surface w ithin each concrete specimen: 0, 5, 10, 15, and 20 mm (0.000, 0.197, 0.394, 0.591, and 0.787 in.). K-type thermocouples were chosen because of their ability to measure the range of temperatures that the concrete might e xperience during testing (Bentley 1998a, 1998b). The maximum and minimum temperatures for K-type th ermocouples are 1250 C (2282 F) and –200 C Figure 3-8. Photo of a series of clos ed-loop wires for detection of spalling.

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80 (-28 F), respectively. In addition, the transient temperatures were used to convert the voltage output from the pressure transducers into pressure values. The calibration of the pressure transducers is based on temperature at the location of measurement. It was therefore necessary to measure temperature at the same distance from the heated surface as the location at which pressure was measured. Similar to the pressure tran sducers and spalling detecti on circuitry, thermocouples were cast directly into the c oncrete specimen. Prior to cas ting, each was secured in place in the specimen mold with fine-gage bare wi re anchored through the bottom of the mold. In addition, all thermocouples were positione d at the same radial distance as the pore pressure transducers and the spalling detection circuitry. 3.1.3 Gas Furnace For simulation of fire conditions, a propa ne-fueled furnace was constructed for the direct application of thermal loading. It wa s constructed in such a manner so that heat could be applied one-dimensionally to a cylindr ical specimens with a diameter of 304.8 mm (12.0 in.). An initial furnace was construc ted for specimens with a diameter of 152.4 mm (6.0 in.), but the specimen size was in creased midway through the experimental program. This increase rendered the first fu rnace geometrically in compatible with the new test specimen size and a new furnace was therefore constructed. 3.1.3.1 Furnace geometry The furnace consisted of three separate elem ents each made of thermal brick: (1) a base, (2) a heat box, and (3) an aperture for placement of th e test specimen. Figure 3-9 shows the geometry of each element, how the furnace was assembled, and the locations

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81 of various ports (for thermo couples, propane torches, and ignition) that were drilled through the walls of the heat box. The base consisted of ten bricks placed in such a manner that two rectangular shaped exhaust ports were created. These ports were necessary to alleviate the pressure within the heat box caused by the propane burners. The inside dimensions of the heat box were 342.9 x 342.9 x 342.9 mm (13.5 x 13.5 x 13.5 in.). The top of the furnace consisted of eight bricks laid flat with a 304.8 mm (12.0 in.) diameter hole cut through them fo r placement of the thermal specimen. Top Heat box Base Holes for thermocouples Holes for propane burners Hole for igniting propane burners Hole for placement of concrete/mortar test specimen, diam.=304.8 mm (12.0 in.) Figure 3-9. Propane furnace for thermal testing

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82 3.1.3.2 Thermal brick Thermal brick used to construct the fu rnace was obtained from Thermal Ceramics and was specifically designed for gas furn aces and electric kilns having a maximum temperature limit of 1788 C (3250 F). This mate rial also had excelle nt strength (modulus of rupture = 1.72 MPa (250 psi)) and durability relative to other insulating brick=. Thermal mortar was used to join individua l bricks and construct each furnace (See Figure 3-10). Figure 3-10. Propane furnace for thermal testing 3.1.3.3 Specimen suspension A suspension system was fabricated to hold each specimen in place above the thermal chamber of the furnace. The goal of the system was to provide a means of achieving one dimensional heat flow on one entire face of the specimen while introducing a minimum amount of lateral conf inement. This was accomplished by using

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83 a combination of bolts and plates in the c onfiguration shown in Fi gure 3-12. Four 101.6 mm (4.0 in.) long bolts were grouted into the specimen at a depth of 12.7 mm (0.5 in.). These bolts were then secured to struts that bear on a second plate spanning across the top of the furnace. Using this support method, one face of the cylindrical sample can be completely exposed to the heat source wit hout impediment and without mechanical restriction of the specimen (the specimen is free to thermally expa nd in the radial and ve rtical directions). In addition, because the anchor bolts terminate a significant distance (63.5 mm (2.5 in.)) from the heated surface, this support method effectively eliminates the influence of the anchor bolts on heat and moisture flow near the heated surface of the specimen. A photo of the experimental setup is shown in Figure 3-11. Figure 3-11. Thermal specimen suspended above the furnace.

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84 A: Bolts for supporting plate, 62.5 mm (2.5 in.) length 6.35 mm (0.25 in.) diameter F: Concrete/mortar test specimen, 304.8 mm (12.0 in.) diameter 76.2 mm (3.0 in.) thickness G: Thermal brick D: Struts (steel flat stock) supporting specimen and resting on plate, 254.0 mm (10.0 in.) length 38.1 mm (1.5 in.) width 5.1 mm (0.2 in.) thickness E: Steel plate for supporting struts, 508.0 mm (20.0 in.) length 152.4 mm (6.0 in.) width 12.7 mm (0.5 in.) thickness C: Bolts for suspending test specimen, 101.6 mm (4.0 in.) length 6.35 mm (0.25 in.) diameter B: Threaded bolt holes for bolts supporting thermal sample, 6.35 mm (0.25 in.) diameter BB BB E D D C C CC FG 11 2 2 (a) Figure 3-12. Apparatus for the suspension of the thermal specimen on top of furnace: (a) Top view, (b) View 1-1, (c) View 2-2

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85 A CAC D FG EB B (b) E G F A ACC DD B B (c) Figure 3-12. Continued 3.1.3.4 Heat supply The burners for supplying h eat to the furnace (Figure 313) were propane fueled and were custom built (Rex Price Company) to provide furnace temperatures similar to those experienced during fires. The amount of heat output by the burners during each thermal test was controlled by a pressure re gulator at the propane source. Typical thermal tests used a regulator setting of 2.36 atm (20 psig) to maintain a furnace timetemperature curve between th at specified by ASTM E119 and ASTM E1529. Multiple burners were simultaneously used to achieve very high temperatur e conditions whereas a single burner was used in instances where some what lower temperatures were desired.

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86 Figure 3-13. Propane burner entering the side of the furnace Figure 3-14 schematically illustrates the system used to internally heat the furnace. A number of safety precautions were taken in the design of the heat supply. Propane was chosen because of the lack of volatility with this type of fuel (minimum energy needed for ignition is higher than ma ny other fuels) and the ability of propane to produce high temperatures when burned. To prevent flame flashback from the burne rs into the tank, an arrestor valve was placed in the source line. 3.2 Experimental Program 3.2.1 One-Dimensional Thermal Loadin g, Fully Instrumented Specimens Five experimental tests were conducted us ing a refined instru mentation method. The refined test method refers to thermal te sting of the specimens with diameters of

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87 Propane tank Regulator Pressure transducer Propane burners Flashback arrestor On/off valves On/off valve Furnace Figure 3-14. Schematic of system for a pplying heat to the furnace from a propane source. 304.8 mm (12.0 in.) having pre ssure transducers embedded w ithout lag bolts. The five mixtures chosen for the experimental progr am consisted of two mortars (M25 and M35), two concretes with granite aggregate (C25 and C45), and one concrete with limerock aggregate (L35). The influence of permeability was investigated by testing both mortar and concrete (with gran ite aggregate) mixtures with diff erent water-binder ratios and thus different pore structures and permeabilities. To evaluate the influence of aggregate type, an additional mixture with limerock aggreg ate was also tested. The ingredient proportions for the mixtures te sted are presented in Table 3-2. Because the mixtures made for permeability and thermal testing were batched at a different time (although with the same proportions), a comparison of the co mposition is also shown in the table.

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88 Table 3-2. Proportions of the conc rete and mortar mixtures produced Mix ID Purpose Waterbinder ratio, w/b Watercement ratio, w/c Binderaggregate ratio, b/a Finecoarse aggregate ratio, fa/ca Silicabinder ratio, s/b Super plasticizerbinder ratio, SP/b Perm.1 0.248 0.275 0.499 0.098 0.0288 Thermal2 0.245 0.270 0.497 0.094 0.0294 M25 Diff.3 -1.2% -1.8% -0.4% -4.1% 2.1% Perm. 0.348 0.386 0.499 0.098 0.009 Thermal 0.346 0.381 0.496 0.094 0.011 M35 Diff. -0.6% -1.3% -0.6% -4.1% 22.2% Perm. 0.248 0.274 0.399 0.097 0.020 Thermal 0.245 0.270 0.397 0.093 0.019 C25 Diff. -1.2% -1.5% -0.5% -4.1% -5.0% Perm. 0.448 0.496 0.399 0.097 0.004 Thermal 0.446 0.492 0.397 0.093 0.004 C45 Diff. -0.4% -0.8% -0.5% 0.625 -4.1% 0.0% Perm. 0.347 0.384 0.398 0.096 0.012 Thermal 0.346 0.382 0.397 0.094 0.014 L35 Diff. -0.3% -0.5% -0.3% 0.625 -2.1% 16.7% 1 Mixture produced for measurement of permeability, porosity, and compressive strength 2 Mixture produced for thermal testing 3 Difference between mixtures 3.2.2 Qualitative Thermal Testing A qualitative experimental testing progr am was initiated to evaluate the susceptibility of moist concrete to explosive spalling due to pore pres sure development. The testing program consisted of subjecting both dry and saturated concrete and mortar materials to a sudden thermal loading and obs erving the resulting behavior. The goal of this program was to evaluate whether the ex istence of pore water within the skeletal structure of concrete had an effect on material fail ure during thermal loading The experimental tests were performed by placing 101.6 x 203.2 mm (4.0 x 8.0 in.) specimens (initially at room temperature) into an electric kiln th at was pre-heated to 1000 C (1832 F). Figure 3-15 shows a schematic diagram of the test setup and the location of the specimens during testing.

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89 Because the heating directions were both ra dial and at the bottom and top of the specimen, water within the specimen will flow toward the center of the specimen creating potentially a very high pore pressure. However, if the specimen has a high enough permeability and tensile strength, it would not exhibit spalling. By testing both saturated and de-saturated mixtures, it can be determined whether moisture has a role in spalling behavior and whether mixture type affects the potential for spalling. Results of the testing of most of the mixtures (all except the M30 mixture due to the lack of available specimens) introduced in Chapter 2 (at both saturated and unsaturated conditions) are presented. Unsaturated specimens were drie d by heating at a te mperature of 105 C (220 F) until the specimen weight reached equilibr ium (two to eight weeks). Wet specimens were taken from the curing tanks (submerged in water) just before testing and thus were considered to be fully saturated. 3.3 Experimental Results The experimental results presented here ar e divided into two sections: one for the fully-instrumented specimens tested one-dimensionally using the propane furnace, and one for the qualitative testing program. For furnace-tested specimens the following information is also described. Air temperature measured at the surface (for comparisons with time-temperature curves specified in ASTM E119 and ASTM E1529) Internal temperature measurements Internal pore pressure measurements Spalling quantification thr ough crack-detection circuitry

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90 Electric kiln Large mass (bricks) to maintain temperature when specimen is introduced Kiln cover Heating coils Thermocouple probe Test specimen Layer of thermal brick for protecting base from spalling concrete or mortar Kiln base Access hole for inserting specimen (a) Electric kiln Large mass (bricks) to maintain temperature whe n specimen is introduced Test specimen Thermocouple probe (b) Figure 3-15. Schematic of test method for qualitative assessment of spalling at high temperatures: (a) Side view of electric kiln, (b) Top view with lid removed. 3.3.1 Mortar Mixture: M25 Two M25 mortar specimens were experiment ally tested using the furnace. Each exhibited significant spalling almo st immediately after the propa ne burners were ignited. Each of the two M25 specimens were tested using a slight variation on the testing apparatus. Test #1 was perf ormed with one propane burner supplying heat while Test #2 used two burners. Therefore, the temperature and heat flux experienced by the test

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91 specimen in Test #2 were higher than those of Test #1. A photo of the M25 specimen (Test #2) is shown in Figure 3-16 after thermal testing. Figure 3-16. M25 mortar specimen (Test #2) after thermal testing. Temperatures measured near the surface of the specimens for each of the tests are shown in Figure 3-17. For Test #1, the air temperature near the surface was measured at three different locations, whereas temperature was measured at two locations for Test #2. Included in both graphs are the time-temperat ure loading curves specified by the ASTM E119 and ASTM E1529 test methods. The te mperatures the specimen experienced in Test #1 are more indicative of those specified by ASTM E1 19, whereas the temperatures in Test #2 were closer to those in the ASTM E1529 specification. Internal temperatures were measured at distances of 8, 10, 15, and 20 mm (0.315, 0.394, 0.591, and 0.787 in.) from the heated su rface for Test #1 and at 5, 10, 15, and 20 mm (0.197, 0.394, 0.591, and 0.787 in.) for Te st #2 (See Figure 318). A measurement of thermocouple depths prior to casting of both specimens re vealed that one of the

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92 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 (a) 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 (b) Figure 3-17. Measured air te mperature near the heated surface during thermal testing of the M25 specimen: (a) Test #1, (b) Test #2

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93 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 8 mm (0.315 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) (a) 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 5 mm (0.197 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) (b) Figure 3-18. Internal temper atures of the M25 specimens measured at various depths from the heated surface: (a ) Test #1, (b) Test #2.

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94 thermocouples in Test #1 was not at the inte nded location (8 mm rather than 5 mm). For Test #2, the thermocouple at 5 mm (0.197 in.) from the surface malfunctioned. During the test, the measured internal temperat ures for Test #2 were higher than those of the Test #1, indicating a more severe heating conditions. Pressures were measured at depths of 10 and 15 mm (0.395 and 0.591 in.) for both Tests #1 and #2 (See Figure 3-19). Unfortunately in each of the tests, one of the pressure transducers did not function prope rly resulting in no data at that location. Pressure was able to be measured at 10 mm (0.395 in.) for the Test #1 and at 15 mm (0.591 in.) for Test #2. Conclusions can still be made by compari ng the pressures at 10 mm for Test #1 (lower surface temperature) and at 15 mm for Test #2 (higher surface temperature). First, even though the surface temperature (and heat fl ux) are lower for Test #1, the peak pore pressure achieved at 10 mm is higher than that measured at 15 mm for Test #2. This demonstrates that locations closer to the surface experience higher pressure than those farther from the heated surface and thus this vicinity is more susceptible to thermally induced spalling. In additi on, the pressure transducer in Test #1 at 10 mm indicated spalling whereas the transducer in Test #2 at 15 mm did not. It is th eorized that spalling occurred in Test #1 at a dept h near the pressure transducer because a sudden drop in pressure occurred rather than a gradual taperi ng off. It is also theorized that spalling occurred at locations close to heated su rface in Test #2 because a minor, but abrupt, increase in pressure occurred at about 660 s econds into the test. Because the pressures measured by the transducers are very sensitiv e to their surroundings explosive spalling (which can be very violent) is suspected to cause the disruption in pressure measurement.

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95 0 2 4 6 8 10 12 0 120 240 360 480 600 720 840 960 1080 1200 0 25 50 75 100 125 150 175 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 15 mm (0.591 in.) (a) 0 2 4 6 8 10 12 0 120 240 360 480 600 720 840 960 1080 1200 0 25 50 75 100 125 150 175 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 15 mm (0.591 in.) (b) Figure 3-19. Measured pressure at 10 a nd 15 mm from heated surface during testing of M25 mixture: (a) Test #1, (b) Test #2.

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96 Spalling during Tests #1 and #2 was quantif ied using the crackdetection circuitry described in Section 3.1.2.2. Results are pr esented in Tables 3-3 and 3-4. Spalling was detected at the approximate point in time that the pressure transducer detected a sudden drop in pore pressure. Although the depths of the transducer and the spalling detection wire were different, the times of spalling were nearly identical. Progressive spalling was detected in Test #1 based on the fact that the wire at 0 mm broke before the wires at 5 and 10 mm (0.197 and 0.394 in.). Therefore, su rface spalling occurred at 658 sec., while deeper spalling occurred at 934 seconds. The depth of the spalling can also be quantified by fact that there was simu ltaneous spalling recorded at 5 and 10 mm (0.197 and 0.394 in.), but none at 15 mm (0.591 in.). This indi cated that the shard of mortar that spalled off at 934 sec. was thicker than 5 mm (0.197 in.) and occurred at a depth between 10 and 15 mm (0.394 and 0.591 in.). The only spallin g detected during Test #2 was at 5 mm (0.197 in.) and was 334 seconds prior to wh en spalling was detected during Test #1. Although the crack detection circuitry work ed well detecting spalling, the results suggest placing the instrumentation at multiple locations across the specimen (at the same distance from the heated surface). This is exemplified through the redundant measurement of spalling at 5 mm (0.197 in.) during Test #1. The two wires measuring spalling at this location were approximately 50.8 mm (2.0 in.) away from each other, but one detected spalling while th e other did not. This indi cates that spalling is not necessarily uniform across the en tire surface. In addition, Test #2 showed no detection of spalling at the surface (0 mm) even though ther e was spalling detected at 5 mm (0.197 in.). These results indicate that ther e should be greater redundancy in spalling measurement when using the crack detecti on circuitry describe d in this study.

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97 Table 3-3. Spalling locati ons and times determined by monitoring resistance through crack-detection circuitry in the M25 specimen, Test #1 Location 0 mm (0.00 in.) 5 mm (0.197 in.) 5 mm (0.197 in.) 10 mm (0.394 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Spalling Yes Yes No. Yes No No No Time of spalling 658 sec. 934 sec. 934 sec. Table 3-4. Spalling locati ons and times determined by monitoring resistance through crack-detection circuitry in the M25 specimen, Test #2 Location 0 mm (0.00 in.) 5 mm (0.197 in.) 5 mm (0.197 in.) 10 mm (0.394 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Spalling No Yes No No Not working No No Time of spalling 600 sec. 3.3.2 Mortar Mixture: M35 Mortar mixture M35 exhibited spalling at the surface, but the spalling was localized and not evenly distributed across the surf ace. Viewing the specimen after testing revealed that some locations had deeper spal ling while at other locations the spalling was relatively shallow (see Figure 3-20). Furthermore, the pressure measurement revealed very high values. Measurements of air temperature were taken throughout the th ermal test at two different locations near the surface of the specimen. Measured temperatures at the surface of the thermal specimen were similar to those applied to the M25 specimens. Figure 3-21 shows the experimentally measur ed temperature along with the temperature curves specified in ASTM E119 and ASTM E15 29. The experimental temperatures were above those specified by ASTM E119, but below ASTM E1529 (except for approximately the first two minutes of the test). This indicates that the temperatures that were applied were similar to those of typical fires.

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98 Figure 3-20. M35 mortar specimen after thermal testing. 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 Figure 3-21. Measured air te mperature near the heated surface during thermal testing of the M35 specimen.

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99 Temperatures were measured at 6, 10 17, and 20 mm (0.236, 0.394, 0.669, and 0.787 in.) from the heated surface. Tw o of the four embedded thermocouples at 6 and 17 mm (0.236 and 0.669) failed to produce usable da ta The locations of the thermocouples were initially placed at 5, 10, 15, and 20 mm (0.197, 0.394, 0.591, and 0.787 in.), but final measurements prior to placement of the mortar mixture produced slightly different distances. The temperat ures measured during the thermal test are shown in Figure 3-22. It should be noted th at the temperature measured at 10 mm (0.236 in.) became erratic at about 240 seconds (4 mi nutes) into the thermal test. Spalling near this location may have shed mo rtar causing the thermocouple to become exposed to air. The surface temperatures measured were si milar to those measured during testing of the M25 specimen as well as those measured internally. For instance, the temperature measured at 20 mm (0.787 in.) from the heat ed surface were similar for the M25 (Test #1 and #2) and M35 mortar specimens tested (see Figure 3-23). This indicates that the heat transfer rate through each of these mixtures was similar. Pressure was measured at 10 and 16 mm (0.394 and 0.630 in.) from the heated surface during the thermal test. Figure 3-24 sh ows the pressures measured at each of the locations. The pressure measured at 10 mm (0.394) was much higher than that measured for the M25 specimen at the same location (Test #1). However, the pressure measured in the M25 specimens was affected by spalling. Because the M35 specimen did not spall near the location of the trans ducer, the pressure c ontinued to rise. If spalling had not occurred in the M25 specimens near the transd ucer, it is assumed that the pressure would have continued to rise, possibly above that measured for the M35 specimen.

