PERFORMANCE CHARACTERIZATION OF HIGH PERFORMANCE CONCRETES
UNDER FIRE CONDITIONS
By
Wasim Khaliq

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Civil Engineering
2012

ABSTRACT

PERFORMANCE CHARACTERIZATION OF HIGH PERFORMANCE CONCRETES
UNDER FIRE CONDITIONS
By

Wasim Khaliq

In recent years, high performance concretes (HPC) are finding increasing applications in
buildings and infrastructure due to numerous advantages, such as higher strength and durability,
these HPC offer over conventional concretes. Structural members made of HPC, when used in
buildings, have to satisfy the fire resistance requirements specified in building codes and
standards. Although conventional concrete members have good fire resistance, same may not be
true for HPC members due to faster degradation of strength with temperature and occurrence of
fire induced spalling. Spalling in HPC columns can be overcome either through the addition of
fibers in the concrete mix or through the provision of 135° bent ties. For evaluating the fire
resistance of HPC columns, as well as to account for the beneficial effects of fibers and 135° tie
configuration on spalling mitigation, high temperature properties of HPC and numerical models
that can take in to account the effect of tie configuration is required. At present, there is lack of
data on high temperature properties specific to different types of HPC (plain and with fibers).
Also, there is no methodology to account for the effect of tie configuration on fire resistance of
RC columns. To overcome these knowledge gaps, an experimental and numerical study is
undertaken as part of this thesis.
Performance characterization of high performance concretes under fire conditions is carried out
at both material and structural level (specifically columns). As part of material characterization,

thermal and mechanical property tests were carried out in 20-800°C temperature range on
different HPC mixes (plain and with different combinations of fibers). Data from measured
property tests was utilized to develop empirical relations for high temperature properties. As part
of structural characterization, fire resistance tests were carried out on two fly ash concrete (FAC)
and two high strength concrete (HSC) columns with different fiber combinations.
As part of numerical study, a macroscopic finite element (MFE) model, originally developed to
evaluate fire resistance of RC columns, was extended to include the effect of tie configuration.
The proposed tie sub-model is based on the approach used in seismic design and involves
calculation of force acting on ties by evaluating stresses resulting from pore pressure, mechanical
loading and thermal effects in RC columns under fire exposure. The force acting on ties is
compared against temperature (time) dependent bond strength (tie-concrete interface) to evaluate
the failure of ties. The model is validated by comparing response predictions against test data and
the model was applied to carry out parametric studies to quantify the influence of HPC properties
and tie configuration on fire response of HPC columns.
Results from high temperature material property tests show that HPC exhibit thermal properties
similar to that in conventional concrete. However, mechanical properties of HPC degrade at
faster rate (much severe) than that in conventional concretes. Results from fire resistance tests
show that plain HPC columns exhibit lower fire resistance due to occurrence of fire induced
spalling and faster degradation of strength. However, presence of different fiber combinations in
HPC columns can significantly enhance the fire resistance of the columns. In addition, presence
of 135° bent ties in HPC columns can significantly enhance the fire resistance of these columns
through confinement action.

DEDICATION
To Amna, Fasih, and Khadija.

iv

ACKNOWLEDGMENTS
I would like to express my greatest gratitude to my advisor, Prof. Venkatesh Kodur, Michigan
State University, for his continued support, encouragement, and guidance during the course of
my studies. I would like to convey my sincere thanks for his ideas and perseverance which made
my graduate studies very rewarding.
I would also like to thank Prof. Parviz Soroushian, Prof. Neeraj Buch and Prof. K.N.
Subramanian for joining my Ph.D. committee, and for their valuable advice throughout my
course of research at MSU.
I would like to thank the lab manager, Mr. Siavosh Ravanbakhsh for his generous support and
help during the experimental program in this research. And, I would also like to extend my
sincere thanks to Laura Taylor, Mary Mroz, and Margaret Conner for all the help they provided.
I would like to thank Monther Dwaikat, Mahmud Dwaikat, Aqeel Ahmad, Rustin Fike, Nikhil
Raut, Nikhil Chaudhary, Sonali Kand, Haihua Gu, Purushutham Pakala, Baolin Yu, Esam Aziz
for their support, particularly in the experimental part of this study. My special thanks to Dr.
Xiaoyong Mao whose continuous help made it possible for me to execute laborious experiments
on HPC columns in this study.
Additionally, I would like to thank all the faculty members and students at the Civil and
Environmental Engineering department at Michigan State University for their help and support
during my doctoral studies.

v

TABLE OF CONTENTS
List of Tables .................................................................................................................................. x
List of Figures ............................................................................................................................... xii
Chapter 1 ......................................................................................................................................... 1
1
Introduction ..................................................................................................................... 1
1.1
General ........................................................................................................................ 1
1.2
High Temperature Properties of Concrete .................................................................. 2
1.3
Response of HPC Columns under Fire Conditions..................................................... 3
1.3.1 General Fire Behavior ............................................................................................. 3
1.3.2 Fire induced Spalling .............................................................................................. 5
1.3.3 Spalling Mitigation ................................................................................................. 6
1.4
Research Objectives .................................................................................................... 7
1.5
Scope ........................................................................................................................... 9
Chapter 2 ....................................................................................................................................... 16
2
State-of-the-Art Review ................................................................................................ 16
2.1
General ...................................................................................................................... 16
2.2
Thermal Properties of Concrete ................................................................................ 17
2.2.1 General .................................................................................................................. 17
2.2.2 Test Methods for High Temperature Thermal Properties ..................................... 19
2.2.3 Previous Studies on Thermal Properties ............................................................... 20
2.2.4 Effect of Temperature on Thermal Properties of Concrete .................................. 24
2.2.5 Summary ............................................................................................................... 27
2.3
Mechanical Properties ............................................................................................... 27
2.3.1 General .................................................................................................................. 27
2.3.2 Testing Methods for High Temperature Mechanical Properties........................... 29
2.3.3 Previous Studies .................................................................................................... 30
2.3.4 Effect of Temperature on Mechanical Properties of Concrete ............................. 38
2.3.5 Summary ............................................................................................................... 40
2.4
Deformation Properties ............................................................................................. 40
2.4.1 General .................................................................................................................. 41
2.4.2 Previous Studies .................................................................................................... 42
2.4.3 Effect of Temperature on Deformation Properties ............................................... 43
2.4.4 Summary ............................................................................................................... 44
2.5
Fire Induced Spalling ................................................................................................ 44
2.5.1 Causes of Spalling................................................................................................. 44
2.5.2 Previous Studies .................................................................................................... 46
2.5.3 Spalling Mitigation ............................................................................................... 48
2.5.4 Summary ............................................................................................................... 49
2.6
Fire Performance of Reinforced Concrete Columns ................................................. 49
2.6.1 Experimental Studies ............................................................................................ 50
2.6.2 Numerical Studies ................................................................................................. 51
2.7
Codes and Standards ................................................................................................. 51
2.8
Summary ................................................................................................................... 52
vi

Chapter 3 ....................................................................................................................................... 67
3
Thermal Properties characterization ............................................................................. 67
3.1
General ...................................................................................................................... 67
3.2
Design of Thermal Property Tests ............................................................................ 68
3.3
Thermal Property Tests ............................................................................................. 70
3.3.1 Mix Proportions .................................................................................................... 70
3.3.2 Test Specimens ..................................................................................................... 72
3.3.3 Test Apparatus ...................................................................................................... 73
3.3.4 Test Procedure ...................................................................................................... 75
3.4
Results and Discussion ............................................................................................. 78
3.4.1 Thermal Conductivity ........................................................................................... 78
3.4.2 Specific Heat ......................................................................................................... 80
3.4.3 Thermal Expansion ............................................................................................... 82
3.4.4 Mass Loss.............................................................................................................. 84
3.4.5 Repeatability of Thermal Property Tests .............................................................. 85
3.4.6 Summary ............................................................................................................... 86
3.5
Relations for Thermal Properties .............................................................................. 87
3.5.1 Relations for Thermal Conductivity ..................................................................... 88
3.5.2 Relations for Specific Heat ................................................................................... 89
3.5.3 Relations for Thermal Expansion ......................................................................... 91
3.5.4 Relations for Mass Loss ........................................................................................ 92
3.6
Summary ................................................................................................................... 93
Chapter 4 ..................................................................................................................................... 118
4
Mechanical Properties characterization ...................................................................... 118
4.1
General .................................................................................................................... 118
4.2
Design of Mechanical Property Experiments ......................................................... 119
4.3
Mechanical Property Tests ...................................................................................... 120
4.3.1 Mix Proportions .................................................................................................. 120
4.3.2 Test Specimens ................................................................................................... 120
4.3.3 Test Apparatus .................................................................................................... 121
4.3.4 Test Procedure .................................................................................................... 123
4.4
Results and Discussion ........................................................................................... 127
4.4.1 Compressive Strength ......................................................................................... 127
4.4.2 Splitting Tensile Strength ................................................................................... 131
4.4.3 Elastic Modulus .................................................................................................. 135
4.4.4 Stress-Strain Curves ............................................................................................ 137
4.4.5 Temperature Induced Spalling ............................................................................ 139
4.4.6 Summary ............................................................................................................. 140
4.5
Relations for Mechanical Properties ....................................................................... 140
4.5.1 General ................................................................................................................ 140
4.5.2 Relations for Compressive Strength ................................................................... 143
4.5.3 Relations for Splitting Tensile Strength .............................................................. 144
4.5.4 Relations for Elastic Modulus ............................................................................. 146
4.6
Summary ................................................................................................................. 147
Chapter 5 ..................................................................................................................................... 178
vii

5

Experimental Studies .................................................................................................. 178
5.1
General .................................................................................................................... 178
5.2
Design and Fabrication of Specimens..................................................................... 179
5.2.1 Design of Columns ............................................................................................. 180
5.2.2 Fabrication of Specimens .................................................................................... 181
5.2.3 Instrumentation ................................................................................................... 183
5.3
Fire Resistance Experiments ................................................................................... 184
5.3.1 Test Equipment ................................................................................................... 184
5.3.2 Preparation of Columns for Fire Tests ................................................................ 186
5.3.3 Test Procedure .................................................................................................... 187
5.3.4 Measured Data and Test Observations ............................................................... 189
5.4
Response of HPC Columns during Fire Exposure .................................................. 190
5.4.1 Thermal Response ............................................................................................... 190
5.4.2 Structural Response ............................................................................................ 192
5.4.3 Spalling Progression ........................................................................................... 199
5.4.4 Failure Modes and Fire Resistance ..................................................................... 200
5.4.5 Summary ............................................................................................................. 201
5.5
Response after Fire Exposure ................................................................................. 202
5.5.1 Tested Columns .................................................................................................. 202
5.5.2 Equipment and Test Procedure ........................................................................... 203
5.5.3 Residual Strength Results ................................................................................... 203
5.6
Summary ................................................................................................................. 204

Chapter 6 ..................................................................................................................................... 228
6
Numerical Model ........................................................................................................ 228
6.1
General .................................................................................................................... 228
6.2
Macroscopic Finite Element Model for Fire Resistance Analysis.......................... 229
6.2.1 General ................................................................................................................ 229
6.2.2 Fire Temperatures ............................................................................................... 230
6.2.3 Thermal Analysis ................................................................................................ 230
6.2.4 Strength Analysis ................................................................................................ 239
6.3
Limitations of Existing Numerical Model .............................................................. 247
6.4
Extension to Macroscopic Finite Element Model ................................................... 247
6.4.1 High Temperature Properties .............................................................................. 248
6.4.2 Approach to Model Tie Configuration ............................................................... 249
6.5
Computer Implementation ...................................................................................... 255
6.5.1 Input Data............................................................................................................ 256
6.5.2 Output Results..................................................................................................... 256
6.6
Validation of Numerical Model .............................................................................. 256
6.6.1 General ................................................................................................................ 256
6.6.2 Validation Studies ............................................................................................... 257
6.7
Summary ................................................................................................................. 263
Chapter 7 ..................................................................................................................................... 280
7
Parametric Studies ...................................................................................................... 280
7.1
General .................................................................................................................... 280
7.2
Factors influencing Fire Resistance ........................................................................ 281
viii

7.3
Parametric Studies .................................................................................................. 282
7.3.1 Selection of RC Columns.................................................................................... 282
7.3.2 Range of Parameters ........................................................................................... 282
7.3.3 Analysis Procedure ............................................................................................. 283
7.4
Results from Parametric Studies ............................................................................. 284
7.4.1 Effect of Permeability (Strength) ........................................................................ 284
7.4.2 Effect of Tie Configuration ................................................................................. 286
7.4.3 Effect of Load Ratio (Level) ............................................................................... 288
7.4.4 Effect of fibers .................................................................................................... 289
7.4.5 Effect of Column Size......................................................................................... 290
7.5
Summary ................................................................................................................. 292
Chapter 8 ..................................................................................................................................... 301
8
Conclusions and Recommendations ........................................................................... 301
8.1
General .................................................................................................................... 301
8.2
Key Findings ........................................................................................................... 301
8.3
Recommendations for Future Research .................................................................. 305
8.4
Research Impact ...................................................................................................... 306
Appendix A ................................................................................................................................. 307
Appendix B ................................................................................................................................. 317
REFERENCES ........................................................................................................................... 333

ix

LIST OF TABLES
Table 3.1 - Test Matrix for evaluation of thermal properties ....................................................... 94
Table 3.2 - Mix proportions of plain HSC, SCC, FAC, and NSC batches ................................... 95
Table 3.3 - Mix proportions for fiber reinforced HSC.................................................................. 96
Table 3.4 - Mix proportions for fiber reinforced SCC .................................................................. 97
Table 3.5 - Mix proportions for FAC and FAC-P ........................................................................ 98
Table 3.6 - Compressive strength of plain HSC, SCC and FAC mixtures ................................... 98
Table 3.7 - Compressive strength of fiber reinforced HSC, SCC and FAC mixtures .................. 99
Table 3.8 - Details of specimens for thermal properties for different batches of concrete......... 100
Table 3.9 - Permeability coefficients for different types of concretes ........................................ 101
Table 4.1 - Test matrix for evaluation of high temperature mechanical properties .................... 148
Table 4.2 - Details of cylinders for different batches of concrete. ............................................. 149
Table 4.3 - Compressive strength reduction factor βT at different temperatures for HSC and fiber
reinforced HSC. .......................................................................................................................... 150
Table 4.4 - Splitting tensile strength reduction factor βT at different temperatures for HSC and
fiber reinforced HSC. .................................................................................................................. 150
Table 4.5 - Compressive strength, tensile strength and elastic modulus reduction factor βT at
different temperatures for SCC and fiber reinforced SCC.......................................................... 151
Table 4.6 - Compressive strength and elastic modulus reduction factor βT at different
temperatures for FAC and FAC-P .............................................................................................. 151
Table 5.1 - Mix proportions for four batches of concrete. .......................................................... 205
Table 5.2 - Summary of test parameters for fire resistance test on columns. ............................. 206
Table 6.1 - Parameters and results for RC columns tested at MSU used in the temperature and
structural response validation study ............................................................................................ 265
Table 7.1 - Results for HPC columns with different load ratios ................................................. 293
Table 7.2 - Results for HPC columns with different fiber combinations ................................... 293
Table 7.3 - Results for HPC columns with different column sizes ............................................. 294
x

Table B.1 - Design parameters used for the columns ................................................................. 318
Table B.2 - Calculated factored capacities of FAC and FAC-P columns ................................... 321
Table B.3 - Calculation of nominal load and moment for P-M diagram for FAC column ........ 324
Table B.4 - Load and moment capacity calculated by moment magnification method. ............ 326
Table B.5 - Calculated factored capacities of HSC-S and HSC-H columns .............................. 327
Table B.6 - Calculation of nominal load and moment for P-M diagram for HSC-S column ..... 330
Table B.7 - Load and moment capacity calculated by moment magnification method. ............ 331

xi

LIST OF FIGURES
Figure 1.1 - Layout of columns used to show comparative response in NSC and HSC columns 12
Figure 1.2 - Comparison of temperature distribution between NSC and HSC columns .............. 12
Figure 1.3 - Comparison of axial deformations between NSC and HSC columns ....................... 13
Figure 1.4 - Different fire scenarios encountered in practical fire situations ............................... 13
Figure 1.5 - Comparison of extent of fire induced spalling in NSC and HSC columns ............... 14
Figure 1.6 - Conventional and improved tie configuration in RC columns.................................. 14
Figure 1.7 - Effect of ties on spalling in RC columns with 90° and 135° bent ties ...................... 15
Figure 2.1 - Variation in thermal conductivity of NSC as a function of temperature .................. 54
Figure 2.2 - Variation in specific heat of NSC as a function of temperature ............................... 54
Figure 2.3 - Variation in linear thermal expansion of NSC as a function of temperature ............ 55
Figure 2.4 - Variation in mass of concrete with different aggregates as a function of temperature
....................................................................................................................................................... 55
Figure 2.5 - Variation in mass of NSC and HSC as a function of temperature ............................ 56
Figure 2.6 - General arrangement of concrete specimen under compressive loading inside
furnace........................................................................................................................................... 56
Figure 2.7 - Specimen heating and loading in stressed test method under preload ...................... 57
Figure 2.8 - Specimen heating and loading in unstressed test method without preload ............... 58
Figure 2.9 - Specimen heating and loading in residual strength measurements ........................... 59
Figure 2.10 - Variation in relative compressive strength as function of temperature for NSC ... 60
Figure 2.11 - Variation in relative compressive strength as function of temperature for HSC .... 60
Figure 2.12 - Variation in relative splitting tensile strength as function of temperature .............. 61
Figure 2.13 - Variation in elastic modulus as a function of temperature ...................................... 61
Figure 2.14 - Typical load deformation of NSC at various temperatures ..................................... 62
Figure 2.15 - Typical load deformation of HSC at various temperatures ..................................... 62

xii

Figure 2.16 - Variation of total strain with temperature for concrete heated under differnet preloads (Anderberg and Thelandersson 1976) ................................................................................. 63
Figure 2.17 - Variation of thermal strain with temperature for limestone concrete heated under
different pre-loads ......................................................................................................................... 64
Figure 2.18 - Illustration of spalling process in concrete (Dwaikat, 2009) .................................. 65
Figure 2.19 - Illustration of thermal dilation mechanism for fire induced spalling ...................... 65
Figure 2.20 - Conventional 90° hook versus modified 135° hook configuration ......................... 66
Figure 3.1 - Steel and polypropylene fibers used in the study .................................................... 102
Figure 3.2 - Typical test specimens for undertaking thermal conductivity and specific heat tests
..................................................................................................................................................... 102
Figure 3.3 - Test setup and apparatus for room temperature and high temperature thermal
conductivity and specific heat tests............................................................................................. 103
Figure 3.4 - Two types of sensors used with Hot Disk TPS 2500S thermal constants analyzer 103
Figure 3.5 - TMA setup for measurement of thermal strain as a function of temperature ......... 104
Figure 3.6 - Room temperature sample holder ........................................................................... 105
Figure 3.7 - Hot Disk (TPS) mica sensor being used between two specimens of concrete........ 105
Figure 3.8 - Time-temperature graph showing heating rate and stabilizing time for Hot Disk tests
..................................................................................................................................................... 106
Figure 3.9 - Time-Temperature graph showing heating rate for thermal expansion tests .......... 106
Figure 3.10 - Measured thermal conductivity as a function of temperature for HSC, SCC, FAC
and NSC ...................................................................................................................................... 107
Figure 3.11 - Measured thermal conductivity as a function of temperature for plain and fiber
reinforced HSC ........................................................................................................................... 107
Figure 3.12 - Measured thermal conductivity as a function of temperature for plain and fiber
reinforced SCC............................................................................................................................ 108
Figure 3.13 - Measured thermal conductivity as a function of temperature for FAC and FAC-P
..................................................................................................................................................... 108
Figure 3.14 - Measured specific heat as a function of temperature for different HSC, SCC, FAC
and NSC ...................................................................................................................................... 109

xiii

Figure 3.15 - Measured specific heat as a function of temperature for plain and fiber reinforced
HSC ............................................................................................................................................. 109
Figure 3.16 - Measured specific heat as a function of temperature for fiber reinforced SCC .... 110
Figure 3.17 - Measured specific heat as a function of temperature for FAC and FAC-P .......... 110
Figure 3.18 - Measured thermal expansion as a function of temperature for HSC, SCC, FAC and
NSC ............................................................................................................................................. 111
Figure 3.19 - Measured thermal expansion as a function of temperature for plain and fiber
reinforced HSC ........................................................................................................................... 111
Figure 3.20 - Measured thermal expansion as a function of temperature for plain and fiber
reinforced SCC............................................................................................................................ 112
Figure 3.21 - Measured thermal expansion as a function of temperature for FAC and FAC-P . 112
Figure 3.22 - Measured mass loss as a function of temperature for HSC, SCC, FAC and NSC 113
Figure 3.23 - Measured mass loss as a function of temperature for plain and fiber reinforced HSC
..................................................................................................................................................... 113
Figure 3.24 - Measured mass loss as a function of temperature for plain and fiber reinforced SCC
..................................................................................................................................................... 114
Figure 3.25 - Measured mass loss as a function of temperature for FAC and FAC-P ............... 114
Figure 3.26 - Thermal expansion plot showing error bars for standard deviation for HSC, SCC,
FAC, and NSC ............................................................................................................................ 115
Figure 3.27 - Thermal conductivity data verses fitted lines for HSC, SCC, and FAC ............... 115
Figure 3.28 - Specific heat data verses fitted lines for HSC, SCC, and FAC ............................. 116
Figure 3.29 - Thermal expansion data verses fitted lines for HSC, SCC, and FAC ................... 116
Figure 3.30 - Mass loss data verses fitted lines for HSC, SCC, and FAC .................................. 117
Figure 4.1 - Arrangement of thermocouples on an instrumented cylinder ................................. 152
Figure 4.2 - Electrical furnace used to heat the small cylinders ................................................. 152
Figure 4.3 - Forney strength test machine used for mechanical properties ................................ 153
Figure 4.4 - Thermal jacket for handling heated cylinders and to preserve heat in cylinders during
compressive strength tests........................................................................................................... 153
Figure 4.5 - Design details of steel bracket frame ...................................................................... 154
xiv

Figure 4.6 - Insulated steel bracket frame for handling heated cylinders and to preserve heat in
cylinders during splitting tensile strength tests ........................................................................... 155
Figure 4.7 - Schematic of temperature and stress increments during heating and loading of test
cylinders ...................................................................................................................................... 156
Figure 4.8 - Time-temperature graph showing ramp and hold times at each target temperature 157
Figure 4.9 - Heating characteristics of test cylinder at 600°C .................................................... 158
Figure 4.10 - Temperature progression at mid-depth of concrete cylinders at various hold times
..................................................................................................................................................... 159
Figure 4.11 - Arrangement for high temperature compressive strength tests and tested cylinder
..................................................................................................................................................... 159
Figure 4.12 - Arrangement for high temperature splitting tensile strength tests and tested cylinder
..................................................................................................................................................... 160
Figure 4.13 - LVDTs and load cell addition to Forney strength test machine for stress-strain
measurements .............................................................................................................................. 160
Figure 4.14 - Measured compressive strength of NSC, HSC, SCC, and FAC ........................... 161
Figure 4.15 - Relative compressive strength of NSC, HSC, SCC, and FAC.............................. 161
Figure 4.16 - Measured compressive strength of HSC and fiber reinforced HSC as function of
temperature ................................................................................................................................. 162
Figure 4.17 - Measured relative compressive strength of HSC and fiber reinforced HSC as
function of temperature ............................................................................................................... 162
Figure 4.18 - Measured compressive strength of SCC and fiber reinforced SCC as function of
temperature. ................................................................................................................................ 163
Figure 4.19 - Measured relative compressive strength of SCC and fiber reinforced SCC as
function of temperature. .............................................................................................................. 163
Figure 4.20 - Measured compressive strength of FAC and FAC-P as function of temperature. 164
Figure 4.21 - Measured relative compressive strength of FAC and FAC-P as function of
temperature ................................................................................................................................. 164
Figure 4.22 - Measured splitting tensile strength of NSC, HSC, SCC, and FAC....................... 165
Figure 4.23 - Relative splitting tensile strength of NSC, HSC, SCC, and FAC ......................... 165
Figure 4.24 - Measured splitting tensile strength of HSC and fiber reinforced HSC as function of
temperature ................................................................................................................................. 166
xv

Figure 4.25 - Measured relative splitting tensile strength of HSC and fiber reinforced HSC as
function of temperature ............................................................................................................... 166
Figure 4.26 - Measured splitting tensile strength of SCC and fiber reinforced SCC as function of
temperature ................................................................................................................................. 167
Figure 4.27 - Measured relative splitting tensile strength of SCC and fiber reinforced SCC as
function of temperature ............................................................................................................... 167
Figure 4.28 - Measured splitting tensile strength of FAC and FAC-P as function of temperature
..................................................................................................................................................... 168
Figure 4.29 - Measured relative splitting tensile strength of FAC and FAC-P as function of
temperature ................................................................................................................................. 168
Figure 4.30 - Measured elastic modulus for plain SCC and fiber reinforced SCC .................... 169
Figure 4.31 - Measured elastic modulus for plain FAC and FAC-P .......................................... 169
Figure 4.32 - High temperature stress-strain curves for SCC ..................................................... 170
Figure 4.33 - High temperature stress-strain curves for SCC-S ................................................. 170
Figure 4.34 - High temperature stress-strain curves for SCC-P ................................................. 171
Figure 4.35 - High temperature stress-strain curves for SCC-H................................................. 171
Figure 4.36 - High temperature stress-strain curves for FAC ..................................................... 172
Figure 4.37 - High temperature stress-strain curves for FAC-P ................................................. 172
Figure 4.38 - Compressive strength test data of SCC with and without fibers compared with
regression based fitted line.......................................................................................................... 173
Figure 4.39 - Compressive strength test data of FAC and FAC-P compared with regression based
fitted line ..................................................................................................................................... 173
Figure 4.40 - Compressive strength relations for plain HSC and fiber reinforced HSC ............ 174
Figure 4.41 - Splitting tensile strength relations for plain HSC and fiber reinforced HSC ........ 174
Figure 4.42 - Compressive strength relations for plain SCC and fiber reinforced SCC ............. 175
Figure 4.43 - Splitting tensile strength relations for plain SCC and fiber reinforced SCC ........ 175
Figure 4.44 - Elastic modulus relations for plain SCC and fiber reinforced SCC ...................... 176
Figure 4.45 - Compressive strength relations for FAC and FAC-P ............................................ 176

xvi

Figure 4.46 - Splitting tensile strength relations for FAC and FAC-P ....................................... 177
Figure 4.47 - Elastic modulus relations for FAC and FAC-P ..................................................... 177
Figure 5.1- Column elevation and cross-section showing design details ................................... 207
Figure 5.2 - Steel cages inside column formwork with instruments wiring ............................... 208
Figure 5.3 - Casting and finishing of columns ............................................................................ 208
Figure 5.4 - Column cross-section showing location of thermocouples (TCs) .......................... 209
Figure 5.5 - Column cross-section showing location of strain gauges (SGs) ............................. 210
Figure 5.6 - View of thermocouples in cross-section and strain gauges attached to steel rebars 210
Figure 5.7 - Column cross-section showing location of linear position transducers (LPTs) ...... 211
Figure 5.8 - Structural fire testing facility at MSU’s Civil Infrastructure Laboratory ............... 212
Figure 5.9 - End conditions for the columns before fire tests ..................................................... 213
Figure 5.10 - Time temperature curve for fire scenario .............................................................. 213
Figure 5.11 - Measured rebars and concrete temperatures for FAC column at Section AA ...... 214
Figure 5.12 - Measured rebars and concrete temperatures for FAC column at Section BB....... 214
Figure 5.13 - Measured rebars and concrete temperatures for FAC column at Section CC....... 215
Figure 5.14 - Measured rebars and concrete temperatures for FAC-P column at Section AA... 215
Figure 5.15 - Measured rebars and concrete temperatures for FAC-P column at Section BB ... 216
Figure 5.16 - Measured rebars and concrete temperatures for FAC-P column at Section CC ... 216
Figure 5.17 - Measured rebars and concrete temperatures for HSC-S column at Section AA... 217
Figure 5.18 - Measured rebars and concrete temperatures for HSC-S column at Section BB ... 217
Figure 5.19 - Measured rebars and concrete temperatures for HSC-S column at Section CC ... 218
Figure 5.20 - Measured rebars and concrete temperatures for HSC-H column at Section AA .. 218
Figure 5.21 - Measured rebars and concrete temperatures for HSC-H column at Section BB .. 219
Figure 5.22 - Measured rebars and concrete temperatures for HSC-H column at section CC ... 219
Figure 5.23 - Comparison of measured temperature distribution for FAC and FACP columns 220
xvii

Figure 5.24 - Comparison of temperature distribution for FAC and HSC columns ................... 220
Figure 5.25 - Measured axial deformations as a function of fire exposure time ........................ 221
Figure 5.26 - Measured lateral deformations as a function of fire exposure time in tested columns
..................................................................................................................................................... 221
Figure 5.27 - Measured axial strains as a function of fire exposure time for FAC column at
Section DD .................................................................................................................................. 222
Figure 5.28 - Measured axial strains as a function of fire exposure time for FAC column at
Section EE................................................................................................................................... 222
Figure 5.29 - Measured axial strains as a function of fire exposure time for FAC-P column at
Section DD .................................................................................................................................. 223
Figure 5.30 - Measured axial strains as a function of fire exposure time for FAC-P column at
Section EE................................................................................................................................... 223
Figure 5.31 - Measured axial strains as a function of fire exposure time for HSC-S column at
Section DD .................................................................................................................................. 224
Figure 5.32 - Measured axial strains as a function of fire exposure time for HSC-S column at
Section EE................................................................................................................................... 224
Figure 5.33 - Measured axial strains as a function of fire exposure time for HSC-H column at
Section DD .................................................................................................................................. 225
Figure 5.34 - Measured axial strains as a function of fire exposure time for HSC-H column at
Section EE................................................................................................................................... 225
Figure 5.36 - State of columns before and after the fire resistance tests .................................... 226
Figure 5.37 - Columns after residual strength tests .................................................................... 227
Figure 5.38 - Load-deformation response of fire exposed columns during residual strength tests
..................................................................................................................................................... 227
Figure 6.1 - Flowchart showing the steps associated with analysis of fire exposed RC column 266
Figure 6.2 - Layout of idealized RC column and discretization of its cross-section for fire
resistance analysis ....................................................................................................................... 267
Figure 6.3 - Variation of strain, stress and internal forces in a cross-section of fire exposed RC
column......................................................................................................................................... 268
Figure 6.4 - Illustration of Curvature Controlled Iterative Procedure used for Structural Analysis
..................................................................................................................................................... 269
xviii

Figure 6.5 - Comparison of fire performance of RC columns with conventional 90° ties and
modified 135° ties ....................................................................................................................... 270
Figure 6.6 - Longitudinal rebar and transverse tie model and assumed forces........................... 271
Figure 6.6 - (cont’d) Longitudinal rebar and transverse tie model and assumed forces ............ 272
Figure 6.7 - Flowchart showing steps to calculate forces in tie configuration subroutine ......... 273
Figure 6.8 - Physical details and location of thermocouples for columns FAC and FAC-P ...... 274
Figure 6.9 - Physical details and location of thermocouples for columns HSC2, HSC3, HSC5 and
HSC6 ........................................................................................................................................... 275
Figure 6.10 - Comparison of measured and predicted temperatures in FAC column ................ 276
Figure 6.11 - Comparison of measured and predicted temperatures in FAC-P column ............. 276
Figure 6.12 - Comparison of measured and predicted axial deformations in FAC, FAC-P
columns ....................................................................................................................................... 277
Figure 6.13 - Predicted pore pressure at cover depth HSC2, HSC3, HSC5, and HSC6 columns
..................................................................................................................................................... 277
Figure 6.14 - Predicted bond strength offered by various ties in selected columns ................... 278
Figure 6.15 - Predicted effective tie force compared to bond strength in 90° tie in NSC, HSC1
and HSC2 columns ..................................................................................................................... 278
Figure 6.16 - Predicted effective tie force compared to bond strength in 135° tie in HSC3 and
HSC4 ........................................................................................................................................... 279
Figure 7.1 - Elevation and cross-sections of RC columns used in parametric study .................. 295
Figure 7.2 – Effect of permeability on pore pressure development in RC columns ................... 296
Figure 7.3 - Effect of tie size on bond strength in RC columns with 90° and 135° ties ............. 296
Figure 7.4 - Comparison of force acting on ties against bond strength in HSC column with 90°
and 135° ties................................................................................................................................ 297
Figure 7.5 - Comparison of force acting on ties against bond strength in NSC column with 90°
and 135° ties................................................................................................................................ 297
Figure 7.6 - Effect of load level on the effective force acting on ties in RC columns................ 298
Figure 7.7 - Temperature response HSC column with different fiber combinations.................. 298
Figure 7.8 - Temperature response of FAC column with different fiber combinations ............. 299
xix

Figure 7.9 - Pore pressure development in RC columns with different fiber combinations ...... 299
Figure 7.10 - Effect of column size on development of pore pressure at 40 mm depth ............. 300
Figure A.1 - The average temperature response as a function of D0(τ) ...................................... 311
Figure A.2 - Modulated temperature (bottom) and the length change (top) both as their first
derivatives. .................................................................................................................................. 314
Figure B.1 - Notations used in calculations ................................................................................ 319
Figure B.2 - Stress-strains and forces in columns....................................................................... 320
Figure B.3 - Cross-section of RC column................................................................................... 321
Figure B.4 - Load-moment interaction diagram for FAC column .............................................. 324
Figure B.5 - Calculation of ultimate load from load-moment interaction diagram for FAC column
..................................................................................................................................................... 327
Figure B.6 - Load-moment interaction diagram for HSC-S column .......................................... 330
Figure B.7 - Calculation of ultimate load from load-moment interaction diagram for HSC-S
column......................................................................................................................................... 332

xx

CHAPTER 1
1

INTRODUCTION

1.1 General
Concrete is one of the most widely used construction material in buildings due to its excellent
strength, durability, ease of fabrication, and fire resistance properties. Over the last three decades
there has been significant research and development activities in concrete technology and this
has led to improved concrete mixes often referred to as high performance concretes (HPC). HPC
which include high strength concrete (HSC), self-consolidating concrete (SCC), fiber reinforced
concrete (FRC), and high strength fly ash concrete (FAC), offer superior strength, durability and
cost advantages, and thus finding wide range of applications in built infrastructure. In recent
years the use of HPC, which was mainly used in bridges, off-shore structures, and infrastructure
projects, has been extended to columns and beams in reinforced concrete (RC) buildings.
Fire represents one of the most severe hazard to which structures may be subjected during their
life time and hence the provision of appropriate fire resistance measures is an important aspect of
building design. This is to enhance safety of occupants, control the spread of fire, and minimize
damage to property and environment in the event of a fire in the building. Fire safety design can
be achieved through active and passive fire protection measures. Active systems generally get
self-activated once the fire is triggered and they include fire detectors, smoke control systems,
and sprinklers. Passive systems are built into the structure (buildings), and do not require specific
operation to control the fire. The need for passive fire protection systems or what is commonly
referred to as fire resistance, can be attributed to the fact that structural integrity is the last line of
defense when other measures for containing the fire fail. Fire resistance is defined as the duration
1

during which a structural member (system) exhibits resistance with respect to structural integrity,
stability, and temperature transmission when exposed to fire (Buchanan, 2002; Purkiss, 2007).
Conventional normal strength concrete (NSC) members generally exhibit good fire resistance
properties. However, recent studies have shown that structural members made of high
performance concrete (similar to HSC, SCC and FAC) have lower fire resistance properties
(Bamonte and Gambarova, 2010; Kodur, 2000; Tang and Lo, 2009). This has been attributed to
differences in thermo-mechanical properties of HPC and also to the occurrence of fire induced
spalling (Castillo and Durrani, 1990; Fu et al., 2005; Kodur and Sultan, 1998; Tang and Lo,
2009). It has also been shown that the spalling in HPC members can be overcome through the
addition of fibers (steel, propylene, and hybrid) in the concrete mix. Whilst most of the high
temperature properties are available for NSC, no data is available for new types of HPC such as
HSC, SCC, and FAC (plain and with different fiber combinations).

