Concrete High Temp.

EXPERIMENTAL STUDIES AND THEORETICAL MODELING OF

CONCRETE SUBJECTED TO HIGH TEMPERATURES

by

JAESUNG LEE

B.A., Architectural Engineering, Hannam University, Korea, 1997

M.A., Architectural Engineering, Hanyang University, Korea, 1999

M.A., Civil Engineering, University of Colorado at Boulder, USA, 2002

A thesis submitted to the

Faculty of the Graduate school of the

University of Colorado in partial fulfillment

of the requirement for the degree of

Doctor of Philosophy

Department of Civil, Environmental, and Architectural Engineering

2006

iii

Lee, Jaesung (Ph.D., Civil, Environmental, and Architectural Engineering)

EXPERIMENTAL STUDIES AND THEORETICAL MODELING OF

CONCRETE SUBJECTED TO HIGH TEMPERATURES

Thesis directed by Professor Yunping Xi

Understanding the properties of concrete under high temperature is essential

to enhance the fire resistance of reinforced concrete structures (RCS) and to provide

accurate information for fire design of RCS. Extensive studies on this important topic

were performed previously. However, the properties of concrete under high

temperature have not been fully understood. Even if there are numerous experimental

and theoretical results available in the literature, contradictions among observations

exist and need to be reconciled.

The studies performed in this thesis can be largely classified as four topics.

Among the four topics, two topics are experimental studies and the other two topics

are theoretical models.

The first experimental study is to find the effects of temperature and moisture

on deformation of concrete. Due to the dependency of the moisture on temperature, it

is not easy to distinguish experimentally the effects of temperature and moisture on

the deformation of concrete. Usually, the thermal strain of concrete, which is called

Conventional Thermal Strain (CTS) in this study, is obtained by measuring the

displacement change without moisture control. In this study, CTS, the strain caused

by temperature increase under constant humidity (Pure Thermal Strain: PTS), and the

strain caused by moisture change under constant temperature (Pure Hygro Strain:

iv

PHS) are measured continually over time. From the data analysis based on the

measured strains, the thermo-hygro coupling effect in the temperature is obtained.

Previous experimental studies on concrete under high temperatures have

mainly concentrated on the strength reduction of concrete, even though the loss of

durability of concrete can severely reduce the remaining service life of the structure.

In the second experimental study, the strength, stiffness, and durability performance

of concrete subjected to various heating and cooling scenarios are investigated.

Variations of concrete under high temperatures result mainly from two

mechanisms. One is the variation of material properties of the constituent phases

under high temperatures, and the other is the transformation of constituent phases

under different temperatures. Therefore, the properties of concrete under high

temperatures must be studied from both mechanical and chemical points of view.

The model for the thermal degradation of elastic modulus of concrete is

obtained by composite damage mechanics. At the level of cement paste, the variations

of volume fractions of the constituents are based on phase transformations taking

place under different temperature ranges. At the levels of mortar and concrete, the

degradations of various sand and gravel are based on available test data.

The model for the thermal strain of cement paste and concrete, considering

micro-structural changes under elevated temperatures ranging from 20°C to 800°C, is

proposed. The model is a combination of a multi-scale stoichiometric model and a

multi-scale composite model. The model can consider characteristics of various

aggregates in the calculation of thermal expansion for concrete.

v

DEDICATION

To my lovely wife, my daughter, my son

Myungsub Kim, Jihyun Lee, and Kisuk Lee

my parents

Sangyoung Lee and Inhee Kim

my parents-in-law

Sangyeal Kim and Soonja Bok

my sisters and brothers

Janghyun Baek, Kyungsook Lee, Ohsung Kwon,

Nammi Lee, Bangsub Lee, and Myunghwa Park

vi

ACKNOWLEDGEMENTS

I appreciate the assistance, guidance, and inspiration of many people without

whom this work would not have been possible. Professor Yunping Xi, my thesis

advisor, provided guidance and support for this thesis and for my professional

development. I am very grateful to him. I would also like to thank Professors

Kaspar J. Willam, Ross B. Corotis, Kevin L. Rens, and Mettupalayam V. Sivaselvan

for their helpful comments regarding this dissertation.

I would like to thank my fellow students at the University of Colorado for

their support, encouragement, and friendship. I am thankful to Keunkwang Lee and

Raeyoung Jung for their sincere encouragement and advice through my student life.

I am thankful to Jaemo Jung, Sunyoung Kim and Junsub Kim for their love. I

am very grateful to my parents (Sangyoung Lee and Inhee Kim), parents-in-law

(Sangyeal Kim and Soonja Bok), brothers-in-law (Janghyun Baek and Ohsung Kwon),

sisters (Kyungsook Lee and Nammi Lee), brother (Bangsub Lee), sister-in-law

(Myunghaw Park) for their faith, life-long support, and love.

The support of the National Science Foundation through grants CMS-0409747

is also gratefully acknowledged.

Finally, I would like to extend my deepest thanks to my wife

(Myungsub Kim), my daughter (Jihyun Lee), and my son (Kisuk Lee) for their

patience, encouragement and love.

vii

CONTENTS

CHAPTER

1. INTRODUCTION ......................................................................................... 1

1.1. Background.................................................................................................... 1

1.2. Thesis objectives............................................................................................ 2

1.3. Thesis organization ........................................................................................ 3

2. LITERATURE REVIEW .............................................................................. 5

2.1. Microstructure variations of concrete due to high temperature ..................... 5

2.1.1. Microstructure of hydrated cement paste................................................. 5

2.1.2. Microstructure changes of cement paste due to high temperature......... 10

2.1.3. Porosity and pore size distribution according to temperature................ 13

2.1.4. Heat deformation of cement paste due to high temperature .................. 15

2.1.5. SEM (Scanning Electron Microscopy) observation of concrete............ 22

2.1.6. SEM observation of concrete used in current research.......................... 25

2.2. Pure concrete exposed to high temperature ................................................. 27

2.2.1. Two major problems when concrete is exposed to fire ......................... 27

2.2.2. Selection of concrete mix....................................................................... 28

2.2.3. Testing methods for mechanical properties of concrete ........................ 35

2.2.4. Concrete properties under high temperatures ........................................ 39

viii

2.2.5. The effects of sustained loading during heating .................................... 47

2.2.6. Combined thermal and mechanical loading histories ............................ 49

2.2.7. Decomposition of the total strain due to coupling effects ..................... 51

2.2.8. The effects of steel and polymer fibers at elevated temperatures.......... 54

2.3. Concrete Structures under High Temperatures............................................ 56

2.3.1. Factors affecting fire performance of concrete structures ..................... 58

2.3.2. Fire scenarios ......................................................................................... 60

2.3.3. Experimental studies on concrete beams ............................................... 63

2.3.4. Experimental studies on concrete columns............................................ 72

2.3.5. Experimental studies on concrete slabs ................................................. 79

3. AN EXPERIMENTAL STUDY FOR THERMO-HYGRO COUPLING

EFFECT OF CONCRETE AT ELEVATED TEMPERATURE................................ 87

3.1. Introduction.................................................................................................. 87

3.2. Experimental details..................................................................................... 88

3.2.1. Material and mixture portion ................................................................. 88

3.2.2. Specimen preparation and test equipments............................................ 91

3.2.3. Thermal compensation function and verification for test method ......... 94

3.3. Test results and discussion........................................................................... 97

3.3.1. Conventional Thermal Strain (CTS) and Pure Hygro Strain (PHS) ...... 97

3.3.2. Pure Thermal Strain (PTS)................................................................... 108

3.3.3. Thermo-hygro coupling effect ............................................................. 111

3.4. Conclusions................................................................................................ 114

ix

4. STRENGTH AND DURABILITY OF CONCRETE SUBJECTED TO

VARIOUS HEATING AND COOLING TREATMENTS...................................... 116

4.1. Introduction................................................................................................ 116

4.2. Specimen preparation, heating equipment and test variables .................... 117

4.3. Temperature distribution and thermal diffusivity ...................................... 123

4.3.1. Test set-up............................................................................................ 123

4.3.2. Results and discussion ......................................................................... 124

4.4. Water permeability..................................................................................... 128

4.4.1. Test set-up............................................................................................ 128

4.4.2. Results and discussion ......................................................................... 130

4.5. Ultrasonic Pulse Velocity (UPV) and residual compression test............... 139

4.5.1. Test equipments and test set-up ........................................................... 139

4.5.2. Results and discussion for UPV (Ultrasonic pulse velocity) ............... 140

4.5.3. Results and discussion for residual compression test .......................... 143

4.5.4. Comparison between Ep and Ei........................................................... 150

4.6. Weight loss................................................................................................. 152

4.7. Cracks and color changes of the specimens............................................... 155

4.8. Conclusions................................................................................................ 157

5. A MULTISCALE CHEMO-MECHANICAL MODEL FOR MODULUS

OF ELASTICITY OF CONCRETE UNDER HIGH TEMPERATURES............... 159

5.1. Introduction................................................................................................ 159

5.2. Hydration kinetics model........................................................................... 162

5.3. Initial volume fractions of constituent phases in concrete......................... 166

x

5.3.1. Volume fractions of the constituent phases at the cement paste level. 166

5.3.2. Volume fractions of the phases at the mortar and concrete levels....... 171

5.4. A multi-scale stoichiometric model for phase transformations ................. 172

5.4.1. Phase transformations at the cement paste level.................................. 172

5.4.2. Validation of current model at cement paste level............................... 177

5.4.3. Volume fractions of the phases according to temperature increase at the

mortar and concrete level.................................................................................. 181

5.5. Composite theories and damage theories................................................... 182

5.6. Thermal degradation of the modulus elasticity of concrete....................... 185

5.7. Comparison between present model and experimental results .................. 188

5.8. Conclusions................................................................................................ 192

6. A MULTISCALE CHEMO-MECHANICAL MODEL FOR THERMAL

STRAIN OF CEMENT PASTE AND CONCRETE UNDER HIGH

TEMPERATURES ................................................................................................... 195

6.1. Introduction................................................................................................ 195

6.2. Model for shrinkage of cement paste and concrete ................................... 196

6.3. Material properties of constituents............................................................. 199

6.4. Comparison between model and experimental results............................... 206

6.5. Conclusions................................................................................................ 211

7. SUMMARY AND CONCLUSIONS ........................................................ 213

REFERNCES............................................................................................................ 220

APPENDIX: RELATIVE HUMIDITY IN UNSATURATED SOIL ...................... 237

xi

TABLES

TABLE

Table. 2.1. Porosity and Pore Size Distribution (Piasta et al, 1984b)......................... 13

Table 2.2. Temperature regimes of chemical reactions of hydrate phase of hardened

cement paste according to Schneider and Herbst (1989).................................... 14

Table 2.3. A summary for heat deformation of cement paste..................................... 21

Table 2.4. Factors influencing spalling of concrete (Khoury, 2000) .......................... 30

Table 2.5. Mix design (Dotreppe et al., 1996) ............................................................ 73

Table 3.1. Typical proportions of materials for normal weight concretes.................. 89

Table 4.1 Coefficients of water permeability for R15_D2 test series....................... 135

Table 4.2 Coefficients of water permeability for R2_D4 test series......................... 135

Table 4.3. Ultrasonic pulse velocity test result ......................................................... 141

Table 4.4. Unit weight measured from specimens used in present study ................. 142

Table 4.5. Elastic modulus ( pE ) from ultrasonic pulse velocity.............................. 142

Table 4.6. Ultimate strength results of residual compression test ........................... 147

Table 4.7. Relative ultimate strength ........................................................................ 148

Table 4.8. Initial tangent modulus from residual compression test .......................... 149

Table 4.9. Relative initial tangent modulus .............................................................. 149

Table 4.10. Effect of heating on weight loss (Initial relative humidity 90%) .......... 153

xii

Table 4.11. Effect of heating on weight loss (RH 100%:Fully saturated)................ 153

Table 5.1. Coefficients of ia , ib , and ic .................................................................. 164

Table 5.2. Diffusion constant and coefficients in the diffusion model..................... 165

Table 5.3. Parameters for the determination of the volume fractions....................... 169

Table 5.4. Volume fractions of constituents at cement paste level (w/c=0.5 and 0.67)

........................................................................................................................... 170

Table 5.5. Density of different rock groups (Road research laboratory, 1959) ........ 172

Table 5.6. Volume fractions at mortar and concrete level (w/c=0.67) ..................... 172

Table 5.7. Processes of decomposition depending on the temperature regime ........ 174

Table 5.8. Theoretical formulas for volume fraction change of each phase (w/c=0.67)

........................................................................................................................... 176

Table 5.9. Mass fractions of clinker phases in the cement ....................................... 177

Table. 5.10. Porosity and pore size distribution [w/c=0.4, (Piasta et al, 1984)]....... 178

Table 5.11. Summary for the results shown in Fig. 5.4 and Fig. 5.5........................ 180

Table 5.12. Volume fraction of phases at mortar level (w/c=0.67) .......................... 181

Table 5.13. Volume fraction of phases at concrete level (w/c=0.67) ....................... 181

Table 5.14. Elastic properties of constituent phases ................................................. 188

Table 5.15. Elastic moduli of each phase used in the present model........................ 189

Table 5.16. Elastic moduli from residual compression test ...................................... 191

Table 5.17. Relative elastic modulus ........................................................................ 191

Table 6.1. Summary for thermal strain of phases in cement paste used in model.... 203

Table 6.2. Elastic modulus and Porosity of each phase............................................ 204

Table 6.3. Elastic properties of various aggregates (Jumijis, 1983) ......................... 205

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Table 6.4. Summary for thermal strain of limestone and sandstone......................... 206

Table 6.5. Thermal strain functions of cement paste from model (w/c=0.5)............ 208

xiv

FIGURES

FIGURE

Figure 2.1. SEM image of tobermorite (C-S-H, Type I) .............................................. 7

Figure 2.2. SEM image of portlandite (CH) crystals .................................................... 7

Figure 2.3. SEM images of ettringite crystals............................................................... 8

Figure 2.4. Model of a well-hydrated Portland cement paste ....................................... 9

Figure 2.5. 2( )Ca OH contents observed from TG and X-ray (Piasta et al, 1984 b).. 11

Figure 2.6. SEM images of calcite crystals................................................................. 12

Figure 2.7. Thermograms of unhydrated clinker minerals and Portland cement:

1) 3C S , 2) 2-C Sβ , 3) 3C A , 4) 4C AF , 5) Portland cement ............................... 16

Figure 2.8. Thermograms of hydrated materials: 1) 3 HC S , 2) 2- HC Sβ , 3) 3 HC A ,

4) 4 HC AF , 5) Portland cement paste, 6) 2( )Ca OH , 7) Ettringite ...................... 17

Figure 2.9. 1) 2( )Ca OH , 2) cement gel [300 °C exposure (1000×), Piasta (1984a)] 19

Figure 2.10. Destroyed grains of unhydrated clinker as a result of different thermal

deformations [500 °C exposure (3000×), Piasta (1984a)] .................................. 20

Figure 2.11. Morphologies of hydrates after 400 ºC exposure (Lin et al, 1996) ........ 22

Figure 2.12. Morphologies of hydrates after 500 ºC exposure (Lin et al, 1996) ........ 23

Figure 2.13. Crakes and honey combs after 900 ºC exposure (Lin et al, 1996) ......... 23

Figure 2.14. Sample under water cooling after 900 ºC exposure (Lin et al, 1996) .... 24

xv

Figure 2.15. SEM images of the concrete used in current research............................ 26

Figure 2.16. Physicochemical process in Portland concrete during (Khoury, 2000) 27

Figure 2.17. Material choices for concrete under high temperature (Khoury, 2000) . 28

Figure 2.18. Mechanism of pore pressure spalling (Schneider and Horbst, 2002)..... 32

Figure 2.19. Gradients of temperature, pore pressure and moisture in a massive

concrete section heated at the unsealed left-hand surface (Khoury, 2000)......... 32

Figure 2.20. Forces acting in heated concrete (Zhukov, 1975) .................................. 34

Figure 2.21. Mechanical property test setup (Phan, 2002) ......................................... 34

Figure 2.22. Test set up, Pore pressure specimen, and Specimen failure (Phan, 2002)

............................................................................................................................. 35

Figure 2.23. Schematic of temperature and loading histories for the three test methods

............................................................................................................................. 38

Figure 2.24. Hot isothermal test results obtained by Castillo and Durani (1990) ...... 40

Figure 2.25. Hot isothermal test results obtained by Abrams (1971) ......................... 42

Figure 2.26. Hot isothermal test results obtained by Morita et al. (1992) .................. 43

Figure 2.27. Hot isothermal test results obtained by Furumura et al. (1995) ............. 44

Figure 2.28. Hot isothermal test results obtained by Noumowe et al. (1996) ............ 46

Figure 2.29. The effects of loading and temperature during heating in uniaxial

compression of unsealed concrete specimens (Khoury, 2002)........................... 48

Figure 2.30. Effect of temperature upon the residual (after cooling) compressive

strength and elastic modulus of unsealed C70 HITECO Concrete -20 percent

load: expressed as a percentage of strength prior to heating (Khoury, 2002)..... 49

xvi

Figure 2.31. Measured total strain in concrete specimens heated to 400 ˚C. Applied

stress is 45 % of compressive strength at 20 ˚C (Anderberg and Thelandersson,

1976) ................................................................................................................... 50

Figure 2.32. Strain of unsealed basalt concrete measured during heating at 1 ˚C/min

under three uniaxial compressive load levels (percent of strength prior to heating)

– excluding the initial elastic strain (Khoury, 2002)........................................... 52

Figure 2.33. Relative proportions of three load induced strains in uniaxial

compression of concrete (Khoury, 2002)............................................................ 52

Figure 2.34. Failure mode with steel fibers (a) and without steel fibers (b) in HSC.. 55

Figure 2.35. The loading frame and the furnace (Fu-ping Cheng et al., 2004) .......... 55

Figure 2.36. High strength concrete blocks after two-hour hydrocarbon fire test:..... 56

Figure 2.37. A fire test of full-scale steel structure built in Cardington Laboratory

(Grosshandler, 2002)........................................................................................... 57

Figure 2.38. Tie configuration for reinforced concrete column: (a) conventional tie

configuration (b) modified tie configuration (Kodur, 1999) .............................. 60

Figure 2.39. Standard fire curves for (ISO 834 (or BS476) and ASTM E119) based on

a typical building fire (Grosshandler, 2002) ....................................................... 61

Figure 2.40. Standard fire scenarios for buildings (ISO 834 or BS 476), offshore and

petrochemical industries (hydrocarbon), and tunnels (RWS, RABT) (Khoury,

2000) ................................................................................................................... 61

Figure 2.41. Temperature vs. Time at different locations (Sanjayan and Stocks, 1991)

............................................................................................................................. 64

Figure 2.42. Weight loss vs. Time in the test (Sanjayan and Stocks, 1991).............. 64

xvii

Figure 2.43. ISO Hydrocarbon Fire Curve, Furnace Temperature, and Time Period

when Spalling was Observed (Hansen and Jensen, 1995).................................. 66

Figure 2.44. Specimen geometry and thermal cycle (Felicetti and Gambarova, 1999)

............................................................................................................................. 67

Figure 2.45. Strength of the three mix designs (Felicetti and Gambarova, 1999)...... 68

Figure 2.46. Fringe pattern and cracking of specimen at T=20 ˚C............................. 69

Figure 2.47. Cracking at failure by mechanical load after one cycle heating up to

500 ˚C (Felicetti and Gambarova, 1999) ............................................................ 69

Figure 2.48. Load-displacement curves at bottom face of mid span and crack patterns

(Felicetti and Gambarova, 1999) ........................................................................ 70

Figure 2.49. (a) Flexural model; (b) strut-and-tie model; (c) beam-end model........ 71

Figure 2.50. Comparison of failure models (Felicetti and Gambarova, 1999) ........... 71

Figure 2.51. Furnace used for tests on columns at the University of Ghent: (a) Overall

view (b) Detail of top hinge and load cell (2000 kN) (c) Detail of bottom hinge

(measurements in millimeters) (Dotreppe at el., 1996) ...................................... 74

Figure 2.52. Furnace used for tests on columns at the University of Liège: (1) Lower

transverse beam (2) Jack with double effect (3.1) Lateral support (3.2) Supports

perpendicular to frame plate (4) Load cell (5) Upper transverse beam (6) Support

for upper transverse beam (7) Furnace (8) Crossing column (Dotreppe at el.,

1996) ................................................................................................................... 74

Figure 2.53. NSC and HSC column after ASTM E119 fire tests (Kodur, 1999) ....... 76

Figure 2.54. Temperature distribution at various depths in NSC and HSC columns

(Kodur, 1999)...................................................................................................... 77

xviii

Figure 2.55. Axial deformation histories of NSC and HSC columns during fire

exposure (Kodur, 1999) ...................................................................................... 78

Figure 2.56. Position of thermo couples and load set-up (di Prisco et al., 2003) ....... 79

Figure 2.57. Comparison between the standard time-temperature curve and the actual

heating curves (di Prisco et al, 2003).................................................................. 80

Figure 2.58. Temperature distribution according to depth inside SFRC slab and

vertical displacement of SFRC and plain concrete slabs (di Prisco et al, 2003) 81

Figure 2.59. Virgin, hot and residual load-deflection of slabs (di Prisco et al, 2003)82

Figure 2.60. Loading frame and test set-up (Foster et al., 2004)................................ 83

Figure 2.61. Supporting frame and heating elements (Foster et al., 2004)................. 83

Figure 2.62. Locations of loads and displacements gages (Foster et al., 2004).......... 84

Figure 2.63. Temperature profiles (Foster et al., 2004) .............................................. 84

Figure 2.64. Yield line mechanism and crack patterns (Foster et al., 2004) .............. 85

Figure 2.65. Mid-span deflections for the tested slabs (Foster et al., 2004)............... 86

Figure 3.1. Granite sand and gravel ............................................................................ 89

Figure 3.2. Relative humidity of 2×4 in. and 4×8 in. cylinder vs. Time .................... 91

Figure 3.3. SHT 75 sensor and EK-H3 data logger .................................................... 92

Figure 3.4. Plastic tube built with the cable and sensor and 2×4 inch cylindrical

specimen embedded a sensor at center ............................................................... 93

Figure 3.5 Equipments and test set up ........................................................................ 93

Figure 3.6. Temp, RH and Strain vs. Time (Aluminum)............................................ 96

Figure 3.7. Temperature and RH inside the chamber vs. Time (No humidity control)

............................................................................................................................. 98

xix

Figure 3.8. Temperature, RH and strain history vs. Time (No humidity control) ...... 99

Figure 3.9. RH, temperature, and strain history vs. time (No humidity control)........ 99

Figure 3.10. Part C magnified in Fig. 3.9. ................................................................ 100

Figure 3.11. Dilatation of solid microstructure induced by decrease of capillary

tension with temperature increase..................................................................... 103

Figure 3.12. Length change of Portland cement paste specimens at elevated

temperature: (a) Philleo (1958); (b) Harada et al. (1972); (c) Cruz and Gillen

(1980); Crowley (1956) .................................................................................... 103

Figure 3.13. Linear thermal expansion of various rocks at elevated temperature: (a)

sand stone; (b) limestone; (c) granite; (d) anorthosite; (e) basalt; (f) limestone; (g)

sandstone; (h) pumice (Soles and Gellers, 1964)............................................. 104

Figure 3.14. Conventional thermal strain by temperature increase from 28 °C to 70 °C

........................................................................................................................... 105

Figure 3.15. Pure-Hygro Strain (PHS) under constant temperature 77.5 0.5C ± ... 106

Figure 3.16. RH, temperature, and strain history vs. time ........................................ 107

Figure 3.17. Shrinkage strain according to internal RH decrease of concrete under

constant temperature 24.5 °C............................................................................ 107

Figure 3.18. Temperature and RH inside the chamber vs. Time .............................. 109

Figure 3.19. Temperature, RH and strain history of the specimen vs. Time ............ 109

Figure 3.20. RH, temperature, and strain history vs. time (Dried specimen) ........... 110

Figure 3.21. Pure thermal strain by temperature increase from 28 °C to 70 °C ....... 110

Figure 3.22. RH (%) and Temp. (Kelvin) versus factor (f) for the range A in Fig. 3.9

........................................................................................................................... 112

xx

Figure 3.23. Equivalent RH (%) at Temp. 77.5°C (350.65 Kelvin) versus factor (f)

........................................................................................................................... 112

Figure 3.24. Thermo-hygro coupling strain between 28-70°C................................. 113

Figure 4.1. Schematic of temperature scenarios ....................................................... 119

Figure 4.2. Test set-up for heating ............................................................................ 119

Figure 4.3. Temperature histories measured at the inside of the mullite tube .......... 122

Figure 4.4. Specimen geometry, locations of thermocouples and test set-up........... 123

Figure 4.5. Transient temperature at each position................................................... 124

Figure 4.6. ∆T Vs. Surface temperature ................................................................... 125

Figure 4.7. Temperature profiles during heating and cooling .................................. 127

Figure 4.8. Thermal diffusivity................................................................................. 128

Figure 4.9. Procedure of the test sep-up ................................................................... 129

Figure 4.10. Test set-up detail................................................................................... 130

Figure 4.11. Cumulative water permeated versus time for the test series R15_D2.. 131

Figure 4.12. Cumulative water permeated versus time for the test series R2_D4.... 132

Figure 4.13. Linear regression for the test series R15_D2 ....................................... 134

Figure 4.14. Linear regression for the test series R2_D4 ......................................... 134

Figure 4.15. Relative water permeability (test series R15_D2)................................ 136

Figure 4.16. Relative water permeability (test series R2_D4).................................. 137

Figure 4.17. Comparison between R2_D4 and R15_D2 subjected to slow cooling. 138

Figure 4.18. Comparison between R2_D4 and R15_D2 subjected to natural cooling

........................................................................................................................... 138

Figure 4.19. Test set-up of the residual compression test......................................... 139

xxi

Figure 4.20. Relative velocity versus maximum temperature exposed .................... 141

Figure 4.21. Relative elastic modulus (from UPV) versus maximum temperature.. 143

Figure 4.22. Stress versus strain (Slow cooling)....................................................... 144

Figure 4.23. Stress versus strain (Natural cooling)................................................... 144

Figure 4.24. Stress versus strain (Water cooling) ..................................................... 145

Figure 4.25. Stress versus strain (Maximum temperature 200˚C) ............................ 145




Figure 4.29. Relative residual strength vs. maximum temperature .......................... 148

Figure 4.30. Relative initial tangent modulus vs. maximum temperature ................ 150

Figure 4.31. Comparison between pE and iE (Slow cooling).................................. 151

Figure 4.32. Comparison between pE and iE (Natural cooling).............................. 151

Figure 4.33. Comparison between pE and iE (Water cooling) ................................ 152

Figure 4.34. Effect of heating on weight loss (RH 100% and 90%) ........................ 154

Figure 4.35. Specimens exposed to heating rate 2 ˚C/min (Natural cooling)........... 156

Figure 4.36. Specimens exposed to maximum temperature 800 ˚C (Natural cooling)

........................................................................................................................... 156

Figure 4.37. Granite concrete melted in the furnace................................................. 157

Figure 5.1. Multiscale internal structure of concrete ................................................ 161

Figure 5.2. Hydration process of cement paste......................................................... 163

Figure 5.3. Change of phase composition with increasing temperature (w/c=0.67) 176

xxii

Figure 5.4. Comparison between current model and test data by Piasta et al. (1984)

........................................................................................................................... 179

Figure 5.5. Comparison between current model and model of Harmathy (1970) .... 179

Figure 5.6. Comparison between current model and test data.................................. 192

Figure 6.1. Simplification to spherical model........................................................... 196

Figure 6.2. Three-phase effective media model........................................................ 197

Figure 6.3. Thermal strain test data of dehydrated substances ................................. 200

Figure 6.4. Thermal strain test data of hydrated substances ..................................... 200

Figure 6.5. Thermal strains of phases in cement paste used in model...................... 204

Figure 6.6. Arrangement of phases in cement paste ................................................. 206

Figure 6.7. Comparison between model and experimental data for cement paste ... 207

Figure 6.8. Arrangement of phases in concrete ........................................................ 208

Figure 6.9. Comparison between model and experimental data (limestone concrete)

........................................................................................................................... 209

Figure 6.10. Comparison between model and experimental data (sandstone concrete)

........................................................................................................................... 210

1

CHAPTER 1

1. INTRODUCTION

1.1. Background

Concrete is a low conductor which exhibits high resistance to temperature

transients. However, extreme and rapid heating from fire can cause large volume

changes due to thermal dilatation, shrinkage due to moisture migration, and eventual

spalling due to high thermal stresses and pore pressure build-up. The large volume

change produces stresses that result in microcracking and large fractures which may

lead to structural failure. The extent of the concrete property variation due to high

temperature depends on many internal and external parameters, such as concrete mix

design, properties of the constituents, heating rate, cooling rate, maximum exposed

temperature, etc. Various studies for concrete exposed to high temperature have been

conducted experimentally and analytically on the importance of different material

parameters to provide essential information to the concrete industry for improving the

fire resistance of concrete. Recently, the research has been concentrated on various

coupling effects of the parameters such as thermo-chemo-mechanical coupling and

thermo-hygro-mechanical coupling.

2

However, more studies on this important topic are still needed, because the

properties of concrete under high temperature have not been fully understood. Even if

there are numerous experimental and theoretical results available in the literature,

contradictions among observations exist and need to be reconciled.

1.2. Thesis objectives

The first objective of this research is to find the coupling effect of temperature

and moisture on deformation of concrete, experimentally. Due to the dependency of

the relative humidity on temperature, it is not easy to measure the temperature effect

and moisture effect on strain separately over time. Usually, the thermal strain of

concrete, which is called Conventional Thermal Strain (CTS) in this study, is

obtained by measuring the displacement change without moisture control. In this

study, CTS, the strain caused by temperature increase under constant humidity (Pure

Thermal Strain: PTS), and the strain caused by moisture change under constant

temperature (Pure Hygro Strain: PHS) are measured continually and simultaneously

over time. PTS and PHS do not have a coupling effect between temperature and

moisture. From the data analysis based on the measured strains, the thermo-hygro

coupling effect is obtained.

The second objective is to investigate the strength, stiffness, and durability

performance of concrete subjected to various heating and cooling scenarios.

Extensive experimental studies on this important topic were performed previously.

The important experimental parameters included maximum temperature, heating rate,

3

types of aggregates used, various binding materials, and mechanical loads under high

temperature conditions. However, the experimental studies have mainly concentrated

on the strength of concrete; very little research focused on the reduction of concrete

durability caused by fire damage. The unstressed residual compressive strength test

and Ultrasonic Pulse Velocity test (UPV) are performed to investigate the strength

and stiffness deterioration by each high temperature scenario. The reduction of the

durability of concrete is investigated using a water permeability test (WPT).

Additionally, weight losses, color changes, and cracks of the specimens are also

studied and reported.

The third objective is to study mechanical properties of concrete under high

temperatures from both mechanical and chemical points of view. The variation of the

mechanical properties of concrete results mainly from two mechanisms. One is the

variation of material properties of the constituent phases under high temperatures, and

the other is the transformation of constituent phases under different temperatures.

Despite various experimental studies, prediction models have not yet been developed

for the thermal strain and thermal degradation of stiffness of concrete in which phase

transformations at the micro-scale level are considered. This study presents multiscale

chemo-mechanical models for thermal strain and modulus of elasticity of concrete

considering phase transformations due to high temperatures.

1.3. Thesis organization

Chapter 1 covers a brief introduction, thesis objectives, and organization.

4

Chapter 2 presents an extensive literature review on the microstructure

variations of concrete subjected to high temperature, the properties of plain

concrete tested in high temperature environments, and the behavior of reinforced

concrete components such as beams, columns, and slabs under high temperatures.

Chapter 3 presents the testing procedure and the test results on Conventional

Thermal Strain (CTS), Pure Thermal Strain (PTS), and Pure Hygro Strain (PHS).

Also, the thermo-hygro coupling effect from the data analysis based on the

measured strains is presented.

Chapter 4 presents the testing procedures and results on the strength, stiffness,

and durability performance of concrete subjected to various heating and cooling

scenarios. Additionally, weight losses, color changes, and cracks of the

specimens are also studied and reported.

Chapter 5 presents the prediction model for the thermal degradation of stiffness

of concrete in which phase transformations at the micro-scale level are

considered.

Chapter 6 presents the model for the thermal strain of cement paste and concrete

considering the phase transformations due to high temperature.

Chapter 7 consists of summary and conclusions.

5

CHAPTER 2

2. LITERATURE REVIEW

2.1. Microstructure variations of concrete due to high temperature

Material properties (such as strength, stiffness, coefficient of thermal

expansion, thermal diffusivity, and moisture diffusivity, etc) of concrete under high

temperature are linked with intricate micro-structural variations, such as the

transformation of constituent phases. At microstructure level, various experimental

studies of cement paste and concrete are summarized in the following sections.

2.1.1. Microstructure of hydrated cement paste

Cement chemists use the following the abbreviations: C CaO= ; 2S SiO= ;

2 3A Al O= ; 2 3F Fe O= ; 3S SO= ; 2H H O= . Anhydrous Portland cement is a gray

powder composed of angular particles typically ranging in the size from 1 to 50 µm.