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100 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 6 mm (0.236 in.) 10 mm (0.394 in.) 17 mm (0.669 in.) 20 mm (0.787 in.) Figure 3-22. Internal temper atures of the M35 specimens measured at various depths from the heated surface. 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Specimen/Test M35 M25Test #1 M25Test #2 Figure 3-23. Internal temperatures measured at 20 mm (0.787 in.) during thermal testing of each of the mortar specimens

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101 0 10 20 30 40 50 60 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 16 mm (0.630 in.) Figure 3-24. Measured pressure at 10 a nd 15 mm from heated surface during testing of M35 specimen. Progressive spalling was quantified by meas uring resistance through seven sets of looped crack-detection wires. The depths from the heated surface, whether spalling was detected, and the time of spalling for each wire are presented in Table 3-5. Spalling is considered to be progressively occurring due to the fact that the wi re at 0 mm broke prior to those at 5 and 10 mm (0.197 and 0.394 in.). In addition, the sp alling at 815 seconds penetrated to at least a depth of 10 mm (0 .394 in.) from the original heated surface because the wire at 15 mm (0.591 in.) did not detect any spalling. Thus, the spalling at 815 seconds was between 10 and 15 mm (0.394 a nd 0.591 in.). The total thickness of the shard of mortar that spalled off was at le ast 5 mm (0.197 in.) in thickness because both wires at 5 and 10 mm (0.197 and 0. 394 in.) broke simultaneously.

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102 Table 3-5. Spalling locations and times determined crack-d etection circuitry in the M35 specimen Location 0 mm (0.00 in.) 5 mm (0.197 in.) 5 mm (0.197 in.) 10 mm (0.394 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Spalling Yes Yes Sensor failed Yes No No No Time of spalling 592 sec. 815 sec. 815 sec. 3.3.3 Concrete Mixture: C25 The C25 specimen exhibited lit tle spalling and low internal pore pressures even though the surface temperatures (heat input) wa s similar to those used for the mortar specimens. This leads to the belief that this particular mixture type (concrete with granite aggregate) is not susceptible to moisture cl og spalling. Because there was very limited spalling, the crack detection ci rcuitry did not provide any usef ul data (i.e., none of the wires broke). Figure 3-25 shows a photo of the specimen after it was removed from the testing apparatus. The air temperature near the heated surf ace was measured with two thermocouples, one of which was damaged during the experi ment. Figure 3-26 shows the temperatures recorded during the thermal test, along with the time-temperature curves specified by ASTM E119 and ASTM E1529. The temperature was above the ASTM E119 curve for the entire duration of the thermal test and was similar to the surface temperature measured during Test #1 of the M25 mortar specimen. Internal temperatures were measured at f our locations (see Figure 3-27) within the C25 concrete specimen. In this test, the temp erature data recorded remained quite stable with very little fluctuation. This is becau se there was a minimal amount of spalling on the surface and each of the thermocouples remained in contact with the surrounding concrete for the entire duration of the thermal test.

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103 Figure 3-25. C25 concrete sp ecimen after thermal testing 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 Figure 3-26. Measured air te mperature near the heated surface during thermal testing of the C25 specimen.

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104 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 5 mm (0.197 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Figure 3-27. Internal temper atures of the C25 specimens measured at various depths from the heated surface. Pressure was measured at 10 and 15 mm (0.394 and 0.591 in.) from the heated surface. Measured pore pre ssures peaked at approximately 4 atm during the thermal testing of the C25 specimen and tran sient data is shown in Figure 3-28 Significant spalling was neith er detected nor observed during the thermal testing of the C25 mixture (see Figure 3-25). Notice the ab sence of spalling at almost all locations. In conjunction with the pressure data, it can be concluded that compared to the mortar thermal test results this mixture is not as su sceptible to pore pressure induced damage and thus has shown to better in typi cal fire conditions. This is due to the increase in tensile strength due to the inclusion of aggreg ate and the increased permeability of such mixtures.

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105 0 1 2 3 4 5 0 120 240 360 480 600 720 840 960 1080 1200 0 10 20 30 40 50 60 70 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 3-28. Measured pore pressure at 10 a nd 15 mm from heated surface during testing of C25 specimen. 3.3.4 Concrete Mixture: C45 After observing only limited sp alling during the thermal te st of the C25 specimen, a more extreme heating cond ition (approximately 1000 C at the 20 minute mark in the thermal test) was applied to the C45 specimen in an attempt to induce higher pore pressures and explosive spalling. Although th e pressures were about twice as high as measured in the C25 specimen, explosive spal ling was still not observed. Figure 3-29 shows a photo of the specimen after thermal testing. Surface temperatures were measured at lo cations on opposite ends of the specimen. The time-temperature curves are shown in Figur e 3-30 and are similar to that of Test #2 of the M25 thermal specimen. Temperatures were measured at 10, 15 and 20 mm (0.197, 0.394, 0.591, and 0.787 in.) from the heated surface (see Figure 3-31).

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106 Figure 3-29. C45 concrete mi xture after thermal testing. 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 Figure 3-30. Measured air te mperature near the heated surface during thermal testing of the C45 specimen.

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107 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 5 mm (0.197 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Figure 3-31. Internal temper atures of the C45 specimens measured at various depths from the heated surface. Pressures were measured at distances of 10 and 15 mm (0.394 and 591 in.) from the heated surface (See Figure 3-32). Because th e specimen did not explosively spall, the pressure time-history curves are continuous (unlike the M25 specimens). The peak pressure was approximately equal in magnitude for both locations, with a time shift of about 360 seconds (6 minutes). This set of pr essure data provides the best proof of the existence of a saturated front moving deeper into the specimen as time progresses. As previously mentioned, the C45 sp ecimen did not exhibit the significant explosive spalling observed in the mortar mi xtures. This was confirmed through the crack detection circuitry, which di d not show any changes in m easured resistance during the test.

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108 0 1 2 3 4 5 6 7 8 9 10 0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 0 20 40 60 80 100 120 140 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 3-32. Measured pressure at 10 a nd 15 mm from heated surface during testing of C45 specimen 3.3.5 Concrete Mixture: L35 The specimen made of the L35 concrete mixt ure did not spall or show signs of high pore pressure development even though the app lied temperature was similar to that which was applied during the testing of the mortar and granite-aggr egate concrete mixtures. A photo of the heated surface of the specimen af ter the testing is shown in Figure 3-33. Only very localized spalling was observed after the specimen was taken out of the furnace.

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109 Figure 3-33. L35 concrete mi xture after thermal testing. The L35 mixture was the most permeable of all of the mixtures thermally tested and thus was probably the leas t susceptible to moisture cl og spalling. A key observation made during this test was that a significant amount of wate r accumulated on the cool side of the specimen, as shown in Figure 3-34. This indicated that the pore pressure was dissipated within the specimen by rapid mois ture migration through the thickness of the specimens (due to the high permeability of the L35 mixture). A specimen of larger thickness would therefore have been preferable. The air temperature measured at the speci men surface (see Figure 3-35) was similar to what was measured during the other therma l tests. The temperature during the entire duration of the thermal test was above that is prescribed by ASTM E119. Except for the

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110 very beginning of the test, the air temperat ure was below time-temperature curve in the E1529 specification. Temperatures were measured internally at 5, 10, 15, and 20 mm (0.197, 0.394, 0.591, and 0.787 in.) from the heated surface throughout the duration of the thermal test (see Figure 3-36). Because the specimen did not spall, the temperature data is useful for comparison to the numerically predicted values. Figure 3-34. Top of the L35 concre te specimen during thermal testing. As previously stated, pressures measured internally at 10 and 15 mm (0.394 and 0.591 in.) from heated surface did not show si gnificant increases during the test (see Figure 3-37). This lack of por e pressure increase is partly due to the specimen thickness

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111 that was too small, but was primarily due to the high permeability of the mixture. The capillary structure had sufficient permeability to relieve the pore pressure development through movement of internal steam and wate r. Although the initia l pressure of the transducer at 15 mm is shown to be approximate ly 2 atm, this was merely due to a loose connection to the data acquisition system and was quickly fixed. 0 200 400 600 800 1000 1200 0 120 240 360 480 600 720 840 960 1080 1200 0 300 600 900 1200 1500 1800 2100 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental ASTM E119 ASTM E1529 Figure 3-35. Measured air te mperature near the heated surface during thermal testing of the L35 specimen. The crack detection circ uitry indicated that no spalling occurred, which corresponds to the surfac e condition of the specimen observed after testing. Therefore, this concrete has therefore b een shown to perform well duri ng typical fire conditions This also provides a positive indication that concrete with limerock (which are typical to Florida) are less susceptible to damage during fires.

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112 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Depth from heated surface 5 mm (0.197 in.) 10 mm (0.394 in.) 15 mm (0.591 in.) 20 mm (0.787 in.) Figure 3-36. Internal temper atures of the L35 specimens measured at various depths from the heated surface. 3.3.6 Qualitative Thermal Testing To confirm the thermal behavior of the concrete and mortar materials presented above (e.g., spalling behavior), a series of radial thermal tests were performed using a different heating method and specimen size. As described in Section 3.2, the specimens in this part of the study were thermally loaded in the radial direction with an instantaneous air temperature of 1000 C (1832 F). Based on re sults from this phase of the test program, a number of conclusions can be made to sup port the previous test results for the mortar and concrete mixtures invest igated. It was found that moisture had an effect on spalling behavior a nd thus pore pressure was si gnificant on material failure.

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113 This verifies the need for transient pore pres sure measurement to quantify the behavior of concrete in fire conditions. 0 1 2 3 4 5 0 120 240 360 480 600 720 840 960 1080 1200 0 10 20 30 40 50 60 70 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Depth from heated surface 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 3-37. Measured pressure at 10 a nd 15 mm from heated surface during testing of L35 specimen Dry specimens of each of the mixtures di d not exhibit spalling whereas all of the saturated specimens explosively spalled, in some cases producing comp lete destruction of the 101.6 x 203.2 mm (4.0 x 8.0 in.) specimens. The saturated mortar specimens performed poorly under this thermal loadi ng. The M20 and M25 saturated specimens were completely destroyed within 15 minutes of introduction into the kiln. Much of the spalling observed during these tests was very lo ud and violent. During the test of the M20 specimen, the lid of the kiln was observed to lift slightly after one of the explosions. The dry specimens did not explosively spall, which indicated the important role of pore

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114 water in initiating failure in the saturated mate rials. Results from this phase of the test program are provided in Table 3-6. Table 3-6. Results from qualitative thermal testing program Specimen condition Mixture type Mixture identification Wet Dry M20 Sample completely destroyed No spalling, specimen cracked at mid-height M25 Sample completely destroyed No spalling, specimen cracked at mid-height M301 Not tested Not tested Mortar M35 Spalling, but sample still intact and cracked No spalling, specimen cracked at mid-height C20 Shallow surface spalling No spalling C25 Shallow surface spalling No spalling C30 Shallow surface spalling No spalling, specimen cracked at mid-height C35 Shallow surface spalling No spalling C40 Shallow surface spalling No spalling Concrete with granite aggregate C45 Shallow surface spalling No spalling L30 Shallow surface spalling No spalling L35 Shallow surface spalling No spalling Concrete with limerock aggregate L40 Shallow surface spalling No spalling 1 Not enough material available to perform this test All of the saturated concrete specimens ( both with granite and limerock aggregate) exhibited the same type of spalling at the surface, whereas the dry specimens showed no signs of spalling. The “surface spalling” observed in the testing of the concrete specimens was typically very shallow, onl y enough to eliminate the surface paste and expose the aggregate. Figure 338 shows photos of the concrete specimens after testing. Because the dry specimens remained intact, th ere is a strong indication that moisture does affect the behavior of concrete under thermal loading. It was also observed that the wet M35 specimen was not completely destroyed af ter thermal testing, although spalling was

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115 significant at the surface and at the top and bo ttom of the specimens. This indicates that there is a spalling dependency on permeability for mortar mixtures. (a) (b) Figure 3-38. Specimens tested in qualitative thermal testing: (a) Mortar, (b) Concrete with granite aggregate, (c) Conc rete with limerock aggregate.

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116 (c) Figure 3-38. Continued. Specimen spalling characteristics for the satu rated concrete mixtures tended to be independent of water-binder ratio. The leas t permeable concrete mixtures performed nearly identically to the most permeable mixtures. Therefore, it can be said that for these types of concrete mixtures (with a w/b be tween 0.30 and 0.40 for limerock concrete and between 0.20 and 0.45 for granite concrete), the permeability and porosity were low enough to cause surface spalling, but still mainta in the original specimen geometry. This does not indicate that the specimen structural integrities were the same as unheated specimens since high temperatur e is known to reduce material strength in many cases. To verify that the structural integrity was compromised as a result of thermal exposure, compressive strength tests were pe rformed on the limerock concrete specimens after cooling. Table 3-7 shows the compressive strength of the mixt ures without thermal loading and after thermal loading (both ini tially dry and saturated conditions). The compressive strengths shown for thermally tested specimens are based on single

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117 specimen tests for each mixture and saturati on condition. Significant strength reduction is observed which indicates that the structural integrity of the thermally tested specimens was compromised and the material was perh aps held together primarily by physical particle interlock. Table 3-7. Compressive strength results from qualitative thermal testing program Compressive strength, MPa (ksi) Post thermal loading2 Mixture identification No thermal loading1 Initially saturated Initially dry 104.1 6.64 4.92 L30 (15.1) (0.96) (0.71) 88.2 5.11 3.14 L35 (12.8) (0.74) (0.45) 78.7 3.64 4.85 L40 (11.4) (0.53) (0.70) 1 As presented in Chapter 2 2 Compression testing of one specimen If the material had been s ubjected to a mechanical comp ressive load during thermal testing, it is theorized that the specimen w ould have been completely destroyed, similar to the M20 and M25 mortar specimens. Furt hermore, if the concrete was in a service condition (e.g., a column in a building) and wa s subjected to an extreme thermal load as in this experimental program, the material woul d probably fail. 3.4 Discussion 3.4.1 Furnace A furnace was constructed that was able to produce transient temperatures similar to those in the ASTM E119 and ASTM E1529 speci fications (similar to fire conditions). The measured temperatures were generall y above what is prescribed in these specifications for the first few minutes of the thermal testing and in between thereafter. Different time-temperature loadings can be produced by the furnace through use of multiple propane burners and with control of the pressure supply of the fuel.

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118 3.4.2 Instrumentation Method Full embedment of the pressure transdu cers, thermocouples, and crack detection circuitry provided a means for measuremen t without introducing significant material discontinuity. Methods were e xplored to make the pressure transducers reusable after thermal testing, but such methods produced erratic measurements. By integrating as much as possible the instrumentation into the su rrounding concrete material, the measured pressures were more reliable based on the continuity through time. 3.4.3 Pressure The one-dimensional thermal testing of the mixtures produced pressure measurements that were quite revealing as to the suscep tibility of the mixtures to explosive spalling. Both mo rtar mixtures spalled during thermal testing, while the concrete mixtures showed little or no spalling even though the heating rates were comparable. The pressures measured in the concrete mixtures were far less than those measured in the mortar mixtures. The concrete with limeroc k aggregate produced extremely low pressure, most likely due to the high permeability and porous aggregates in the mixture. The mortar mixtures spalled significantly during thermal testing, which limited the amount of reliable pore pressure data obtained (for the M25 specimen). However, this was not a deficiency of the e xperimental test, but rather a result of the actual material behavior. If the material had not failed in the M25 specimens, the measured pressure would most likely have increased to the significant levels seen in the M35 specimen. Additionally, measured pressure was highe r during the thermal testing of the C45 mixture than in the C25 specimen. This wa s most likely due to the porosity difference

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119 between the mixtures. Although the permeab ility of the C45 mixture was much higher that of the C25 mixture, the difference was not sufficient to overcome the difference in porosity and initial water content. 3.4.4 Spalling Detection The spalling detection circui try that was designed for thes e experiments was able to identify when spalling failure of the materi al occurred. However, because the sloughing off of material was not particularly uniform across the face of the sp ecimen, identification of spalling from an individual crack detector did not necessarily indi cate spalling at that depth for all locations. Although redundanc y was included in the measurement of spalling occurred by placing multiple detection wi res at the same depths from the heated surface, there was insufficient redundancy to quantify sloughing off of material across the entire surface. It is theref ore recommended that further re dundancy be considered in any future thermal tests using this instrumentation. 3.4.5 Qualitative Testing A means of assessing the in fluence of moisture on sp alling behavior has been presented. By suddenly expos ing both dry and wet cylindric al specimens to elevated temperatures (using a kiln pre-heated to 1000 C (1832 F)), the influe nce of moisture has been assessed. All of the saturated concre te specimens exhibited surface spalling, and complete destruction was observe in some of the mortar spec imens. In contrast, the dry specimens retained their original geometry a nd showed minimal signs of spalling. This indicated that moisture plays an important ro le in material behavi or of concretes and mortars subjected to elevated temperatures and that ther mal stress development should not be the only failure mechanism.

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120 CHAPTER 4 MODELING HEAT AND MASS FLOW WITHIN CONCRETE DURING FIRE EXPOSURE CONDITIONS This chapter describes procedures for perf orming numerical simula tions of heat and mass transfer in concrete and mortar duri ng fire exposure conditions. Subsequently, numerical simulation results are compared to experimental results. An existing numerical program, TOUGH2 (Preuss 1987, 1991), was ut ilized based on its ab ility to perform transient heat and mass flow simulations fo r applications of water, steam, and air movement through porous media. The primar y goal in performing the type of modeling treated in this study was to cr eate a method for predicting po re pressure and temperature in concrete materials during extreme thermal loading. Models are created that represent the thermally tested mixtures (previously described) using experimentally determin ed material propert ies (intrinsic gas permeability, slip flow factor, intrinsic wate r permeability, and porosity). Results from numerical simulations are then compared w ith those measured experimentally and the validity of the models discussed. Afte r making comparisons between the numerical solution and the experimentally measured values, procedures for applying thermal loading typical of fire co nditions (ASTM E119 and ASTM E1529) are addressed and comparisons made. 4.1 Background of the TOU GH2 Numerical Simulator TOUGH2 was chosen to perform the numeri cal modeling of heat and mass flow in this study because it was successfully previ ously used for this type of application

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121 (Consolazio et al. 1998). TOUGH2 is the successor to TOUGH (Transport Of Unsaturated Groundwater and Heat), written by the Lawrence Berkeley Laboratory at the University of California and is a numerical program for simulating heat and multi-phase mass flow through porous media. The program has many of the capabilities needed to perform modeling of concrete and mortar under exposure to fire. Furthermore, source code for the program (written in FORTRAN) is available. As a result, modifications to the solution process may be added to the pr ogram to better represent the physical properties and behavior of cementitious materials. TOUGH2 is based on an implicit finite di fference solution of heat and mass flux equations through a user-specified volumetric st ructure. One of the basic equations that the program solves is the cons ervation of heat an d mass equation (also referred to as the material time derivative of volume integral): Heat and mass Heat and Heat and mass accumulationmass fluxproductionVV nnnd M dvdqdv dtFn (4-1) where n is the index of the volume element under consideration, nV is the volume of the element, is the specie (water, air, or heat), M is either the heat or mass (depending on the specie) n, is the control surface of the element, F is either the heat or mass flux (depending on the specie), n is the normalization vector, nV is the volume of the element, and q is either the heat or mass flux (depending on the specie). The first term of the equation indicates the amount of heat and mass accumulated or lost in a particular volume over time (the material ti me derivative of the volume integral). The second term of the equation describes the net heat and mass entering or leaving the

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122 volume through its boundary surfaces. The third term is the rate increase of mass or heat within the control volume and can either be used to describe a chemical or physical change of state to the mass or a source of heat or mass (e.g., thermal loading). To implement a finite difference solution, the terms in Equations 4-1 are represented as a discrete set of element volumes: nn V n M dvMV (4-2) nmnm m ndAF Fn (4-3)nn V nqdvVq (4-4) where n represents the element and m represents the surfaces surrounding the element. From this discretization into elements, the im plicit finite difference formulation is then constructed for time step k: ()1()1()()11kkkkk nnnnmnmnn n mt RMMAFVq V (4-5) where n R represents a residual that the numerical solver in TOUGH2 minimizes using the Newton-Rhapson method. Each volume in the model will be represented by three of these equations (one for each of species) and will be solved simultaneously at each time step. Variables that are solved using Equati on 4-5 are the primary variables that define the thermodynamic state of the system. Fo r the two-phase condition found in concrete during heating, the primary variables are pre ssure, gas saturation, and temperature.