1.2 High Temperature Properties of Concrete
Evaluating fire resistance of a structural system requires knowledge of high temperature
properties of constituent materials (Buchanan, 2002; SFPE, 2008). The properties of concrete
that are needed for fire resistance analysis are thermal, mechanical, deformation, and special
properties such as fire induced spalling. Thermal properties include thermal conductivity,
specific heat, thermal diffusivity, thermal expansion, and mass loss. Deformation properties such
as creep and mechanical properties such as strength, stress-strain curves, and elastic modulus
significantly influence the fire response of a structural system. In addition, fire induced spalling
which occurs in concrete under certain fire conditions can alter the response of a reinforced
concrete structural system. All these properties vary with temperature and are influenced by the

2

mix proportions, type of aggregate, presence of fibers, and mineral and chemical admixtures
(Bažant and Kaplan, 1996; Buchanan, 2002; Phan, 1996; SFPE, 2008).
HPC are typically made through addition of binders such as silica fume, fly ash, blast furnace
slag, and other smaller amounts of mineral and chemical admixtures. These binders introduce
specific properties to HPC such as flow ability and workability in fresh form and high strength
and dense microstructure in the hardened form. Thus thermal and mechanical properties of HPC
can be different from that of conventional concrete (Kodur and Sultan, 1998). When these HPC’s
are subjected to high temperatures, their performance is affected by changes in its thermal and
mechanical behavior. Understanding the behavior of these HPC’s at the material level and
characterizing their high temperature properties is important for predicting the fire response of
HPC structural members. However, at present there is very limited information on high
temperature thermal and mechanical properties for these new types of HPC.

1.3 Response of HPC Columns under Fire Conditions
1.3.1

General Fire Behavior

One of the major applications for high performance concrete is in columns of high rise buildings
since high compressive strength can effectively be utilized. The behavior of RC columns under
fire is quite different from that at room temperature mainly due to the fact that under fire
conditions, the strength and stiffness of the column deteriorate with temperature. Columns made
of conventional NSC generally exhibit good fire resistance and can offer 3 to 4 hours of fire
resistance rating without any additional measures. However, it has been shown through
numerous experimental and numerical studies that HPC columns may not exhibit the same level
fire resistance as that of NSC (Kodur, 2003; Kodur and Sultan, 1998). The effect of various
parameters such as cross sectional size, cover thickness, reinforcement ratio, aggregate type,
3

load, and load eccentricity on fire resistance was investigated previously through series of fire
experiments (Kodur and McGrath, 2003).
Data from reported fire tests can be used to illustrate the typical behavior of an RC column under
fire. Figure 1.1shows the elevation and cross-section of a typical NSC and HSC column tested in
the laboratory under ASTM E119 (ASTM Standard E119, 2007) standard fire (Figure 1.2), and
Figure 1.3 shows the variation of axial deformation of a NSC and HSC column with fire
exposure time (Kodur and Sultan, 1998; Lie and Woolerton, 1988). Concrete compressive
strength for the HSC and NSC columns was 97 MPa and 36 MPa respectively. The HSC column
was loaded with 2000 kN or 60% of the ultimate resistance whereas NSC column was subjected
to a load of 1067 kN or 60% of its ultimate resistance. HSC column had four while NSC column
had eight 20 mm longitudinal rebars as main reinforcement. The columns were provided with
135° bent ties. The NSC column had 8 mm at 305 mm spacing, whereas the HSC column had 10
mm ties at a spacing of 225 mm.
When a concrete column is exposed to fire, the cross-sectional temperatures increase with time
as shown in Figure 1.2. At the beginning of fire exposure concrete and steel expand due to rising
cross-sectional temperatures, as shown in Figure 1.3. The expansion in the initial stages of fire
exposure is mainly due to the thermal expansion occurring in both concrete and steel. With the
increase in temperature, concrete and steel rebars start to lose strength. Since the reinforcing
rebars are in the outer core of the column, the temperature rises much faster in rebars than the
inner core of concrete as shown in Figure 1.2. When the steel yields, as a result of rising
temperatures, the concrete carries a progressively increasing portion of the load. The strength of
the concrete also decreases with temperature due to deteriorating properties of concrete, and
ultimately as it can no longer support the load, failure of the column occurs.

4

The difference between temperature progression in NSC and HSC can be seen in Figure 1.2.
Since HSC has higher thermal conductivity, it displays higher temperature development at
quarter depth and mid depth to that of NSC. Both NSC and HSC columns also display different
deformation patterns, and these differences can be attributed to ductile behavior of NSC and
differences in thermal expansion and elastic modulus properties of NSC and HSC (Kodur, 1999).
The lower deformation (expansion and contraction) in HSC column can be attributed to the
lower thermal expansion and high stiffness properties of HSC. The failure time for HSC column
in the fire test was reported as 225 minutes as compared to 366 minutes for NSC column,
indicating HSC columns has much lower fire resistance in comparison to NSC columns.
The above comparative illustration clearly indicates that NSC and HSC columns have significant
difference in fire behavior. This difference in fire response of RC columns of two concrete types
is attributed to difference in their high temperature thermal and mechanical properties. Although
conventional NSC members have good fire resistance as illustrated above, same may not be true
for HSC columns due to faster degradation of strength and occurrence of fire induced spalling.
HPC columns having concrete properties identical to that of HSC members are also assumed to
have lower fire performance. Therefore there is a need to characterize the high temperature
properties specific to HPC. There is substantial amount data in literature on high temperature
thermal and mechanical properties of NSC and to some extent for HSC as well. However, in the
case of new types of HPC such as FAC, SCC (both plain and with fibers) this high temperature
property data is very limited.
1.3.2

Fire induced Spalling

An RC column can be exposed to different fire scenarios (other than standard fire) during the life
time of a structure as shown in Figure 1.4. Once exposed to some of these fire scenarios the
5

cross-section of RC columns can experience high thermal gradients which in turn can
significantly influence the fire behavior of structural members. These thermal gradients can be
moderate to severe, depending on thermal properties, cross-sectional size, and microstructure of
concrete. The high thermal gradients resulting from rising temperatures in the cross-section lead
to rapidly increasing pore pressure that cause fire induced spalling. Fire induced spalling that is
caused by pore pressure buildup in concrete, is not a problem with NSC columns and is mostly
associated to HSC columns due to low permeability (Ali, 2002; Ali and Nadjai, 2008; Kodur,
1999; Kodur, 2000).
Figure 1.5 shows a comparison of post fire status of NSC and HSC columns and extent of fire
induced spalling in HSC. If the cross-sectional temperatures rise at faster rate, high pore pressure
will build up due to moisture converting to vapors. This fire induced pore pressure in concrete
increases with temperature while the tensile strength of concrete degrades with temperature.
Since tensile strength of concrete is inherent resistance to spalling, when pore pressure exceeds
the tensile strength of concrete spalling occurs. Spalling depends on a number of factors such as
heating rate, permeability, moisture content, configuration of lateral (tie) reinforcement, and
strength of concrete. Depending on all these factors the columns may undergo fire induced
spalling thus hampering their strength and stiffness properties. HPC such as FAC, SCC which
are characterized by dense microstructure similar to HSC are also prone to fire induced spalling.
1.3.3

Spalling Mitigation

To mitigate fire induced spalling in HSC, researchers have suggested addition of different fiber
combinations, such as polypropylene fibers (Ali et al., 2004; Behnood and Ghandehari, 2009;
Bilodeau et al., 2004), steel fibers (Kodur, 1999; Rossi, 1994) and hybrid fibers (Ali and Nadjai,
2008). Polypropylene fibers melt at relatively low temperatures (about 167-170°C) thus leaving
6

micro and macro channels randomly oriented inside the concrete that help diffusion of pore
pressure (Bilodeau et al., 2004) resulting in spalling mitigation. Steel fibers enhance the tensile
strength of concrete which provides resistance against pore pressure and thus helps mitigate
spalling. Hybrid fibers take advantage of both types of fibers to mitigate spalling, by increase in
porosity of concrete with melting of propylene fibers at higher temperatures and improvement in
tensile strength with use of steel fibers.
Tests have also shown that modifying the tie configuration in HSC columns from conventional
90° to 135° is beneficial to reduce the effect of spalling (Kodur and McGrath, 2003). It was
experimentally established that, (1) spalling occurs throughout the cross-section of columns
when the ties are bent in a conventional pattern at 90° and (2) spalling only occurs in the outer
layer of steel cage when ties are bent at 135° into the concrete core (Kodur and McGrath, 2006;
Kodur et al., 2002). Figure 1.6 shows arrangements of conventional 90° and improved 135° ties
and Figure 1.7 shows the failure modes of HSC columns with 90° and 135° ties respectively. It
can be seen that extent of spalling has been reduced in column with improved tie configuration.
For this reason, ACI 216.1 (2007) specifies that for fire design, cross ties in the column shall be
anchored through 135° end hooks which turn around longitudinal bars and are embedded in the
concrete core. Though based on experimental studies, the prescriptive approach has been adopted
by ACI 216.1 to take into account the effect of tie configuration; however, there is lack of
understanding of fundamental principles as to how it contributes in enhancement of fire
resistance of RC columns.

1.4 Research Objectives
The difference in fire behavior of NSC and HSC columns results from different thermal and
mechanical properties at high temperature. One of the major problems that affects the fire
7

behavior in HSC members is fire induced spalling. With the increased use of new types of HPC
in RC columns, there is a need to characterize its’ thermal and mechanical properties both at
material and structural level. For evaluating the fire resistance of HPC columns, as well as to
account for beneficial effects of fibers and 135° tie configuration on spalling mitigation, high
temperature material properties of HPC (plain and with different fiber combinations) and
including the effect of tie configuration is required. However, there is lack of data on high
temperature properties specific to different HPC (plain and with fibers) as well as established
mechanism with which fire resistance in RC columns is enhanced with provision of modified
135° tie configuration. To overcome the current knowledge gaps, this research is aimed at
addressing the following objectives:
Undertake a detailed state-of-the-art review on the high temperature properties of present day
concrete mixes. The comprehensive review will compile the current state of experimental
and numerical studies on HSC columns and code provisions on thermal, mechanical,
deformation and special properties like fire induced spalling and technique to overcome
problem of spalling in HSC.
Undertake material property tests to generate database on high temperature thermal and
mechanical properties of new types of HPC namely HSC, FAC, and SCC (plain and with
different fiber combinations). Data from these tests will be utilized to develop empirical
thermal and mechanical property relationships.
Undertake fire resistance tests on two fly ash concrete (FAC) and two high strength concrete
(HSC) columns with different fiber combinations as part of structural characterization of
HPC structural members. Extensive data will be collected in the form of axial and lateral

8

deformations, cross-sectional temperatures and strains in steel rebars. Data from fire resistance
tests was utilized to validate the numerical model for fire resistance predictions of HPC columns.

Develop an approach for modeling the effect of tie configuration on fire resistance of HPC
columns. This will include evaluation of the mechanics involved in opening and failing of
ties by taking into account the forces acting on ties resulting from high temperature thermomechanical stresses and fire induced pore pressure. Effect of modification of tie
configuration on spalling mitigation and enhancement of fire resistance of RC columns will
be studied.
Incorporate the high temperature properties of HPC and tie sub-model in to macroscopic
finite element (MFE) model. Validate the extended MFE model for evaluating the fire
response of HPC columns tested earlier by computing thermal and structural response
predictions for HPC columns under different tie configurations.
Carry out parametric studies to quantify the significant factors that influence the fire response
of HPC columns with 90° and 135° bent ties.

1.5 Scope
The research proposed here involves experimental and numerical studies on characterization of
fire performance of HPC both at material and structural levels. As part of experimental research,
extensive high temperature experiments on small specimens were carried out for characterizing
thermal and mechanical properties of FAC, SCC, and HSC (plain and with different fiber
combinations) at material level. At structural level, four full scale RC columns made of FAC and
HSC were fabricated and tested under design fire to evaluate the structural fire response of FAC
columns with and without fibers to that with HSC columns. To develop a fundamental
understanding on the effect of tie configuration on fire response of RC columns a numerical ‘tie
9

sub-model’ was developed and incorporated into a macroscopic finite element model. The effect
of tie configuration on fire resistance is modeled through mechanics based principles, similar to
the approach used in seismic analysis of structures. Data from fire resistance tests is utilized to
validate the fire resistance model. The validated MFE model was then applied to carry out
parametric studies to quantify influence of various factors on fire response of HPC columns.
The thesis is organized into eight chapters:
Chapter 1 provides background information on fire resistance of HPC and high temperature
properties needed for fire resistance evaluation of HPC columns.
Chapter 2 provides a review of the literature on the high temperature thermal and mechanical
material properties of conventional NSC and HSC, the variability in existing data and also
highlights limitations of available methods for fire resistance evaluation of HPC columns. A
review of recent experimental and analytical studies on fire resistance evaluation of RC
columns is also provided.
Chapter 3 presents experimental studies on high temperature thermal properties of HSC,
SCC, and FAC (plain and with different fiber combinations) and the development of
empirical relationships for high temperature material properties.
In Chapter 4 experimental studies on high temperature mechanical properties of HSC, SCC,
and FAC (plain and with different fiber combinations) are presented. The chapter also
provides empirical relationships developed for high temperature mechanical properties of
HPC.
In Chapter 5 details on fire resistance experiments on two FAC and two HSC columns (with
different fiber combinations) under non-standard fire scenarios are presented. Results from

10

the fire tests are used to discuss the comparative response of FAC and HSC columns under
fire conditions.
In Chapter 6 covers the details on macroscopic finite element numerical model and analysis
details for fire resistance predictions of RC columns. Development of subroutines based on
high temperature material properties of HPC and tie configuration sub-model is also
presented. Incorporation of these subroutines into macroscopic finite element (MFE) model
and validation of the extended MFE model are covered in this chapter.
Chapter 7 presents results from parametric studies showing influence of the significant
factors such as high temperature thermal and mechanical properties and effect of different tie
configurations on fire response of HPC columns.
Chapter 8 summarizes the key findings, recommendations for future work and research
impact based on this study.

11

P

4-20 mm main rebars

305 mm

3810 mm

Ties

50 mm effective
cover

305 mm

Elevation

Cross-section

Figure 1.1 - Layout of columns used to show comparative response in NSC and HSC columns

Temperature (°C)

1000

800

600

400

ASTM E119
NSC rebar
HSC rebar
NSC quarter depth
HSC quarter depth
NSC mid depth
HSC mid depth

200

0
0

30

60

90

120

150

180

Time (minutes)

Figure 1.2 - Comparison of temperature distribution between NSC and HSC columns

12

210

Axial deformation (mm)

15
NSC
HSC

10
5
0
-5
-10
-15
-20
-25
0

100

200
Time (min)

300

400

Figure 1.3 - Comparison of axial deformations between NSC and HSC columns

Temperature (°C)

1000
Severe fire

800

Moderate fire
ASTM E119 standard fire

600

ISO 834 Standard fire
400
200
0
0

20

40

60
80
Time (min)

100

120

Figure 1.4 - Different fire scenarios encountered in practical fire situations

13

140

NSC

HSC

Figure 1.5 - Comparison of extent of fire induced spalling in NSC and HSC columns
(For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation)
Plate 406×406×25 mm

A

3300 mm

A

Angle 100×100×12 mm

10 mm Stirrups (135° @ 200 mm c/c
)

90˚ Hook

135˚ Hook

Plate 406×406×25 mm

Figure 1.6 - Conventional and improved tie configuration in RC columns
14

Column with 90˚ ties

Column with 135˚ ties

Figure 1.7 - Effect of ties on spalling in RC columns with 90° and 135° bent ties

15

CHAPTER 2
2

STATE-OF-THE-ART REVIEW

Part of this chapter is based on the following journal papers:
•

Kodur, V., and Khaliq, W. (2011). "Effect of Temperature on Thermal Properties of
Different Types of High Strength Concrete." Journal of Materials in Civil Engineering,
ASCE, 23(6), 793-801.

•

Khaliq, W., and Kodur, V. (2011). "High temperature properties of fiber reinforced high
strength concrete." Innovations in Fire Design of Concrete Structures - ACI SP 279, 3-1-42.

•

Khaliq, W., and Kodur, V. (2011). "Thermal and mechanical properties of fiber reinforced
high performance self-consolidating concrete at elevated temperatures." Cement and
Concrete Research, 41(11), 1112-1122.

2.1 General
Concrete generally exhibits good fire resistance properties and thus finds wide applications in
buildings and other built infrastructure, where fire safety is one of the primary considerations.
However, recent studies show that structural members made of new concrete types (HSC, SCC
and FAC) known as HPC, may not have same level of fire resistance like conventional concrete
(NSC) (Bamonte and Gambarova, 2010; Kodur, 2000; Tang and Lo, 2009). Typically, new types
of HPC have lots of applications in columns of building because of the advantage of higher
strength which is utilized to reduce size (cross-section) of columns. The fire resistance of
concrete structural members is governed by high temperature thermal and mechanical properties
16

of constituent concrete. For predicting fire resistance of concrete structural members, knowledge
of high temperature material properties is very critical which includes thermal, mechanical and
deformation properties. In addition to that, fire induced spalling might significantly influence the
fire resistance of HSC, therefore properties related to spalling are also important and should be
known.
In this chapter previous studies related to the high temperature properties of concrete are
reviewed. The phenomenon of fire induced spalling and methods for mitigating spalling are also
presented. Moreover, previous experimental and numerical studies carried out to evaluate fire
resistant of RC columns are also reviewed.

2.2 Thermal Properties of Concrete
2.2.1

General

For evaluating fire resistance of concrete structural members the temperature distribution within
the member is to be established. This temperature distribution is dependent on high temperature
thermal properties of concrete. The thermal properties that govern the temperature distribution
are thermal conductivity and specific heat (or heat capacity). Other thermal properties that
influence the fire behavior of RC structural members are thermal expansion and mass loss that
have an effect on development of thermal stresses and specific heat respectively.
Thermal conductivity is defined as the ratio of rate of heat flow to temperature gradient, and
represents the uniform flow of heat through concrete of unit thickness over a unit area subjected
to a unit temperature difference between the two opposite faces. Concrete contains moisture in
different forms and, type and amount of moisture has significant effect on thermal conductivity.
Thermal conductivity is usually measured by means of 'steady state' or 'transient' test methods
(Bažant and Kaplan, 1996). Transient methods are preferred to measure thermal conductivity of
17

moist concrete over steady-state methods (Shin et al., 2002), as physicochemical changes of
concrete at higher temperatures cause intermittent direction of heat flow.
Specific heat is the amount of heat per unit mass, required to change the temperature of a
material by one degree and is generally expressed in terms of thermal (heat) capacity which is
the product of specific heat and density. Specific heat is highly influenced by moisture content,
aggregate type, and density of concrete (Kodur and Sultan, 1998; Phan, 1996). Specific heat
represents the energy absorbed by the concrete and accounts for sensible heat and latent heat
involved during temperature change. Sensible heat ascribes to the heat involved in
thermodynamic reaction during temperature change. Latent heat refers to the energy absorbed or
released by the material during phase transition. The material absorbs considerable amount of
energy during physiochemical changes and hence specific heat values are highly influenced by
the phase transition in materials.
The coefficient of thermal expansion is defined as the percentage change in length of a specimen
per degree temperature rise. Linear thermal expansion is the thermal strain resulting from
increased temperature. Thermal expansion of concrete is generally influenced by cement type,
water content, aggregate type, temperature and age (Lie, 1992). Thermal expansion of concrete is
further complicated by other contributing factors such as additional volume changes caused by
changes in moisture content, by chemical reactions (dehydration, change of composition), and by
creep and micro-cracks resulting from non-uniform thermal stresses (Bažant and Kaplan, 1996).
In some cases thermal shrinkage can also result from loss of water due to heating, along with
thermal expansion, and this might lead to overall volume change to be negative, i.e. shrinkage
rather than expansion.

18

Mass is a property that enables concrete to absorb and store significant amounts of heat. Mass
loss can affect the enthalpy and amount of latent heat which directly affects all the thermal
properties of concrete. Higher mass in concrete acts as heat sink, by absorbing and holding heat
for longer time. This delays the heat transfer through material in an RC member, thus mass loss
influences thermal properties of the concrete as well as strength and stiffness properties of RC
members. Mass loss of conventional NSC and HSC has been investigated earlier with most of
the information pertaining to NSC.
2.2.2

Test Methods for High Temperature Thermal Properties

There are many ways to measure the thermal conductivity of a given material and the results can
vary depending on the test method used (Flynn, 1999). The general idea behind these testing
techniques is to monitor the difference of temperature between two ends of the material
specimen. Among various methods, hot wire method (ASTM C1113, 2009) and guarded heat
flow meter method (ASTM E1530, 2011) are commonly used for measuring thermal
conductivity of concrete. Hot wire method is used to measure the thermal conductivity of
"refractories" such as insulating bricks, concrete and powder or fibrous materials. Because it is
basically a transient radial flow technique, isotropic specimens are required. In guarded heat flow
meter method a small sample of the material to be tested is held under a compressive load
between two polished metal surfaces, each controlled at a different temperature. The lower
surface is part of a calibrated heat flux transducer. As heat flows from the upper surface through
the sample to the lower surface, an axial temperature gradient is established in the stack. By
measuring the temperature difference across the sample along with the output from the heat flux
transducer, thermal conductivity of the sample can be determined with known thickness. These

19

test methods for measuring thermal conductivity can also be applied for higher temperatures up
to 850°C and above, but measuring at higher temperatures becomes cumbersome and costly.
Many techniques are available to measure the specific heat of concrete at room temperature;
however, these methods can be used at elevated temperatures but they would become costly and
time-consuming. Of these methods differential scanning calorimetry (DSC) is most common to
measure specific heat of concrete (ASTM C1269, 2011). This technique is based on measuring
the energy necessary to establish a nearly zero temperature difference between a substance and
an inert reference material, as the two specimens are subjected to identical temperature regimes
in an environment heated or cooled at a controlled rate. DSC hence can be used to establish the
heat energy required to raise a certain amount of material to a certain temperature, which can
lead to the determination of the specific heat of that material.
Among various techniques to measure linear thermal expansion, dilatometric technique and
thermomechanical analysis technique (ASTM E831, 2006) are most common. Both these
thermal expansion measurement techniques are similar where dimension change in specimens is
measured as a function of temperature and percentage change is calculated. The mass loss with
temperature is usually measured by means of thermogravimetric analyzer technique (ASTM
E1868, 2010). A specimen of known mass is heated at a constant temperature while its mass is
continuously measured as a function of time. At the end of a pre-determined time interval or
temperature, the mass loss of the specimen is calculated as a percent of the original mass.
2.2.3

Previous Studies on Thermal Properties

There have been quite a few test programs for characterizing high temperature thermal properties
of concrete. Harmathy (1970), Harmathy and Allen (1973), Lie and Kodur (1996), VanGeem et
al. (1997), Shin et al. (2002) and Kodur and Sultan (2003) have evaluated the thermal properties
20

of NSC concrete. Based on the test data, empirical formulae for thermal properties of NSC have
been developed (ASCE, 1992; Eurocode 2, 2004; Kodur and Sultan, 2003; Lie and Kodur,
1996). Some of the notable studies are reviewed here:
Harmathy and Allen (1973) studied the effect of temperature on thermal properties of NSC
through thermogravimetry and dilatometry tests. In these tests the temperature of the specimen
was raised form room temperature to 1000°C at a rate of 5°C/min and thermal properties namely,
thermal conductivity, specific heat, thermal diffusivity, and mass loss were measured. It was
concluded by the authors that heat flow in concrete at elevated temperatures cannot be accurately
predicted unless latent heat effects associated with the process are properly considered. It was
found that variation in apparent specific heat due to elevated temperatures was difficult to obtain
and supplemental theoretical considerations were suggested. It was also concluded that the
spalling of concrete in fire is not caused by the presence of quartz in the aggregate, but it is due
to high moisture content in concrete.
Lie and Kodur (1996) measured high temperature thermal properties of steel fiber reinforced
concrete in 0-1000°C range. These thermal properties comprised of thermal conductivity,
specific heat, thermal expansion, and mass loss. They also proposed empirical relations for these
properties as a function of temperature. It was concluded by the authors that thermal properties
of steel fiber reinforced concrete are similar to conventional plain NSC. They proposed
mathematical relations that can be used as input data in analytical models for fire resistance
calculations of structural members.
Van Geem et al. (1997) experimentally investigated thermal properties of HSC at elevated
temperatures. The HSC used in this study ranged from 69-138 MPa with water to cement ratio
ranging from 0.26 to 0.32. Mineral admixtures such as silica fume and fly ash were also used in

21

the concrete mixes. They tested thermal conductivity, specific heat, thermal diffusivity and
drying rates at 30, 150, and 370°C. They used different test methods to evaluate the thermal
properties and found that these properties differed depending upon the test method used. Thermal
conductivity using hot plate method, hot wire method and graduated hot plate apparatus was
found to be similar and was within 1.7 to 2.6 W/m.K range. It was found that thermal
conductivity of HSC decreases with increasing temperature. The specific heat values of HSC
were also reported to be similar to those conventional NSC. Thermal diffusivity of HSC reduced
with increasing temperature and was found to decrease significantly at 540°C and was attributed
to increase rate of mass loss near this temperature. Mass loss of HSC was also found to be
similar to that of NSC at elevated temperatures.
Shin el al. (2002) experimentally studied the thermal behavior of indigenous Korean concrete
mixes (similar to US basaltic concrete) exposed to high temperature conditions. They tested
density, thermal conductivity, thermal diffusivity and specific heat in 20-1100°C temperature
range. It was found that most thermal properties except for specific heat decrease with increasing
temperature. The thermal properties of concrete were found to be strongly temperature
dependent. The density, thermal conductivity, and thermal diffusivity decrease with temperature,
and particularly the conductivity and the diffusivity which have a 50% decrease at 900°C as
compared to room temperature values. The specific heat was found to increase until 500°C,
decrease in 700 to 900°C temperature range, and then increase again above 900°C. It was also
concluded that the measurement beyond 1100°C is not accurate enough because the concrete
decomposes to a liquid phase from a solid phase at that temperature.
Kodur and Sultan (2003) also carried out tests to measure thermal conductivity, specific heat,
thermal expansion, and mass loss of plain HSC and steel fiber-reinforced HSC made of siliceous

22

and carbonate aggregate. Based on the measured property data, empirical relations were
proposed for thermal properties as a function of temperature in the temperature range of 0 and
1000°C. It was concluded in this study that the type of aggregate has a significant influence on
the thermal properties of HSC at elevated temperatures. The measured results showed that the
presence of carbonate aggregate in HSC increases fire resistance. The authors also concluded
that the thermal properties, at elevated temperatures, exhibited by steel fiber-reinforced HSC are
similar to those of plain HSC.
Hu et al. (1993) investigated the thermal properties of construction materials commonly
available in China. In this study mass loss was measured as a function of temperature up to
1000°C. It was found in this study that mass loss in carbonate aggregate concrete was only up to
97% for temperature up to 650°C, but mass loss was rapid in 650-900°C as it dropped to 75% in
this range. It was reported that mass loss in siliceous aggregate concrete was not high and it
dropped to only 97% at 1000°C.
Lie and Kodur (Lie and Kodur, 1996) investigated the mass loss of steel fiber reinforced
conventional NSC made of siliceous and carbonate aggregates at elevated temperatures. Mass
loss was measured using thermogravimetric analyzer in room temperature to 1000°C. It was
found in this study that mass loss in concrete was small up to 600°C where only 3% mass was
lost. However, mass was lost considerably up to about 30% of in 600-800°C in carbonate
aggregate concrete, which was attributed to dissociation of dolomite in carbonate aggregate.
However, in siliceous aggregate concrete on 3-4% of mass was lost in entire temperature range
of 20-1000°C. It was also found that mass loss of concrete is not significantly affected by
presence of steel fiber reinforcement in concrete in entire temperature range.

23

Kodur and Sultan (2003) measured the mass loss in plain and steel fiber reinforced HSC in
temperature range of 0-1000°C. Mass loss was measured using thermogravimetric analyzer
(TGA) up to 1000°C. The mass loss for both siliceous and carbonate concrete was very small
until about 600°C, where it was about 3% of the original mass. Between 600 and 700°C, the
mass of carbonate aggregate concrete dropped considerably with the temperature. Above 750°C,
the mass loss again decreased slowly with temperature. The substantial mass loss and decrease in
density for carbonate aggregate concrete was attributed to the dissociation of dolomite in the
concrete.
2.2.4

Effect of Temperature on Thermal Properties of Concrete

The review of previous studies presented above is utilized to draw inferences on effect of
temperature on thermal properties namely thermal conductivity, specific heat, thermal expansion
and mass loss of concrete. The presented data shows that there is significant variation on test
procedures, measurement techniques, range of measured temperatures and test results. Also it
helped identify the drawbacks in state-of-the-art and availability of these properties for HPC.
2.2.4.1 Thermal Conductivity
Figure 2.1 illustrates variation of thermal conductivity of NSC as a function of temperature based
on test data and empirical relations. The test data is compiled from different studies (Harada et
al., 1972; Harmathy, 1970; Harmathy and Allen, 1973; Kodur and Sultan, 2003; Lie and Kodur,
1996; Shin et al., 2002) and standards (ASCE, 1992; Eurocode 2, 2004). It can be seen that there
is large variation in available data in literature as shown by upper and lower bounds of the
plotted. These variations in reported data can be attributed to different measurement techniques,
test conditions, and environmental conditions adopted by various researchers (Bažant and
Kaplan, 1996; Harada et al., 1972; Kodur et al., 2008; Phan, 1996). It should be noted that there
24

are very few standardized methods available for measuring thermal properties. On average, the
thermal conductivity of conventional NSC, at room temperature, ranges between 1.4 and 3.6
W/m°C (Bažant and Kaplan, 1996). However, the thermal conductivity decreases graduallyS
with temperature and this decrease is dependent on the concrete mix properties, specifically
moisture content and permeability. It can be noted that as HPC are made of low w/c ratio and use
of different binders, therefore thermal conductivity of FAC, SCC, and FRC will be different
from that of NSC.
2.2.4.2 Specific Heat
Figure 2.2 illustrates the variation of specific heat for NSC with temperature as reported by test
data and different standards. The data is compiled based on experimental data (Harmathy, 1970;
Harmathy and Allen, 1973; Kodur and Sultan, 1998; Shin et al., 2002) and empirical relations
given in different standards (ASCE, 1992; Eurocode 2, 2004). The variation in data is depicted
by upper and lower bounds and this variation is mainly attributed to moisture content, type of
aggregate, test conditions and measurement techniques used in experiments (Harmathy and
Allen, 1973; Kodur and Sultan, 2003; Lie, 1992; Phan, 1996). The specific heat property is
sensitive to various physical and chemical transformations that take place in concrete at elevated
temperatures. This includes the vaporization of free water at about 100°C, the dissociation of
Ca(OH)2 into CaO and H2O between 400-500°C and the quartz transformation of some
aggregates above 600°C. Specific heat is therefore highly dependent to moisture content and
considerably increases with higher w/c ratio.