It is produced by pulverizing the clinker being a heterogeneous mixture of several

compounds produced by high-temperature reactions between calcium oxide (CaO ),

silica ( 2SiO ), alumina ( 2 3Al O ), and iron oxide ( 2 3Fe O ) with a small amount of

6

calcium sulfate (gypsum: 4 2.2CaSO H O ). The major compounds of Portland cement

are 3C S (tricalcium silicate called as alite phase), 2C S (dicalcium silicate called as

belite), 3C A (tricalcium aluminate called as aluminate phase), and 4C AF

(tetricalcium aluminoferrite called as ferrite phase). In ordinary Portland cement,

their respective amounts usually range between 45 and 60, 15 and 30, 6 and 12, and 6

and 8 percent. The hydrated cement pastes can be classified as four principal

substances described below:

Calcium silicate hydrate (tobermorite gel): The calcium silicate hydrate

phase (C-S-H) makes up 50 percent to 60 percent of the volume of solids in a

completely hydrated Portland cement paste. Thus, C-S-H is the most important phase

determining the properties of the paste. The term hyphenated of C-S-H indicates that

C-S-H is not a well-defined compound. Actually, the ratio of cement to sand (c/s)

varies between 1.5 and 2.0, and the structural water content varies even more. The

morphology of C-S-H also varies from poorly crystalline fibers to reticular network.

In accordance with Diamond (1978), the morphology of C-S-H gels has been divided

into 4 types. Type I is fibrous particles that are a few micrometers long in the form of

a spine, prism, rod, or rolled sheet. Type II is reticular or honeycomb-shaped structure

formed in conjunction with Type I. Type III is the nondescript or flattened particles

under 0.1 µm. Type IV is compact and dimpled appearance, which is generally

formed in a later hydration period (Ramachandran, 1981). Fig. 2.1 shows SEM

(Scanning-Electron-Microscopy) image of tobermorite in concrete.

7

Figure 2.1. SEM image of tobermorite (C-S-H, Type I)

Calcium hydroxide (portlandite): Calcium hydroxide crystals [ 2( )Ca OH ]

comprise 20 percent to 25 percent of the volume of solids in the hydrated paste. In

contrast to the C-S-H, calcium hydroxide is a compound with a definite stoichiometry.

It tends to form large crystals with distinct hexagonal-prism morphology. Later in

hydration the morphology usually varies to massive structure that loses its hexagonal

form. Fig. 2.2 shows SEM image of portlandite.

Figure 2.2. SEM image of portlandite (CH) crystals

8

Calcium sulfoaluminates hydrates: Calcium sulfoaluminate hydrates occupy

15 percent to 20 percent of the solids volume in the hydrated paste. Thus, it takes part

in only a minor role in the microstructure-property relationships. During the early

stages of hydration, the sulfate/alumina ionic ratio of the solution phase is generally

the formation of trisulfate hydrate ( 36 32C AS H ), which also called ettringite. Ettringite

forms into long rods or needles with parallel sides that have no branches. In pastes of

ordinary portland cement, ettringite eventually transforms to the monosulfate hydrate

( 4 18C ASH ), which forms hexagonal-plate crystals. The presence of the monosulfate

hydrate in portland cement concrete makes the vulnerable concrete to sulfate attack. It

should be noted that both ettringite and the monosulfate contain small amounts of

iron, which can substitute for the aluminum ions in the crystal structure. Fig. 2.3

shows SEM (Scanning-Electron-Microscopy) images of ettringite crystals.

(a) Hexagonal form (b) Tubular form

Figure 2.3. SEM images of ettringite crystals

9

Unhydrated clinker grains: Depending on the particle size distribution of the

anhydrous cement and the degree of hydration, some unhydrated clinker grains may

be found in the microstructure of hydrated cement paste, even long after hydration.

As stated earlier, the clinker particles in modern portland cement generally conform

to the size range 1 µm to 50 µm. With the progress of the hydration process, the

smaller particles dissolve first and disappear from the system, then the larger particles

become smaller. Because of the limited available space between the particles, the

hydration products tend to crystallize in close proximity to the hydrating clinker

particles, which gives the appearance of a coating formation around them. At later

ages, hydration of clinker particles due to the lack of available space results in the

formation of a very dense hydration product, the morphology of which may resemble

the original clinker particle. Fig. 2.4 shows a model of well-hydrated Portland cement

paste.

Figure 2.4. Model of a well-hydrated Portland cement paste

In Fig. 2.4, A represents aggregation of poorly crystalline C-S-H particles

which have at least one colloidal dimension (1 µm to 100 µm). Inter-particle spacing

10

within an aggregation is 0.5 nm to 3.0 nm (average 1.5 nm). H represents hexagonal

crystalline products such as CH , 4 18C ASH , 4 19C AH . They form large crystals,

typically 1 µm wide. C represents capillary cavities or voids which exist when the

spaces originally occupied with water do not get completely filed with the hydration

products of cement. The size of capillary voids ranges from 10 nm to 1 µm, but in

well-hydrated pastes with low water ratio to cement, they are less than 100 nm.

2.1.2. Microstructure changes of cement paste due to high temperature

A common link throughout all concrete types is the use of cement paste as a

matrix. The response of the cement paste correlated with temperature is essential to

understanding characteristics of concrete exposed to high temperature.

Piasta et al (1984 b) investigated the microstructure and phase composition of

cement pastes from 20-800 °C. The reactions of 2( )Ca OH , 3CaCO , C-S-H, non-

evaporable water and micropores to heat were investigated using thermal analysis

(TA), X-ray diffraction analysis, infrared spectroscopy analysis and mercury porosity.

Ordinary Portland cement (OPC) specimens (initial w/c=0.4) were cured for 28 days

under the curing condition of relative humidity of about 95 percent at temperature

20 2 C± . The hardened OPC specimens were dried at temperature 105 5 C± and

then the specimens were kept for 3 hours in each of the invesgated temperatures, in

the range of 200 °C to 800 °C in intervals of 100 °C. Water content in cement paste

decreases up to 600 °C. Beyond this temperature water content holds fairly consistent

with a slight increase. This fact is the same as the results obtained from the

11

measurement for weight loss of the concrete specimens in current research, even

though the materials (cement paste in the research of Pista et al. and concrete in

current research) and heating conditions are different with those used in the research

of Piasta et al (see section 4.7). Water vapor created in the concrete between 100-

300 °C causes high pressure in the paste. This forms most ideal conditions for internal

autoclaving because steam is liberated most intensively in this temperature range. In

this temperature range, additional hydration of unhydrated cement grains occurs as

the result of steam effect under the internal autoclaving. This is manifested by

increase of the content of 2( )Ca OH that is observable from the TG [Fig. 2.5 (a)] and

X-ray method [Fig. 2.5 (b)] and decrease of unhydrated cement grain quantities

( 3 2-C S C Sβ+ ) observable from the X-ray method.

(a) 2( )Ca OH and 3CaCO (TG) (b) 2( )Ca OH and 2 3-C S C Sβ + (X-ray)

Figure 2.5. 2( )Ca OH contents observed from TG and X-ray (Piasta et al, 1984 b)

The difference of TG method (decrease) and X-ray method (increase) for

calcium hydroxide between 200 °C and 300 °C is due to different sensitivities of both

12

methods to cement paste structure. The indications of TG method are not practically

dependent on the structure. On the other hand, the X-ray method exhibits higher

sensitivity to change in the structure, particularly to the degree of its crystallization.

Keeping this in mind, up to 300 °C progressing recrystallization of amorphous

2( )Ca OH by the internal autoclaving conditions occurs in the hardened cement paste.

The results observed from TG method also show that the carbonization

kinetics of 2( )Ca OH in the temperature range of 200-500 °C increases as indicated

by a decrease in 2( )Ca OH in favor of 3CaCO . 2( )Ca OH , which has not undergone

carbonization, is decomposed with the emission of calcium oxide between 450 °C

and 550 °C. In the temperature range of 500-800 °C, the increase in the 2( )Ca OH

content is a result of humidity effect from air on free lime CaO being formed in this

temperature range. The content of 3CaCO decreases gradually as a result of its

dissociation at temperature above 500 °C. In opinion of Tsivilis et al (1998), 3CaCO

begin to decompose in the temperature range of 600-800 °C (decaonation of calcite)

and thus increases the content of calcium oxide (CaO ).

Figure 2.6. SEM images of calcite crystals

13

2.1.3. Porosity and pore size distribution according to temperature

Table 2.1 shows the results of porosity tests between 20-800 °C. Total

porosity at room temperature is the lowest.

Table. 2.1. Porosity and Pore Size Distribution (Piasta et al, 1984 b)

At 200 °C porosity is not significantly affected in either total porosity or pore

size distribution. Between 300-500 °C, total porosity along with simultaneous slight

changes in mercury porosity increases significantly due to an increase in the

percentage of pores greater than 7500 nm in diameter. In mercury porosity, there is a

decrease in the 5-10 nm pores with 25-75 nm pores increasing. The formation of

microcracks would cause the increase in pores with diameters greater than 500 nm in

the temperature range of 300-500 °C. At 600 °C an almost doubling of the total

porosity occurs. Also at this temperature capillary pores, 250-500 nm diameters, are

significantly increased. This rapid increase in porosity is caused by two chemical

14

processes, liberation of water from the decomposition of 2( )Ca OH

[ 2 2( )Ca OH CaO H O→ + ] and the liberation of 2CO resulting from 3CaCO

dissociation [ 3 2CaCO CaO CO→ + ]. 700 °C shows the highest total porosity. The

percentage of pores in the 25-75 nm diameter range decrease with capillary pores in

the range of 250-1000 nm increasing. Total porosity decreases at 800 °C. 5-10 nm

pores are significantly reduced with 500-1000 nm pores increasing significantly. The

beginning of cement paste sintering may cause this.

Table 2.2 shows a summary of temperature regimes of chemical reactions of

hydrate phase of hardened cement paste according to Schneider and Herbst (1989).

Table 2.2. Temperature regimes of chemical reactions of hydrate phase of hardened

cement paste according to Schneider and Herbst (1989)

15

But, the temperature range of decomposition of 3CaCO (calcite) is different

from the results of Lach (1970) and Tsivilis et al (1998). In their results, the

decomposition of calcite was occurred in temperature range of 600-800 °C. The result

is very similar to that of Piasta et al (1984b). In results of Piasta et al, the

decomposition of calcite was started above 500 °C.

2.1.4. Heat deformation of cement paste due to high temperature

One of the destructive causes to concrete failure is the heat deformation in the

micro and macro components. Due to differential thermal expansions of phases in

hardened cement paste, micro-cracking occurs on the phase boundaries. This micro-

cracking leads to significant destruction of the concrete structure.

Piasta (1984a) conducted experiments under the purpose of defining the

character and course of heat deformation of phases present in hardened cement paste,

and to determine initial temperatures, in temperature range of 20-800 °C. The thermal

analysis was performed with differential thermal analysis (DTA), thermal dilatometry

(TD), and differential thermal dilatometric analysis (DTD). The TD tracked heat

deformations while the DTD tracked the velocity of changes and the DTA observes

the kind of chemical processes occurring. Portland cement as well as 3C S , 2-C Sβ ,

3C A , and 4C AF which are the mineralogical composition of Portland cement were

studied in both the unhydrated and hydrated states. The mineralogical composition of

Portland cement used in the experiments was the followings: 3C S -63.2 %, 2-C Sβ -

15.4 %, 3C A -9.9 %, and 4C AF -8.1 %. The contents of free calcium oxide ( CaO ),

16

magnesium oxide ( MgO ), alkali ( 2 2Na O K O+ ), and gypsum were 1.1, 0.8, 0.5, and

3.4 % respectively. A heating rate10 ˚C/min was used.

Figure 2.7. Thermograms of unhydrated clinker minerals and Portland cement:

1) 3C S , 2) 2-C Sβ , 3) 3C A , 4) 4C AF , 5) Portland cement

In the temperature range of 20-900 °C, the test results from DTD (heat

deformation intensity) and DTA (endothermal phenomenon) showed no chemical

processes of 3C S , 3C A , and 4C AF , whereas 2-C Sβ showed a weak endothermal

phenomenon and a strong heat deformation intensity between 630-700 °C due to a

polymorphous transformation of 2-C Sβ into '2-C Sα (see Fig. 2.7). Thermal

17

expansions of the clinker minerals were tracked with temperature. All minerals

showed a linear expansion except for 2-C Sβ , which shows a nonlinear segment

between 600-700 °C. This expansion is also connected to the polymorphous

transformation. Thermal expansion of 3C A was the lowest followed by 3C S and

4C AF . Portland cement also showed a linear thermal expansion that was higher than

all but 2-C Sβ .

Figure 2.8. Thermograms of hydrated materials: 1) 3 HC S , 2) 2- HC Sβ , 3) 3 HC A ,

4) 4 HC AF , 5) Portland cement paste, 6) 2( )Ca OH , 7) Ettringite

18

Hydrated clinker materials and cement paste has performed differently from

that of unhydrated materials. From TD analysis, the hydrated materials between 20-

200 °C showed a low volume expansion similar to that of the unhydrated materials

(see Fig. 2.8). Beyond 200 °C they start to contract at varying intensities. 2- HC Sβ

showed the least contraction followed by 4 HC AF , 3 HC S and 3 HC A . Shrinkage

continues up to the temperature of dehydration decay for hydrates. After dehydration,

hydrates expand with rising temperature. On the other hand, 2( )Ca OH had the

greatest expansion that lasted from 200 °C to 450 °C. At 450 °C decomposition

begins and 2( )Ca OH begins to shrink. Ettringite had the shortest and least thermal

expansion up to 50 °C. However, Ettringite had the greatest shrinkage of all materials

tested. All materials showed non-linear heat deformations with a correlation in the

heat deformation intensity (DTD) and the endothermal phenomena (DTA) concluding

the influence of chemical processes on the heat deformations.

The common trend of all materials is the initial expansion up until the onset of

dehydration. The dehydration causes shrinkage of the hydrated materials until full

dehydration is reached. After dehydration, hydrates expand again up to 800 °C.

150 °C is the point at which shrinkage of the hydrated materials takes a significant

role in the thermal deformations. At 550-600 °C the hydrated materials are fully

dehydrated. After that, the materials are expanded with temperature increase. The

diverse nature of concrete microstructure leads to thermal deformations in both the

hydrated and unhydrated components. As mentioned in the heat deformations of the

unhydrated state, the unhydrated materials were subjected to thermal expansion over

19

all temperature range. Expansion in the unhydrated components with a corresponding

shrinkage in the hydrated components leads to stress concentrations along the

boundaries. The stress concentrations are linked with microcracks.

In SEM observation of Piasta (1984a), micro-cracks first appeared at 300 °C

around 2( )Ca OH . The cracks are linked with the different heat deformations between

2( )Ca OH and other materials. A great number of micro-cracks were observed to

between large unhydrated particles and the cement paste at 400 °C. The cracks are

linked with the stress concentrations. At 500 °C the interior of unhydrated clinker was

completely destroyed. The rehydration of free lime (CaO ), which has 44 % volume

expansion, is correlated to severe cracking due to rapid cooling. Table 2.3 is a

summary for heat deformation of cement paste.

Figure 2.9. 1) 2( )Ca OH , 2) cement gel [300 °C exposure (1000×), Piasta (1984a)]

20

Figure 2.10. Destroyed grains of unhydrated clinker as a result of different thermal

deformations [500 °C exposure (3000×), Piasta (1984a)]

21

Table 2.3. A summary for heat deformation of cement paste

Temperature Heat deformation & chemical reaction (Unhydrated substances):

3C S , 2-C Sβ , 3C A , 4C AF , and Portland cement

20-900 °C 3C S , 3C A , 4C AF : No chemical reaction

630-700 °C Polymorphous transformation of 2-C Sβ into '2-C Sα

20-900 °C

Thermal expansion (No contraction): 2 4 3 3-C S Potland cement C AF C S C Aβ > > > >

* Portland cement, 4C AF , 3C S , 3C A : Linear thermal expansion * 2-C Sβ : Nonlinear thermal expansion in temperature range 600- 700 °C due to a polymorphous transformation of '

2-C Sα

Temperature Heat deformation & chemical reaction (Hydrated substances):

3 HC S , 2- HC Sβ , 3 HC A , 4 HC AF , Portland cement paste, 2( )Ca OH , and Ettringite

20-900 °C All materials: chemical reaction and nonlinear heat deformation 20-200 °C Low thermal expansion of all hydrated materials

20-600 °C 1. Shrinkage of the materials due to dehydration of hydrates

(except for 2( )Ca OH ) 2. 2( )Ca OH : Greatest thermal expansion up to 450 °C

300 °C Occurrence of initial micro-cracks due to different heat

deformation between 2( )Ca OH (expansion) and other materials (shrinkage)

400 °C

Occurrence of a great number of micro-cracks between large unhydrated particles and the cement paste

* Due to stress concentrations along the boundaries by different

heat deformations between the unhydrated components (expansion) and hydrated components (shrinkage)

500 °C Interior of unhydrated clinker is completely destroyed 550-600 °C The hydrated materials are fully dehydrated. 600-800 °C After full dehydration of hydrates, they expand again up to 800 °C

Cooling Rehydration of free lime (CaO ):

2 2( ) ( )CaO H O From air or water Ca OH+ → 44 % volume expansion → Correlation to severe cracking

22

2.1.5. SEM (Scanning Electron Microscopy) observation of concrete

In a study conducted by Lin et al. (1996), the microstructure of concrete

exposed to elevated temperatures in both actual fire and laboratory conditions were

evaluated with the use of SEM and stereo microscopy. Thermal stresses, due to

thermal gradients, decomposition of calcium hydroxide, calcinations of the limestone

aggregates and phase transformation of quartz aggregate, cause spalling and cracking

during heating and disintegration during cooling. When temperatures rise about

100 ºC evaporable moisture reduces cohesive forces between C-S-H layers and gel

surface. In samples exposed to temperatures below 200 ºC no noticeable cracks were

observed. Exposure to 400 ºC causes the collapse of crystals. Buildup of internal

pressure is caused by vaporization of free water, dehydration of calcium hydroxide,

which occurs exclusively between 440-580 ºC, above 350 ºC, and partial

volatilization of C-S-H gels above 500 ºC. At 573 ºC the crystal structure of quartz in

siliceous aggregate transforms from low temperature α crystal to high temperature

β crystal.

Figure 2.11. Morphologies of hydrates after 400 ºC exposure (Lin et al, 1996)

23

Fig. 2.11 shows the morphology of hydrates after an exposure to 400 ºC.

Above 350 ºC calcium hydroxides dissociates into lime (CaO ) and water. This leads

to damage as free lime expands during cooling. Dehydroxylation of calcium

hydroxide occurs exclusively between 440 ºC and 580 ºC (above 350 ºC).

Figure 2.12. Morphologies of hydrates after 500 ºC exposure (Lin et al, 1996)

.

Figure 2.13. Crakes and honey combs after 900 ºC exposure (Lin et al, 1996)

24

Fig. 2.12 shows the hydrates after 500 ºC exposure. Calcium hydroxide

appears layered plates with ettringite and C-S-H from about 400 ºC. Fig. 2.13 also

shows the layered plates. Significant shrinkages, cracks and honeycombs were

observed in concrete samples exposured to 900 ºC. Fig. 2.14 shows the morphology

of a sample after 900 ºC exposure. After the sample was heated to 900 ºC, the sample

under water-curing formed a different microstructure as compared with compared

with that under air-curing. This is due to the presence of water. With the presence of

water, CH is formed as a result of rehydration of calcium oxide. The C-S-H forms

honeycomb and filigree networks with small pore spaces.

Figure 2.14. Sample under water cooling after 900 ºC exposure (Lin et al, 1996)

Wang et al. (2005) used SEM to examine the cracking of high performance

concrete (HPC) exposed to high temperatures under axial compressive loading of

about 200 N. The compressive loading mainly restricted the loose deformation of the

sample at high temperature. The study observed the initiation and propagation of

cracks and micro-cracks in HPC. Temperatures were increased from 25 ºC to 100,

25

200, 300, 400, 500 ºC. The interfacial transition zone (ITZ) has higher porosity than

the surrounding matrix. Micro-cracking is affected not only by the applied stress but

also by the exposure temperature. Cracks formed around the aggregate become

significant as temperature increases. This is most likely due to the changed properties

along the ITZ and dilation differentials. Micro-cracks formed in the direction of the

applied load. Between 100 ºC and 200 ºC micro-cracking was initiated in loading

direction although this did not lead to the cleavage failure of aggregate particles.

However micro-cracking did not continue to propagate in this direction from 300-

500 ºC. In this temperature range the combination of C-S-H becoming soft and

increased adhesion between intermixed and hydrated phases begins to close cracks.

Therefore 200 ºC is a critical temperature for the formation of micro-cracks of HPC

under service conditions.

2.1.6. SEM observation of concrete used in current research

SEM observation was conducted from the concrete sample used in the current

research. The average size of samples used was 15-20 mm in diameter. The samples

were heated with rate of 2 ºC/min. After heating up to the desired temperature, the

specimens were cooled naturally inside the closed furnace. The exposed maximum

temperatures were 24, 500, 700, and 900 ºC. Fig. 2.15 (a) shows hydration products

of calcium silicate gel (C-H-S), CH, ettringite in unheated sample. The ettringite are

in the form of rods interspersed between hydrates. Fig. 2.15 (b) shows well-developed

ettringite and micro-cracks developing between calcium hydroxide in the cement

26

paste. Fig. 2.15 (c) shows the morphologies of C-S-H and CH, and ettringite after

exposure 700 ºC. Fig. 2.15 (d) shows severe shrinkage cracks and honeycombs in

cement paste after exposure at 900 ºC. The results of the SEM are relatively similar to

those from literature review.

(a) 24 ˚C exposure (3000×) (b) 500 ˚C exposure (2500×)

(c) 700 ˚C exposure (5000×) (d) 900 ˚C exposure (2400×)

Figure 2.15. SEM images of the concrete used in current research

Ett

CH

CH

CSH

CH

CH

CSH

Ett CH

Honey combs (CSH)

Shrinkage Cracks

27

2.2. Pure concrete exposed to high temperature

2.2.1. Two major problems when concrete is exposed to fire

Fire incurs two major problems in concrete. One is the deterioration in

mechanical properties of concrete, such as physicochemical changes of the cement

paste and aggregate, thermal incompatibility between the aggregate and the cement

paste according to temperature level, heating rate, applied load, and moisture loss.

The other problem is spalling of concrete. Spalling can lead to severe reduction of the

cross sectional area, which leads to the exposure of the reinforcing steel to excessive

temperatures. Fig. 2.16 illustrates the physicochemical processes taking place in

concrete at various temperature ranges. A detailed review of concrete spalling and the

physical mechanisms behind this phenomenon is presented in Sec. 2.2.2.

Figure 2.16. Physicochemical process in Portland concrete during (Khoury, 2000)

28

2.2.2. Selection of concrete mix

Selection of the concrete mix design is very important in the fire design for

reinforced concrete structures. The individual material constituents should be selected

considering spalling and strength loss. Fig. 2.17 presents a schematic for the two

arguments of appropriate material choice.

Figure 2.17. Material choices for concrete under high temperature (Khoury, 2000)

a. Mix designs considering strength loss

The mechanical properties of concrete under high temperature can be

improved significantly by intelligent mix design. There are three items to be

considered: aggregate, cement paste and the interaction between them. The choice of

aggregate is very important in concrete mix design since its thermal stability depends

29

strongly on the type of aggregate being used. In general, flint gravel breaks up at

relatively low temperatures (below 350 ˚C), while granite exhibits thermal stability up

to 600 ˚C. Other important features of the aggregate are low thermal expansion, rough

angular surfaces and the presence of reactive silica. Under high temperature,

aggregates expand and cement paste shrinks due to rapid moisture loss which cause

crack on the interface between aggregate and paste. Therefore, aggregates with low

coefficient of thermal expansion can reduce the thermal incompatibility between

cement paste and aggregate, hence use of low coefficient of thermal expansion

reduces the thermal damage. Also, rough and angular surface of the aggregate

improves the physical bond with the cement paste. An important fire design

parameter is the cement/sand (c/s) ratio. A low c/s ratio results in a low calcium

hydroxide (Ca(OH)2) content in the original mix and ensures beneficial hydrothermal

reaction. Calcium hydroxide is not desirable because it dissociates at about 400 ˚C

into CaO and 2CO . CaO rehydrates expansively and detrimentally upon cooling

and exposure to moisture. So, the reduction of C/S ratio using blast furnace slag, fly

ash, and silica fume can lead to an improvement of concrete strength upon fire. Tests

by Khoury at el., (1995 (a)) show that the use of slag produces the best results at high

temperature, followed by fly ash and then the silica fume. Particularly, the relatively

poor performance of the silica fume cement paste (contrary to its high durability at

room temperature) may be attributed to the dense, low permeability structure of the

paste which does not readily allow moisture to escape from heated concrete, which

results in high pore pressures and occurrence of micro-cracks.

30

b. Mix designs considering spalling

Spalling is the break off of layers or pieces of concrete from the surface of a

structural element. The spalling of normal strength concrete (NSC) occurs due to

rapid temperature change - typically 20 ˚C/min (Khoury, 2000). High strength

concrete (HSC) has a significantly higher potential for explosive spalling than normal

strength concrete (NSC) due to its low permeability. Explosive spalling of HSC may

occur even at relatively low heating rate - less than 5 ˚C/min (Phan, 2002). However,

spalling occurs only in narrow regions of the concrete specimen, which has been

observed by many researchers. There has been no explanation as regards to why

spalling does not occur in all specimens. Many researchers have been arguing about

what is the main cause of explosive spalling.

Table 2.4. Factors influencing spalling of concrete (Khoury, 2000)

Spalling of concrete can be classified into four categories. They are aggregate

spalling, surface spalling, explosive spalling as violent breaking and corner spalling

as non-violent breaking. The main factor responsible for the first three types is the

31

heating rate, while the fourth type is influenced more by the maximum temperature.

The following table summarizes the natures and the main influential factors for

concrete spalling. The main factors are heating rate, permeability of concrete,

moisture content, presence of reinforcement and level of externally applied load.

In order to prevent the occurrence of concrete spalling, it is very important to

understand what happens in concrete that causes spalling, that is, to understand the

fundamental mechanisms that cause concrete spalling. There are several theories

explaining the spalling mechanisms, which may be classified in three categories:

(a) pore pressure spalling, (b) thermal stress spalling, and (c) combined pore pressure

and thermal stress spalling.

- Pore pressure spalling: Fig. 2.18 shows the mechanism of pore pressure spalling.

High temperature causes the evaporation of free water near the concrete surface. The

high vapor pressure in the surface layer drives the water vapor to diffuse in two

opposite directions: to the surface and into the deeper part of the concrete specimen.

With a sharp temperature increase at the concrete surface (under rapid heating), the

interior temperature of concrete remains low. When the free water evaporates the

vapor diffuses into the interior part of the concrete (cooler part), where it condensates.

The condensation of vapor increases the moisture content of the concrete in that layer

and thus reduces the permeability of the concrete, which results in the formation of a

barrier in the interior, the so-called moisture clog (see Figs. 2.18 (b) and 2.18 (c)).

The interior water vapor is blocked by the clog, and the vapor pressure starts to build

up rapidly. As soon as the pressure exceeds the tensile strength, then spalling takes

32

place. Fig. 2.19 shows the conceptual distribution of temperature, pore pressure and

moisture in a massive concrete section heated at the unsealed surface on the right side.

Figure 2.18. Mechanism of pore pressure spalling (Schneider and Horbst, 2002)

Figure 2.19. Gradients of temperature, pore pressure and moisture in a massive

concrete section heated at the unsealed left-hand surface (Khoury, 2000)

33

In this process, the sharp temperature reduction (high temperature gradient)

from the surface plays an important role, and the high gradient occurs only under very

rapid heating of massive concrete components. This is why fast heating is a necessary

condition for the spalling. Other necessary conditions are low permeability of

concrete and the size of the concrete structure, otherwise the vapor would readily

escape to the surface and there would be no pressure build-up. On the other hand,

high temperature causes the dehydration of chemically bonded water in the cement

paste, which contributes to the high pore pressure and spalling. This is why spalling

takes place in the HPC concretes with low moisture content. This also explains that

high initial water content in concrete is not a necessary condition for spalling.

- Thermal stress spalling: This mechanism is the result of thermo-mechanical

coupling, in which the temperature gradient upon rapid heating causes severe thermal

stress gradients in the concrete component. In the high temperature zone (on the

surface) concrete expands more than in the low temperature zone (the interior part).

As a self-equilibrating thermal stress state develops, a thin layer near the surface is in

compression while the interior part is in tension. Because of the high temperature

gradient, the compressive stress in the thin surface layer can be very high, which

causes buckling and delamination of the outer layer, observed in the form of spalling.

Therefore, the main factor of thermal stress spalling is the excessive thermal stress

generated by rapid heating of massive concrete components and structures.

- Combined pore pressure and thermal stress spalling: In most cases, a

combination of the two mechanisms takes place. Fig 2.20 shows forces acting in

heated concrete.

34

Figure 2.20. Forces acting in heated concrete (Zhukov, 1975)

Explosive spalling generally occurs under the combined effect of pore

pressure, and compression in the exposed surface region induced by thermal stress

and external loading and internal cracking. Consequently the pore pressure needs to

be considered together with both the thermal and the load-induced stresses before the

occurrence of explosive spalling.

Figure 2.21. Mechanical property test setup (Phan, 2002)

35

Figure 2.22. Test set up, Pore pressure specimen, and Specimen failure (Phan, 2002)

Fig. 2.21 and Fig. 2.22 show the experimental setup for testing concrete

spalling and the fractured concrete specimens at NIST. The methods of improving

concrete mix design to prevent spalling will be introduced in later sections.

2.2.3. Testing methods for mechanical properties of concrete

► Idealized testing methods: There are six idealized test methods for testing

concrete at high temperature. Four of which belong to the category of steady state,

36

isothermal temperature experiments, and two belong to the category of the transient,

isotonic temperature experiments. Steady state tests include stress rate or strain rate

controlled tests, steady state creep and relaxation tests. Transient tests include

transient creep and relaxation experiments (Phan, 1996).

- Steady state tests: The difference between strain and stress controlled tests depends

on the load control method used in the experiment. The test specimen is heated up to

the target temperature with a constant heating rate. After the concrete specimen has

reached a uniform temperature distribution, the specimen is subjected to a constant

rate of stress or strain until the ultimate stress level or strain level is reached. This test

method is also called “unstressed test”, because the specimen is stress free (or strain

free) during the heating period. Data from this type of test can be used to determine

the compressive strength, the modulus of elasticity, the strain at ultimate strength, and

the dissipated mechanical energy as function of temperatures. The steady creep test is

designed to measure creep deformations at different target temperatures (isothermal

creep test). The test specimen is slowly heated to the target temperature until a

uniform temperature distribution is reached in the concrete specimen. After that the

mechanical load is applied. The loading period is typically much longer than the

loading period of stress rate controlled or the strain rate controlled experiments. Once

the load level is reached, both the target temperature and the mechanical load are kept

constant during the test period. The measured results are creep deformations due to

sustained constant load at different temperatures. The elastic deformation which

occurs instantaneously upon loading is separated from the creep deformations which

result from long term, sustained loading. This type of test is not applicable to a

37

concrete structure under fire since the testing duration is normally far longer than the

duration of building fires. The steady relaxation test is similar to the steady state

creep test. Under each steady temperature condition, an initial (elastic) strain resulting

instantaneously from the applied deformation is recorded. Thereafter the initial

deformation and the target temperature are kept constant during the testing period and

measurements of stress as a function of time are recorded. The steady relaxation test

also has little relevance to the performance of concrete under fire situation because its

duration exceeds the duration of building fires in real life (Phan, 1996).

- Transient tests: In the case of a transient creep test, the specimen is subjected to a

constant applied load, usually a percentage of the specimen’s ultimate strength

measured at room temperature before heating, and then the specimen is heated with a

constant heating rate until failure occurs. In case of a transient relaxation test, the

specimen is subjected to a constant applied strain measured at room temperature. The

strain is maintained for the duration of the test by adjusting the applied load (usually

by reducing the applied load in order to keep the constant strain), while the specimen

is heated at a specified rate. The test is terminated when the applied stress level

diminishes to zero. Unlike the steady state creep and relaxation tests, where the test

durations far exceed the practical duration of building fires, the transient creep and

the transient relaxation tests simulate the transient conditions which concrete

members might experience in real structures. Thus data obtained from the transient

tests have relevance to the performance of concrete structures during fires (Phan,

1996), see also the workshop papers (Willam et al., 2003; Willam et al., 2004).

38

► Commonly used test methods: Three testing methods are commonly referred to

as stressed tests, unstressed tests, and unstressed residual strength tests. The

schematic of the three test methods is shown in Fig. 2.23.

Figure 2.23. Schematic of temperature and loading histories for the three test methods

Stressed tests are a modified version of stress or strain controlled experiments

performed under isothermal temperature conditions. A preload, generally in the range

of 20 percent to 40 percent of the ultimate compression strength at room temperature,

is applied to the concrete specimen prior to heating, and the load is sustained during

the heating period. After the specimen reaches a steady state temperature condition,

the stress or the strain is increased with a prescribed loading rate until the specimen

fails. The test results of this test are most suitable for representing fire performance of

concrete in a column or in the compression zone of beams and slabs.

Unstressed tests are carried out identically to the stress or strain controlled

experiments of the steady state type. The test results are most suitable for representing

39

the performance of concrete in the tension zone of beam and slabs or concrete

elements with low stress levels under service conditions.

Unstressed residual strength tests are experiments where the specimen is first

cooled to room temperature after one or several cycles of heating without preloading.

The load is then applied at room temperature under stress or strain control until the

specimen fails. The results of this test are most suitable for assessing the post fire (or

residual) properties of concrete (Phan, 1996).