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1234.2 Program Input 4.2.1 Geometry The finite difference solution is geometrically based on element volumes, distances between element centroids and element inte rfaces, interface surf ace areas, and surface orientations. Two different geometrical mode ls (one and two dimensional models) were constructed to represent the one -dimensional heating of concrete and mortar studied here. A two-dimensional model with nearly the ex act geometry and test conditions of the experimental thermal test was constructed to account for local effects in the vicinity of embedded pore pressure transducers. The instrumentation used to measure pressure (Chapter 3) contained a sma ll void near the point of pre ssure measurement, which was included in the two-dimensional model but not the one-dimensional model. The onedimensional model was used primarily for predictions of pore pressure during ASTM E119 and ASTM E1529 thermal loading (discussed later). 4.2.1.1 One-dimensional model The one-dimensional model consisted of 227 total elements in series (See Figure 4-1). Each of the interior 225 elements had a finite volume and was assigned the heat and mass flow properties of concre te, whereas the two boundary el ements (hereafter referred to as super-elements) were modeled as air and had very large vol umes relative to the concrete elements. Because the super-elements had such large volumes with respect to the concrete elements, they acted as sinks for mass flow. Mass (air, water, or steam) that flowed into the super-elements from the conc rete elements did not result in a significant increase in pressure or saturation level becau se of the extremely large volumes. One of the super-elements acted as a source of heat input by specification of the element temperature through the duration of the numerical simulation (discussed in greater detail

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124 later). The super-element at the opposite end of the mode l acted as a heat sink because any heat flux from the concrete elements into this super-element did not result in a rise in temperature. 200 Elements @ 0.25 mm (0.0098 in.) = 50 mm (1.97 in.) 25 Elements @ 1.00 mm (0.0394 in.) = 25 mm (0.98 in.) 75 mm (2.95 in.) Heat and mass sink superelement Volume = 1.00x1050 m3 (6.10x1054 in3) Concrete/mortar elements: Volume = 2.50 x10-8 m3 (1.53 x10-3 in3) Concrete/mortar elements: Volume = 1.00x10-7 m3 (6.10x10-3 in3 ) Cool surface of concrete/mortar, Cross-sectional area = 1.00x10-4 m2 (0.155 in2) Element B Element A d2 Ad1 Ad2 Bd1 B D istance to flux surface of element Heat and mass sink superelement Volume = 1.00x1050 m3 (6.10x1054 in3) Heated surface of concrete/mortar, Cross-sectional area = 1.00x10-4 m2 (0.155 in2) Figure 4-1. One-dimensional model used for numerical simulations Based on results from preliminary numerical simulations, it was observed that pore pressure, saturation, and temperature changed mo st significantly in the elements near the heat source. As individual element volumes increased, accuracy decreased with respect to quantifying maximums and minimums of pore pressure, temperature, and saturation level because the state variables are averaged over larger volumes. Therefore, elements

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125 near the heated super-element were chosen to be of smaller volume to increase the accuracy of the solution. To demonstrate the importance of choosing an appropriate element volume, a series of simulations were performed on one-dime nsional models with different element volumes. The element volumes for the 50 mm (1.97 in.) closest to the heated super-element were decreased incrementally from 100 to 5 mm3 (61.0x10-4 to 3.1x10-4 in3) while the total number of el ements in this region was increased from 50 to 1000. The elements ranging from 50 to 75 mm (1.97 to 2. 95 in.) from the heated surface were kept at a constant volume for all of the models. Geometric data for each of the models is provided in the Table 4-1. All other aspects for th is series of models, such as permeability, thermal properties, and saturation level remained constant and were representative of the M35 mortar mixture produced in the experimental progr am. Thermal load was applied to the boundary super-element as a temperature tim e-history conforming to the ASTM E119 specification (discussed later in this chapter). The key parameters used in the numerical models (which were also kept cons tant) are provided in Table 4-2. Figure 4-2 shows computed pore pressure pr ofiles across the depth for each for the models at time 1200 seconds. Each profile was filtered with a Gaussian smoothing function (using Mathcad software) and a bandwidth of 4 mm (0.157 in.). Profiles of temperature (see Figure 4-3) for each of the models were similar, whereas the profiles of saturati on level and pore pressure were quite different. The pore pressure profiles show that the peak pore pressure generally decr eased as the element volumes decreased. Therefore, the models with element heights of 0.5 and 1.0 mm

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126 Table 4-1. Geometry of elements in the m odels for investigation into the effect of element volume size on the numerical solution Elements Parameter Model 1 Model 2 Model 3 Model 4 Element volume, mm3 (x10-4 in3) 100 (61.0) 50 (20.5) 25 (15.3) 10 (6.10) Element flux area, mm2 (in2) 100 (0.155) Element height, mm (in) 1.00 (0.0394) 0.50 (0.0197) 0.25 (0.00984) 0.10 (0.00394) Elements closest to the heated super element Number of elements 50 100 200 500 Element volume, mm3 (x10-4 in3) 100 (61.0) Element flux area, mm2 (in2) 100 (0.155) Element height, mm (in) 1.00 (0.0394) Elements farthest from heated super element Number of elements 25 Table 4-2. Properties of materials in th e models for evaluating element geometry Parameter Value Parameter Value Dry conductivity 0.5 W/mC (0.289 Btu/hftF) Slip flow constant, at 25 C (77F) 4.497 atm Wet conductivity 1.0 W/mC (0.578 Btu/hftF) Water permeability 4.120x10-21 m2 (6.386x10-18 in2) Specific heat 921.1 J/kgC (219 Btu/(lbmF) Porosity 15.0 % Emissivity 0.88 Saturation level 0.50 Coefficient of thermal expansion 6.5x10-6 (m/m)/C (3.6x10-6 (m/m)/F) Thermal loading E119 Mass density 2400 kg/m3 (150 lbm/ft3) Simulation duration 1200 sec Gas permeability 1.097x10-18 m2 (1.700x10-15 in2) Maximum applied temperature 795 C (1463 F) at 1200 sec

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127 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 0 100 200 300 400 500 600 700 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Pore pressure (atm) Pore pressure (psia)Distance from heated surface (mm) Distance from heated surface (in.) Element height 1.0 mm (0.0394 in.) 0.50 mm (0.0197 in.) 0.25 mm (0.0984 in.) 0.10 mm (0.00394 in.) Figure 4-2. Profiles of pore pressure at 1200 seconds for the one-dimensional models with different element heights (or volumes) (0.0197 and 0.0394 in.) were not chosen becau se the resolution of the model geometry did not produce reliable valu es of pore pressure. Final choice of element geometry was then limited to element heights of either 0.10 or 0.25 mm (0.00394 and 0.00984 in.). Both models showed very similar values of peak pore pressure, but with only a slight shift of location of across the depth. After studying the saturation level profiles (see Figure 44), the element height chosen for the onedimensional model was 0.25 mm (0.00984 in.) based on the high variability observed in the results for the model with an el ement height 0.10 mm (0.000394 in.).

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128 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 40 0 200 400 600 800 1000 1200 1400 1600 1800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Temperature (C) Temperature (F)Distance from heated surface (mm) Distance from heated surface (in.) Element height 1.0 mm (0.0394 in.) 0.50 mm (0.0197 in.) 0.25 mm (0.0984 in.) 0.10 mm (0.00394 in.) Figure 4-3. Profiles of te mperature at 1200 seconds acr oss the depth of the onedimensional models with different element heights (or volumes) 4.2.1.2 Two-dimensional model To simulate the two-dimensional flow around the pore pressure transducers and laterally through the sides of the experime ntal thermal samples, a model with twodimensional geometry was constructed. Th e initial two-dimensional (axisymmetric) model was nearly a complete representation of the experimental thermal test in respect to the boundary conditions and size of the test specimen (see Figure 4-5). Edge effects (radial flow of heat and ma ss into the thermal bricks) were not as significant as initially expected. After an alyzing output from pr eliminary numerical simulations, it was observed that pore pressure temperature, and sa turation did not vary significantly in the radial dire ction. In addition, the reso lution of the system mesh was

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129 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 5 10 15 20 25 30 35 40 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Saturation levelDistance from heated surface (mm) Distance from heated surface (in.) Element height 1.0 mm (0.0394 in.) 0.50 mm (0.0197 in.) 0.25 mm (0.0984 in.) 0.10 mm (0.00394 in.) Figure 4-4. Profiles of saturation level at 1200 seconds across the depth of the onedimensional models with different element heights (or volumes) found to be too coarse to provide reliable results. Initial choice of volume size was based on the solution capabilities of the numerical code. Considering the combination of limited edge effects and necessity for a more refined mesh, an axisymmetric model with smaller elements and a reduced overall geometry was constructed. The revised mode l was axisymmetric with a radius of 10 mm (0.394 in.) and a height of 75 mm (2.95 in.). Because pore pressure was experimentally measured at 10 and 15 mm (0.394 and 0.591 in.) from the heated surface, two models were created representing the transducer locatio ns at each of the these distances. Figure

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130 4-6 shows the geometry of th e refined two-dimensional mode l with the pore pressure transducer at 10 mm (0.394 in.) from the heated surface. Boundary super-elements, volume = 1x1050 m3(3.53x1051 ft3) Porosity = 99.9% Liquid saturation = 0.1% Thermal Brick Porosity = 50% Liquid Sat = 0.1% 20 elem. @ 1 mm (0.0394 in.) 18 elem. @ 3 mm (0.118 in.) 80 mm (3.15 in.) 74 mm (2.91 in.) Concrete/mortar elements Void from pressure transducer No interface between elements Boundary super-elements, volume = 1x1050 m3(3.53x1051 ft3) Porosity = 99.9% Liquid saturation = 0.1% Figure 4-5. Initial two-di mensional (axisymmetric) model used for numerical simulations

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131 75 mm (2.95 in.) 40 elements @ 0.5 mm = 20 mm (0.79 in.) 20 elements @ 1.0 mm = 20 mm (0.79 in.) 7 elements @ 5 mm = 35 mm (1.38 in.) 10 mm (0.394 in.) 17 @ 0.5 mm (0.0197 in.) 8.5 mm (0.335 in.) 1.0 mm (0.0394 in.) 9.5 mm (0.374 in.) 1.5 mm (0.0591 in.) From left to right: 0.89, 0.36, and 0.25 mm (0.0350, 0.0141, 0.0098 in.) Steel Concrete/mortar Air Material legend Boundary super-elements (heat sink): volume = 1x1050 m3 (3.53x1051 ft3) Boundary super-elements (heat source): volume = 1x1050 m3 (3.53x1051 ft3) From left to right: 0.89, 0.36, and 0.25 mm (0.0350, 0.0141, 0.0098 in.) Figure 4-6. Final two-dimens ional (axisymmetric) model used for numerical simulations

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132 To model the geometry of the pore pressure transducer, four elements were used to represent the void near the poi nt of pressure measurement. This void, which was modeled as air, was present in the experime ntal testing and therefore needed to be included in the TOUGH2 models to accurately represent the in-situ conditions of the transducers. In addition to modeling the voi d space, the steel casi ng of the transducer was also approximated. Material properties used for the void and the steel casing are provided in Table 4-3. Table 4-3. Properties of the mate rials in the two dimensional model Value Parameter Steel Void Conductivity 47.0 W/mC (27.2 Btu/hftF) 0.02763 W/mC (0.01596 Btu/hftF) Porosity 0.001 0.999 Specific heat 490.0 J/kgC (117 Btu/(lbmF) 1000.0 J/kgC (239 Btu/(lbmF) Mass density 7850 kg/m3 (490 lbm/ft3) 2.4 kg/m3 (0.15 lbm/ft3) Gas permeability 1.2x10-31 m2 (1.3x10-30 ft2) 1.2x10-13 m2 (1.3x10-12 ft2) 4.2.2 Thermal Loading Using Boundary Super-Elements Thermal loading was applied to the concre te model by prescribing the temperature time-history in the super-element. TOUGH2 program modifications (Consolazio et al. 1998) permitted super-element modeling of radiation boundary condition. Transient temperatures specified for the super-element are then used for radiation heat transfer into the adjacent concrete element. Several specifications are available that prescribe tr ansient temperature data representing fire conditions. The cases incl uded in this study—excl uding experimentally

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133 measure furnace temperatures—were ASTM E119 and ASTM E1529. A related specification, ISO 834 (Interna tional Organization for Sta ndardization (ISO) 1999) was also considered but was found to be very si milar to ASTM E119 standard and therefore did not warrant separate simulations. 4.2.2.1 ASTM E119 Focus in the ASTM E119 specification is given to the analysis of structural members subjected to typical building fire conditions (combustion of interior building components where the primary fuel source is solid in nature). The time-temperature curve provided in ASTM E119 represents such conditions (see Figure 4-7). This curve is based on measurement of temperature in si mulated fire conditions and was developed through a number of separate research initiatives. 0 200 400 600 800 1000 1200 1400 0 3600 7200 10800 14400 18000 21600 25200 28800 0 400 800 1200 1600 2000 2400 0 60 120 180 240 300 360 420 480 Temperature (C) Temperature (F)Time (sec.) Time (min.) Points from ASTM E119, Appendix X1 Linear interpolation between points Figure 4-7. ASTM E119 time-temperature curve

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134 Although the total duration of the fire pr esented in Figure 4-7 is 480 minutes, only the first 40 minutes of temperature data were used in the numerical models studied here. The shortened duration was used because expl osive spalling is a phenomenon that is most likely to occur during periods of rapi d temperature change. The ASTM E119 specification provides discrete temperatures in tabular form at only 0, 5, 10, 15, 20, 25, 30, 35, and 40 minutes (see Appendix X1 of ASTM E119) rather than providing a functional form. Therefore, a sixth order pol ynomial of this data was performed which resulted in the following formula for temperat ure for the first 40 minut es of the test fire: 176135194 63326.262105.792102.17810 4.269104.646102.79120.0 ttt T ttt (4-6) where, T is temperature in degrees Celsius and t is time in seconds. Figure 4-8 shows the fitted formula (Equation 4-6) and nine discrete points specified by ASTM E119. 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 40 0 200 400 600 800 1000 1200 1400 1600 1800 0 300 600 900 1200 1500 1800 2100 2400 Temperature (C) Temperature (F)Time (min) Time (sec) Fitted curve From specification Figure 4-8. ASTM E119 time-temperature curve fitted for the first 40 minutes

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1354.2.2.2 ASTM E1529 An alternate standard time-temperature cu rve that represents fire conditions is included in the ASTM E1529 Standard Test Method for Determining Effects of Large Hydrocarbon Pool Fires on St ructural Members. The thermal loading in this specification represents fire s that are large, outdoor (meaning high air-flow), and hydrocarbon-fueled. Although this speci fication was intended for the hydrocarbon processing industry, it is applicable to other civil engineering struct ures such as highway bridge overpasses. For example, a highway overpass in Birmingham, Alabama at the I65-I59 interchange was subjecte d to an intense gasoline fire due to a tanker-truck crash (see Figure 1-2). The rate of temperature increase from such an explosion is better modeled by ASTM E1529 than ASTM E119. ASTM E1529 provides two crit eria for applying the thermal loading. The first stipulates that the heat flux applied to a structural memb er shall be at least 158 kW/m2 (50000 Btu/hr-ft2) and must be reached in the first fi ve minutes of exposure. The second states that the minimum environmental temp erature shall be 815 C (1500 F) at three minutes and that temperature between 1010 C (1850 F) and 1180 C (2150 F) must be maintained at all times after the first five minutes. A temperaturehistory curve was fitted to this criterion: 3322time350 sec 6.432101.240106.44020.0 time350 sec 1032 ttt T (4-7) where, T is temperature in degrees Celsius and t is time in seconds. Figure 4-9 shows the fitted curve along with the time-temperatu re criteria specified by ASTM E1529. It is difficult to satisfy both criteria in the nume rical model because the heat flux and super-

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136 element temperature cannot both be specified as boundary conditions using a radiation heating method. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 5 10 15 20 25 30 35 40 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 300 600 900 1200 1500 1800 2100 2400 Temperature (C) Temperature (F)Time (min) Time (sec) Fitted curve From specification Minimum temperatur e at 3 minutes Range for which the temperature must be maintained after 5 minutes Figure 4-9. ASTM E1529 time-temperature curve Thus, two separate cases were used: a h eat flux input and a time temperature-curve (through a radiation boundary super-element). Both methods used a super-element at the location of the heated surf ace to act as a mass sink. 4.2.2.3 Heat flux Estimation is required when specifying time-histories of temperature rather than time histories of flux because heat input is not solely dependent upon fire temperature. The actual heat flux that may exist in a fire is dependent upon factors such as convection during airflow, distance from heat source, and quantity of particles related to smoke that is in the air (Schrefler et al. 2002). Ho wever, ASTM E1529 and ASTM E119 indicate

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137 that radiative heating is the pr imary source of heat flux during fires. Therefore, in this study, the heat flux has been assumed to be solely dependent upon thermal radiation. During non-blackbody radiation heat transfer a number of factors affect the thermal energy flux across the surface of the concrete. Primary factors that were considered for the numerical model are show n in the following equation (Consolazio et al. 1998, Holman 1990): 44 12 12 12 12121211 1 TT qA F FF (4-8) where, q is the heating rate, is the Stefan-Boltzmann constant which is equal to 8245.66910 W/mK (8240.171410 Btu/hftR ), 1T is the absolute temperature of the fire, 2T is the absolute concrete surface temperature, A is the surface area susceptible to flux, 12F and 21F are view factors, 1 is the fire emissivity (1.0 for a perfectly radiating fire), and 2 is the concrete emissivity. Each of terms in the denominator of Equa tion 4-8 represents a resistance to heat flux (Holman 1990). The first term, 1112211 F F, represents the resistance of the heat source (which is equated to zero because of the assumption of a perfectly radiating fire). The second term, 211F, represents the resistance over space between the two bodies (the fire and the concrete) a nd is quantified through the view factor 21F. 21F varies from zero to one and is dependent on the orientation and location of the heat source in regards to the surf ace area of the concrete subjected to heat flux. Because ASTM E119 and ASTM E1529 do not require a ny specific location or orientation of the heat source in regards to the test specimen, th e view factor in the second term is assumed

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138 to be one (perfect orientation). The third term, 221 represents the resistance of the concrete to absorbed energy, which is quantified through the emi ssivity value of the concrete. Rearrangement and cancellation of Equation 4-8 with the above conditions yields the more familiar form of the radiation heat transfer formula: 44 212q TT A (4-9) which represents the heat flux per unit area and is dependent on the model geometry ( A ), the forth order difference in absolute temp erature between the c oncrete surface and the fire 44 12TT and the emissivity value of the concrete (2 ). For all of the models presented in this chapter, a thermal emissivity value of 0.88 was used for concrete (Gieck and Gieck 1997) This value is defined in the TOUGH2 model through the specification of a factor representing the de nominator of Equation 4-8. Letting the view factors and ra diation heat source emissivity equal unity, the denominator reduces to 21 or 1.1364. 4.2.3 Estimations of Material Properties Due to the scope of this study, estimations were made of some ma terial properties. Values of these material properties for input into the numerical models were based on a collection of results from previous re search programs (Klieger and Lamond 1994). 4.2.3.1 Permeability at High Temperatures Values of permeability and slip-flow fo r each of the numerical models were specific to a temperature of 25 C (77 F). Three steps were taken to account for variation in permeability with temperature. Ea ch was based on relationships found through experimental testing, physical theory of ga ses, and previously published research (Kundt

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139 and Warburg 1879, Scheideggar 1957, Schneid er and Herbst 1989, Li and Horne 2001). Subroutines that have been added to the T OUGH2 source code to calculate such effects are displayed in the flow chart shown in Figure 4-10. A subroutine was included to capture the increase in intrin sic permeability with temperature due to micro-cracking during expansion and chemical reactions. Tw o different subroutines were implemented within the TOUGH2 source code to account fo r the change in the slip flow parameter with temperature. The slip flow parameter will change with temperature due to a change in the mean free path of the gas molecules and due to a change in the intrinsic permeability of the concrete. Input : intrinsic permeability and slip flow factor (measured experimentally at some temperature) Modify i ntrinsic permeability based on skeleton changes with temperature Modify slip flow factor based on increase in intrinsic permeability. Modify slip flow factor based change in gas mean free path with temperature change Output : new intrinsic permeability and slip flow factor at a particular temperature Figure 4-10. Flowchart of modifications to intrinsic permeability and slip flow factor based on a change in temperature