25

2.2.4.3 Thermal Expansion
Figure 2.3 illustrates the variation of thermal expansion in conventional concrete with
temperature (ASCE, 1992; Eurocode 2, 2004), where upper and lower bounds indicate the range
of values reported by different researchers. The thermal expansion increases from zero at room
temperature to about 1.3% at 700°C and then generally remains constant through 1000°C.
Thermal expansion of concrete is complicated by other contributing factors such as additional
volume changes caused by changes in moisture content, by chemical reactions (dehydration,
change of composition), and by creep and micro-cracks resulting from non-uniform thermal
stresses (Bazant and Kaplan 1996). In some cases thermal shrinkage can also result from loss of
water due to heating, along with thermal expansion, and this might lead to overall volume
change to be negative, i.e. shrinkage rather than expansion.
2.2.4.4 Mass Loss
Figure 2.4 illustrates the variation in mass of concrete as a function of temperature for concretes
made with carbonate and siliceous aggregates. It can be seen that there is significant difference
for mass loss in concretes made with two types of aggregates. In the case of siliceous aggregate
concrete, the mass loss remained insignificant even above 600°C. The mass loss for steel fiberreinforced HSC was found to be similar to plain HSC up to about 800°C. Above 800°C, in the
case of the carbonate aggregate mix, the mass loss in steel fiber-reinforced HSC was slightly
lower than that of plain HSC. Figure 2.5 shows variation in mass loss for conventional NSC and
HSC at elevated temperatures. It is evident that significant variation exists between the mass loss
of two types of concretes.
Mass loss of concrete at elevated temperatures is highly influenced with the type of aggregate
(Kodur and Sultan, 1998; Lie and Kodur, 1996). The mass loss is minimal for both carbonate and
26

siliceous aggregate concretes up to about 600°C. However, in beyond 600°C, carbonate
aggregate concrete experiences larger percentage of mass loss as compared to siliceous aggregate
concrete. This higher percentage of mass loss in carbonate aggregate concrete is attributed to
dissociation of dolomite in carbonate aggregate around 700°C (Kodur and Harmathy, 2008).
2.2.5

Summary

Thermal conductivity, specific heat, thermal expansion, and mass loss are important thermal
properties which are desired for predicting the temperature profiles as well as spalling in
concrete structures under fire exposure. As indicated by the review, there have been quite a few
studies on NSC that show the influence of thermal properties on fire resistance of structural
members. However, there is lack of data on these properties for new types of HPC (HSC, SCC
and FAC). In order to predict the temperature rise in concrete members as well as fire induced
forces, high temperature thermal properties specific to concrete type are to be determined which
is one of the main objectives of this research.

2.3 Mechanical Properties
2.3.1

General

The mechanical properties that are of primary interest in fire resistance design are compressive
strength, tensile strength, elastic modulus, and stress-strain response in compression. Mechanical
properties of concrete at elevated temperatures have been studied extensively in literature in
comparison to thermal properties. High temperature mechanical properties at small level are
generally carried out on concrete specimens that are typically cylinders or cubes of different
sizes. Unlike room temperature property measurements, where there are specified specimen sizes
as per standards, the high temperature mechanical properties are usually carried out on a wide

27

range of specimen sizes due to lack of test standards for high temperature testing. The cylinder
specimens of size 75x150, 100x200, and 150x300 mm whereas cube specimens of size 100x100,
150x150 and prism specimens of size 100x300 are usually used for high temperature.
The primary difference between HSC and NSC relates to the compressive strength that refers to
the maximum resistance of a concrete sample to applied pressure. Although there is no precise
point of separation between HSC and NSC, these days HSC is defined as concrete with a
compressive strength greater than 70 MPa (Kodur et al., 2008).
Compressive strength of concrete depends upon water-cement ratio, aggregated-paste interface
transition zone, curing conditions, aggregated type and size, admixture types and type of stress
(Mehta and Monteiro, 2006). The tensile strength of concrete is much lower than compressive
strength, due to ease with which cracks can propagate under tensile loads (Mindess et al., 2003).
It is normal practice to neglect the tensile strength of concrete in strength calculations at room
and elevated temperature. However, under fire conditions tensile strength of concrete can be
crucial in cases where fire induced spalling occurs in a HSC structural member. Also tensile
strength is an important property, because cracking in concrete is generally due to tensile stresses
and the structural damage of the member in tension is often generated by progression in
microcracking (Mindess et al., 2003).
Another property that influences fire resistance is the modulus of elasticity of concrete which
decreases with temperature. At high temperature disintegration of hydrated cement products and
breakage of bonds in microstructure of cement paste reduces elastic modulus and the extent of
reduction depends on moisture loss, high temperature creep and type of aggregate.
The high temperature compressive stress-strain behavior of concrete is of significant importance
in the fire resistance analysis of RC structural members. These high temperature stress-strain

28

curves are helpful to trace the structural response of RC structural members under fire
conditions. The high temperature stress-strain response of concrete is dependent on factors such
as aggregate-paste interface transition zone, curing conditions, aggregated type and size. The
aggregate type has a significant effect on the ultimate strain attained in HSC exposed to elevated
temperatures; carbonate aggregate HSC attains higher peak strains as compared to siliceous
aggregate HSC (Cheng et al., 2004).
2.3.2

Testing Methods for High Temperature Mechanical Properties

Three steady-state test methods (conditions) are utilized to determine high temperature strength
properties namely, stressed, unstressed and residual test methods (Fu et al., 2004; Phan, 1996).
Figure 2.6 illustrates the general arrangements for heating and loading to measure high
temperature mechanical properties. Figures 2.7, 2.8 and 2.9 graphically illustrate the main
difference in three test methods to evaluate the high temperature mechanical properties of
concrete. In the case of stressed test method, specimens are preloaded to a certain load usually
30-60% of room temperature ultimate compressive strength of concrete. Specimens are then
exposed to the desired temperature and further loaded to failure.
In unstressed test method, specimens are heated to target temperature without and preload. Once
equilibrium conditions are met, and the target temperature is reached, the specimens are
subjected to loading (leading to failure). In the case of residual test method, test specimen is
heated to a target temperature till reaching steady-state, and then allowed to cool down to room
temperature. Specimen is then loaded to failure at ambient temperature to obtain the residual
strength of concrete. Residual strength, representative of post fire exposure behavior of concrete,
is less applicable for predicting high temperature mechanical properties of concrete.

29

2.3.3

Previous Studies

There have been significant test programs for characterizing high temperature mechanical
properties of concrete. In the high temperature property tests, the response is measured while
specimens are hot at a target temperature. Such high temperature tests (both stressed and
unstressed) were carried out by limited researchers to measure the mechanical response (Castillo
and Durrani, 1990; Khoury, 1992 ; Khoury, 2008; Khoury et al., 1985; Lie, 1992; Lie and Kodur,
1996). However, research on high temperature properties was mostly done through residual
property tests after exposure to high temperatures (Chen and Liu, 2004; Felicetti and
Gambarova, 1998; Felicetti et al., 1996; Fu et al., 2005; Fu et al., 2004; Li et al., 2004; Li and
Guo, 1993; Xiao and König, 2004). Some of the notable studies on high temperature mechanical
properties are presented in the following section.
2.3.3.1 Compressive Strength
Compressive strength of concrete is influenced by water-cement ratio, aggregate-paste interface
transition zone, curing conditions, aggregate type and size, admixture types and type of stress
(Mehta and Monteiro, 2006). Good amount of data is available on compressive strength of
concrete at elevated temperatures for both NSC and HSC (Castillo and Durrani, 1990; Fu et al.,
2005; Poon et al., 2001; Tang and Lo, 2009; Xu et al., 2001). Few of the notable studies
presented here generate information on high temperature compressive strength of concrete.
Carette et al. (1982) did an important study on use of pozzolans in NSC at elevated temperatures.
They reported that addition of fly ash and slag in NSC did not improve the residual compressive
strength of concrete after exposure to high temperatures. Even change in water-cement ratio of
NSC with these pozzolans did not show any effect on high temperature mechanical properties
behavior of concrete.
30

Lie and Kodur (1996) investigated high temperature strength properties of NSC with and without
steel fibers. They reported that compressive strength steel fiber reinforced concrete degrades at a
much higher rate with temperature than similar concrete without steel fibers. They also
concluded that effect of aggregate type on the compressive strength is not significant.
Chan et al. (1999) investigated the residual compressive strength of both NSC and HSC after
exposure to high temperatures. He identified three distinct temperature ranges having an effect
on loss of compressive strength of concrete namely, 20-400°C, 400-800°C, and 800-1200°C. He
reported that only small part of strength was lost in 20-400°C (1-10% for HSC and 15% for
NSC), however severe loss occurred in 400-800°C range. This severe loss in 400-800°C range
was attributed to deterioration of calcium silicate hydrate (C-S-H) gel and cementing ability due
to dehydration in concrete. They suggested the temperature range of 400-800°C be regarded as
critical strength-loss range for concrete. Above 800°C the residual strength was reported as only
a small part of original strength.
Li et al. (2004) experimentally studied the residual mechanical properties of NSC and HSC at
elevated temperatures. They investigated the influence of temperature, water content, specimen
size, strength grade and temperature profiles on mechanical properties. Authors reported that the
compressive strength of HSC drops with temperature after 200°C. The strength loss in HSC was
higher (36.8%) in 20-400°C as compared to NSC (28.8%), and this higher loss was attributed to
dense microstructure and impermeability of HSC. It was also reported that water content had
minimum effect on high temperature strength loss of concrete. As for specimen size, it was
concluded that compressive strength loss of larger concrete specimens was lower than that in
smaller size specimens.

31

Noumowé (2005) investigated the behavior of high temperature mechanical properties of plain
HSC and polypropylene fiber reinforced HSC up to 200°C. He reported that the HSC containing
polypropylene fibers has higher compressive strength loss as compared to plain HSC.
Sideris (2007) investigated the compressive strength characteristics of SCC exposed to elevated
temperatures up to 700°C. For comparison, he also tested and compared the results with
conventional concretes. Residual strength properties were tested after exposure to 100, 200, 500,
and 700°C. He reported that the residual strength loss trend of both SCC and conventional
concretes was similar in 20-700°C. Both SCC and HSC suffered explosive spalling at
temperatures beyond 380°C.
Kim et al. (2009) recently investigated the compressive strength characteristics of HSC exposed
to elevated temperatures up to 700°C through stressed test method. During heating, the
specimens were subjected to a pre-load of 25% of the ultimate compressive strength at room
temperature, and then loaded to failure at target temperature. It was concluded by the researchers
that with increase in strength of concrete, the loss of strength due to high temperature exposure
also increase. It was also concluded from this research that HSC loses minimum strength in 100400°C temperature but the rate of strength loss is significant beyond 400°C.
The review of compressive strength properties above shows that good amount of research has
taken place for high temperature behavior of both NSC and HSC. However, it can be observed
that the strength trends for both NSC and HSC are not consistent and there are significant
variations in strength loss, as reported by various authors. Moreover, there is very limited data in
literature on high temperature strength properties of new types of concrete such as SCC, FAC
and fiber reinforced HPC. Therefore data on strength properties of new types of concretes as a

32

function of temperature is needed for evaluating fire response of structural members made of
HPC.
2.3.3.2 Tensile Strength
Tensile strength of concrete at ambient temperatures can be evaluated through three methods
namely, flexural tensile, direct tension, and splitting tensile strength tests. Flexure tensile
strength is obtained through subjecting a concrete beam to third-point flexural loading (ASTM
C78, 2009). The direct tensile strength is measured by testing cylinder or prism specimens by
applying axial tensile load in a suitable test machine until specimen breaks in direct tension
(ASTM C1583, 2004). Direct tension test is less reliable as the specimen holding devices (grips)
introduce secondary stresses leading to unreliable strength data. In splitting tensile test a
compressive load is applied on the generatrices of the specimen which are diametrically opposite
(ASTM C496, 2004). The load is increased until failure occurs by splitting of the specimen along
the vertical diameter. At ambient temperature, splitting tensile strength is usually 50-70% greater
than direct tension strength, where as it is 40-50% lower than flexure tensile strength (Popovics,
1998).
Tensile strength of concrete is dependent on compressive strength of concrete, water/cement
ratio, aggregate-paste interface transition zone, presence of any flaws, and microstructure of
concrete (Neville, 2004). A review of the literature indicates that there have been limited studies
on high temperature tensile strength of concrete. It is also worth noting that all previous studies
on high temperature tensile strength of concrete are based on residual strength tests that are
applicable for concrete members cooled after fire exposure. This residual tensile strength
property cannot represent the tensile strength behavior of hot concrete (during fire exposure)

33

which is required for predicting spalling. Some of the notable studies presented here generate
information on high temperature tensile strength behavior of concrete.
Carette et al. (1982) investigated the temperature effect on the tensile strength of NSC. He tested
concrete cylinders in 75-600°C temperature range through residual strength technique. He
reported 65-70% reduction in splitting tensile strength at 600°C. He concluded that water cement
ratio and type of aggregate has significant influence on the splitting tensile strength of NSC.
Felicetti et al. (1996) investigated the residual tensile strength of two types of HSC from room
temperature to 600°C by testing through direct tension method. They noticed reduction in tensile
strength to zero at about 600°C. It was also observed in this study that concrete softens at high
temperature and that temperature has a marked effect on its tensile strength.
Recently, Bahnood and Ghandehari (2009) reported residual splitting tensile strength of plain
and polypropylene fiber reinforced HSC up to 600°C. The authors inferred that the decrease in
splitting tensile strength is due to decomposition of hydrated cement products and thermal
incompatibility between aggregates and cement paste. They also observed that there was no
noticeable difference in the splitting tensile strength of polypropylene fiber reinforced HSC up to
600°C in comparison to plain HSC.
Li et al. (2004) conducted tests for residual splitting tensile strength of HSC in 200-1000°C
temperature range. HSC batch mix contained 27 per cent fly ash as cement replacement. 100 mm
concrete cubes were used to measure splitting tensile for HSC at 200, 400, 800 and 1000°C
temperatures. A retained splitting tensile strength of 51.9% at 800°C and 16.9% at 1000°C was
reported which is significant at these temperatures. Appearance and propagation of cracks was
observed to be more obvious in tensile strength as compared to compressive strength tests.

34

Reduction in splitting tensile strength with temperature was attributed to thermal stresses induced
in dense microstructure of HSC that resulted in micro and macro cracks.
Chen and Liu (2004) experimentally studied the residual splitting tensile strength of HSC and
hybrid fiber reinforced concrete at various temperatures in 20-800°C ranges. The authors found
that higher residual splitting tensile strength was obtained by hybrid fiber reinforced HSC. Steel
fibers in concrete were observed to provide restriction against initiation and expansion of
cracking, while polypropylene fibers provided micro-channels resulting in reduction of thermal
stresses.
Anagnostopoulos et al. (2009) investigated the residual splitting tensile strength properties of
SCC with different fillers at 20, 300, and 600°C temperatures respectively. Sharp loss in tensile
strength was observed and was attributed to micro and macro cracks produced in specimens due
to thermal incompatibility. SCC with limestone filler was reported to have displayed better
performance at high temperature by preserving splitting tensile strength. In this study, explosive
spalling was also reported in high strength SCC at 600°C temperature.
Eurocode (2004) fire provisions recommend accounting for tensile strength properties of
concrete in fire resistance calculations. It treats both NSC and HSC alike for temperature
dependent tensile strength of concrete by provision of a simple relationship for representation of
tensile strength of concrete with temperature. On the other hand ACI 216.1 (2007) does not
provide any guideline or relationship for tensile strength of concretes.
2.3.3.3 Elastic Modulus
Another property that influences fire response of concrete structures is the elastic modulus of
concrete which decreases with temperature. Elastic modulus of concrete degrades with

35

temperature and thus influences the fire resistance of structural members. At high temperature,
disintegration of hydrated cement products and breakage of bonds in microstructure of cement
paste reduces the elastic modulus and the extent of reduction depends on moisture loss, high
temperature creep and type of aggregate (Bažant and Kaplan, 1996).
Some of the prominent studies undertaken on high temperature elastic modulus are discussed
below:
Castillo and Durrani (1990) experimentally studied the effect of temperature on elastic modulus
of both NSC and HSC in 20-800°C temperature range. Modulus was measured using closed-loop
servo-controlled hydraulic testing machine integrated with an electric furnace. The authors
reported that both NSC and HSC have similar loss of modulus under elevated temperature. Slight
loss was recorded up to 400°C and faster loss was observed between 400-600°C. The higher loss
above 400°C was attributed to progressive dehydration and loss of bond between materials.
Bamonte and Gambarova (2010) tested HSC and SCC cylinders up to 90 MPa for elastic
modulus at 20, 200, 400, and 600°C. They reported that the elastic modulus is much lower in hot
state than residual which was attributed to thermal affects. It was also concluded that there is no
difference in the elastic modulus of HSC and SCC.
Perrson (2004) did extensive experimental investigation on the elastic modulus of SCC at
elevated temperatures and as residual property. Tested temperatures consisted of 20, 200, 400,
600 and 800°C. He observed a lower elastic modulus for SCC, as compared to HSC, throughout
the temperature range in both hot state and as residual property.
2.3.3.4 Stress-Strain Curves
Limited information is available on the compressive stress-strain curves of HSC exposed to
elevated temperatures. The main reason for limited data is the complexity involved to generate
36

high temperature stress-strain curves through stressed or unstressed test methods. However,
researchers have carried out investigation on stress-strain curves of concrete under all three test
conditions (stressed, unstressed and residual) to study the effect of elevated temperatures on
stress-strain behavior. Some of the previous studies are discussed here to generate information on
high temperature stress-strain response of concrete:
Castillo and Durrani (1990) studied the effect of transient high temperature on stress-strain
response of HSC and NSC under both stressed and unstressed test conditions in 23-800°C range.
It was found in this study that effect of temperature on stress-strain curves is same for HSC and
NSC in entire temperature range. For both NSC and HSC the strain at peak stress did not
significantly vary in 100-200°C range. There was a slight increase in strain at peak stress in 300400°C range. However, there was a significant increase in strain at peak stress in 500-800°C
range. At 800°C the recorded strain was measured to be four times to the strain at room
temperature.
Furumura et al. (1995) tested cylinders to generate stress-strain curves for NSC and HSC, during
heating and after heating. The test data indicated that the stress-strain curves for HSC are quite
different from NSC. For HSC stress-strain curves showed brittle response below 500°C.
However the stress-strain curves above 500°C showed more ductile response, and it was
attributed to internal microcracks developed due to thermal stresses caused by contraction of
cement paste, expansion of aggregates and thermal gradients. For both NSC and HSC the strains
at maximum strength during heating and after heating increased rapidly with increasing
temperature above 300-400°C temperature. It was concluded in this study that concrete strength
has only a little effect on the strain at maximum strength.

37

Felicetti et al. (Felicetti et al., 1996) studied residual mechanical properties, including stressstrain curves, for HSC after heating to 105, 250, 400 and 500°C temperatures. It was shown by
stress-strain curves that there was significant decrease in the peak stress after exposure to high
temperature. The peak stress decreased by 2.5% at 105°C, 25% at 250°C, 75% at 400°C, and
94% at 500°C. Above 500°C, residual strength was so small (10%) that HSC was considered to
be unsuitable for bearing any loads.
2.3.4

Effect of Temperature on Mechanical Properties of Concrete

The review of previous studies presented above is utilized to draw inferences on effect of
temperature on mechanical properties. The presented data shows that there is significant
variation in reported mechanical properties which is attributed to test procedures and test
techniques. Presented state-of-the-art also indicated that there is lack of high temperature
propertied data on HPC.
2.3.4.1 Compressive Strength
Figure 2.10 and 2.11 illustrate the variation of compressive strength ratio of NSC and HSC
concrete at elevated temperatures respectively with upper and lower bounds showing limit of
variation in reported data.
In the case of NSC, the compressive strength of concrete is marginally affected by elevated
temperatures up to 400°C. NSC is usually highly permeable and allows easy diffusion of pore
pressure as a result of water vapors. This shows that NSC is most suited for concrete
infrastructure exposed to fire hazards. On the other hand, use of different binders in HPC
produce a superior and dense microstructure with less amount of calcium hydroxide which
ensures a beneficial effect on compressive strength. Binders such as use of slag and silica fume
gives best results to improve compressive strength which is attributed to dense microstructure.
38

However, as mentioned earlier, the compact microstructure is highly impermeable and under
high temperature becomes detrimental as it does not allow moisture to escape resulting in
buildup of pore pressure and rapid development of microcracks in HSC leading to its
deterioration and spalling.
2.3.4.2 Tensile Strength
Figure 2.12 illustrates the variation of splitting tensile strength ratio of NSC and HSC as a
function of temperature as reported in previous studies and recommended by Eurocode standard
(Behnood and Ghandehari, 2009; Carette et al., 1982; Eurocode 2, 2004; Felicetti et al., 1996).
The ratio of tensile strength at given temperature, to that at room temperature is plotted. The
upper and lower bounds shown in Figure 2.12 shows range of variation in splitting tensile
strength obtained by various researchers for NSC with conventional aggregates. The decrease in
tensile strength of NSC with temperature can be attributed to weak microstructure of NSC
allowing initial microcracks. At 300°C concrete loses about 20% of its initial tensile strength.
Above 300°C temperature, the tensile strength in NSC drops at a faster rate. This is due to more
pronounced thermal damage in the form of microcracks.
2.3.4.3 Elastic Modulus
Figure 2.13 illustrates variation of ratio of elastic modulus at target temperature (ET) to that at
room temperature (E0) for HSC (Castillo and Durrani, 1990; Phan, 1996). It can be seen from the
figure that the trend of loss of elastic modulus of both concretes with temperature is similar, but
there is significant variation in the reported data. Figure 2.13 also illustrates the ratio of elastic
modulus for SCC as reported in two studies (Bamonte and Gambarova, 2010; Persson, 2004). It
can be observed that loss of elastic modulus in SCC is similar to HSC. This lower modulus in
39

both HSC and SCC can be attributed to the excessive thermal stresses and physical and chemical
changes in concrete microstructure.
2.3.4.4 Stress-Strain Curves
Figure 2.14 and 2.15 illustrate the load-deformation response of NSC and HSC respectively
(Castillo and Durrani, 1990). In general, it is established that HSC has steeper and more linear
stress-strain curves in comparison to NSC in 20-800°C. High temperature has significant effect
on the stress-strain response of both NSC and HSC, as with the rise in temperature, the strain at
peak stress starts to increase, especially above 500°C this increase is significant and the strain at
peak stress can reach four times to strain at room temperature. HSC specimens exhibit brittle
response as indicated by post peak behavior of stress-strain curves shown in Figure 2.15.
2.3.5

Summary

Compressive strength, tensile strength, elastic modulus and stress-strain curves are central
mechanical properties that are required for predicting fire performance of RC structural
members. The above review illustrates that good amount of data exists for high temperature
mechanical properties for NSC and also limited data exists on HSC. But this data is not available
for HPC such as FAC and SCC with and without fibers. This data is desirable especially for high
temperature tensile strength, elastic modulus and stress-strain curves for these HPC. Thus one of
the major objectives of this research is to evaluate high temperature mechanical properties for
these new types of concrete. The generated test data can be used to develop mathematical
relations for various properties as a function of temperature.

2.4 Deformation Properties

40

2.4.1

General

Deformation properties of concrete include creep and transient strains and are mainly influenced
by strength, aggregate type, sustained stress and chemical and physical reactions that take place
in concrete under fire conditions (Schneider, 1988). Creep is defined as the time-dependent
plastic strain under constant stress and temperature. At room temperature sustained external
stress becomes the driving force for the movement of the physically absorbed water and water
held in small capillaries (Mehta and Monteiro, 2006). Due to limited moisture movement in
concrete at room temperature, creep deformations are slow to occur. However, at elevated
temperatures, moisture movement is usually significant in concrete that leads to higher creep
strains. High temperature creep strains are thus largely influenced by concrete temperature
(Dwaikat, 2009). Because high temperature creep affects strains, deflections, and stress
redistribution at elevated temperatures, it plays an important role on the fire resistance of
structural members.
Transient strain on the other hand occurs during the first time heating of concrete, but it does not
occur upon repeated heating (Khoury et al., 1985). Transient strain is independent of time and is
essentially caused by the thermal incompatibilities between the aggregate and the cement paste
(Purkiss, 2007). Exposure of concrete to high temperature induces complex changes in the
moisture content and chemical composition of the cement paste. Moreover there exists a
mismatch in thermal expansion between the cement paste and the aggregate. Therefore factors
such as changes in chemical composition of concrete and mismatches in thermal expansion lead
to internal stresses and micro-cracking in the concrete constituents (aggregate and cement paste)
and results in transient strain in the concrete (Schneider, 1988).

41

2.4.2

Previous Studies

Literature review shows that there is very limited information on creep and transient strain of
concrete at elevated temperature (Kodur et al., 2008). Anderberg and Thelandersson (1976)
carried out tests to evaluate transient and creep strains under elevated temperatures. Figure 2.16
shows influence of initial moisture content on deformations under transient conditions. They
found that pre-dried specimens at 45 and 67.5% of load level were less liable to deformation in
‘positive direction’ (expansion) under load. At 22.5% pre-load, specimen displayed no
significant difference for strains. They also found that the influence of water saturation was not
very significant except for free thermal expansion (0% preload), which was found to be smaller
for water saturated specimens.
Khoury (1985) studied creep strain of initially moist concretes at four load levels measured
during first heating at 1°C/min as shown in Figure 2.17. An important feature of these results
was that considerable contraction under load was observed as compared to free (unloaded)
thermal strains. This contraction is referred to as the 'load-induced thermal strain' and the actual
thermal strain is considered to consist of total thermal strain minus the load-induced thermal
strain.
Schneider (1988) also investigated the effect of transient and creep restraint on deformation of
concrete. He concluded that the transient test for measuring total deformation or restraint of
concrete have the strongest relation to building fires and are supposed to give most realistic data
with direct relevance to fire. The important conclusions from the study were (1) w/c ratio and
original strength are of little importance on creep deformations under transient conditions. (2)
Aggregate cement ratio has a great influence on the strains and critical temperatures, the harder
the aggregate the lower the thermal expansion therefore total deformation in transient state will

42

be lower. (3) Curing conditions are of great importance in 20-300°C range. Air cured and ovendried specimens have lower transient and creep strains than water cured specimens.
Anderberg and Thelandersson (1976) developed constitutive models for creep and transient
strain in concrete at elevated temperatures. These equations for creep and transient strain at
elevated temperatures as suggested by Anderberg and Thelandersson are:

ε

ε

cr

tr

= β

=k

σ
1 f

)

(2.1)

t e

c, T

σ
2 f

(

d T − 293

ε

(2.2)

th

c, 20

where: εcr = creep strain, εtr = transient strain,

-6 -0.5

β1 = 6.28×10 s

, d = 2.658×10

-3

-1

K ,T=

concrete temperature (°K) at time t (s), fc,T = concrete strength at temperature T, and σ = stress in
the concrete at the current temperature, k2 = a constant ranges between 1.8 and 2.35, εth =
thermal strain, and fc,20 = concrete strength at room temperature.
2.4.3

Effect of Temperature on Deformation Properties

Time dependent deformations in concrete such as creep, get highly enhanced at elevated
temperatures under compressive strains (Bažant and Kaplan, 1996). Creep in concrete under high
temperatures increases due to moisture movement out of concrete matrix. This phenomenon is
further intensified by moisture dispersion and loss of bond in cement gel (C-S-H). Therefore the
process of creep is caused and accelerated mainly by two processes, (1) moisture movement and
dehydration of concrete due to high temperatures and (2) acceleration of the process of bond
breaking.
43

2.4.4

Summary

High temperature creep and transient strain of concrete are complex phenomenon and are
influenced by factors such as temperature, strength, moisture content, loading, and mix
proportions. The creep deformation generally increases with temperature, with low-modulus
aggregates (Schneider, 1988) and also with increasing load levels at elevated temperatures.
Transient strain is independent of time and does not recur as it is encountered only in first
heating of concrete.

2.5 Fire Induced Spalling
Spalling occurs when concrete member is exposed to rapidly rising temperatures as encountered
in a fire and is one of the major concerns with HSC. Low permeability and dense microstructure
in HSC prevent easy dissipation of pore pressure that is generated due to moisture converting to
vapors under elevated temperatures leading to buildup of high pore pressure. When this pore
pressure exceeds the tensile strength of concrete, which also degrades temperature, spalling
occurs. Previous studies have shown that spalling in HSC is affected by concrete strength,
permeability, concrete density, moisture content, fire intensity, presence of fibers and specimen
dimensions (Ali, 2002; Kodur and McGrath, 2003; Kodur and Sultan, 1998; Phan, 1996).
2.5.1

Causes of Spalling

A review of literature presents a conflicting data on the probability of occurrence of fire induced
spalling and also on the exact mechanism for spalling. While some investigators reported
explosive spalling in concrete structural members under fire conditions, few others reported little
or no significant spalling at all. One explanation to this conflicting trend of observations is
possibly the large number of factors and their inter-dependency that influence the fire induced

44

spalling in concrete. However, it has been established and agreed upon by most researchers that
the major causes for fire induced spalling in concrete are low permeability of concrete and high
moisture migration at elevated temperatures.
There are two general theories on which the spalling phenomenon can be explained (Kodur,
2003):
2.5.1.1 Pore pressure build-up
High strength concrete has low permeability as compared to NSC (Mindess et al., 2003) and
therefore this low permeability is believed to be more detrimental in pore pressure built-up. The
extremely high vapor pressure, generated during moisture converting to vapor under fire
exposure, cannot escape due to the low permeability of HSC. This build-up of pore pressure is
believed to be the major cause of spalling during heating. As the pore pressure builds up with
temperature, tensile strength of concrete offers resistance against pore pressure which is
degrading with temperature as shown in Figure 2.18. When the pore pressure exceeds the tensile
strength of concrete, pieces/fragments of concrete break away from the structural member
(Figure 2.18) and thus spalling occurs. This breaking off can often is explosive depending on the
fire and concrete characteristics (Harmathy, 1993).
2.5.1.2 Brittle Fracture
Bažant (1997) presented a different hypotheses for fire induced spalling. According to him, high
pore pressure develops at a certain distance inside heated surface of concrete and creates a crack
as shown in Figure 2.19. However, as the crack starts to open up, the water vapor and liquid flow
into the crack and increase in volume. Once no additional water is available to fill into the crack
from surrounding concrete, the pore pressure drops while crack starts to open up and spalling

45

occurs. This shows that pore pressure plays a secondary role to trigger a crack but does not cause
the explosion or cause the crack to open widely. Therefore, the spalling is assumed to be caused
by another source of energy, which is basically present in the form of potential energy from
thermal stresses. This hypothesis is consistent with high magnitude of pore pressure and spalling
in wet concretes, and less spalling observation in pre-dried concrete specimens.
2.5.2

Previous Studies

A number of experimental studies have been performed to investigate fire induced spalling in
high strength concrete specimens which include both large scale structural members and small
scale laboratory specimens such as cubes and cylinders. Kalifa (2001), Hertz (2003), and Phan
(2007) have conducted some noteworthy studies on small scale specimens. Kodur (2003), Kodur
and McGrath (2003), and Bilodeau et al. (2004) have conducted studies on large scale
specimens. It has been well established through all these experimental studies that HSC is more
susceptible to fire induced spalling compared to NSC.
Kalifa et al. (2001) investigated 120-mm thick RC slabs by exposing them to rapid heating from
one side (underneath) to study fire induced spalling in HSC concrete. Two types of HSC mix
with and without polypropylene fibers were considered. A heating rate of 5°C/sec was used for
the first two minutes and then the temperature was kept at 600°C. Within the depth of slab, pore
pressure and temperatures were measured at different locations. It was concluded from the study
that polypropylene fibers significantly facilitate the increase in permeability of HSC and thus
decrease the pore pressure at elevated temperature. As a results fire induced spalling is mitigated
due to lower pore pressure in concrete.
Hertz (2003) conducted tests on concrete prisms to investigate the influence of thermal stresses
on fire induced spalling in dense concrete. Ten 600x600x20 mm prisms of dense concrete were
46

heated at a limited area of 200x200 mm at the center of one side of each specimen. These
specimens were exposed to constant high temperature from a hole in an oven. He concluded that
susceptibility of concrete to spall is less if it does not have pozzolans like silica fume and that if
moisture content is below 3%. He also concluded that spalling mostly occurs at about 374°C
which is the critical temperature of water when water becomes vapor. He also found that
polypropylene fibers were effective in mitigating spalling in less permeable concrete.
Kodur (2003) investigated the fire resistance RC columns by conducting full-scale fire tests. The
parameters that were investigated in this study were concrete strength, column dimensions, type
of aggregate, tie configuration, use of fibers and their type, and load intensity. The columns were
of 3810 mm long and were of square cross-section 305x305 mm. The compressive strength of
NSC was 34 MPa and that of HSC was 110 MPa. It was concluded that HSC columns have
lower fire endurance and are susceptible to spalling as compared to NSC columns. This study
(Kodur, 2003) also showed that type of aggregate, concrete strength, concrete density, load
intensity, fire intensity and tie configuration have an influence on the fire performance (both
spalling and fire endurance) of HSC columns.
In another study, Kodur and McGrath (2003) experimentally investigated the fire endurance of
HSC by testing six columns designated as HSC1 to HSC6. The main factors varied in the test
included cross-sectional size, quantity of longitudinal reinforcement, tie configuration, and
aggregate type. This study also established that HSC was more prone to fire induced spalling
than NSC. It was also concluded that carbonate aggregate concrete experiences less fire induced
spalling than siliceous aggregate HSC. HSC columns exhibited better fire endurance by closer tie
spacing and better detailing. Once ties were bent 135° back into the core of the column and

47

amount of lateral reinforcement was increased, it also reduced the potential for fire induced
spalling in HSC columns.
From these experimental studies it is clear that spalling of concrete is a very complex
phenomenon that depends on many factors, namely strength, moisture content, density, heating
rate, and specimen size. Strength of concrete is one of the primary causes as HSC is more
susceptible to spalling, similarly higher moisture content in concrete also increases the potential
of spalling. Concrete density is another factor that influences spalling as lightweight aggregate
concrete is more susceptible to spalling. Heating rate also effects the fire induced spalling as
higher heating rate increases the occurrence of fire induced spalling in concrete. An increase in
specimen size also increases the risk of explosive. Type of aggregate can reduce the occurrence
of spalling e.g. use of carbonate aggregate concrete is effective in minimizing the fire induced
spalling in concrete than siliceous aggregate.
2.5.3

Spalling Mitigation

To minimize the occurrence of fire induced spalling in HSC, researchers have recommended
addition of polypropylene fibers to concrete (Ali et al., 2004; Behnood and Ghandehari, 2009;
Bilodeau et al., 2004; Kodur, 2000). Polypropylene fibers melt at relatively low temperatures
(about 167-170°C) and create randomly oriented micro and macro channels inside concrete.
These channels facilitate dispersion of high vapor pressure. Another approach to overcome the
spalling is through enhancing tensile strength of concrete by addition of steel fibers (Kodur,
1999; Rossi, 1994). Ali and Nadjai (2008) recently carried out investigation on spalling
mitigation through use of hybrid fibers (mix of polypropylene and steel fibers) in the concrete
and found it very useful in minimizing the fire induced spalling in HSC columns.