2.2.4. Concrete properties under high temperatures

The compressive strength of concrete at high temperature is largely affected

by the following factors: 1) Individual constituent of concrete, 2) Sealing/moisture

condition, 3) Loading level during heating period, 4) Testing under ‘hot’ or ‘cold

residual’ conditions, 5) Rate of heating or cooling, 6) Duration at constant

temperature, 7) Time maintained in moist conditions after cooling before the test is

carried out, and 8) Number of thermal cycles (Khoury, 2002). In this section, we will

focus on the general trends of the test data without giving a detailed description of

concrete mix design, curing time and experimental conditions.

The effect of elevated temperatures on concrete strength and load-deformation

behavior of HSC and NSC were investigated by Castillo and Durani (1990). Type Ι

Portland cement with natural river sand and crushed limestone were used for

preparing the concrete specimens in the form of 51 mm×102 mm cylinders. Fig. 2.24

shows the test results. In the case of the stressed experiment, 40 percent of the

40

ultimate compressive strength at room temperature was applied to the specimens and

sustained during the heating period. In the unstressed experiment, when exposed to

temperatures in the range of 100 °C to 300 ˚C, HSC showed a 15 percent to

20 percent loss of compressive strength, whereas the NSC showed no strength loss

(Figure 2.24 (a)).

(a) Compressive strength vs. Temperature (b) Modulus of Elasticity vs. Temperature

(c) Load-deformation of HST (d) Load-deformation of NSC

Figure 2.24. Hot isothermal test results obtained by Castillo and Durani (1990)

HSC recovered its strength between 300 °C and 400 ˚C, reaching a maximum

value of 8 percent to 13 percent above room temperature. At temperature above

41

400 ˚C, HSC progressively lost its compressive strength which dropped to about

30 percent of the room temperature strength at 800 ˚C. The trend of NSC was also

similar to that of HSC. The elastic modulus in the range of 100 ˚C to 300 ˚C was

decreased by 5 percent to 10 percent for both HSC and NSC (Fig. 2.24 (b)). At

800 ˚C, the elastic modulus was only 20 percent to 25 percent of the value at room

temperature. Beyond 300 ˚C, the elastic modulus decreased at a faster rate with

increase in temperature. The load-deformation plots for HSC and NSC are shown at

Fig. 2.24 (c) and (d). NSC specimens did exhibit ductile failure except for 200 ˚C.

Between 300 ˚C and 800 ˚C, the NSC specimens were able to undergo large post-

peak strains while the decrease in strength was more gradual. HSC showed brittle

failure up to 300 ˚C, and with further increasing temperature, the HSC specimens

began to exhibit a more gradual failure.

Abrams (1971) conducted a study of four variables including aggregate types

(carbonate dolomite sand and gravel, siliceous, and expanded shale lightweight

aggregates), testing methods (unstressed, stressed and unstressed residual

experiments), concrete strengths (ranging from 22.8 MPa to 44.8 MPa), and

temperatures (from 93 ˚C to 871 ˚C). The specimens were 75 mm×150 mm cylinders.

Fig. 2.25 summarizes the test results. The following conclusions were reported: Up to

about 480 ˚C, all three concretes exhibited similar strength loss characteristics under

each test condition (stressed, unstressed, and unstressed residual). Above 480 ˚C, the

siliceous aggregate concrete had greater strength loss and retained less strength for all

three test conditions. Specimens made of carbonate aggregates and lightweight

aggregates behaved about the same over the entire temperature range and retained

42

more than 75 percent of their original strength at temperatures up to 649 ˚C in

unstressed tests.

(a) Carbonate aggregate concrete (b) Siliceous aggregate concrete

(c) Lightweight aggregate concrete (d) Stressed tests

(e) Unstressed tests (f) Unstressed residual tests

Figure 2.25. Hot isothermal test results obtained by Abrams (1971)

43

For the siliceous aggregate, the strength was 75 percent of the original

strength at 430 ˚C. Compressive strengths of specimens with preload (stressed tests)

were generally 5 percent to 25 percent higher than those without preload (unstressed

tests). Also the preloads of 25, 40, and 55 percent of the room temperature

compressive strength, had insignificant effect on compressive strength of the stressed

specimens. The unstressed residual specimens had the lowest strength compared with

the stressed and unstressed specimens tested at high temperatures. The test results of

Abrams (1971) indicate that strength recovery took place only in a limited

temperature range in the case of the stressed and unstressed experiments.

(a) Residual compressive strength (b) Residual normalized strength

(c) Residual elastic modulus (d) Residual normalized elastic modulus

Figure 2.26. Hot isothermal test results obtained by Morita et al. (1992)

44

Morita et al. (1992) conducted unstressed residual strength tests. The

specimens were 100 mm×200 mm cylinders. The heating and cooling rate were

1 ˚C/min and target temperatures were 200, 350, and 500 ˚C. The keeping time at

target temperatures to allow a steady state was 60 min. Fig. 2.26 shows the test results.

High strength concrete has a higher rate of reduction in residual compressive strength

and modulus of elasticity than normal strength concrete after being exposed to

temperatures up to 500 ˚C. The study did not report any spalling problems during

heating.

(a) Compressive strength (b) Elastic modulus

(c) Stress-strain curves (FR-42) (d) Stress-strain curves at 300˚C

Figure 2.27. Hot isothermal test results obtained by Furumura et al. (1995)

45

Furumura et al. (1995) performed unstressed tests and unstressed residual tests

on 50 mm×100 mm concrete cylinders using three compressive strength levels:

21 MPa (normal strength concrete FR-21), 42 MPa (intermediate strength concrete

FR-42), and 60 MPa (high strength concrete FR-60). The heating rate was 1 ˚C/min

and target temperatures were from 100 ˚C to 700 ˚C with an increment of 100 ˚C. The

time at target temperatures to allow a steady state was two hours. The concrete was

made from ordinary Portland cement. They observed that, for the unstressed tests, the

compressive strength decreased at 100 ˚C, recovered to room temperature strength at

200 ˚C and then decreased monotonically with increasing temperature beyond 200 ˚C.

For the unstressed residual tests, the compressive strength decreased gradually with

increasing temperature for the entire temperature range without any recovery. The

modulus of elasticity, in general, decreased gradually with increase of temperature.

Fig. 2.27 shows the test results. As expected, the stress-strain curves for HSC are

different from those of normal strength concrete (Fig. 2.27 (d)). High strength

concretes exhibited steeper slopes than the NSC at temperature up to 300 ˚C to

400 ˚C in the unstressed test.

Noumowe et al (1996) conducted unstressed residual strength tests to compare

the performance of HSC exposed to high temperatures with NSC. The specimens

were 160 mm×320 mm cylinders and 100 mm×100 mm×400 mm prisms. A normal

strength (38.1 MPa) and high strength (61.1 MPa) were used. The prismatic

specimens had enlarged ends and were used to measure tensile strength. Calcareous

aggregates were used for both concretes. The specimens were heated at a rate of

46

1 ˚C/min to target temperatures of 150, 300, 450, 500, and 600 ˚C, which was

maintained for 1 hour, and then allowed to cool at 1 ˚C/min to room temperature.

(a) Residual tensile strengths (b) Elastic Modulus of HSC and NSC

(c) Porosity vs. temperature (d) Mass loss vs. temperature

Figure 2.28. Hot isothermal test results obtained by Noumowe et al. (1996)

Uniaxial compressive, splitting tensile, and direct tensile tests were performed

to obtain residual compressive strength, modulus of elasticity, and residual tensile

strength versus temperature relationships. Figs. 2.28 (a) and (b) show the latter two

relationships. Residual tensile strengths for NSC and HSC decreased similarly and

almost linearly with increase of temperature. Tensile strengths of HSC at all

47

temperatures were 15 percent higher than those of NSC. Also, the tensile strengths

measured by splitting tension experiments were higher than those obtained in direct

tension. The residual modulus of elasticity remained approximately 10 percent to

25 percent higher than those of NSC for the entire temperature range. Measurements

of porosity after exposure to different temperatures were performed for both

concretes using a mercury porosimeter. Fig. 2.28 (c) shows the results of porosity

measurements. Fig. 2.28 (d) illustrates the percentage loss in mass for different

temperature. Porosity measurements indicated that between 25 ˚C and 120 ˚C, the

porosity of both concretes was not altered. As the temperatures increased, NSC

became increasingly more porous compared with HSC. Mass losses in both concretes

were also similar up to 110 ˚C. The highest rate of mass loss occurred in the

temperature range of 110 ˚C to 350 ˚C. The rate of weight loss stabilized at

temperatures above 350 ˚C. At any temperature, mass loss in NSC was higher than

that in HSC.

2.2.5. The effects of sustained loading during heating

Preloading during heating has positive effects on both the compressive

strength and the elastic modulus. Fig. 2.29 demonstrates the positive effects

(measured in the ‘hot’ state for unsealed CRT HITECO ultra-high performance

concrete). Comparison of Figs. 2.29 (a) and (b) shows that the compressive strength

and elastic modulus of the specimen under sustained loading is larger than those of

specimens without the sustained loading. This aspect can be explained from the fact

48

that compressive preloading inhibits crack development - although this explanation

has not been fully validated. Mechanical properties such as strength and stiffness

generally decrease with increasing temperature. Each of Figs. 2.29 (a) and (b) shows

that the compressive strength as well as the elastic modulus decrease as the

temperature increases. In other words, the elevated temperature has a very significant

effect on the degradation of the mechanical concrete properties.

(a) For 0 % load (b) For 20 % load

Figure 2.29. The effects of loading and temperature during heating in uniaxial

compression of unsealed concrete specimens (Khoury, 2002)

Fig. 2.30 (Khoury, 2002) shows the positive effect of temperature upon the

residual (after cooling) compressive strength and the elastic modulus of unsealed C70

HITECO concrete containing thermally stable Gabbro Finnish aggregate. The

specimens are heated with heating rate 2 ˚C/min under 0 percent and 20 percent

49

preloaded in compression. The results are shown in terms of percentage of strength

and elastic modulus prior to heating.

Figure 2.30. Effect of temperature upon the residual (after cooling) compressive

strength and elastic modulus of unsealed C70 HITECO Concrete -20 percent load:

expressed as a percentage of strength prior to heating (Khoury, 2002)

2.2.6. Combined thermal and mechanical loading histories

Anderberg and Thelandersson (1976) conducted experiments to determine

thermal and mechanical interaction effects. Fig. 2.31 shows the heating scenario and

the results of the experiment. The uniaxial strains were measured in two unsealed

concrete specimens. In the first case (curve 1 in Fig. 2.31), a uniaxial compressive

stress was applied after heating was completed, while in the second case (curve 2 in

50

Fig. 2.31), the same stress was applied from beginning. Fig. 2.31 shows that the total

strain (the final part of curve 1) can not be regarded as simple summation of the

curves from the stress test and temperature test. It could be argued that the difference

between point A and B is caused by creep in the loaded specimen.

Figure 2.31. Measured total strain in concrete specimens heated to 400 ˚C. Applied

stress is 45 % of compressive strength at 20 ˚C (Anderberg and Thelandersson, 1976)

But tests on the same concrete under isothermal conditions show very clearly

that creep strains in the temperature range 0 - 400 ˚C are much smaller than the

observed difference in Fig. 2.31. Therefore, if the observed path dependence is to be

interpreted as creep, one must postulate that the creep strain depends on the rate of

temperature change. The phenomenon is called transitional thermal creep, a term

which was originally introduced by Illston and Sanders (1973). The notation of creep

51

in this context is confusing, since transitional thermal creep is not a long-term effect.

In relation to the time scale of isothermal creep it can be regarded as quasi-

instantaneous response to temperature change similar to that of free thermal strain.

Several experiments showed rather clearly that the extra deformation caused by

change in temperature distinctly occurs during the period of changing temperature,

while the deformation under load after this period is just the basic creep (Illston and

Sanders, 1973).

2.2.7. Decomposition of the total strain due to coupling effects

Decomposition of total strain of concrete due to combined thermal and

mechanical loadings is a complicated issue, mainly because the definitions of the

terminologies used in the literature are not consistent among researchers. In this

report, we will restrict to the definitions and explanations given by Khoury (1985 a &

2002). When the temperature and sustained mechanical load are applied to the

specimen simultaneously, the total thermo-mechanical strain will be observed. The

decomposition of the total strain can be considered experimentally or numerically to

estimate the effect of combined thermal and mechanical action or the influence of

each strain component of the total strain. The total strain decomposes into the

following components:

Total strain = FTS(Free Thermal Strain) – LITS(Load Induced Thermal Strain) (2.1)

52

Figure 2.32. Strain of unsealed basalt concrete measured during heating at 1 ˚C/min

under three uniaxial compressive load levels (percent of strength prior to heating) –

excluding the initial elastic strain (Khoury, 2002)

Figure 2.33. Relative proportions of three load induced strains in uniaxial

compression of concrete (Khoury, 2002)

53

Figs. 2.32 and 2.33 provide the conceptual argument of LITS. The definition

for each terminology is as follows.

FTS (Free thermal strain) - FTS is a function of temperature and time. It

includes drying shrinkage (due to moisture loss) and expansive strains.

Load induced thermal strain (LITS) - LITS is the strain that develops when

concrete is heated for the first time under load. LITS is composed of transient creep,

basic creep, and the elastic strain that occurs during the heating process. The term

‘basic creep’ is used cautiously here, because this strain strictly occurs when concrete

is loaded at constant temperature and after all internal reactions have been completed

(Khoury 1985 b).

LITS = Transient Creep + Basic Creep + Elastic strain (during the heating) (2.2)

Transient creep is classified as transitional thermal creep and drying creep in

case of unsealed specimen.

Transient Creep (unsealed specimen) = Transitional Thermal Creep (TTC)

(sealed specimen) + Drying Creep (2.3)

TTC (Transitional thermal creep) - TTC develops irrecoverably during, and

for a few days following, first-time heating of sealed concrete under load. It appears

in addition to the increase in elastic strain and basic creep (flow and delayed elastic)

components with temperature. TTC is generally developed within a month from the

54

start of heating (Khoury, 1985 a). The strains developed under combined thermal and

mechanical loading have not been considered systematically in the constitutive

models for structural analysis.

2.2.8. The effects of steel and polymer fibers at elevated temperatures

Recent research has been performed by several researchers to improve the fire

resistance of concrete. Polypropylene fibers and steel fibers are very useful materials

for improving fire resistance of concrete. They are particularly useful to enhance the

spalling resistance of HSC.

Kodur’s test results (2000) show that the addition of polypropylene fibers

minimizes spalling in HSC members under fire conditions. One of the well-accepted

theories is that by melting at a relatively low temperature of 170 °C, the

polypropylene fibers create “channels” for the steam pressure in concrete to escape,

thus preventing internal pressurization causing spalling. The study showed that the

amount of polypropylene fibers needed to minimize spalling is about 0.1 percent to

0.25 percent (by volume). On the other hand, the fibers increase the tensile strength of

concrete (below the melting point of the fibers), which also provides higher resistance

to the pore pressure.

The presence of steel fibers increases the ultimate strain and concrete ductility

according to the results of Lie and Kodur (1995 a). Cheng et al. (2004) carried out

compression experiments to study the influence of various aggregates and steel fibers

at elevated temperature in HSC. The test results were similar to that of NSC.

55

(a) with steel fibers (b) without steel fibers

Figure 2.34. Failure mode with steel fibers (a) and without steel fibers (b) in HSC

Figure 2.35. The loading frame and the furnace (Fu-ping Cheng et al., 2004)

56

Figure 2.36. High strength concrete blocks after two-hour hydrocarbon fire test:

(a) without polypropylene fibers; (b) with polypropylene fibers (Bilodeau et al., 1998)

Further research is being carried out to determine the optimum fiber content

for different types of concrete. The effect of polypropylene fibers on spalling is

illustrated in Fig. 2.36, which shows HSC concrete blocks after two hours of fire

exposure.

2.3. Concrete Structures under High Temperatures

Local high temperature due to fire results in damage in concrete structural

members such as beams, columns, walls, and slabs. The damage in concrete may be

manifested as deterioration in strength or stiffness or as spalling. In the case of severe

damage in key structural members, localized damage may lead to structural failure. In

the past two decades, the research on the behavior of plain concrete under fire has

57

been conducted extensively at material level. However, the research on the behavior

of reinforced concrete structures under fire (at structural level) has not been very

active as compared to the research on plain concrete.

Literature review indicates that the behavior of a structural member in a

structure is different from that of a single member under the same fire conditions. As

an example, the full scale test of an eight story steel structure was conducted at the

Building Research Establishment’s Cardington Laboratory in England during 1995

and 1996 (Fig. 2.37).

Figure 2.37. A fire test of full-scale steel structure built in Cardington Laboratory

(Grosshandler, 2002)

The test data demonstrated that the requirements for fire safety in structural

design were overly conservative at the level of structural elements. The reason is that

due to continuity, restraint conditions, and the interaction of members in a complete

structure, an alternative load path is developed by the rest of the structure to bridge

58

over the members failed due to the local fire, thus enhancing the fire performance of

the entire structure. Therefore, in principle, different local fire scenarios in a

structural system should be considered in order to assess the realistic fire resistance of

the structure. In practice, however, very limited experimental data on overall

structural behavior in real fire conditions are available due to the complexity and cost

of carrying out such experimental studies. Therefore, in the following sections we

will focus on experimental results on behaviors of reinforced concrete structural

members under high temperature. It is worthwhile to mention that the lack of

experimental results on structural performance under high temperature has generated

an interest in developing numerical models, which can be used to simulate different

fire scenarios. Currently, there is a pressing need for developing reliable simulation

models to characterize the behavior of concrete structures under high temperatures.

2.3.1. Factors affecting fire performance of concrete structures

The factors related to spalling-damage in concrete structures can be

summarized as follows. Some of the factors were already introduced in Chapter 2.2.

Concrete strength: While it is difficult to specify the exact strength range,

based on the available information, concrete strengths higher than 55 MPa are more

susceptible to spalling and may result in lower fire resistance.

Moisture Content: The moisture content, expressed in terms of relative

humidity, RH, influences the extent of spalling. Higher RH levels lead to greater

regions of spalling. Fire-resistance tests on full scale HSC columns have shown that

59

significant spalling occurs when the RH is higher than 80 percent. The time required

to attain an acceptable RH level (below 75 percent) in HSC structural members is

longer than that required for NSC structural members because of the low permeability

of HSC.

Type of Aggregate: For the two commonly used aggregates, carbonate

mineral aggregate (predominantly limestone) provides higher fire resistance and

better spalling resistance than siliceous mineral aggregate (predominantly quartz).

This is mainly because carbonate aggregate has a substantially higher heat capacity

(specific heat), which is beneficial in preventing spalling.

Concrete Density: The extent of spalling of structural members made with

lightweight aggregate is much greater than concrete made of normal-weight aggregate.

This is mainly because lightweight aggregate contains more free moisture, which

creates higher vapor pressure under fire exposures.

Fire Intensity: High heating rates are critical for the occurrence of spalling.

Spalling of HSC is much more severe than NSC under the same heating rate.

Specimen Dimensions: The risk of explosive thermal spalling increases with

increasing specimen size. This is due to the fact that the size is directly related to the

heat and moisture transport through the structural member. Larger members can store

more energy. Therefore, careful consideration must be given to the size of structural

members when evaluating spalling; fire tests are often conducted on small-scale

specimens, which may provide misleading non-conservative results.

Lateral Reinforcement: The spacing and configuration of ties have

significant effects on the performance of HSC columns. Both closer tie spacing (at

60

0.75 times that required for NSC columns) and the bending of ties at 135° back into

the core of the column, as illustrated in Fig. 2.38, enhance fire performance. The

provision of cross ties also improves fire resistance. Fire tests on HSC columns, with

additional confinement through cross ties and bending of ties back into the core of the

column, have shown that spalling is significantly reduced (Kodur, 1998).

Figure 2.38. Tie configuration for reinforced concrete column: (a) conventional tie

configuration (b) modified tie configuration (Kodur, 1999)

Load Intensity: A HSC structural member loaded in compression will spall

to a greater degree than an unloaded member because the mechanical stress adds to

the thermal stresses, as shown in Fig. 2.22.

2.3.2. Fire scenarios

The idealized fire curves (standard fire curves) based on experience in real

fires are used in fire testing, analysis and design. The standard fire curves differ from

country to country and depend on the structural application. There are three main

categories of fire curves: building, offshore/petrochemical and tunnel fires. Figs. 2.39

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and 2.40 show the standard fire curves ISO 834 (or BS476) and ASTM E119 for

buildings based on typical building fires, the hydrocarbon curve used in the offshore

and petrochemical industries, and the RWS/RABT curves used in tunnels.

Figure 2.39. Standard fire curves for (ISO 834 (or BS476) and ASTM E119) based on

a typical building fire (Grosshandler, 2002)

Figure 2.40. Standard fire scenarios for buildings (ISO 834 or BS 476), offshore and

petrochemical industries (hydrocarbon), and tunnels (RWS, RABT) (Khoury, 2000)

62

The standard furnace curve represents a typical building fire in which the fuel

source is usually wood, paper, fabric, etc. In ISO 834, the temperature increases from

20 ˚C to 842 ˚C after the first 30 min. (i.e., equivalent to an average heating rate of

27.4 ˚C/min). This fire profile has a slow temperature rise up to 1000 ˚C over a period

of 120 min. This curve represents only one possible exposure condition at the growth

and the fully developed fire stages, and does not include the final decay stage. By

comparison, real fires may exhibit a slower or longer growth phase, and once they are

established, the temperatures can be higher than the furnace temperature, though they

are rarely sustained because they are subject to pronounced fluctuations. The standard

temperature–time curve, therefore, corresponds to a severe fire, but not to the most

severe possible fire.

In the 1970s, the Mobil Oil company investigated hydrocarbon fuel fires and

developed temperature–time profiles with a rapid temperature rise in the first 5 min.

up to 900 ˚C (i.e. 176 ˚C/min) and a peak of 1100 ˚C/min. This research laid the

foundation for assessing the performance of fire protection materials in the offshore

and petrochemical industries.

In the Netherlands, the Ministry of Public Works, the Rijswaterstaat (RWS),

and the TNO Centre for Fire Research established a fire curve for the evaluation of

passive protection materials in tunnels. This RWS fire curve simulates the most

severe hydrocarbon fire, rapidly exceeding 1200 ˚C and peaking at 1350 ˚C (melting

temperature of concrete) after 60 min. and then falling gradually to 1200 ˚C at

120 min., the end of the curve. The RWS fire curve was established on the basis of

63

Dutch experience in tunnel fires. However, the maximum temperatures attained in

recent major fires did not reach RWS levels, e.g. Channel (1100 ˚C), Great Belt

(800 ˚C), Mont Blanc (1000 ˚C), Tauern (1000 ˚C). The RWS fire curve, therefore,

represents the most severe form of tunnel fire in terms of initial heating rates and

maximum temperature. The RABT German fire curve in Fig. 2.40, with a descending

branch, represents a less severe fire scenario in tunnels than the RWS fire curve,

reaching a maximum temperature of 1200 ˚C (melting point of some aggregates)

sustained up to one hour before decaying to ambient conditions (Khoury, 2000).

2.3.3. Experimental studies on concrete beams

Sanjayan and Stocks (1991) conducted fire tests with two full-scale T-beams,

one made of high-strength concrete with silica fume (105 MPa) and one made of

normal strength concrete (27 MPa). For both specimens, the length was 2.5 m, the

width of the flange was 1.2 m, the depth of the web from the top surface was 45 cm,

and the width of the web was 25 cm. Different flange thicknesses of 20 cm and 15 cm

were cast for both beam specimens on each side of the web. To study the effect of

reinforcement cover, the cover of steel in the 20 cm flange was 7.5 cm, and for 15 cm

flange the cover was 2.5 cm. In addition, the main bars in the web were staggered

diagonally to obtain reinforcement covers of 2.5, 5.0, and 7.5 cm along the web. The

beams were stored in the laboratory for three and half months prior to testing.

Standard fire scenario ASTM E-119 was used and temperature profiles were obtained

at 2.5, 5.0, and 7.5 cm from the bottom of the web with thermocouples. Weight loss

64

versus time was measured for both specimens while the test was in progress.

Figs. 2.41 and 2.42 show the temperature profiles and weight loss versus time,

respectively.

Figure 2.41. Temperature vs. Time at different locations (Sanjayan and Stocks, 1991)

Figure 2.42. Weight loss vs. Time in the test (Sanjayan and Stocks, 1991)

65

Moisture began to drop from several vertical cracks in both specimens at the

average temperature of 695 ˚C of the furnace (about 15 min. into the test). Explosive

spalling occurred in the 20 cm flange of HSC specimen between 20 min and 40 min.,

but there was no spalling in the web, possibly because the distance for the moisture to

escape was much shorter as compared to the flange due to exposure of three sides of

the web for fire, and because wider flexural cracks existed in the web. However, in

case of NSC, there was no spalling, even though the temperatures inside the NSC

specimen were only slightly lower than in the HSC specimen. The range of spalling is

indicated in Figs. 2.41 and 2.42.

Hansen and Jensen (1995) conducted beam tests using three types of concretes

in the Norwegian Fire Research Laboratory. The test specimens included reinforced

and prestressed concrete beams having dimensions of 150 mm×200 mm×2850 mm.

Three types of concrete were used, normal density concrete, lightweight aggregate

concrete (Liapor aggregate), and lightweight aggregate concrete with fibers (Fibrin

fiber types 1823). The concrete specimens (100 mm×100 mm×100 mm cubes) were

designed to have a target 28-day cube strength of 75 MPa and 95 MPa. In addition,

some beams were provided with a coating of Lightcem concrete (manufactured by

LightCem A/S, Norway) for passive fire protection. Standard bars of quality K500TS

according to the requirements of Norwegian Standard NS 3570 were used as

reinforcement. The longitudinal reinforcement included 20 mm and 32 mm bars, and

8 mm stirrups. For prestressing, 26 mm, Dywidag bars, of the type St 835/1030 were

used. A prestressing force of 300 kN was centrically applied at the ends of the beams,

resulting in a mean prestress of approximately 10 MPa. Fire tests were performed in

66

an oil-heated furnace. The furnace has horizontal exposure openings with dimensions

2.5 m×5.0 m and a depth of 1.5 m. The concrete beams were exposed to a

hydrocarbon fire on three sides. The test procedure was in accordance with ISO 834.

Thermocouples were installed on the longitudinal and shear reinforcement at two

locations in each beam. The beams were exposed to the ISO 834 hydrocarbon fire for

two hours, and the maximum oven temperature reached approximately 1100 ˚C. The

furnace temperature history and the period when spalling was observed are shown in

Fig. 2.43.

Figure 2.43. ISO Hydrocarbon Fire Curve, Furnace Temperature, and Time Period

when Spalling was Observed (Hansen and Jensen, 1995)

The test date obtained in this study showed that (a) severe spalling (exposed

reinforcement) occurred in the high strength lightweight aggregate beams, while

spalling without exposed reinforcement occurred in normal weight density concrete

67

beams; (b) shallow spalling or no spalling was observed for high strength lightweight

concrete beams with fibers; and (c) no spalling was observed for the lightweight

beams with fibers and the passive protective coating.

Deep beams are structural elements loaded as beams in which a significant

amount of the load is transferred to the supports by a compression thrust joining the

load and the support reaction. As a result, the strain distribution is no longer linear

along the depth of the beam, and the shear deformations become significant when

compared to pure flexure. Floor slabs under horizontal load, short span beams

carrying heavy loads, and transfer girders are examples of deep beams. Although a lot

of studies have been conducted on deep beams, the structural behavior of deep beam

is still not completely understood. In particular, the behavior of deep beams when

exposed to high temperatures has not been studied very well.

Figure 2.44. Specimen geometry and thermal cycle (Felicetti and Gambarova, 1999)

Felicetti and Gambarova (1999) conducted high temperature deep beam tests

with high strength concrete using siliceous aggregate (predominantly quartz), which

is weaker than carbonate aggregate in terms of fire resistance. The purpose of the

study was to find whether the deep beam fails in bending, shear-bending or shear-

68

compression in a high-temperature environment. Fig. 2.44 shows specimen geometry

and thermal cycle used in their tests.

(a) Siliceous HSC (b) Calcareous HSC (c) Typical NSC

Figure 2.45. Strength of the three mix designs (Felicetti and Gambarova, 1999)

Compression tests and tension tests were conducted prior to the deep beam

experiment. Fig. 2.45 shows compression and tensile strength values for three kinds

of concretes after a temperature cycle as the ratio 20Tc cf f and 20T

ct ctf f . The residual

strength decreased with increasing target temperature in all tests. The test results of

typical NSC were very interesting, in which the compressive strength at high

temperature was higher than that measured after cooling down to room temperature

(i.e. after a thermal cycle). Little difference between the “hot” and “cold residual”

tensile strength was found under slow cooling condition of the residual specimens.

However, no explanation was provided about these results.

To determine the crack pattern in the beam tests, the back face of the beams

was covered with Moiré grid having 40 vertical lines/mm, and a “reference” grid

(40.1 lines/mm) was superimposed. In this way, the interference between the distorted

grid glued to the specimen and the reference grid produced a fringe pattern with a

69

sensitivity of 1/80 mm. Cracks appear as discontinuities in the fringe patterns.

Fig. 2.46 shows fringe pattern and cracking of specimen at T=20 ˚C, and Fig. 2.47

shows the extent of cracking at failure by mechanical load after one cycle heating up

to 500 ˚C. Fig. 2.48 shows load-displacement curves at the bottom face of mid span

and the crack patterns.

Figure 2.46. Fringe pattern and cracking of specimen at T=20 ˚C

(Felicetti and Gambarova, 1999)

Figure 2.47. Cracking at failure by mechanical load after one cycle heating up to

500 ˚C (Felicetti and Gambarova, 1999)

70

Figure 2.48. Load-displacement curves at bottom face of mid span and crack patterns

(Felicetti and Gambarova, 1999)

The load-displacement diagrams show a marked decay of the mechanical

behavior after a high temperature cycle. However, up to the 400 °C cycle the ultimate

load capacity (peak load) was only marginally affected, while the stiffness was more

temperature-sensitive. Above 400 °C the load capacity decreased dramatically, and

the overall behavior became very ductile. Such occurrence is certainly not ascribable

to the reinforcement, but to the loss of compressive strength in the concrete. In their

test results, the collapse mode was mostly in the form of bending (20 °C and 250 °C)

or shear-bending (400 °C). Under the heating condition 500 °C the beam exhibited a

completely different behavior, since the mechanical decay of the mortar was

accompanied by chemo-physical transformations in the highly siliceous aggregates,

whose color and surface turned from white to red, and from glossy to opaque, with

many particles split, owing to the expulsion of the bound water. In the end, failure

was triggered off by the lack of compressive strength in one of the inclined struts.

The experimental evidence showed that different ultimate behaviors may

occur, depending on the severity of the thermal cycle. Three models were considered

71

in their paper (see Fig. 2.49). The first refers to the bending failure which assumes

linearity of the strain distribution in the mid-span section (which is consistent with the

actual value of the ratio h/L ≈ ½); the second refers to the shear-compression failure,

and is based on a strut-and-tie resistant system; and the third predicts the shear-

bending failure, assuming an inclined shear plane (beam-end model).

Figure 2.49. (a) Flexural model; (b) strut-and-tie model; (c) beam-end model

Figure 2.50. Comparison of failure models (Felicetti and Gambarova, 1999)

72

The comparison between the test results and the three models is shown in

Fig. 2.50. The temperature level T = 400 °C forms a threshold condition. Below this

value bending failure (flexural model) is the only failure mode, while above this value

other failure modes become more or equally probable. Between 400 °C and 450 °C

bending (flexural failure mode) and shear-bending modes (beam-end mode) seem to

be equally probable. The high reduction of the compressive strength above 300 °C

results in a downward trend of the ultimate load capacity of the strut-and-tie

mechanism. The shear-compression mode (strut-and-tie model) becomes as probable

as the other two failure modes after a cycle at 450 °C. Above 450 °C, the deep beam

tends to fail definitely in shear-compression.

2.3.4. Experimental studies on concrete columns

Diederichs et al. (1995) reported that the use of fibers helps to reduce spalling

in HSC columns and suggested that further studies be conducted on the effects of

fiber contents.

The document ENV 1992-1-2 (Structural fire design developed by European

Commission for Standardization (CEN)) is essentially based on tabulated data

containing the dimensions of the cross sections and values for the concrete cover.

Dotreppe et al. (1996) conducted experimental studies on the determination of the

main parameters affecting the behavior of reinforced concrete columns under fire

conditions. The parameters used were the load level, the dimensions of the cross

section, the length of columns, the main reinforcement, the concrete cover and the

73

eccentricity of the axial load. The concrete mix design used in the test program is

summarized in Table 2.5.

Table 2.5. Mix design (Dotreppe et al., 1996)

Gravel 4/14 1100 kg Coarse sand 800 kg Cement P40 280 kg

Water 185 kg

The fire resistance tests were performed according to the Belgian Standard

NBN 713.020 and the columns were exposed to fire on four sides. The support

conditions of the columns were hinges at both ends. The dimensions of the cross

section were: 200 mm×300 mm, 300 mm×300 mm, and 400 mm×400 mm. The

column lengths were 3.95 m and 2.10 m. Concrete covers of 25 mm, 35 mm, and

40 mm were used. Eccentricities of (-20 mm, 20 mm), (20 mm, 20 mm), and (0 mm,

0 mm) were used with respect to the central axis of the 300 mm×300 mm cross

section.