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1404.2.3.1.1 Intrinsic permeability. The apparatus built in this study for measuring gas permeability (and thus intrinsic pe rmeability) was not designed to withstand temperatures above room temperature and t hus gas permeability was only measured for concrete and mortar samples at this thermal condition. This limitation was predominately the result of the low melting te mperature of the epoxy collars, gaskets, brass fixtures, and plastic tubing used in the construction of the gas permeameter. Within the scope of the present study then, an estimated relati onship between intrinsic permeability and temperature (Gawin et al. 1999) was used: 2 () 21 110g A TT k gK K (4-10) where 2 g K (m2) is the intrinsic permeability at temperature 2T (K), 1 g K (m2) is the intrinsic permeability measured at room temperature 1T (K), and kA (K-1) is a constant based on the type of concrete. Based on pr evious experimental work (Schneider and Herbst 1989), the value of kA was found to equal 0.005 K-1 for silicate concrete. Since the mixtures in this study ha d 10% silica, this value of kA and the estimation of the permeability-temperature relationship given by Equation 4-10 was adopted and added to the TOUGH2 code. 4.2.3.1.2 Slip flow factor (in relation to skeleton changes). A subroutine was added to the TOUGH2 code that modified th e slip flow factor based on the increase in intrinsic gas permeability as described in Chap ter 2. Because an increase in intrinsic permeability causes a decrease in the slip flow constant (as observed during experimental testing of the mortar mixtures in Chapter 2) a modification was made to the slip flow factor based on the change in intrinsic permeability. Equation 2-10 which describes

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141 the relationship between the slip flow factor and intrinsic gas permeability can be expressed in ratio form: 12 12sfsf B B ggbb AKAK (4-11) where A and B are parameters that are dependent on the type of mixture. In Equation 411, 1 g K and 1 s fb are specified in the TOUGH2 input file and represent the intrinsic permeability and slip flow factor at ambient conditions. 2 g K is the intrinsic permeability that results from a change in the concrete micro structure and is calculated from Equation 4-10. 2 s fb is the slip flow factor calculated for a change in the skelet al structure of the concrete and is given by: 2 () 21 110 B sf ATT k sfb b (4-12) where B equals –0.1725 for the mortar mixtures pr oduced in the experimental phase of this study. Because the concrete mixtures did not demonstrat e a reliable relationship between the intrinsic gas permeability and the slip flow factor (see Chapter 2), this subroutine was only included in modeling the mortar mixtures. 4.2.3.1.3 Slip flow factor (in relation to mean free path). While the permeant used in this study to measure gas permeability was nitrogen, the methods and permeability data collected are also applicable to other gases such as air and steam. Slip flow constants, however, vary with the type of gas permeant because gas slippage is directly related to the molecular mean free path of the gas. While the s fb values obtained in this study are sp ecific to nitrogen, correspondi ng constants for other gases

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142 may be determined from by making use of a relationship proposed by Li and Horne (2001): sfsf M bb M (4-13) where, s fb, and M are the slip flow constant, viscosity, and molecular weight of the base permeant (nitrogen for this study) and s fb , and M are the corresponding parameters for the gas for which the slip flow constant is desired. As an example of using this conversion, c onsider that the slip flow constant is desired for oxygen flow through the M20 mortar mixture. For nitrogen gas flow through the M20 material used in this study, we have s fb = 7.748 atm, = 1.77 x 10-5 Pa-s, and M = 28.0135 g/mol. If it was desired to fi nd the slip flow constant for oxygen where = 2.03 x 10-5 Pa-s and M = 31.999 g/mol, Equation 4-12 yields s fb= 8.313 atm. Thus, the slip flow factors summarized in Table 22 can be used for a va riety of gases other than nitrogen by making appropriate use of E quation 4-13. Because air has values of viscosity and molecular weight th at are very similar to nitrogen, the slip flow factor for air calculated using Equation 4-13 will be nearly identical to that obtained from nitrogen permeability testing. An additional modification was made to E quation 4-13 to account for changes in slip flow factor that occur at high temperat ure. The following de rivation (Carman 1956, Collins 1961, Scheidegger 1957, Churaev 1990, Moran and Shapiro 1995, Street et al. 1996) demonstrates how the slip flow constant varies with temperature due to a change in

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143 the mean free molecular path. The deriva tion begins with Chapman’s equation (of viscosity) for rigid spherical molecules: 1 2v (4-14) where is viscosity, is mass density, v is the mean thermal molecular velocity, and is the mean free molecular path. The mean thermal molecular velocity ( v) is defined as: 8 R T v M (4-15) where R is the universal gas constant, T is absolute temperature of the gas, and M is the molecular weight. Substitution of mean thermal molecular velocity (Equation 4-15) into Chapman’s equation (Equation 4-14) lead s to the following equation for viscosity: 18 2 R T M (4-16) Rearranging the terms in Equation 4-16 lead s to an expression for mean free path: 2 8 M R T (4-17) Using the ideal gas law ( / p MRT where p is the mean pressure), Equation 4-17 simplifies to: 2 R T pM (4-18) This equation is used to cal culate the mean free path fo r a gas based on common physical properties.

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144 Quantifying the mean free path becomes cr itical when evaluating the slip flow using the equation (Klinkenberg 1941): 4 s fb c rp (4-19) where c is a proportionality factor (a value slightly less than 1), r is an effective capillary radius, and s fb is slip flow parameter. R earranging and substituting Equation 4-18 into Equation 4-19 yields the followi ng expression for the gas slip factor: 8sfcRT b rM (4-20) Using Equation 4-20, a ratio is derived that relates the slip flow factor for two different ideal gases (gases 1 and 2) at two different temperatures (g as 1 is at temperature 1 and gas 2 is at temperature 2): 12 12 12 12 1288sfsf TTbb R TRT cc rMrM (4-21) Canceling and rearranging terms, the follo wing relationship permits the calculation of the slip flow factor for a gas at a particul ar temperature using th e slip flow data for another gas at a different temperature. 2 2 221 1112 1 T sf sf Tb TM bTM (4-22) Equation 4-22 was used in this study to conve rt the ambient conditi on slip flow factor specified in each TOUGH2 model (based on nitrogen at room temperature) into a slip flow factor for steam at variable temperatures. At each time step in the numerical

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145 simulation the temperature was evaluated fo r each element volume and the slip flow factor was determined using Equation 4-22. 4.2.3.2 Relative Permeability Relative permeability refers to the ratio of effective permeability to intrinsic permeability that is a function of saturation level (Martin 1986, Jacobs 1998). The relative permeability function used in TOUGH2 for this study is based on previous research (Consolazio and Chung 2003) and is therefore only described briefly here. The key parameters that the relative permeability to water (rwK ) and gas (rgK) are based upon are the saturation level ( L S) and porosity ( ): 0.0522.5110S L rwwKK (4-23) 0.0522.50.0522.51010S L rggKK (4-24) These functions were used by the numerical code to find the effective permeability to gas and liquid for every element at each time step. Figure 4-11shows the relative permeability functions for the mortar and concrete mixtures that were produced in this study. As these graphs indicate, the relative permeability functions increase as the porosity decreases (from M35 to M20, C45 to C 20, and L40 to L30). The effect of this ratio with porosity has an impact on the numerical solution process and mass flux calculations. It is therefore important to use an accurate porosity value, preferably determined through experimental measurement (s ee Chapter 3), in order that an accurate relative permeability function be generated.

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146 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Permeability ratio kr/kSaturation level Permeability function, mixture krw/kw, M20 (porosity=11.2%) krw/kw, M35 (porosity=15.0%) krg/kg, M20 (porosity=11.2%) krg/kg, M35 (porosity=15.0%) (a) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Permeability ratio kr/kSaturation level Permeability function, mixture krw/kw, C20 (porosity=7.9%) krw/kw, C45 (porosity=19.3%) krg/kg, C20 (porosity=7.9%) krg/kg, C45 (porosity=19.3%) (b) Figure 4-11. Relative permeability functions for: (a) mortar, (b) concrete with granite aggregate, and (c) concrete with limerock aggregate.

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147 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Permeability ratio kr/kSaturation level Permeability function, mixture krw/kw, L30 (porosity=13.7%) krw/kw, L40 (porosity=16.6%) krg/kg, L30 (porosity=13.7%) krg/kg, L40 (porosity=16.6%) (c) Figure 4-11. Continued. 4.2.3.3 Porosity at High Temperatures Due to thermal expansion, porosity increases will accompany increases in temperature and will vary directly with the coefficient of thermal expansion of the solid matrix. Such coefficients were estimated fo r the mortar and concrete mixtures studied here and reflect typical values found in pr evious research (Klieger and Lamond 1994). The work of Klieger and Lamond also suggests that the thermal expansivity does not vary significantly with the water-binder ratio of mixt ures made of the same aggregate type due to the high volume percentage of aggreg ate in typical mixtures. The value 6.5x10-6 K-1 (3.6 x10-6 F-1) was chosen as the expansivity of all the mixtures, based on an average value found in published data (Klieger and Lamond 1994).

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1484.2.3.4 Thermal conductivity, specific heat, and mass density Dry and wet thermal conductivities for the mixtures in this study were estimated based on previous research (Klieger and Lam ond 1994). All of the mortar models used conductivities of 0.5 and 1.0 W/mK (0.289 a nd 0.578 Btu/hrftF) for the dry and wet conditions, whereas the concrete mixtures were given values of 1.4 and 2.6 W/mK (0.809 and 1.502 Btu/hrftF). Thermal c onductivity is a challe nging parameter to quantify, especially in partia lly saturated concrete. In a ddition, conductivity is believed to vary with temperature (Kodur and Sultan 2003), which is currently not accounted for in the numerical code. Estimated conductivity values were temper ature independent in this study, but it is recommended that these pa rameters be measured experimentally in future test programs (using ASTM C 177 or C518 standard test methods). Specific heat does not exhibit a strong dependence on the geology of different aggregates (Klieger and Lamond 1994). Th erefore, a value of 921.1 J/kgK (220.0 Btu/lbmF) was used for all of the numerical simulations. To facilitate more accurate future simulations, the ASTM D2766 sta ndard test method may be utilized to experimentally quantify the sp ecific heat of concrete. Mass density was estimated to be 2403 kg/m3 (150 lb/ft3) for all of the concrete and mortar mixtures. 4.3 Modeling Program Each of the concrete and mortar mixtures presented in Chapter 2 were simulated using the TOUGH2 program. Four different thermal loadings were applied during the numerical modeling study: 1. Furnace time-temperature curves measured during thermal testing 2. ASTM E119 time-temperature curve (40 minutes)

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149 3. ASTM E1529 time-temperature curve (40 minutes) 4. ASTM E1529 flux loading The ASTM E119 and both ASTM E1529 ther mal-loading conditions were applied to one-dimensional models of each mixture. Experimental furnace time-temperature curves were applied to the one and two-di mensional models and were limited to the mixtures that were actually tested (M25, M35, C25, C45, and L35) in the thermal testing phase of the study. Table 4-4 provides a more de tailed description of the analysis study. Because the saturation level of the concrete has the potenti al to affect pore pressure, multiple simulations with different initial li quid saturation levels (25, 50, 75, and 90%) were conducted for each of mixtures w ith the E119 and E1529 thermal loading conditions. Furnace-test models were analyzed with an initial satura tion of 90% as this was the approximate specimen condition during testing (see Appendix C). Table 4-4. TOUGH2 simula tions performed on the concrete and mortar mixtures E15291 Furnace 2D4 Mixture ID E1191 Temperature2Flux3 1D 10 mm 15 mm M20 5 M25 M35 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 1 Only one-dimensional simulations run for E119 and E1529 thermal loading 2 Thermal loading specified as time-temperature curve 3 Thermal loading is specifi ed as surface heat flux 4 Location of pressure transducer 5 Shaded region indicates the simulation was performed

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1504.4 Modeling Results 4.4.1 Comparisons Between Numerical Models and Experimental Testing The two-dimensional TOUGH2 models us ed for simulating the experimental thermal testing did not initially produce pressures that were similar to those measured. Two explanations for the differences are as fo llows. First, the mortar mixtures spalled significantly during thermal testing which affected the heat and mass flow within the material. The heated surface was continually redefined during testing due to spalling and thus the distance from heated surface to the pressure transducer changed. Spalling also caused changes in the location of the ambi ent pressure boundary condition, which was originally at the heated surface. Second, the assumptions made in regard to material properties used in TOUGH2 affected the results. For instance, the vari ation in intrinsic permeability with temperature added to the numerical code was based on previous published research and may not precisely represent the behavior of the materials considered in this study. An attempt was therefore made to improve the models by using results from the permeability testing phase of this study. The effects of cement dehydration which results in an additional pore water and increased porosity was not included in the numerical models after evaluation of the necessary time to include this in the experimental program. The process of comparing nume rical model results to the experimental testing data is summarized in the flowchart in Figure 4-12. As the flowchart shows, the ultimate goal for the numerical modeling is to create pore pr essure and temperature data to be used in stress analysis. Therefore, comparison betw een experimentally measured pressure and air void pressure predicted by the two-dimensional numerical models was an intermediate

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151 step. One-dimensional models were then us ed to predict pore pressure and temperature in non-instrumented concrete systems. Measured Surface Temperature Compare Numerically Predicted Inte rnal Temperature with Thermocouple Data Experimental Thermal Testing 2-D Numerical Modeling (with pressure transducer geometry) 1-D Numerical Modeling (without pressure transducer geometry) Pore Pressure, Internal Temperature Internal Temperature Overestimated Stress Analysis (See Chapter 5) Decrease Transient Surface Temperatures Compare Numerically Predicted Inte rnal Pressure with Thermocouple Data Increase Permeability Temperature Dependance Factor, Ak Internal Pressure Underestimated Figure 4-12. Flowchart detai ling numerical modeling process

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1524.4.1.1 Thermal loading curves For each of the thermal specimens, a one-dimensional simulation was performed. Measured furnace temperatures were prescr ibed as the temperatures of the boundary super-elements. For each of the simulations, the temperatures of the element volumes at 10 and 15 mm (0.394 and 0.591 in.) from the heated surface were compared to those measured internally during expe rimental testing. If the temperatures in the model were significantly different at thes e locations, the heat input into the model (through the boundary super-element) was adjusted. Although the air temperature was measured near the surface of the specimen, the actual th ermocouple location was approximately 50 mm (2 in.) from the heated surface. Therefore, the thermocouple data may not have indicated the temperature at locations closer to the surf ace. It was assumed, however, that the timetemperature curve was similar in shape at lo cations closer to the surface, but with a different overall magnitude. Therefore, the entire time-temperature history of the superelement was adjusted and numerical simulati ons were run again until the temperature at 10 and 15 mm (0.394 and 0.591 in.) matched the experimental data. The super-element time-temperature curves did not need to be modified for all three thermal tests of the mortar mixtures because the numerical and experimental temperature results matched well. Howeve r, the numerical solutions for all three concrete mixtures over-predic ted internal temperatures. Therefore, the super-element temperatures were reduced by 10 and 20% a nd the internal temperatures were again compared. The super-element temperatures were reduced by 10% for the C25 model, 20% for the C45 model, and 20% for the L35 specimen to obtain internal temperatures that more closely resembled t hose measured experimentally.

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153 Figure 4-13 shows the air temperature meas ured during the thermal testing of the M25 specimen (Test #1) and filtered data points at 10 second intervals (linearly interpolated). This filtering process was perfor med for each of the six experimental tests. Resulting curves are pres ented in Appendix D. 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered Figure 4-13. Filtering of the experimental air temperature for Test #1 of the M25 specimen for the TOUGH2 boundary super-element 4.4.1.2 Comparison of results The time-history of pressure was obtained from the numerical simulation results of each mixture at the locations representing the pore pressure transducers. As previously discussed, a void of air was introduced into the models at the locations of the pore pressure transducers. The pore pressure in the void was then extracted from the TOUGH2 output data and was filtered using a Gaussian smoothing technique to eliminate

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154 0 20 40 60 80 100 0 300 600 900 1200 0 200 400 600 800 1000 1200 1400 0 5 10 15 20 Pore pressure (atm) Pore pressure (psia)Time (sec) Time (min) Mixture ID M25-1 M25-2 M35 C25 C45 L35 (a) 0 20 40 60 80 100 0 300 600 900 1200 0 200 400 600 800 1000 1200 1400 0 5 10 15 20 Pore pressure (atm) Pore pressure (psia)Time (sec) Time (min) Mixture ID M25-1 M25-2 M35 C25 C45 L35 (b) Figure 4-14. Pore pressures predicted by numerical models using the experimental furnace time-temperature loading curves: (a) 10 mm (0.394 in.), (b) 15 mm (0.591 in.)

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155 high frequency fluctuations. Finally, pore pressure out put was obtained from onedimensional numerical simulations representi ng the thermal tests. Figure 4-14 shows a summary of the pore pressure output for each numerical model. The details of how each of these curves was obtained are given in the following sections. Following the procedure outlined in Figure 4-modifications to the applied surface temperatures and permeability temperature dependency factors (kA ) for each of the mixtures was performed (Table 4-5). The transient surface temperatures required only minor modifications, but still produced values between those prescribed by the ASTM E119 and ASTM E1529 standard test fires. Detailed comparisons of numerically predicted internal temperatur e and thermocouple data are presented in Appendix E. Measured surface temperatures were sometime s overestimated due to the proximity of the thermocouples to the propane burners. Table 4-5. Calibration factors for numerical modeling Calibration Factors Mixtures Percentage of Experimentally Measured Surface Temperature Permeability Temperature Dependence Factor, Ak M25 (Test #1) 100 % 0.005 M25 (Test #1) 100% 0.005 C25 90% 0.010 C45 80% 0.010 L35 80% 0.010

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156 The permeability temperature-dependency factors show that for the models representing the mortar mixtures, a value of 0.005 which was based on previous research by Gawin et al. (1999) accurately predicted pressures. However, all three concrete mixtures required this factor to be increased to 0. 010. Aggregate type, mixture proportions, and test methods used by Gawin et al. were not available to the author and may have been different from the properties of the mixtures consider ed in this study. 4.4.1.2.1 M25 mortar specimens. Two thermal tests were conducted on specimens made of M25 mortar mixture, each with a different time-temperature thermal loading curve (air temperature at the surface). The M25 specimens exhibited significant spalling (observed through crack-detection circuitry and visual assessment) during thermal testing and this material failure was responsible for the limited pressure data in Test #1. Figure 4-15 shows a comparison between the pore pressures measured during Test #1 of the M25 mortar specimen at 10 mm (0 .394 in) from the heated surface and the output from the numerical models. Two of th e curves plotted in the figure represent numerically determined pressures. One is from the two-dimensional model in which an element has been used to represent the void at the tip of the pressure transducer and the other is from the one-dimensional model. Experimentally measured pressure demonstrated similar values to those predicted by the numerical models. The extreme decrease in experimentally measured pore pre ssure at about 660 seconds (11 minutes) is indicative of spalling in the vicinity of the transducer. The pressure difference between the numerical and experimental results is most likely the

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157 result of estimations made in the TOUGH2 c ode concerning the behavior of the material at high temperatures (e.g., pe rmeability and porosity). 0 20 40 60 80 100 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2d Model) Pore pressure (1d model) Figure 4-15. Comparison between pressure measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M25 specimen (Test #1) Figure 4-16 shows a comparison between th e pressures measured at 15 mm (0.394 in) from the heated surface of test #2 of th e M25 mortar specimens and output from the numerical models. The numerically determin ed pressure is from the two-dimensional model using the element representing the void at the tip of the pressure transducer. Although there was not an abrupt change in pressure that a ccompanies spalling, there was a sudden change in slope of the experimenta lly measured pressure at about 900 seconds (15 minutes). It is believed that there wa s spalling near the transducer, but not in a

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158 manner that would expose the transducer s uddenly to ambient pressure. If spalling occurred near the transducer the pressure at the point of measurement could stop increasing as observed during Test #2 of the M25 specimen. Spalling was detected at 5 mm (0.0197 in.) from the original heated su rface at 600 seconds into the thermal test by the crack-detection circuitry. 0 20 40 60 80 100 120 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2D model) Pore pressure (1D model) Figure 4-16. Comparison between pressure measured experimentally and predicted numerically at 15 mm (0.591 in.) from the heated surface for the thermal testing of the M25 specimen (Test #2) Again, the numerical model seemed to slightly overestimate the pressure as it did for the simulation of Test #1 of M25. As previously discussed, there may have been spalling near the pressure transducer. This idea is reinforced by observing that a rate increase of temperature at about 780 seconds (13 minutes) into the thermal test measured by the thermocouple at 15 mm (0.591 in.) from the original location of the heated surface.