48

Alongside use of fibers, bending of ties in columns similar to that in seismic region have been
found to be useful and attractive to reduce the fire induced spalling and to enhance the fire
resistance of columns (Kodur and McGrath 2003). In this technique, it was experimentally
established that bending the ties at 135° as compared to conventional 90° bent ties, spalling can
be minimized. These two tie configurations are shown in Figure 2.20. When ties are bent at 135°
in to the core of concrete column, these provide additional confinement to concrete thus keeping
the section intact in case of exposure to fire.
2.5.4

Summary

The moisture transformation and mass transport in concrete have a unique influence on its
temperature profile and development of pore pressure. HPC due to impermeability and low
porosity can experience significant pore pressure build-up and thus are more susceptible to fire
induced spalling. Spalling in HPC is therefore a major concern that has to be overcome to
enhance the fire resistance of structural members made of these concretes.

2.6 Fire Performance of Reinforced Concrete Columns
Concrete has generally good performance and it is well established that up to 6 hours of fire
resistance rating can easily be obtained by provision of conventional NSC columns (Ali et al.,
2004; Kodur, 2003; Lie and Woolerton, 1988). HSC due to high compressive strength are
preferred in columns of high rise buildings. However, columns made of HSC have lower fire
resistance due to deterioration of material properties and occurrence of fire induced spalling.
There are a number of studies on high temperature performance of RC columns that are available
in literature, only limited review on effect of tie configuration on fire response of RC columns is
presented in this section.

49

2.6.1

Experimental Studies

A detailed review has recently been done by Kodur and Raut (2010) and Raut (2011) on fire
performance of RC columns. In the state-of-the-art, experimental and analytical studies related to
fire performance of RC columns is elaborated along with a review of fire resistance provisions in
various codes and standards. It is evident from the review that there is lack of data on fire
performance of RC columns made of new types of HPC. There are absolutely no studies on HPC
columns made of FAC and SCC.
Since fire resistance of HSC columns is seriously hampered by fire induced spalling, fibers are
often added to the mix to mitigate spalling. The fire performance of HSC columns with steel and
with polypropylene fibers have been experimentally well studied before (Ali, 2002; Ali et al.,
2004; Kodur, 2003). However, there is only one study done by Ali and Nadjai (2008) in which
effect of hybrid fibers is investigated on fire response of HSC columns.
Alongside use of fibers, bending of ties in columns similar to that in seismic region have been
found to be useful and attractive to reduce the fire induced spalling and to enhance the fire
resistance of columns (Kodur and McGrath 2003). However, there is no fundamental
understanding as to how the tie configuration helps improve the fire resistance. Further, the
numerical models do not account for effect of tie configuration in fire resistance predictions of
columns which is an important factor.
It can be inferred from the review that, the fire resistance of columns changes with type of
concrete, mix design, use of different combination of fibers and tie configuration. Although, the
tests have generated valuable data for understanding the behavior and for validation of computer
models, the types of concrete investigated are only NSC and HSC.

50

2.6.2

Numerical Studies

A fair number of analytical studies have also been conducted to study the fire behavior of RC
columns. The main objective in many of these studies is to trace the response and fire resistance
of RC columns under fire conditions. Few of these studies were done on HSC columns and
important factors such as high temperature material properties of specific concrete type, spalling,
addition fibers and tie configuration were not fully incorporated in the analysis. A detailed
review of studies for numerical modeling of fire response of columns is also done by Kodur and
Raut (2010) and Raut (2011).
Review of numerical studies illustrates that numerical models used to predict the fire response of
RC structural members simplify the calculations by making some ideal assumptions. These
models do not incorporate the factors that are critical for accurate fire resistance calculations.
Factors such as high temperature properties of new types of HPC, effect of different fibers and
tie configuration have not been considered and need to be included in numerical models for
realistic fire resistance predictions.

2.7 Codes and Standards
The specifications for fire resistant design are included in building codes and national standards
of various countries. These provisions are usually prescriptive in nature, as the codes and
standards provide tabulated values of fire resistance which are based on standard fire tests. These
tabulated fire resistance values are mostly dependent on concrete cover thickness and minimum
dimensions of structural members.
In the USA, concrete structures are designed in accordance with the American Concrete Institute
(ACI-318) (2008) standard. While ACI-318 does not contain any fire provisions, it refers to ACI
216.1 (2007) standard which gives prescriptive based specifications for fire design of concrete
51

and masonry structures. ACI 216.1 standard specifies concrete cover thickness and minimum
sectional dimensions required for achieving a desired fire resistance rating in RC columns.
Similarly, Eurocode 2, Part 1–2 (2004) gives simplified approach for determining fire resistance
of RC columns based on tables and advanced methods. For example, to reduce fire induced
spalling; Eurocode suggests a reinforcement mesh with a nominal cover of 15 mm to HSC
columns.
It can be seen that these provisions provide prescriptive approaches based on experimental
studies. Tables, which are based on this approach, provide the faster and most direct method for
determining the minimum dimensions and cover thickness in RC columns. The simplified
equations may give more economical fire resistant designs, especially for small columns and/or
high fire resistance periods. However, the important factors such as HPC, use of different
combination of fibers and effect of tie configuration are not comprehensively taken into account
by these standards.

2.8 Summary
Based on information presented in this chapter, it is evident that high temperature material
properties are crucial for modeling the fire response of RC members. Good amount of data exists
on high temperature thermal, mechanical and strength properties including elastic modulus of
NSC and to some extent for HSC as well. However, there very limited property data on HPC
(HSC, SCC, FAC) is available at elevated temperatures. It is also established that mostly the fire
resistance tests were conducted on RC columns made of NSC and HSC, but these tests are not
existent for HPC columns such as FAC and SCC. Moreover, limited data is available on effect of
hybrid fibers on spalling mitigation in HPC columns. Further, the guidelines put forward by
experimental studies have not been fully incorporated in numerical models. Important factors
52

such as high temperature material properties of HPC, use of hybrid fibers, and effect of tie
configuration are not fully incorporated in numerical models.

53

3
Thermal conductivity (W/m-°
C)

Eurocode (lower)
Eurocode (upper)

2.5

Test – upper bound

ASCE (carbonate)

2
1.5
1

Test – lower bound

0.5
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 2.1 - Variation in thermal conductivity of NSC as a function of temperature
20
ASCE Manual
Specific heat (MJ/m3-°
C)

Eurocode 2
16

Kodur and Sultan

Test – upper bound

12

8

Test – lower bound
4

0
0

200

400
600
Temperature (°
C)

800

Figure 2.2 - Variation in specific heat of NSC as a function of temperature
54

1000

ASCE model

Thermal expansion (%)

1.6

Test – upper bound (siliceous)

Eurocode carbonate
Eurocode siliceous

1.2

Test – upper bound
(carbonate)

0.8

Test – lower
bound (siliceous)

0.4

Test – lower bound (carbonate)
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 2.3 - Variation in linear thermal expansion of NSC as a function of temperature

Mass (% of original)

100

Hu et al. - Carbonate
Hu et al. - Silieous
Lie and Kodur - Carbonate
Lie and Kodur - Siliceous
Kodur and Sultan - Carbonate
Kodur and Sultan - Silieous

80

60
0

200

400
600
Temperature (°
C)

800

1000

Figure 2.4 - Variation in mass of concrete with different aggregates as a function of temperature

55

Mass (% of original)

100

80

Noumowe et al. - NSC
Noumowe et al. - HSC
VanGeem - NSC
Kodur and Sultan -HSC

60
0

200

400
600
Temperature (°
C)

800

1000

Figure 2.5 - Variation in mass of NSC and HSC as a function of temperature
Loading mechanism

Furnace
Concrete specimen
TC3 TC2 TC1
TC - Thermocouple
TC1 - Center
TC2 - Surface
TC3 - Furnace

Loading mechanism

Figure 2.6 - General arrangement of concrete specimen under compressive loading inside
furnace
56

Start loading with
strength test machine

Temperature

T

Temperature increase to target
tempearture T in time t

t

Time

Move to strength
test machine

Stress (or strain)

(a) Heating scheme

Preloading 40 % of
capacity and further
stress increase after
heating time t
0.4 f'c

t

Time
(b) Loading scheme

Figure 2.7 - Specimen heating and loading in stressed test method under preload
57

Start loading with
strength test machine

Temperature

T

Temperature increase to target
tempearture T in time t

t

Time

Start loading with
strength test machine

Stress (or strain)

(a) Heating scheme

No preloading and
further stress increase
after heating time t

t

Time
(b) Loading scheme

Figure 2.8 - Specimen heating and loading in unstressed test method without preload
58

Temperature

T

Start loading with
strength test machine

Temperature increase to target
tempearture T in time t

t

Time

Start loading with
strength test machine

Stress (or strain)

(a) Heating scheme

No preloading and
further stress increase
after cooling down of
concrete

t

Time
(b) Loading scheme

Figure 2.9 - Specimen heating and loading in residual strength measurements
59

Relative compressive strength

1.2

Test – upper bound
1
0.8
0.6

Test – lower bound
0.4

ASCE model
Eurocode (siliceous)
Eurocode (carbonate)

0.2
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 2.10 - Variation in relative compressive strength as function of temperature for NSC

Relative compressive strength

1.2

Test – upper bound

1
0.8
0.6

Test – lower bound
0.4

Kodur et al. model
Eurocode - HSC (Class 2)
Eurocode- HSC (Class 3)
Castillo 1990 - HSC

0.2
0
0

200

400
600
Temperature (°
C)

800

Figure 2.11 - Variation in relative compressive strength as function of temperature for HSC

60

Relative splitting tensile strength

1

Test – upper bound

0.8

Bahnood 2009
Eurocode
Felicetti 1996
SFPE HB

0.6
0.4

Test – lower bound

0.2
0
0

200

400

600

800

Temperature (°
C)
Figure 2.12 - Variation in relative splitting tensile strength as function of temperature
1.2

Test – upper bound
1

ET/E0

0.8

Phan - HSC
Castillo 1990 - HSC
Persson - SCC
Bamonte - SCC

0.6
0.4

Test – lower bound

0.2
0
0

200

400
Temperature (°
C)

600

Figure 2.13 - Variation in elastic modulus as a function of temperature
61

800

35

23°C
100°C
200°C
300°C
400°C
500°C
600°C
700°C
800°C

30

Load (kips)

25
20
15
10
5
0
0

5000

10000

15000

20000

Deformation xe-5 (in)
Figure 2.14 - Typical load deformation of NSC at various temperatures
35

23°C
30

100°C
200°C

25
Load (kips)

300°C
20

400°C
500°C

15

600°C
10

700°C
800°C

5
0
0

5000

10000

15000

Deformation xe-5 (in)
Figure 2.15 - Typical load deformation of HSC at various temperatures

62

20000

14

0.0%
22.5%
35%

10

45%
67.50%

Total strain (%)

6

2

-2

-6

-10
0

200

400

600

800

Temperature (°
C)

Figure 2.16 - Variation of total strain with temperature for concrete heated under differnet preloads (Anderberg and Thelandersson 1976)

63

0.0%
8000

0.10%

Strain x 106

0.20%
0.30%
4000

0

-4000
0

200

400

600

Temperature (°
C)

Figure 2.17 - Variation of thermal strain with temperature for limestone concrete heated under
different pre-loads

64

Tensile strength

Spalling
point

Porosity ×
Pore pressure
in concrete

Porosity × Pore pressuure

Heat

Tensile strength
of concrete

Heat

Heat

Heat
Spalling Zone

0

100

200

300

400

500

Temperature (°C)
Figure 2.18 - Illustration of spalling process in concrete (Dwaikat, 2009)

Temperature
distribution

Compressive
strength

Heat

Heat

Crack
development

Restraint
Thermal
stresses

(a) Restrained concrete

(b) Developed stresses

Figure 2.19 - Illustration of thermal dilation mechanism for fire induced spalling

65

90˚ Hook

135˚ Hook

Figure 2.20 - Conventional 90° hook versus modified 135° hook configuration

66

CHAPTER 3
3

THERMAL PROPERTIES CHARACTERIZATION

This chapter is mainly based on the following journal papers:
•

Kodur, V., and Khaliq, W. (2011). "Effect of Temperature on Thermal Properties of
Different Types of High Strength Concrete." Journal of Materials in Civil Engineering,
ASCE, 23(6), 793-801.

•

Khaliq, W., and Kodur, V. (2011). "High temperature properties of fiber reinforced high
strength concrete." Innovations in Fire Design of Concrete Structures - ACI SP 279, 3-1-42.

•

Khaliq, W., and Kodur, V. (2011). "Thermal and mechanical properties of fiber reinforced
high performance self-consolidating concrete at elevated temperatures." Cement and
Concrete Research, 41(11), 1112-1122.

•

Khaliq, W., and Kodur, V. K. R. (2011). "Effect of high temperature on tensile strength of
different types of high-strength concrete." ACI Materials Journal, 108(4), 394-402.

3.1 General
Thermal properties of concrete are critical for evaluating temperature rise in concrete members,
which are needed for determining strength and stiffness degradation and ultimately fire
resistance of concrete structural members. These thermal properties vary with temperatures and
thus accurate predictions of temperatures in concrete members require temperature dependent
thermal property relations. As discussed in Chapter 2, there is lack of data specific to high
temperature thermal properties of new types of high performance concrete. To develop such

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information characterization of high temperature thermal properties of various HPC is
undertaken and is presented in this Chapter.
The main thermal properties that influence the temperature rise and fire induced forces in
concrete structural members are thermal conductivity, specific heat, thermal expansion and mass
loss. At present, some codes and design standards provide thermal property relations as a
function of temperature (ASCE, 1992; Eurocode 2, 2004). These relations are mainly derived
from the experimental studies on conventional NSC and in some cases for conventional HSC.
However, thermal properties of HPC, especially at high temperature, are influenced by factors
such as presence of fibers, fly ash or silica fume, mix proportions, w/c ratio and permeability. To
quantify influence of some of these factors, a series of thermal property tests were conducted on
different type of HPC specimens and the effect of some of these factors on thermal properties of
HPC is quantified. Based on the test data obtained from these thermal property tests, simple
empirical relations for high temperature thermal properties are also presented. A detailed
description of the tests and discussion of test results on thermal properties is presented here.

3.2 Design of Thermal Property Tests
A comprehensive test program was designed to undertake high temperature thermal property
tests on four types of concrete namely HSC, SCC, and FAC and NSC. To quantify the effect of
fibers on thermal properties three types of fibers namely steel, polypropylene and hybrid fibers
were added to some of these mixes. This led to a total of eleven mix designs for measuring
thermal properties. The effect of steel, polypropylene and hybrid fibers was studied in HSC and
SCC, whereas to reduce the number of total tests (effort) only effect of polypropylene fibers was
studied in FAC. Thermal properties namely specific heat, thermal conductivity, thermal
expansion, and mass loss are measured for these concretes. Thermal conductivity and specific
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heat measurements were made in the temperature range of 20-800°C (due to equipment
limitations), while thermal expansion measurements were made in the temperature range of 201000°C. Mass loss measurements were done in the temperature range of 100-800°C at 100°C
increments. The test matrix for evaluating thermal properties is given in Table 3.1.
Thermal conductivity and specific heat measurements were done using the state-of-the-art test
equipment namely ‘Hot Disk’. Hot Disk is relatively new equipment and it combines the
measurement of three heat transfer properties (thermal conductivity, thermal diffusivity, and
specific heat) in a single test unlike other existing test apparatus which require separate
equipment for measuring thermal conductivity, thermal diffusivity, and specific heat. In the case
of Hot Disk thermal conductivity and thermal diffusivity are measured directly and specific heat
is internally calculated based on the measured thermal conductivity and thermal diffusivity.
Description of the Hot Disk equipment together with the principles used in evaluating thermal
properties is explained in Appendix A.
Thermal expansion is also measured using state-of-the-art test equipment namely
thermomechanical analyzer (TMA). This equipment measures real time thermal expansion of the
sample as a function of temperature through linear variable displacement transducer. Equipment
details and the principles used in the measurement of thermal expansion are described in
Appendix A.
Mass loss measurements were relatively simple in which the dimensions of a cylinder specimen
was first accurately measured using a precise vernier caliper for volume calculations and a
sensitive balance was used to calculate room temperature weight. The cylinder was exposed to a
target high temperature in an electric furnace, and then weight of heated cylinder was recorded.

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Mass loss was then evaluated using room temperature and high temperature weight
measurements of cylinder.

3.3 Thermal Property Tests
Thermal property tests namely thermal conductivity, specific heat, thermal expansion and mass
loss were carried out on HSC, SCC, FAC and NSC specimens as per design matrix given in
Table 3.1. This section covers details on all thermal property tests.
3.3.1

Mix Proportions

Four concretes namely HSC, SCC, FAC, and NSC were used to fabricate the test specimens for
measuring thermal properties. In addition, three types of fibers, namely steel, polypropylene and
hybrid fibers were added to these mixes. The specimens are designated as HSC, HSC-S, HSC-P,
and HSC-H for HSC, and SCC, SCC-S, SCC-P, and SCC-H for SCC, and FAC, and FAC-P for
FAC where S, P and H designations indicate the presence of steel, polypropylene and hybrid
(steel + polypropylene) fibers respectively. In addition to these HPC, a conventional NSC mix,
designated as NSC was also included in the program for generating a bench mark data. These
mixes had ordinary Portland cement (Type I), limestone (carbonate) based coarse aggregate of
maximum size 10 mm, and natural source sand fine aggregate. In the FAC and FAC-P batch
mixes, 25% fly ash (Type C) was used as replacement of cement. To achieve desired strength
and workability properties, optimum amount of mineral admixtures, such as silica fume and slag
(Grade 120), were added to batch mix. Silica fume, fly ash, and slag are the industrial byproducts having cementitious properties used to produce HPC.
Silica fume is an industrial by-product of the induction arc furnaces in the silicon metal and
ferrosilicon alloy industries (Mehta and Monteiro, 2006). Reduction of quartz to silicon at

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temperatures up to 2000°C produces SiO vapors, which oxidize and condense in the lowtemperature zone of the furnace to tiny spherical particles consisting of non-crystalline silica.
The material removed by filtering the outgoing gases in bag filters possesses an average diameter
2

on the order of 0.1 µm and surface areas in the range 15 to 25 m /g which is extremely fine as
compared to normal portland cement. Silica fume is highly pozzolanic, but it is hard to handle
and it increases the water requirement in concrete significantly unless water-reducing admixtures
are used. Fly ash has cementitious and pozzolanic properties and is produced during the
combustion of powdered coal in thermal power plants. As coal passes through high-temperature
zone in the furnace the volatile matter and carbon are burned off. During combustion most of the
fine particles fly out with the chimney gas stream and are called fly ash. This ash is subsequently
removed from the gas by special filtration techniques. Blast furnace slag is produced in the
production of cast iron when the slag is cooled slowly in air; the mineral components are usually
present as crystalline melilites that do not react with water at ordinary temperature. When ground
to very fine particles, we get blast furnace slag, a material which is cementitious and pozzolanic
(Mehta and Monteiro, 2006).
For fiber reinforced HSC, SCC, and FAC mixes, commercially available fibers, NOVOCON XR
type steel fibers and MONOFILAMENT (multi-plus) type polypropylene fibers were added.
Figure 3.1 shows the steel and polypropylene fibers used in this study. Steel fibers were 38 mm
in length and 1.14 mm equivalent diameter and had a specified tensile strength of 966 MPa.
Polypropylene fibers are non-absorbent type with 20 mm length, 0.91 specific gravity and 162°C
melting point. Steel fibers in HSC-S and SCC-S were 42 kg in a cubic meter of concrete
representing 0.54% by volume. Polypropylene fibers in HSC-P, SCC-P, and FAC-P were 1
3

kg/m representing 0.11% by volume. In the case of HSC-H and SCC-H the proportion of steel
71

3

3

and polypropylene fibers were 42 kg/m steel, and 1 kg/m polypropylene, representing 0.54%
and 0.11% by volume respectively.
Details of the mix proportions, laboratory conditions at time of casting of plain HSC, SCC, FAC,
and NSC are given in Table 3.2, and details of fiber reinforced HSC, SCC, and FAC are given in
Table 3.3, 3.4, and 3.5 respectively. After casting, the test specimens were cured in curing room
with controlled environment of 22°C temperature and 98% relative humidity. Specimens were
pored with one mix at a time. The tests were completed over a period of 18 months with
concretes casted first were tested first. Thermal property tests for a particular concrete were
carried out over a period of 6 months to 10 months after casting of specimens. The 28 day
compressive strength measured on specimens and for different concretes ranged from 16-81 MPa
for plain HSC, SCC, FAC, and NSC as given in Table 3.6. The 28 days compressive strength of
fiber reinforced HSC, SCC, and FAC ranged between 56-89 MPa as given in Table 3.7.
Chemical admixtures such as superplasticizer, retarder, and water reducer were added to batch
mixes to achieve desired concrete properties in HSC, SCC, FRC and FAC. For SCC, result for
VSI was ‘1.0’ and it was observed that mix was even with very less signs of segregation. Very
little poppying of air was observed in slump patty in SCC. FAC displayed significantly high
strength as compared to other types of concrete. HSC and SCC mixes were supplied by
commercial concrete plants while FAC and FAC-P were mixed in laboratory under controlled
conditions. This could be the main reason for FAC to achieve higher strength as compared to
HSC and SCC.
3.3.2

Test Specimens

From each batch of concrete two 100×100×300 mm size prism specimens were fabricated. The
specimens were demolded one day after casting and cured under controlled conditions of 90%
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humidity and 20°C temperature. Test specimens of 60×60×25 mm size were machine cut from
100×100×300 mm prisms and prepared for determining thermal properties at elevated
temperatures. Thermal property tests were carried out over 4 months period after 6 months of
concrete pour.
Square specimens of size 60 mm on sides and 25 mm in height as shown in Figure 3.2(a) were
used for carrying out thermal conductivity and specific heat tests. As the accuracy of test result
greatly depends on the specimen-to-sensor contact, these specimens were ground smooth to
ensure uniformity of the surface and enhance specimen-to-sensor contact. For thermal expansion
tests, specimens of 10×10×18 mm size machine cut from same prisms described above. Sides of
these specimens were smoothened carefully to have a balanced fit under thermal expansion
probe as shown in Figure 3.2b. For mass loss measurements, 75×150 mm cylinders were used at
different temperatures. The details and number of specimens for thermal properties are given in
Table 3.8.
3.3.3

Test Apparatus

The thermal properties were measured using commercially available instruments. The specific
heat, and thermal conductivity were measured using “Hot Disk TPS 2500S” thermal constant
analyzer as shown in Figure 3.3a. This procedure follows ISO/DIS22007 (2008) test standards
for measurement of thermal conductivity and specific heat properties. This equipment is
connected to a furnace in which a specimen can be exposed to desired high temperature as shown
in Figure 3.2(b). This state-of-the-art equipment utilizes transient plane source (TPS) technique
to measure thermal properties of materials from room temperature to 800°C. A flat source sensor
is placed between two halves of the specimens and it acts like a heater (constant effect generator)
and as detector (resistance thermometer) at the same time (Adl-Zarrabi et al., 2006). This sensor
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is either insulated with mica or kapton layers and accordingly called mica or kapton sensor as
shown in Figure 3.4. Kapton sensor can be used for measurements up to 200°C, and mica sensor
can be used for measurements in 100-800°C temperature range (Adl-Zarrabi et al., 2006). When
a constant heat source is applied, the temperature in sensor rises and heat flow starts in the
specimen being tested. The test specimen must have uniform temperature distribution throughout
the specimen at the time of measurement.
For thermal expansion measurements, thermo-mechanical analysis (TMA) apparatus (Q-400
EM) was used as per ASTM E831-06 (2006) test procedure. TMA (Figure 3.5a) utilizes a
movable-core linear variable differential transducer (LVDT), which generates an output signal
directly proportional to specimen dimension change. TMA can be used for measuring
dimensional changes in concrete specimens from room temperature to 1000°C. For thermal
expansion tests, a flat-tipped standard expansion probe (Figure 3.5b) is placed on the concrete
specimen with a small static force is applied to it so that probe stays steadily on the specimen.
The specimen is subjected to temperature increase regimen according to user defined ramp and
probe movement records the sample expansion or contraction. The TMA test is run through
computer program while the input parameters such as heating rate, static load and maximum
temperature are provided by the user.
The test equipment for mass loss calculations consisted of an electrical furnace and weight
balance. The mass loss measurements, both at room and high temperatures, were carried out by
utilizing a highly sensitive balance that has accuracy up to 0.001 gram. The concrete specimens
were exposed to target temperatures of 100, 200, 400, 600, and 800°C in an electric furnace at a
heating rate of 2°C/minute and were kept for two hours at the target temperature till steady state

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conditions were attained. Heated specimens were then quickly taken out (without much heat
loss) and weighed.
3.3.4

Test Procedure

3.1.1.1. Thermal Conductivity and Specific Heat
For thermal conductivity and specific heat measurements were carried out using Hot Disk (TPS
2500S) apparatus on 60×60×25 mm test specimens. The specimens were air dried and surfaces
were ground smooth for ensuring good sensor contact. Thermal conductivity and specific heat of
concrete were measured at thirteen temperature points namely 20, 100, 200, 300, 400, 450, 500,
550, 600, 650, 700, 750, and 800°C. The smaller increments towards higher temperatures were
to capture effect of phase changes in concrete on thermal properties. The age of concrete at the
time of thermal property measurements tests was 6 months or older.
Kapton sensor was used to undertake tests at room temperature (20˚C). This Kapton sensor is
sandwiched between two halves of concrete test specimens and is connected to Hot Disk. The
specimen and sensor assembly rests on a platform of room temperature specimen holder (Figure.
3.6). A small pressure is applied to ensure good contact between the specimen and the sensor.
The equipment sends and receives signal through the sensor connected to the TPS 2500S (Figure
3.3a), and is monitored with a computer program. The measurements at room temperature with
kapton sensor are important to figure out the best test parameters as reasonable test results
obtained at room temperature provide suitable parameters to be used for high temperature tests.
For high temperature tests, mica sensor was sandwiched between two specimens and the
assembly was subjected to high temperatures in a furnace connected to the Hot Disk apparatus.
Figure 3.7 illustrates mica sensor being placed between two specimens of concrete in the holder

75

assembly. This holder assembly is further placed inside the furnace (Figure 3.3b) for exposure to
high temperature. The computer program controls the temperatures of specimen and furnace. The
concrete specimens are exposed to high temperature in a furnace connected to Hot Disk
apparatus as per defined test conditions. The test condition parameters namely, probing depth,
sensor type, initial thermal coefficient of resistance (TCR), hold time at steady state,
measurement power, and measurement times are to be programmed (as input) in to Hot Disk
apparatus by user. For these tests, initial TCR of 0.004693 /K, probing depth of 20 mm, sensor
measurement power of 0.9 W, hold time of 60 minutes and measurement time of 40 seconds was
used. For high temperature measurements, a built-in value of TCR at each temperature as per
sensor type was used. At each target temperature, once the thermal equilibrium is attained,
thermal conductivity and specific heat are recorded. Then the temperature in the furnace is
increased to next target temperature and this procedure is continued till 800°C. It took an average
of 25 minutes to reach a target temperature with 100°C increments and an average of 17 minutes
to attain a target temperature with 50°C increments. Average stabilizing time to obtain uniform
temperature throughout the specimens was 300 minutes for 100°C increments and was 210
minutes for 50°C increments. This resulted in average time of running a complete test on each
specimen to approximately 52 hours. Figure 3.8 illustrates time-temperature increments and
stabilizing times at different target temperatures.
In order to verify reliability of measurements, thermal property tests were repeated on additional
specimens from the same batch of concrete. For this, three SCC-P and two HSC samples were
selected and Hot Disk tests were repeated in the entire temperature range. The variability in the
thermal conductivity and specific heat was with in ±5% indicating good reliability of the

76

measurements. To keep the results consistent with other concretes, data from one batch of
measurements is presented here.
For thermal expansion measurement, samples were prepared as per ASTM E 831-06 (2006).
Since concrete is a heterogeneous material, the specimens were selected from concrete prisms in
a manner that they contained aggregate and cement matrix in equal representative amount. After
carefully placing the specimen on expansion probe (Figure 3.5c) a small load of 0.02 N was
applied to the specimen through expansion probe to maintain static contact between the
specimen and the probe. The test equipment was first calibrated and zeroed to make the TMA
ready for new test. The initial length of the specimen and ambient temperatures were recorded by
the TMA before start of test. Three TMA tests were performed for each type of concrete
throughout the temperature range of 20-1000°C. The temperature increase for thermal expansion
depends on the temperature ramp (heating rate) set by the user for that particular test. Once
specimen is placed in position, inside TMA furnace, the test is run and controlled by software
that records dimensional change with increasing temperature. For concrete specimens, the
selected ramp was 5°C per minute. It took three hours and twenty minutes for each specimen to
reach target temperature of 1000°C. Figure 3.9 illustrates the temperature ramp used in thermal
expansion tests. To ensure repeatability of the test results, 3 tests were conducted for each type of
concrete and average value was considered as final results.
Mass loss of all concretes was measured at various temperatures using 75 mm dia and 150 mm
height concrete cylinders. Mass loss measurement procedure involved weighing the cylinder at
room temperature before it was exposed to high temperatures. Cylinders were taken out form the
curing room and then air dried at room temperature for one hour before taking measurements and
testing. The dimensions of the cylinder were measured using a precise vernier caliper at three

77

places along length and diameter and average of the dimensions were used for volume
calculations. Room temperature density and mass calculations were then based on weight of the
cylinders measured at ambient temperature.
Following room temperature density and mass calculations, the cylinders were then exposed to
higher temperatures in an electric furnace at a heating rate of 2°C/minute to target temperature.
Specimens were then allowed to stabilize for two hours to reach steady state conditions
throughout the specimen. Then the heated specimens were quickly transferred to a sensitive
balance (with accuracy of 1000

th

of a gram) and weighed to record change in weight at that

target temperature. Mass loss was then evaluated at high temperature using both recorded room
temperature and high temperature weights. This procedure was repeated for various target
temperatures.

3.4 Results and Discussion
The measured thermal conductivity (kt), specific heat (cp), thermal expansion (εth) and mass
loss properties for plain and fiber reinforced HSC, SCC, and FAC are presented in this section.
Results of thermal property tests on NSC are utilized to compare the thermal properties of
different concrete types. Data from these tests is also used to discuss the effect of various
parameters on high temperature thermal properties.
3.4.1

Thermal Conductivity

The measured thermal conductivity of HSC, SCC, FAC, and NSC are plotted in Figure 3.10 as a
function of temperature. Thermal conductivity of these three concrete types is between 2.4 and
3.3 W/m°K at room temperature range. For all three concretes, thermal conductivity initially
decreases with temperature up to 400°C, then it remains almost constant between 400 and
78

500°C, and finally decreases again up to 800°C. This trend in thermal conductivity can be
attributed to variation of moisture content with increase in temperature (Bažant and Kaplan,
1996). The initial steep slope of thermal conductivity up to 400°C can be attributed to moisture
loss at a faster pace resulting from the evaporation of free and pore water in concrete with rise in
temperature. The minor variation in thermal conductivity between 400°C and 500°C is due to
dissociation of small amounts of physically bound water present in concrete as a result of phase
change. Beyond 500°C, there is slow decrease in thermal conductivity due to liberation of small
amount of strongly held moisture left within calcium silicate hydrate (CSH) layers.
Thermal conductivity for FAC follows quite similar trend and lie closer to that of HSC and NSC,
therefore it is deduced that there is not much difference in thermal conductivity values of HSC,
NSC and FAC. Thermal conductivity of NSC follows trend close to these concretes till 600°C,
however, after the thermal conductivity of NSC seems to stay constant. The main reason for
constant thermal conductivity of NSC beyond 600°C is that maximum dehydration of NSC has
already taken place and there is not much physically or chemically bound water left to lose. This
is not the case with other concretes, as high permeability allows retaining some chemically
bound water till higher temperature range and therefore cause further thermal conductivity
variation.
Thermal conductivity of SCC also follows a similar trend to HSC, except that it is slightly higher
as compared to other concrete types within 600°C temperature range. This might be attributed to
the fact that SCC is produced by excessive use of chemical admixtures, and thus it has increased
amount dissolved chemical ions in mixed water. This higher concentration of chemical ions
slightly increases thermal conductivity of SCC (Ganguli et al., 2008).