Experiments on 3.95 m high columns were performed at the University of

Ghent. Fig. 2.51 shows the furnace used for the tests on the RC columns at the

University of Ghent. The 2.10 m high column experiments were performed at the

University of Liège. Fig. 2.52 shows the furnace used for the tests on columns at the

University of Liège. Longitudinal reinforcing bars of 12, 16, and 25 mm in diameter

were used (see Dotreppe et al., 1996 for detailed information). Although the type and

arrangement of stirrups was not a parameter, buckling of some individual longitudinal

reinforcements may occur between two stirrups at column failure.

74

Figure 2.51. Furnace used for tests on columns at the University of Ghent: (a) Overall

view (b) Detail of top hinge and load cell (2000 kN) (c) Detail of bottom hinge

(measurements in millimeters) (Dotreppe at el., 1996)

Figure 2.52. Furnace used for tests on columns at the University of Liège: (1) Lower

transverse beam (2) Jack with double effect (3.1) Lateral support (3.2) Supports

perpendicular to frame plate (4) Load cell (5) Upper transverse beam (6) Support for

upper transverse beam (7) Furnace (8) Crossing column (Dotreppe at el., 1996)

75

Therefore, decreasing the spacing between stirrups might improve the

behavior of the column under fire conditions, however theoretical and experimental

research should be performed in order to quantify this effect. A summary of the test

results follows:

- In all problems involving fire resistance, the load level (column stress) is the

most important factor. The fire resistance decreases when the load increases.

- The dimensions of the cross section influence the fire resistance. The fire

resistance of 200 mm×300 mm sections was between 1 hour and 2 hour, while in

most of the 300 mm×300 mm sections the fire resistance was greater than 2 hours.

However the applied load must be limited and reinforcement with large diameters

rebars should be avoided.

- In the case of 400 mm×400 mm columns, the fire resistance time was

appreciably shorter than expected. For one of the columns, the fire resistance time

was shorter than 1 hour, and for the other, the fire resistance time was between 1 hour

and 2 hours. These inconsistent results may be partly explained by the existence of

reinforcement with large diameters in one case, and by the use of a section with large

dimensions and small concrete cover in both cases.

- The increase of column length had a negative influence on column failure at

normal as well as at high temperature because of geometrically nonlinear effects.

- In principle, the increase of the concrete cover should result in an increase of

the fire resistance or of the admissible load level, since the temperature in the main

reinforcement increases less rapidly when the column begins to deflect laterally. The

76

test results showed that the increase of concrete cover had a positive effect on the fire

resistance.

- The use of eight 16 mm diameter reinforcement instead of four 25 mm

diameter reinforcement showed a positive effect on the fire resistance in terms of

strength. But, additional tests on columns involving reinforcing with large diameter

bars are still required to clarify the effect of the bar diameters of longitudinal

reinforcement.

- Test results of eccentrically loaded columns (-20 mm, 20 mm) and

(0 mm, 0 mm) showed approximately the same failure results. On the contrary, the

use of eccentricities (20 mm, 20 mm) exhibited a decrease of the load capacity levels.

(a) NSC column (b) HSC column

Figure 2.53. NSC and HSC column after ASTM E119 fire tests (Kodur, 1999)

77

Kodur (1999) conducted an experimental study to compare the fire resistance

of NSC and HSC columns. He also proposed guidelines for improving the fire

resistance of HSC structural members. Tests were performed under both laboratory

and actual fire conditions. Fig. 2.53 shows the conditions of HSC and NSC columns

after concluding the fire resistance tests. In the HSC column, the reinforcement (both

longitudinal and transverse) is completely exposed and there is significant spalling.

However, there was no spalling in the NSC column. Since spalling occurs during the

initial stage of fires in HSC columns, it may pose a risk to evacuating occupants and

firefighters. As discussed in Chapter 2.2, spalling is attributed to the building up of

pore pressure during heating. HSC is believed to be more susceptible to this pressure

build-up because of its low permeability.

Figure 2.54. Temperature distribution at various depths in NSC and HSC columns

(Kodur, 1999)

78

Figure 2.55. Axial deformation histories of NSC and HSC columns during fire

exposure (Kodur, 1999)

Fig. 2.55 shows that the axial deformation of the HSC column is significantly

lower than that of the NSC column. This can be explained in part by the lower

thermal expansion of HSC and the slower rise in temperature in the HSC column

during the initial stages of fire exposure due to the compactness of HSC. As the

temperature is continuously rising, the steel reinforcement in the NSC column and the

HSC column gradually reaches the yield capacity and the RC column contracts.

When this happens, the concrete carries a progressively increasing portion of the axial

load. The strength of the concrete also decreases with time and, ultimately, when the

column can no longer support the load, failure occurs. At this stage, the column

behavior depends primarily on the strength of concrete. There is significant

contraction in the NSC column leading to gradual (ductile) failure. The lower

contraction in the HSC column can be attributed to the fact that at elevated

79

temperatures HSC becomes brittle and loses strength faster than NSC. For the NSC

columns, the fire resistance time to failure was approximately 366 min, while for

HSC column it was 225 min (Kodur, 1999).

2.3.5. Experimental studies on concrete slabs

Di Prisco et al (2003) conducted tests to study the thermal and mechanical

behavior of plain concrete slabs and steel fibers reinforcement concrete slabs, SFRC.

The concrete were loaded mechanically and then exposed to a standard fire up to

failure.

Figure 2.56. Position of thermo couples and load set-up (di Prisco et al., 2003)

80

The size of the slab specimens was 1800 mm× 600 mm× 60 mm. The purpose

of these tests were (a) to find thermal parameters of SFRC as compared to the plain

concrete, and (b) to obtain data on the structural behavior under fire which can be

used as a reference to validate computational models. Fig. 2.56 shows the furnace, the

position of thermo couples and the load set-up of the slab experiments. Fig. 2.57

compares the standard time-temperature curve and the actual heating curves in the

three furnace compartments. In the experiments, the actual mean temperature-time

curve was satisfactorily close to the standard heating curve (ISO 834). The

temperature dips in Test 2 and Test 3 occurred by a temporary flame-out of the

burners due to debris falling from the specimens.

Figure 2.57. Comparison between the standard time-temperature curve and the actual

heating curves (di Prisco et al, 2003)

Fig. 2.58 shows on the left the temperature distribution at different depth

levels inside Test 1-SFRC slab (unloaded). At the right it illustrates the vertical

displacement of the SFRC slab as compared to the plain-concrete slab under time-

temperature conditions (Test 2 and Test 3) and application of a bending moment that

81

corresponds to some portion (11, 24, and 40 percent, di Prisco et al., 2003) of the

ultimate bending moment at the reference temperature. The experiments were aimed

at quantifying the time required to failure for different levels of mechanical loading.

The temperature distribution curves at different depths of the SFRC slab show

parabolic trends, which are similar to the actual heating curve (Fig. 2.57, Test 1). The

SFRC slab was more ductile than the plain concrete slab due to the addition of steel

fibers. The performance of the test slabs during the temporary flame-out of the

burners was not jeopardized, as indicated in Fig. 2.58 (under load).

Figure 2.58. Temperature distribution according to depth inside SFRC slab and

vertical displacement of SFRC and plain concrete slabs (di Prisco et al, 2003)

Fig. 2.59 shows the mean value of the load-displacement curves of the SFRC

slabs (using low carbon fibers) in 4-point bending in the virgin state and after

exposure to high temperature (T = 600 ˚C) but tested after cooling. The temperature

effects under hot and residual test conditions were very large as compared to the

flexural test performed at room temperature. The fire resistance after cooling was

slightly higher than that at high temperature. However, the general behavior of the

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SFRC slab did not exhibit a large difference between residual and hot testing as

shown in Fig. 2.59.

Figure 2.59. Virgin, hot and residual load-deflection of slabs (di Prisco et al, 2003)

Foster et al. (2004) conducted an investigation on the influence of thermal

curvature on the failure mechanisms of rectangular slabs. The loading frame and test

set-up are shown in Fig. 2.60. Fig. 2.61 shows the heating elements and the

supporting frame.

To satisfy similar boundary conditions to slabs used in the eight story steel

structure tested at the Cardington Laboratory (see Fig. 2.37), the slab was placed on a

supporting frame, providing vertical support around the perimeter. The four corners

of the slab were loosely clamped to restrain the vertical upward movement without

restraining the horizontal movement at the support edges. The applied load remained

vertical with the aid of ball-joints which allowed the loading system to rotate as the

slab deflected.

83

Figure 2.60. Loading frame and test set-up (Foster et al., 2004)

Figure 2.61. Supporting frame and heating elements (Foster et al., 2004)

Fig. 2.62 shows the locations of the applied loads and displacements gages

(horizontal and vertical displacement). The slabs were reinforced with smooth or

deformed (ribbed) steel wire meshes which were arranged isotropically. The

deformed wire was made by indenting the smooth wire using a purpose-built machine.

Fourteen slabs were used for testing and one of them was used to obtain a

temperature profile without loading.

84

Figure 2.62. Locations of loads and displacements gages (Foster et al., 2004)

Fig 2.63 shows the temperature history profile at different positions at each of

the three levels through the thickness of the slab tested without mechanical loading.

Figure 2.63. Temperature profiles (Foster et al., 2004)

Thirteen slabs were loaded before the heating elements were switched on. The

formation of yield lines was depending on the applied load level. After the initial slab

85

deflected into double curvature a crack was generated across its short span through

the full-depth. Thereafter a less distinctive yield line mechanism developed at high

temperature which resulted into significant thermal bowing. All slabs behaved

similarly.

(a) Yield line mechanism

(b) Topside (c) Bottom

Figure 2.64. Yield line mechanism and crack patterns (Foster et al., 2004)

Approximately 15 min. after the furnace was switched on, diagonal cracks

occurred across the corners as the slab deflected into double curvature. After 20 min.,

a single transverse crack could be seen forming on the topside of the slab in its central

86

region. Over time this crack developed outwards in the short-span direction towards

the long edges of the slab (Fig. 2.64 (b)). Most of the slabs developed crack patterns

resembling a yield line mechanism towards the end of the test, usually occurring after

2 hours. The crack patterns resemble those of similar slabs tested at ambient

temperature.

The mid-span deflections for the tested specimens are shown in Fig. 2.65. The

rate of deflection of the slab reinforced with smooth wires (Test 13) was less than the

equivalent slab using deformed wires (Test 12). The reinforcing bars across the large

tensile cracks were exposed to high temperature early on. These results imply that

slabs reinforced with smooth wire meshes perform better than those reinforced with

deformed wire meshes.

Figure 2.65. Mid-span deflections for the tested slabs (Foster et al., 2004)

87

CHAPTER 3

3. AN EXPERIMENTAL STUDY FOR THERMO-HYGRO COUPLING EFFECT

OF CONCRETE AT ELEVATED TEMPERATURE

3.1. Introduction

At elevated temperature, the thermal strain of concrete is related to changes of

both temperature and moisture. The measurements of thermal expansion of solid

materials in ASTM [ASTM E 831-03, C 531-00, and E 228-95] are obtained by

measurement of the displacement change of the material in accordance with

temperature change from initial temperature up to a target temperature without

moisture control. Usually, the thermal strain of concrete (CTS), is obtained by

measurement of the displacement change without moisture control.

It is not easy to experimentally measure the temperature effect and moisture

effect on strain separately over time. In this experimental study, CTS, the strain

caused by temperature increase under constant humidity (PTS), and the strain caused

by moisture change under constant temperature (PHS) are measured continually and

simultaneously over time. The maximum temperature in the chamber, which can

control both humidity and temperature simultaneously, is 80 °C. Since high heating

88

rates will lead to large specimen temperature gradients, a low heating of rate

0.1 °C/min is used for the test. The objectives of this experimental study can be

explained as follows.

The first objective is to measure the strain as the temperature and humidity

changes continually and simultaneously over time. It appears that there has been no

experimental study adopting such a testing method. The second objective is to

examine the difference between CTS and PTS experimentally. The third objective is

to identify the thermo-hygro coupling effect based on test data and analysis.

3.2. Experimental details

3.2.1. Material and mixture portion

Only one aggregate (granite) is used for this test. With respect to density

aggregates are classified as light weight (less than 1120 kg/m3), normal weight (1520-

1680 kg/m3) and heavy weight aggregates (larger than 2080 kg/m3). Most of normal

weight aggregates such as limestone and granite are classified as natural mineral

aggregate. For this experiment, granite is chosen over limestone due to the advantages

of being more durable and the fact that it readily bonds to concrete mix. Fig. 3.1

shows the granite sand and gravel used in the research. Table 3.1 shows typical

proportions of materials for producing low, moderate, and high-strength concretes

using normal-weight aggregates. Among the three mix designs, the moderate-strength

mix design is used for the present test. However, the water/cement (w/c) ratio used

89

for this experiment is different (0.71 by weight) from the table because the

workability could not be obtained from the mix design; this is due to dry aggregates

and the non-negligible contents of very fine size aggregates in crushed granite sand.

Figure 3.1. Granite sand and gravel

Table 3.1. Typical proportions of materials for normal weight concretes

To calculate the real w/c ratio considering moisture contents of the aggregates,

the oven dry (OD) and saturated surface dry (SSD) moisture contents are measured.

The test for OD moisture content follows test method B in ASTM D 2216. The

moisture contents for OD and SSD are calculated by Eqs. (3.1) and (3.2).

90

(%)100)]/()[()( ×−−= ccdscdscms MMMMODMC (3.1)

(%)100)]/()[()( ×−−= ccsscsscms MMMMSSDMC (3.2)

Where )(ODMC is the moisture content based on oven dry (%), )(SSDMC is

the moisture content based on saturated surface dry (%), cmsM is the mass of

container and moist aggregates (g), cssM is the mass of container and saturated

surface dry aggregates (g), cdsM is the mass of container and oven dry aggregates (g),

and cM is the mass of container (g).

)(SSDMC and )(ODMC obtained from above equations are -0.36 % and

0.42 % respectively. The negative value of )(SSDMC means that pores in the

concrete are partially filled with water. Absorption capacity (AB) for the aggregates

is then calculated by Eq. (3.3). Absorption capacity is a measure of the mount of

water in pores.

( ) 100 (%) /SSD OD ODAB W W W= − × (3.3)

In which, SSDW is the unit weight of aggregates in saturated surface dry and

ODW is the unit weight of aggregates in oven dry. The absorption capacity of

aggregates is about 0.78 %. By subtracting the water absorption capacity of the

aggregates from original water content, the finalized real w/c ratio is 0.67 by weight.

The maximum size of coarse aggregates is 3/8 inch.

91

3.2.2. Specimen preparation and test equipments

Fig. 3.2 shows the relative humidity variation over time measured at the center

of a 2×4 inch cylinder and a 4×8 inch cylinder under standard room conditions.

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100Time (Days)

RH

(%)

2*4 cyinderical specimen

4*8 cylinderical specimen

Figure 3.2. Relative humidity of 2×4 in. and 4×8 in. cylinder vs. Time

Using a 2×4 inch cylindrical specimen reduces the testing time because of the

rapid humidity reduction ratio compared with 4×8 inch cylindrical specimen, as

shown in Fig. 3.2. Four specimens are used for each test. Two specimens are used to

measure relative humidity and temperature from a sensor embedded at center of each

specimen. Two other specimens are used to measure the strain from two strain gages

attached on surface of each specimen.

The model SHT 75 sensor and EK-H3 data logger produced by SENSIRION

as shown in Fig. 3.3 are used to measure temperature and relative humidity. The

92

sensor can measure both temperature and relative humidity simultaneously. The

capacities of the sensor recommended by the manufacturer are 0-100 % for relative

humidity and -40-120 ˚C for temperature. The strain gage (Model N2A-06-20CBW-

120) by VISHAY and the data logger (Model CR10X) by CAMBELL SCIENTIFIC

are used to measure strain.

Figure 3.3. SHT 75 sensor and EK-H3 data logger

In the specimens with a sensor, a plastic tube is used to keep the sensor settled

in center of the specimen because the simple cable connection is too loose for the

purpose of this experiment. The cable is inserted through the plastic tube until the

sensor connected to the cable reaches the other side, then the gap between the cable

and tube on end sides of the tube are sealed using sealant (with temperature resistance

up to 200 ˚C) to prevent moisture and temperature loss through the tube. The sensor is

wrapped with GORE-TEX fabric to protect it from being damaged from concrete

paste. Fig. 3.4 shows the plastic tube built with the cable and sensor, and the 2×4 inch

cylindrical specimen embedded with a sensor. The specimens are cured in a curing

room (Temp. 24 ˚C and RH 92 %) for 28 days.

93

Figure 3.4. Plastic tube built with the cable and sensor and 2×4 inch cylindrical

specimen embedded a sensor at center

Figure 3.5 Equipments and test set up

The RUSSELLS environmental chamber (Model RD-5-1) is used to control

relative humidity and temperature. The temperature and humidity control range of the

chamber is from -30 ˚C to 177 ˚C and 0 % to 95 % respectively. Fig. 3.5 shows the

equipments and test set up.

94

3.2.3. Thermal compensation function and verification for test method

The data obtained from the strain gage require thermal compensation because

the grid alloy used on the strain gage also changes with temperature. The strain gage

used is a resistance strain gage. Since the gage grid is made from a strain-sensitive

alloy, the resistance change of the strain gage is also proportional to the thermally

induced strain. The strain function with thermal compensation for concrete is

obtained from the following derivation.

When the thermal expansion coefficient of the gage grid is different from that

of a specimen used for the test, the net resistance change of the gage for temperature

can be expressed as follows:

TFRR

GSGGo

∆⋅−⋅+=∆ )]([ ααβ (3.4)

In which, oR R∆ is the net resistance change of gage, Gβ is the thermal

coefficient of resistivity of grid material, )]24(1[ CTcFF RG °−+= (gage factor as

calculated in an uniaxial stress state), 61.2 10 /c C−= × (temperature coefficient of

gage factor), RF is the gage factor at room temperature 24°C (given as 2.1 by

manufacturer), GS αα − is the difference in thermal expansion coefficients between

specimen and grid, and T∆ is the temperature change from arbitrary initial reference

temperature. Thus, thermal output in strain units is expressed by Eq. (3.5).

95

I

GSGG

I

oSG F

TFF

RRT

∆⋅−⋅+=

∆=

)]([/)( /

ααβε (3.5)

In which, SGT /)(ε is the thermal output for grid gage G on specimen material

S and IF is the instrument gage factor setting employed in recording thermal output

data (2.0 for all alloy gages). From Eq. (3.5), the thermal outputs of the concrete and

1018 steel are:

I

GCONCRETEGGCONCRETEG F

TFT

∆⋅−⋅+=

)]([)( /

ααβε (for concrete) (3.6)

I

GSTEELGGSTEELG F

TFT

∆⋅−⋅+=

)]([)( 1018

1018/

ααβε (for 1018 steel) (3.7)

By subtracting thermal output of the 1018 steel from that of the concrete, the

thermal strain function of the concrete with thermal compensation is expressed as

Eq. (3.8).

TTTFF

T STEELSTEELGCONCRETEGI

GCONCRETE ∆⋅+−= 10181018// ])()([)( αεεε (3.8)

The coefficient of thermal expansion of 1018 steel is C°× − /1012 6 and

STEELGT 1018/)(ε is given from the thermal output data sheet of the strain gage tested on

1018 steel provided from the manufacturer.

96

To verify the thermal compensation function and test method, the thermal

expansion of aluminum is tested with the same strain gage (model N2A-06-20CBW-

120) as the concrete test. The range of the coefficient of thermal expansion for

aluminum is from 61021 −× to C°× − /1025 6 .

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250

Time (hrs)

RH

(%) &

Tem

p (C

)

0

200

400

600

800

1000

1200

1400

1600

Stra

in (x

10-6

)

Temp (Chamber)RH (Chamber)Aluminum Strain

Figure 3.6. Temp, RH and Strain vs. Time (Aluminum)

Fig. 3.6 shows the result of the aluminum thermal expansion test. The

aluminum sample is equilibrated to ambient temperature inside the chamber (about

28 °C) and then the temperature inside the chamber is increased up to 80 °C without

moisture control. Fig. 3.6 shows the change of the ambient temperature, relative

humidity inside the chamber, and aluminum thermal strain over time. The coefficient

of thermal expansion of the aluminum, from the thermal compensation function, is

found to be C°× − /105.22 6 which falls in the known range given above.

97

3.3. Test results and discussion

3.3.1. Conventional Thermal Strain (CTS) and Pure Hygro Strain (PHS)

As mentioned earlier, temperature and humidity histories at the center of the

specimens and inside the chamber are measured over time. The strains of the concrete

specimens are measured from the surfaces of the concretes because setting-up strain

gages in the center of specimens is not possible. The strain of the specimens are

measured under temperature control (heating rate 0.1 °C/min and maximum

temperature 80 °C) without humidity control inside the chamber. After 28 days of

curing, the relative humidity of the specimens in the curing room is about 92 % at

24 °C. The specimens are taken out of the curing room and left in the laboratory until

the relative humidity measured at the center of the specimens reaches the target

relative humidity of 70 % at 24 °C. Then, the specimens are placed in the chamber

and kept for 4-5 days allowing them to reach thermal equilibrium at an ambient

temperature of about 28 °C. After the equilibrium state is reached, the temperature

inside the chamber is increased to the target temperature of 80 °C at a rate of

0.1 ˚C/min without humidity control.

Fig. 3.7 shows the histories of relative humidity and temperature inside the

chamber. Relative humidity (RH) is expressed as the ratio of the partial vapor

pressure to the saturated vapor pressure [see Eq. (3.9)].

98

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250

Time (hrs)

RH

(%) &

Tem

p (C

)

Temp (Chamber)

RH (Chamber)

Figure 3.7. Temperature and RH inside the chamber vs. Time (No humidity control)

satv

v

vsatv

vv

satv

v

PP

RTwP

RTwP

RH,,,

===ρρ

(3.9)

In which, vρ is the vapor density, satv,ρ is the saturated vapor density, vP is

the partial vapor pressure, ,v satP is the saturated vapor pressure, vw is the molar mass

(molecular mass) of water vapor, R is the universal gas constant, and T is the

temperature in Kelvin. The saturated vapor pressure is a temperature function that is

the maximum amount of humidity air can hold at the specific temperature. The

saturated vapor pressure increases exponentially as the temperature increases in a

closed system, therefore the increase of the temperature generally leads to the

decrease in relative humidity as shown in Fig. 3.7.

99

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250

Time (hrs)

RH

(%) &

Tem

p (C

)

-400

-200

0

200

400

600

800

1000

1200

Stra

in (x

10-6

)

Temp (Specimen)RH (Specimen)Strain_average

Figure 3.8. Temperature, RH and strain history vs. Time (No humidity control)

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250

Time (hrs)

RH

(%) &

Tem

p (C

)

-400

-200

0

200

400

600

800

1000

1200

Stra

in (x

10-6

)

Temp (Chamber)RH (Chamber)Temp (Specimen)RH (Specimen)Strain_average

Range B

Range A Range C

Figure 3.9. RH, temperature, and strain history vs. time (No humidity control)

100

0

1

2

3

4

5

170 180 190 200 210

Time (hrs)

RH

(%) &

Tem

p (C

)

RH (Chamber)

RH (Specimen)

Figure 3.10. Part C magnified in Fig. 3.9.

Fig. 3.8 shows the histories of the internal temperature and internal relative

humidity at the center of the specimen, and the strain on the surface of the specimen.

Comparing Fig. 3.8 with Fig. 3.7, one can see that when the temperature increases,

the chamber RH decreases in Fig. 3.7, while the internal RH of the specimen

increases. Fig 3.9 is the overlap plot of Fig. 3.7 and Fig. 3.8, which shows the two

opposite RH variations more clearly. The heating period in Fig. 3.9 is called Range A,

in which the internal relative humidity of the specimen increases with temperature

increase. After Range A, it is Range B in which the temperature is kept constant and

the internal RH decreases. Range C follows Range B, which is magnified and shown

in Fig. 3.10. In Range C, when the temperature drops the internal relative humidity in

the concrete drops, too. These three ranges in Fig. 3.9 need more detailed explanation.

Range B shows the diffusion process of the internal RH under constant

temperature. The diffusion of moisture is driven by the moisture gradient (i.e. higher

internal RH in the concrete and lower external RH in the chamber). The measured

101

strain in Range B is the Pure Hygro Strain (the so-called true shrinkage strain without

the effect of thermal expansion). In Range A and Range C, the internal relative

humidity in concrete is changed in proportion to the temperature variation. The

experimental study for hardened cement paste by Grasley and Lange (2004) shows

the same trend, that the internal relative humidity in hardened cement paste increases

as temperature increases. The variation of internal RH in Range A and Range C

cannot be explained simply based on Eq. (3.9), which is valid in a large closed system

and not suitable for porous material with very small pores. To this end, the

relationship between RH and temperature in porous medium needs to be introduced.

For temperatures below the critical point of water (374.15 °C), concrete is

distinguished as saturated and nonsaturated concrete. But, for higher temperature

there is no such distinction because the liquid phase does not exist (Bažant, 1996). In

a partially saturated pore system, if it is assumed that a local thermodynamic

equilibrium always exists between the phases of pore water (vapor, liquid) within a

very small element of concrete, the static force equilibrium based on a capillary tube

model is expressed with Eq. (3.10) [see APPENDIX A for detailed explanation].

2 cos( ) sa w

TP Pr

ασ ⋅= − = (3.10)

In which, ( )a wP P− , called suction, is the pressure difference between air and

water in a pore, sT is the surface tension of the pore fluid, r is the average radius of

meniscus, and α is the contact angle between air and water.

102

While mechanical equilibrium is expressed by Eq. (3.10), physicochemical

equilibrium between the vapor and liquid is satisfied according to the Kelvin equation,

Eq. (3.11) [see APPENDIX A].

2 cos ln( )s

w

T RT RHr v

α⋅= − (3.11)

In which R is the universal gas constant and wv is the molar volume of water.

Thus, the relative humidity in a partially saturated porous medium from Eq. (3.10)

and (3.11) is expressed by Eq. (3.12).

( - ) 2 cosexp - exp -a w w s wP P v T vRHRT r RT

α⎛ ⎞ ⎛ ⎞= = ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(3.12)

Eq. (3.12) has been widely used to describe the relationship of temperature

and relative humidity in partially saturated pore systems such as partially saturated

soil (Lu and Likos, 2004), cement paste, and concrete [Power and Brownyard (1947),

Bažant (1996), Grasley and Lange (2004)]. From Eq. (3.12), it can be seen that under

constant ( )a wP P− (or sT , α , and r ), when temperature increases, the RH in

concrete increases. However, ( )a wP P− (or sT , α , and r ) depends on temperature.

When temperature increases, water expands (swelling pressure), which means that

( )a wP P− decreases, the surface tension ( sT ) of water decreases, the contact angle

(α ) increase, cosα decreases, and the radius of the meniscus curvature increases

103

(Power and Brownyard, 1947). All these changes in sT , α , and r lead to an increase

in internal RH in concrete, which is the same as the direct effect of increasing T in

Eq. (12). Fig. 3.11 shows a schematic for dilatation of solid microstructure induced

by a decrease of capillary tension with a temperature increase.

Soild Soild

Swelling Pressure

RH= 50%

Water Soild Soild

Swelling Pressure

Water

Increasing temperature

RH= 80%Capillary tension

Capillary tension

Soild Soild

Swelling Pressure

RH= 50%

Water Soild Soild

Swelling Pressure

Water

Increasing temperature

RH= 80%Capillary tension

Capillary tension

Figure 3.11. Dilatation of solid microstructure induced by decrease of capillary

tension with temperature increase

Figure 3.12. Length change of Portland cement paste specimens at elevated

temperature: (a) Philleo (1958); (b) Harada et al. (1972); (c) Cruz and Gillen (1980);

Crowley (1956)

104

Figure 3.13. Linear thermal expansion of various rocks at elevated temperature: (a)

sand stone; (b) limestone; (c) granite; (d) anorthosite; (e) basalt; (f) limestone; (g)

sandstone; (h) pumice (Soles and Gellers, 1964)

Under the same concept Dettling (1964) attributed the initial expansion (see

Fig. 3.13) of hardened cement paste, up to about 150 °C, to kinetic molecular

movements in the paste plus an increase of swelling pressures. When we consider the

relationship between temperature and strain for aggregates and hardened cement paste

as components of concrete, it is clear that the internal relative humidity (RH) of

concrete increases as temperature increases.

Fig. 3.12 and 3.13 show the length change of hardened cement pastes and

aggregates at elevated temperature, respectively. Almost all of the aggregates expand

as the temperature increases up to about 800 °C. While initially the hardened cement

pastes expand when heated to about 150 °C, beyond 150 °C the hardened cement

pastes shrinks. This means that there is no shrinkage of concrete by dehydration (a

105

decrease of relative humidity) during heating up to about 150 °C. It is also expected

that the shrinkage effect due to a decrease in internal relative humidity (dehydration)

of cement is contained in the overall expansion of concrete beyond 150 °C.

0

100

200

300

400

500

600

20 30 40 50 60 70 80

Temperature (C)

Stra

in (x

10-6

)

CTSCTS_Linear

Figure 3.14. Conventional thermal strain by temperature increase from 28 °C to 70 °C

Fig. 3.14 shows CTS at elevated temperatures from 28-70 °C from Range A

in Fig. 3.9. The CTS curve in Fig. 3.14 is not exactly linear because of the moisture

effect. Pure Hygro Strain (PHS), which is the moisture effect under constant

temperature measured in this study, is nonlinear. For temperatures ranging of 28-

70 °C, the linear function for the CTS is expressed as Eq. (3.13). T is the temperature

in Celsius.

( ) 612.85 359.8 10CTS Tε −= ⋅ − ⋅ for 28 70C T C≤ ≤ (3.13)

106

From Range B in Fig. 3.9, Pure Hygro Strain (PHS) under constant

temperature 77.5 °C is plotted in terms of internal relative humidity of concrete in

Fig. 3.15. In Range B, the fluctuation range of the internal temperature of concrete is

77.5 0.5C ± . The PHS function in terms of RH (%) from curve fitting is expressed

as Eq. (3.14). For RH 5-84 % at constant temperature 77.5°C, the PHS is:

11 4 9 3 7 2

7 7

3 10 ( ) 7 10 ( ) 5.463 10 ( )

1.953 10 ( ) 7.614 10PHS RH RH RH

RH

ε − − −

− −

= − ⋅ + ⋅ − ⋅

+ ⋅ − ⋅ (3.14)

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90

RH (%)

Stra

in (x

10-6

)

PHS_constant temperature 77.5C

Figure 3.15. Pure-Hygro Strain (PHS) under constant temperature 77.5 0.5C ±

Theoretically, PHS should be linear with respect to humidity under constant

temperature. An interesting result is that the PHS according to humidity increase is

nonlinear. It is difficult to explain the trend clearly. The measurement for the strain

107

caused by humidity loss under constant room temperature shows the same result, that

the strain caused by humidity loss is nonlinear.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700

Time (hrs)

RH

(%) &

Tem

p (C

)

-400

-200

0

200

400

600

800

1000

1200

1400

Stra

in (x

10-6

)

Temp (Room)RH (Room)Temp (Specimen)RH (Specimen)Strain_average

Figure 3.16. RH, temperature, and strain history vs. time

-300

-250

-200

-150

-100

-50

0

30 35 40 45 50 55 60 65 70 75 80RH (%)

Stra

in (x

10-6

)

Strain_average

Trend line

Figure 3.17. Shrinkage strain according to internal RH decrease of concrete under

constant temperature 24.5 °C

108

Fig. 3.16 shows the strain due to humidity loss under constant room

temperature 24.5 ˚C. The strain versus internal relative humidity in concrete is plotted

in Fig. 3.17. The strain, which is measured on the surface of the specimen, shows

fluctuation relative to violent fluctuation of the relative humidity curve of the

laboratory room. From the trend line in Fig. 3.17, it is shown that the strain due to

humidity loss under constant room temperature 24.5 ˚C is also nonlinear. It is likely

linked to complicated physiochemical reactions in concrete with humidity change.

3.3.2. Pure Thermal Strain (PTS)

PTS is measured using dried specimens. Prior to the test the specimens are

dried in an oven at a constant temperature of 102 °C for 3 days. The specimens are

then left in standard room conditions to come to equilibrium for 1 day, at a

temperature of about 24 °C. The test results are presented in Fig. 3.18 through 3.20 in

the same format as those of the tests done under no humidity control (Fig. 3.7 to 3.9).

As shown in Fig. 3.19, the internal relative humidity of concrete increases as

the temperature increases. However, the increase of the internal relative humidity is

very small (3 % at temperature 28 °C and 8 %, the peak value at temperature 77 °C).

If the increase of the internal relative humidity during heating is neglected the strain

measured from the dried specimen can be regarded as PTS. The PTS is potted versus

temperature in Fig. 3.21. As shown in Fig. 3.21, the PTS is linear because there is no

moisture effect, unlike the CTS. For temperature ranging from 28 °C to 70 °C, the

function of the PTS is expressed with Eq. (3.15). T is the temperature in Celsius.