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159 The change in the rate of temperature increase indicates that the original heated surface moved closer to the point of measurement. 4.4.1.2.2 M35 mortar specimen The two-dimensional numerical model created for the simulation of thermal testing of th e M35 specimen had convergence difficulties and there is limited output for comparison to the experimental results. Although the numerically predicted pressures in the air void were consistently lower than the experimentally measured values, spalling of th e mortar in the thermal test affected the results. Figure 4-17 shows the experimentally measured and numerical ly predicted (from 0 20 40 60 80 100 120 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2d Model) Pore pressure (1d model) Spalling Figure 4-17. Comparison between pressure measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M35 specimen the 2D model) for the M35 specimen. Noted on the graph is the suspected time of spalling during the experimental testing wh ich caused instability in the measured pressure. The M35 thermal specimen exhibi ted extensive spalling during experimental

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160 testing. Therefore, the data presented must by evaluated in light of the fact that spalling may have affected the temperatur e and pore pressure development. 4.4.1.2.3 C25 concrete specimen A pair of two-dimensional numerical simulations was conducted representing th e thermal test of the C25 specimen, representing transducers at 10 and 15 mm (0.394 and 0.591 in.) from the heated surface. Figure 4-18 shows the comparison between the e xperimentally measured and numerically 0 5 10 15 20 0 120 240 360 480 600 720 840 960 1080 1200 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2D model) 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 4-18. Comparison between pressure measured experimentally and predicted numerically for the thermal testing of the C25 specimen predicted values of pore pressure for 10 a nd 15 mm (0.394 and 0.591 in.) from the heated surface. The magnitudes of the pressures output by the numerical model and those measured experimentally were both low comp ared to other mixtures, indicating a lower susceptibility to failure due to pore pressure development.

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161 Figure 4-19 shows the extracted pore pressure values from each of theses models for both depths (10 and 15 mm (0.394 and 0.592 in .) from the heated surface. The results show that the peak of the pore pressure prof ile is moving away from the heated surface, as expected with the moisture clog spalling theo ry. This plot shows the first signs in the study that the theory holds true for concre te as it does for mortar. Even though the permeability is far higher for the C25 mixture co mpared to the mortar mixtures, there is migration of steam and water causi ng a moving pressure buildup. 0 5 10 15 20 0 120 240 360 480 600 720 840 960 1080 1200 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) 15 mm 10 mm Figure 4-19. Pore pressure output from one-dimensional numeri cal modeling of C25 specimen 4.4.1.2.1 C45 concrete specimen Figure 4-20 shows the pressure measured experimentally and predicted numerically for 10 and 15 mm (0.394 and 0.591 in.) from the heated surface. This plot shows that bot h experimentally measured pore pressure and

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162 numerically predicted pressures are higher than those of the less permeable C25 mixture. This proves to be an intrigui ng new aspect to the moisture clog spalling phenomena. A more permeable mix may be more susceptible to higher pore pressures in fire conditions. The key difference between these two mixtures is the porosity. Because porosity was higher in the C45 mixtures, this also meant th at there was a higher initial volume of water within the concrete pore structure. 0 5 10 15 20 0 120 240 360 480 600 720 840 960 1080 1200 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2D model) 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 4-20. Comparison between pressure measured experimentally and predicted numerically for the thermal testing of the C45 specimen The equivalent pore pressures (from th e one-dimensional models) are shown in Figure 4-21. Interestingly, the pore pressures were similar in magnitude to those of the void pressures from the two-dimensional models This is also most likely due to the

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163 higher porosity and permeability. The air void at the pore pressure transducer essentially acted less as a reservoir for moisture migration. 0 5 10 15 20 0 120 240 360 480 600 720 840 960 1080 1200 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Pressure (Air void in 2D model) Pore pressure (1D model) 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 4-21. Comparison between pressure of air void in 2D model and pore pressure from 1D model for the numerical modeling of the C45 specimen 4.4.1.2.5 L35 concrete specimen The pore pressure measured in the experimental program was the lowest of all the mixtures and the same was true in the numerical modeling program. As mentioned in Chapter 3, there was significant moisture observed exiting the cool surface of th e specimen during the thermal test, which may have reduced the internal pore pressure. This was acc ounted for in the numerical simulation by modeling the exact thickness of the specime n and providing a large super-element which acted as a sink for heat and mass flow on the last concrete element (farthest from the

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164 heated surface). A comparison between the experimentally measured and numerically predicted pore pressure is shown in Figure 4-22. 0 1 2 3 4 5 6 7 8 9 10 0 120 240 360 480 600 720 840 960 1080 1200 0 20 40 60 80 100 120 140 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Experimentally measured pressure Pressure (Air void in 2D model) 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 4-22. Comparison between pore pressu re measured experimentally and predicted numerically for the thermal testing of the L35 specimen The pore pressures predicted by the one-d imensional models at 10 and 15 mm (0.394 and 0.591 in.) from the heated surface ar e presented in Figure 4-23. Note how the magnitude at the peak pore pressure for each location is about the same. These pore pressures may also be over-estimated ba sed on the air-void pressures in the twodimensional model being higher than the expe rimentally measured pressure. However, the magnitudes of the pore pressure are extr emely low compared to the other mixtures tested; indicating that failure due to pore pr essure development is less likely with this mixture design.

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165 0 1 2 3 4 5 6 7 8 9 10 0 120 240 360 480 600 720 840 960 1080 1200 0 20 40 60 80 100 120 140 0 2 4 6 8 10 12 14 16 18 20 Pressure (atm) Pressure (psia)Time (sec.) Time (min.) Pressure (Air void in 2D model) Pore pressure (1D model) 10 mm (0.394 in.) 15 mm (0.591 in.) Figure 4-23. Comparison between pressure of air void in 2D model and pore pressure from 1D model for the numerical modeling of the L35 specimen 4.4.2 ASTM E119 and ASTM E1529 Thermal Loading This section discusses the e ffects of material properties and thermal loadings on the distribution of pore pressure saturation, and temperature across a one-dimensional model. The effects of permeability and porosity on the distribution of pore pressure were investigated through numerical modeling of the concrete and mortar mixtures presented in Chapter 2. It is more realistic to vary both permeability and porosity simultaneously rather than individually because permeability is generally dependent upon porosity within mixtures made of the same constituents. For example, the C-class concrete mixtures

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166 presented in Chapter 2 had a relationship be tween intrinsic gas permeability and porosity, while the mixture proportions (with exception of the water-binder ratio) were the same. Two different thermal loading methods ASTM E119 and ASTM E1529, were applied to each of the numerical models to evaluate the difference pore pressure buildup caused by two fire curves. The time-temperat ure curves described in the specifications were applied to each of the one-dimensional models representing the concrete and mortar mixtures. ASTM E1529 specifies an applie d heat flux in conjunction with a boundary temperature, but specifying both was beyond the limitations of the numerical code. In order to simulate fire exposure of c oncrete under varied field conditions having variable saturations levels, numerical simu lations of the ASTM E119 and ASTM E1529 thermal loadings were performe d for concrete and mortar mixt ures over a range of initial saturation levels. In particular, simulations were performed with initial saturation levels of 25, 50, 75, and 90%. A saturation level of 90% was typical for the mixtures in this study (see Appendix C) at the time of testing, but in-service concrete often have values that are far lower. 4.4.2.1 Effects of Permeability and Porosity During extreme thermal loading of saturated or partially saturated concrete, porosity and permeability are key parameters for quantifying steam and water migration, and thus pore pressure development. It is de monstrated in this section that pore structure and permeability affect the por e pressure within concrete when heated. Relationships between pore pressure and para meters describing the pore structure (e.g., porosity, water permeability, and gas permeability) are presented using the TOUGH2 database of simulations of the concrete and mortar mixtur es presented in Chapter 2. It should be noted that this is not necessarily a sensitivity analysis of permeability or porosity, but

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167 rather a sensitivity analysis of water-binder ratio. Gas permeability, water permeability, and porosity all vary with water-binder ratio, as measured for each of the mixtures. To compare numerical simulations of th e mixtures, a number of data filtering procedures were developed (see Figure 4-24). First, pore pressure profiles through the depth of the one-dimensional models were ex tracted from the TOUGH2 output files at increments of 10 seconds. Second, each of the profiles was filtered (across the depth) using a Gaussian-kernel smoothing technique Third, the maximum value of pore pressure (i.e., peak pore pressure) was recorded for each of the smoothed pore pressure Pore pressureDepth from heated surface time2time1 (a) Pore pressureDepth from heated surface time2time1 Peak pore pressures (b) Pore pressureSimulation time time2time1 (c) Pore pressureSimulation time Absolute maximum pore pressure (d) Figure 4-24. Data filtering procedure for determining absolute maximum pore pressure: (a) Output from simulation, (b) Smoothed prof iles, (c) Peak pore pressure at each time step, (d) Smoothed peak pore pressure at each time step and extraction of absolute maximum pore pressure profiles at each time step. Finally, the peak pore pressures were fi ltered (through time), again using a Gaussian-kernel smoothing techni que. This procedure produces a singular

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168 pore pressure that represents the statistica lly smoothed (through time and space) absolute maximum value in the entire geometry and duration of the model. Figure 4-25 shows the relationship between the peak pore pressure versus the intrinsic gas permeability for the all of the mixtures (from the experiment al program presented Chapter 2) with an initial saturation level of 90%, thermally loaded with both the ASTM E119 and ASTM E1529 time-temperature curves. The mortar and concrete with limerock aggregate mixtures both show tre nds of higher pore pressure with lower intrinsic gas permeability, which is a relati onship that agrees with past research (Anderberg 1997, Kalifa et al. 2000, Hertz 2003) An opposite relationship is revealed for the concrete with granite aggregate, wh ich agrees with the experimental results 20 40 60 80 100 1 10 100 1000 10000 100000 0 200 400 600 800 1000 1200 1400 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic gas permeability, Kg (x10-20 m2) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) C20 C25 C30 C35 C40 C45 L30 L35 L40 M35 M30 M25 M20 Figure 4-25. Variation of absolute ma ximum pore pressure with intrinsic gas permeability (90% initial saturation level)

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169 presented by Ali (2002). The graph of absolute maximum pore pressure with water permeability (see Figure 4-26) shows a similar trend as that which was revealed with intrinsic gas permeability. Although the concrete mixtures produced highly variable data between mixtures, the results showed that maximum pore pressure was higher for mixtures with higher water permeability. This suggests that porosity which was wide ranging within this mixture set had a significant effect on th e pore pressure results. In contrast, both the mortar and the limerock concrete mixtures showed increasing values of absolute maximum pore pressure with decreasing intrinsic water permeability. The maximum pore pressure for each of the simulation times plotted for the granite-aggregate concrete mixtures demonstr ates a positive relationship with intrinsic 0 20 40 60 80 100 0 2 4 6 8 10 12 0 200 400 600 800 1000 1200 1400 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic water permeability, Kw (x10-21 m2) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C45 C40 C35 C30 C25 C20 L40 L35 L30 Figure 4-26. Variation of absolute maxi mum pore pressure with intrinsic water permeability (90% initial saturation level)

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170 gas permeability. This is an unusual relationship because it is assumed that materials with lower permeability (i.e., a lower ability for pore constituent migration) would have higher maximum pore pressures, thus yielding a line of negative slope as demonstrated with the mortar and limerock-aggregate c oncrete mixtures. A negative relationship would almost certainly be true if all the ma terials had the same porosity. However, the porosity was quite different between the conc rete mixtures (ranging from 7.9 to 19.3% for the C-class concrete mixtures). In addition, the water permeability values did not increase significantly from the least to most porous mixtures. Therefore, the change gas and water permeability from mixture to mixt ure was not high enough to keep pace with the change in porosity. Stated another way, the volumetric amount of pore constituents (i.e., water, air, and steam) increased more rapidly from the C20 to the C45 mixture than did the ability of the pore network to tr ansport them. This trend in pore pressure development agrees with the experimental m easurement of pore pressure on the C25 and C45 specimens. Figure 4-27 shows the relatio nship between maximum pore pressure and porosity. Similar trends were found for mixtures with lo wer initial saturation le vels (presented in Appendix F). The key finding that is revealed through this series of models is that permeability alone does not indicate the suscepti bly of mixtures to high pore pressure. This was proven through the use of experime ntally measured permeability and porosity for a number of different mixtures (with vary ing water-binder ratios and aggregate types). This is not to say that the conclusions reached in the past concerning the increasing susceptibility of spalling of concrete in fires with strength are incorrect. The mixtures in this study showed both trends. Since all of the mixtures in this study

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171 0 20 40 60 80 100 0 2 4 6 8 10 12 14 16 18 20 0 200 400 600 800 1000 1200 1400 Maximum pore pressure (atm) Maximum pore poressure (psia)Porosity (%) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 4-27. Variation of absolute maximu m pore pressure with porosity (90% initial saturation level) were high-strength, the primary conclusion re ached from the numerical simulations is that the magnitude of pore pressure devel oped during fires for high performance concrete depends on the permeability and porosity of th e mixtures, not the strength (see Figure 428). 4.4.2.2 Effects of Thermal Loading Severity of thermal loading will have a direct effect on the magnitude of pore pressure within concrete due to the interrel ation of heat and mass flow. This section evaluates the sensitivity of pore pressure with intensity of thermal loading using the ASTM E119 and ASTM E1529 time-temperature curves.

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172 As previously shown in Figures 4-25, 426, 4-27, and 4-28 the absolute maximum pore pressure was generally higher for the ASTM E1529 rather than ASTM E119 thermal loading of the concrete and mortar mixtures at 90% initial saturation. However, this was not true for lower saturation levels such as 25% initial saturation (see Appendix F). The absolute maximum pore pressures were approximately equal for both thermal-loading conditions at this saturation level. This indicat es that, for the mixtures considered in this study, at low saturation levels the magnitude of the absolute maximum pore pressure is independent of whether ASTM E119 or ASTM E1529 is considered. 0 20 40 60 80 100 0 20 40 60 80 100 120 140 160 0 200 400 600 800 1000 1200 1400 0 5 10 15 20 Maximum pore pressure (atm) Maximum pore pressure (psia)Compressive strength, f'c (MPa) Compressive strength, f'c (ksi) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C45 C40 C35 C30 C25 C20 L30 L35 L40 Figure 4-28. Variation of absolute maximu m pore pressure with compressive strength (90% initial saturation level) Although the pore pressures may be the sa me, the locations at which the peak pressures occur within the concrete are different as are the resulting internal stress states.

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173 Figure 4-29 shows the locations of the p eak pore pressures through time for the C45 mixture at 25 and 90 % initial saturati on for both E119 and E1529 thermal loading conditions. The figure indicates that the peak pore pressure will not only be higher for the E1529 thermal loading (at high saturations), but it will also occur at a point earlier in time than would occur under the ASTM E119 thermal loading. 0 20 40 60 80 0 300 600 900 1200 1500 1800 2100 2400 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 5 10 15 20 25 30 35 40 Distance from heated surface (mm) Distance from heated surface (in.)Time (sec) Thermal loading, Initial saturation E119, 25% E119, 90% E1529, 25% E1529, 90% Figure 4-29. Variation of absolute maximu m pore pressure with thermal loading and initial saturation level for the C45 mixture Two conclusions can be drawn from the data in Figure 4-29. First, the absolute maximum pore pressure will be farther from the heated surface for the E1529 than the E119 thermal loading (for the same saturation le vels). This is a result of the higher early temperatures that exist for the ASTM E1529 than the ASTM E119 thermal loading curve (see Figures 4-8 and 4-9). A higher heat inpu t and thus an earlier development of pore pressure occur for the ASTM E1529 thermal loading. Second, lower saturation levels

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174 result in the location of the peak pressure being farther away from the heated surface (for the same loading condition). A concrete mi xture with lower saturation level has less impedance to flow because the initial relati ve permeability (which depends in saturation level) is higher. 4.4.2.3 Effects of Saturation Level By comparing the maximum pore pressures in Figures 4-25, 4-26, 4-27, and 4-28 and comparing them to the data presented in the figures of Appendix F, initial saturation level is noted to greatly affect the devel opment of pore pressure. Figure 4-30 shows a comparison between absolute maximum pore pre ssure for concrete and mortar mixtures 20 40 60 80 100 1 10 100 1000 10000 100000 0 200 400 600 800 1000 1200 1400 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic gas permeability, Kg (x10-20 m2) Saturation level, Mixture type 90%, Mortar 90%, Concrete (granite) 90%, Concrete (limerock) 25%, Mortar 25%, Concrete (granite) 25%, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 4-30. Variation of absolute maximu m pore pressure with saturation level for ASTM E119 thermal loading with different saturation levels. This figure is essentially a combination of Figure 4-25 and the equivalent figure in Appendix F. As shown, the pore pressures are very different for the saturation levels of 25 and 90%.

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175 The same trend of higher pore pressures was also found for the ASTM E1529 thermal loading when comparing initial sa turation levels of 25 and 90% (see Figure 431). This indicates that regardless of the t ype of fire (hydrocarbon fueled (ASTM E1529) or building fire (ASTM E119)), the pore pressure is sensitive to saturation level. 20 40 60 80 100 1 10 100 1000 10000 100000 0 200 400 600 800 1000 1200 1400 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic gas permeability, Kg (x10-20 m2) Saturation level, Mixture type 90%, Mortar 90%, Concrete (granite) 90%, Concrete (limerock) 25%, Mortar 25%, Concrete (granite) 25%, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 4-31. Variation of absolute maximu m pore pressure with saturation level for ASTM E1529 thermal loading 4.5 Summary and Conclusions From the numerical modeling program in itiated to accompany the experimental testing program, a number of key conclusions were made: A method to quantify heat and mass flow in concrete and mortar was presented and compared to experimental results. Additions were made to the numerical c ode to account for ch anges in intrinsic permeability and the slip flow factor with temperature.

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176 It was shown that the measurement of pre ssure was not equal to the pore pressure due to the void space at the tip of the pre ssure transducer. This volume of air must be included in numerical modeling for proper comparison to experimental data. The development of pore pressure duri ng thermal loading is dependent upon porosity, permeability, saturation level, and the intensity of transient temperature loading (as shown in the m odels with the E119 and E1529) It was shown that the more permeable concrete mixtures were more susceptible to higher pore pressures due to the high porosity. Unlike the mortar and concrete with limerock aggregate, the permeability did not increase eno ugh (from the least to most permeable mixtures, C20 to C45) to overcome th e increase porosity for these mixtures.

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177 CHAPTER 5 STRESS DEVELOPMENT DUE TO PORE PR ESSURE IN CONCRETE MATERIALS EXPOSED TO FIRE In this chapter, focus is placed on th e task of merging pore pressure and temperature data output from TOUGH2 simulati ons together with finite element models for the purpose of conducting stress analyses. Comparisons of predicted stress are then made for the concrete and mortar mixtures presented in Chapter 2. While Chapter 4 focused on quantifying pore pressure numerically a necessary step in analyzing material failure of concrete during fire conditions involves the process of stress evaluation. Methods based on previous research (Chung 2003) are used to compute stresses in concrete using pore pressure and temper ature data obtained from the TOUGH2 simulations described in Chapter 4. Results developed in the present chapter may serve as a basis for future modeling of concre te spalling during thermal exposure. 5.1 Finite Element Program ADINA, the finite element program that wa s used in this study was developed by ADINA R&D (1997). The program offers the capabilities necessa ry for the present application: Ability to map pore pressure and temperature as nodal loads Thermo-elastic material model Ability to use output from numerical models as input for finite element models Ability to perform time varying analyses

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178 5.2 Input Parameters 5.2.1 Geometry of Models Geometrically, the models considered here are similar to the one-dimensional model discussed in Chapter 4. Three items of data were specified in the TOUGH2 model that were also used in the creation of the finite element model: element volume, distances between the element centers and flux surfaces and flux surface areas. The size of each element in the finite element model was based on the element volume used in the TOUGH2 model and the state variables (i.e., pore pressure, temper ature, and saturation level) calculated by TOUGH2 at the elem ent centroids. Therefore, each volume centroidal location was equated to a nodal coordinate in the fi nite element model so that the state variables could be prescribed as nodal boundary conditions (Chung 2003). Distances between nodes in the finite el ement model were based on the distances between the centroids of the element volumes in the TOUGH2 models. Figure 5-1 shows the correlation between the numerical and finite element models for nodal locations. Two-dimensional plane strain continuum solid elements were used to model the concrete system for stress analysis. The volume of each finite element was equal to distance between nodes multiplied by the flux ar ea specified in the numerical model. 5.2.2 Material Models A linear elastic material having a modulus th at varied with temperature was defined for all elements. The modulus data were chosen based on a number of equations by Collins and Mitchell (1991) that relate material parameters to compressive strength. From this set of equations, the secant modulus ( s E ) was estimated for each of the mixtures in this study and equa ted to the elastic modulus ( E ).