79

Figures 3.11 and 3.12 and 3.13 show the effect of fibers on the thermal conductivity of HSC,
SCC, and FAC as a function of temperature respectively. For HSC, the trends indicate that
addition of steel, polypropylene, and hybrid fibers to concrete does not significantly alter the
thermal conductivity up to 600°C. However, beyond 600°C fibers have marginal influence on
thermal conductivity of fiber reinforced HSC. This minor influence can be attributed to
dehydration of the CSH, and also due to contribution of higher thermal conductivity of steel
fibers present in the concrete mix.
For SCC the presence of fibers does have an effect as thermal conductivity is higher for SCC-S
and SCC-H as compared to SCC-P. This modification might have been due to contribution from
higher thermal conductivity of steel fibers as compared to polypropylene fibers. However, it can
be observed form Figure 3.12 that reduction in thermal conductivity of SCC with three types of
fibers follow similar trend throughout the temperature range tested.
In case of FAC, polypropylene fibers do not affect the thermal conductivity, as it is almost same
for both FAC and FAC-P concretes. Thermal conductivity of FAC at room temperature was a
little higher as compared to FAC-P, this can be attributed to the polypropylene fiber matrix that
hinders flow of heat at room temperature, however, as the polypropylene fiber melt at about
169°C, the thermal conductivity of both concretes follow similar trend throughout the tested
temperature.
3.4.2

Specific Heat

The variation of specific heat for HSC, SCC, FAC, and NSC with temperature is illustrated in
Figure 3.14. The specific heat for all the concrete types remains almost constant up to 400°C,
then increases up to about 650°C and then remains constant between 650-800°C range. SCC and
FAC exhibit slightly higher values of specific heat throughout the temperature range. This could
80

be attributed to varying permeability characteristics of concrete. The permeability coefficients
for different concrete types as reported in literature are tabulated in Table 3.9. It can be observed
that SCC and FAC are less permeable than that of HSC and NSC. Since extra heat is absorbed
for releasing bound water in less permeable concretes, SCC and FAC display higher specific heat
values. Kodur and Sultan (2003) observed that the specific heat of HSC is affected by
physiochemical processes that occur in the cement paste and aggregate above 600°C. This is
generally true with FAC and SCC as well. Above 600°C enormous amount of heat is required to
raise the temperature of the carbonate aggregate concrete. The substantial increase in specific
heat of SCC and FAC between 600 and 700°C, as compared to HSC, can be attributed to
presence of mineral and chemical admixtures in SCC and FAC. NSC has the specific heat closer
to HSC between 600-800°C, porosity and dehydration resulting from loss of water at early
temperatures is the cause of these decreasing values of NSC towards high temperature.
The effect of fibers on specific heat of HSC, SCC, and FAC as a function of temperature is
illustrated in Figures 3.15, 3.16 and 3.17 respectively. Addition of steel, polypropylene, and
hybrid fibers to HSC and SCC has marginal influence on the specific heat of concrete. Specific
heat up to 400°C is constant for three types of fiber reinforced HSC and SCC, but beyond 400°C
there is slight influence of fibers. Influence of steel and hybrid fibers on specific heat is similar
as compared to polypropylene fibers concrete up to 600°C; however between 600 and 800°C,
polypropylene fiber reinforced concrete experiences drop in specific heat. Steel fibers present in
HSC-S and HSC-H help to control cracking and its propagation at higher temperatures and hence
density of the concrete does not get reduced resulting in higher specific heat. However, in case of
HSC-P, polypropylene fibers decompose (after burning) leading to increase in porosity of
concrete. As a result HSC-P becomes more permeable with high crack density, which gives

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lower specific heat for HSC-P in higher temperature range. Similar observations of crack control
and preserved density (in the case of steel fibers) are noted for SCC-S and SCC-H concrete as
compared to SCC-P and are illustrated in Figure 3.16.
In the case of FAC and FAC-P, the specific heat remains constant up to 400°C; however there is
a marginal difference between the two concretes beyond 400°C. Higher specific heat in FAC can
be attributed to the dense microstructure that does not allow easy evaporation of chemically
bound water and thus requires extra heat. On the other hand easy evaporation and dehydration in
the case of FAC-P is facilitated by enhanced porosity due to burning of polypropylene fibers.
Over all there is significant difference in the specific heat of the FAC and FAC-P beyond 400°C.
3.4.3

Thermal Expansion

The variation of thermal expansion of HSC, SCC, FAC, and NSC is plotted as a function of
temperature in Figure 3.18. Thermal expansion generally increases with temperature for all three
concrete types. This increase is substantial in 20-600°C temperature range, and is mainly due to
high thermal expansion resulting from constituent aggregates and cement paste in concrete. The
expansion rate subsidizes between 600-800°C for all three concretes, as loss of chemically bound
water in hydrates causes shrinkage. Thermal expansion again rises substantially after 800°C and
this can be attributed to decarbonation of limestone based aggregates, when macro crack
development is observed (Fu et al., 2004). Since calcium hydroxide, which is found in concrete
matrix, dehydrates above 800°C, maximum thermal expansion occurs between 800 and 1000°C.
At this point, the physically bound water held by limestone aggregate would also evaporate and
lead to this higher thermal expansion in concrete. In case of NSC the expansion follows a trend
similar to HSC and FAC, however expansion remains consistent till 800°C with significant

82

changes (contraction or degradation). It can be attributed to consistent properties associated with
less damaged microstructure of NSC as compared to HSC or FAC.
It can be seen in Figure 3.18 that SCC has slightly higher thermal expansion as compared to
other two concretes throughout the temperature range. This can be attributed to higher chemical
and mineral admixtures present in SCC mix and also due to lower permeability of SCC. Thermal
shrinkage, instead of expansion, is observed in FAC between 800 and 1000°C and this can be
attributed to presence of fly ash (25%) in the mix. This has also been established by Shehata et
al. (2000), who inferred that use of fly ash in concrete reduces the expansion of concrete and this
reduction is dependent on the volume of fly ash in concrete mix.
The effect of fibers on thermal expansion of HSC, SCC, and FAC is illustrated in Figures 3.19,
3.20 and 3.21 respectively. The presence of fibers influences thermal expansion all three types of
HPC. In case of HSC, the addition of fibers reduces thermal expansion. Generally this effect of
fibers is much pronounced in 400-1000ºC temperature range. This can be attributed to
differential thermal expansion of steel and also due to crack control effect facilitated by steel
fibers. The addition of fibers shows an increased trend in thermal expansion in case of SCC. The
addition of polypropylene fibers has the least expansion in HSC and SCC. Overall, SCC
displayed 0.4% higher values of thermal expansion as compared to HSC over the entire
temperature range.
In the case of FAC and FAC-P, the thermal expansion is higher in FAC; especially it is
significant beyond 400°C. Higher thermal expansion in FAC can also be attributed to the
impermeable and dense microstructure that does not allow easy dehydration and therefore causes
extensive micro and macro cracks resulting from thermal stresses. Whereas this is not the case

83

with FAC-P, as the thermal expansion is quite gradual and smooth throughout 20-800°C
temperature range.
3.4.4

Mass Loss

The variation in mass loss (ratio of mass at a specified temperature (M) to mass at room
temperature (M0)), as obtained from tests, is plotted in Figure 3.22 as a function of temperature
for plain HSC, SCC, FAC, and NSC. It can be seen that no significant mass loss occurs till
600°C in all concrete types; however moderate mass loss that is about 10% of room temperature
mass takes place in 600-800°C in the case of SCC and FAC. Higher mass loss takes place in
HSC in 600-800°C (about 20% at 800°C), which can be attributed to the relatively easy
dehydration in HSC which has comparatively less dense microstructure. The main reason for
sudden higher mass loss beyond 600°C is the loss of the hidden moisture present in carbonate
aggregate that vaporizes at temperatures above 600°C due to dissociation of dolomite. This is an
endothermic reaction which absorbs lots of heat. All these concretes were made of carbonate
aggregate; the mass loss in these concretes follows almost similar trends throughout 20-800°C.
Compared to HPC, mass loss in conventional NSC is higher and this loss starts from the early
stages of heating. This higher and early mass loss is attributed to easy loss of moister form NSC
due to its permeable microstructure. However, ultimate mass loss in NSC at 800°C is quite
similar to other types of concrete, therefore it can be deduced that earlier moisture retention in
HPC is due to low permeability and therefore higher thermal properties as compared to NSC.
This is the reason that conventional NSC behaves entirely different from HPC under elevated
temperatures and suffers less from the detrimental effects of pore pressure that builds up in HPC.

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The effect of fibers on mass loss of HSC, SCC, and FAC is illustrated in Figures 3.23, 3.24 and
3.25 respectively. It can be seen that there is no significant effect of fibers on mass loss of these
HPC at elevated temperatures. This is explained by the plotted data (Figures 3.23, 3.24 and 3.25)
which shows that fiber reinforced HSC, SCC, and FAC have almost similar trend of mass loss as
compared to plain form of the concrete.
3.4.5

Repeatability of Thermal Property Tests

Thermal conductivity and specific heat measurements were carried out by testing one pair of
specimens for each test. Since high temperature measurements were to be carried out at 12
temperatures (100, 200, 300, 400, 450, 500, 550, 600, 650, 700, 750, and 800°C) on each
specimen type. Three measurements were carried out at target temperature in a single test with a
time difference of 60 minutes at each temperature with Hot Disk equipment. However, the tests
were not repeated for thermal conductivity and specific heat to save on time and resources. It
should be noted that the sensors used for the high temperature thermal property measurements
get destroyed after the test and these sensors are very expensive. Moreover, a single test on Hot
Disk equipment took an average of 52 hours (about 3 work days). However, to ensure the
repeatability of measurements and thermal conductivity and specific heat tests were repeated by
conducting three tests for SCC-P and two tests for HSC specimens throughout the 20-800°C
temperature range. The variability was with in ±5% and thus the authors are quite confident on
the reliability of the measurements.
Thermal expansion measurements were carried out by testing three samples of each type of
concrete throughout the temperature range. For statistical analysis, the y-error bars are shown on
the TMA test on four types of concrete in Figure 3.26. These error bars shown in the line graph
represent a description of confidence on mean representing the true expansion value as a function
85

of temperature. The more the original data values range above and below the mean, the wider the
error bars and less confident you are in a particular value. The maximum standard deviation is
depicted by HSC values that are within 10% of the measured range; values for all other concretes
are much lower than 10%. Mass loss measurements were also done using one sample at each
temperature. Like thermal conductivity and specific heat, mass loss is also time consuming test
with each temperature test taking a day to complete. These tests were therefore only repeated to
confirm results once mass loss property at a given temperature was a significant outlier.
3.4.6

Summary

Temperature has significant influence on thermal properties of HSC, FAC, and SCC. The
thermal conductivity of all three concrete types generally decreases with temperature, while the
thermal expansion increases with temperature up to 800°C. Conversely, specific heat of all three
concrete types remains constant up to about 400°C, and then increases up to about 650°C before
following a constant trend in 650-800°C range. Results show that SCC possesses higher thermal
conductivity and thermal expansion as compared to HSC and FAC in the temperature range of
20-800°C. However, specific heat of SCC lie in-between that of HSC and FAC in 20-800°C
temperature range. Compared to HSC and SCC, FAC has higher thermal expansion in 550850°C, and it shrinks in 850-1000°C. No significant mass loss occurs in HSC, SCC, and FAC up
to 600°C, and moderate mass loss occurs in 600-800°C.
The addition of steel, polypropylene, and hybrid fibers to HSC, SCC, and FAC does not
significantly alter the thermal conductivity. However addition of fibers increases specific heat of
SCC and HSC in 400-800°C, while in case of FAC the specific heat drops in 400-800°C
temperature range. In the case of thermal expansion addition of fibers to SCC increases thermal
expansion in 400-800°C, while in case of HSC and FAC the addition of fibers decreases the
86

thermal expansion in 20-800°C temperature range. Fibers do not have any effect on mass loss in
HSC, SCC and FAC in the entire 20-800°C temperature range.

3.5 Relations for Thermal Properties
Data generated from the thermal property measurements is utilized to develop thermal property
relations for plain and fiber reinforced HSC, SCC and FAC. These properties are expressed in
the form of empirical relations over temperature range of 20-800°C for thermal conductivity,
specific heat and mass loss, and in 20-1000°C for thermal expansion. These empirical relations
were arrived at based on linear regression. For the regression analysis, measured thermal
properties were used as response parameter with temperature as their predictor parameter. Three
data points based on three measurements taken at a target temperature were used for regression
analysis.
For regression analysis, linear regression was selected based on the fact that thermal properties
are measured as a function of temperature and therefore linear relation of property verses
temperature is simple and more suitable. The procedure for estimating the parameters of any
linear model (linear fitting), the method of least squares can be used simply by fitting a straight
line to a set of data points (Wackerly et al., 2008 ). The least-squares procedure is used for fitting
a line through a set of ‘n’ data points where it is desired that the differences between the
observed values and corresponding points on the fitted line to be minimum overall. A convenient
way to accomplish this, and one that yields estimators with good properties, is to minimize the
sum of squares of the standard deviations from the fitted line. These deviations in the response
value (thermal property) given by the predicted value (temperature) is called the error and to
reduce these deviations in response values, sum of squares of deviations/error is utilized. This
quantity is referred to as sum of squares of error (SSE).
87

If the simple linear regression model fits the data well, the differences between the observed and
predicted values are small, leading to a smaller for SSE. On the other hand if the regression
model fits poorly, SSE will be large leading to a quantity known as coefficient of determination
2

2

R (Wackerly et al., 2008 ). This R can be interpreted as the proportion of the total variation in
the response that is explained by the variable prediction in a simple linear regression model. The
2

accuracy of the statistical model is represented by coefficient of determination ‘R ’, that
represents proportion of the sum of squares of deviations of the response values about their
2

predictor (Mendenhall and Sincich, 2007). The value of R is always between 0 and 1, where 1 is
the perfect fit of the equation to underlying data. For this study commercially available statistical
2

software (Minitab) was used to find a linear fit through regression analysis. The R value
obtained for the proposed equations lies between 0.84-0.9 that represents a reasonably high
confidence level in light of high variability in thermal properties. Since fibers do not
significantly influence the thermal properties, the relations presented here are also applicable for
fiber reinforced HSC, SCC and FAC unless stated otherwise. Selected fitted line plots for HSC,
SCC and FAC obtained by regression analysis are illustrated in Figures 3.27 to 3.30 against their
measured data for thermal conductivity, specific heat, thermal expansion, and mass loss
respectively. In these figures, the fitted lines obtained by regression analysis show least deviation
and thus provide a near perfect fit for the measured data. Due to property variations in different
temperature ranges, the proposed equations give either linear or bi-linear and tri-linear relations.
3.5.1

Relations for Thermal Conductivity

The test data clearly indicate that thermal conductivity is influenced mainly by the type of high
strength concrete, moisture retention in concrete and temperature range. To capture this trend
88

separate expressions are developed for thermal conductivity of HSC, SCC, and FAC. For each
concrete type, thermal conductivity relations are presented in two temperature ranges i.e.
between 20-400°C and 400-800°C. These relations are presented in Eqs 3.1 to 3.6.
HSC
kt = 2.5-0.0033T

20°C ≤ T ≤ 400°C

(3.1)

kt = 2.3-0.002T

400°C ≤ T ≤ 800°C

(3.2)

kt = 3.12-0.0045T

20°C ≤ T ≤ 400°C

(3.3)

kt = 3-0.0028T

400°C ≤ T ≤ 800°C

(3.4)

kt = 3-0.0045T

20°C ≤ T ≤ 400°C

(3.5)

kt = 2.6-0.0025T

400°C ≤ T ≤ 800°C

(3.6)

SCC

FAC

3.5.2

Relations for Specific Heat

The specific heat is mainly influenced by type of concrete mix (HSC, FAC, SCC) and
temperature range. The effect of steel and hybrid fibers is minimal throughout the range of
temperature specified. However, polypropylene fibers have some influence on specific heat of
HSC and SCC in 650-800°C temperature range. To capture this trend separate equations are
proposed for polypropylene fiber reinforced HSC and SCC in 400-800°C temperature range.
These relations are presented in Eqs 3.7 to 3.21.

89

HSC
cp = 2.4+0.0002T

20°C ≤ T ≤ 400°C

(3.7)

cp = 2.4+0.0006T

400°C ≤ T ≤ 800°C

(3.8)

cp = 2.4+0.0002T

20°C ≤ T ≤ 400°C

(3.9)

cp = 1.0+0.0043T

400°C ≤ T ≤ 650°C

(3.10)

cp = 9.1+0.009T

650°C ≤ T ≤ 800°C

(3.11)

cp = 2.4+0.0001T

20°C ≤ T ≤ 400°C

(3.12)

cp = 0.6+0.006T

400°C ≤ T ≤ 800°C

(3.13)

cp = 2.4+0.0001T

20°C ≤ T ≤ 400°C

(3.14)

cp = 0.6+0.006T

400°C ≤ T ≤ 650°C

(3.15)

cp = 10.6-0.01T

650°C ≤ T ≤ 800°C

(3.16)

cp = 2.7+0.0004T

20°C ≤ T ≤ 400°C

(3.17)

cp = 0.3+0.0065T

400°C ≤ T ≤ 600°C

(3.18)

For HSC-P only:

SCC

For SCC-P only:

FAC

90

600°C ≤ T ≤ 800°C

(3.19)

cp = 2.63+0.00074T

20°C ≤ T ≤ 400°C

(3.20)

cp = 0.34+0.0021T

400°C ≤ T ≤ 800°C

(3.21)

cp = 3.6+0.0014T

FAC-P

3.5.3

Relations for Thermal Expansion

The expression for thermal expansion of HSC, SCC and FAC are presented in Eqs 3.22-3.28.
Since thermal expansion of HSC has a direct correlation with temperature, a single equation is
developed over entire temperature range. However, as it is observed that low permeability and
presence of mineral and chemical admixtures of SCC and FAC have different influence at
different temperature range; three different thermal expansion relations are presented to capture
the trend. As fibers have no pronounced effect on thermal expansion of HSC or SCC, same
relations can be used for fiber reinforced HSC and SCC.
HSC

εth= -0.5+0.001T

20°C ≤ T ≤ 1000°C

(3.22)

εth= -0.03+0.001T

20°C ≤ T ≤ 200°C

(3.23)

εth= -0.2+0.0017T

200°C ≤ T ≤ 700°C

(3.24)

εth= -0.5+0.002T

700°C ≤ T ≤ 1000°C

(3.25)

SCC

91

FAC

εth= -0.03+0.001T

20°C ≤ T ≤ 200°C

(3.26)

εth= -0.17+0.0013T

200°C ≤ T ≤ 600°C

(3.27)

εth= -0.5+0.0005T

600°C ≤ T ≤ 1000°C

(3.28)

3.5.4

Relations for Mass Loss

Mass of HSC, SCC and FAC are presented in Eqs 3.29-3.37. Since mass loss does not vary
significantly throughout temperature range, a single equation is developed over entire
temperature range for all these concretes. As fibers have no pronounced effect on mass loss of
HSC, SCC and FAC, same relations can be used for fiber reinforced HSC, SCC, and FAC.
HSC
M/M0 = 1

20°C

(3.29)

M/M0 = 1.01-0.0002T

20°C ≤ T ≤ 600°C

(3.30)

M/M0 = 1.25-0.00055T

600°C ≤ T ≤ 800°C

(3.31)

M/M0 = 1

20°C

(3.32)

M/M0 = 1.01-.00014T

20°C ≤ T ≤ 600°C

(3.33)

M/M0 = 1.01-.00016T

600°C ≤ T ≤ 800°C

(3.34)

SCC

92

FAC
M/M0 = 1

20°C

(3.35)

M/M0 = 1.004-.00016T

20°C ≤ T ≤ 600°C

(3.36)

M/M0 = 1.004-.00019T

600°C < T ≤ 800°C

(3.37)

3.6 Summary
Tests were performed to measure high temperature thermal properties of different types of high
performance concrete. For all three HPC (HSC, FAC and SCC), thermal conductivity was
observed to have very little variation, however; specific heat had significant variation with
temperature. Thermal expansion of three HPC increased with temperature and followed almost
similar trend with slight variation for SCC. Similarly, the mass loss did not show any significant
variation as a function of temperature. The presence of fibers in these HPC has an influence on
the specific heat and thermal expansion, but has no effect on thermal conductivity and mass loss
property. Data from tests is utilized to develop high temperature relations for thermal properties
as a function of temperature. The proposed relations for the thermal properties can be used as
input data in computer programs for validations and evaluating the response of HPC structures
exposed to fire.

93

Table 3.1 - Test Matrix for evaluation of thermal properties

S/No

Property

1

Thermal
conductivity

2

Specific heat

3

Thermal
expansion

Temperature
range (and
interval)
(°C)
20 to 400°C
@100°C interval
and 400 to 800°C
@50°C interval
20 to 400°C
@100°C interval
and 400 to 800°C
@50°C interval
20 to 1000°C
@5° C per
minute heating
rate

Test equipment

Hot Disk

Hot Disk

TMA

Concrete types (mixes)
tested
HSC, HSC-S, HSC-P,
HSC-H, SCC, SCC-S,
SCC-P, SCC-H, FAC,
FAC-P, NSC
HSC, HSC-S, HSC-P,
HSC-H, SCC, SCC-S,
SCC-P, SCC-H, FAC,
FAC-P, NSC
HSC, HSC-S, HSC-P,
HSC-H, SCC, SCC-S,
SCC-P, SCC-H, FAC,
FAC-P, NSC

Sensitive
HSC, HSC-S, HSC-P,
balance, calipers HSC-H, SCC, SCC-S,
4
Mass loss
and electric
SCC-P, SCC-H, FAC,
heating furnace FAC-P, NSC
* All types of concrete had 20% extra specimens prepared for testing
20, 100, 200,
300, 400, 500,
600, 700, 800°C

94

Number of
specimens
tested

Total
number of
tests
carried out

28*

14 (11 + 3
repetitions)

28*

14 (11 + 3
repetitions)

33*

33

99*

99

Table 3.2 - Mix proportions of plain HSC, SCC, FAC, and NSC batches
Components

HSC

SCC

FAC

NSC

560

327

420

390

630

735

708

831

1090

904

1040

1038

42

-

42

-

-

-

140

-

76

-

-

3

140

143

105

157

Water cement ratio (w/c)

0.25

0.44

0.25

0.4

Water to cementitious ratio (w/cm)

0.23

0.28

0.18

Air entraining admixture ASTM C3
260, kg/m

-

3

-

.24

-

.80

-

1.63

-

.45

-

-

81

-

230

440

100

150

-

1.0

-

-

Humidity, %

44

45

42

42

Ambient temperature, °C

23

23

24

22

Concrete mix temperature, °C

20

20

20

21

Cement Type I ASTM C-150, kg/m
Fine aggregate ASTM C-33, kg/m

3

3

Course aggregate ASTM C-33 (max
3
size 10 mm), kg/m
Silica Fume, kg/m

3

Fly Ash (Class C) ASTM C-618
3
(25% replacement of cement), kg/m
Slag St Lawrence, kg/m
Water, kg/m

Superplastizer , kg/m

3

3

Retarding Admixture, kg/m

3

High range water reducer ASTM C3
494 (Type F), kg/m
Slump, mm
VSI index

95

-

-

-

Table 3.3 - Mix proportions for fiber reinforced HSC

Components

HSC

HSC-S

HSC-P

HSC-H

560

560

560

560

630

630

630

630

1090

1090

1090

1090

42

42

42

42

-

-

1

1

-

42

-

42

3

140

140

140

140

Water cement ratio (w/c)

0.25

0.25

0.25

0.25

3403

3403

3403

3403

Slump, mm

230

200

100

50

Ambient humidity at casting (%)

44

45

44

44

Ambient temperature, °C

23

23

24

24

Concrete mix temperature at casting, °C

20

20

20

20

Cement Type I ASTM C-150, kg/m
Fine aggregate ASTM C-33, kg/m

3

3

Course aggregate ASTM C-33 (max size 10
3
mm/0.4 inch), kg/m
Silica fume, kg/m

3

Polypropylene fibers, kg/m
Steel fibers, kg/m
Water, kg/m

3

3

Retarding admixture, ASTM C494, mL/m

3

96

Table 3.4 - Mix proportions for fiber reinforced SCC
Components

SCC

SCC-S

SCC-P

SCC-H

327

327

327

327

735

735

735

735

Course aggregate ASTM C-33
3
(maximum size 10 mm), kg/m

904

904

904

904

Slag St Lawrence ASTM C-989, (Grade
3
120), kg/m

76

76

76

76

3

143

143

143

143

Water cement ratio (w/c)

0.44

0.44

0.44

0.44

Water to cementitious ratio (w/cm)

0.35

0. 35

0. 35

0. 35

Air entraining admixture, ASTM C-260,
3
kg/m

3

3

3

3

High range water reducer & plasticizer,
3
ASTM C-494 (Type F), kg/m

81

81

81

81

Slump flow/spread, mm

440

410

420

410

VSI index

1.0

1.0

1.0

1.0

Humidity at casting, %

45

45

45

45

Ambient temperature at casting, °C

23

23

23

23

Concrete mix temperature at casting, °C

20

20

20

20

-

42

-

42

-

-

1

1

Cement type-I ASTM C-150, kg/m
Fine aggregate ASTM C-33, kg/m

water, kg/m

Steel fibers, kg/m

3

3

3

Polypropylene fibers, kg/m

3

97

Table 3.5 - Mix proportions for FAC and FAC-P
Components

FAC

FAC-P

420

420

708

708

1040

1040

42

42

140

140

76

76

-

1

3

135

135

Water cement ratio (w/c)

0.32

0.32

3403

3403

27

27

Slump, mm

100

100

Ambient humidity at casting (%)

47

47

Ambient temperature at casting, °C

24

24

Concrete mix temperature at casting, °C

20

20

Cement (Type I), kg/m
Fine aggregate, kg/m

3

3

Course aggregate (max size 10mm), kg/m
Silica fume, kg/m

3

3

Fly ash - Class C (25% replacement of
3
cement), kg/m
Slag - Grade 120), kg/m

3

Polypropylene fibers, kg/m
Water, kg/m

3

Retarding admixture, mL/m

3

Superplasticizer - Type F, kg/m

3

Table 3.6 - Compressive strength of plain HSC, SCC and FAC mixtures
Compressive strength (MPa)

Age of concrete
(days)

HSC

SCC

FAC

NSC

7

71

46

53

20

28

81

61

72

41

90

90

72

86

50

98

Table 3.7 - Compressive strength of fiber reinforced HSC, SCC and FAC mixtures
Compressive strength (MPa)

Age of concrete
(days)

HSC-S

HSC-P

HSC-H

SCC-S

SCC-P

SCC-H

FAC-P

7

80

72

74

48

45

46

50

28

89

71

67

57

56

57

68

90

90

82

86

70

68

72

74

99

Table 3.8 - Details of specimens for thermal properties for different batches of concrete.

Casted
samples for
thermal
properties

Extracted samples thermal properties

Type of
concrete

Mass loss

Thermal conductivity and specific
heat

Thermal
expansion

100×100×300
mm prisms

S
No

60×60×25 mm prisms

10×18 mm
prisms

75×150 mm
cylinders

1

HSC

2

4

4

12

2

HSC-P

2

4

4

12

3

HSC-S

2

4

4

12

4

HSC-H

2

4

4

12

5

SCC

2

4

4

12

6

SCC-P

2

4

4

12

7

SCC-S

2

4

4

12

8

SCC-H

2

4

4

12

9

FAC

2

4

4

12

10

FAC-P

2

4

4

12

11

NSC

2

4

4

12

100

Table 3.9 - Permeability coefficients for different types of concretes

S No

Concrete type

Permeability
coefficient

1

SCC

2.1×10

2

FAC

1.8×10

3

HSC

1.5×10

4

NSC

2.4-6.8×10

-17
-16
-16

2

Gas permeability (Boel et al., 2008)

2

Gas permeability (Shi et al., 2008)

2

Gas permeability (Noumowé et al., 2009)

m
m
m

Permeability measurement type

-12

Liquid and gas permeability procedures
m/s (Mindess et al., 2003)

101

Steel

Polypropylene

Figure 3.1 - Steel and polypropylene fibers used in the study

(a)

(b)

Figure 3.2 - Typical test specimens for undertaking thermal conductivity and specific heat tests

102

(a) Hot Disk TPS 2500S thermal constants analyzer

(b) Furnace

Figure 3.3 - Test setup and apparatus for room temperature and high temperature thermal
conductivity and specific heat tests

(a) Mica sensor

(b) Kapton sensor

Figure 3.4 - Two types of sensors used with Hot Disk TPS 2500S thermal constants analyzer

103

(a)

(b)

(c)

Figure 3.5 - TMA setup for measurement of thermal strain as a function of temperature
strain

104

Figure 3.6 - Room temperature sample holder

(a) Hot disk sensor being placed
between two concrete specimens

(b) Concrete specimens ready
for thermal property tests
with sensor placed inside

Figure 3.7 - Hot Disk (TPS) mica sensor being used between two specimens of concrete

105

Specimen temperature (°C)

800
700
600
500
400
300
200
100
0
0

5

10

15

20 25 30
Time (hours)

35

40

45

50

Figure 3.8 - Time-temperature graph showing heating rate and stabilizing time for Hot Disk tests
1000

Temperature (°C)

800
600
400
200
0
0

0.5

1

1.5

2

2.5

3

3.5

Time (hours)
Figure 3.9 - Time-Temperature graph showing heating rate for thermal expansion tests

106

Thermal conductivity (W/m.°
C)

4
HSC
SCC
FAC
NSC

3.5
3
2.5
2
1.5
1
0.5
0
0

200

400
Temperature (°
C)

600

800

Figure 3.10 - Measured thermal conductivity as a function of temperature for HSC, SCC, FAC
and NSC

Thermal conductivity (W/m.°
C)

4
HSC
HSC-S
HSC-P
HSC-H

3.5
3
2.5
2
1.5
1
0.5
0
0

200

400
Temperature (°
C)

600

800

Figure 3.11 - Measured thermal conductivity as a function of temperature for plain and fiber
reinforced HSC

107

Thermal conductivity (W/m.°
C)

4
SCC

3.5

SCC-S

3

SCC-P

2.5

SCC-H

2
1.5
1
0.5
0
0

200

400
Temperature (°
C)

600

800

Figure 3.12 - Measured thermal conductivity as a function of temperature for plain and fiber
reinforced SCC

Thermal conductivity (W/m.°
C)

4
FAC

3.5

FAC-P
3
2.5
2
1.5
1
0.5
0
0

200

400
Temperature (°
C)

600

800

Figure 3.13 - Measured thermal conductivity as a function of temperature for FAC and FAC-P

108

6
HSC
Specific heat (MJ/m3K)

5

SCC
FAC

4

NSC

3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 3.14 - Measured specific heat as a function of temperature for different HSC, SCC, FAC
and NSC
6
HSC
Specific heat (MJ/m3K)

5

HSC-S
HSC-P

4

HSC-H

3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 3.15 - Measured specific heat as a function of temperature for plain and fiber reinforced
HSC

109

6
SCC
Specific heat (MJ/m3K)

5

SCC-S
SCC-P

4

SCC-H

3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 3.16 - Measured specific heat as a function of temperature for fiber reinforced SCC
6
FAC
Specific heat (MJ/m3K)

5

FAC-P

4
3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 3.17 - Measured specific heat as a function of temperature for FAC and FAC-P

110

HSC

1.4
Thermal expansion (%)

1.6

SCC
FAC

1.2

NSC

1
0.8
0.6
0.4
0.2
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 3.18 - Measured thermal expansion as a function of temperature for HSC, SCC, FAC and
NSC
1.6
HSC

Thermal expansion (%)

1.4

HSC-S

1.2

HSC-P

1

HSC-H

0.8
0.6
0.4
0.2
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 3.19 - Measured thermal expansion as a function of temperature for plain and fiber
reinforced HSC

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1.6
SCC

Thermal expansion (%)

1.4

SCC-S

1.2

SCC-P

1

SCC-H

0.8
0.6
0.4
0.2
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 3.20 - Measured thermal expansion as a function of temperature for plain and fiber
reinforced SCC

Thermal expansion (%)

1.6

FAC

1.4

FAC-P

1.2
1
0.8
0.6
0.4
0.2
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 3.21 - Measured thermal expansion as a function of temperature for FAC and FAC-P

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Mass loss (%)

1

0.9

HSC
0.8

SCC
FAC
NSC

0.7
0

200

400
600
Temperature (°C)

800

Figure 3.22 - Measured mass loss as a function of temperature for HSC, SCC, FAC and NSC

Mass loss (%)

1

0.9

HSC

0.8

HSC-S
HSC-P
HSC-H

0.7
0

200

400
600
Temperature (°C)

800

Figure 3.23 - Measured mass loss as a function of temperature for plain and fiber reinforced HSC

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Mass loss (%)

1

0.9

SCC
SCC-S
SCC-P
SCC-H

0.8

0.7
0

200

400
600
Temperature (°C)

800

Figure 3.24 - Measured mass loss as a function of temperature for plain and fiber reinforced SCC

Mass loss (%)

1

0.9

0.8
FAC
FAC-P
0.7
0

200

400
Temperature (°C)

600

800

Figure 3.25 - Measured mass loss as a function of temperature for FAC and FAC-P

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HSC

Thermal expansion (%)

1.5

SCC
FAC

1.2

NSC
0.9
0.6
0.3
0
0

200

400
600
Temperature (°
C)

800

1000

Figure 3.26 - Thermal expansion plot showing error bars for standard deviation for HSC, SCC,
FAC, and NSC

Thermal conductivity (W/m.°
C)

4
HSC - test data

3.5

HSC - fitted line

3

SCC - test data

2.5

SCC - fitted line
FAC - test data

2

FAC - fitted line

1.5
1
0.5
0
0

200

400
Temperature (°
C)

600

Figure 3.27 - Thermal conductivity data verses fitted lines for HSC, SCC, and FAC

115

800

7
HSC - test data
HSC - fitted line
SCC - test data
SCC - fitted line
FAC - test data
FAC - fitted line

Specific heat (MJ/m3K)

6
5
4
3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 3.28 - Specific heat data verses fitted lines for HSC, SCC, and FAC
HSC - test data

1.4
Thermal expansion (%)

1.6

HSC - fitted line

1.2

SCC - test data
SCC - fitted line

1

FAC - test data
0.8

FAC - fitted line

0.6
0.4
0.2
0
0

200

400
600
Temperature (°
C)

800

Figure 3.29 - Thermal expansion data verses fitted lines for HSC, SCC, and FAC

116

1000

Mass loss (%)

1

0.9
HSC - test data
HSC - fitted line
SCC - test data
SCC - fitted line
FAC - test data
FAC - fitted line

0.8

0.7
0

200

400
600
Temperature (°C)

Figure 3.30 - Mass loss data verses fitted lines for HSC, SCC, and FAC

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800

CHAPTER 4
4

MECHANICAL PROPERTIES CHARACTERIZATION

This chapter is mainly based on the following journal papers:
•

Khaliq, W., and Kodur, V. K. R. (2010). "Effect of high temperature on tensile strength of
different types of high-strength concrete." Conference Presentation, ACI Spring Convention,
Chicago, IL.

•

Khaliq, W., and Kodur, V. K. R. (2011). "Effect of high temperature on tensile strength of
different types of high-strength concrete." ACI Mater Journal, 108(4), 394-402.