109

( ) 610.995 307.86 10PTS Tε −= ⋅ − ⋅ for 28 70C T C≤ ≤ (3.15)

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Time (hrs)

RH

(%) &

Tem

p (C

)Temp (Chamber)

RH (Chamber)

Figure 3.18. Temperature and RH inside the chamber vs. Time

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Time (hrs)

RH

(%) &

Tem

p (C

)

-400

-200

0

200

400

600

800

1000

1200

Stra

in (x

10-6

)

Temp (Specimen)RH (Specimen)Strain_average

Figure 3.19. Temperature, RH and strain history of the specimen vs. Time

110

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Time (hrs)

RH

(%) &

Tem

p (C

)

-400

-200

0

200

400

600

800

1000

1200

Stra

in (x

10-6

)

Temp (Chamber)RH (Chamber)Temp (Specimen)RH (Specimen)Strain_average

Figure 3.20. RH, temperature, and strain history vs. time (Dried specimen)

0

100

200

300

400

500

600

20 30 40 50 60 70 80

Temperature (C)

Stra

in (x

10-6

)

PTS

PTS Trend

Figure 3.21. Pure thermal strain by temperature increase from 28 °C to 70 °C

111

3.3.3. Thermo-hygro coupling effect

From experimental data, the thermo-hygro coupling effect can be obtained

using Eq. (3.16).

CTS PTS PHS coupling = + + - ( )thermo hygro couplingε ε ε ε (3.16)

To plot the thermo-hygro coupling effect ( couplingε ) on the plane of strain

versus temperature with CTSε and PTSε , the factor f is defined as Eq. (3.17).

( )a w wP P vf

R−

= − (3.17)

Thus, from Eq. (3.12),

( )T In RH f⋅ = (3.18)

The factor f of Range A, where both temperature and internal humidity of

concrete vary, in Fig. 3.9 is calculated using Eq. (3.18). To find an equivalent RH at a

constant temperature of 77.5 °C corresponding to Range A in Fig. 3.9, the calculated

f and temperature 77.5 °C are placed into Eq. (3.18). In the equation, T is the

temperature in Kelvin.

Fig. 3.22 shows the internal relative humidity and temperature in Kelvin

versus the factor f for concrete in Range A of Fig. 3.9. Fig. 3.23 is the equivalent

112

relative humidity at constant temperature 77.5 °C (350.65 Kelvin) versus the factor

f , which is the same as that in Fig 3.22.

0

10

20

30

40

50

60

70

80

90

100

1200 1250 1300 1350 1400 1450 1500 1550 1600

f (factor)

RH

(%)

290

300

310

320

330

340

350

360

Tem

pera

ture

(Kel

vin)

RH (%)Temperature (Kelvin)

Figure 3.22. RH (%) and Temp. (Kelvin) versus factor (f) for the range A in Fig. 3.9

0

10

20

30

40

50

60

70

80

90

100

1200 1250 1300 1350 1400 1450 1500 1550 1600

f (factor)

RH

(%)

290

300

310

320

330

340

350

360

Tem

pera

ture

(Kel

vin)

Equivalent RH (%) at 350.65 KelvinTemperature (350.65 Kelvin)

Figure 3.23. Equivalent RH (%) at Temp. 77.5°C (350.65 Kelvin) versus factor (f)

113

Now, thermo-hygro coupling effect ( couplingε ) can be plotted on the plane of

strain versus temperature with CTSε and PTSε because the PHS at constant temperature

77.5 °C (350.65 Kelvin) was already obtained in the relation of strain versus RH (%)

as shown in Fig. 3.15. The thermo-hygro coupling strain with CTS, PTS, and PHS in

the temperature range between 28-70 °C is shown in Fig. 3.24.

-100

0

100

200

300

400

500

600

20 30 40 50 60 70 80

Temperature (C)

Stra

in (x

10-6

)

CTSPTSPHSThermo-hygro coupling strain

Figure 3.24. Thermo-hygro coupling strain between 28-70°C

In Fig 3.24, PTS is less than CTS because the there is no additional hygro

strain as the temperature increases. PHS is nonlinear. At higher temperatures, PHS

increases more rapidly. The thermo-hygro coupling strain is negative in the tested

temperature range for this study. This means that there is no shrinkage due to

114

dehydration (decrease of relative humidity) in the CTS of concrete. The thermo-hygro

coupling strain from curve fitting is expressed with Eq. (3.19). T is the temperature in

Celsius.

10 3 8 2

6 6

23.275 10 30.541 10

13.151 10 179.877 10coupling T T

T

ε − −

− −

= − ⋅ + ⋅

− ⋅ + ⋅ for 28 70C T C≤ ≤ (3.19)

3.4. Conclusions

The Conventional Thermal Strain (CTS), Pure Thermal Strain (PTS), and Pure

Hygro Strain (PHS) with respect to temperature and humidity changes were measured

continually and simultaneously over time. From the measured strains, the thermo-

hygro coupling effect in the temperature range 28-70 °C was obtained. The

conclusions from this study are as follows;

1. If it is assumed that a local thermodynamic equilibrium always exists between the

phases of pore water (vapor, liquid) within a very small element of concrete, the

phenomenon, which is the increase of internal relative humidity of concrete with

temperature increase, can be explained using Eq. (3.12). This equation is based on

static force equilibrium from a capillary tube model and physicochemical equilibrium

by the Kelvin equation. When we consider the strain change of aggregates and

hardened cement paste as components of concrete at elevated temperatures, it is clear

that the internal relative humidity of concrete increases as the temperature increases.

115

2. Pure Thermal Strain (PTS), because the there is no additional moisture effect by

swelling pressure increase (increase of relative humidity) according to temperature

increase, was less than Conventional Thermal Strain (CTS) in the range of

temperatures used in this study.

3. Pure Hygro-Strain (PHS) was nonlinear. At higher temperatures, Pure Hygro Strain

(PHS) increased more rapidly. It is likely linked to complicated physiochemical

reactions in concrete as humidity changes, i.e. the increase of swelling pressure (RH

increase) is not directly proportional to temperature increase.

4. The thermo-hygro coupling effect was negative in the tested temperature range.

That means that the internal relative humidity of concrete increases as the temperature

increases in the tested temperature range.

5. The shrinkage effect due to a decrease in internal relative humidity (dehydration)

of cement may be contained in the overall expansion of concrete beyond 150 °C.

However, it should be noticed that concrete expands as temperature increases because

aggregates, which make up about 70 % of concrete by volume, expand continually as

the temperature increases.

116

CHAPTER 4

4. STRENGTH AND DURABILITY OF CONCRETE SUBJECTED TO VARIOUS

HEATING AND COOLING TREATMENTS

4.1. Introduction

Under rapid heating, concrete experiences large volume changes resulting

from thermal dilatation of aggregate, shrinkage of cement paste due to moisture loss,

and spalling damage due to high thermal stresses and pore pressure build-up.

Therefore, it is very important to study residual mechanical and durability properties

after concrete is subjected to high temperatures with different heating and cooling

rates. These special features of concrete will provide essential information to the

concrete industry for improving the fire resistance of concrete.

Extensive experimental studies on this important topic were performed in the

past. The important experimental parameters included maximum temperature, heating

rate, types of aggregates used, various binding materials, and mechanical loads under

high temperature conditions. However, the experimental studies have mainly

concentrated on the strength of concrete, very little research focused on the reduction

of concrete durability caused by fire damage. Poon et al. (2001) conducted an

117

experimental study on the strength and durability performance of normal and high

strength concretes, but the study did not consider the effects of heating and cooling

rates which are very important factors on degradation of concrete due to fire. From a

strength point of view, the reduction of concrete strength is affected strongly by the

heating rate, and the residual strength of concrete depends strongly on the cooling rate.

The purpose of this experimental study is to investigate both the strength and

durability performance of concrete subjected to various high temperature scenarios.

The test variables are heating rates, holding times at target temperatures, and cooling

rates. Thermal diffusivity, which is one of the fundamental thermal properties of

concrete, is evaluated after various heat treatments. The reduction of the durability of

concrete is investigated using a water permeability test (WPT). The unstressed

residual compressive strength test and ultrasonic pulse velocity test (UPV) are

performed to investigate the strength and stiffness deterioration by each high

temperature scenario. Additionally, weight losses, color changes, and cracks of the

specimens are also studied and reported.

4.2. Specimen preparation, heating equipment and test variables

The mix proportion and materials used to produce the concrete specimens are

the same as that previously described in chapter 3.2.1. Concrete cylindrical specimens

with dimensions of 4×8 inch are made for the experimental study. The maximum size

of coarse aggregate in concrete specimen is 3/4 inch. The specimens are cured under

the standard condition (Temperature 23 ˚C and RH 93 %) for 8 weeks in a fog room.

118

For the weight loss and water permeability tests 4×2 inch slices are needed. To make

the slices the concrete cylinders are cured for 21 days in the fog room and then cut

into the slices. To make the cuts from 4×8 inch cylinders the bottom and top

1.5 inches of the specimens are removed, the remaining portion of the cylinders is cut

in half, and then put into the fog room for another five weeks of curing.

An electrically heated furnace (Model RHF 15/8 of CARBOLITE) designed

for maximum temperature up to 1600 ˚C is used. The interior size of the furnace is

7.8"W×11.4"D×6.6"H. The temperature history inside the furnace is measured and

recorded from type K-thermocouples installed inside. The data logger used along with

the thermocouples is the model OM-CP-OCTTEMP produced by OMEGA.

The water permeability test is performed after the specimen experiences one

of the temperature scenarios. The test variables are heating rates (2 and 15 ˚C/min),

holding times (2 and 4 hrs) at each maximum temperature and cooling conditions,

which include slow cooling (1 ˚C/min), natural cooling in the furnace and water

cooling. The target maximum temperatures are 200, 400, and 600 ˚C.

For the unstressed residual compressive strength test and ultrasonic pulse

velocity test (UPV), the test variables are the cooling condition (slow cooling, natural

cooling, and water cooling) and maximum temperatures 200, 400, 600, and 800 ˚C.

The heating rate is 2 °C/min, and holding time at the maximum temperature is 4 hrs.

In the cases of natural and slow cooling, the specimen is left in the furnace

and the temperature change is recorded over time. For water cooling, the specimen is

taken out of the furnace and put in a tank of water that is initially at 20 ˚C. Fig. 4.1 is

the schematic of the temperature scenarios used for this test.

119

Figure 4.1. Schematic of temperature scenarios

Figure 4.2. Test set-up for heating

The furnace is heated using two groups of three heating elements on either

side of the specimen. In order to protect the heating units from potential spalling

damage of concrete, the concrete specimen is placed inside a hollow tube made of

mullite with a maximum operational temperature of 1700 ˚C. This provided a more

uniform thermal condition inside the specimen. Fig. 4.2 shows the test-set up for

heating. Fig 4.3 shows the temperature histories measured in the mullite tube with the

K-thermocouple.

Thermocoup

Mullite

120

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Time (min)

Tem

pera

ture

(C)

R15_200D2S1

R15_200D2N

R15_200D2W

Water cooling

Slow cooling

Natural cooling

(a) Heating rate 15 °C/min, target temperature 200 °C, and different cooling regimes

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Time (min)

Tem

pera

ture

(C)

R15_400D2S1

R15_400D2N

R15_400D2WWater cooling

Slow cooling

Natural cooling

(b) Heating rate 15 °C/min, target temperature 400 °C, and different cooling regimes

121

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Time (min)

Tem

pera

ture

(C)

R15_600D2S1

R15_600D2N

R15_600D2W

Slow cooling

Natural cooling

Water cooling

(c) Heating rate 15 °C/min, target temperature 600 °C, and different cooling regimes

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Time (min)

Tem

pera

ture

(C)

R2_200D4S1

R2_200D4N

R2_200D4W

Water cooling

Slow cooling

Natural cooling

(d) Heating rate 2 °C/min, target temperature 200 °C, and different cooling regimes

122

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600Time (min)

Tem

pera

ture

(C)

R2_400D4S1

R2_400D4N

R2_400D4W

Water cooling

Slow coolingNatural cooling

(e) Heating rate 2 °C/min, target temperature 400 °C, and different cooling regimes

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Time (min)

Tem

pera

ture

(C)

R2_600D4S1

R2_600D4N

R2_600D4W

Slow cooling

Natural cooling

Water cooling

(f) Heating rate 2 °C/min, target temperature 600 °C, and different cooling regimes

Figure 4.3. Temperature histories measured at the inside of the mullite tube

123

4.3. Temperature distribution and thermal diffusivity

4.3.1. Test set-up

Thermal diffusivity is one of the fundamental thermal properties, such as gas

or liquid permeability, used to evaluate the bearing capacity of a fire-exposed

concrete structure. The thermal diffusion is evaluated with a 4×8 concrete cylinder.

(a) Specimen geometry (b) Positions of thermocouples

(c) Set-up of thermal couples (Type K) (d) Specimen placed inside the furnace

Figure 4.4. Specimen geometry, locations of thermocouples and test set-up

124

One thermocouple is used to measure ambient temperature between the

specimen and mullite hollow tube, and four additional K thermocouples are installed

inside and on the surface of the specimen to measure the temperature distribution in

the concrete cylinder. Fig. 4.4 shows the specimen geometry, locations of

thermocouples and test set-up. The heating rate is 1 ˚C/min, maximum temperature

900 ˚C, holding time at the maximum temperature 2 hrs, and the cooling method is

natural cooling.

4.3.2. Results and discussion

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25 30 35 40Time (hrs)

Tem

pera

ture

(C)

Position 1

Position 2

Position 3

Position 4

Ambient

Figure 4.5. Transient temperature at each position

125

Fig. 4.5 shows temperature histories over time measured at each thermocouple

location. One can see that in the heating phase the surface temperature is higher than

the internal temperature and in the cooling phase the surface temperature is lower

than the internal temperatures, which are expected experimental results. The two

vertical drops in the cooling phase in Fig. 4.5, near 540 ˚C at the center and 330 ˚C at

mid-radius, are due to the damage of the two thermocouples in position 1 and

position 2.

0

10

20

30

40

50

60

70

0 200 400 600 800 1000

Surface temperature (C)

Del

ta T

(C)

The first peak The third peak

The second peak

Figure 4.6. ∆T Vs. Surface temperature

An interesting result in Fig. 4.5 is the radial distribution of temperatures

measured at different locations during the testing period. Fig. 4.6 shows the

temperature difference between the surface and center of the specimen at different

temperature ranges. One can see that the temperature difference varies during the

126

entire testing period, which means that a steady state condition in the concrete was

never reached. This is mainly due to the phase transformations taking place at

different temperatures in the concrete. The three peaks shown in the figure are related

to the micro-structural changes due to complex physicochemical transformations in

the concrete under different high temperatures. The peaks are closely related to the

results of DTA (Differential Thermal Analysis) conducted by Lankard (1970). The

first peak occurs at 200 ˚C. This peak is associated with the evaporation of free water

and the dehydration of calcium silicate hydrate (C-S-H). In fact, the weight of the

concrete is decreased rapidly up to about 200 ˚C due to the evaporation of free water.

This result is shown more clearly in the weight loss measured in this study, which

will be discussed later. The second peak between 550 ˚C and 650 ˚C is related to the

decomposition of calcium hydroxide (CH) and calcium silicate hydrate (C-S-H). The

peak occurring at 850 ˚C is occasionally observed in DTA. It is likely that the third

peak is due to the decomposition of calcium carbonate ( 3CaCO ) observed in the DTA

test results by Lankard (1970).

Fig. 4.7 shows the temperature profiles measured at positions 1, 2, and 3,

when temperatures at the center in the specimen have reached about 600 ˚C and

800 ˚C, during both heating and cooling. The surface temperature corresponding to

each temperature profile is indicated in the figure. While undergoing natural cooling,

the temperature difference between the center and the surface is two times larger than

that during heating. This means that the damage of the concrete is strongly affected

by cooling method. One of the important applications of the temperature profiles is to

determine the thermal diffusivity of the cylindrical concrete specimens. The

127

simplified expression, developed by Khoury et al (1985 a), for linear heat conduction

in a solid cylinder subjected to constant surface temperature increase relates the

thermal diffusivity ( D ) to the temperature difference ( T∆ ) between the surface and

the center. It does not account for moisture transport.

2 / 4hD v R T= ∆ (4.1)

hv is the rate of temperature of the specimen at the surface and R is the

radius of the specimen.

During heating [Surface Temp: 1179.66 F (637.59 C)]

609.43600

609.43

636.86 636.86

580

680

-40.8 -20.4 0 20.4 40.8

During cooling [Surface Temp: 976.98 F (524.99 C)]

575.49

600.22

575.49

550.55 550.55

530

630

-40.8 -20.4 0 20.4 40.8

During heating [Surface Temp: 1572.75 F (855.97 C)]

822.75

811.06

822.75

845.49 845.49

790

890

-40.8 -20.4 0 20.4 40.8

During cooling [Surface Temp: 1302.01 F (705.56 C)]

796.15

812.21

796.15

741.48 741.48

730

830

-40.8 -20.4 0 20.4 40.8

Figure 4.7. Temperature profiles during heating and cooling

Fig. 4.8 is the plot of thermal diffusivity versus temperature based on the

temperature profiles. One can see that there is a large drop in thermal diffusivity up to

about 200 ˚C, which is related to the loss of the free water, and it remains relatively

constant thereafter with increasing temperature.

128

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500 600 700 800 900

Temperature (C)

D*1

000

(m2 /h

)

Figure 4.8. Thermal diffusivity

4.4. Water permeability

4.4.1. Test set-up

Water permeability is a measurement of the transport property of concrete,

and a very good indicator of the change of microstructure in concrete under different

temperature treatments. As shown in this section, the permeability is far more

sensitive to temperature treatment than the associated degradation of strength and

stiffness which will be discussed in the subsequent section.

Figs. 4.9 and 4.10 show the procedure of the test sep-up and the experimental

apparatus used in the present study for measuring water permeability of concrete,

129

respectively [see Ludirdja et al. (1989)]. The flow of water is measured from the drop

of water level in the pipette during the test. The water level is filled to the original

level periodically. After the specimen is exposed to a temperature cycle, it is placed in

an air vacuum for 3 hours to remove air in the specimen, and then it is placed in a

water vacuum for 1 hour. The water used for the water vacuum is boiled to make sure

it is free of air and then it is cooled to room temperature. The specimens are then

immersed for 18 hrs in the de-aerated water and finally placed in the water

permeability apparatus. The vacuum process follows ASTM C 1202.

(a) Put specimen into plastic tube (b) Combine top and bottom cover

(c) Put water into bottom and top cover (d) Test set-up

Figure 4.9. Procedure of the test sep-up

130

Figure 4.10. Test set-up detail

4.4.2. Results and discussion

The test results for the test series R15_D2 (heating rate15 ˚C/min and 2 hrs

holding time at target temperature) are plotted in Fig. 4.11 as the cumulative water

permeated versus time. In Fig. 4.11, the plot (a), (b) and (c) show the test results

subjected to different target temperatures under the same cooling regime. The plots

(d), (e), and (f) show the effect of different cooling regimes for the same target

temperature. The test results for the test series R2_D4 (heating rate 2 ˚C/min and

4 hrs holding time at target temperature) are plotted in Fig. 4.12 with same format as

those of the test series R15_D2.

131

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)

R15_200D2S1

R15_400D2S1

R15_600D2S1

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


R15_200D2N

R15_400D2N

R15_600D2N

(a) Slow cooling (b) Natural cooling

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)R15_200D2WR15_400D2WR15_600D2W

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


R15_200D2S1R15_200D2NR15_200D2W

(c) Water cooling (d) Maximum temperature 200 ˚C

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)R15_400D2S1R15_400D2NR15_400D2W

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


(e) Maximum temperature 400 ˚C (f) Maximum temperature 600 ˚C

Figure 4.11. Cumulative water permeated versus time for the test series R15_D2

132

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)R2_200D4S1R2_400D4S1R2_600D4S1

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)R2_200D4NR2_400D4NR2_600D4N

(a) Slow cooling (b) Natural cooling

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)

Reference (No heating)R2_200D4WR2_400D4WR2_600D4W

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


(c) Water cooling (d) Maximum temperature 200 ˚C

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000

Time (min)

Q (m

l)


(e) Maximum temperature 400 ˚C (f) Maximum temperature 600 ˚C

Figure 4.12. Cumulative water permeated versus time for the test series R2_D4

133

The nonlinearity of the curves may be attributed to the absorption of the water

into a partially empty pore system in the specimens. The test results show that the

initial slope of cumulative water flow through the specimen increases as the target

temperature and cooling rate increase. There is linearity in the plots of the specimens

exposed to a maximum temperature over 400 ˚C using water cooling. This may be

due to the severe damage caused by rapid cooling. These trends are also shown in the

test series R2_D4.

The coefficient of permeability is obtained from Darcy’s law:

/pV K Ah L= (4.2)

By integrating the above equation,

tKhALQ p ⋅=⋅⋅ )/( (4.3)

Where V is the rate of flow dQ dt per unit area ( / secm ), Q is the total

water permeated ( 3m ), A is the cross section of the specimen ( 2m ); L is the

thickness ( m ), h is the head of water ( m ), and pK is the coefficient of permeability

( sec/m ). Note that A and L in our specimens are constants, and h is also assumed to

be constant if the small difference in pressure head during the test is neglected.

Fig. 4.13 (Test series R15_D2) and 4.14 (Test series R2_D4) are the plots of

linear regression of )/( hALQ ⋅⋅ versus time after the steady state flow is nearly

established. The coefficient of permeability pK is calculated from the slope found

from the linear regression.

134

y = 1.45E-05x + 4.13E-07

y = 1.42E-06x + 2.36E-05

y = 2.68E-08x + 1.09E-05

y = 7.98E-09x - 6.14E-07

y = 1.03E-08x + 1.70E-06

y = 3.37E-08x + 1.59E-05

y = 1.82E-08x - 1.41E-07

y = 1.89E-08x + 1.40E-06

y = 1.49E-08x + 4.17E-06

y = 7.70E-09x - 4.11E-07

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 1000 2000 3000 4000 5000 6000 7000

Time (min)

QL

/Ah

(m)

REF (No heating)

R15_200D2S1

R15_200D2N

R15_200D2W

R15_400D2S1

R15_400D2N

R15_400D2W

R15_600D2S1

R15_600D2N

R15_600D2W

Regression functions

Figure 4.13. Linear regression for the test series R15_D2

y = 1.97E-05x - 4.03E-19

y = 2.31E-08x + 1.58E-05

y = 1.89E-08x + 1.63E-05

y = 1.09E-08x + 3.84E-06

y = 2.24E-08x + 1.16E-05

y = 1.39E-08x + 3.66E-06

y = 1.53E-08x + 3.75E-06

y = 7.70E-09x - 4.11E-07

y = 8.64E-09x - 4.36E-07

y = 2.63E-06x + 1.66E-05

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (min)

QL

/Ah

(m)

Ref (No heating)

R2_200D4S1

R2_200D4N

R2_200D4W

R2_400D4S1

R2_400D4N

R2_400D4W

R2_600D4S1

R2_600D4N

R2_600D4W

Regression functions

Figure 4.14. Linear regression for the test series R2_D4

135

Table 4.1 and 4.2 show the values of the coefficient of permeability for the

test series R15_D2 and R2_D4 respectably.

Table 4.1 Coefficients of water permeability for R15_D2 test series

Temp (˚C)

Slow cooling Kp, (10-10 m/s)

Natural cooling Kp, (10-10 m/s)

Water cooling Kp, (10-10 m/s)

25 ˚C 1.28 1.28 1.28 200 ˚C 1.33 1.72 2.48 400 ˚C 3.03 3.15 236.67 600 ˚C 4.47 5.62 2416.67

Table 4.2 Coefficients of water permeability for R2_D4 test series

Temp (˚C)

Slow cooling Kp, (10-10 m/s)

Natural cooling Kp, (10-10 m/s)

Water cooling Kp, (10-10 m/s)

25 ˚C 1.28 1.28 1.28 200 ˚C 1.44 1.82 3.73 400 ˚C 2.32 2.55 438.33 600 ˚C 3.15 3.85 3283.33

Effects of the maximum temperature and cooling rate

The results shown in Table 4.1 and Table 4.2 indicate that the value of pK

increases when the specimen is subjected to higher temperatures and faster cooling

rates. In terms of the development of damage in concrete, it increases as the

maximum temperature and cooling rate increase, which leads to an increase in pK .

Increasing the cooling rate affects the level of damage to the concrete because of the

136

increasing temperature gradients. Particularly, the pK values of the specimens

subjected to the target temperature 400 or 600 °C under water cooling are very high

when compared with those subjected to other cooling regimes (natural cooling and

slow cooling) as shown in Table 4.1 and Table 4.2.

Column 1 of Table 4.1 and Table 4.2 show that under slow cooling, the

permeability increases very little. The last column of the two tables shows the effect

of fast cooling where a very large increase in permeability can be observed. This is

evidence that permeability is very sensitive to the variation of the microstructure of

concrete, which changes depending on the applied temperature treatment. The cooling

rate appears to be a significant factor in the damage development of concrete which

was exposed to high temperatures.

1.00 1.04

2.36

3.48

1.34

4.38

1.94

2.45

0.0

1.0

2.0

3.0

4.0

5.0

25 200 400 600Temperature (C)

Rel

ativ

e w

ater

per

mea

bilit

y

R15D2_Slow cooling

R15D2_Natural cooling

R15D2_Water cooling

Figure 4.15. Relative water permeability (test series R15_D2)

137

1.00 1.12

1.81

2.45

1.42

1.99

3.002.91

0.0

1.0

2.0

3.0

4.0

5.0


Rel

ativ

e w

ater

per

mea

bilit

y

R2D4_Slow coolingR2D4_Natural coolingR2D4_Water cooling

Figure 4.16. Relative water permeability (test series R2_D4)

Fig. 4.15 and 4.16 are the plots of relative water permeability versus

maximum temperature for the test series R15_D2 and R2_D4, respectively. These

figures clearly show the effects of target temperature and cooling rate.

Effects of the holding time at target temperature and heating rate

The comparisons between test series R2_D4 and R15_D2 are shown in Fig.

4.17 and Fig. 1.18. For the specimens exposed to a target temperature over 400 ˚C

(Fig. 4.17 and Fig. 1.18), the effect of the heating rate is more significant than the

holding time. Under lower temperature ranges, up to a target temperature of 200 ˚C,

the difference between the two effects is not as significant.

138

1.00

1.81

2.45

1.00

2.36

3.48

1.121.04

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0


Rel

ativ

e w

ater

per

mea

bilit

y

R2D4_Slow cooling

R15D2_Slow cooling

Figure 4.17. Comparison between R2_D4 and R15_D2 subjected to slow cooling

1.00

1.99

3.00

1.00

2.45

4.38

1.421.34

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0


Rel

ativ

e w

ater

per

mea

bilit

y



Figure 4.18. Comparison between R2_D4 and R15_D2 subjected to natural cooling

139

4.5. Ultrasonic Pulse Velocity (UPV) and residual compression test

4.5.1. Test equipments and test set-up

For this test, 4×8 inch cylinders are used. An ultrasonic pulse velocity (UPV)

test is performed prior to the residual compression test. The equipment for UPV is V-

METER from JAMES INSTRUMENTS. The longitudinal wave pulse velocity

determination method is popular for nondestructive testing of concrete because of its

simplicity and cost effectiveness.

Figure 4.19. Test set-up of the residual compression test

There are three standards in arranging transducers, which are direct

transmission (located direct opposite to each other), diagonal transmission (located

140

diagonally to each other), and indirect transmission (located on same surface and

separated by known distance). The direct transmission method is used in this research

because the direct method is the most sensitive among the three methods (Komloš at

al, 1996).

In residual compression test, axial deformation is measured with MTS model

632.94E-20, which delivers the average value automatically from two extensometers.

Displacement control of 0.0001 inch/sec is used for the test. Fig. 4.19 shows the set-

up of the residual compression test. As mentioned earlier, the test variables are the

maximum temperature exposed and cooling regimes with constant heating rate of

2 °C/min and holding time of 4 hrs at the maximum temperatures. The target

temperatures are 200, 400, 600, and 800 ˚C.

4.5.2. Results and discussion for UPV (Ultrasonic pulse velocity)

Table 4.3 shows the results from ultrasonic pulse velocity test (UPV). The

pulse frequency used for testing concrete is much lower than that used in metal

testing. The 54 kHz transducers are used for concrete testing. The signal wave length

is about 3 inches. Fig. 4.20 is a plot for relative velocity versus maximum temperature

exposed. As shown in the test results, the pulse velocity decreases as the exposed

maximum temperature increase for all cases of cooling methods. In other words, the

level of damage is fairly proportional to maximum temperature. In the subject of

cooling rate, it is observed that the velocity of specimens subjected to slow cooling

are higher than that of specimens subjected to natural cooling. This implies that faster

141

cooling contributes to increase of damage. However, this tendency does not apply to

the comparison of the water cooling to slow or natural cooling because the specimens

were temporarily (about 10 min) submerged in the water, and some water penetrates

to pores and cracks of the specimen. Thus, the test results from the specimens

subjected to water cooling can not be an accurate indication of level of damage.

Table 4.3. Ultrasonic pulse velocity test result

Velocity (m/sec) Temp. (°C) Slow cooling Natural cooling Water cooling

25 3.97E+03 3.97E+03 3.97E+03 200 3.23E+03 3.20E+03 3.03E+03 400 2.43E+03 2.36E+03 2.22E+03 600 1.10E+03 1.01E+03 1.17E+03 800 6.55E+02 3.81E+02 6.77E+02

0.0

0.2

0.4

0.6

0.8

1.0

1.2

25 200 400 600 800

Temperature (C)

Rel

ativ

e ve

loci

ty

R2D4_Slow cooling


R2D4_Water cooling

Figure 4.20. Relative velocity versus maximum temperature exposed

The elastic modulus is calculated using the test result of pulse velocity. The

function is shown below:

142

( )2 1 (1 2 )(1 )

longp

VE

ρ ν νν

⋅ ⋅ + ⋅ −=

− (4.4)

Where pE is elastic modulus, longV is longitudinal pulse velocity (P-wave), ρ

is density of the solid material, and ν is Poisson’s ratio of the solid material (0.2).

Table 4.4. Unit weight measured from specimens used in present study

Unit weight ( 3kN m ) Temp. (°C) Slow cooling Natural cooling Water cooling

25 2.304 2.304 200 2.184 2.178 400 2.162 2.158 600 2.129 2.133 800 2.098 2.098

2.304

Table 4.5. Elastic modulus ( pE ) from ultrasonic pulse velocity

pE (psi) Temp. (°C)

Slow cooling Natural cooling Water cooling 25 4.75E+06 4.75E+06 4.75E+06 200 2.97E+06 2.91E+06 2.76E+06 400 1.67E+06 1.57E+06 1.49E+06 600 3.37E+05 2.81E+05 4.10E+05 800 1.18E+05 3.96E+04 1.38E+05

Table 4.4 is a summary for unit weights measured from concrete samples used

in present study. In the calculation of elastic modulus, the unit weights in Table 4.4

are used. In case of the water cooling, the unit weight measured from no heating

specimens is used. Table 4.5 shows the elastic modulus calculated from the ultrasonic

pulse velocity. Fig. 4.21 is a chart of relative elastic modulus (obtained from UPV)

versus maximum temperature. The elastic modulus obtained from ultrasonic pulse

143

velocity (UPC) is compared to initial tangent modulus obtained from the residual

compression test in section 4.5.4.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

25 200 400 600 800

Temperature (C)

Rel

ativ

e dy

nam

ic m

odul

us

R2D4_Slow cooling


R2D4_Water cooling

Figure 4.21. Relative elastic modulus (from UPV) versus maximum temperature

4.5.3. Results and discussion for residual compression test

Fig 4.22, 4.23, and 4.24 plot stress versus strain for the specimens that were

subjected to slow, natural, and water cooling, respectively. The compressive strength

and elastic modulus decrease significantly as the maximum temperature increases.

The elastic region of the specimens subjected to slow or natural cooling and

temperatures of 600 ˚C and beyond are nonlinear. For the case of water cooling, the

same trend is shown for the range of maximum temperatures of 400 ˚C and beyond.

This may be due to thermally induced cracks formed during high temperature

treatment. In the initial stage of loading the cracks are closed as the load gradually

144

increases. After the cracks are closed, the curves follow the general trend of a

compression strength test.

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)R2_200D4S1R2_400D4S1R2_600D4S1R2_800D4S1

Figure 4.22. Stress versus strain (Slow cooling)

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)R2_200D4NR2_400D4NR2_600D4NR2_800D4N

Figure 4.23. Stress versus strain (Natural cooling)

145

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)R2_200D4WR2_400D4WR2_600D4WR2_800D4W

Figure 4.24. Stress versus strain (Water cooling)

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)

R2_200D4S1

R2_200D4N

R2_200D4W

Figure 4.25. Stress versus strain (Maximum temperature 200˚C)

146

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)R2_400D4S1R2_400D4NR2_400D4W


0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)

R2_600D4S1

R2_600D4N1

R2_600D4W


147

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (p

si)

Ref (No heating)

R2_800D4S1

R2_800D4N

R2_800D4W


The effect of different cooling methods is shown in Fig. 4.25 through

Fig. 4.28. Faster cooling contributes to decrease in strength and elastic modulus of the

concrete as shown in Figs.

Table 4.6. Ultimate strength results of residual compression test

'cf : ultimate strength (psi) Temp. (°C)

Slow cooling Natural cooling Water cooling 25 3068.59 3068.59 3068.59 200 3067.76 3011.87 2221.44 400 2856.25 2695.97 1978.69 600 1734.85 1554.84 1163.05 800 538.65 463.03 425.22

Table 4.6 is a summary of the ultimate strengths from the residual

compression test. Table 4.7 and Fig. 4.29 show the residual strength normalized by

148

the reference strength (25 ˚C) for three cooling methods as a function of the target

temperature. The residual strength rapidly drops beyond 400 ˚C. The strength of the

specimens subjected to water cooling decreases more rapidly than the specimens

subjected to other cooling methods. The strength of the specimens exposed to the

target temperature of 600 ˚C is less than 57 % of the reference strength. For 800 ˚C,

the strength is less than 18 % of the reference strength.