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179 Boundary super-element is not mapped into finite element model z y Distances specified in numerical model Distance specified in specified in finite element model Volume centroid Node Numerical model Finite element model Figure 5-1. Locating nodes in the finite element model based on the geometry of the numerical model (Chung 2003) The stress-strain relationship used in this study is parabolic in shape and is based and has the following form (Collins and Mitchell 1991): ' 1'c c nk c cnee f f nee (5-1) where c f is the compressive stress in MPa (ksi), 'c f is the maximum compressive strength in MPa (ksi), n is a curve fitting factor, e is the compressive strain, 'ce is the compressive strain at the maxi mum compressive strength, and k is a post peak-stress decay factor. Although Equation 5-1 contains the factor k for post-peak stress-strain behavior, this was not included in the material model (equals unity). Therefore, the only parameters that needed to be estimated were n and 'ce The curve-fitting factor (n) was calculated as follows:

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180 0.8 17c f n (f’c in ksi) (5-2a) 0.8 2.5c f n (f’c in MPa) (5-2b) This curve-fitting factor is also useful in calculating 'ce if the following relationship is also invoked: t tsE n EE (5-3) where tE is the tangent modulus at the or igin or zero-strain condition and s E is the secant modulus and is equal to ''cc f e. The tangent modulus (tE), is calculated with the following formula, which is particular to mixtures with high compressive strength: 3.32'6900tcEf (Et and f’c in ksi) (5-4a) 31265'1.010tcEf (Et and f’c in MPa) (5-4b) Rearrangement of Equation 5-3 yields the fo llowing relationship for calculation of the secant modulus: 1 1 s tEE n (5-5) The secant modulus was then equated to th e elastic modulus of the material in both the tension and compression. When analyzing the stress output from the simulations, it is important to determine when the tensile stresses have reached the tensile strength. However, the simple linear elastic material model used in this study would, in general, allow stresses to exceed the tensile strength or modulus of rupture. Therefore, to detect the occurrence of tensile failures, th e first principal stresse s were computed and

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181 compared to the tensile strength, which wa s computed based on an empirical equation by Nawy (2001) for high strength concrete: '0.59'tc f f (ft and f’c in ksi) (5-6a) '0.234'tc f f (ft and f’c in MPa) (5-6b) A geometric representation of the variable s calculated above is shown in Figure 52. Each of the variables calculated for each of the mixtures in this study are presented in Table 5-1 fc ft ete`c EsEt Es = Secant modulus Et = Tangent modulus ft = Tensile strength et = Strain at tensile strength f’c = Compressive strength e’c = Strain at compressive strength Figure 5-2. Derivations of the stress-str ain curve for concrete using the Collins and Mitchell formulation (1991)

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182 Table 5-1. Strength parameters for constructin g stress-strain relationships for mixtures in the experimental program Maximum compressive strength, f’c MPa (ksi) Curvefitting factor, n Tangent modulus, Et MPa (ksi) Strain at maximum compressive stress, e’c Secant modulus, Es MPa (ksi) Maximum tensile stress, f’t MPa (ksi) Mix ID Measured Eq. 5-2 Eq. 5-4 f’c/Et Eq. 5-5 Eq. 5-6 127.2 8.3 44342 0.00326 38988 6.65 M20 (18.4) (8.2) (6433) (0.00327) (5646) (1.01) 127.0 8.3 44312 0.00326 38953 6.65 M25 (18.4) (8.2) (6428) (0.00326) (5641) (1.00) 96.9 6.5 39588 0.00289 33500 5.81 M30 (14.1) (6.4) (5743) (0.00290) (4849) (0.88) 85.9 5.9 37676 0.00275 31241 5.47 M35 (12.5) (5.8) (5465) (0.00276) (4521) (0.83) 139.0 9.0 46037 0.00340 40907 6.96 C20 (20.2) (8.9) (6679) (0.00340) (5925) (1.05) 122.8 8.0 43685 0.00321 38239 6.54 C25 (17.8) (7.9) (6337) (0.00322) (5537) (0.99) 109.3 7.2 41608 0.00305 35853 6.17 C30 (15.9) (7.1) (6036) (0.00305) (5191) (0.93) 106.4 7.1 41145 0.00301 35316 6.09 C35 (15.4) (7.0) (5969) (0.00302) (5113) (0.92) 91.1 6.2 38585 0.00282 32319 5.63 C40 (13.2) (6.1) (5597) (0.00282) (4677) (0.85) 79.7 5.5 36540 0.00267 29882 5.27 C45 (11.6) (5.4) (5301) (0.00267) (4323) (0.80) 104.1 6.9 40770 0.00298 34880 6.02 L30 (15.1) (6.8) (5914) (0.00299) (5049) (0.91) 88.2 6.0 38076 0.00278 31716 5.54 L35 (12.8) (5.9) (5524) (0.00279) (4590) (0.84) 78.7 5.4 36347 0.00265 29650 5.23 L40 (11.4) (5.4) (5273) (0.00266) (4290) (0.79) The ADINA finite element program offers a concrete material model that has a similar overall shape to that produced by Equa tion 5-1 and is temper ature dependent. In addition, the material model also allows for a tensile failure conditi on. The stress-strain formula associated with the ADINA concrete model (ADINA R&D 1997) is as follows:

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183 23/' 1/'/'/'tscc c c ccccccEEee f f AeeBeeCee (5-7) where A, B and C are constants based on following equations: 3232 22231 21tutsEEppEEpp A ppp (5-8) 232t sE B A E (5-9) 2t sE CA E (5-10) where 'uc p ee ue is the ultimate strain past the peak stress, uE is the modulus at the ultimate strain and is equal to uu f e, and u f is the ultimate stress at ue. In Figure 5-3, a comparison is shown of the Collins and M itchell formulation, ADINA concrete model, and the linear elastic model based on the secant modulus. Because the strength of concrete varies with temperature, a thermal dependence of strength was also included in the finite element material model. The compressive strength versus temperature curve for high-st rength concretes shown in Figure 5-4 (Phan and Carino 1998) was used to soften the el astic modulus and the relationship. The compressive strength stays constant up to 400 C (752 F) and decreases linearly to 30% of the maximum strength at 800 C (1472 F). The strength remains constant at 30% of the maximum at temperatures above 800 C (1472 F). Because all of the properties (tE, 'ce, and t f ) calculated for the material model were based on compressive strength, this method of approximating temperature dependence was used to determine the elastic modulus of mixtures at high temperatures.

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184 0 30 60 90 120 150 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0 5 10 15 20 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 Stress (MPa) Stress (ksi)Strain (mm/mm) Strain (in./in.) Collins and Mitchell formula (1991) ADINA formula for concrete (Bathe 1997) Linear elastic based on secant modulus Figure 5-3. Stress-strain curves for the Collins and Mitchell, ADINA concrete model, and linear elastic formulations for the C20 concrete mixture f'c(T) / f'cTemperature, T 1.0 0.3 400 C (752 F) 800 C (1472 F) Figure 5-4. Variation of compressive stre ss with temperature (Phan and Carino 1998)

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185 A linear thermo-elastic material model was used to represent the concrete in the finite element models. s E and t f were calculated for each mixture at the critical points in the strength-temperature curve that co rrespond to temperatures of 400 and 800 C (752 and 1472 F). An example of the variation of the strength parameters (for the C20 mixture) between 400 and 800 C (752 to 1472 F) is shown in Figure 5-5. Although the compressive strength decreased by 70%, the elastic modulus and tensile strength decreased less because these parameters are based on empirical formulas. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 100 200 300 400 500 600 700 800 900 1000 200 400 600 800 1000 1200 1400 1600 1800 Ratio (see legend)Temperature, T (C) f'c(T)/f'c Es(T)/Es ft(T)/ft Figure 5-5. Variation of strength paramete rs with temperature for the C20 mixture The values of the strength parameters fo r the mixtures at temperatures below 400 C (752 F) are as shown previously in Table 51. Table 5-2 shows the strength parameters at temperatures above 800 C (1472 F). The pr ocedures and equations for calculation of

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186 n, tE, 'ce, s E, and 't f at 800 C (1472 F) were the same as those previously used, but were based on the reduced compressive strength (0.3'c f ). Table 5-2. Strength parameters for cons tructing stress-strain relationships for temperatures above 800 C (1472 F) Maximum compressive strength, f’c MPa (ksi) Curvefitting factor, n Tangent modulus, Et MPa (ksi) Strain at maximum compressive stress, e’c Secant modulus, Es MPa (ksi) Maximum tensile stress, f’t MPa (ksi) Mix ID 30% of measured f’c Eq. 5-2 Eq. 5-4 f’c/Et Eq. 5-5 Eq. 5-6 38.2 3.0 27408 0.00207 18405 3.64 M20 (5.5) (3.0) (3976) (0.00208) (2656) (0.55) 38.1 3.0 27391 0.00207 18383 3.64 M25 (5.5) (3.0) (3973) (0.00208) (2653) (0.55) 29.1 2.5 24804 0.00195 14925 3.18 M30 (4.2) (2.5) (3598) (0.00196) (2151) (0.48) 25.8 2.3 23757 0.00191 13501 3.00 M35 (3.7) (2.3) (3446) (0.00192) (1945) (0.45) 41.7 3.3 28336 0.00212 19623 3.81 C20 (6.0) (3.2) (4110) (0.00213) (2833) (0.58) 36.8 3.0 27048 0.00205 17930 3.58 C25 (5.3) (2.9) (3923) (0.00206) (2587) (0.54) 32.8 2.7 25911 0.00200 16415 3.38 C30 (4.8) (2.7) (3758) (0.00201) (2367) (0.51) 31.9 2.7 25657 0.00199 16074 3.33 C35 (4.6) (2.7) (3722) (0.00200) (2318) (0.50) 27.3 2.4 24255 0.00193 14179 3.08 C40 (4.0) (2.4) (3518) (0.00194) (2043) (0.47) 23.9 2.2 23134 0.00189 12650 2.89 C45 (3.5) (2.2) (3356) (0.00190) (1821) (0.44) 31.2 2.6 25451 0.00198 15798 3.30 L30 (4.5) (2.6) (3692) (0.00199) (2278) (0.50) 26.5 2.4 23976 0.00192 13800 3.03 L35 (3.8) (2.3) (3478) (0.00193) (1988) (0.46) 23.6 2.2 23029 0.00189 12505 2.87 L40 (3.4) (2.2) (3340) (0.00190) (1800) (0.43) Material input data for the finite element models of each of the mixtures presented in Chapter 2 and numerically modeled in Chap ter 4 is shown in Table 5-3. A constant Poisson’s ratio (0.20 ) was used in the analysis fo r all the mixtures and at all

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187 temperatures since this value is generally independent of temperat ure and mixture type (Phan and Carino 1998). Table 5-3. Parameters for c onstructing stress-strain relations hips for temperatures above 800 C (1472 F) Elastic modulus, MPa (ksi) Mix ID Poisson’s Ratio Coefficient of thermal expansion, C-1 (F-1) T 400 C (T 752 F) T 800C (T 1472 F) 38988 18405 M20 (5646) (2656) 38953 18383 M25 (5641) (2653) 33500 14925 M30 (4849) (2151) 31241 13501 M35 (4521) (1945) 40907 19623 C20 (5925) (2833) 38239 17930 C25 (5537) (2587) 35853 16415 C30 (5191) (2367) 35316 16074 C35 (5113) (2318) 32319 14179 C40 (4677) (2043) 29882 12650 C45 (4323) (1821) 34880 15798 L30 (5049) (2278) 31716 13800 L35 (4590) (1988) 29650 12505 L40 0.20 6.5x10-6 (3.61x10-5) (4290) (1800) 5.2.3 Loading Methods For each of the numerical simulations presented in Chapter 4, each of the output files contained the pore pressure and temperat ure data for each of the elements at every time step. These time-histories (for the one-dimensional numerical models) were mapped

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188 as nodal loads (as pore pressure loading and te mperature loading) into the finite element models (see Figure 5-6). A program was wr itten to convert data extracted from the TOUGH2 output files into noda l boundary load data for input in to the ADINA input file. Pore pressure and temperature output from the numerical models are the average at the center of the volumes. Pore pressure and temperature output from the numerical models are mapped into finite element model as nodal loads. 2d solid elements, thickness = width = 1.0 mm Pore pressure, temperature Figure 5-6. Mapping of pore pressure and te mperature results from numerical models into finite element models (Chung 2003) ADINA interprets nodal pore pressure as a hydrostatic pressure. Therefore, the pore pressures that were mapped as nodal load s were converted to effective stresses by using equilibrium of forces (see Figu re 5-7 for a simplified free body diagram): 1 P (5-11) where is the hydrostatic tensile st ress caused by the pore pressure, P is the pore pressure, and is the porosity. The conve rsion used in this project which is often referred to as the effectiv e stress concept (Terzaghi 1936) is one of the simpler methods for applying pore pressure as a stre ss. Other methods are also available (De Buhan and Dormieux 1999).

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189 Skeleton Pore (a) Pore pressure Tensile stress Tensile stress (c) Tensile stress (b) L L P P = pore pressure = tensile stress = P /(1) = porosity (d) Figure 5-7. Free body diagram for calcula ting hydrostatic tens ile stress from pore pressure: (a) Geometrical representation, (b) Developed Stresses, (c) Quadrant showing stresses, (d) Ca lculation of stresses 5.2.4 Boundary Conditions Choosing the boundary conditions for the models is critical for analysis of stress development due to the sensitivity of ther mal stresses on displacement restriction. Because the temperature was increasing in the elements, thermal expansion was quantified with the coefficient of thermal expansion. If the elements were restricted from

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190 expanding, stresses may develop and in so me cases could become extremely large relative to those caused by the pore pressure. In reference to the one-dimensional finite element model presented above, if this mode l was to represent the conditions of a structural member (e.g., the surface of a slab being heated), a fully restrained condition would be appropriate for the out of plane direct ions (in the x and y-di rections as shown in Figure 5-8). For other types of structur al members, alternative boundary conditions would need to be used. The boundary conditions that were used in this study were chosen to allow free expansion in the z-direction while restricting displacement in the y and x directions (see Figure 5-8). This condition is typical for slab systems with uniform surface heating. To facilitate this set of boundary conditions, plan e strain elements were used (strain in xdirection equals zero). 5.3 Stress Output Two major stress quantifications were inve stigated for the evaluation of material failure within these models. The first and third principal stresses were used for comparison to the maximum tensile and compre ssive strength. The first principal stress was always positive and thus was always comp ared to the tensile strength. The third principal stress was found to always be nega tive, indicating a stat e of compression and thus comparisons to compressive strength were performed. The failure criteria intended for this stress analysis is when the first principal stresses exceed ft or the third principal stresses exceed f’c. A more advanced stress analysis should include the investigation of the octahedral shear stre ss and stress invariants.

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191 z y Plane strain elements Original geometry Deformed shape Figure 5-8. Boundary conditions for the finite element models (full restrain in x and y directions) 5.3 Modeling Study A database of finite element solutions based on the output from the numerical simulations presented in Chapter 4 was construc ted for stress analysis. Considering that there were 104 numerical simulations perfor med (thirteen mixtures, two thermal loading conditions for each mixture, and four initial saturation levels for each thermal loading), the database of finite element models al so consisted of 104 heat and mass transport

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192 solutions, one for each numerical simulation. Given the size of the database, the finite element models were solved only at a single simulation time of 1200 seconds into thermal loading. From the database, a number of comparisons and data analyses were made based on similar variables presented in Chapter 4 (intrinsic gas permeability, water permeability, porosity, and compressive strength ). Particularly, results are presented in the form of principal stresses as a percentage of strength: First principal stress versus tensile strength Second/third principal stress ve rsus compressive strength. From these stress-percentages, the influence of pore pressu re and temperature on stress was quantified for the mixtures presented in Chapter 2 using the E119 and E1529 thermal loading. 5.4 Modeling Results Output data from the finite element pr ogram was calculated at one time (1200 sec) during thermal heating. The principal st resses at each location were divided by the strength (tensile strength fo r first principal stress and co mpressive strength for second principal stress), which was reduced based on the temperature at that location. Figure 5-9 shows how the stress-percenta ges varied across the depth for the granite concrete mixtures with E119 thermal loading. The va lue at the peak of the stress-percentage distribution was then calculat ed and used for the comparisons in the following sections.

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193 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Stress percentage (%)Distance from the heated surface (mm) Distance from the heated surface (in.) Mixture type C20 C25 C30 C35 C40 C45 Figure 5-9. First principal st ress as a percentage of tensile strength versus distance from the heated surface for E119 thermal loadi ng with an initial saturation level of 90% 5.4.1 Effects of Permeability Permeability has been commonly thought to be the main factor affecting pore pressure development (higher permeability re sulting in lower pore pressure). It was shown in Chapter 4 however that this was not always true after analyzing the numerical modeling results of the granite-aggregate co ncrete mixtures. Because first principal stress is directly proportional to pore pressure, the resulti ng trends with intrinsic gas permeability are also mixture-type dependent. Figure 5-10 shows the first principal stress as a percentage of tensile strength versus intrinsic gas permeability for the mixtures of this study.

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194 0 5 10 15 20 25 30 10 100 1000 10000 100000 Stress as a percentage of strength (%)Intrinsic gas permeability, Kg (x10-20 m2) Mixture type Mortar Concrete (granite) Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 5-10. First principal stress as a percen tage of tensile strengt h versus intrinsic gas permeability for E1529 thermal loading with an initial saturation level of 90% The stress-percentage was approximately c onstantfor each of the mortar mixtures (approximately 15%) and the limerock-aggregate concrete mixtures (approximately 4%), whereas the granite-aggregate concrete mixtur es showed a variation with intrinsic gas permeability (4 to 22%). This increase in stre ss-percentage is due to the trend of higher pore pressures produced by the numerical model, higher porosity (and thus higher effective-stress factor), and lower strength of the mixtures with higher permeability (e.g., C45 versus C20). The stress-percentages of a ll the mixtures indicate s that pore pressure is a significant contributor to the tensile stress of mortar mixtures and potentially for granite aggregate concrete mixtures depe nding on water-binder ra tio, but not for the limerock-aggregate mixtures of this study unde r the thermal loading conditions studied.

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195 5.4.2 Effects of Porosity Porosity is an extremely important paramete r for mapping pore pressure into stress. Figure 5-11 shows the first principa l stresses as a percentage of tensile stress for all of the mixtures subjected to the E1529 thermal loading curve. 0 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 18 20 Stress as a percentage of strength (%)Porosity (%) Mixture type Mortar Concrete (granite) Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 5-11. First principal stress as a percen tage of tensile strength versus porosity for E1529 thermal loading with an in itial saturation level of 90% The plotted data shows that the stress-p ercentage was not solely a function of porosity for the mixtures. Mixtures with th e same porosity but di fferent aggregate did not produce the same stress percentage. Mixt ures with approximately the same water binder ratio (0.30 and 0.35 for comparison betw een the three mixture types) and different aggregate produced different stress-percentage s. This indicates that the water-binder

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196 ratio is also not the sole i ndicator of potential stress deve lopment (due to pore pressure) in concrete materials during fires (Ali 2002). 5.4.3 Effects of Thermal Loading Second principal stresses are more depende nt on temperature than pore pressure. Due to the boundary conditions of limiting thermal of the concrete at high temperature, compressive stresses are developed. Under severe thermal loading, these stresses may contribute to the failure of the material. This was especially true at locations near the heated surface where computed compressive stresses may be above the compressive strength. Figure 5-12 shows the second principal stresses as a percentage of compressive strength versus porosity. The trend for all of the mixtures was a slightly increasing stress percentage with water binder-ratio. This was predominately because the temperature profiles were essentially the same for all of the mixtures while the strengths decreased with increasing porosity, thus produc ing a higher percentage of stress. The second principal stresses were cons iderably higher for the E1529 than the E119 thermal loading because of the higher temperatures across the depth and thus greater thermal expansion. Figure 5-13 s hows the temperature di stribution comparison for the E119 and E1529 thermal loading of the granite aggregate concrete mixtures. The stress-percentage was further magnified by the reduced strength with higher temperatures (70% reduction of compressive strength at 800 C (1472 F)).