•

Khaliq, W., and Kodur, V. (2011). "High temperature properties of fiber reinforced high
strength concrete." Innovations in Fire Design of Concrete Structures - ACI SP 279, 3-1-42.

•

Khaliq, W., and Kodur, V. (2011). "Thermal and mechanical properties of fiber reinforced
high performance self-consolidating concrete at elevated temperatures." Cement and
Concrete Research, 41(11), 1112-1122.

•

Khaliq, W., and Kodur, V. K. R. (2012). "High temperature mechanical properties of high
strength fly ash concrete with and without fibers." ACI Mater Journal, submitted and
reviewed.

4.1 General
For evaluating fire response of concrete structural members, mechanical properties of high
performance concretes (HPC) are required. These properties include strength, elastic modulus,
stress-strain curves which vary with temperature. As discussed in the literature review Chapter,
there is lack of data on high temperature mechanical properties of HPC. Availability of high
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temperature mechanical property relations for HPC is critical for evaluating the strength
degradation of structural members made of such concrete types.
In order to evaluate the effect of temperature on mechanical properties of HPC, high temperature
property tests on compressive strength, tensile strength, elastic modulus and stress-strain
behavior were carried out. The generated property data was utilized to develop relations for
various mechanical properties as a function of temperature in 20-800°C. Details of experimental
design, test equipment, test procedures and obtained results are discussed in this chapter.

4.2 Design of Mechanical Property Experiments
The test program was designed to undertake high temperature mechanical property tests on three
types of high performance concrete mixes namely HSC, SCC, and FAC. To further study the
effect of fibers on mechanical properties, three types of fibers namely steel, polypropylene and
hybrid fibers were added to HSC, SCC, and FAC concrete mixes. For the tests, a number of
cylinders were fabricated from each batch of concrete. These cylinder specimens were tested at
various temperature points in 20-800°C temperature range to evaluate mechanical properties. For
comparison purpose NSC specimens were also tested for compressive strength and splitting
tensile strength behavior at elevated temperatures. As sufficient data is available for stress-strain
curves and elastic modulus in literature on HSC and NSC mixes, therefore, these tests were not
carried out for NSC, HSC and fiber reinforced HSC to reduce time and effort.
In the absence of standardized test methods for high temperature strength tests on concrete in
ASTM standards, RILEM (2000; 1995) test procedures were mostly followed to evaluate the
mechanical properties of concrete. Special handling techniques were developed as part of this
study to transfer heated cylinders from furnace to strength test machine. For this purpose a
thermal jacket was used to transfer the specimens for compressive strength and stress-strain tests

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and insulated steel bracket frame was used to transfer specimens for splitting tensile strength
tests. The strength test machine was also upgraded to accomplish high temperature tests on
concrete (HPC) cylinders.

4.3 Mechanical Property Tests
Mechanical property tests, namely compressive strength, splitting tensile strength, elastic
modulus and stress-strain curves were carried out on HSC, SCC, FAC and NSC as per test
matrix given in Table 4.1. Details on specimen fabrication, test equipment, and test procedure are
presented in this Section.
4.3.1

Mix Proportions

For mechanical property tests, cylinders were prepared from the same concrete batch mixes
(HSC, SCC, FAC and NSC) as those used for thermal properties and the cylinders were cast at
the same time under similar conditions. The details of the mix proportions, laboratory conditions
at time of casting of these concretes are given in Chapter 3 in Tables 3.1 to 3.4. Room
temperature compressive strength details of for plain and fiber reinforced HSC, SCC, FAC, and
NSC at 7, 28, and 90 days are given in Chapter 3 in Tables 3.5 and 3.6 respectively. The 28 day
compressive strength of different concretes ranged from 52-81 MPa for plain NSC, HSC, SCC,
and FAC as given in Table 3.6. The 28 days compressive strength of fiber reinforced HSC, SCC,
and FAC ranged between 56-89 MPa as given in Table 3.7.
4.3.2

Test Specimens

From each batch of HSC, SCC, FAC, and NSC, two sizes of cylinders were fabricated; 100×200
mm cylinders for room temperature compressive strength tests and 75×150 mm cylinders for
high temperature compressive strength, stress-strain curves, and splitting tensile strength tests.

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The use of smaller cylinders for high temperature properties was due to limitations on heating
chamber of the electrical furnace. The heating chamber is of 150×200 mm size and specimen
smaller than the furnace chamber can fit inside for exposure to high temperature. RILEM (2000;
1995) test standards do not impose a limitation on size of specimens for high temperature
mechanical properties; therefore a specimen size of 75×150 mm cylinder was selected for this
study.
The details on size and number of cylinders for high temperature mechanical properties are given
in Table 4.2. In this table the difference in quantities of cylinders for high temperature strength
tests is due to number of target temperatures tested for that particular concrete type. Two type K
thermocouples (TCs) were embedded in cylinders one in the middle and one on the surface of the
cylinder. Figure 4.1 illustrates these locations of thermocouples on a cylinder. For calibration
purpose, 25% of test cylinders were instrumented with TCs to measure the temperature rise and
stabilization times in the cylinder’s cross-section during heating and also to measure the
temperature drop during the testing process. The age of concrete at the time of mechanical
property tests was 6 months or older.
4.3.3

Test Apparatus

The test setup for measuring mechanical properties consisted of an electric furnace (see Figure
4.2) to heat the concrete cylinders and Forney strength test machine to carry out compressive
strength (including elastic modulus and stress-strain curve tests) and splitting tensile strength
tests. In evaluating strength property at elevated temperatures, appropriate heating conditions
have to be simulated. The electric furnace used to expose cylinders to heating was specially
designed for simulating high temperature conditions and could produce a maximum temperature
up to 927°C. It is equipped with internal heating electric elements, with a ramp and hold

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temperature controller, capable of generating different heating rates. The furnace heating
chamber, with 150×200 mm internal dimensions, is lined with steel jacket to withstand any
possible spalling in concrete cylinders.
Forney strength test machine as shown in Figure 4.3, is a load controlled test machine which
allows to manually control rate of loading during testing. This strength test machine that was
utilized to undertake compressive and splitting tensile strength tests is an 1800 kN load
controlled compressive test machine which is capable of loading cylinders up to 318 metric tons.
For stress stain response tests, modifications were done to the Forney strength test machine by
introducing a 900 kN load cell and two linear variable displacement transducers (LVDTs). These
instruments were connected to a state-of-the-art data acquisition system for recording loaddisplacement response. This data acquisition equipment is based on ‘LabVIEW’ measurement
software, which helps in real-time data recording by automating several measurements from
multiple instruments. Load-displacement measurements were recorded at a frequency of 100
readings/sec and were averaged out to 10 readings/sec as final results.
For handling (transporting) and loading the heated cylinders in compression and splitting tensile
strength tests, special arrangements were made. A thermal jacket was used for moving the heated
cylinders from the furnace to the Forney strength test machine for compressive strength tests (see
Figure 4.4). This thermal jacket composed of 50 mm thick ‘fiberfrax’ high temperature
insulation blanket sheet material (made of refractory ceramic fibers) and was designed to wrap
tightly around heated cylinders. Use of thermal jacket allowed safe and easy transfer of cylinders
for carrying out the compressive strength and stress-strain tests for temperatures up to 800°C.
The thermal jacket also helped to minimize heat loss in the cylinders during testing and it was

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noted through observations on instrumented cylinders that from start of the test to the end of the
test an average temperature drop of only 10°C was recorded in cylinder’s temperature.
Splitting tensile strength test is more complicated as it requires placing of cylinders in a precise
manner under test machine to apply a diametral compressive force as per ASTM C 496 (2011).
This gets further challenging under elevated temperatures when cylinder is heated (up to 800°C)
and it becomes cumbersome to position (align) the cylinder precisely along its diametral lines.
To overcome this problem, a specially designed and insulated steel bracket frame was used to
transfer the heated cylinders from furnace to tensile strength test machine as shown in Figure 4.5.
This frame had an opening of 45x172 mm at the bottom and was designed in such a manner that
the cylinder could be placed on side extending out of this opening. Also two 38 mm wide and 19
mm deep rectangular notches were made on vertical sides of frame so that a steel loading strip of
38x25 mm cross-section would precisely run along and align on top of other diametral side of
cylinder (opposite side of bottom opening in frame) as shown in Figure 4.5. To preserve the
temperature in the cylinder, this frame was insulated with fiberfrax material. Alignment lines
were marked on bracket, as well as on platens of strength test machine, to facilitate aligned
placement. The frame thus helped carrying out splitting tensile strength tests at elevated
temperatures with safe transfer and precise positioning of cylinders (see Figure 4.6).
4.3.4

Test Procedure

4.3.4.1 General Procedure
The mechanical property tests were carried out at various temperature points using unstressed
test method as describe in Section 2.3.2. Figure 4.7 shows the two stages for this test; first the
cylinders are heated without preload to the target temperature, and then moved to strength test
machine for loading. The test parameters, such as age of concrete at testing, loading and heating
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conditions, were followed as per RILEM (2000; 1995). A heating rate (ramp) of 2°C/minute was
selected based on the cylinder size and type of tests as per RILEM test procedure (2000; 1995).
The time-temperature graph shown in Figure 4.8 illustrates the heating ramp used to heat and
hold times required to achieve steady state temperature in the cylinders at a given target
temperature.
Figure 4.9 illustrates the temperature progression in the furnace, on the surface and at the center
of 75×150 mm test cylinder for the case of 600°C target temperature. Three type K
thermocouples (TC), two on the cylinder and one in the furnace (see Figure 4.9(a)) were used to
record temperatures in the furnace, at the surface and mid-depth of the cylinder. As expected, the
rise in temperature at the center of the cylinder was much slower than the surface and furnace
temperature and this is due to low thermal conductivity of concrete (Figure 4.9(b)). It was
observed that a hold time of two hours was required to reach the steady state (uniform
temperature distribution) in the cylinder at all the target temperatures.
To further confirm effect of hold time required for reaching thermal equilibrium, additional
calibration tests were repeated at 100°C with different hold times of 60, 90 and 120 mins. The
effect of different hold times on moisture loss is plotted in Figure 4.10. It can be seen in Figure
4.10 that at 100°C, the core (mid-depth of cylinder) temperature was 68, 87, and 100°C at 60, 90
and 120 mins hold time respectively. The corresponding moisture loss with selected hold times
was 0.65, 0.6, and 0.4% respectively. These results illustrate that a hold time of 120 mins (2
hours) ensures complete thermal equilibrium to be attained across the cross-section of the
cylinder at a target temperature.

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4.3.4.2 Compressive Strength
After achieving steady state condition, the heated cylinders were covered in thermal jacket and
transferred to strength test machine to undertake compressive strength and stress-strain tests. The
cylinders were then moved to strength test machine and gradually loaded at a loading rate of 0.5
MPa per second with a precision of ±1 % (as per RILEM test procedure) till failure occurred and
the failure load was recorded. Figure 4.11(a) shows the cylinder prior to undertaking
compression (and stress-strain) test and Figure 4.11(b) shows a failed cylinder after compression
test. For high temperature compressive strength, one cylinder was tested at each target
temperature. Test was repeated to confirm results at select temperatures where recorded result
was unusual or lied outside the tolerance range. Compressive strength tests for NSC and HSC
(plain and with fibers) were carried out at temperatures 20, 100, 200, 300, 400, 500, 600, and
800°C. For SCC (plain and with fibers) these tests were carried out 20, 100, 200, 400, 600, and
800°C. For FAC and FAC-P the compressive strength tests were done at 20, 200, 400, 600, and
800°C temperatures. The details on the tested temperatures and intervals for compressive
strength are given in Table 4.1.
4.3.4.3 Tensile Strength
After heating, the cylinders were carried in steel bracket frame and transferred to strength test
machine for undertaking splitting tensile strength tests. The cylinders were then gradually loaded
at a loading rate of 0.25 MPa per second till failure occurred and the failure load was recorded.
Figure 4.12(a) illustrates the cylinder prior to undertaking splitting tensile strength test, whereas
Figure 4.12(b) shows a failed cylinder after failure. For high temperature splitting tensile
strength tests, one cylinder was tested at each target temperature. Similar to compressive strength
tests, some tests were repeated only at temperatures where recorded data were unusual or lied

125

outside the tolerance range. Splitting tensile strength tests for NSC and HSC (plain and with
fibers) were carried out at temperatures 20, 100, 200, 300, 400, 500, 600, and 800°C. For SCC
(plain and with fibers) these tests were carried out 20, 200, 300, 400, 600, and 800°C. For FAC
and FAC-P the splitting tensile strength tests were done at 20, 200, 400, 600, and 800°C
temperatures. The details on the tested temperatures and intervals for splitting tensile strength are
also given in Table 4.1.
4.3.4.4 Stress-Strain Curves and Elastic Modulus
Stress-strain curve tests were carried out on SCC and FAC cylinders both with and without
fibers. Figure 4.13 illustrates a cylinder prior to undertaking stress-strain curve test. Test
procedure similar to one for compressive strength test was adopted for stress-strain curve tests.
Load-deformation data was recorded with data acquisition system by loading the cylinders at a
rate of 0.5 MPa per second till failure of the cylinders. While carrying out the tests for stressstrain curves, the failure load was also recorded through control panel of Forney test machine.
This failure load was used to counter check the failure loads from compressive strength tests.
Collected load-deformation data was used to evaluate stress-strain curves for tested concretes.
Elastic modulus for SCC and FAC was calculated from the measured stress-strain curves. Elastic
modulus at room temperature is generally evaluated as the slope of compressive stress-strain
curve corresponding to 40% of stress (ASTM C39, 2009). This approach was extended to
evaluate the modulus at high temperatures. For SCC (plain and with fibers), stress strain curves
and elastic modulus was evaluated 20, 100, 200, 400, 600, and 800°C temperatures, whereas for
FAC and FAC-P, these properties were evaluated at 20, 200, 400, 600, and 800°C temperatures.
The details on the tested temperatures and intervals of these stress-strain tests are given in Table
4.1.

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4.4 Results and Discussion
Results from above tests are utilized to discuss the effect of temperature on strength and modulus
properties of plain and fiber reinforced HSC, SCC, and FAC in this section. To compare the
strength loss with temperature, compressive and tensile strength results of conventional NSC are
also discussed included with plain HSC. Effect of fibers on high temperature strength for
particular type of concrete is also discussed in separate sub-sections.
4.4.1

Compressive Strength

The recorded applied load at which the heated cylinder failed in compression was used to
compute compressive strength at each temperature and these values are plotted as a function of
temperature for NSC, HSC, SCC and FAC in Figure 4.14. For all four concretes, compressive
strength decreases with temperature which can be attributed to physical and chemical changes
that occur in concrete at higher temperatures. This loss is significant in HSC and FAC as
compared to NSC and SCC especially at temperatures beyond 300°C. SCC exhibits minimum
strength loss throughout 20-800°C temperature range. The higher drop of compressive strength
at 100°C in SCC can be attributed to excessive moisture loss at 100°C as SCC has the higher
amount of initial moisture content (higher w/c ratio). Of different concretes, FAC exhibits
maximum compressive strength loss especially in 20-400°C temperature range.
The relative compressive strength loss in NSC, HSC, SCC and FAC follows similar trend to its
absolute strength as shown in Figure 4.15. NSC displays the least loss of compressive strength
ratio as compared to HSC. It can be seen that both SCC and NSC exhibit better compressive
strength ratio with about 35% of retention of compressive strength at 800°C as compared to HSC
and FAC. Moisture content in concrete plays a significant role in retention of compressive

127

strength in high performance concretes. As in the case of HSC and FAC, low moisture content
caused early desiccation leading to higher strength loss as compared to SCC and NSC.
4.4.1.1 High Strength Concrete
The compressive strength evaluated at each temperature is plotted as a function of temperature
for HSC with and without fibers in Figure 4.16. In all types of concrete, physical and chemical
changes that occur at elevated temperatures lead to significant reduction of compressive strength.
HSC (plain and with fibers) gradually lose strength with temperature in 20-800°C range in a
similar trend. This loss is slightly higher in 20-400°C and can be attributed to dense
microstructure of HSC that undergoes more thermal stresses from evaporation of moisture up to
400°C and does not let water vapors to escape easily. This effect has been established by Castillo
and Durrani (Castillo and Durrani, 1990) that moisture in concrete has detrimental effect on high
temperature compressive strength of HSC. It can be seen that fibers do not have much effect on
high temperature compressive strength of HSC. Beyond 400°C, all four HSCs exhibit similar
trend of slower strength loss. This degradation in strength can be attributed to slow disintegration
of microstructure due slower loss of chemically bound water in 400-800°C temperature range.
The ratio of recorded compressive strength f’c,T/f’c for HSC with and without fibers is shown
in Figure 4.17. The strength loss is higher in 20-400°C range and lowers in 400-800°C range.
This can be attributed to higher loss of physically bound moisture in concrete up to 400°C as
explained above. Fibers do not have much pronounced effect on the compressive strength of
HSC both at room temperature and at higher temperature.

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4.4.1.2 Self-Consolidating Concrete
Measured compressive strength of SCC and fiber reinforced SCC is plotted as a function of
temperature in Figure 4.18. For SCC, there is an initial reduction in compressive strength at
100°C and then strength regain at 200°C. SCC is produced with higher water cement ratio;
therefore the strength loss at 100°C can be attributed to initial moisture loss which is higher in
case of SCC. The increase in strength in 100-200°C temperature range can be attributed to
rehydration and moisture migration (Dias et al., 1990; Fares et al., 2010).
It has been established that moisture in concrete has significant effect on high temperature
compressive strength of concrete (Castillo and Durrani, 1990). For initial moisture loss up to
100°C, due to evaporation of free water, the strength drops sharply; however, with excess loss of
free water (SCC is produced with higher w/c ratio), compressive strength stabilizes at
temperatures between 100 and 400°C. Beyond 400°C the strength loss becomes gradual with
increase in temperature for SCC and fiber reinforced SCC. This gradual degradation of strength
(without substantial drop) can be attributed to slow loss of chemically bound water due to
dehydration and disintegration of C-S-H in concrete (FIB Bulletin 38, 2007). In the case of fiber
reinforced SCC the loss of compressive strength with temperature is about same for SCC-S,
SCC-P and SCC-H throughout temperature range. This can be deduced that the addition of fibers
does not have much effect on the variation of compressive strength of SCC with temperature.
The ratio of recorded compressive strength at target temperature f’c,T to compressive strength at
room temperature f’c for SCC and fiber reinforced SCC is shown in Figure 4.19. The relative
strength loss in all concretes follow similar trend to its absolute strength. The initial strength
reduction at 100°C temperature is attributed to excess moisture lost as SCC (plain and with

129

fibers) is produced with higher w/c ratio. There is noticeable strength retention in SCC (with and
without fibers) even at 800°C and this range from 30 to 44%. This level of strength retention is
much higher than conventional HSC, which has less than 20% relative compressive strength at
800°C (Chen and Liu, 2004; Felicetti and Gambarova, 1998). This observation confirms that
high strength SCC has superior microstructure and therefore displays better compressive strength
even at higher temperatures.
4.4.1.3 Fly-ash Concrete
The compressive strength of FAC and FAC-P, which is plotted in Figure 4.20, decreases with
temperature in 20-800°C. In the case of FAC, which has a compressive strength of 86 MPa at
room temperature, there is high reduction in compressive strength at 200°C initially, followed by
gradual loss in 200-600°C and then again rapid decrease in 600-800°C range. The initial strength
loss up to 200°C can be attributed to damage caused by thermal stresses from pore pressure.
After the moisture is driven out and pore pressure reduces, the strength loss becomes gradual in
200-600°C and this is mainly due to spreading of microcracks. The high degradation of
compressive strength of FAC above 600°C can be attributed to both physical and chemical
transformation of concrete that takes place between 600 and 800°C, resulting in decomposition,
softening and loss of binder property in concrete (Khoury et al., 1985).
Unlike FAC, FAC-P experiences gradual loss in compressive strength throughout 20-800°C
range. Despite lower initial compressive strength at room temperature (than FAC), FAC-P shows
significant retention in tensile strength throughout 20-800°C. The moisture in concrete turns in to
vapors above 100°C and induces pore pressure resulting in thermal stress on microstructure of
concrete. This pore pressure gets alleviated due to increased porosity by melting of
polypropylene fibers around 162°C temperature and reduces thermal stresses, which is a reason
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for low degradation of compressive strength in FAC-P. In comparison to conventional HSC,
FAC follows almost similar trend of strength loss in the entire temperature range. This shows
that compressive strength variation of FAC is almost similar to that of conventional HSC.
The ratio of recorded compressive strength at target temperature (f’c,T) to that at room
temperature (f’c) for FAC, FAC-P is shown in Figure 4.21. The relative strength loss in FAC and
FAC-P follows similar trend to absolute strength variation, however, FAC-P shows much
improvement in strength retention in 200-600°C range as compared FAC. This can be attributed
to less damage to microstructure of FAC-P, facilitated through increased porosity resulting from
melting of polypropylene fibers.
4.4.2

Splitting Tensile Strength

The recorded applied load at which the cylinders failed were used to compute splitting tensile
strength (T) as per ASTM C496 (2004), using formula T=2P/πld, where (P) is the failure load,
(l) is the length and (d) is the diameter of the tested cylinder. Measured splitting tensile strength
of NSC, HSC, SCC and FAC is plotted as a function of temperature in Figure 4.22. It can be
seen that all concrete types experience loss in tensile strength with temperature. Loss in splitting
tensile strength is dependent on the physical and chemical changes that occur at higher
temperatures. Except SCC, other concrete types exhibit similar trend in loss of splitting tensile
strength throughout 20-800°C temperature range; however in SCC tensile strength was degrade
less in 20-400°C temperature range. FAC exhibited lower splitting tensile strength among tested
HPC. Beyond 400°C all concretes significantly lose splitting tensile strength mainly because of
excessive thermal stresses and thermal incompatibility within the concrete matrix. Moreover

131

development and spread of micro and macro cracks effect loss of tensile strength more as
compared to compressive strength as these expedited the splitting of cylinder under compression.
The relative splitting tensile strength loss in NSC, HSC, SCC and FAC is illustrated in Figure
4.23. Loss of splitting tensile strength in HSC and FAC is similar to conventional NSC. In
comparison, SCC exhibits higher tensile strength ratio, especially this ratio is significant and
noteworthy in 20-400°C temperature range. This increase in tensile strength is of much
advantage in mitigating the fire induced spalling in SCC and therefore can enhance the fire
resistance rating of RC members made of SCC.
4.4.2.1 High Strength Concrete
Figure 4.24 illustrates the splitting tensile strength as a function of temperature for HSC with and
without fibers. Splitting tensile strength reduces with temperature in all four concretes up to
800°C. In both HSC-S and HSC-H, significant retention in splitting tensile strength is observed
up to 300°C which can be effective in minimizing fire induced spalling. This retention in tensile
strength can be attributed to effectiveness of steel fibers in bridging cracks under tensile loading.
Shah (1991) deduced that fibers substantially enhance room temperature tensile strength of
concrete, as fibers suppress localization of microcracks into macrocracks and consequently
tensile load capacity of concrete increases. In case of plain HSC and HSC-P the tensile strength
loss is higher in 20-800°C temperature range compared to HSC-S and HSC-H.
The ratio of recorded splitting tensile strength f’t,T/ f’t for HSC and fiber reinforced HSC (HSCS, HSC-P, and HSC-H) is shown in Figure 4.25. The ratio of tensile strength loss is higher for
HSC and HSC-P in 20-400°C where as it is least for HSC-S and HSC-H. This can be attributed
to effectiveness of steel fibers which arrest crack initiation and propagation. Test data indicates

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that HSC and fiber reinforced HSC retain about 35% to 45% of original tensile strength at 600°C
which is quite significant and can be effective to mitigate spalling.
4.4.2.2 Self-Consolidating Concrete
Figure 4.26 illustrates the degradation of splitting tensile strength in SCC and fiber reinforced
SCC (SCC-S, SCC-P, and SCC-H) as a function of temperature. In the case of SCC which has a
lower tensile strength of 4 MPa at room temperature, the reduction in tensile strength is gradual
and almost linear in SCC up to 400°C and then there is sharp reduction in tensile strength to
800°C. This sharp reduction in splitting tensile strength beyond 400°C can be attributed to the
development of excessive micro and macro cracks resulting from thermal stresses and thermal
incompatibility within SCC. This is in line with the reported data by Sideris (2007), Chan (1999)
and Khoury (1992 ).The slower degradation of strength (without substantial changes) at early
stages in all SCC’s can be attributed to its higher stiffness as compared to fiber reinforced SCC.
Both SCC-S and SCC-H display higher ratio of splitting tensile strength in 300-800°C
temperatures range which can be attributed to presence of steel fibers which help arrest the
development and propagation of micro and macro crack under tensile loading. SCC-P has the
lowest splitting tensile strength beyond 250°C which indicates that after melting of
polypropylene fibers at about 180°C there is significant degradation in its microstructure
resulting from increased porosity.
Figure 4.27 illustrates the ratio of recorded splitting tensile strength at a target temperature f’t,T
to the splitting tensile strength at room temperature f’t for SCC (plain and with different fiber
combinations). The ratio plotted in these figures indicates that addition of polypropylene fibers to
SCC caused more reduction in splitting tensile strength as can be observed for SCC-P and SCC133

H. Also the figure shows that SCC and fiber reinforced SCC retain about 40 -50% of its tensile
strength at 600°C and this is quite significant as compared to plain HSC which has only 30% of
its retained tensile strength at 600°C.
4.4.2.3 Fly-ash Concrete
Figure 4.28 shows the splitting tensile strength for FAC and FAC-P as a function of temperature.
For FAC, which has a lower initial tensile strength of 4.2 MPa, the reduction in tensile strength is
gradual and is almost linear in 20-800°C. This gradual degradation of strength (without
substantial changes) can be attributed to enhanced microstructure that results from reaction of fly
ash with calcium hydroxide formed during hydration of cement. In the case of FAC-P, the loss in
tensile strength is similar to FAC up to 200°C. In both FAC and FAC-P, the early loss of tensile
strength in 20-200°C can be attributed to the progression of microcracks resulting from the
temperature induced pore pressure.
FAC-P retains significant tensile strength in 200-800°C range and this can be attributed to lesser
microstructural damage in concrete facilitated through increased porosity resulting from melting
of polypropylene fibers at about 162°C. This increased porosity helps in alleviation of pore
pressure generated from moisture movement in FAC-P and reduces the extent of microstructure
damage within the matrix and this helps in retention of higher tensile strength up to 600°C.
The ratio of recorded splitting tensile strength at target temperature (f′t,T) to splitting tensile
strength at room temperature (f′t) for FAC and FAC-P is shown in Figure 4.29. Measured test
data indicates that FAC and FAC-P have about 23, 48% of f′t,T / f′t at 600°C respectively that is
in the range of reported data for high strength concretes, by other authors (Behnood and

134

Ghandehari, 2009; Li et al., 2004). The improved tensile strength of FAC-P in entire temperature
range, as compared to other two concrete types, is mainly due to the beneficial effect of
polypropylene fibers that minimizes cracking in concrete as shown in Figure 4.29.
4.4.3

Elastic Modulus

The elastic modulus of concrete is dependent on moisture content and microstructure of hydrated
cements products in paste (Bažant and Kaplan, 1996). As physical and chemical changes occur
in concrete due to increase in temperature, elastic modulus degrades with temperature. Data
generated from compressive stress-strain curves was used to obtain elastic modulus of different
concretes at various temperatures.
4.4.3.1 Self-Consolidating Concrete
Figure 4.30 illustrates the relative elastic modulus (Ec,T/Ec) for SCC (plain and fiber reinforced)
as a function of temperature. The elastic modulus for all four concretes decrease in 20-800°C
temperature range. SCC exhibits lower elastic modulus which can be attributed to thermal
damage to dense microstructure of SCC as compared to SCC-S, SCC-P and SCC-H. Use of
fibers in SCC mix helped reduce (slow down) the degradation in modulus. This is achieved
through melting of polypropylene fibers as they help alleviate pore pressure (thermal stresses),
steel fibers help reduce propagation of micro and macro cracks and hybrid fibers help reduce
both of these affects combined. SCC-H therefore exhibits the least deterioration in elastic
modulus as compared to other types. The reduction in elastic modulus in SCC is similar to that
reported by Persson (2004) and Bamonte and Gambarova (2010). However, the ratio of
reduction for elastic modulus of fiber reinforced SCC is much less compared to SCC which is

135

attributed to presence of different fibers to SCC mix that enhances its elastic modulus at higher
temperatures.
Modulus for SCC-S and SCC-H initially remains constant up to 100°C and then sharply reduces
up to 200°C before gradual decay in the temperature range of 200-800°C. The higher modulus
observed in SCC-S and SCC-H can be attributed to increased ductility due to the presence of
steel fibers which act as crack arresters as these provide necessary bond against development of
cracks. The addition of polypropylene fibers in SCC-P show higher degradation of elastic
modulus in 20-200°C temperature range, in comparison to SCC-S and SCC-H. This higher loss
in elastic modulus is higher in 20-200°C, but this degradation reduces above 200°C, after
melting of polypropylene fibers.
4.4.3.2 Fly-ash Concrete
Measured elastic modulus for FAC and FAC-P at various temperatures is shown in Figure 4.31.
For both FAC and FAC-P, the modulus of elasticity remains almost constant up to 200°C,
decreases at a faster rate up to 600°C, and then finally stabilizes in 600-800°C reaching to about
7-8% at 800°C. This loss in elastic modulus with temperature is attributed to physical and
chemical changes and thermal incompatibility of constituents. The loss of moisture due to high
temperature and degradation of microstructure concrete results development of and propagation
of micro and macro cracks that lead to degradation of elastic modulus.
In 200-600°C, FAC-P retains higher elastic modulus as compared to FAC and this can be
attributed to relatively lower damage that occurs in FAC-P facilitated by melting of
polypropylene fibers that reduces crack propagation under thermal stresses. Also, FAC has lower
elastic modulus than that of conventional HSC in 200-600°C range and this is primarily due to

136

higher temperature induced damage in FAC resulting from dense microstructure and reduced
permeability because of secondary hydration of fly ash in the mix (Nasser and Marzouk, 1979).
4.4.4

Stress-Strain Curves

The recorded load-deformation data in compressive stress-strain response was utilized to
generate stress-strain curves at various temperatures for different HPC. The stress-strain response
was obtained by measuring load-deformation through load controlled technique; as a result the
descending branch of most of the curves could not be captured in totality. However, in some
cases (such as SCC-S and SCC-H) where steel fiber was used in the mix, short descending
branch of nonlinear portion of the curves could be captured due to their ductile response. As high
temperature stress-strain response of HSC is available in literature, the stress-strain curves for
SCC and FAC (with and without fibers) are presented in this section.
4.4.4.1 Self-Consolidating Concrete
Stress-strain curves for SCC, SCC-S, SCC-P, and SCC-H are plotted in Figures 4.32 to 4.35
respectively. At room temperature, both SCC and SCC-S, show linear-elastic response up to
about 80% of peak stress. It can also be observed that room temperature peak stress decreases
and peak strain increases in SCC-S and SCC-H as compared to SCC and SCC-S. It can be
inferred that polypropylene fibers in SCC-P and SCC-H do not contribute much to the ductility
of concrete. However, presence of steel fibers in both SCC-S and SCC-H has significantly
enhanced the ductility of these concretes as shown in Figures 4.33 and 4.35.
For SCC and fiber reinforced SCC, the gradient (slope) of stress-strain curves decrease with
temperature showing a drop in peak stress, and increase in peak strain. The plotted total strain is
mainly composed of mechanical stain due to loading and thermal strain due to temperature. As

137

the tested were done by unstressed test method (heating without applied load), therefore the
creep and transient strains are not significant in the measured (total) strain. In all these concrete,
development of micro and macro cracks due to high temperatures lead to rapid increase in peak
strains. Figures 4.32 to 4.35 illustrate that SCC-S and SCC-H attains higher peak strains as
compared to SCC and SCC-P with increasing temperature. The attainment of higher strains in
SCC-S and SCC-H can be attributed to two factors, namely stress-induced thermal strain and
arresting of crack development due to presence of steel fibers. It is reported by Bažant and Chern
(1987) that the stress-induced thermal strain in concrete is due to micro diffusion of pore water
between capillary pores and gel pores. Therefore, higher peak strain in SCC-S and SCC-H can be
attributed to additional thermal strain caused by easy diffusion of pore water facilitated due to
increased ductility resulting from steel fibers.
4.4.4.2 Fly-ash Concrete
Figures 4.36 and 4.37 illustrate the stress-strain curves for FAC and FAC-P respectively at
various temperatures. At room temperature, both FAC and FAC-P, show linear-elastic response
up to about 80% of peak stress similar to high strength SCC and SCC-P. For FAC-P, short
descending branch of nonlinear portion of the curves could be captured due to ductile response
of FAC-P. It can also be observed that room temperature peak stress decreases and peak strain
increases in FAC-P as compared to FAC. It can be seen that presence of polypropylene fibers has
some contribution on its improved ductility.
For both FAC and FAC-P, the gradient of stress-strain curves decrease with temperature showing
a drop in peak stress, and increase in peak strain. The plotted total strain is mainly composed of
mechanical stain due to loading and thermal strain due to temperature due to similar reasons that
the tested cylinders were not loaded during heating. Therefore the creep and transient strains are

138

not significant in the measured (total) strain for FAC and FAC-P too. In both FAC and FAC-P
cylinders, larger macrocracks develop at temperatures above 400°C and these cracks further
widen around 600°C leading to rapid increase in strains above 400°C. Figures 4.37 illustrates
that FAC-P attains higher peak strains as compared to FAC at higher temperature. The
attainment of higher strains in FAC-P can also be attributed the phenomenon explained for
higher strains in SCC-S and SCC-H. Therefore, higher peak strain in FAC-P can be attributed to
additional thermal strain caused by easy diffusion of pore water facilitated due to increased
porosity resulting from burning of polypropylene fibers and increase in macrocracks due to
elevated temperature.
4.4.5

Temperature Induced Spalling

While carrying out the high temperature material property tests on HSC, SCC, and FAC (plain
and with different fiber combinations), no spalling was observed during heating or testing at
elevated temperatures. It should be noted that the heating ramp selected for tests was 2°C per
minute as per RILEM test standards for high temperature mechanical property tests (RILEM TC
129-MHT, 2000; RILEM TC 129-MHT, 1995). Fire induced spalling is generally associated
with faster heating rates, therefore a heating rate of 2°C per minute is considered to be quite low
to cause any spalling in HPC. It is envisaged that a higher heating rate has an effect on the
spalling behavior of concrete; however, the increased splitting tensile strength and porosity in
case of fiber reinforced concrete will help to minimize the spalling associated with fire. A fiber
dosage of 0.1 – 0.5% by volume has been suggested (Ali et al., 2004; Bentz, 2000; Kodur, 2000)
to mitigate spalling in HPC, however, the present dosage of 0.11% of polypropylene fibers and
0.54% of steel fibers by volume could not verify it due to the lower heating rate.