Table 4.7. Relative ultimate strength

Relative ultimate strength Temp. (°C) Slow cooling Natural cooling Water cooling

25 1 1 1 200 0.9997 0.9815 0.7239 400 0.9308 0.8786 0.6448 600 0.5654 0.5067 0.3790 800 0.1755 0.1509 0.1386

0.0

0.2

0.4

0.6

0.8

1.0

1.2

25 200 400 600 800

Temperature (C)

Rel

ativ

e st

reng

th

R2D4_Slow cooling


R2D4_ Water cooling

Figure 4.29. Relative residual strength vs. maximum temperature

149

Table 4.8 summarizes the test results for the initial tangent modulus from the

residual compression test.

Table 4.8. Initial tangent modulus from residual compression test

iE : initial tangent modulus (psi) Temp.(°C)

Slow cooling Natural cooling Water cooling 25 3.60E+06 3.60E+06 3.60E+06 200 2.34E+06 2.09E+06 1.63E+06 400 1.14E+06 1.04E+06 3.53E+05 600 1.91E+05 1.38E+05 5.77E+04 800 4.39E+04 2.44E+04 1.30E+04

Table 4.9 and Fig. 4.30 show the values of the initial tangent modulus with

different temperatures, normalized by the reference specimen tested at room

temperature. The basic trend of the variation of initial tangent modulus shown in

Fig. 4.30 is similar to that of the residual strength shown in Fig. 4.29. However, the

initial tangent modulus of concrete is more sensitive to elevated temperature than the

compression strength. The initial tangent moduli of the specimens exposed to a

maximum temperature of 600 ˚C are less than 5.3 % of the initial reference tangent

modulus. For 800 ˚C, the moduli are less than 1.3 % of the reference values.

Table 4.9. Relative initial tangent modulus

Relative initial tangent modulus Temp. (°C) Slow cooling Natural cooling Water cooling

25 1.0000 1.0000 1.0000 200 0.6510 0.5816 0.4537 400 0.3183 0.2896 0.0983 600 0.0530 0.0385 0.0161 800 0.0122 0.0068 0.0036

150

0.0

0.2

0.4

0.6

0.8

1.0

1.2

25 200 400 600 800

Temperature (C)

Rel

ativ

e in

itial

tang

ent m

odul

us

R2D4_Slow cooling


R2D4_Water cooling

Figure 4.30. Relative initial tangent modulus vs. maximum temperature

Therefore the results show that faster cooling contributes to more significant

decreases in both the strength and stiffness of concrete.

4.5.4. Comparison between Ep and Ei

The comparisons between elastic modulus ( pE ) obtained from the ultrasonic

pulse velocity and initial tangent modulus ( iE ) obtained from residual compression

test are shown in Fig. 4.31 through Fig. 4.33.

The trend for thermal degradation of pE and iE is similar as shown in Fig.

4.31 through Fig 4.33. However, the elastic modulus ( pE ) is evaluated higher than

the initial tangent modulus ( iE ).

151

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

25 200 400 600 800

Temperature (C)

E (p

si)

Ep from UPV (Slow cooling)Ei_ initial tangent modulus (Slow cooling)

Figure 4.31. Comparison between pE and iE (Slow cooling)

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

25 200 400 600 800

Temperature (C)

E (p

si)

Ep from UPV (Natural cooling)Ei_ initial tangent modulus (Natural cooling)

Figure 4.32. Comparison between pE and iE (Natural cooling)

152

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

25 200 400 600 800

Temperature (C)

E (p

si)

Ep from UPV (Water cooling)Ei_ initial tangent modulus (Water cooling)

Figure 4.33. Comparison between pE and iE (Water cooling)

4.6. Weight loss

Concrete is a porous material having many discrete and interconnected pores

of different sizes and shapes. Water in the visible voids and large capillaries is called

free water while the water in the combined form in hardened cement paste is called

combined water or water of hydration [Ravindrarajah et al, (2000)].

When hardened concrete is gradually heated, the weight loss occurs. The

weight loss relative to exposed temperature can be explained as follows.

-Range 0-200 °C (Drying stage): Evaporation of water from capillary pores

-Range 200 °C-600 °C (Dehydration stage): Loss of non-evaporable water

from gel pores can evaporate. The substantial shrinkage of concrete is accompanied.

153

The slope of weight loss is less than that in range 0-200°C due to the difficulty in

removing the water from smaller pore size.

-Range 600 °C-1000 °C (Decomposition stage): The several changes

including decomposition of CH (calcium hydroxide) and CHS (calcium silicate

hydrate) phase in the cement paste occurs in the concrete system.

- Above 1000 °C: The combined water from hardened concrete is completely

released. This causes the lost of the cementing property of concrete.

The weight loss for the specimens with initial relative humidity 90 % and

100 % (fully saturated condition) are measured for each temperature history. The

weight loss measurement does not include water cooling specimens because they are

submerged in water immediately after the high temperature treatment.

Table 4.10. Effect of heating on weight loss (Initial relative humidity 90 %)

Initial relative humidity 90% Temp. (˚C) R2D4S (%) R2D4N (%) R15D4N (%) R2D2N (%)

25 0 0 0 0 200 5.21 5.46 5.61 5.03 400 6.13 6.33 6.01 6.04 600 7.58 7.41 7.39 7.22 800 8.90 8.93 9.10 8.85

Table 4.11. Effect of heating on weight loss (RH 100 %:Fully saturated)

Fully saturated Temp. (˚C) R2D4S (%) R2D4N (%) R15D4N (%) R2D2N (%)

25 0 0 0 0 200 8.03 8.48 8.08 7.78 400 9.33 9.06 9.16 8.91 600 9.69 9.99 10.30 9.82 800 10.04 11.57 12.09 11.00

154

0

2

4

6

8

10

12

14

0 100 200 300 400 500 600 700 800 900

Temperature(C)

Wei

ght l

oss (

%)

R2D4S1(90%)R2D4N (90%)R15D4N (90%)R2D2N (90%)R2D4S1 (100%)R2D4N (100%)R15D4N (100%)R2D2N (100%)

Notation

R: heating rateD: holding time at max. temp.S1: cooling rate:1˚C/minN: natural cooling in the furnace

Figure 4.34. Effect of heating on weight loss (RH 100 % and 90 %)

Table 4.10 and 4.11 show the results of the weight losses of concrete

specimens with initial RH 90 % and 100 %, respectively. The two initial RH values

are used to study the effect of initial RH on weight loss of concrete under different

temperatures. The weight losses for both RH 90 % and 100 % are plotted in Fig. 3.34.

The weight loss in concrete increases as the temperature increases. However, the

weight loss and maximum temperature is not linearly proportional over the entire

temperature range. The slope of the weight loss plot above 200 °C is considerably

less than that in the range of 25-200 °C because of different mechanisms of weight

loss. In the lower temperature range, the weight loss is due mainly to the evaporation

of free water in voids and capillary pores. When all free water is evaporated further

weight loss comes from the removal of adsorbed water in smaller pores, which needs

more energy. Moreover, at high temperature, some phase transformations take place

and a certain amount of chemically bound water is released and evaporated. The

155

amount of adsorbed water and released chemically bound water is less than the free

water in the concrete specimens with RH 90 % and 100 %. This leads to the reduced

slope in the weight loss curve above 200 °C.

The initial weight loss plot of fully saturated specimens is steeper than those

for RH 90 % specimens up to 200 ˚C. This is because the fully saturated specimens

contain more free water than the specimens of RH 90 %. At temperatures higher than

200 ˚C, the slopes for both saturation levels are almost the same. This means that the

evaporation of the free water in the voids and capillary pores is almost complete at a

temperature of 200 ˚C. Therefore, regardless of the initial moisture content of

concrete, after 200 ˚C, the rate of weight loss is similar for all specimens. This

indicates that up to 800 ˚C the weight loss of concrete is governed by the same

mechanism. The test results, for both RH 90 % and RH 100 %, show that the weight

loss is governed by target temperature, not by heating rate, cooling method, or

holding time (2 hrs and 4 hrs in this research).

4.7. Cracks and color changes of the specimens

Red spots and distributed cracks were observed on every specimen to a

maximum temperature of exposed to maximum temperature 600 ˚C and above. It is

likely that the distributed cracks on the bottom and top surfaces of the specimens

occurred because of the differences in the thermal deformations between the

aggregate and cement paste matrix. The chemical composition of granite is composed

mostly of silica ( 2SiO ) and alumina ( 2 3Al O ). The colors of the specimens subjected

156

to slow and natural cooling are generally pink, while the colors of the specimens

subjected to water cooling are dark pink. The colors of the particles and aggregate on

the specimens are gold in patches.

(a) maximum temperature 600˚C (b) maximum temperature 800˚C

Figure 4.35. Specimens exposed to heating rate 2 ˚C/min (Natural cooling)

(a) Heating rate: 2˚C/min (b) Heating rate: 15˚C/min

Figure 4.36. Specimens exposed to maximum temperature 800 ˚C (Natural cooling)

The crack widths of the specimens exposed to a maximum temperature of

800 ˚C are visibly wider than those of the specimens exposed to a maximum

Cracks

157

temperature of 600 ˚C in shown in Fig. 4.35. Also, in the specimens exposed to

maximum temperature 800 ˚C, the crack widths of the specimens heated quickly

(15 ˚C/min) are significantly larger than those of the specimens heated slowly

(2 ˚C/min) in shown in Fig. 4.36.

Figure 4.37. Granite concrete melted in the furnace

Generally, concrete is melted between about 1150 ˚C and 1300 ˚C. Fig. 4.37

shows a granite concrete lump (which was a 4×8 inch cylinder) inside the furnace

melted from its exposure to the temperature of 1200 ˚C.

4.8. Conclusions

1. There were three distinct peaks in the plot of the temperature difference between

the surface and center of the specimen. The three peaks are related to the micro-

structural changes due to complex physicochemical transformations in the concrete

158

under high temperature. The first peak is associated with the dehydration of calcium

silicate hydrate (C-S-H) and the evaporation of free water. The second peak is related

to the decomposition of calcium hydroxide (CH) and calcium silicate hydrate (C-S-H).

The third peak may be due to the decomposition of calcium carbonate ( 3CaCO ).

2. The results of the water permeability test (WPT) showed that the pK (coefficient of

permeability) of the specimen increased as the temperature and cooling rate increases.

Also, the test results of the specimens subjected to slow or natural cooling showed

that the effect of the cooling rate on thermal damage in concrete is more significant

than that of the holding time at target temperatures.

3. Strength and stiffness of the concrete decreased significantly as the maximum

temperature and the cooling rate increase.

4. The trend for thermal degradation of pE (obtained from the ultrasonic pulse

velocity) and iE (obtained from residual compression test) was similar. However, the

elastic modulus ( pE ) was evaluated higher than the initial tangent modulus ( iE ).

5. The weight loss below 200 °C was steeper than that above 200 °C, for RH 90%

and full saturation, because it is governed by the evaporation of the free water. The

weight loss at temperatures above 200 °C is due to the loss of adsorbed and

chemically bound water in the specimen. The weight loss was governed by the target

temperature rather than the heating rate, cooling method, or holding time (2 hrs and

4 hrs in this research).

6. The crack width increased with an increase in temperature and also with heating

rate which means they both contribute to the damage of concrete.

159

CHAPTER 5

5. A MULTISCALE CHEMO-MECHANICAL MODEL FOR MODULUS OF

ELASTICITY OF CONCRETE UNDER HIGH TEMPERATURES

5.1. Introduction

Stiffness of concrete degrades under high temperatures. The degradation

results mainly from two mechanisms. One is the variation of material properties of

the constituent phases under high temperatures, and the other is the transformation

of constituent phases under different temperatures. Therefore, the degradation of

mechanical property of concrete under high temperatures must be studied from both

mechanical and chemical points of view. Since the sizes of the constituent phases in

concrete vary from centimeter to micrometer, and the phase transformations and

property variations in the cement paste take place at a broad range of scale levels, a

comprehensive mathematical model for characterizing the degradation of stiffness of

concrete under high temperatures must be a multiscale model including the chemo-

mechanical characteristics of the constituent phases under high temperatures.

Extensive experimental studies have been performed by previous researchers.

Piasta (1984 a) conducted experiments to study thermal deformation of phases

160

present in hardened cement paste and to determine initial temperatures in the range of

20-800 °C which initiate the destruction of the micro structure of cement paste.

Schneider and Herbst (1989) and Piasta and co-workers (1984 b) investigated

chemical reactions and the behaviors of 2( )Ca OH , 3CaCO (calcite), - -C S H , non-

evaporable water and micropores under various temperatures. In a study conducted by

Lin et al. (1996) the microstructure of concrete exposed to elevated temperatures in

both actual fire and laboratory conditions was evaluated with the use of Scanning-

Electron-Microscopy (SEM) and stereo microscopy. Also, Wang et al. (2005) used

SEM to examine the cracking of high performance concrete (HPC) exposed to high

temperatures under axial compressive loading of about 200 N. Despite the

experimental studies, a prediction model has not yet been developed for the thermal

degradation of stiffness of concrete in which phase transformations at the micro-scale

level are considered.

This study is a new attempt to predict the thermal degradation of the elastic

modulus of concrete considering phase transformations under different temperature

ranges. Stoichiometric models are used to handle the volumetric variations of the

constituent phases, and composite mechanics models are used to obtain effective

elastic modulus of concrete based on the volumetric variations under high

temperatures.

The degradation of stiffness of concrete results from the phase transformations

taking place in the cement paste as well as in aggregates. In this study, we focused on

phase transformations taking place in the cement paste, while the effect of various

aggregates is included in the model by using a degradation factor representing

161

different aggregates. The internal structure of concrete can be divided into the

following four scale levels (Constantinides and Ulm 2004):

Level 1( 8 610 ~ 10 m− − ,the - -C S H level): A characteristic length scale of

8 610 10 m− −− is the smallest material length scale. At this scale, the - -C S H exists in

at least two different forms with different volume fractions (inner and outer C-S-H).

Level 2 ( 6 410 ~ 10 m− − , the cement paste level): Homogeneous - -C S H with

large CH crystals, aluminates, cement clinker inclusions, and water.

Level 3 ( 3 210 ~ 10 m− − , the mortar level): Sand particles embedded in a

homogeneous cement paste matrix.

Level 4 ( 2 110 ~ 10 m− − , the concrete level): Concrete as a composite material;

course aggregates embedded in a homogeneous mortar matrix.

-2 1

Level 4(10 10 )m−− -3 2

Level 3(10 10 )m−− -6 4

Level 2(10 10 )m−− -8 6

Level 1(10 10 )m−−

Figure 5.1. Multiscale internal structure of concrete

In this study, the lowest scale level is at the micro-scale, i.e. the cement paste

level (or Level 2). The decomposition of C-S-H under high temperatures will be

considered in stoichiometric models, but the nanostructure of C-S-H will not be

considered.

162

In Chapter 5.2, a kinetic model for hydration reactions of Portland cement will

be described first. This model is necessary and important to calculate the initial

volume fractions (prior to the exposure to high temperature) of the constituent phases

in cement paste. In Chapter 5.3, initial volume fractions of the constituents in

concrete will be calculated based on the kinetic model described in Chapter 5.2 and

concrete mix design parameters. In Chapter 5.4, the variations of the initial volume

fractions under elevated temperatures will be described by stoichiometric models

based on phase transformations of the constituent phases taking place at different

temperature ranges. In Chapter 5.5, the composite theory is briefly introduced which

can be used at every scale level to obtain effective mechanical properties. In Chapter

5.6, the composite theory is used to predict the effective modulus of elasticity of

concrete based on the volume fractions of the constituents at different temperature

ranges. In Chapter 5.7, the model predictions are compared with available test data in

the literature and with our own test data. Chapter 5.8 is conclusions.

5.2. Hydration kinetics model

Typically four clinkers ( 3C S , 2C S , 3C A , and 3C AF ) in Portland cement are

considered as reactants in the hydration reactions of cement, which are considered to

have five periods, namely the initial reaction period (Period 1), the induction period

(Period 2), the acceleratory period (Period 3), the decelerating period (Period 4), and

the slow period (Period 5). Periods 1 and 2 correspond to the early stage of hydration

reaction, Periods 3 and 4 to the middle stage, and Period 5 to the late stage

163

(Taylor, 1997). The hydration reactions of cement are largely classified as two

processes. The first one is the process of nucleation and growth reaction of the clinker

phases, which is developed over 0-20 hours. The second is a diffusion controlled

process where the kinetics of the hydration reaction is controlled by the rate of

diffusion of dissolved ions through the layers of hydrates, which is formed around the

clinker, and is developed at ages of 1 day and beyond. The rate of hydration of the

second process depends strongly on the water to cement (w/c) ratio (Berliner et al,

1998). Fig. 5.2 is a schematic for the hydration process of cement paste.

water20hrs

Outer ProductAfter 20hrs

Inner product

1α =

Clinker phasesOuter Product

Inner product

Clinker phases

water20hrs

Outer ProductAfter 20hrs

Inner product

1α =

Clinker phasesOuter Product

Inner product

Clinker phases

Figure 5.2. Hydration process of cement paste

Eq. (5.1) (called Avrami equation) has been commonly employed to model

the nucleation and growth reaction kinetics, the first 20-30% of the reaction, in

cement chemistry:

ln[1 ( )] [ ( ) ]mi oi ok t tα α− − − = − (5.1)

In which, iα is the hydration degree of reaction of clinker i at the time t . oiα

is the hydration degree of reaction of clinker i at the time ot , when the nucleation

and growth process dominate the hydration. k is a rate constant that considers the

164

effects of nucleation, multidimensional growth, geometric shape factors, and the

diffusion process. m is an exponent defining the reaction order.

1 exp[ ( ) ]ici i ia t bα = − − − (5.2)

In which, ia , ib , and ic are coefficients, which were determined empirically

with the specific Portland cement. The empirical equation, Eq. (5.2) proposed by

Taylor (1987), is based on the Avrami equation. The coefficients are shown in Table

5.1. Also, Eq. (5.2) is used as an approximate equation for the hydration reaction of

cement paste for large values of time.

Table 5.1. Coefficients of ia , ib , and ic

Compound ia ib ic

3C S 0.25 0.9 0.7

2C S 0.46 0.0 0.12

3C A 0.28 0.9 0.77

3C AF 0.26 0.9 0.55

For a long duration of time ( 1t day> ), the hydration reaction, controlled by

the rate of diffusion, has been addressed by researchers such as Berliner et al (1998),

Fuji and Kondo (1974). According to Fuji and Kondo (1974), the rate of hydration

reaction is

1/3 1/ 2 * 1/ 2 * 1/3(1 ) (2 ) ( ) / (1 )i i iD t t Rα α− = − − + − (5.3)

165

In which, *iα is the degree of reaction of clinker i at the time *t . The

hydration reaction is governed by the rate of diffusion of dissolved ions. iD is the

diffusion constant ( 2 /cm h ) of clinker i , and R is the initial radius of the clinker

grains. An average particle size 45 10 cm−× can be used as the initial radius of the

clinker grains (R). The parameter iD and coefficients taken from Berliner (1998) and

Bernard (2003) are summarized in Table 5.2.

Table 5.2. Diffusion constant and coefficients in the diffusion model

Diffusion model Clinkers w/c

iD ( 2 /cm h ) *( )t h *iα

0.3 100.42 10−× 0.5 102.64 10−× 3C S 0.7 1015.6 10−× 0.3 0.5 2C S 0.7

106.64 10−×

0.3 0.5 3C A 0.7

102.64 10−×

0.3 100.42 10−× 0.5 102.64 10−× 3C AF 0.7 1015.6 10−×

20 or 30 0.60

The hydration reaction of the cement paste based on the diffusion theory is

very fast as compared with that from the empirical equation, Eq. (5.2). The overall

degree of hydration, α , of the cement-based material systems is related to the

individual degree of hydration of clinkers. The overall degree of hydration may be

expressed with Eq. (5.4).

166

( )( )

i ii

ii

m tt

m

αα =

∑∑

(5.4)

In which, 3 2 3

, ,i C S C S C Am m m m= , and 4C AFm are the mass fractions of the

clinker phases in the cement.

5.3. Initial volume fractions of constituent phases in concrete

5.3.1. Volume fractions of the constituent phases at the cement paste level

The initial volume fraction of the phases is calculated on the basis of

parameters and equations developed by Bernard (2003). At the cement paste level, the

total volume is composed of reactants (remaining water and cement grains) and

products of the hydration reactions (such as - -C S H , CH, products by aluminates,

and capillary voids). The total volume is expressed with Eq. (5.5).

_ . capillary voids( ) ( ) ( ) ( ) ( ) ( )total cklevel c p w i C S H CH AL

i

V V t V t V t V t V t V t− −= + + + + +∑ (5.5)

The volume of remained water in the reactant phases is obtained by

subtraction of the water consumed during hydration from the initial water content.

( ) ( ) 0o iw w w i

iV t V V tα= − × ≥∑ (5.6)

167

In which, wV is the volume of remaining water, owV is the initial volume of

water in the matrix, and iwV is the volume of the consumed water for complete

hydration of clinker i . iwV is calculated by Eq. (5.7).

* //

iiw i iwo

c w w

V NV

ρ µρ µ

= × ; * i ii co

c ii

M mV m

ρ ρ= =∑

(5.7)

In which, ocV is the initial cement volume, im (

3 2 3 4, , ,C S C S C A C AFm m m and m ) is

the mass fraction of clinker phases in the cement, and iµ is molar mass of phase i .

/iw w iN n n= denotes the number, wn , of moles of the consumed water during the

hydration of 1in = mol of the clinker phase i of mass density *iρ . For example, the

hydration reactions of 3C S and 2C S compound are expressed by Eq. (5.8) and (5.9).

3 3.4 2 82 10.6 - - 2.6C S H C S H CH+ → + (5.8)

2 3.4 2 82 8.6 - - 0.6C S H C S H CH+ → + (5.9)

In Eq. (5.8), the ratio of consumed water to the hydration of 3C S is 5.3.

Among them, 1.1 moles are chemically bound, and 2.9 moles are absorbed in the

- -C S H pores. In Eq. (5.9), the ratio of consumed water to the hydration of 2C S is

4.3. Thus, 3C SwN and 2C S

wN are 5.3 and 4.3 respectively. Eq. (5.8) and (5.9) also show

168

that the hydration of 3C S and 2C S leads to the formation of 1.3 moles of CH and

0.3 moles of CH respectively.

The volume of the hydrated clinker phases in the cement is calculated with

Eq. (5.10). In Eq. (5.10), _ck oiV is the initial volume of the clinker phases in the

cement.

_( ) [1 ( )]ck ck oi i iV t V tα= − (5.10)

- -C S H and CH are produced by the hydration of 3C S and 2C S . The

volume of - -C S H is calculated with Eq. (5.11).

3 2

3 2( ) ( ) ( )C S C S

C S H C S H C S C S H C SV t V t V tα α− − − − − −= × + × (5.11)

3C SC S HV − − and 2C S

C S HV − − , which are asymptotic volumes produced by the hydration

of 3C S and 2C S , are calculated by Eq. (5.12) and (5.13) respectively.

33 33

* //

C SC S C SC SC S H

C S Hoc C S H C S H

V NV

ρ µρ µ

− −− −

− − − −

= × ; 3 3

3

* C S C SC S co

c ii

M mV m

ρ ρ= =∑

(5.12)

22 22

* //

C SC S C SC SC S H

C S Hoc C S H C S H

V NV

ρ µρ µ

− −− −

− − − −

= × ; 2 2

2

* C S C SC S co

c ii

M mV m

ρ ρ= =∑

(5.13)

169

The volume of CH is calculated using Eqs. (5.14) - (5.16), which are similar

to Eqs. (5.11) - (5.13).

3 2

3 2( ) ( ) ( )C S C S

CH CH C S CH C SV t V t V tα α= × + × (5.14)

33 33

* //

C SC S C SC SCH

CHoc CH CH

V NV

ρ µρ µ

= × (5.15)

22 22

* //

C SC S C SC SCH

CHoc CH CH

V NV

ρ µρ µ

= × (5.16)

The parameters used in these equations are taken from Bernard (2003) and

summarized in Table 5.3.

Table 5.3. Parameters for the determination of the volume fractions

Reactants Products Parameters

3C S 2C S 3C A 4C AF W C 3.4 2 8C S H− − CH* 3[ / ]i g cmρ

3

*C Sρ

2

*C Sρ

3

*ACρ

3

*AFCρ 1 3.15 2.04 2.24

im 0.543 0.187 0.076 0.073 - - - - [ / ]i g molµ 228.32 172.24 270.20 430.12 18 - 227.2 74

iC S HN − − 1.0 1.0 - - - - - -

iCHN 1.3 0.3 - - - - - -

iwN 5.3 4.3 10.0 10.75 - - - -

The capillary voids produced by the chemical shrinkage of the hydrates

occurring during the hydration can be approximately calculated using Eq. (5.17) [see,

Bentz (2006)].

170

capillary voids ( )os c cV C V tρ α= ⋅ ⋅ ⋅ (5.17)

sC is the chemical shrinkage per gram of cement. The value of 0.07 /ml g by

Bentz (2006) is used in this study. All volume fractions are calculated using

Eq. (5.18). _ .total

level c pV is calculated from the initial volume of the cement and water in

the mixture because the value is constant with time. The volume fraction occupied by

aluminates is calculated from Eqs. (5.18) and (5.19).

_ .

1oi i ci i ctotal o o

wlevel c p c w

V V wf V VcV V V

ρρ

⎛ ⎞= = = ⋅ + ⋅⎜ ⎟+ ⎝ ⎠

(5.18)

capillary voids1 ckAL C S H i CH w

i

f f f f f f− −⎛ ⎞= − + + + +⎜ ⎟⎝ ⎠

∑ (5.19)

Under the condition of complete hydration ( 1α = ), the volume fractions of

the cement paste, with a w/c ratio of 0.5 and 0.67, are calculated using the described

equations and summarized in Table 5.4. The w/c ratio of 0.67 was used for residual

compression tests in the present study.

Table 5.4. Volume fractions of constituents at cement paste level (w/c=0.5 and 0.67)

Volume fractions % (w/c=0.5) % (w/c=0.67) C S Hf − − 53.69 44.45

CHf 15.71 13.01

ALf 15.76 13.04

capillary voidf 8.56 7.09

wf 6.28 22.41

171

In the cement paste with w/c ratio of 0.5, the remaining water and capillary

void form a macro porosity of 14.84 % ( 14.84%capillary void wf f+ = ). These values

agree with the results from Taylor (1997) and Hansen (1986) quite well.

5.3.2. Volume fractions of the phases at the mortar and concrete levels

The volume fractions of the constituent phases at the mortar and concrete

levels are related to the mass proportions of the concrete mix design. At the mortar

level, the volume fractions of the cement paste and sand can be calculated from

Eq. (5.20).

/ ; 1/ / /

os s s

s cp so o oc w s c c w w s s

f uf f ff f f u u u

ρρ ρ ρ

= = = −+ + + +

(5.20)

In which, cu , wu , and su are the masses per unit volume for cement, water,

and sand respectively. cρ , wρ , and sρ are the mass densities of cement, water, and

sand respectively. cpf and sf are the volume fractions of cement paste and sand in

mortar respectively. The volume fractions at the concrete level are obtained by

considering the coarse aggregate (gravel) in Eq. (5.21).

/; 1

/ / / /

og g g

g m go o o oc w s a c c w w s s g g

f uf f f

f f f f u u u uρ

ρ ρ ρ ρ= = = −

+ + + + + + (5.21)

172

In which, gu is the mass of coarse aggregate per unit volume. gρ is the mass

density of coarse aggregate. mf and gf are the volume fraction of mortar and coarse

aggregate in concrete respectively.

Table 5.5. Density of different rock groups (Road research laboratory, 1959)

Rock group Range of specific gravity

Average specificgravity Density ( 3/kg m )

Basalt 2.6-3.0 2.80 2800 Flint 2.4-2.6 2.54 2540

Granite 2.6-3.0 2.69 2690 Gritstone 2.6-2.9 2.69 2690 Hornfels 2.7-3.0 2.82 2820

Limestone 2.5-2.8 2.66 2660 Porphyry 2.6-2.9 2.73 2730 Quartzite 2.6-2.7 2.62 2620

Table 5.6. Volume fractions at mortar and concrete level (w/c=0.67)

Contents Mix Design( 3/kN m )

Density ( 3/kg m )

oif Mortar level Concrete level

Cement 3.49 3150.00 0.012Sand 8.32 2690.00 0.032 sf = 0.47 gf =0.37

Water 2.33 1000.00 0.024Coarse agg 10.12 2690.00 0.039 cpf =0.53 mf =0.63

5.4. A multi-scale stoichiometric model for phase transformations

5.4.1. Phase transformations at the cement paste level

It is difficult to calculate each phase transformation exactly with temperature

increase because, with respect to temperature increase, the stoichiometric reactions

173

have not yet been conclusively established with experimental data. Therefore, some

hypotheses are required to predict each phase transformation. In the present model,

the following hypotheses are used.

First, the total volume of hardened cement paste varies under different

temperatures (Bazant and Kaplan, 1996). It expands during heating up to about

150 °C; the maximum expansion is 0.2 %. No further expansion occurs between

150 °C and 300 °C. Between 300 °C and 800 °C the hardened paste shrinks, where

shrinkage is between 1.6 and 2.2 % at 800 °C. The expansion and shrinkage of

cement paste are quite small comparing with the total volume. Therefore, the initial

total volume of the cement paste is considered as a constant.

Secondly, volume fraction of each phase in a phase transformation is assumed

as a linear function between the beginning and ending temperature. For instance,

- -C S H is decomposed continually up to 800 °C. The free water is evaporated at

about 100-120 °C and bound water is gradually released up to 800 °C. The loss of the

bound water is assumed to be a linear function between 100 °C and 800 °C.

Thirdly, loss of carbonation between 600°C and 900°C and the increase of

calcite ( 3CaCO ) between 600 °C and 800°C are neglected.

Lastly, the aluminum hydrates are regarded as non-reactive substances

regardless of temperature increase.

The capillary void, the remaining water, and the water in gel pores are

regarded as the initial total void at the cement paste level.

_void cement w capillary void water in gel poresf f f f= + + (5.22)

174

By Copeland and Hayes (1953), the water volume in gel pores is about

28 % of the total volume of the gel. In the present model, the volume of the water in

gel pores is considered as 28 % of - -C S H volume.

Table 5.7. Processes of decomposition depending on the temperature regime

Temperature Decomposition 20-120°C Evaporation of free water, Dehydration of C-S-H and ettringite 120-400°C Dehydration of C-S-H 400-530°C Dehydration of C-S-H, Dehydration of CH 530-640°C Dehydration of C-S-H, Decomposition of poorly crystallized 3CaCO640-800°C Dehydration of C-S-H , Decomposition of 3CaCO

Different processes of decomposition obtained from literature are summarized

in Table 5.7 with respect to different temperature ranges (from 20 °C to 800 °C).

Since the water in the gel pores is assumed as the initial void, it should be noted that

Eq. (5.8) and (5.9) are balanced assuming all of the hydration products are saturated.

After evaporation of free water in gel pores, the chemical formula of C-S-H is

regarded as 3.4 2 3- -C S H [Tennis and Jennings, 2000]. This means that 5 moles of

2H O (free water in gel pores) per 1 mole of - -C S H is evaporated between 100-

120 °C. Thus, after evaporation of free water in gel pores, the decomposition of

- -C S H is described by Eq. (5.23). Between 400 °C and 530 °C, the decomposition

of calcium hydroxide (CH) is expressed using Eq. (5.24).

2 2 2 23.4 2 3 3.4 2 3CaO SiO H O CaO SiO H O⋅ ⋅ → ⋅ + ↑ (5.23)

2 2( )Ca OH CaO H O→ + ↑ (5.24)

175

The volume of water decomposed from - -C S H and CH is regarded as an

additive void. It is assumed that CH and - -C S H are completely decomposed at

530 °C and 800 °C, respectively. Under this assumption the volume fraction of the

decomposed total water from - -C S H (between 120 °C and 800 °C) and CH

(between 400 °C and 530°C) is calculated using Eq. (5.25).

//

w i i ii i w

w w

f f N ρ µρ µ

= × × (5.25)

In which, wif is the volume fraction of water decomposed from phase i

[i= 3.4 2 3C S H and CH] in the cement paste. if is the initial volume fraction of phase i.

Particularly, it should be noted that C S Hf − − is the volume fraction after evaporation of

the free water in C-S-H gel pores. /iw w iN n n= denotes the value wn as a number of

moles of water decomposed from 1in = mol of phase i ( C S HwN − − =3.0 and CH

wN =1.0).

The density and molar mass of 3.4 2 3C S H are 31.75 /g cm and 365 /g mol respectively

(Tennis and Jennings, 2000). The parameters for CH and water are listed in Table 5.3.

Finally, the volume of calcium oxide (CaO) produced from the decomposition

of CH is obtained by deducting the decomposed water volume from initial volume of

CH. From the same methodology, the volume of 3.4 2C S produced from the

decomposition of 3.4 2 3C S H is obtained by deducting the decomposed water volume

from initial volume of 3.4 2 3C S H .