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197 0 50 100 150 200 250 300 350 0 2 4 6 8 10 12 14 16 18 20 Stress as a percentage of strength (%)Porosity (%) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) C20 C25 C30 C35 C40 C45 M20 M25 M30 M35 L30 L35 L40Figure 5-12. Second principal stress as a pe rcentage of compressive strength versus porosity for E1529 and E119 thermal loadi ngs with an initial saturation level of 90% The compressive stresses are extraordinarily high for two reasons. First, the boundary conditions allowed no lateral expansion, which caused high stresses during thermal expansion. Second, these percentage s were the maximum values extracted from all locations within the models Temperatures in the elements near the heated surface were much higher in comparison to deep er locations which would cause higher compressive stresses in this region. Fi gure 5-14 shows the distribution of stresspercentage (second principal stresses versus compressive strength) across the depth for the granite-aggregate concrete mixtures. No tice how the stresses are similar for all the concrete mixtures for within each ASTM heating rate. Also note that the stresses are

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198 much higher for the ASTM E1529 curves due th e more intense heating rates which thus causes higher temperatures and greater expansion. 0 200 400 600 800 1000 0 10 20 30 40 50 60 70 80 0 200 400 600 800 1000 1200 1400 1600 1800 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Temperature (C) Temperature (F)Distance from the heated surface (mm) Distance from the heated surface (in.) E1529 thermal loading E119 thermal loading Figure 5-13. Temperature versus depth for E1529 and E119 thermal loadings of the granite-aggregate concrete mixtures with an initial saturation level of 90% 5.4.4 Effects of Init ial Saturation Level The initial saturation level greatly affect ed the pore pressure produced in the numerical modeling program. This resulted in lower stresses when mapping those results into the finite element models. Figure 5-15 shows a comparison between the stresspercentages for initial saturation levels of 25 and 90%. At 25% saturation, the stresspercentages for all of the mixtures did not exceed 7%, indicating that the induced stress due to pore pressure development is not a significant contributor to spalling at low saturation levels (for these mixtures and thermal loadings).

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199 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Stress percentage (%)Distance from the heated surface (mm) Distance from the heated surface (in.) E119 thermal loading E1529 thermal loading Figure 5-14. Second principal stress as a pe rcentage of compressive strength versus depth for E1529 and E119 thermal loadings of the granite-ag gregate concrete mixtures with an initial saturation level of 90% Another valuable observation made when comparing the second principal stresses at different saturation levels was that the second princi pal stress-percentages were typically 5 to 10 % higher for mixtures with lower initial saturation levels (See Figure 516). This was mainly due to the higher numerically predicted temperatures that occurred in models with lower saturation levels. Hi gher temperatures caused greater expansion of the concrete and resulted in smaller compre ssive strengths. Because this was observed for all of the mixtures in th e study, it can be concluded that high saturation levels caused larger first principal stresses, but smaller s econd principal stresses (f or this simple onedimensional model and associated boundary conditions).

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200 0 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 18 20 Stress as a percentage of strength (%)Porosity (%) Saturation level, Mixture type 90%, Mortar 90%, Concrete (granite) 90%, Concrete (limerock) 25%, Mortar 25%, Concrete (granite) 25%, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure 5-15. First principal stress as a percen tage of tensile strength versus porosity for E119 thermal loading with initial saturation levels of 25 and 90% 5.5 Discussion By mapping pore pressure and temperature da ta from numerical heat and mass flow models into finite element models for the co ncrete and mortar mixt ures in this study, it was shown that trends of stress percentage with gas permeability, water permeability, porosity, and strength depended on the mixture type. Each of these material properties played a role in the development of stresses and a culmination of these variables should be considered when evaluating the susceptibil ity of a concrete mixture to spalling.

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201 150 160 170 180 190 200 210 220 230 240 250 0 2 4 6 8 10 12 14 16 18 20 Stress as a percentage of strength (%)Porosity (%) Saturation level, Mixture type 90%, Mortar 90%, Concrete (granite) 90%, Concrete (limerock) 25%, Mortar 25%, Concrete (granite) 25%, Concrete (limerock) M20 M30 M35 M40 C20 C25 C30 C35 C40 C45 L30 L40 L35 Figure 5-16. Second principal stress as a pe rcentage of compressive strength versus porosity for E119 thermal loading with in itial saturation levels of 25 and 90% It has been commonly thought that the suscep tibility for spalling of concrete during fires was directly related to st rength. Moreover, this is due to the notion that permeability rapidly decreases with strength and thus pr ovides a greater restri ction to moisture movement. However, a decrease in porosity which also accompanies an increase in concrete strength affects both the potential for higher initial amount of water within the pore structure and the stress factor (for conve rsion of pore pressure to stress). From numerical modeling results, it was shown that the increasing permeability from the higher to lower strength granite aggregate concrete mixtures did not outweigh the increasing porosity. The resulting pore pressures were higher for the lower-strength graniteaggregate concrete mixtures. In addition to hi gher pore pressure in lower strength granite

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202 aggregate concrete, the stresses were magnified even further due to the higher effective stress factors (see Table 5-4). Therefore, for these mixtures, the pore pressures and corresponding applied stresses (w hich resulted in higher prin cipal stresses) were larger for the lower strength materials. In addition, the stress-percentages (f irst principal versus tensile strength) for the mixtures with even higher for the granite aggregate concrete mixtures with lower water-binder ratios becau se the tensile strength was also decreasing. Table 5-4. Effective stress fact ors for mixtures in this study Mixture type Mixture I.D. Porosity (%), Factor on pore pressure to find effective stress, 1 M20 11.2 0.126 M25 11.9 0.135 M30 13.0 0.149 Mortar M35 15.0 0.176 C20 7.9 0.085 C25 10.1 0.113 C30 13.0 0.150 C35 14.8 0.174 C40 16.0 0.190 Concrete with granite aggregate C45 19.3 0.239 L30 13.7 0.159 L35 15.0 0.176 Concrete with limerock aggregate L40 16.5 0.198 Although the numerically predicted pore pres sures were larger for both the mortar and limerock-aggregate mixtures with lower water-binder ratios (higher strength), the resulting stress-percentages (f irst principal versus tensil e strength) were about equal within each mixture type. After multiplying the pore pressure output from the numerical models by the effective stress factors (which increased with porosity and thus decreased with strength) and dividing the resulting first principal stresses by the tensile strength the result stress-percentages were indepe ndent of the water-binder ratio.

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203 All of the mixtures had smaller second principal stresses-percentages as the strength increased. This is a result of the temperature profiles be ing approximately equal while the concrete strength and modulus increased as the water-binder ratio decreased. Due to the tendency of all the mixtures to expa nd at the same rate (i.e., same coefficient of thermal expansion) and strength differe nces between mixtures, the higher strength concrete and mortar mixtures had a tendency to have lower stress-pe rcentages. Another way to evaluate such tendencies is to di vide the compressive st rength by the elastic modulus to obtain the strain at which compressi ve failure occurs (see Table 5-1) and then compare that to the thermal strains. Since al l of the mixtures had an equal coefficient of expansion, the resulting poten tial for element expansion (or the amount of potential strain) is approximately equal for a particular thermal load ing condition. Therefore, it can be concluded that material failure in compression (for boundary conditions used in this analysis) is more likely in the lower strength materials.

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204 CHAPTER 6 FINDINGS AND CONCLUSIONS Quantification of pore pressure developmen t within concrete materials during fire conditions is a challenging but important step in improving our understanding of the behavior of concrete stru ctural systems under extreme thermal conditions. The experimental and numerical programs pres ented in the previous chapters have demonstrated methods by which such qua ntification may be addressed. 6.1 Importance of Quality Control Quality control of the experimental methods and materials was a key goal for the program presented. Because parameters such as permeability and pore pressure are highly sensitive to the specific measurement methods used, efforts were made throughout the experimental program to ensure accuracy. 6.2 Quantification of Permeability 6.2.1 Findings This dissertation has presented equipm ent and test methods developed and fabricated to quantify gas and water permeability of cementitious materials. Particularly, a new gas permeameter was presented that is able to quantify slip-flow and intrinsic permeability for both concrete and mortar mixt ures with a high-degree of accuracy. As expected, measured intrinsic gas permeabilities increased with water-binder ratio due to the increased size of the capillary structure within the mixtures. In each individual mixture type, intrinsic gas pe rmeability was very sensitive to the water-binder ratio.

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205 Small variations in water-binder ratio (on the order of 0.05 to 0.1) resulted in order of magnitude differences in intrinsic gas permeability. The theory of molecular slippage dur ing gas flow through porous media was verified in all of the mixtures through the experimental gas permeability testing program. Each specimen tested demonstrated a strong re lationship between mean test pressure and measured gas permeability. It was previously theorized that the s lip-flow factor should increase with decreasing intrinsic gas pe rmeability. Although this relationship was found to be true for the mortar mixtures, it was not found to be true for the concrete mixtures. The exact opposite relationship was found fo r the concrete mixtures with granite aggregate. Water permeability was also measured fo r each of the mixtures and it was found that the values were not si gnificantly different between mi xture types. All of the mixtures had water permeability values of the same magnitude (10-21 m2) regardless of aggregate type or water-binder ratio whereas the intrinsic gas permeability had four orders of magnitude difference (10-20 to 10-16 m2) between the least and most permeable mixtures. Therefore, when approaching a pplications of water and gas flow through cement-based materials such as concrete, independent measurement of permeability should be made with both water and gas as the permeant. 6.2.2 Recommendations As significant differences in water versus gas permeability of the cementitious materials were observed in this study, (due to physical and chemical reactions), it is important to measure both parameters in futu re pursuance of this topic. Based on the consistent experimental proof that slip-flow occurred in all of the concrete and mortar mixtures, it is also recommended to measure gas permeability at multiple pressures in

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206 order to quantify the effects of slip-flow. Ga s slippage could have a significant effect on gas (air, steam) flow through concrete during fire conditions and numerical models that include such behavior are more accurate. Because the gas permeameter described here was not capable of measuring flow at higher than room temperatures, an estimation of the increase of intrinsic gas permeability with temperature was made for all of the mixt ures (Gawin et al. 1999) and used in later numerical modeling. This enhancement to the numerical code was beneficial for predicting heat and mass flow within concrete at high temperatures, but additional studies need to take place in the future to quantify the increase of permeability with temperature. 6.3 Experimental Thermal Testing 6.3.1 Findings Experimental measurement of internal pressure in cementitious materials exposed to fire has demonstrated that inclusion of the effects of ma ss flow within concrete is essential for a rational evalua tion of material behavior. Information regarding methods and equipment for application of thermal loading (similar to fire conditions) of concrete specimens has been presented together w ith techniques for measuring of internal pressure, temperature, a nd detecting spalling. A furnace was designed and constructed th at could provide heating conditions similar to those specified in ASTM E119 and ASTM E1529. Atop the furnace, an apparatus for suspension of a concrete speci men was designed in a manner that allowed free expansion without introduction of mech anical boundary conditi ons. Allowing free expansion ensured the elimination of stresses that would result if the specimens were confined radially. As such, a test condition was established in which material spalling would result directly from pore pressure and thermal gradient stresses.

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207 A new method of instrument installation was explored and incorporated into the thermal testing of both concrete and mortar mixtures. Pore pressure was quantified in mortar and concrete specimens during hea ting conditions simila r to fires by using embedded pressure transducers. Spalling wa s detected with embedded fine-gage wire that broke during material failure. By measuring electric current in the wire during testing the time and location of spalling was quantified. Five different mixtures we re experimentally tested: two mortar, two graniteaggregate concrete, and one limerock-aggreg ate concrete mixtures. Strategically, choosing these five mixtures for thermal testing allowed for good comparisons of the effect of material properties on spalling behavior and pore pre ssure development. From the thermal testing program, a number of observations were made. First, the mixtures without coarse aggr egate did not exhibit signifi cant explosive spalling during thermal testing, compared to the almost immediate spalling observed in the mortar mixtures. Two differences in the mixtures may have caused this dissimilarity in behavior: Due to the existence of coarse aggregate, tensile strength of the concrete mixtures was greater than that of the mortar mixtur es and therefore capable of resisting stress caused by pore pressure. Measured intrinsic gas permeability was much higher for concrete mixtures than mortar mixtures, which resulted in a hi gher rate of steam migration through the heated surface. The mortar specimens demonstrated much high pore pressure development during experimentation than did the concrete specime ns. This was especially apparent in the M35 mortar mixture where the pore pressure was measured to be almost 31 atm (450 psia) at 10 mm (0.394 in.) from the heated su rface (prior to suspected spalling). Pore

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208 pressure in the M25 specimens would have sim ilarly continued to rise to such levels if spalling had not occurred near the pressure transducers. The C45 concrete specimen exhibited higher pore pressure than those measured in the C25 specimen. This is due to the higher porosity of the C45 mixture (19.3 %) in comparison to the C25 mixture (10.2 %). W ith a higher porosity and equal saturation level (90%), the C45 mixtures had nearly twice the initial water within the pore system than did the C25 mixtures. Although the intr insic permeabilities (both gas and water) of the C45 were much larger than in C25, they were not large enough to offset the effects of the increase of the porosity. Qualitative thermal testing of the specimens in the electric kiln demonstrated that saturated concrete is more likely to spall than unsaturated concrete. In the case of high strength mortar mixtures (e.g., M20-M35) explosive spalling is probable, based upon the complete destruction of the M20 and M25 satu rated specimens, in less than 15 minutes of thermal loading. This type of destruc tion was also observed in the one-dimensional thermal testing of M25 and M35 specimens. For all mixtures, de-saturated specimens did not exhibit spalling. However, these were specimens that were not subjected to any mechanical stress during thermal loading and the structural integrity of the specimens was most certainly compromised based on pos t thermal testing compressive strengths. The objective of this testing program was to quantify pore pressure buildup heated concrete and mortar specimens. Additionally, thermal gradient stresses caused by the sudden application of high temperature appli cation were not sufficient to cause spalling in any of the tests of th e desaturated specimens.

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209 6.3.2 Recommendations A framework for future thermal testing was established through development of experimental methods for quant ifying pore pressure. Future studies will need to increase the scope of the test materials to include a broa der set of concrete mixtures. In particular, the focus should be on concrete materials th at are typically used in structures and admixture modifications to those material s that limit the amount of pore pressure development. For example, the effect of polypropylene fibers on pore pressure development in concrete should be explored. Concerning the experimental study presen ted, a key observation that became apparent during testing was the need fo r more redundancy in the measurement of pressure, temperature, and spal ling. In future testing, c onsideration should be given to providing multiple measurements of internal variables for added confidence. The reason for providing this recommendation was the observation of nonuniform surface spalling during the thermal testing of mortar. Sloughing of material during these test s occurred at considerably different depths across the face of the specimens. 6.4 Numerical Modeling 6.4.1 Findings A numerical program has been introduced for the prediction of pore pressure, temperature, and saturation level in concrete exposed to fire. Models were created to mimic the specimens and boundary conditions th at were present during the experimental thermal testing of the materials. Input parameters such as intrinsic gas and water permeability, and porosity were measured for each of the mixtures in the experimental testing program and were then us ed in the numerical models.

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210 Modifications were made to the numerical code for adaptation to simulating concrete materials and corresponding changes in permeability with temperature. Previously, this was absent from the nume rical code and is im portant for the proper modeling of concrete materials. Permeability increases with temperature and thus causes a greater alleviation of pore pressure due to an increased ability for pore constituent transport. Although the relationship that was added into the code was based on previous research (Gawin et al. 1999), it can be easil y changed for adaptation to materials where the change in permeability with temperatur e has been experimentally established. Numerical solutions of the concrete and mortar mixtures —for which permeability and porosity were measured— exposed to time -temperature curves from the ASTM E119 and E1529 specifications provided interesting trends of behavior. It has been traditionally assumed that pore pressures are higher in concrete with higher strength. Through numerical modeling, it was found that this assumption is not always accurate. For the granite aggregate concrete simulati ons, it was found that numerically predicted pore pressures were higher for mixtures with higher water-binder ratios (and thus lower strength). The cause of this trend, which is opposite of conventiona l thought, is the result of large differences in porosity between the mixtures. Although the permeability was higher for the mixtures with lower strength, the porosity was much higher and thus there was a higher initial volume of water within the pore structure. Other mixtures studied (mortar and limerock concrete), however, did exhibit the expected trends. Numerical solutions of these models showed that pore pressures were higher for the higher strength materials within each mixture set. The rami fications of these different trends for each

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211 mixture show that strength is not necessarily a determinant of pore pressure development and thus spalling suscepti bility of concrete. By performing simulations at different initial saturation levels, it was found that mixtures with higher initial amounts of liqui d water are far more susceptible to pore pressure development and spalling. Theref ore, numerical modeling of heat and mass flow should be utilized when evaluating the fire susceptibility of concrete under high humidity or nearly saturated conditions (e .g., offshore drilling platforms). Neglecting pore pressure development in such cases provi des an incomplete projection of material performance. 6.4.2 Recommendations Numerical models presented here were capab le of predicting pressures that were similar to those measured during the experi mental program. When comparing numerical model data with experimental data, it is r ecommended that twoor threedimensional models be used with precise descriptions of the physical conditions under which pressure was measured (e.g., the inclusion of an air vo id at point of measurement in the present study). Simple (one-dimensional) models may not be capable of pr oviding data that is indicative of the conditions measured. After us ing twoor threedi mensional models to compare with experimentally measured data, a one-dimensional model can then be used (with the same material and thermal loading characteristics) to obtain predictions of system response in the abse nce of instrumentation. In this study, non temperature-dependent material parameters were used for quantities such as thermal conductivity, speci fic heat, and porosity due to practical limitations of the scope. Preliminary enhancem ents were made to the simulation code to address permeability changes with temperature, and a similar approach should be taken

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212 with these variables. In addition, the pr ocess of cement skeleton dehydration at high temperature and the effects on porosity and wate r content should be considered in future code development. 6.5 Stress Analysis 6.5.1 Findings A finite element analysis method was e xplored to quantify the tensile-stress induced by the pore pressure, thermal gradient s, and thermal restraint. Mapping methods were developed to link the numerical heat a nd mass transport solution and finite element model for quantifying stress. The results indica ted that the tensile stresses caused by pore pressure were significant enough to cont ribute to material failure. The failure susceptibility of granite-a ggregate concrete mixtures was further brought to light when performing stress analyses It was found that pore pressures were higher for the lower strength mixtures (in the granite aggregate conc rete). The porosity was larger for the lower strength materi als, causing a greater magnification of pore pressure when converting to e ffective stress. Finally, because the strength was lower for the mixtures with higher eff ective stress (due to pore pressure), the tensile stress predicted by the finite element model yielded a stress relative to the material strength. The opposite trend was found for the mortar a nd limerock-aggregate concrete mixtures. 6.5.2 Recommendations Estimations were made during the finite element modeling program that should be addressed in future research programs. The ma terial models used were very simplified. Use of a thermal-elastic material model provided only an estimation of stress. The material softening of the concrete at elevat ed temperatures was estimated from previous research and should be refined in the future. Ultimate strengths of th e materials were also

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213 neglected in the models. Elastic representation of the materials allowed stresses to increase indefinitely and thus did not include a limit based on strength. A more reliable material model would include the full stre ss-strain behavior in both tension and compression at multiple temperatures. This will require an extensive amount of experimental material testing, but will be helpful when quantifying stresses and making comparisons of mixtures. Based on the combination of results from the numerical and experimental program Table 6-1 was constructed to show how each measured parameter within this study affects the susceptibility of concrete to failure under fire loading. From what is presented, it is apparent that there is no singular variable that can be used as the primary Table 6-1. Parameters affecting pore pres sure and material failure of concrete Parameter Effect on Heat and Ma ss Effect on Stress Solution Porosity Higher porosity results in a greater volume of water that needs to be transported through the capillary systems and thus a tendency for higher pore pressures (all else equal) Higher porosity results in an increase in the factor used to convert pore pressure into effective stress. Water Permeability Higher water permeability will increase the movement of liquid water through the system (away from the heated surface) and thus result in a lower pore pressure. Higher water permeability decreases the pore pressure resulting in lower tensile stresses, but may increase the compressive stresses (for the finite element model used) due to the change in thermal properties that accompanies the different profile of saturation across the material. Gas Permeability Higher intrinsic permeability will result in lower pore pressures due to the ability of steam to move more easily out of the heated surface, thus alleviating the pore pressure at the saturated front. Lower tensile stresses (due to lower pore pressure) and possibly higher compressive stress (due to a change in the saturation profile) accompany higher gas permeability. Strength None Higher strength results in a greater resistance to tensile and compressive stresses.

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214 determinant of material failure due to por e pressure developmen t during fires. For instance, higher permeability usually accompanie s an increase in porosity, but may not be high enough not overcome the effects of additi onal initial pore wa ter and conversion to effective stress. 6.4 Concluding Remarks The coupled experimental and numerical program presented in this dissertation provides a framework for future research ende avors of the same topic. The key points from this research program were: Extensive steps were taken to use consiste nt test methods and high quality mixtures to provide valuable and worthwhile data for others to reference. Intrinsic gas permeability and slip-flow beha vior were quantified for each concrete and mortar mixture. Results showed a large difference in intrinsic gas permeability between mixtures, and thus the effect on the numerical simulations and spalling tendency was significant. Instrumentation methods were presented to measure internal pore pressure, temperature, and material failure (spalling) in concrete during fires. The existence of pore pressure buildup wa s verified through experimental testing and the sensitivity of numerical predictions on permeability and porosity were presented. Concrete mixtures tended not to spall under fi re loading, while mortar mixtures did. Including large aggregate reduced the susceptibility to spalling. A framework was provided for simulating h eat and mass flow as well as analyzing stress in concrete materials exposed to fire.