139

4.4.6

Summary

The mechanical properties of HPC namely, compressive strength, splitting tensile strength,
elastic modulus and stress-strain response deteriorates with temperature. Addition of steel,
polypropylene, and hybrid fibers do not have much effect on high temperature compressive
strength of HPC. However, addition of polypropylene fibers slows down degradation of
compressive strength in FAC with temperature. Steel fibers significantly reduce the degradation
of tensile strength, elastic modulus and stress-strain response in HSC and SCC. The low
degradation on tensile strength up to 400°C in HSC and SCC can be beneficial to reduce fire
induced spalling. Polypropylene fibers do not have much effect on stress-strain curves of SCC-P,
however strain at peak stress was increased in FAC-P. Elastic modulus of FAC and FAC-P does
not degrade significantly up to 200°C, however rapid deterioration of elastic modulus occurs in
200-600°C. Comparatively FAC experiences higher degradation of elastic modulus as compared
to FAC-P in entire 20-800°C range.

4.5 Relations for Mechanical Properties
4.5.1

General

Data generated from the mechanical property measurements is utilized to develop mechanical
property relations for HSC, SCC, and FAC (plain and with different fibers). These properties are
expressed in the form of empirical relations over temperature range of 20-800°C for compressive
strength, splitting tensile strength and elastic modulus. The empirical relations were arrived at
based on linear regression. For the regression analysis, measured mechanical properties were
used as response parameter with temperature as their predictor parameter.

140

The procedure used for linear regression analysis for mechanical properties is similar to that
adopted in developing for thermal property relations as discussed in Chapter 3, Section 3.4. The
procedure for estimating the parameters of any linear model (linear fitting), the method of least
squares can be used by fitting a straight line to a set of data points (Wackerly et al., 2008 ). The
least-squares procedure is used for fitting a line through a set of ‘n’ data points where it is
desired that the differences between the observed values and corresponding points on the fitted
line should be minimum. A convenient way to accomplish this, and one that yields estimators
with good properties, is to minimize the sum of squares of the standard deviations from the fitted
line. In the case of mechanical properties, these deviations in the response value (mechanical
property) given by the predicted value (temperature) is called the error and to reduce these
deviations in response values, sum of squares of deviations/error called sum of squares of error
(SSE) is utilized.
Commercially available statistical software (Minitab) was also used to carry out the regression
analysis of the mechanical property experimental results similar to thermal properties. For
2

regression analysis, coefficient of determination R (Wackerly et al., 2008 ) defines the accuracy
2

of the best fit equations. This, R can be interpreted as the proportion of the total variation in the
response that is explained by the variable prediction in a simple linear regression model. The
2

accuracy of the statistical model is represented by coefficient of determination ‘R ’, that
represents proportion of the sum of squares of deviations of the response values about their
2

predictor (Mendenhall and Sincich, 2007). The values of coefficient of determination ‘R ’
obtained for the proposed mechanical property equations lies between 0.8-0.95 that represents a
reasonably high confidence level in light of high variability in mechanical properties.

141

Figures 4.38 and 4.39 illustrate the measured compressive strength of SCC and FAC with and
without fibers along with typical fitted line by regression analysis for similar concretes. It can be
seen in these figures that the plots predicted by the empirical relations are in good agreement
with the test data.
The variation of compressive strength (f’c,T), tensile strength (f’t,T) and elastic modulus (ET)
with temperature can be related through a coefficient βT representing ratio of respective strength
at target temperature to that at room temperature (f’c, f’t, and E0) given by Eqns 4.1 to 4.3. Due
to least variation in compressive strength of HSC and SCC (with and without fibers); single
representative relation is presented for compressive strength. However, because of significant
variation in tensile strength relations are presented separately for HSC and SCC (with and
without fibers). Also separate relations are presented for SCC (with and without fibers) due to
significant variation of high temperature elastic modulus. Due to property variations in different
temperature ranges, the proposed equations give either linear or bi-linear and tri-linear relations.
These empirical relations can be used for HPC up to a compressive strength of 100 MPa and
tensile strength of 7 MPa. The strength reduction coefficient ratio (βT) for compressive strength,
splitting tensile strength and elastic modulus is given as:

βT,compressive= f’c,T/ f’c

(4.1)

βT,tensile= f’t,T/ f’t

(4.2)

βT,modulus= ET/ E0

(4.3)

142

The value of βT for respective mechanical property at different temperatures can be obtained
from Eqns 4.4 to 4.42 for plain and fiber reinforced HSC, SCC and FAC. In lieu of equations,
Table 4.3 and 4.4 give reduction factor βT for compressive and splitting tensile strength of HSC
and fiber reinforced HSC. Similarly, Table 4.5 and 4.6 give reduction factors βT for
compressive, splitting tensile strength and elastic modulus of plain and fiber reinforced SCC and
FAC respectively. This reduction factor βT at different temperatures can be used for evaluating
compressive strength, splitting tensile strength and elastic modulus for these concretes. Using
these values of reduction factors βT for compressive, splitting tensile strength, and elastic
modulus of plain and fiber reinforced HSC, SCC, and FAC the constitutive curves are obtained
as shown in Figures 4.40 to 4.47. These figures show the constitutive plots based on the
empirical relations derived from the experimental data in this study.
4.5.2

Relations for Compressive Strength

HSC, HSC-S, HSC-P and HSC-H
βT,compressive = 1.0

20°C

(4.4)

βT,compressive = 1.0 -0.0016T

100°C ≤ T ≤ 400°C

(4.5)

βT,compressive = 0.74 -0.0008T

400°C ≤ T ≤ 800°C

(4.6)

20°C

(4.7)

SCC, SCC-S, SCC-P, and SCC-H:
βT,compressive = 1.0

143

βT,compressive = 0.99 -0.002T

100°C ≤ T ≤ 200°C

(4.8)

βT,compressive = 0.73 -0.0005T

200°C ≤ T ≤ 800°C

(4.9)

βT,compressive = 1.0

20°C

(4.10)

βT,compressive = 0.78 -0.0009T

200°C ≤ T ≤ 800°C

(4.11)

βT,compressive = 1.0

20°C

(4.12)

βT,compressive = 1.09 -0.0012T

200°C ≤ T ≤ 800°C

(4.13)

βT,tensile = 1.0

20°C

(4.14)

βT,tensile = 0.97 -0.0011T

100°C ≤ T ≤ 800°C

(4.15)

βT,tensile = 1.0

20°C

(4.16)

βT,tensile = 0.9

100°C

(4.17)

βT,tensile = 1.42 -0.0018T

300°C ≤ T ≤ 800°C

(4.18)

FAC

FAC-P

4.5.3

Relations for Splitting Tensile Strength

HSC

HSC-S

HSC-P

144

βT,tensile = 1-0.002T

20°C ≤ T < 200°C

(4.19)

βT,tensile = 0.82-0.001T

200°C ≤ T ≤ 800°C

(4.20)

βT,tensile = 1.0

20°C

(4.21)

βT,tensile = 0.78

100°C ≤ T < 300°C

(4.22)

βT,tensile = 1. 28-0.0016T

400°C ≤ T ≤ 800°C

(4.23)

βT,tensile = 1.0

20°C

(4.24)

βT,tensile = 0.98-0.001T

100°C ≤ T < 800°C

(4.25)

βT,tensile = 1.0

20°C

(4.26)

βT,tensile = 1.1-0.001T

100°C ≤ T < 800°C

(4.27)

βT,tensile = 1.0

20°C

(4.28)

βT,tensile = 1.05-0.0013T

200°C ≤ T < 800°C

(4.29)

20°C

(4.30)

HSC-H

For SCC and SCC-P:

For SCC-S and SCC-H:

FAC

FAC-P
βT,tensile = 1.0

145

βT,tensile = 1.0

20°C

(4.30)

βT,tensile = 0.98-.0006T

200°C ≤ T < 400°C

(4.31)

βT,tensile = 1. 44-0.0017T

400°C < T ≤ 800°C

(4.32)

4.5.4

Relations for Elastic Modulus

For SCC and SCC-P:
βT,modulus = 1.0

20°C

βT,modulus = 0.84-0.001T

100°C ≤ T ≤ 800°C

(4.33)
(4.34)

For SCC-S and SCC-H:
βT,modulus = 1.0

20°C

(4.35)

βT,modulus = 1.1-0.002T

100°C ≤ T < 200°C

(4.36)

βT,modulus = 0.88-0.008T

200°C ≤ T ≤ 800°C

(4.37)

FAC
βT,modulus = 1.0

20°C

(4.38)

βT,modulus = 0.97

200°C

(4.39)

βT,modulus = 0.74-0.0009T

400°C ≤ T ≤ 800°C

(4.40)

FAC-P
βT,modulus = 1.0

20°C

146

(4.41)

βT,modulus = 1.24-0.0015T

200°C ≤ T ≤ 800°C

(4.42)

4.6 Summary
Tests were performed to characterize high temperature compressive strength, splitting tensile
strength, elastic modulus and stress-strain curves for HPC. For all tested HPC, these high
temperature properties deteriorate with temperature. Addition of steel, polypropylene and hybrid
fibers do not influence the high temperature compressive strength, however it does have an effect
on splitting tensile strength and elastic modulus as fibers (steel, polypropylene, and hybrid) help
reduce deterioration in these properties due to rising temperatures. Data from the tests is utilized
to develop high temperature relations for compressive strength, splitting tensile strength, and
elastic modulus of HPC. The proposed relations can be used as input data in computer programs
for evaluating the fire response of HPC structures exposed to fire.

147

Table 4.1 - Test matrix for evaluation of high temperature mechanical properties

S/No

1

Property

Compressive
strength

Temperature
range (and
interval)
(°C)

Test
equipment

20-800°C @100
and 200°C
interval**

Elect furnace,
thermal jacket,
Forney strength
test machine

Concrete types
(mixes) tested
NSC, HSC, HSC-S,
HSC-P, HSC-H,
SCC, SCC-S, SCCP, SCC-H, FAC,
FAC-P, NSC
NSC, HSC, HSC-S,
HSC-P, HSC-H,
SCC, SCC-S, SCCP, SCC-H, FAC,
FAC-P, NSC

Elect furnace,
20-800°C @100 steel bracket
Tensile
2
and 200°C
frame, Forney
strength
interval**
strength test
machine
Elect furnace,
20-800°C @100
SCC, SCC-S, SCCElastic
thermal jacket,
3
and 200°C
P, SCC-H, FAC,
modulus
Forney strength
interval**
FAC-P, NSC
test machine
Elect furnace,
20-800°C @100
SCC, SCC-S, SCCStress-strain
thermal jacket,
4
and 200°C
P, SCC-H, FAC,
curves
Forney strength
interval**
FAC-P, NSC
test machine
* All types of concrete had 20% extra cylinders prepared for testing
** Temperature intervals varied for different concretes

148

Number of
cylinders
tested
(75x150
mm)

222*

222*

108*

108*

Table 4.2 - Details of cylinders for different batches of concrete.

S No

Type of
concrete

Room
temperature
compressive
strength

High temperature
compressive
strength

High temperature
tensile strength

Cylinder sizes
100×200 mm
cylinders

1
2
3
4
5
6
7
8
9
10
11

HSC
HSC-P
HSC-S
HSC-H
SCC
SCC-P
SCC-S
SCC-H
FAC
FAC-P
NSC

75×150 mm
cylinders

75×150 mm
cylinders

18
18
18
18
15
15
15
15
15
15
12

24
24
24
24
18
18
18
18
18
18
18

24
24
24
24
18
18
18
18
18
18
18

149

Table 4.3 - Compressive strength reduction factor βT at different temperatures for HSC and fiber
reinforced HSC.

Temperature -°C
20
100
200
300
400
600
800

Compressive strength reduction factor ሺ઺‫ ܂‬ሻ
HSC
1
0.9
0.8
0.7
0.52
0.35
0.2

HSC-P
1
0.9
0.9
0.9
0.7
0.5
0.34

HSC-S
1
0.8
0.6
0.52
0.45
0.38
0.3

HSC-H
1
0.78
0.78
0.78
0.66
0.52
0.36

Table 4.4 - Splitting tensile strength reduction factor βT at different temperatures for HSC and
fiber reinforced HSC.

Temperature -°C
20
100
200
300
400
600
800

Splitting tensile strength reduction factor ሺࢼࢀ ሻ
HSC
1
0.86
0.75
0.64
0.53
0.42
0.31

HSC-P
1
0.90
0.90
0.90
0.70
0.52
0.34

150

HSC-S
1
0.82
0.60
0.52
0.42
0.32
0.22

HSC-H
1
0.78
0.78
0.78
0.64
0.48
0.32

Table 4.5 - Compressive strength, tensile strength and elastic modulus reduction factor βT at
different temperatures for SCC and fiber reinforced SCC.
Reduction factor ሺࢼࢀ ሻ
Temperature -°C

20
100
200
300
400
600
800

Compressive
strength
SCC and
SCC with
fibers
1
0.79
0.59
0.56
0.53
0.43
0.33

Tensile strength

Elastic Modulus

SCC-P

SCC, SCC-S,
SCC-H

SCC and
SCC-P

SCC-S and
SCC-H

1
0.89
0.79
0.69
0.59
0.39
0.19

1
0.95
0.9
0.8
0.7
0.5
0.3

1
0.74
0.64
0.54
0.44
0.34
0.04

1
0.9
0.72
0.64
0.56
0.4
0.24

Table 4.6 - Compressive strength and elastic modulus reduction factor βT at different
temperatures for FAC and FAC-P

Temperatur
e (°C)

20
200
400
600
800

Reduction factor (βT)
Compressive strength
FAC
FAC-P
1
1
0.6
0.85
0.42
0.61
0.24
0.37
0.06
0.13

Splitting tensile strength
FAC
FAC-P
1
1
0.79
0.86
0.53
0.76
0.27
0.42
0
0.08

151

Elastic Modulus
FAC
FAC-P
1
1
0.97
0.94
0.38
0.64
0.2
0.34
0.02
0.04

TC1

TC1
TC2

TC2

TC – Thermocouple
TC1 – Centre
TC2 – Surface

Specimen 75x150 mm
(a) Cylinder inside furnace

(b) Thermocouples position in cylinder

Figure 4.1 - Arrangement of thermocouples on an instrumented cylinder

Figure 4.2 - Electrical furnace used to heat the small cylinders

152

Figure 4.3 - Forney strength test machine used for mechanical properties

Figure 4.4 - Thermal jacket for handling heated cylinders and to preserve heat in cylinders during
compressive strength tests

153

140 mm
19 mm

38 mm

172 mm

48 mm

76 mm

57 mm

45 mm
250 mm
25 mm
38 mm

Insulation

Insulation

Figure 4.5 - Design details of steel bracket frame

154

Handles

Figure 4.6 - Insulated steel bracket frame for handling heated cylinders and to preserve heat in
cylinders during splitting tensile strength tests

155

Start loading with
strength test machine

Temperature

T

Temperature increase to
target tempearture T in time t

Inside furnace

t

Time

Start loading with
strength test machine

Stress (or strain)

(a) Heating scheme

No preloading and
further stress increase
after heating time t

Inside furnace

t

Time
(b) Loading scheme

Figure 4.7 - Schematic of temperature and stress increments during heating and loading of test
cylinders

156

900
Heating rate = 120°C/h
Hold period = 2 h

800
Temperature (°C)

700
600
500
400
300
200
100
0
0

2

4
6
Time (hours)

8

10

Figure 4.8 - Time-temperature graph showing ramp and hold times at each target temperature

157

Furnace
Specimen - 75mm
TC3 TC2 TC1
TC - Thermocouple
TC1 - Center
TC2 - Surface
TC3 - Furnace

(a) Location of thermocouples on cylinder specimen and in furnace

Temperature (°
C)

600
500
400
300

Time required to reach
steady state at 600°C

200

Specimen center
Specimen surface
Furnace

100
0
0

60

120

180

240

300

360

Time (minutes)
(b) Temperature rise recorded by thermocouples at different locations
Figure 4.9 - Heating characteristics of test cylinder at 600°C

158

420

100°C Exposure

0.65
0.6

0

0.4
Core temp 100°C

0.2

0.6

Core temp 87°C

0.4

Core temp 68°C

Moisture loss per m3,%

0.8

60

90
Hold time (mins)

120

Figure 4.10 - Temperature progression at mid-depth of concrete cylinders at various hold times

(a)

(b)

Figure 4.11 - Arrangement for high temperature compressive strength tests and tested cylinder

159

(a)

(b)

Figure 4.12 - Arrangement for high temperature splitting tensile strength tests and tested cylinder

Figure 4.13 - LVDTs and load cell addition to Forney strength test machine for stress-strain
measurements

160

100
Compressvie strength (MPa)

NSC
HSC

80

SCC
FAC

60
40
20
0
0

200
400
Temperature (°
C)

600

800

Figure 4.14 - Measured compressive strength of NSC, HSC, SCC, and FAC
NSC

1

HSC
SCC

0.8

f'c,T/f'c

FAC
0.6
0.4
0.2
0
0

200

400
Temperature (°
C)

600

Figure 4.15 - Relative compressive strength of NSC, HSC, SCC, and FAC

161

800

Compressive strength (MPa)

100
HSC
HSC-S

80

HSC-P
60

HSC-H

40
20
0
0

200

400

600

800

Temperature (°
C)
Figure 4.16 - Measured compressive strength of HSC and fiber reinforced HSC as function of
temperature

1.2
HSC

1

HSC-S
HSC-P

f'c,T/f'c

0.8

HSC-H

0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°
C)
Figure 4.17 - Measured relative compressive strength of HSC and fiber reinforced HSC as
function of temperature

162

Compressive strength (MPa)

80
SCC

70

SCC-S

60

SCC-P

50

SCC-H

40
30
20
10
0
0

200

400

600

800

Temperature (°C)
Figure 4.18 - Measured compressive strength of SCC and fiber reinforced SCC as function of
temperature.
1.2
SCC
1

SCC-S
SCC-P

f'c,T/f'c

0.8

SCC-H

0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Figure 4.19 - Measured relative compressive strength of SCC and fiber reinforced SCC as function
of temperature.

163

FAC
Compressive strength
(MPa)

80

FAC-P

60

40

20

0
0

200

400
600
Temperature (°C)

800

Figure 4.20 - Measured compressive strength of FAC and FAC-P as function of temperature.

1

FAC
FAC-P

f'c,T/f'c

0.8
0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Figure 4.21 - Measured relative compressive strength of FAC and FAC-P as function of
temperature

164

Splitting tensile strength (MPa)

5
NSC
HSC

4

SCC
FAC

3
2
1
0
0

200

400
Temperature (°
C)

600

800

Figure 4.22 - Measured splitting tensile strength of NSC, HSC, SCC, and FAC
NSC

1

HSC
SCC

0.8

f't,T/f't

FAC
0.6
0.4
0.2
0
0

200

400
Temperature (°
C)

600

800

Figure 4.23 - Relative splitting tensile strength of NSC, HSC, SCC, and FAC

165

Splitting tensile strength (MPa)

7
HSC
6

HSC-S
HSC-P

5

HSC-H

4
3
2
1
0
0

200

400

600

800

Temperature (°
C)
Figure 4.24 - Measured splitting tensile strength of HSC and fiber reinforced HSC as function of
temperature
HSC

1

HSC-S
0.8

HSC-P
HSC-H

f't,T/f't

0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°
C)
Figure 4.25 - Measured relative splitting tensile strength of HSC and fiber reinforced HSC as
function of temperature

166

Splitting tensile strength (MPa)

6
SCC
5

SCC-S
SCC-P

4

SCC-H

3
2
1
0
0

200

400

600

800

Temperature (°C)
Figure 4.26 - Measured splitting tensile strength of SCC and fiber reinforced SCC as function of
temperature
1.2
SCC
1

SCC-S
SCC-P

f't,T/f't

0.8

SCC-H

0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Figure 4.27 - Measured relative splitting tensile strength of SCC and fiber reinforced SCC
as function of temperature

167

Splitting tensile strength (MPa)

FAC

5

FAC-P

4
3
2
1
0
0

200

400

600

800

Temperature (°
C)

Figure 4.28 - Measured splitting tensile strength of FAC and FAC-P as function of temperature
FAC

1

FAC-P

f't,T/f't

0.8
0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°
C)

Figure 4.29 - Measured relative splitting tensile strength of FAC and FAC-P as function of
temperature

168

1.2
SCC
1

SCC-S
SCC-P

ET/E0

0.8

SCC-H
0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Figure 4.30 - Measured elastic modulus for plain SCC and fiber reinforced SCC
1
HFAC-P

ET/E0

0.8

HSC

0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

Figure 4.31 - Measured elastic modulus for plain FAC and FAC-P

169

800

20°C

Compressive stress
(MPa)

80

100°C
200°C

60

400°C
600°C
800°C

40

20

0
0

0.003

0.006
0.009
0.012
Strain (mm/mm)

0.015

Figure 4.32 - High temperature stress-strain curves for SCC
20°C

80
Compressive stress
(MPa)

100°C
200°C

60

400°C
600°C

40

800°C

20

0
0

0.003

0.006
0.009
0.012
Strain (mm/mm)

Figure 4.33 - High temperature stress-strain curves for SCC-S

170

0.015

20°C

80
Compressive stress
(MPa)

100°C
200°C
60

400°C
600°C

40

800°C

20

0
0

0.003

0.006
0.009
0.012
Strain (mm/mm)

0.015

Figure 4.34 - High temperature stress-strain curves for SCC-P
20°C

80
Compressive stress
(MPa)

100°C
200°C
60

400°C
600°C

40

800°C

20

0
0

0.003

0.006
0.009
0.012
Strain (mm/mm)

Figure 4.35 - High temperature stress-strain curves for SCC-H

171

0.015

Compressive stress
(MPa)

20°C
200°C

80

400°C
60

600°C
800°C

40
20
0
0

0.003

0.006

0.009

Strain (mm/mm)
Figure 4.36 - High temperature stress-strain curves for FAC
20°C

Compressive stress
(MPa)

80

200°C
400°C

60

600°C
800°C

40

20

0
0

0.003

0.006
Strain (mm/mm)

0.009

Figure 4.37 - High temperature stress-strain curves for FAC-P

172

1.2

SCC - test data
SCC-S - test data

1

SCC-P - test data
SCC-H - test data

0.8

f'c,T/f'c

SCC (all) - fitted line
0.6
0.4
0.2
0
0

200

400
600
Temperature (°C)

800

Figure 4.38 - Compressive strength test data of SCC with and without fibers compared with
regression based fitted line
FAC - test data

1

FAC - fitted line

f'c,T/f'c

0.8

FAC-P - test data
FAC-P - fitted line

0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

800

Figure 4.39 - Compressive strength test data of FAC and FAC-P compared with regression based
fitted line

173

HSC

1

HSC-S

f'c,T/f'c

0.8

HSC-P
HSC-H

0.6
0.4
0.2
0
0

200

400

600

800

Temperature (°C)

Figure 4.40 - Compressive strength relations for plain HSC and fiber reinforced HSC
HSC

1.0

HSC-S
0.8

HSC-P
HSC-H

f't,T/f't

0.6
0.4
0.2
0.0
0

200

400
Temperature (°
C)

600

800

Figure 4.41 - Splitting tensile strength relations for plain HSC and fiber reinforced HSC

174

1

f'c,T/f'c

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

800

Figure 4.42 - Compressive strength relations for plain SCC and fiber reinforced SCC
1

SCC-P
SCC, SCC-S, SCC-H

f't,T/f't

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

800

Figure 4.43 - Splitting tensile strength relations for plain SCC and fiber reinforced SCC

175

1

SCC, SCC-P
SCC-S, SCC-H

E/E0

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

800

Figure 4.44 - Elastic modulus relations for plain SCC and fiber reinforced SCC
FAC

1

FAC-P

f'c,T/f'c

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

Figure 4.45 - Compressive strength relations for FAC and FAC-P

176

800

1

FAC
FAC-P

f't,T/f't

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

800

Figure 4.46 - Splitting tensile strength relations for FAC and FAC-P

FAC

1

FAC-P

ET/E0

0.8
0.6
0.4
0.2
0
0

200

400
Temperature (°C)

600

Figure 4.47 - Elastic modulus relations for FAC and FAC-P

177

800

CHAPTER 5
5

EXPERIMENTAL STUDIES

Part of this chapter is mainly based on the following journal papers:
•

Kodur, V., and Khaliq, W. (2011). “Behavior of High Strength Fly Ash Concrete Columns under Fire
Conditions." ASCE Journal of Structural Engineering, Submitted.

•

Kodur, V. Mao, X. Raut, N. and Khaliq, W. (2011). “Simplified Approach for Evaluating Residual
Strength of Fire-Exposed Reinforced Concrete Columns.” ASCE Structural Journal, submitted.

•

Khaliq, W., and Kodur, V. (2012). "High temperature mechanical properties of high strength
fly ash concrete with and without fibers." ACI Materials Journal, submitted and reviewed.

5.1 General
Literature review presented in Chapter 2 indicates that there is large amount of data on
conventional NSC and HSC columns tested under standard fire scenarios. Also limited data is
available on fire response of polypropylene fiber reinforced HSC columns. However, there is no
data on fire performance of HPC columns fabricated with fly ash or with steel and hybrid fiber
reinforcement. Moreover, for structural characterization of high temperature thermal and
mechanical properties of HPC (as presented in Chapter 3 and Chapter 4), full scale fire tests are
deemed essential. To overcome these shortcomings, an experimental program was designed to
undertake four HPC columns. Since there is large amount of data on HSC columns, fire
resistance tests were carried out on two FAC and two HSC columns (with different fiber
combinations). This is to limit the number of experiments, due to high cost of fire tests. The

178

varied parameters included HPC type (FAC to HSC), addition of polypropylene fibers in FAC
column and addition of steel and hybrid fibers in HSC columns.
To HPC columns (FAC, FAC-P, HSC-S and HSC-H) were designed, fabricated as per and ACI
318 (2008) and were tested under design fire scenario. These columns were well instrumented
and collected a considerable amount of response data comprising cross-sectional temperatures,
axial and lateral deformations and strains in rebars. This data from the fire tests helped to
characterize the fire response of HPC columns and validate the numerical model. Discussion on
results is presented based on fire response of columns comprising the thermal and structural
response of these columns. Since columns were tested under design fires that present practical
scenario during which the columns may not fail, three out of four tested columns survived the
fire resistance tests. These three columns (FACP, HSC-S, HSC-H) were further subjected to
post-fire strength tests to evaluate their residual strength capacity. Full details on residual
strength tests are also presented in this Chapter.

5.2 Design and Fabrication of Specimens
The experimental program consisted of conducting fire resistance tests on four reinforced
concrete columns, two of which were made of fly ash concrete and the other two made of fiber
reinforced HSC. Of the two FAC columns, one was fabricated with plain FAC, while the other
was fabricated with polypropylene fibers, referred to as FAC and FAC-P columns respectively.
Of two HSC columns, one was steel fiber reinforced HSC and other with hybrid fiber (mix of
polypropylene and steel fibers) reinforced HSC column, designated as HSC-S and HSC-H
columns respectively. For comparison of results, the HSC columns were designed to have similar
characteristics as that of FAC columns.

179

5.2.1

Design of Columns

The size of the test columns were dictated by the dimensions of furnace and loading equipment
available for testing. The columns were designed as per ACI 318 (2008) and ACI 216.1 (2007)
provisions as high strength slender columns having minimum of two hours fire resistance rating.
As per ACI 216.1 Section 2.5.3, for two hours of fire resistance, 50 mm concrete cover is
required, however, as per ACI 216.1 Table 2.3, minimum 250 mm columns dimension is
required for same fire resistance. As column size could not be increased from 203 mm sides,
therefore the actual fire resistance was estimated less than 2 hours base on both cover and size
provisions. The design details are given in Appendix B where calculations for one column from
each set of FAC and HSC columns is presented. The capacity of the columns was calculated
using load-moment (P-M) interaction diagrams generated for these columns (Figures B.5 and B.7
Appendix B). The actual end conditions of these columns were partially-fixed, but for
conservative P-M capacity calculations, pin-pin end conditions were considered which lead to a
slenderness ratio of 55. Both FAC and FAC-P columns had higher load and moment capacities
as compared to HSC-S and HSC-H columns. The overall load capacity of FAC and FAC-P
columns was 2144 and 2020 kN respectively while for HSC-S and HSC-H columns it was 1612
and 1665 kN respectively. Similarly the moment capacity of FAC and FAC-P columns was 68
and 69 kN-m to that of 51 and 53 kN-m for HSC-S and HSC-H columns. These ultimate loads
and moment capacities of columns are given in Table 5.2 as per Appendix B.
All four columns were 3300 mm long and were of square cross section of 203×203 mm. The
columns had four 19 mm dia rebars as longitudinal reinforcement and 10 mm ties, at 200 mm
spacing, as transverse reinforcement. The steel of main reinforcing rebars and ties had specified
yield strength of 420 MPa. The details of column dimensions and provided reinforcement are

180

given in Figure 5.1. Generally, 135° bent ties are to be provided as lateral reinforcement for
columns in seismic areas, however, recent studies have shown that fire resistance of columns
also gets enhanced with the provision of 135° bent ties (Kodur and McGrath, 2003). Therefore
the ties in the columns were bent at 135° and anchored in the concrete core to a length of 75 mm
as shown in Figure 5.1. For minimum fire rating of two hours, 50 mm of concrete cover was
provided as per ACI 216.1(2007).
5.2.2

Fabrication of Specimens

5.2.2.1 Mix Proportions
Four batches of concrete were used for fabricating these columns namely FAC, FAC-P, HSC-S
and HSC-H. All four batches of concrete had ordinary Portland cement (Type I), carbonate
coarse aggregate and natural source sand as fine aggregate. Fly ash (Type C) was used as
replacement (25%) to cement in FAC and FAC-P mixes. To achieve desired high strength and
workability, optimum amount of mineral admixtures, such as silica fume and slag (Grade 120),
were added to batch mix. In FAC-P and HSC-H mixes, 2 kg/m

3

(0.22% by volume),

MONOFILAMENT (multi-plus) type polypropylene fibers, were added. The 20 mm long
polypropylene fibers were of nonabsorbent type and have a specific gravity of 0.91 and a melting
3

point 162°C. In HSC-S and HSC-H mixes 42 kg/m (0.54% by volume) NOVOCON XR type
steel fibers were added. Steel fibers were 38 mm in length and 1.14 mm (0.045 in) equivalent
diameter and had a specified tensile strength of 966 MPa. Mix proportions and attained
compressive strengths at different ages for four batches of concrete (FAC and FAC-P, HSC-S
and HSC-H) used for fabricating the columns are tabulated in Table 5.1. The compressive
strength of different concrete mixes measured on 100×200 mm cylinders at 28 days ranged from

181

67-102 MPa. It can be seen from Table 5.1 that 28 days compressive strength of FAC and FACP concrete was significantly higher (102 and 100 MPa respectively) as compared to HSC-S and
HSC-H (67 and 68 MPa respectively). Same is true for strength of these concretes at 90 days and
on the test day. It should be noted that the quantity of silica fume was almost similar in batch
3

mixes of both HSC and FAC columns (43 and 41 kg/m respectively) therefore the additional
improvement in strength properties of FAC and FAC-P concrete is attributed to fly ash in the
mix. Strength in HSC-S and HSC-H was lower even with the addition of steel fibers. However, it
should be noted that the real contribution of steel fibers in concrete is to increase the toughness
of concrete as the fibers tend to increase the strain at peak load, and provide a higher energy
absorption in post-peak portion of the load-deflection response (Mehta and Monteiro, 2006).
5.2.2.2 Fabrication of Columns
Horizontal wooden formwork was prepared to cast the columns. Longitudinal steel rebars were
tied with lateral ties using binding wire to create the reinforcement cage. This reinforcement cage
was placed inside the formwork as shown in Figure 5.2. At this stage, instrumentation consisting
of strain gauges and thermocouples were attached to the steel rebars. All four concrete columns
were cast and finished by placing the formwork in horizontal position. Fifteen 100x200 mm
cylinders were also cast for strength measurements at different concrete age. In fabrication of
columns, vibrators were used at moderate speed to ensure quality finish. The columns were then
physically leveled and finished on the open side of the formwork as shown in Figure 5.3. After
casting, the columns were initially moist cured in the forms for 7 days and then removed from
the forms and stored at ambient conditions (more than six months) till tests were done. During
storage, the conditions were maintained at about 22°C temperature and 40% relative humidity.