176

Table 5.8. Theoretical formulas for volume fraction change of each phase (w/c=0.67)

Temperature Formulas (%)

3.4 2 3

24.706 10 37.649C S Hf T−= − ⋅ +

3.4 2

23.488 10 4.185C Sf T−= ⋅ − 120 T 800C C≤ ≤

3.4 2 3

21.218 10 1.462wC S Hf T−= ⋅ −

0.10 53.028CHf T= − ⋅ + 24.554 10 18.215CaOf T−= ⋅ − 400 T 530C C≤ ≤

25.452 10 21.806wCHf T−= ⋅ −

0

20

40

60

80

100

20 150 280 410 540 670 800

Temperature (C)

Rel

ativ

e vo

lum

e (%

)

Non-reactive substances

C-S-H

CH

CS

CaO

Pore space

Figure 5.3. Change of phase composition with increasing temperature (w/c=0.67)

The theoretical formulas for the volume fraction change of each phase

considering temperature ranges and w/c ratio are obtained from schemes described

above. Table 5.8 shows the theoretical formulas of each phase in cement paste with a

w/c ratio of 0.67 for the given temperature ranges. Fig. 5.3 shows the result for the

177

volume fraction change with the transformations of each phase up to 800 °C using the

formulas presented in Table 5.8.

5.4.2. Validation of current model at cement paste level

There has been no quantitative measurements considering changes of all the

phases ( - -C S H , CH , CaO , solid grains, and so on) in cement paste with respect to

temperature increase. Thus, the validation of the present model is done by (1) using

the variation of pore volume under elevated temperatures measured experimentally by

Piasta et al. (1984), and (2) comparing the theoretical calculation for the porosity

change by Harmathy (1970).

Table 5.9. Mass fractions of clinker phases in the cement

Clinker phases 3C Sm

2C Sm 3C Am

4C AFm Others Piasta et al. (1984) 0.632 0.154 0.099 0.080 0.035 Harmathy (1970) 0.470 0.270 0.116 0.090 0.054

Table 5.9 shows the mass fractions of clinker phases for the cements used in

the experiments of Piasta et al. (1984) and the theoretical calculation of Harmathy

(1970). Piasta et al. (1984) performed various experimental studies related to the

thermal properties of concrete with w/c of 0.4 at elevated temperatures. Harmathy

(1970) calculated the porosity, the true density, and the bulk density of an idealized

cement paste with w/c of 0.5 at elevated temperature using formulae based on the

work of Powers (1960).

178

Table 5.10 shows the result of porosity tests between 20 °C and 800 °C by

Piasta et al. (1984). To compute the volume fraction of the voids in cement paste

from the test data of Piasta et al. (1984), the density of cement paste is approximated

using Eq. (5.26).

(1 / )1 ( / ) ( / )

cp w c ccp

cp w c c w

m m m w cV V V w c

ρρρ ρ

+ ⋅ += = =

+ + ⋅ (5.26)

The volume fraction of the voids from the test data is calculated as the product

of the density of cement paste using Eq. (5.26) and the value of total porosity.

Table. 5.10. Porosity and pore size distribution [w/c=0.4, (Piasta et al, 1984)]

In Eq. (5.6), ( )wV t has a positive value beyond the w/c ratio of 0.45 for the

cement used in their test. For w/c ratio of 0.4, the volume fraction of completely

hydrated cement compounds is 0.89. The remaining 11 % of cement compounds

exists as solid grains (non-reactive substances) in the cement paste. To reflect this

179

volume fraction of completely hydrated grains in Eqs (5.6), (5.11), (5.14), and (5.17),

( )i tα , the hydration degree, is multiplied by the factor of 0.89 for these equations. The

remaining procedures are the same as mentioned in Chapter 5.4.1.

0

20

40

60

80

100

0 100 200 300 400 500 600 700 800 900Temperature (C)

Vol

ume

frac

tion

of p

ore

spac

e (%

)

w/c=0.4 [Piasta et al. (1984)]

w/c=0.4 [Current model]

Figure 5.4. Comparison between current model and test data by Piasta et al. (1984)

0

20

40

60

80

100

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Vol

ume

frac

tion

of p

ore

spac

e (%

)

w/c=0.5 [Harmathy (1970)]

w/c=0.5 [Current model]

Figure 5.5. Comparison between current model and model of Harmathy (1970)

180

Table 5.11. Summary for the results shown in Fig. 5.4 and Fig. 5.5

Volume fraction of pore space (%) Temp. (°C) Piasta et al.

(w/c=0.4) Prediction(w/c=0.4) Diff. Harmathy

(w/c=0.5) Prediction (w/c=0.5) Diff.

100 22.64 23.28 0.65 44.00 28.04 15.96 200 22.44 24.43 1.99 47.00 29.18 17.82 300 23.81 25.86 2.05 51.00 30.61 20.39 400 26.34 27.29 0.95 52.00 32.05 19.95 500 28.68 35.58 6.90 54.00 39.11 14.89 600 41.17 39.07 2.10 57.00 42.23 14.77 700 47.81 40.51 7.30 58.00 43.66 14.34 800 43.51 41.94 1.58 61.00 45.10 15.90

The comparison for pore volume fractions between the present model and the

test data by Piasta et al. (1984) is shown in Fig. 5.4. Fig. 5.5 shows the comparisons

between the present model and the theoretical calculation by Harmathy (1970).

Table 5.11 is a summary of the results shown in Fig. 5.4 and Fig. 5.5. The current

model predicts the test results by Piasta et al. (1984) very well. The difference

between the present model and the model by Harmathy (1970) is larger than the

difference between the present model and the test results by the Piasta et al. because

the model of Harmathy (1970) assumed that cement was only composed of 3C S

(0.653 as the weight fraction) and 2C S (0.365 as the weight fraction). In other words,

for the prediction of voids in a cement paste, Harmathy’s model only considered two

phases ( - -C S H and CH), which are formed from the 3C S and 2C S components, as

the total volume of cement paste. This assumption might cause a larger error than the

present model because the model overestimates the volume of voids with respect to

temperature increase.

181

5.4.3. Volume fractions of the phases according to temperature increase at the

mortar and concrete level

At an elevated temperature, aggregates expand. However, the total volume of

aggregates is assumed to be constant in the calculation for the volume fractions of

sand and gravel.

Table 5.12. Volume fraction of phases at mortar level (w/c=0.67)

Temperature (°C) Volume (%) 20 T 120C C≤ ≤ 200°C 400°C 600°C 800°C

3.4 2 3C S H 16.87 14.88 9.92 4.96 0.00

3.4 2C S 0.00 1.47 5.15 8.82 12.50 CH 6.86 6.86 6.86 0.00 0.00 CaO 0.00 0.00 0.00 3.12 3.12 AL 6.88 6.88 6.88 6.88 6.88

_void cement 22.11 22.62 23.91 28.93 30.21 sand 47.29

Table 5.13. Volume fraction of phases at concrete level (w/c=0.67)

Temperature (°C) Volume (%) 20 T 120C C≤ ≤ 200°C 400°C 600°C 800°C

3.4 2 3C S H 10.71 9.45 6.30 3.15 0.00

3.4 2C S 0.00 0.93 3.27 5.60 7.93 CH 4.35 4.35 4.35 0.00 0.00 CaO 0.00 0.00 0.00 1.98 1.98 AL 4.36 4.36 4.36 4.36 4.36

_void cement 14.03 14.36 15.17 18.36 19.18 sand 30.02

gravel 36.53

182

The volume fractions of each phase with respect to temperature increase at the

mortar and concrete levels are calculated with Eq. (5.27) and (5.28).

'_ _i mortar i cp mortarf f f= ⋅ ; _s motar sf f= , at mortar level (5.27)

'_i con i cp mf f f f= ⋅ ⋅ ; _s con s mf f f= ⋅ ; _g con gf f= , at concrete level (5.28)

In which, if is the volume fraction for 3.4 2 3C S H , CH , AL , 3.4 2C S , CaO ,

and _void cement which changed with temperature increase at the cement paste

level. Table 5.12 and Table 5.13 show volume fractions of each phase at the mortar

level and concrete levels respectively (w/c=0.67).

5.5. Composite theories and damage theories

Based on composite mechanics theory the effective modulus, Eeff, of a two-

phase composite can be expressed with Eq. (5.29).

( )2 1eff jE f c E= (5.29)

In which, 1E is the modulus of phase 1 (may be considered as the matrix). c2 is

the volume fraction of phase 2 (may be considered as the inclusion) for the total

volume, which contains volume 1V for phase 1 and volume 2V for phase 2, in such a

manner that 1 2V V V+ = . Depending on the volume fraction and distribution of the

183

phase 2 in the phase 1, ( )2jf c represents the variation of the effective modulus due

to the appearance of phase 2. Subscript j represents different types of distributions of

the phase 2.

If the phase 2 is distributed parallel to the loading direction, ( )2jf c is

expressed with Eq. (5.30) and the corresponding effE gives the upper bound for the

modulus.

2 2 2 2 1( ) (1 ) ( / )parellelf c c c E E= − + (5.30)

It is also known as Voigt’s model, an iso-strain model, because the strains in

phase 1 and phase 2 are the same in a representative volume element (RVE).

If the phase 1 and the phase 2 are distributed serial to the loading direction,

( )2jf c is expressed with Eq. (5.31) and the corresponding effE gives the lower

bound for the modulus.

( )2 2

1 22

1

11/

( )serial

c cE E

f cE

⎡ ⎤−⎧ ⎫+⎨ ⎬⎢ ⎥

⎩ ⎭⎣ ⎦= (5.31)

It is also known as Ruess’s model, an iso-stress model, because the stresses in

phase 1 and phase 2 are the same in RVE.

If the phase 2 is in a spherical shape of different sizes and distributed

randomly within phase 1, ( )2jf c is expressed with Eq. (5.32)

184

]1)//[(13/)1(

1)(122

22 −+−

+=EEc

ccfspherical (5.32)

Eq. (32) is called the spherical model for damage distribution or generalized

self-consistent model for effective modulus of two-phase composite. The

corresponding effE is between the lower and upper bounds.

As long as analytical solutions for ( )2jf c are available, Eq. (5.29) can be

used for the effective modulus of composites with any distribution of phase 2,

although only three different types of distributions, i.e. j = parallel, serial, and

spherical are shown here.

It is worthwhile to point out that when the parallel model is used and the

phase 2 is considered as the damaged phase with modulus 2 0E = , Eq. (5.29) and

(5.30) become Eq. (5.33) and (5.34), respectively.

( )2 11effE c E= − (5.33)

)1()( 22 ccf parellel −= (5.34)

As one can see, Eq. (5.33) is the fundamental equation used in conventional

scalar damage mechanics developed by Kachanov in 1958 (Lemaitre 1992;

Krajcinovic 1996). This implies that the conventional scalar damage mechanics

considered a special distribution for the damaged phase, i.e. parallel distribution of

the damaged phase in distressed materials. Therefore, the conventional scalar damage

185

mechanics represents the upper bound of all possible damage distributions and

developments.

Recently developed composite damage mechanics is a more general damage

theory, capable of handling various types of damage distributions and developments

(Xi 2002; Xi and Nakhi 2005; Xi et al. 2006). In this study, the composite damage

mechanics together with the spherical model is used, Eq. (5.29) and Eq. (5.32), under

the assumption that the transformed phases in the concrete due to high temperatures

are distributed randomly as spherical shape of different sizes within the original

phases.

5.6. Thermal degradation of the modulus elasticity of concrete

When phase transformations take place in concrete under high temperatures.

Some phases with high moduli convert to other phases with lower moduli and might

even have a modulus equal to zero (i.e. void). Nucleation of voids in this case, is due

to the evaporation of water at high temperature. As described in section 4, water

includes the existing water in the concrete as well as the water generated by the phase

transformations.

By considering the phase transformations taking place in the concrete as

independent processes (which could be simultaneous but with no coupling effect), the

following equation, Eq. (5.35) for the effective modulus of concrete can be developed

based on the composite damage mechanics, Eq. (5.29).

186

( )3.4 2 3

3.4 2 3

,, ,_ _

,_

....T C S HT T i T CHeff spherical con ref spherical spherical con ref

NT i

spherical con refi C S H

E f E f f E

f E=

= = ⋅ ⋅

⎛ ⎞= ⋅⎜ ⎟

⎝ ⎠∏

(5.35)

Eq. (5.35) considers the phase transformations described in Chapter 5.4. The

function ,T isphericalf , which denotes the thermal degradation factor of the elastic modulus

from each original phase to their respective decomposed phases. Eq. (5.35) is a result

of recursive applications of Eq. (5.29), with each transformation described by its own

function ,T isphericalf . For example, 3.4 2 3C S H is decomposed into 3.4 2C S and 2H O

(considered as new void) with temperature increase as shown in Eq. (5.23). 2c is the

volume fraction of the decomposed phase 3.4 2C S with respect to the original phase

3.4 2 3C S H , and 2 1/E E is the ratio for the elastic modulus of the decomposed phase

3.4 2C S ( 2E ) to the original phase 3.4 2 3C S H ( 1E ). The effective stiffness considering

the original phase 3.4 2 3C S H and the decomposed phase 3.4 2C S is obtained by putting

Eq. (5.32) into Eq. (5.29).

To obtain the finalized thermal degradation factor for the original phase

3.4 2 3C S H , Eq. (5.32) is applied again for the second decomposed phase 2H O . In

Eq. (5.33), the stiffness of original phase, 1E , is the effective stiffness 3.4 2 3.4 2 3_C S C S HeffE ,

which is obtained from 3.4 2 3C S H and the previous transformation 3.4 2C S . The volume

fraction and stiffness of the 2H O (new void) phase are c2 and E2 (where the phase is

void, 2E =0). Eq. (5.36) is the function for the thermal degradation factor of the

187

elastic modulus transformed from 3.4 2 3C S H (the original phase) to 3.4 2C S and 2H O

(the respective decomposed phases).

23.4 2 3

3.4 2 3.4 2 3

2 2

,_1

(1 ) / 3 1/[( / ) 1]H OT C S H

spherical C S C S HH O H O eff

cf

c E E= +

− + − (5.36)

In the determination of the order of the decomposed phases in application of

the composite damage mechanics, it is noticed that effE obtained from the first

decomposed phase should be higher value than the elastic modulus of the second

decomposed phase because the thermal degradation factor should always be less than

or equal to 1. In summary, the modulus ratios in ,T isphericalf is not simply the stiffness

ratio of the product and the reactant, but the stiffness ratio of the product and the

effective media.

It is important to point out that Eq. (5.35) does not include the effect of

thermal degradation of aggregates used in concrete. The aggregates experience

various phase changes during thermal treatments of different heating and cooling

rates. Therefore, another function, agg_degf , for the thermal degradation of aggregates

is introduced. Eq. (5.37) is the final thermal degradation function for the elastic

modulus of concrete. Eq. (5.38) is the total thermal degradation factor of concrete

( )3.4 2 3

,agg_deg _ _

NT T ieff spherical con ref con ref

i C S H

E f f E F T E=

⎛ ⎞= ⋅ ⋅ =⎜ ⎟

⎝ ⎠∏ (5.37)

188

3.4 2 3

,agg_deg( )

NT i

sphericali C S H

F T f f=

⎛ ⎞= ⋅⎜ ⎟

⎝ ⎠∏ (5.38)

5.7. Comparison between present model and experimental results

To calculate the thermal degradation of elastic modulus of concrete using the

present model, the stiffness of each phase must be evaluated. Table 5.14 is a summary

for elastic properties of the constituent phases obtained from literatures.

Table 5.14. Elastic properties of constituent phases

Phases ( )E Gpa ( )v − References

CSH 31 4± 29.4 2.4±

- 0.24

Acker Constantinides and Ulm

3C S 135 7± 147 5±

0.3 0.3

Acker Velez et al.

2C S 140 10± 130 20±

0.3 0.3

Acker Velez et al.

CH

35.24 48

39.77 44.22− 36 3± 38 5±

- -

0.305 0.325−- -

Beaudoin Wittmann

Monteriro and Chang Acker

Constantinides and UlmCaO 194.54 0.5± 0.207 Oda et al.

3C A 160 10± 145 10±

- -

Acker Velez et al

3C AF 125 25± - Velez et al

It is noticed that the elastic modulus of CS decomposed from - -C S H and

CaO decomposed from CH vary depending on the porosity of the phases. The

porosities of CaO and 3.4 2C S are therefore calculated using the volume fractions of

189

the phases decomposed from CH and 3.4 2 3C S H . The functions are shown in

Eq. (5.39).

2

2

_

_ _

H O CHCaO

CaO CH H O CH

Vp

V V=

+; 2 3.4 2 3

3.4 2

3.4 2 3.4 2 3 2 3.4 2 3

_

_ _

H O C S HC S

C S C S H H O C S H

Vp

V V=

+ (5.39)

Table 5.15. Elastic moduli of each phase used in the present model

Phases ip (Porosity) E (Gpa )

3.4 2 3C S H - 32.0

3.4 2C S 0.26 29.79 [from3.4 2

120 (1 )nC SE p= ⋅ − , n=4.65]

CH - 40.2 CaO 0.54 8.35 [from 194.54 (1 )n

CaOE p= ⋅ − , n=4] Void - 0

Table 5.15 is a summary for the elastic modulus of each phase used in the

present model. The functions for the elastic modulus of CaO and 3.4 2C S with respect

to porosity are based on empirical functions by Velez et al (2001). The fixed variable

(n) in the function, on Table 5.15, for the elastic modulus of CaO is assumed as 4,

which is an average value for variables used in the functions for 2C S and 2C A by

Velez et al (2001). ,T ALsphericalf for the aluminum hydrates is 1 because they were

assumed to be a non-reactive substance. Thus, the elastic moduli of the aluminum

hydrates are not used in the calculation of the thermal degradation.

0.002agg_deg 0.03921 Tf e−= + (5.40)

190

The thermal degradation ( agg_degf ) of the aggregates is taken from Bazant and

Kaplan (1996).

Finally, the prediction model for the thermal degradation of elastic modulus

can be expressed in terms of temperature, combining the relevant equations in

previous sections. Since the capillary void, remaining water, and water in gel pores of

- -C S H are assumed as the initial total void from 20°C to 120°C in the model, the

thermal degradation factor of concrete for 20-120°C is the same as the thermal

degradation ( agg_degf ) for the elastic modulus of the aggregates. Eq. (5.41) through

(5.43) are the thermal degradation factors of concrete according to temperature ranges.

For 120-400°C,

3 0.002 3 6

3 6

(39.21 10 ) (697.126 10 253.828 10 )( )(651.437 10 126.914 10 )

Te TF TT

− − − −

− −

⋅ + ⋅ ⋅ − ⋅=

⋅ + ⋅ (5.41)

For 400-530°C,

4 2 0.002

2 5 3 6

563.948 10 (3.921 10 )(178.434 10 279.418 10 ) (697.126 10 253.828 10 )

( )(77.1825 ) (5132.91 )

TeT T

F TT T

− −

− − − −

⎡ ⎤⋅ ⋅ ⋅ + ⋅⎢ ⎥

⋅ − ⋅ ⋅ ⋅ − ⋅⎣ ⎦=+ ⋅ +

(5.42)

For 530-800°C,

( )3 2 0.002 3 6

3 6

357.689 10 (3.921 10 ) (697.126 10 253.828 10 )( )651.437 10 126.914 10

Te TF TT

− − − − −

− −

⋅ ⋅ ⋅ + ⋅ ⋅ − ⋅=

⋅ + ⋅

(5.43)

191

The prediction model is compared with the test data from previous researchers

including our own study (Lee et al., 2006). Table 5.16 is a summary for the results of

elastic modulus (chord modulus calculated by ASTM C 469) obtained from the

residual compression test. Table 5.17 shows the values of the relative elastic modulus

for the three cooling methods.

Table 5.16. Elastic moduli from residual compression test

E : Elastic modulus (psi) Temp.(°C) Slow cooling Natural cooling Water cooling

25 2.96E+06 2.96E+06 2.96E+06 200 2.02E+06 1.94E+06 1.60E+06 400 1.07E+06 9.90E+05 4.53E+05 600 2.12E+05 1.64E+05 7.94E+04 800 4.61E+04 2.82E+04 1.87E+04

Table 5.17. Relative elastic modulus

Relative elastic modulus Temp. (°C) Slow cooling Natural cooling Water cooling

25 1.0000 1.0000 1.0000 200 0.6818 0.6568 0.5414 400 0.3631 0.3345 0.1531 600 0.0715 0.0555 0.0268 800 0.0156 0.0095 0.0063

Fig. 5.6 shows the comparison between the present model and the test data in

our study and by previous researchers. The present model satisfactorily predicts the

trend of the test results. In the tests by previous researchers, the experimental

conditions [such as w/c ratios, curing ages, heating rates, holding times at each target

temperature, loading time (unstressed test and residual test)] are different from each

other. However, it is shown in Fig. 5.6 that the trend for the thermal degradation of

192

the elastic modulus of concrete is similar. The model predicts the test results with

relatively good accuracy.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 100 200 300 400 500 600 700 800

Temperature (C)

Rel

ativ

e e

last

ic m

odul

us (E

)

Slow coolingNatural cooingWater coolingCurrent modelPimienta and Hager (2002)Felicetti et al. (1996)Morita et al. (1992)Diederichs et al. (1988)

Figure 5.6. Comparison between current model and test data

5.8. Conclusions

1. A multiscale model was established for predicting the thermal degradation of the

modulus of elasticity of concrete under different temperature ranges. The internal

structure of concrete was considered at three scale levels: cement paste, mortar, and

concrete. Cement paste is considered as a multiple phase composite with cement

particles and all hydration products; mortar is a mixture of cement paste and sand;

and concrete is a mixture of mortar and gravel.

193

2. At the cement paste level, the phase transformations in cement paste under high

temperature were modeled by stoichiometric relations, which give the volume

fractions of the products of the phase changes. The effective elastic modulus of

cement paste under a certain temperature was then calculated based on composite

models and using the volume fractions of the constituent phase at the temperature.

The water released during the heating process is considered as part of voids with zero

modulus of elasticity.

3. The variation of pore volume with increasing temperature was predicted by the

present model, and compared with the test data by Piasta et al. (1984). The present

model predicted the test results very well. The change of porosity by the present

model was also compared with the model prediction by Harmathy (1970), which

showed some difference. The difference was due to the assumption used in

Harmathy’s model, that is, the cement is only composed of 3C S (0.653 as the weight

fraction) and 2C S (0.365 as the weight fraction), and other phases were neglected.

4. At the mortar and concrete levels, the effective elastic moduli of mortar and

concrete under a certain temperature was calculated based on composite models and

using the volume fractions and moduli of cement paste, sand, and gravel. The elastic

modulus of cement paste came from the effective modulus obtained from the lower

level model, and the variations of elastic moduli of various sand and gravels were

established based on available test data in the literature.

5. The present model for the thermal degradation of elastic modulus of concrete

predicted satisfactorily the basic trend shown in the available test results which

included various concrete mix design parameters and heating and cooling conditions.

194

6. The multi-scale chemo-mechanical model provided a general framework that can

be used in the prediction for thermal degradations of elastic modulus as well as other

properties of concrete, such as thermal strain and diffusivity of concrete under high

temperatures.

195

CHAPTER 6

6. A MULTISCALE CHEMO-MECHANICAL MODEL FOR THERMAL STRAIN

OF CEMENT PASTE AND CONCRETE UNDER HIGH TEMPERATURES

6.1. Introduction

The expansion of concrete subjected to extreme elevated temperature is linked

with intricate micro-structural variations. This study proposes a model to predict the

thermal strains of cement paste and concrete considering micro-structural changes

under elevated temperatures ranging from 20°C to 800°C. The model can consider

characteristics of various aggregates in the calculation of thermal expansion for

concrete. The model is a combination of the multi-scale stoichiometric model, which

was described in Chapter 5.2 through 5.4, and a multi-scale composite model, which

was proposed by Xi and Jennings (1997). At the cement paste level, the model

satisfactorily predicted a test result. At the concrete level, upper bounds from the

model were matched relatively well with test results by previous researcher. If the

mechanical properties, such as elastic modulus (E), Poisson’s ratio (ν), and thermal

deformation, of the aggregates used in concrete are given, it is likely that the model

will reasonably predict experimental results. In Chapter 6.2, the model for shrinkage

of cement paste and concrete using the effective homogeneous theory proposed by Xi

196

and Jennings (1997) is briefly introduced. In Chapter 6.3, the information for the

stiffness, Poisson’s ratio, and thermal expansion of each phase are analyzed from

literature review. The analyzed results are used in the model. In Chapter 6.4, the

model predictions are compared with available test data in the literature. Chapter 6.5

is conclusions.

6.2. Model for shrinkage of cement paste and concrete

Concrete is a heterogeneous material in which constituents are distributed

randomly. Thus, there is no exact solution in modeling material properties

considering constituents in concrete. To simplify the internal structure of a material,

composite models for effective properties have been developed. The three phase

model developed by Cristensen (1979 a, 1979 b) was originally developed for elastic

properties only, but Herve and Zauoi (1990) have shown that the model can be

extended to nonlinear materials.

(a) Concrete (b) Partitioning (c) Spherical model

Figure 6.1. Simplification to spherical model

197

Effective homogeneous medium (Phase 3)

Phase1

Phase2

Effective homogeneous medium (Phase 3)

Phase1

Phase2

Figure 6.2. Three-phase effective media model

In Fig. 6.1, the meso-structure of concrete [Fig. 6.1 (a)] can be expressed as

Fig. 6.1 (b) by partitioning aggregate and matrix. In the spherical model the partitions

are simplified using spherical elements, Fig. 6.1 (c), such that the volume fraction of

each phase and internal structure in an element are the same regardless of the size of

elements. The spherical elements have three dimensional features, reducing the

problem to one dimension [Xi and Jennings (1997)]. On the nanometer and

micrometer scales, the spherical model can be applied. Fig. 6.2 shows the three-phase

effective media model, where phase 3 is the effective homogeneous medium made

equivalent to the heterogeneous medium.

Xi and Jennings (1997) proposed a model for shrinkage of cement paste and

concrete using the effective homogeneous theory. The proposed model is obtained by

combining the model for shrinkage proposed by them and the multi-scale

stoichiometric model described in Chapter 5. Although the model by Xi and Jennings

is for shrinkage, it can also be used for effective thermal expansion in a

heterogeneous medium. The effective bulk modulus and strain for the effective

198

homogeneous phase shown in Fig. 6.2 are expressed using Eq. (6.1) and (6.2)

respectively.

( )11 2

12 1 22

1 1 2

1 22 2

1 1 43

eff

V K KV V

K K

V K KV V K G

⎛ ⎞⋅ −⎜ ⎟+⎝ ⎠= +

⎛ ⎞⎜ ⎟⎛ ⎞ −

+ − ⋅⎜ ⎟ ⎜ ⎟+⎝ ⎠ +⎜ ⎟⎝ ⎠

(6.1)

( ) ( )

( ) ( )

1 11 1 2 2 2 2 1 2

12 1 2 1 2

12 2 2 2 2 1

1 2

3 4 1 3 4

3 4 4eff

V VK K G K K GV V V V

VK K G G K KV V

ε εε

⎛ ⎞ ⎛ ⎞⋅ + + − ⋅ +⎜ ⎟ ⎜ ⎟+ +⎝ ⎠ ⎝ ⎠=

⎛ ⎞+ − ⋅ ⋅ −⎜ ⎟+⎝ ⎠

(6.2)

In which, iK , iV , and iG are the bulk modulus, volume fraction, and shear

modulus of phase i , respectively. The general forms of effective bulk modulus and

strain are delineated as Eq. (6.3) and (6.4), respectively [see, Xi and Jennings (1997)].

( ) ( )

( ) ( )

1, 1

11,1 1 4

3

i i eff iieff ii

eff iii i

i i

c K KK K

K Kc

K G

− −

−−

⎡ ⎤⋅ −⎣ ⎦= +⎡ ⎤

−⎢ ⎥+ − ⋅ ⎢ ⎥

+⎢ ⎥⎣ ⎦

(6.3)

( ) ( ) ( ) ( ) ( ) ( )( ) ( )

1, 1,1 1 1

1,1 1

3 4 1 4 3

3 4 4eff eff i i i i i i i i i effi i i

eff ii eff i i i i i effi i

K c K G K c G K

K K G c G K K

ε εε

− −− − −

−− −

⎡ ⎤+ + − ⋅ +⎣ ⎦=⎡ ⎤ ⎡ ⎤+ − ⋅ −⎣ ⎦ ⎣ ⎦

(6.4)

In which, 2N i≥ ≥ ; ( ) 11effK K= and ( ) 11effε ε= . Parameter 1,i ic − is:

199

1

1,1 1

i i

i i j jj j

c V V−

−= =

= ∑ ∑ for 2N i> ≥ and 1

1,1

1N

N N j Nj

c V V−

−=

= = −∑ for i N= (6.5)

The parameters iG and iK can be expressed easily in terms of elastic modulus

and Poisson’s ratio. From elastic theory, / 3(1 2 )i i iK E ν= − and / 2(1 )i i iG E ν= + .

6.3. Material properties of constituents

To predict thermal expansion the information for the stiffness, Poisson’s ratio,

and thermal expansion of each phase should be given.

Experimental studies for heat deformations of cement paste were performed

by Piasta (1984 a). Thermal strains of dehydrated and hydrated substances were

measured using the dilatometer. The samples for the test were sleeve shaped with an

inner diameter of 5 mm, an outer diameter of 10 mm, and a height of 50 mm. The

dehydrated samples were compacted imparting a pressure of 40 Mpa. Paste samples

were prepared with a w/c ratio of 0.5 and compacted by means of vibration. The

investigation into heat deformation of the dehydrated substances was performed

directly after forming. The paste samples were examined after curing for 28 days

under a relative humidity of 95 % and a temperature of 20 2± °C. A heating rate of

10 °C/min was used to measure heat deformation for all substances. Thermal strain of

CaO (decomposed from CH), was calculated using the test data from the coefficient

of thermal expansion by Okayama (1978). Fig. 6.3 and Fig. 6.4 are the test data

regarding thermal strains of dehydrated and hydrated substances respectively.

200

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

C2S

Potland Cement

C4AF

C3SCaOC3A

Figure 6.3. Thermal strain test data of dehydrated substances

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

C2SH

Cement pasteC4AFH

C3SH

Ettringit

C3AH

Expansion

Contraction Ca(OH)2

Figure 6.4. Thermal strain test data of hydrated substances

201

Generally up to 150 °C hydrate substances expand because the expansion in

the dehydrated parts is more prevalent than the shrinkage of hydrated parts [Piasta

(1984 a)]. At temperatures above 150 °C shrinkage prevails due to dehydration.

In phases considered for the model at the cement paste level are 3.4 2 3C S H ,

3.4 2C S , CH , CaO , aluminum hydrates, and void space. The test data of CaO in

Fig. 6.3 and CH in Fig. 6.4 are used in the model. However, because there is no

exact information for the thermal strain of the chemical components 3.4 2C S and

3.4 2 3C S H from literature, the thermal stain of 3.4 2C S is assumed on the basis of the

test data for 2C S and 2C S in Fig. 6.3. For 3.4 2 3C S H , the average thermal strain of

2 HC S and 3 HC S is used in the model.

In the model, the thermal strain for alumina hydrates should be considered

because the thermal deformations of alumina hydrates, i.e. ettringite and 3 HC A , are

large compared to other components as shown in Fig. 6.4. In cement paste, alumina

hydrates exist in various chemical components. It is difficult to create a model that

contains the all chemical components for alumina hydrates. Usually, the hydration of

3C A and 3C AF in Portland cement involve reactions with sulfate ions which are

supplied by the dissolution of gypsum. The primary reactions of 3C A and 3C AF are

expressed with Eq. (6.6) and (6.7) respectively. (See, Sidney et al, 2002).

3 2 6 3 323 ( ) 26 ( )C A CSH gypsum H C AS H ettringite+ + → (6.6)

4 2 6 3 32 33 ( ) 21 ( , ) ( , )C AF CSH gypsum H C A F S H A F H+ + → + (6.7)

202

Ettringite (Eq. 6.6) is the first hydrate to crystallize because of the high ratio

of sulfate to aluminates in the solution phase during the first hour of hydration. In

Portland cement, which contains 5-6 percent gypsum, ettringite contributes to early

strength development. After the depletion of sulfate when the aluminate concentration

goes up again due to renewed hydration of 3C A and 4C AF , ettringite becomes

unstable and is gradually converted into monosulfate, the final product (Mehta, 1986).

Eq. (6.8) contains the chemical reaction from ettringite to monosulfate. Eq. (6.9)

shows the chemical reaction converting from 6 3 32( , )C A F S H to 4 123 ( , )C A F SH .

6 3 32 3 4 12( ) 2 4 3 ( )C AS H ettringite C A H C ASH monosulfate+ + → (6.8)

6 3 32 4 4 12 3( , ) 7 3 ( , ) ( , )C A F S H C AF H C A F SH A F H+ + → + (6.9)

In Eq. (6.7) and (6.9), iron oxide plays the same role as alumina during

hydration. F can substitute for A in the hydration products. The use of a formula such

as 6 3 32( , )C A F S H indicates that iron oxide and alumina occur interchangeably in the

compound, but the A/F ratio need not be the same as that of the parent compound.

When monosulfate comes in contact with a new source of sulfate ions ettringite can

be formed once again. This potential for reforming ettringite is the basis for sulfate

attack on Portland cement (Sidney et al, 2002).

In the present model alumina hydrates are assumed as monosulfate. However,

the information for thermal strain of monosulfate could not be found in the literature.