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215 APPENDIX A GAS PERMEABILITY DATA FOR ALL MIXTURES This appendix contains results of the experimental gas permeability testing for all of mixtures mentioned in Chapter 2. E ach graph shows results from each of the specimens tested within that particular mixt ure. Data for each specimen consists of an apparent gas permeability value with a corresponding reciprocal mean pressure. Figures A-1 through A-4 show the results for the mortar mixtures (M20-M35). Figures A-5 through A-10 show the results for the concrete mixt ures with granite aggregate (C20-C45). Figures A-11 through A-13 show the results for the concrete mixtures with limerock aggregate (L30-L40). Note that the scale on the y-axis may be different for each graph.

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216 0 1 2 3 4 5 0.00 0.05 0.10 0.15 0.20 0 10 20 30 40 50 Gas permeability, Kg (x10-19 m2) Gas permeability, Kg (x10-19 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-1. M20 Mixture

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217 0 1 2 3 4 5 0.00 0.05 0.10 0.15 0.20 0 10 20 30 40 50 Gas permeability, Kg (x10-19 m2) Gas permeability, Kg (x10-19 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Specimen #5 Figure A-2. M25 Mixture

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218 0 2 4 6 8 10 0.00 0.05 0.10 0.15 0.20 0 20 40 60 80 100 Gas permeability, Kg (x10-19 m2) Gas permeability, Kg (x10-19 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-3. M30 Mixture

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219 0 4 8 12 16 20 0.00 0.05 0.10 0.15 0.20 0 40 80 120 160 200 Gas permeability, Kg (x10-19 m2) Gas permeability, Kg (x10-19 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-4. M35 Mixture

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220 0 1 2 3 4 5 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 10 20 30 40 50 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-5. C20 Mixture

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221 0 4 8 12 16 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 40 80 120 160 200 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-6. C25 Mixture

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222 0 4 8 12 16 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 40 80 120 160 200 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-7. C30 Mixture

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223 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 100 200 300 400 500 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-8. C35 Mixture

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224 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 100 200 300 400 500 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-9. C40 Mixture

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225 0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 200 400 600 800 1000 Gas permeability, Kg (x10-18 m2) Gas permeability, Kg (x10-18 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-10. C45 Mixture

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226 0 1 2 3 4 5 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 10 20 30 40 50 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-11. L30 Mixture

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227 0 4 8 12 16 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 40 80 120 160 200 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Figure A-12. L35 Mixture

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228 0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 200 400 600 800 1000 Gas permeability, Kg (x10-17 m2) Gas permeability, Kg (x10-17 ft2)Reciprocal of mean pressure (1/atm) Specimen #1 Specimen #2 Specimen #3 Specimen #4 Figure A-13. L40 Mixture

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229 APPENDIX B CALIBRATION GRIDS FOR PRESSURE TRANSDUCERS This appendix contains the calibration gr ids for the pressure transducers used during the thermal testing portion of this study. Each table caption gives the transducer serial number, test specimen within which it was installed, and the embedment location from the heated surface.

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230 Table B-1. Serial number 6579-9-231, M251 specimen, 10 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) -1.07 -2.20 -2.56 -2.78 -2.86 8.5 atm (125 psia) 20.54 19.79 19.42 19.04 18.68 17.0 atm (250 psia) 42.21 41.79 41.43 40.88 40.22 25.5 atm (375 psia) 63.67 63.78 63.42 62.71 61.75 34.0 atm (500 psia) 85.39 85.71 85.35 84.50 83.24 Table B-2. Serial number 6579-9-238, M251 specimen, 15 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) -0.47 -0.96 -1.13 -1.16 -1.25 8.5 atm (125 psia) 21.07 20.90 20.76 20.57 20.23 17.0 atm (250 psia) 42.64 42.79 42.67 42.32 41.74 25.5 atm (375 psia) 64.18 64.66 64.55 64.06 63.23 34.0 atm (500 psia) 85.66 86.48 86.39 85.76 84.67

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231 Table B-3. Serial number 6579-9-233, M252 specimen, 15 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) -0.80 -1.68 -2.30 -2.81 -3.53 8.5 atm (125 psia) 20.55 20.08 19.53 18.95 18.02 17.0 atm (250 psia) 41.89 41.87 41.41 40.75 39.57 25.5 atm (375 psia) 63.21 63.64 63.28 62.53 61.12 34.0 atm (500 psia) 84.46 85.36 85.11 84.29 82.64 Table B-4. Serial number 6757-7-338, M35 specimen, 10 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.38 0.22 -0.36 -0.94 -1.52 -1.74 17.0 atm (250 psia) 50.79 50.75 50.46 49.80 48.90 48.05 34.0 atm (500 psia) 101.11 101.24 101.28 100.56 99.27 97.79 Table B-5. Serial number 6757-7-339, M35 specimen, 16 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.09 0.14 0.38 0.81 1.35 2.04 17.0 atm (250 psia) 50.45 50.66 51.24 51.56 51.65 51.58 34.0 atm (500 psia) 100.78 101.15 102.08 102.29 101.89 101.09

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232 Table B-6. Serial number 6757-7-341, C25 specimen, 10 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.18 0.00 -0.66 -1.27 -1.86 -2.40 17.0 atm (250 psia) 50.22 50.20 49.92 49.23 48.22 46.94 34.0 atm (500 psia) 100.30 100.49 100.58 99.84 98.41 96.40 Table B-7. Serial number 6757-7-173, C25 specimen, 15 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.61 0.76 1.38 2.04 2.78 3.87 17.0 atm (250 psia) 50.58 50.86 51.79 52.36 52.69 53.09 34.0 atm (500 psia) 100.62 101.08 102.30 102.83 102.76 102.45 Table B-8. Serial number 6757-7-179, C45 specimen, 10 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 3.27 3.04 2.22 1.39 0.58 0.04 17.0 atm (250 psia) 53.29 53.21 52.68 51.74 50.55 49.31 34.0 atm (500 psia) 103.45 103.55 103.32 102.30 100.70 98.73

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233 Table B-9. Serial number 6757-7-176, C45 specimen, 15 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.18 0.25 0.62 1.07 1.49 2.19 17.0 atm (250 psia) 50.52 50.74 51.45 51.82 51.79 51.72 34.0 atm (500 psia) 100.92 101.35 102.40 102.71 102.23 101.40 Table B-10. Serial number 6757-7-174, L35 specimen, 10 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) -0.42 -0.32 0.15 0.67 1.24 2.17 17.0 atm (250 psia) 56.25 56.72 58.25 59.39 60.18 60.99 34.0 atm (500 psia) 112.97 113.83 116.46 118.22 119.24 119.95 Table B-11. Serial number 6757-7-180, L35 specimen, 15 mm from heated surface; grid terms are in millivolts Temp. Pressure 23.9 C (75 F) 37.8 C (100 F) 93.3 C (200 F) 148.9 C (300 F) 204.4 C (400 F) 260.0 C (500 F) 0.0 atm (0.0 psia) 0.21 0.33 0.92 1.57 2.35 3.58 17.0 atm (250 psia) 50.25 50.55 51.54 52.15 52.58 53.07 34.0 atm (500 psia) 100.32 100.84 102.22 102.84 102.89 102.64

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234 APPENDIX C CALCULATION METHOD FOR DETERMI NING INITIAL SATURATION LEVEL OF THERMALLY TESTED MIXTURES Two M25 specimens were used to calcul ate the initial saturation level of the mixtures for input into the numerical mode ls. The specimens were conditioned in the same manner as the thermal specimens (subm erged in water for curing and in ambient conditions for four days). The masses was th en recorded and the sp ecimens placed in an oven at 105 C (220 F). After the weight of the oven-dried specimens reached equilibrium, their masses were measured. By then using the porosity which was previously calculated on the same mixture and the estimated mass density, the saturation level was calculated (as shown in the table in this Appendix). In the table, specimen #1 was cast when the thermal specimen for Test #1 of the M25 mixture was cast and specimen #2 was cast when the thermal specimen for Test #2 of the M25 mixture was cast. The saturation level was then rounded to 90% and used as the in itial level for all of the numerical models of thermal sample mixtures.

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235 Table C. Calculation of saturation level for M25 thermal specimens Parameter Specimen #1 Specimen #2 Porosity of M25 mixture, 11.9 % Water density, wat 1000 kg/m3 (62.4 lb/ft3) Dry density (estimated), dry 2197 kg/m3 (137 lb/ft3) Dry mass of specimen, mdry 1628.5 g (3.591 lb) 1518.9 g (3.349 lb) Ambient mass of specimen, mamb 1706.5 g (3.763 lb) 1590.8 g (3.508 lb) Mass for full saturation, msat = mdry+wat(mdry/dry) 1716.7 g (3.785 lb) 1601.1 g (3.530 lb) mamb-mdry 78.0 g (0.172 lb) 71.9 g (0.159 lb) msat-mdry 88.2 g (0.194 lb) 82.2 g (0.181 lb) Saturation level, (mamb-mdry)/(msat-mdry)100 88.4 % 87.5 %

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236 APPENDIX D FILTERED EXPERIMENTAL THERMAL LOADING CURVES FOR USE IN THE NUMERICAL MODELING PROGRAM The graphs in this appendix represen t the time-temperature curves measured experimentally and filtered for use in th e TOUGH2 simulations. A Gaussian kernel smoothing technique with a bandwidth of th irty seconds was used to filter the temperature data. After filter ing, individual points were ex tracted at ten second intervals and were then used as the prescribed boundary super-element temperatures for the numerical simulations. The time-temperat ure curves for the C25, C45, and L35 specimens were reduced by 10, 20, and 20% based on comparisons between the results from preliminary one-dimensional models a nd experimentally measured data for the internal temperatures at 10 and 15 mm (0. 394 and 0.591 in.) from the heated surface.

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237 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered Figure D-1. Filtering of the experimentally measured air temperature for Test #1 of the M25 specimen

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238 Figure D-2. Filtering of the experimentally measured air temperature for Test #2 of the M25 specimen 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered

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239 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered Figure D-3. Filtering of the experimentally measured air temperature for M35 specimen

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240 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered (and reduced by 10%) Figure D-4. Filtering of the experimental ly measured air temperature for the C25 specimen

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241 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered (and reduced by 20%) Figure D-5. Filtering of the experimental ly measured air temperature for the C45 specimen

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242 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Filtered (and reduced by 20%) Figure D-6. Filtering of the experimental ly measured air temperature for the L35 specimen

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243 0 100 200 300 400 500 600 700 800 900 1000 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 1000 1200 1400 1600 1800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) M25-Test #1 M25-Test #2 M35 C25 C45 L35 Figure D-7. Filtering of the experimentally measured air temperature: all thermal tests

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244 APPENDIX E COMPARISON PLOTS OF EXPERIMENTALLY MEASURED AND NUMERICALLY PREDICTED TEMPERATURES This appendix contains comparison plots of temperature based on the experimental thermal testing program described in Chap ter 3 and the numerical modeling program described in Chapter 4.

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245 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (1d model) Figure E-1. Comparison betw een temperature measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M25 specimen (Test #1)

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246 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (1d model) Figure E-2. Comparison betw een temperature measured experimentally and predicted numerically at 15 mm (0.591 in.) from the heated surface for the thermal testing of the M25 specimen (Test #2)

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247 0 50 100 150 200 250 300 350 400 450 500 0 120 240 360 480 600 720 840 960 1080 1200 0 100 200 300 400 500 600 700 800 900 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (1d model) Figure E-3. Comparison betw een temperature measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the M35 specimen

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248 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (90% thermal loading) Figure E-4. Comparison betw een temperature measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the C25 specimen

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249 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (90% Thermal loading) Figure E-5. Comparison betw een temperature measured experimentally and predicted numerically at 15 mm (0.394 in.) from the heated surface for the thermal testing of the C25 specimen

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250 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (80% thermal loading) Figure E-6. Comparison betw een temperature measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the C45 specimen

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251 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (80% Thermal loading) Figure E-7. Comparison betw een temperature measured experimentally and predicted numerically at 15 mm (0.394 in.) from the heated surface for the thermal testing of the C45 specimen

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252 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (80% thermal loading) Figure E-8. Comparison betw een temperature measured experimentally and predicted numerically at 10 mm (0.394 in.) from the heated surface for the thermal testing of the L35 specimen

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253 0 100 200 300 400 500 0 120 240 360 480 600 720 840 960 1080 1200 0 200 400 600 800 0 2 4 6 8 10 12 14 16 18 20 Temperature (C) Temperature (F)Time (sec.) Time (min.) Experimental Numerical (100% thermal loading) Numerical (80% Thermal loading) Figure E-9. Comparison betw een temperature measured experimentally and predicted numerically at 15 mm (0.394 in.) from the heated surface for the thermal testing of the L35 specimen

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254 APPENDIX F ABSOLUTE MAXIMUM PORE PRESSURE RESULTS FROM THE NUMERICAL MODELING PROGRAM This appendix contains plots of absolu te maximum pore pressure obtained through numerical simulations of the E119 and E1529 th ermal loading on the concrete and mortar materials presented in Chapter 2. The met hods for constructing these plots was presented in Chapter 4. Plots are provided for the E119 and E1529 thermal loading conditions for all of the mixtures at an initial saturation level of 25%.

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255 5 10 15 20 25 30 35 1 10 100 1000 10000 100000 50 100 150 200 250 300 350 400 450 500 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic gas permeability, Kg (x10-20 m2) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure E-10. Variation of absolute ma ximum pore pressure with intrinsic gas permeability (25% initial saturation level)

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256 0 5 10 15 20 25 30 35 0 2 4 6 8 10 12 0 50 100 150 200 250 300 350 400 450 500 Maximum pore pressure (atm) Maximum pore pressure (psia)Intrinsic water permeability, Kw (x10-21 m2) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 L30 L35 L40 Figure E-11. Variation of absolute maxi mum pore pressure with intrinsic water permeability (25% initial saturation level)

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257 0 5 10 15 20 25 30 35 0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 250 300 350 400 450 500 Maximum pore pressure (atm) Maximum pore poressure (psia)Porosity (%) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L35 L40 Figure E-12. Variation of absolute maximu m pore pressure with porosity (25% initial saturation level)

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258 0 5 10 15 20 25 30 35 0 20 40 60 80 100 120 140 160 0 50 100 150 200 250 300 350 400 450 500 0 5 10 15 20 Maximum pore pressure (atm) Maximum pore pressure (psia)Compressive strength, f'c (MPa) Compressive strength, f'c (ksi) Thermal loading, Mixture type E1529, Mortar E1529, Concrete (granite) E1529, Concrete (limerock) E119, Mortar E119, Concrete (granite) E119, Concrete (limerock) M20 M25 M30 M35 C20 C25 C30 C35 C40 C45 L30 L40 L35 Figure E-13. Variation of absolute maximu m pore pressure with compressive strength (25% initial saturation level)

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260 American Society for Testing and Material (ASTM) C 518-02, “Standard Test Method for Steady-State Thermal Transmission Pr operties by Means of the Heat Flow Meter Apparatus,” Annual Book of ASTM Standards, 2002, V 04.06, American Society for Testing and Material s (ASTM), West Conshohocken, Pa. American Society for Testing and Material (ASTM) D 2766-95, “Standard Test Method for Specific Heat of Liquids and Solids, ” Annual Book of ASTM Standards, 1997, V 05.01, American Society for Test ing and Materials (ASTM), West Conshohocken, Pa. American Society for Testing and Material (ASTM) E 119-00a, “Standard Test Methods for Fire Tests of Building Constructi on and Materials,” Annual Book of ASTM Standards, 2000, V 04.07, American Soci ety for Testing and Materials (ASTM), West Conshohocken, Pa. American Society for Testing and Material (ASTM) E 1529-00, “Standard Test Methods for Determining Effects of Large Hydro carbon Pool Fires on St ructural Members and Assemblies,” Annual Book of ASTM Standards, 2000, V 04.07, American Society for Testing and Material s (ASTM), West Conshohocken, Pa. Bamforth, P. B., “The Relationship Between Permeability Coefficients for Concrete Obtained Using Liquid and Gas,” Magazine of Concrete Research, 1987, V. 30, No. 138, pp. 233-241. Bazant, Z. P., “Analysis of Pore Pressure, Thermal Stress and Fracture in Rapidly Heated Concrete,” International Workshop on Fire Performance of High-Strength Concrete, NIST Special Publication 919, 1997, pp. 155-164. Bentley, R., Handbook of Temperature Measurement, Volume 1: Theory and Practice of Thermoelectric Thermometry, Springer-Verlag, Singapore, 1998 (a). Bentley, R., Handbook of Temperature Measurement, Volume 3: Temperature and Humidity Measurement, Springer-Verlag, Singapore, 1998 (b). Cabrera J., and Lynsdale C., “New Gas Pe rmeameter for Measuring the Permeability of Mortar and Concrete,” Mag azine of Concrete Research, 1988, V. 40, No. 144, pp. 171-182. Carman, P. C., Flow of Gases through a Porous Media, Academic Press Inc., New York, NY, 1956. Carrasquillo, R. L., Nilson, A. H., and Slate, F. O., “Properties of High Strength Concrete Subject to Short-Term Loads,” ACI Materi als Journal, 1981, V. 61, No. 2, pp. 195211. Churaev, N. V., Liquid and Vapor Flows in Porous Bodies, Surface Phenomena, Gordon and Breach Science Publishers, Canada, 1990.

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261 Chung, J., “Numerical Simulation of HydroThermo-Mechanical Behavior of Concrete Structures Exposed to Elevated Temperatur es,” Ph.D. Dissertation, University of Florida, Department of Civil and Coastal Engineering, 2003. Collier, J. G., Convective Boiling and Condensation, McGraw-Hill, Inc., New York, NY, 1972. Collins, M., and Mitchell, D., Prestressed Concrete Structures, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1991. Collins, R. E., Flow of Fluids through Porous Materials, Reinhold Publishing Corporation, New York, NY, 1961. Consolazio, G, and Chung J., “Numeric Simu lation of Near-Surface Moisture Migration and Stress Development in Concrete Expos ed to Fire,” Computers and Concrete, 2004, V. 1, No. 1. Consolazio, G. R., McVay, M. C., and Rish, J. W., “Measurement and Prediction of Pore Pressures in Saturated Mortar Subjecte d to Radiant Heating,” ACI Materials Journal, 1998, V. 95, No. 5, pp. 525-536. De Buhan, P., and Dormiuex, L., “A Microm echanics-Based Approach to the Failure of Saturated Porous Media,” Transport in Porous Media, 1999, V. 34, pp. 47-62. Dhir, R., Hewlett, P., and Chen, Y., “Near Su rface Characteristics of Concrete: Intrinsic Permeability,” Magazine of Concrete Research, 1989, V. 41, No. 147, pp. 87-97. Dhir, R., Hewlett, P., Byars, E., and Shaab an, I., “A New Technique for Measuring Air Permeability of Near Surface Concrete,” Ma gazine of Concrete Research, 1995, V. 47, No. 171, pp. 167-176. Gawin, D., Majorana, C. E., and Schrefler, B. A., “Numerical Analys is of Hygro-thermal Behaviour and Damage of Concrete at High Temperature,” Mechanics of Cohesive-Frictionless Materials, 1999, V. 4, pp. 37-74. Gieck, K., and Gieck, R., Engineering Formulas, McGraw-Hill, Inc., New York, NY, 1997. Halliday, D., and Resnick R., Fundamentals of Physics, John Wiley and Sons, Inc., New York, NY, 1988. Hamarthy, T. A., “Effect of Moisture on the Fire Endurance of Building Elements,” ASTM Publication STP 385, 1965, American Society for Testing and Materials (ASTM), West Conshohocken, Pa. Hewlett, P., Lea’s Chemistry of Cement and Concrete, John Wiley & Sons, Inc., New York, NY, 1988.

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265 BIOGRAPHICAL SKETCH The author is originally from the state of New Jersey before moving to the state of Florida in 1999, where he now resides. Before pursuing the degree of Doctor of Philosophy at the University of Florida, the author received Bach elor of Science and Master of Science degrees from Rutgers, The State University of New Jersey, in 1997 and 1999. The bachelor’s degree held a concen tration in structural engineering while the master’s degree had a focus of transportation ma terials engineering. Currently, the author is engaging a career in the structural de sign of buildings at Desimone Consulting Engineers and has designed medical, resi dential, and resort facilities.