203

Table 6.1. Summary for thermal strain of phases in cement paste used in model

Phase Temperature Strain 20 T 600C C< ≤ 7 6149.664 10 299.328 10Tε − −= ⋅ − ⋅ 600 T 700C C< ≤ 7 5183.974 10 235.795 10Tε − −= ⋅ − ⋅ 3.4 2C S 700 T 800C C< ≤ 7 6152.974 10 187.949 10Tε − −= ⋅ − ⋅

CaO 20 T 800C C< ≤ 7 6126.923 10 253.846 10Tε − −= ⋅ − ⋅ 20 T 200C C< ≤ 8 6722.222 10 144.444 10Tε − −= ⋅ − ⋅ 200 T 270C C< ≤ 8 5464.286 10 222.286 10Tε − −= − ⋅ + ⋅ 270 T 300C C< ≤ 7 5178.846 10 580.385 10Tε − −= − ⋅ + ⋅ 300 T 400C C< ≤ 7 5215.513 10 690.385 10Tε − −= − ⋅ + ⋅ 400 T 600C C< ≤ 7 2321.667 10 1.115 10Tε − −= − ⋅ + ⋅ 600 T 650C C< ≤ 5 32.1 10 4.45 10Tε − −= − ⋅ + ⋅

3.4 2 3C S H

650 T 800C C< ≤ 6 25 10 1.245 10Tε − −= ⋅ − ⋅ 20 T 200C C< ≤ 7 6111.111 10 222.222 10Tε − −= ⋅ − ⋅ 200 T 300C C< ≤ 5 32.2 10 2.4 10Tε − −= ⋅ − ⋅ 300 T 400C C< ≤ 6 38.0 10 1.8 10Tε − −= ⋅ + ⋅ 400 T 430C C< ≤ 7 5266.667 10 566.667 10Tε − −= ⋅ − ⋅ 430 T 500C C< ≤ 7 4542.857 10 291.429 10Tε − −= − ⋅ + ⋅ 500 T 590C C< ≤ 6 4144.444 10 742.222 10Tε − −= − ⋅ + ⋅ 590 T 650C C< ≤ 7 5166.667 10 116.667 10Tε − −= − ⋅ − ⋅ 650 T 700C C< ≤ 5 32.4 10 3.6 10Tε − −= − ⋅ + ⋅

CH

700 T 800C C< ≤ 6 38.0 10 7.6 10Tε − −= − ⋅ − ⋅ 20 T 50C C< ≤ 5 42.2 10 4.4 10Tε − −= ⋅ − ⋅ 50 T 120C C< ≤ 6 38.0 10 1.06 10Tε − −= − ⋅ + ⋅ 120 T 175C C< ≤ 7 5654.545 10 795.455 10Tε − −= − ⋅ + ⋅ 175 T 300C C< ≤ 4 21.44 10 2.17 10Tε − −= − ⋅ + ⋅ 300 T 375C C< ≤ 5 39.3 10 6.4 10Tε − −= − ⋅ + ⋅ 375 T 400C C< ≤ 4 21.13 10 1.39 10Tε − −= − ⋅ + ⋅ 400 T 450C C< ≤ 5 36.4 10 5.7 10Tε − −= − ⋅ − ⋅ 450 T 500C C< ≤ 5 36.0 10 7.5 10Tε − −= − ⋅ − ⋅ 500 T 600C C< ≤ 8 4833.333 10 333.333 10Tε − −= − ⋅ − ⋅ 600 T 650C C< ≤ 7 4173.333 10 279.333 10Tε − −= − ⋅ − ⋅

4 123C ASH (Monosulfate)

650 T 800C C< ≤ 7 5533.333 10 453.333 10Tε − −= − ⋅ − ⋅

204

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

C3.4S

C3.4S2H3

Monosulfate

CaOExpansion

Contraction Ca(OH)2

Figure 6.5. Thermal strains of phases in cement paste used in model

As a matter of fact, there is no known mineral of monosulfate. Thus, the

thermal strain of the monosulfate is assumed on the basis of the test data of 3 HC A and

ettringite shown in Fig. 6.4. Table 6.1 is a summary for thermal strain functions

according to the temperature range of each phase in cement paste used in the model.

Fig. 6.5 is a plot for the thermal strains of phases from the functions.

Table 6.2. Elastic modulus and Porosity of each phase

Phases ip (Porosity) E (Gpa )

3.4 2 3C S H - 32.0

3.4 2C S 0.26 29.79 [from3.4 2

120 (1 )nC SE p= ⋅ − , n=4.65]

CH - 40.2 CaO 0.54 8.35 [from 194.54 (1 )n

CaOE p= ⋅ − , n=4] Monosulfate 0.25 40.0

Void - 0

205

Table 6.2 shows the porosity and elastic modulus of phases used in the model.

The methodology to obtain the elastic modulus of each phase except for monosulfate

was already described in Chapter 5.7. The elastic modulus and Poisson’s ratio for

monosulfate are assumed as 4 Gpa and 0.25, respectively.

Generally, the volume portion of aggregates is between 60 % and 80 % of the

total volume of concrete. Therefore, they have a very important effect on the volume

changes of concrete. The material properties of various aggregates are summarized in

Table 6.3. It should be noticed that there is no consistency for the properties in the

Table. 6.3 because the chemical portions constituting rock are different, even if the

rocks are called by the same name.

Table 6.3. Elastic properties of various aggregates (Jumijis, 1983)

Rock ( )E Gpa ( )v − Basalt 19.1-111.5 0.14-0.25

Diabase 22.0-114.0 0.103-0.333 Gabbro 58.4-107.8 0.125-0.48 Granite 21.3-68.5 0.125-0.338

Igneous rocks

Syenite 58.8-86.3 0.15-0.319 Dolomite 19.6-93.0 0.08-0.37 Limestone 8.0-78.5 0.10-0.33 Sandstone 4.9-84.5 0.066-0.62 Sedimentary rocks

Shale (clay) 7.8-44.0 0.04-0.54 Gneiss 14.2-70.0 0.091-0.25 Marble 28.0-100.0 0.11-0.38

Quartzite 25.5-97.5 0.11-0.23 Schist 4.0-70.5 0.01-0.20

Metamorphic

Slate - 0.06-0.44

Table 6.4 shows the thermal strain functions of sandstone and limestone

obtained from curve fitting of test data by Soles and Geller (1964).

206

Table 6.4. Summary for thermal strain of limestone and sandstone

Phase Temperature Strain 20 T 600C C< ≤ 14 4 11 3 8 2

6

4.0 10 2.0 10 2.0 109.0 10 0.0002

T T TT

ε − − −

−

= × ⋅ − × + ×

+ × −

600 T 650C C< ≤ 5 31.75 10 2.625 10Tε − −= ⋅ + ⋅ Sandstone

650 T 800C C< ≤ 6 23.80 10 1.153 10Tε − −= ⋅ + ⋅ Limestone 20 T 800C C< ≤ 12 3 8 2 64.0 10 1.0 10 9.0 10 0.0003T T Tε − − −= × + × + × −

6.4. Comparison between model and experimental results

To apply the multi-scale composite model, arrangement of the phases in

cement paste is shown in Fig. 6.6.

Phase1

Phase2 Phase 4: Cement paste

(Effective medium)

Phase 2: Crystal Phases

(CH & Monosulfate)Phase 3: Gel Phase (CSH)

Phase 1: Void

Phase3 Phase4

Temperature increase (Decomposition of Phases)

Phase 1: Void

Phase 5: CS123456

Phase 2: CaOPhase 3: CHPhase 4: Monosulafate

Phase 6: CSHPhase 7: Cement paste

(Effective medium)7

Phase1

Phase2 Phase 4: Cement paste

(Effective medium)

Phase 2: Crystal Phases

(CH & Monosulfate)Phase 3: Gel Phase (CSH)

Phase 1: Void

Phase3 Phase4

Temperature increase (Decomposition of Phases)

Phase 1: Void

Phase 5: CS123456

Phase 2: CaOPhase 3: CHPhase 4: Monosulafate

Phase 6: CSHPhase 7: Cement paste

(Effective medium)7

Figure 6.6. Arrangement of phases in cement paste

207

Before cement paste is exposed to high temperature, void and crystal phases

are surrounded by gel phase. When cement paste is exposed to high temperature, the

decomposed solid phases, i.e. CaO from CH and 3.4 2C S from 3.4 2 3C S H , are located

in close proximity to primary phases and the decomposed voids from 3.4 2 3C S H and

CH are located at the center of cement paste in the model. Finally, the model is

obtained by combination of the multi-scale composite model considering the

arrangement for phases shown in Fig. 6.6 and the multi-scale stoichiometric model

described in Chapter 5.

The model is compared with the test result with w/c ratio of 0.5. The model

satisfactorily predicts the test result as shown in Fig. 6.7.

-0.015

-0.013

-0.011

-0.009

-0.007

-0.005

-0.003

-0.001

0.001

0.003

0.005

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

Cement paste_Exp. [(Piasta, 1984a), w/c=0.5]

Cement paste_Model (w/c=0.5)

Figure 6.7. Comparison between model and experimental data for cement paste

208

Table 6.5 is a summary for the thermal strain functions according to

temperature rage of cement paste with w/c=0.5 obtained from the model.

Table 6.5. Thermal strain functions of cement paste from model (w/c=0.5)

From model Temperature Strain 20 T 50C C< ≤ 7 6117.667 10 235.333 10Tε − −= ⋅ − ⋅ 50 T 120C C< ≤ 8 6462.857 10 121.571 10Tε − −= ⋅ + ⋅ 120 T 175C C< ≤ 6 38.60 10 1.709 10Tε − −= − ⋅ + ⋅ 175 T 300C C< ≤ 6 430.032 10 54.596 10Tε − −= − ⋅ + ⋅ 300 T 400C C< ≤ 5 32.493 10 3.929 10Tε − −= − ⋅ + ⋅ 400 T 425C C< ≤ 5 33.80 10 9.157 10Tε − −= − ⋅ + ⋅ 425 T 500C C< ≤ 5 35.712 10 17.283 10Tε − −= − ⋅ + ⋅ 500 T 530C C< ≤ 5 33.66 10 7.023 10Tε − −= − ⋅ + ⋅ 530 T 575C C< ≤ 8 4466.667 10 148.483 10Tε − −= ⋅ − ⋅ 575 T 625C C< ≤ 6 39.32 10 17.524 10Tε − −= ⋅ − ⋅ 625 T 650C C< ≤ 5 31.264 10 19.599 10Tε − −= ⋅ − ⋅

Cement paste

650 T 800C C< ≤ 8 4508.667 10 146.893 10Tε − −= ⋅ − ⋅

Phase1

Phase2Concrete

Phase 3: Concrete

(Effective homogeneous medium)

Phase 2: Cement paste (From effective medium considering phases)

Phase 1: Aggregates

Phase1

Phase2Concrete

Phase 3: Concrete



Phase 1: Aggregates

Phase1

Phase2Concrete

Phase 3: Concrete



Phase 1: Aggregates

Figure 6.8. Arrangement of phases in concrete

In calculation of thermal strain of concrete from model, the arrangement of

cement paste and aggregates is shown in Fig. 6.8. The aggregates are surrounded by

209

cement paste. The bulk moduli of cement paste according to temperature increase are

calculated using Eq. (6.3) with the volume fractions of phases according to

temperature increase from the multi-scale stoichiometric model. In application of

Eq. (6.2) to calculate thermal expansion of concrete from the model, shear modulus of

cement paste is calculated using the mixture theory of Eq. (6.10).

1

N

cp i ii

G f G=

= ⋅∑ (6.10)

In which, iG and if , which changed with temperature increase, are the shear

modulus and the volume fraction for 3.4 2 3C S H , CH , Monosulfate, 3.4 2C S , and CaO

calculated at cement paste level.

-0.005

0.000

0.005

0.010

0.015

0.020

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

LimestoneConc._Exp. [(Schneider, 1982), w/c=0.6]

LimestoneConc._Upper bound from model (w/c=0.6)

LimestoneConc._Lower bound from model (w/c=0.6)

Figure 6.9. Comparison between model and experimental data (limestone concrete)

210

-0.005

0.000

0.005

0.010

0.015

0.020

0 100 200 300 400 500 600 700 800 900

Temperature (C)

Stra

in

SandstoneConc._Exp. [(Schneider, 1982), w/c=0.62]

SandstoneConc._Upper bound from model (w/c=0.62)

SandstoneConc._Lower bound from model (w/c=0.62)

Figure 6.10. Comparison between model and experimental data (sandstone concrete)

In the ranges of material properties of aggregates given in Table 6.3, the upper

and lower bounds from the model for strains of limestone concrete (w/c = 0.6) and

sandstone concrete (w/c = 0.62) are shown in Fig. 6.9 and Fig. 6.10 with the test data

by Scheider (1982), respectively. The functions, which are based on the test data of

Soles and Geller (1964), in Table. 6.4 were used as the thermal strains of the

aggregates in the model. The test samples by Schneider (1982) were sleeve shaped

with diameter 80 mm and height 300 mm. The samples were cured for 750 days

under the condition of 65 % relative humidity at a temperature of 20 2± °C after

water curing for 7 days.

The test data for the sandstone concrete is contained between the upper and

lower bound from the model. While the test data of the limestone concrete is a little

211

higher than the upper bound from the model. The upper bounds from the model are

matched relatively well with the test results. The rocks have different material

properties due to different chemical portions in the rocks, even if they have the same

name, the thermal strains are also different from each other. In the model, the test data

of the aggregates by Soles and Geller (1964) was used to calculate the thermal strains

of limestone concrete and sandstone concrete. The test data for the concretes used to

compare with the model is from Schneider (1982). When aggregates and concrete

(containing the same aggregates) undergo the same test conditions, and the material

properties of the aggregates are given, it is likely that the proposed model predicts the

thermal expansion of concrete reasonably.

6.5. Conclusions

1. At cement paste level, the model, obtained by a combination of the multi-scale

composite model and the multi-scale stoichiometric model, was compared with test

results from Piasta (1984 a), and satisfactorily predicted them.

2. The test data for the sandstone concrete was contained in the upper bound and

lower bound from the model. While the test data for limestone concrete was a little

higher than the upper bound from the model.

3. At concrete level, the upper bounds from the model matched relatively well with

test results by Scheider (1982).

4. The thermal deformation of the aggregates used is an important factor in the

thermal deformation of concrete because aggregates occupy about 70 % of the total

212

volume of concrete. When aggregates and concrete (containing the same aggregates)

undergo the same test conditions, and the material properties of the aggregates are

given, it is likely that the proposed model will predict the thermal expansion of

concrete reasonably.

213

CHAPTER 7

7. SUMMARY AND CONCLUSIONS

The studies performed in this thesis are largely classified as two experimental

studies and two theoretical models. One of the experimental studies is to find the

effects of temperature and moisture on strain of concrete and the other one is to

investigate the strength, stiffness, and durability performance of concrete subjected to

various heating and cooling scenarios.

In Chapter 3, the effects of temperature and moisture on strain of concrete

were investigated. The strain caused by temperature increase without moisture control

(Conventional Thermal Strain: CTS), the strain caused by temperature increase under

constant humidity (Pure Thermal Strain: PTS), and the strain caused by moisture

change under constant temperature (Pure Hygro Strain: PHS) were measured

continually and simultaneously over time. From the measured strains, the thermo-

hygro coupling effect in the temperature range 28-70 °C was obtained. The

conclusions from the study are as follows;

- If it is assumed that a local thermodynamic equilibrium always exist between

the phases of pore water (vapor, liquid) within a very small element of concrete, the

phenomena, which is the increase of internal relative humidity of concrete with

214

temperature increase, can be explained using Eq. (3.12). This equation is based on

static force equilibrium from the capillary tube model and physicochemical

equilibrium by the Kelvin equation. When we consider the strain change of

aggregates and hardened cement paste as components of concrete at elevated

temperatures, it is clear that the internal relative humidity of concrete increases as the

temperature increases.

- Pure Thermal Strain (PTS), because the there is no additional hygro strain by

swelling pressure increase (increase of relative humidity) according to temperature

increase, was less than Conventional Thermal Strain (CTS) in the range of

temperatures used in this study.

- Pure Hygro-Strain (PHS) was nonlinear. At higher temperatures, Pure

Hygro-Strain (PHS) increased more rapidly. It is likely linked to complicated

physiochemical reactions in concrete as humidity changes, i.e. the increase of

swelling pressure (RH increase) is not directly proportional to temperature increase.

- The thermo-hygro coupling effect was negative in the tested temperature

range. That means that the internal relative humidity of concrete increases as the

temperature increases in the tested temperature range.

- The shrinkage effect due to a decrease in internal relative humidity

(dehydration) of cement may be contained in the overall expansion of concrete

beyond 150 °C. However, it should be noticed that concrete expands as temperature

increases because aggregates, which make up about 70 % of concrete by volume,

expand continually as the temperature increases.

215

In Chapter 4, the strength, stiffness, and durability performance of concrete

subjected to various heating and cooling scenarios were investigated. The strength

and stiffness performance of concrete were investigated with the aid of Ultrasonic

Pulse Velocity test (UPV) and residual compressive strength testing. The durability of

the concrete was investigated using a water permeability test (WPT). Additionally,

the thermal diffusivity, weight losses, color changes, and cracks of the specimens

were reported. The conclusions from the study are as follows;

- There were three distinct peaks in the plot of the temperature difference

between the surface and center of the specimen. The three peaks are related to the

micro-structural changes due to complex physicochemical transformations in the

concrete under high temperature. The first peak is associated with the dehydration of

calcium silicate hydrate (C-S-H) and the evaporation of free water. The second peak

is related to the decomposition of calcium hydroxide (CH) and calcium silicate

hydrate (C-S-H). The third peak may be due to the decomposition of calcium

carbonate ( 3CaCO ).

- The results of the water permeability test (WPT) showed that the pK

(coefficient of permeability) of the specimen increased as the temperature and cooling

rate increases. Also, the test results of the specimens subjected to slow or natural

cooling showed that the effect of the cooling rate on thermal damage in concrete is

more significant than that of the holding time at target temperatures.

- Strength and stiffness of the concrete decreased significantly as the

maximum temperature and the cooling rate increase.

216

- The trend for thermal degradation of pE (obtained from the ultrasonic pulse

velocity) and iE (obtained from residual compression test) was similar. However, the

elastic modulus ( pE ) was evaluated higher than the initial tangent modulus ( iE ).

- The weight loss below 200 °C was steeper than that above 200 °C, for RH

90 % and full saturation, because it is governed by the evaporation of the free water.

The weight loss at temperatures above 200 °C is due to the loss of adsorbed and

chemically bound water in the specimen. The weight loss was governed by the target

temperature rather than the heating rate, cooling method, or holding time (2 hrs and

4 hrs in this research).

- The crack width increased with an increase in temperature and also with

heating rate which means they both contribute to the damage of concrete.

Variations of concrete under high temperatures result mainly from two

mechanisms. One is the variation of material properties of the constituent phases

under high temperatures, and the other is the transformation of constituent phases

under different temperatures. Therefore, the properties of concrete under high

temperatures must be studied from both mechanical and chemical points of view.

In Chapter 5, the model for the thermal degradation of elastic modulus of

concrete was proposed by composite mechanics at three scale levels: concrete, mortar,

and cement paste level. At the level of cement paste, the variations of volume

fractions of the constituents were evaluated based on phase transformations taking

place under different temperature ranges. Stoichiometric models were used to

calculate the volumetric changes of the constituents. The conclusions from the study

are as follows;

217

- A multiscale model was established for predicting the thermal degradation of

the modulus of elasticity of concrete under different temperature ranges. The internal

structure of concrete was considered at three scale levels: cement paste, mortar, and

concrete. Cement paste is considered as a multiple phase composite with cement

particles and all hydration products; mortar is a mixture of cement paste and sand;

and concrete is a mixture of mortar and gravel.

- At the cement paste level, the phase transformations in cement paste under

high temperature were modeled by stoichiometric relations, which give the volume

fractions of the products of the phase changes. The effective elastic modulus of

cement paste under a certain temperature was then calculated based on composite

models and using the volume fractions of the constituent phase at the temperature.

The water released during the heating process is considered as part of voids with zero

modulus of elasticity.

- The variation of pore volume with increasing temperature was predicted by

the present model, and compared with the test data by Piasta et al. (1984). The present

model predicted the test results very well. The change of porosity by the present

model was also compared with the model prediction by Harmathy (1970), which

showed some difference. The difference was due to the assumption used in

Harmathy’s model, that is, the cement is only composed of 3C S (0.653 as the weight

fraction) and 2C S (0.365 as the weight fraction), and other phases were neglected.

- At the mortar and concrete levels, the effective elastic moduli of mortar and

concrete under a certain temperature was calculated based on composite models and

using the volume fractions and moduli of cement paste, sand, and gravel. The elastic

218

modulus of cement paste came from the effective modulus obtained from the lower

level model, and the variations of elastic moduli of various sand and gravels were

established based on available test data in the literature.

- The present model for the thermal degradation of elastic modulus of concrete

predicted satisfactorily the basic trend shown in the available test results which

included various concrete mix design parameters and heating and cooling conditions.

- The multi-scale chemo-mechanical model provided a general framework that

can be used in the prediction for thermal degradations of elastic modulus as well as

other properties of concrete, such as thermal strain and diffusivity of concrete under

high temperatures.

In Chapter 6, the model for the thermal strain of cement paste and concrete,

considering micro-structural changes under elevated temperatures ranging from 20 °C

to 800 °C, was proposed. The model was obtained by the combination of a multi-

scale stoichiometric model and a multi-scale composite model. The model can

consider characteristics of various aggregates in the calculation of thermal expansion

for concrete. The conclusions from the study are as follows;

- At cement paste level, the model, obtained by a combination of the multi-

scale composite model and the multi-scale stoichiometric model, was compared with

test results from Piasta (1984 a), and satisfactorily predicted them.

- The test data for the sandstone concrete was contained in the upper bound

and lower bound from the model. While the test data for limestone concrete was a

little higher than the upper bound from the model.

219

- At concrete level, the upper bounds from the model matched relatively well

with test results by Scheider (1982).

- The thermal deformation of the aggregates used is an important factor in the

thermal deformation of concrete because aggregates occupy about 70 % of the total

volume of concrete. When aggregates and concrete (containing the same aggregates)

undergo the same test conditions, and the material properties of the aggregates are

given, it is likely that the proposed model will predict the thermal expansion of

concrete reasonably.

220

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237

APPENDIX A

9. RELATIVE HUMIDITY IN UNSATURATED SOIL

238

A.1. Definition of relative humidity

There are three assumptions in relative humidity in most practical

geotechnical applications.

First assumption is that the composition of air excluding the water vapor

component remains essentially unchanged over time.

Second assumption is that the mixture of the component gases as a whole, as

well as each of the component gases that make up air, follows ideal gas behavior.

Third assumption is that all components of air, including the water vapor

component, reach local thermodynamic equilibrium. Thermodynamic equilibrium

requires that chemical potentials among all components of all phase in the system are

the same.

R.H in the atmosphere is expressed as Eq. (A.1). From the ideal-gas equation

of state,

)( ρν

⋅⋅⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⋅= T

wRTRP g

(A.1)

Where P is the absolute pressure, gR R w= (gas constant), R is the universal

gas constant, w is the molar mass (molecular mass), T is the temperature, 1ν ρ= is

the specific volume, ρ is the density.

Notice: Definition of mol is that the mole (abbreviation, mol) is the Standard

International (SI) unit of material quantity. One mole is the number of atoms in 12 g

239

of C-12 (carbon-12). This number is equal to approximately 236.022169 10× , and is

also called the Avogadro constant.

RTPw

VM

==ρ (A.2)

Thus, the density can be expressed by Eq. (A.2). Relative humidity is defined

as the ratio of the absolute humidity ( vρ ) in equilibrium with any solution to the

absolute humidity in equilibrium with free water ( satv,ρ ) at the same temperature.

satv

v

vsatv

vv

satv

v

PP

RTwP

RTwP

RH,,,

===ρρ

(A.3)

Where vρ is the vapor density, satv,ρ is the saturated vapor density, vP is the

partial water vapor pressure, ,v satP is the saturated vapor pressure, vw is the molar

mass (molecular mass) of water vapor, R is the universal gas constant, and T is the

temperature in Kelvin.

A.2. Capillary tube model for unsaturated soil

A simple capillary tube model has been developed to analyses of unsaturated

soil. The complex geometries for various shapes and sizes of particles and pore

240

fabrics formed among adjacent particles are simplified with the following

assumptions. First assumption is that sand particles have identical spherical shape,

second assumption is that an air-water interface described by the so-called toroidal

approximation.

The idealized geometry of the air-water interface between two spherical soil

grains, which can be characterized by two radii of curvature r1 and r2, is shown in

Fig. A.1.

Soild

AirWater

A

A’

r1r2

A

B

A’

r1

r2

r3

α

αTs

Ts

T = Ts × sinα

r3

T

dθθ

r3

Soild

B’

(a) Water meniscus between two particles (b) Free-body diagram for water meniscus

(c) Section B-B’ (d) Small area of section B-B’

Ts

Ts

Soild

AirWater

A

A’

r1r2

A

B

A’

r1

r2

r3

α

αTs

Ts

T = Ts × sinα

r3

T

dθθ

r3

Soild

B’

(a) Water meniscus between two particles (b) Free-body diagram for water meniscus

(c) Section B-B’ (d) Small area of section B-B’

Ts

Ts

Figure A. 1. Idealized air-water interface geometry in unsaturated soil

Consider force balance in the horizontal direction and the free body diagram

in Fig. A.1. There are three force contributions in the free-body diagram: surface

241

tension along the interface described by r1 that results in the positive direction

horizontally, surface tension along the interface described by r2 that results in the

negative direction horizontally, and air and water pressure applied on either side of

the interface. The projection of surface tension in the positive horizontal direction is

21 3 3 30

4 cos 4 4 sinsF T r d r T r Tπ

θ θ α= ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ ⋅∫ (A.4)

The projection of the surface tension in the negative horizontal direction (if

α is very small, sinα α= ) is

2 1 1 12 (2 ) 4 4 sins s sF T r r T r Tα α α= − ⋅ ⋅ ⋅ ⋅ = − ⋅ ⋅ ⋅ ≈ − ⋅ ⋅ ⋅ (A.5)

Also, the projection of air and water pressure aP and wP in the horizontal

direction (assuming 2 3r r= ) is

3 1 2 1 2( ) (2 sin ) (2 ) 4 ( ) sina w a wF P P r r r r P Pα α= − ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ − ⋅ (A.6)

Balancing all three forces leads to

1 2

1 1( )a w sP P Tr r

⎛ ⎞− = ⋅ −⎜ ⎟

⎝ ⎠ (A.7)

Eq. (A.7) provides a simple mathematical expression describing the pressure

change across an air-water-solid interface between two idealized soil grains. The

242

quantity ( )a wP P− is called as the matric suction. The matric suction depending on the

relative magnitudes of 1r and 2r can be positive, zero, or negative. Most likely, the

value of matric suction is positive due to the fact that 1r is mostly less than 2r under

unsaturated conditions. The matric suction can be also expressed in terms of soil pore

radius ( r ), contact angle between air and water (α ), and surface tension sT . Fig. A.2

shows two dimensional free-body diagrams for pressure and surface tension across a

spherical phase interface between air and water.

Air phase

Water phase Pw

Pa

TsTs

r

TsTsRδA’

δAPa

Pw

α

αAir phase

Water phase Pw

Pa

TsTs

r

TsTsRδA’

δAPa

Pw

α

α

Figure A. 2. Free-body diagrams for pressure and surface tension across a spherical

phase interface between air and water.

The projection of incremental force due to pressure on both sides of interface

over an area Aδ in the vertical direction is as follows:

( ) cos ( ) 'v a w a wF P P A P P Aδ δ α δ↓ = − − ⋅ ⋅ = − − ⋅ (A.8)

243

Where 'Aδ is the projection of Aδ in the horizontal axis. The total vertical

force due to the pressure difference acts over the area of the interface as follows:

2( )v a wF P P rπ↓ = − − ⋅ ⋅ (A.9)

The projection of surface tension around the circumference of the cut in the

vertical direction is

2 cosv sF r Tπ α↑ = ⋅ ⋅ ⋅ ⋅ (A.10)

Applying force equilibrium leads to

2 cos( ) sa w

TP Pr

α⋅− = (A.11)

A.3. Kelvin’s equation

Consider a simple three phase system comprised of air, water, and soil at a

state of equilibrium in a closed container. The air phase consists of two components

of dry air ( daP ) and water vapor ( vP ). The total air pressure ( aP ) is equal to the sum

of the partial pressures of dry air and water vapor. The composition and amount of

dry air will not vary in the container, but the amount of water vapor may indeed vary

under concurrent condensation and evaporation processes. Assume that the water

phase is free (i.e. free of influence by the solid, the solid container, and dissolved

solute) and that the air-water interface is perfectly flat (Fig. A.3).

244

Air

Water

Solid

Pa=Pda+Pv

Pw

Air

Water

Solid

Pa=Pda+Pv

Pw

Figure A. 3. A simple three phase system comprised of air, water, and soil

For relatively incompressible materials such as solid, mechanical force

considerations are usually the only criteria necessary to arrive at an equilibrium

relationship. However, for highly deformable materials such as dry air, water vapor,

or liquids, it is necessary to also consider chemical equilibrium. For this thought

experiment, mechanical and chemical equilibrium between the air and water phases

are considered. Because the air-water interface is flat, mechanical equilibrium

requires that the air pressure ( aP ) be equal to the total water pressure ( wP ). Chemical

equilibrium requires that the total chemical potential, or more conveniently, the

change in the total chemical potential, be the same in each coexisting phase (i.e., air

and water).

For mechanical equilibrium,

a da v wP P P P= + = (A.12)

For chemical equilibrium,

a da v w w w a a da da v vRT P v P v P v P vµ µ µ µ= + = = = = = + (A.13)

245

Where iµ and iv mean the chemical potential and the partial molar volume for

each component, respectively. Assuming ideal gas behavior for the dry air and water

vapor, the dry air pressure and vapor pressure can be expressed as Eq. (A.14) and

(A.15) respectively.

dada

da da da

M RTP RTV w v

= = (A.14)

vv

v v v

M RTP RTV w v

= = (A.15)

Where M is the mass, V is the volume, and w is the molecular mass. Since

any ideal gas has 22.4 L/mol, the partial molar volume can be calculated from

molecular weight and the volume fraction of each respective gas.

From chemical equilibrium,

w da da v vP v P vµ = + (A.16)

At mechanical and chemical equilibrium, the vapor pressure of pure water

reaches its saturated value ,v satP under the prevailing temperature and pressure

condition. In other words, a state of 100 % relative humidity is reached. This state is

defined as reference state.

246

Air

Water Droplets,

Solid

r

Pa=Pda+Pv

Pw

Air

Water Droplets,

Solid

r

Pa=Pda+Pv

Pw

Figure A. 4. Air-water-solid system at mechanical and chemical equilibrium

Let’s suppose that all of the water in the container is in the form of spherical

droplets having uniform radii r (Fig. A.4). The solid container consists of a perfectly

water repellent material such that the contact angle 180°, implying that no water

potential change can occur due to surface wetting. Here, a new state of pressure and

potential for the air and water phase must be established. If water vapor follows the

ideal gas law and the change in chemical potential of dry air is negligible compared to

the change in chemical potential of the water vapor, the change in chemical potential

for the total air phase with respect to the previous case for the flat air-water interface

can be expressed by Eq. (A.17).

,

ln va da v v

v sat

PRTP

µ µ µ µ∆ = ∆ + ∆ = ∆ = − (A.17)

The last assumption in the development of above the equation is based on the

fact that the total pressure change is small and that the partial molar volume of dry air

remains unchanged in the closed container.

247

The chemical potential change in the liquid phase is expressed by Eq. (A.18).

w w wv Pµ∆ = ∆ (A.18)

In the geometry of the water droplets (contact angle 0° between water and air:

Fig. A.4.), the pressure change across the air-water is expressed by Eq. (A.19).

2 sw a w

TP P Pr

∆ = − = Thus, (A.19)

,

2ln ( )v s ww a w a w

v sat

P T vRT v P PP r

µ µ∆ = ∆ = − = − = or (A.20)

,

2ln ( )v sa w

w v sat

P TRT P Pv P r

− = = − (A.21)

Eq. (A.21) is Kelvin’s equation applied to equilibrium between a water drop

and its vapor pressure.

Air

Capillary Tubes,

Solid

α

Pa=Pda+Pv

r

Pw

Air

Capillary Tubes,

Solid

α

Pa=Pda+Pv

r

Pw

Figure A. 5. Air-water-solid system at mechanical and chemical equilibrium

248

To apply to unsaturated soil, consider the idealized system of capillary tubes

partially filled with water, each having a radius r and a solid-liquid contact angle α

(Fig. A.5). From the geometry of Fig. A.5, Kelvin’s equation can be expressed as

Eq. (A.22).

,

2 cosln v s ww a

v sat

P T vRTP r

αµ µ∆ = ∆ = − = (A.22)

The relative humidity of the pore air phase in saturated soil is fundamentally

linked to the change of chemical potential and the pressure difference between air and

water (suction). Eq. (A.23) is obtained from Eq. (A.11) and (A.22) using the capillary

tube model. Finally, the relative humidity in unsaturated soil is expressed with Eq.

(A.24).

( ),

2 cosln lnv sa w

w v sat w

P TRT RTP P RHv P v r

α− = − = − =

(A.23)

( - ) 2 cosexp - exp -a w w s wP P v T vRHRT r RT

α⎛ ⎞ ⎛ ⎞= = ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(A.24)

Date post:	28-Apr-2015
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Concrete High Temp.

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