182

Three cylinders from each batch were tested to evaluate compressive strength at 7, 28, 90 days
and on test day (about 8 months after casting of columns).
5.2.3

Instrumentation

The instrumentation in the columns included thermocouples (TCs) to record concrete and rebar
temperatures, strain gauges (SGs) to record strain in steel rebars, and linear position transducers
(LPTs) to measure axial and lateral deformations. Thirteen type-K (Chromel-alumel)
thermocouples of 0.91 mm thickness were installed at three different cross-sections namely midheight, top three-quarter, and bottom one-quarter cross-section in the fire exposed portion of the
columns.
Figure 5.4 illustrates the position of three cross-sections and precise location of TCs at each
cross-section. The arrangement for thermocouples was same for all four columns. At Section
AA, TC 1 to TC 3 were attached to record rebars’ temperatures, TC 4 and TC 5 for surface
temperatures, TC 6 and TC 7 to record concrete temperatures at center and quarter depth of the
cross-section. At section BB, TC 8 was attached to record rebar temperature, while TC 9 and TC
10 were installed to record temperatures of center the cross-section and ties. At Section CC, TC
11, TC 12, and TC 13 were attached to record rebar, concrete at quarter depth and tie
temperatures respectively. Two high-temperature and one regular strain gauge namely HTSG 1,
HTSG 2, and SG 3 were used at geometric mid-height (Section DD) of the columns and another
three regular strain gauges namely SG 1, SG 2, and SG 3 were used at three-quarter-height
(Section EE) of columns as shown in Figure 5.5. These strain gauges were attached to the steel
rebars and the arrangement was similar in all four columns. Physical placement of thermocouples
and strain gauges on to steel cage is shown in Figure 5.6.

183

The axial deformation of the columns was measured by placing two linear position transducers
(LPTs) orthogonal to each other on top of each column attached to the top plate of the columns.
The recording of axial deformation by two LPTs placed orthogonally helped to record data on
two axes and compute actual axial deformation by comparing the two measurements. The
columns were oriented in East-West and North-South directions of the furnace. The LPTs were
placed North-East and North-West sides of the columns as shown in Figure 5.7.
Measurement of lateral deformations in a fire exposed column inside the furnace becomes very
difficult due to harsher environment (very high temperatures). This difficulty was overcome
through a specialized technique by using Chromel wires inside the furnace. Chromel wires that
can resist high temperatures (up to 1350°C) were pulled out of Type-K (Chromel-alumel)
thermocouples and were attached to columns by wrapping around and tying to columns. These
wires were then extended outside of the furnace so as to attach to LPTs positioned outside of
furnace for recording lateral deformations of the column. Figure 5.7 illustrates that these
Chromel wires were attached to LPTs on two orthogonal faces of the column at mid height. The
position of each axial and lateral LPT to measure axial and lateral deformation in all four
columns is also illustrated in Figure 5.7. Two columns were tested at the same time in the
furnace by placing them in east and west positions. Depending on the available openings, the
lateral LPTs on east column were placed on north and east sides of the furnace, whereas for west
column these LPTs were placed north and west sides of the furnace as shown in Figure 5.7

5.3 Fire Resistance Experiments
5.3.1

Test Equipment

The fire resistance tests were carried out by placing the columns in the structural fire test furnace
at the Civil Infrastructure Laboratory (CIL) of Michigan State University (MSU). The test
184

furnace, integrated with a loading frame, has been specially designed to produce conditions, such
as temperature, loads and heat transfer, to which a structural member might be exposed during a
fire as shown in Figure 5.8(a). The furnace has the capacity to supply both heat and applied loads
to the structural member that are present in a typical structural member exposed to fire.
The furnace consists of a steel loading frame (framework) supported by four steel columns, with
a fire chamber that is 2440 mm wide, 3050 mm long, and 1775 mm high as shown in Figure
5.8(b). The maximum heat power the furnace can produce is 2.5 MW. Six natural gas burners
located within the furnace provide thermal energy, while eight type-K thermocouples distributed
throughout the test chamber as per ASTM E119 (2008), help monitor and control the furnace
temperatures. Data from fire tests, which include temperatures, displacements, forces and strains,
are collected using a “Darwin Data DA100/DP120-13” acquisition system. This system contains
70 thermocouple channels, 10 voltage channels for measuring displacements and forces, and 10
strain-gauge channels. These channels are connected to data acquisition system, which transfers
the data at five second intervals throughout the fire test to a personal computer that stores it in a
“.CSV” file using the “DAQ 32” computer program.
During the fire test, temperatures recorded in the furnace are used to manually adjust fuel supply
and air intake, to maintain a temperature course consistent with the pre-determined standard or
design fire scenarios (Kodur and Fike, 2009). In this way, the furnace temperature can be
maintained along a desired time-temperature curve. Two small view ports on either side of the
furnace wall are provided for visual monitoring of the fire-exposed columns during a test. The
furnace accommodates two columns at a time and different load levels can be applied on each
column.

185

5.3.2

Preparation of Columns for Fire Tests

The columns after curing for about 6 months (or more) were prepared for safe and secure testing.
The columns were placed in furnace in a predetermined arrangement to fit precisely under
vertical actuators and also to attach to bottom steel plate of size 406×406×60 mm that is fixed to
the floor. A steel plate of size 406×406×25 mm was also attached to the top of the column where
actuator loading head makes a contact with the column. These steel plates were bolted at each
end of the column using four steel angles of 100×100×12 mm which helped to fix the column in
position and for facilitating load transfer from the actuator. These end plate and angle
attachments are illustrated in Figure 5.7. With these end conditions at the top and bottom, the
column can be assumed to be partially restrained against rotation. The actuator sits on top of the
fixed plate and provides a rotational stiffness of 250 kN.m/µrad. Figure 5.9 illustrates attached
parts and the end restraint conditions at the top and bottom of the columns before testing.
On the test day, just prior to undertaking the fire tests, the room temperature moisture conditions
(relative humidity) of the columns and compressive strength of concrete were measured. The
relative humidity of concrete columns was measured at two different locations on the columns
using a “Sensirion” relative humidity sensor (probe). For placing the probe, 8 mm holes were
drilled at two different locations in each column and then the probe was placed in the hole and
the hole was sealed for about 5 minutes until equilibrium of relative humidity and temperature
was achieved. Once the equilibrium conditions were reached, the relative humidity at that
position was recorded. The average of two relative humidity measurements for each column at
the time of testing was between 90 and 91% as shown in Table 5.2. Higher relative humidity
readings in the tested high columns, as compared to typical normal strength concrete columns

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(Raut and Kodur, 2011), can be attributed to dense microstructure and compactness of high
performance concrete mixes which minimizes evaporation of moisture.
Test day cylinder compressive strength of all four concretes was not much different from 90 days
compressive strength, but it was significantly higher (ranging 5-19%) than 28 days compressive
strength as shown in Table 5.1. Both fly ash and silica fume enhance concrete strength over time
as the pozzolans react with calcium hydroxide continuously during the hydration process (Mehta
and Monteiro, 2006; Mindess et al., 2003; Neville, 2004) and contribute to enhanced strength.
The improvement in strength in all four concretes (FAC, FAC-P, HSC-S and HSC-H) is
therefore attributed to the age of the specimens and continuous hydration process in presence of
pozzolans.
The test day compressive strength was used to calculate the capacity of the columns and to
evaluate the test load that was to be applied on columns during fire tests. As per ACI 318 (2008)
design guidelines, a column is said to be slender when the slenderness ratio of columns is greater
than 40, therefore these four columns, with slenderness ratio of 55, were designed as slender
columns and the capacity was evaluated based on axial load-moment (P-M) interaction diagrams.
The detailed capacity calculations and resulting P-M interaction diagrams of these columns are
given in Appendix B. The calculated capacities for all the columns are also tabulated in Table
5.2.
5.3.3

Test Procedure

The fire resistance tests were carried out by placing two columns in the furnace and exposing
them to selected design fire scenario. The columns were exposed to fire from all sides. First test
was carried out on FAC and FAC-P columns, while second test was carried out on HSC-S and
HSC-H columns. During the fire test, middle 1775 mm of the 3300 mm height of the columns

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was exposed to fire. The columns were tested under a parametric (design) fire exposure which
comprised of a growth phase as per ASTM E119 (2008) standard fire exposure and followed by
a decay phase as shown in Figure 5.10. In test-I decay phase of 4.16°C/min was based on
Eurocode design fire (Eurocode 1, 2002), whereas in test-II a faster decay rate of 11°C/min was
selected to depict early extinguishing of fire.

As fire resistance of RC columns is significantly enhanced with use of fibers and also with 135°
bent ties, a fire exposure of 3 hours was selected to see the failure of the columns against
estimated fire resistance of 2 hours (or under) as per ACI 216.1. However, the decay (cooling)
phase was 4 hours for test with cooling phase based on Eurocode design fire and 1.5 hours for
second test with faster cooling rate. Total fire exposure duration for FAC and FAC-P columns in
first test was 7 hours, and for HSC-S and HSC-H columns was 4.5 hours. The well-defined
decay (cooling) phase was achieved by controlling temperatures (cooling) in the furnace (by
blowing air through the vents in the furnace) so as the fire to decay at a predetermined cooling
rate representing typical fire in a building.
All four columns were tested under a concentric axial load representing a load ratio of 0.4 for
FAC and FAC-P columns and a load ratio of 0.6 for HSC-S and HSC-H columns. The load ratio
is the ratio of the applied (test) load to the column capacity computed according to ACI 318
(2008). Earlier studies (Raut and Kodur, 2011) have shown that HSC columns perform better
under 0.4 load ratio, therefore a higher load ratio of 0.6 was selected for HSC columns in this
study. Another reason for selecting higher load ratio of 0.6 was the expected better fire
performance of steel and hybrid fiber reinforced HSC columns.

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The loading was applied approximately 30 minutes prior to start of the fire resistance tests and
was maintained either until the column failed under fire exposure or to the end of the test. During
the fire resistance tests on columns, temperature was controlled in such a way that the average
temperature in the furnace followed, as closely as possible, the parametric fire scenario (Design
fire 1 and Design fire 2). At the end of the fire test, once the furnace temperatures were down to
room temperature, the surviving columns were unloaded and allowed to cool while still inside
the furnace. These survived columns were used for residual strength tests as discussed in Section
5.5. A summary of test parameters and results from fire resistance tests for four columns namely
FAC, FAC-P, HSC-S, and HSC-H is given in Table 5.2.
5.3.4

Measured Data and Test Observations

The test data comprising of furnace temperatures, column temperatures, axial deformations,
lateral deformations, rebar strains and loading were recorded at every 5 seconds interval through
data acquisition system. Visual observations were made every 5 minutes through the view ports
in the furnace to record any major changes in the columns such as fire induced spalling, visible
crack propagation and excessive deformations. Also photographs of columns were taken at
regular intervals during the test. After completion of fire resistance tests, post-test observations
were made to record failure pattern, extent of physical deterioration due to heat (fire) and
spalling, concrete discoloration and condition of reinforcement. Volumetric measurements were
done on fire exposed columns to quantify the extent of spalling resulting from fire exposure. The
exposed length of each column was divided into a number of segments and the volume of each
segment is computed by taking measurements with respect to a reference axes system. The total
volume of a damaged column was then computed as the sum of the volumes of all the segments,
and used to compute overall spalling. FAC column was the only column that failed during the

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fire test as hydraulic jack could no longer maintain the load, whereas other three columns in this
test program did not fail under the given fire exposure time.

5.4 Response of HPC Columns during Fire Exposure
Data generated from the above fire tests was utilized to compare the fire behavior of FAC, FACP, HSC-S, and HSC-H columns under different conditions. The test variables included concrete
strength, effect of type of concrete, and effect of different fibers. A summary of results of fire
resistance tests on the columns are tabulated in Table 5.2. The fire performance of these columns
is evaluated in the form of thermal response, structural response, spalling behavior as well as fire
resistance time.
5.4.1

Thermal Response

During fire tests, the temperature progression was recorded through thirteen thermocouples
located at three cross-sections (sections AA, BB and CC) as shown in Figure 5.4. The thermal
response of all four columns (FAC, FAC-P, HSC-S, and HSC-H) is shown in Figures 5.11 to
5.22 by plotting measured temperature profiles in rebars, and concrete as a function of fire
exposure time. In all columns, an initial plateau can be seen in rebar and concrete temperatures
around 100°C and this can be attributed to heat from fire being utilized for evaporation of free
water in concrete. After this initial plateau, the temperatures in concrete and rebars increase with
fire exposure time. It can be noted that, in all four columns, the progression of temperatures in
concrete (at mid-depth) is lower than that in rebars. This can be attributed to lower thermal
conductivity and higher specific heat of concrete which delays temperature rise to inner layers of
concrete.

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The temperatures profiles at sections AA and BB show inconsistent trend and this can be
attributed to displacement (or damage) of TC’s (TC3, TC4, TC5 at Section AA and TC8, TC9,
TC10 at Section BB) at these locations resulting from fire induced spalling and direct exposure
of rebars to fire temperatures. This disturbance in temperature profiles was not observed in FACP, HSC-S and HSC-H at all three cross-sections since there was no fire induced spalling. These
temperature profiles show that addition of fibers (both steel and polypropylene) is quite
beneficial in mitigating the fire induced spalling and retaining cross-sectional integrity of HPC
columns.
A comparison of temperature rise in FAC and FAC-P columns indicates that temperatures in
FAC column are slightly higher than that in FAC-P column throughout the fire exposure time
(see Figure 5.23). The higher temperatures in FAC column can be attributed to two factors,
occurrence of fire induced spalling leading to loss of concrete cross-section, and higher thermal
conductivity of FAC (Kodur and Khaliq, 2011). The peak rebar temperatures attained in FAC
column was 681°C at 270 minutes into the fire exposure, as compared to 645°C in FAC-P
column. This lower temperature in FAC-P column can also be attributed to reduced thermal
conductivity of FAC-P resulting from increased permeability (due to melting of polypropylene
fibers).
To compare the performance of different types of HPC under fire conditions, fire resistance of
the two types of concrete columns (FAC and HSC) tested in this program is also compared. The
thermal response of FAC and FAC-P columns is compared with measured temperatures of HSCS and HSC-H columns (see Figure 5.24). It can be seen that the temperature progression in both
FAC and FAC-P columns follow similar trends to that of HSC-S and HSC-H columns, however
both FAC and FAC-P columns had slightly higher temperature profiles. This can be attributed to

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slightly higher thermal conductivity and specific heat of FAC (as compared to HSC) (Kodur and
Khaliq, 2011).
5.4.2

Structural Response

Structural response of column is generally assessed by measuring axial and lateral deformations
in column, and also strain in rebars under fire exposure. Both axial and lateral deformations were
recorded in four columns and strain data was measured in steel rebars in the fire resistance tests
is presented here. To gauge the relative performance of two types of HPC (FAC and HSC) the
comparison of structural response for all four columns is presented.
5.4.2.1 Axial Deformations
The structural response of four columns is evaluated by comparing measured axial deformations
as a function of fire exposure time, which is shown in Figure 5.25. An RC column, when
exposed to fire, expands initially due to thermal expansion occurring both in steel rebars and in
concrete. With increasing fire exposure time, temperatures in rebars rise and the steel
(reinforcement) yields at about 600°C, a temperature that is critical for steel since it loses 50% of
its yield strength (Lie, 1992). After steel yields, concrete core in the column progressively carries
higher percentage of applied load. With increasing temperatures, strength and stiffness properties
also deteriorate in concrete (Kodur and McGrath, 2003) leading to increased load induced
mechanical strains which in turn results in contraction of the columns. With increasing fire
exposure time, the strength of the concrete also decreases due to deteriorating properties of
concrete, and ultimately, when the column can no longer support the load, failure of column
occurs.
Results plotted in Figure 5.25 indicate that all four columns underwent expansion in the initial
stages of fire exposure. Higher initial expansion in the case of FAC column can be attributed to
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higher thermal strains. Further fire induced spalling that occurred in FAC column led to loss of
cross section which resulted in loss of strength and contraction (100 minutes) much earlier than
that in FAC-P column which led to failure of FAC column in 165 minutes. At this failure time,
the rebars temperature in FAC column reached 630°C and mid-depth (concrete) temperature
reached 560°C (as opposed to 570 and 470°C respectively in FAC-P column). This indicates that
steel rebars had also lost strength entirely in FAC column due to fire exposure. Previous fire
resistance studies have shown that the large deformation prior to failure results from high
mechanical strains (due to significant loss of strength and stiffness of the columns) and also from
significant levels of high temperature creep (Lie, 1992). Significant increase in the deformations
in column FAC-P towards later stages of fire exposure can be attributed to effect of high
temperature creep, which can be quite high when steel and concrete temperatures exceed 600°C.
The effect of fire on structural response of both HSC-S and HSC-H columns can also be gauged
by reviewing the progression of axial deformation with time (Figure 5.25). These columns were
exposed to similar fire scenario as that of FAC columns. Both these columns exhibit expansion
phase followed by contraction similar to FAC columns. However, the axial expansion in both
HSC-S and HSC-H columns is lesser than that in FAC column. It should be noted that HSC
columns were subjected to higher load ratio (0.6) as compared to FAC columns (0.4). Therefore
the lower axial expansion in case of HSC columns was due to influence of higher applied load.
Both HSC-S and HSC-H columns expanded smoothly up to three hours before they started
contracting. Also no spalling or major cracking was observed in HSC-S and HSC-H columns,
this in turn led to their better fire performance than that of FAC column.
The axial deformation-time plot in Figure 5.25 illustrates that higher initial axial deformation and
early contraction occurred in FAC column. Since FAC column had lost its cross-section in initial

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30 minutes of fire exposure, it resulted in direct fire exposure of rebars leading to higher
expansion of FAC column. Loss of cross-section in FAC column also compromised the
structural integrity due to higher degradation in stiffness; this resulted in early contraction under
load and led to failure. FAC-P column on the other hand sustained lesser axial deformation and
contraction in initial stages for fire than that in FAC column. Moreover, as a result of spalling
mitigation, due to melting of polypropylene fibers, the column cross-section in FAC-P column
remained unchanged, thus lower degradation to stiffness occurred. As a result FAC-P column
exhibited better fire resistance than FAC column.
Comparison of results from the tests on FAC and FAC-P columns with those of HSC-S and
HSC-H columns in Figure 5.25 illustrates that axial deformations in FAC-P, HSC-S, and HSC-H
columns follow almost similar trends in early stages of fire test. The gradual increase in
expansion and contraction in HSC-S and HSC-H columns can be attributed to higher applied
load (60% of ultimate load capacity) and enhanced ductility facilitated by presence of steel
fibers. Even under higher axial loads, both HSC-S and HSC-H columns survived the entire fire
test up to 4.5 hours. Fly ash concrete column had better strength properties as compared to HSCS and HSC-H resulting from fly ash in the mix (as described in Section 5.2), however, the steel
fibers improved the toughness and tensile strength properties in HSC-S and HSC-H concrete that
resulted in higher fire resistance in HSC-S and HSC-H columns.
5.4.2.2 Lateral Deformations
The lateral deformation measured at mid-height is plotted as a function of fire exposure time for
all four columns in Figure 5.26. All four columns had similar end (restraint) conditions with
bottom end completely fixed and the top end partially fixed (as shown in Figure 5.9). All these
columns exhibited lateral deformation in the expansion phase (in the initial stages of fire) and the

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deformation reached 25 mm at 100 minutes in to fire exposure (see axial deformation plot in
Figure 5.25). However, in FAC column, the lateral deformation significantly increased to 121
mm, at the time of failure, when the column moved in to contraction phase. Two factors that
contributed to this excessive lateral deformation in FAC column are; reduced cross-section due
to fire induced spalling and temperature induced stiffness degradation. This excessive lateral
deformation led to failure of FAC column in 165 minutes through global buckling. Lateral
deformation in FAC-P column increased to 45 mm at 180 minutes and then stabilized and
slightly reversed in the cooling phase of fire. This onset of reversal and stabilization of lateral
deformation in FAC-P column coincides with start of its axial contraction after undergoing initial
expansion (as can be seen in Figure 5.25). The enhanced performance of FAC-P column can be
attributed to its sustained integrity (without any loss of cross-section) due to mitigation of
spalling facilitated by the melting of polypropylene fibers.
As shown in Figure 5.26, lateral deformation in HSC-S and HSC-H columns increased to about
30 mm at 150 minutes and then almost remained steady. This steadiness in lateral deformation in
HSC-S and HSC-H columns, in comparison to FAC columns, can be attributed to slower
degradation of stiffness in these columns resulting from presence of steel fibers. The other factor
that enhanced the fire performance of HSC-S and HSC-H columns was sustained cross-sectional
integrity of these columns facilitated by spalling mitigation.
5.4.2.3 Strain in Steel Reinforcement
The strains in the longitudinal reinforcement in the columns were monitored during the fire tests
through high temperature and regular (room temperature) strain gages as explained in Section
5.2.3 and illustrated in Figure 5.5. The high temperature strain gauges can give reliable strain
measurements in steel rebars for temperatures up to 300°C, whereas regular strain gauges are

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reliable only up to 100°C. Due to limit of workable temperature range, functionality of these
strain gauges is limited as data collected by them may be unstable and unreliable in high test
temperatures up to 600-800°C. During the fire test, few of these strain gages (mostly regular)
malfunctioned during fire tests, these strain gauges either got disconnected or simply broken due
to fire exposure (temperature limitation). The measured strain from strain gauges attached to the
longitudinal reinforcement at two sections of the tested columns is plotted as a function of fire
exposure time in Figures 5.27-5.34. It can be seen from these figures that the strain data from
tested columns appeared to be reliable only up to 20 minutes or less in to fire exposure.
Moreover not all data gave good results and some of these results were irrational due to
significant variation. The malfunctioning and bad results in strain gauges can be attributed to the
cracking of concrete near the strain gauge, or intermittent de-bonding of the strain gauge from
the reinforcing steel due to the sudden rise (thermal shocks) in rebar temperature due to fire
exposure.
Results from two of the survived high temperature strain gauges (HTSG 1 and HTSG 2) in FAC
column at Section DD (mid-height of column as shown in Figure 5.27) show that they recorded
thermal expansion in steel rebars between 6 and 10 minutes. The recorded thermal strain was
between 100-300 micrometer/m range. This is in good agreement to the load-axial deformation
trends in FAC column as shown in Figure 5.25 where the FAC column is seen expanding in
initial stages of the fire test. However, after 10 minutes in to fire exposure the strain data
collected by both strain gauges became irrational either due to malfunctioning or deboning from
steel rebars. On the other hand only one regular strain gauge (SG 2) survived at Section EE
(three-quarter-height of column as shown in Figure 5.28). This strain gauge recorded thermal
expansion in steel rebar up to 13 minutes and the maximum recorded stain was 500

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micrometer/m before it stopped recording data. The small disturbance in the measurement
recording at about 5 minutes into the fire test might have resulted from cracking and spalling that
was in progress in FAC column at that time. The thermal strain in steel rebar is again rational
and in good agreement to load-deformation of FAC column.
In the case of FAC-P column, all three stain gauges survived at Section DD (mid-height of
column as shown in Figure 5.29) and recorded strain data correctly up to about 140 minutes with
very little disturbance. The recorded thermal strain remained constant under 100 micrometer/m
up to 120 minutes and increased up to 1500 micrometer/m before malfunctioning. The stain in
steel rebars also depicts correctly the lower load-axial deformation in FAC-P column (Figure
5.25) up to 140-150 minutes before it started to contract. Only one stain gauge (SG 3) survived at
Section EE (three-quarter-height of column as shown in Figure 5.29) and recorded strain data
correctly up to about 25 minutes but with some disturbance. The maximum recorded strain was
800 micrometer/m at about 11 minutes of the fire exposure but then it shows contraction in steel
rebar. This is not in line (agreement) with the load-deformation response of FAC-P in which
expansion continued till 150 minutes. This result may have occurred due to some local
disturbance concrete-steel rebar interaction and therefore deemed unreliable.
For HSC-S column, two high temperature strain gauges (HTSG 1 and HTSG 2) at Section DD
and two regular strain gauges (SG 1 and SG 2) at Section EE survived and recorded strain data
up to about 30 minutes as shown in Figures 5.31 and 5.32 respectively. The strain recorded by
HTSG1 and HTSG2 at Section DD show expansion with a maximum thermal strain of 1500
micrometer/m before both the strain gauges malfunctioned. However data recorded till about 20
minutes is in good agreement with the load-deformation plot of column HSC-H (see Figure
5.25). The strain recorded by SG1 and SG2 at Section EE show irrational response data as these

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show expansion and contraction at the same time at this section within 30 minutes. In the case of
HSC-H, all three strain gauges survived at both cross-sections DD and EE and recorded thermal
strains in steel rebars up to 20 and 40 minutes respectively as shown in Figures 5.33 and 5.34
respectively. At Section DD the two high temperature strain gauges recorded strains up to 1000
micrometer/m in 7-10 minutes. However, the strain recorded by SG3 at this section seems
irrational as it might have gone bad under high temperature. At Section EE all three regular
strain gauges show different strain progression and therefore measurements seem irrational. The
SG1 shows increase in thermal strain up to 40 minutes in steel rebars that correlates with the
actual load-deformation behavior of HSC-H column. However, SG2 shows no change in thermal
strain and SG3 shows increase in thermal strain after about 30 minutes, therefore data recorded
by both of these strain gauges is unreliable.
It should be noted that both regular and high temperature strain gages have temperature
limitations for reliable operation (100 and 300°C respectively), therefore these are less reliable
due to harsher temperature environments and complex physical and chemical processes that
occur in structural members at elevated temperatures (Dwaikat, 2009). It should also be noted
that the fire temperatures in fire test can reach up to 1000°C and steel rebar temperature can go
as high as 800°C and therefore strain gauges cannot stably operate at these high temperatures.
The problem associated with the reliability of high temperature strain gages was also
encountered by other researchers (Dwaikat, 2009; Raut, 2011; Williams, 2004). Some previous
researchers attributed the problem in strain gages to the electrical interference from the operation
of the high voltage ignition and the control systems (Williams, 2004) associated with fire tests.
One other reason for this problem could be that the strain gages are designed for low heating
rate. Whereas in actual very high heating rate is encountered (about 10°C per minute for rebars),

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and also these strain gauges could be directly exposed to fire when spalling occurs in the vicinity
of the strain gauges. Due to the lack of consistency in strain gages, the strain data recorded by
them should be cautiously used to infer any strain trends in the tested columns.
5.4.3

Spalling Progression

The progression and extent of spalling in columns was recorded qualitatively through visual
observations made through the observation windows of the furnace during the fire test. Also,
after the fire test, the quantity of spalling was evaluated by measuring the volumetric loss of
concrete in fire exposed columns. The quantity of spalled concrete was evaluated by subtracting
the remaining concrete section from the original volume of column and this is tabulated in Table
5.2.
In the case of FAC column, spalling due to high temperature started at about 12 minutes in to the
test and continued till about 25 minutes. After its initial occurrence, spalling gradually subsided
in FAC column and did not further penetrate into the concrete core inside steel cage. Figure 5.35
illustrates the columns status under fire conditions observed through view ports of furnace at 60
minutes into the fire test. The figure shows that out of four tested columns only plain FAC
column suffered spalling. The extent of spalling in FAC column was moderate as compared to
typical HSC column, which can be attributed to superior microstructure in FAC column.
In contrast, FAC-P, HSC-S, and HSC-H columns experienced no spalling throughout the fire
exposure. The absence of fire induced spalling in FAC-P, and HSC-H columns can be attributed
to enhanced permeability in concrete due to melting of polypropylene fibers at around 160°C.
The increased permeability facilitated dissipation of steam and thus helped to limit pore pressure
build-up so as not to exceed the tensile strength of concrete. The absence of spalling in HSC-S
column columns can mainly be attributed to increased tensile strength at higher temperature

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facilitated by the presence of steel fibers. In the case of HSC-H column, both mechanisms
increased tensile strength through steel fibers and increased permeability through melting of
polypropylene fibers prevented occurrence of spalling in concrete.
It has been shown in Chapter 4 that the presence of steel fibers decelerates the degradation of
tensile strength in HPC. The improved high temperature tensile strength in HSC-S and HSC-H
columns also helps to mitigate fire induced spalling. This beneficial effect in HSC-S and HSC-H
can be seen Figure 5.36 which illustrates the state of the post fire conditions of columns after
completion of fire tests as spalling was not encountered in these columns.
Post fire test volumetric measurements indicated the spalled concrete in FAC column was about
17% of its exposed volume, whereas this was about 40% in case of a typical HSC column (Raut
and Kodur, 2011). These volumetric calculations indicate that spalling was less severe in FAC
column compared to that of plain HSC columns (Raut and Kodur, 2011). This can be partly
attributed to higher tensile strength of fly ash concrete which is about 20% higher than that of
conventional high strength concrete as reported by Khaliq and Kodur (2012).
5.4.4

Failure Modes and Fire Resistance

The fire response of FAC and FAC-P columns was quite different from each other. Fire induced
spalling in FAC column led to loss of cross-section in early stages of test. The reduced crosssection in FAC column suffered increased degradation in strength and stiffness due to high
temperatures and led to failure of FAC column in 165 minutes. In the case of FAC-P column,
melting of polypropylene fibers mitigated the fire induced spalling by dissipation of pore
pressure. Melting of polypropylene fibers creates micro channels that help diffuse pore pressure
build-up (Bilodeau et al., 2004) and its detrimental effects. Due to spalling mitigation and

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survival of cross-sectional integrity, FAC-P column displayed better fire resistance than FAC
column and survived the burnout conditions during the test.
In the case of HSC-S and HSC-H columns, fire induced spalling was also not encountered. The
steel and hybrid fibers in HSC-S, and HSC-H columns decreased degradation of tensile strength,
mitigated spalling and also increased toughness of concrete under fire conditions. The better fire
resistance of HSC-S and HSC-H columns can therefore be attributed to presence of steel and
hybrid fibers. A comparison of fire resistance of all four columns is tabulated in Table 5.2. With
similar degradation in strength and stiffness to FAC and FAC-P columns, but with higher applied
load, HSC columns exhibited better fire resistance than FAC and FAC-P columns.
Out of four tested columns, three columns (FAC-P, HSC-S, and HSC-H) survived the fire
exposure conditions; this is typically a case once buildings are exposed to fire. However,
significant strength and stiffness reduction is anticipated in fire exposed columns after the test.
To characterize the post-fire capacity of the fire exposed columns and to establish their
serviceability, residual strength tests were performed on survived (FAC-P, HSC-S, and HSC-H)
columns.
5.4.5

Summary

Results from the fire resistance tests show that plain FAC column exhibits lower fire resistance
performance compared to steel and hybrid fiber reinforce HSC columns. The fire resistance in
FAC column was significantly affected by loss of cross-section due fire induced spalling. The
fire response of FAC-P column was almost similar to HSC-S and HSC-H columns. However,
HSC-S and HSC-H columns displayed lesser axial deformations than FAC and FAC-P columns.
The fire resistance of FAC-P column was also enhanced due to spalling mitigation facilitated by
burning of polypropylene fibers. Similarly presence of steel and hybrid fibers in HSC-S and

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HSC-H columns also slowed the degradation of tensile strength and mitigated spalling, thus
significantly enhanced the fire resistance of these columns.

5.5 Response after Fire Exposure
In many practical situations RC columns survive in burn-out fire scenarios. In such situations,
repair of fire exposed RC structures is often more economical both in terms of cost and time,
than to demolish and rebuild the structure. One of the major challenges therefore is to determine
the extent of damage to fire exposed columns. To assess such damage and the capacity of
structure for feasibility of repair, determination of residual strength in fire exposed RC columns
an important factor.
The extent of strength loss in RC columns due to fire exposure is dependent on a number of
factors, including type of fire exposure, temperatures in the concrete and steel, concrete and steel
properties (including strength) and load level. Due to high thermal capacity and low thermal
conductivity of concrete, RC columns may retain much of their initial strength under most
realistic fires, particularly if the columns do not experience significant fire-induced spalling. In
order to develop data on residual capacity of HPC columns, additional strength tests were carried
out on the survived RC columns tested for fire resistance.
5.5.1

Tested Columns

Since FAC-P, HSC-S, and HSC-H columns did not fail during the fire resistance tests, residual
strength tests were conducted on these three columns to determine the capacity of these columns
after exposure to fire. These columns survived the fire exposure which lasted from 4 to 7 hours.
After the fire tests, these columns were unloaded and left to cool down in the furnace for 24
hours before conducting residual strength tests at room temperature.

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5.5.2

Equipment and Test Procedure

The residual strength tests were carried out using the same loading frame as used for fire
resistance tests, but with the furnace lids removed. In the residual strength tests, the columns
were gradually loaded with vertical actuators at a prescribed rate and axial deformations were
recorded through LPTs attached to the top of the columns assembly. Each column was tested to
failure under axial load with semi fixed support conditions as shown in Figure 5.9. The load was
increased gradually at a rate of about 10 kN per minute and displacement was recorded as a
function of load till failure of the columns. Due to severe fire exposure, these columns had
already signs of cracks and surface scaling had occurred during the fire tests. During the loading
for residual strength tests, significant cracking and spalling was observed in the columns due to
the crushing of concrete under increasing load and this is illustrated in Figure 5.37.
5.5.3

Residual Strength Results

The results of axial load carrying capacity and post-fire residual strength of FAC-P, HSC-S, and
HSC-H columns is tabulated in Table 5.2. It can be seen that all three columns (FAC-P, HSC-S,
and HSC-H) displayed significant residual load-carrying capacity after exposure to fire. FAC-P
column retained lowest residual capacity of 697 kN that is about 34.5% of its ultimate strength
capacity while in HSC-S and HSC-H columns, higher residual strength capacity was retained as
839 and 741 kN, which is about 44.5 and 52% of their ultimate strength capacity respectively.
This is despite the fact that severe fire-induced degradation in strength and stiffness is
encountered in RC members during fire resistance tests. The higher residual capacity in FAC-P,
HSC-S, and HSC-H columns can be attributed to the partial regain of strength by concrete and
steel upon cooling, and strain hardening of the steel reinforcement.

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The measured load deformation response for the three columns during the residual strength tests
is captured in Figure 5.38. It can be seen that the axial deformation is higher in HSC-S and HSCH columns as compared to that in FAC-P column. This higher load-deformation capacity in
HSC-S and HSC-H can be attributed to presence steel fibers in the mix which induced toughness
and ductility of these columns. This improvement is in agreement with the fact that after
exposure to high temperatures, fiber reinforced HSC shows a higher overall residual compressive
and flexural strength and a higher elastic modulus (Lau and Anson, 2006) as compared to plain
HSC. After fire exposure FAC-P column acted more like plain HSC showing less loaddeformation capacity as compare to both HSC-S and HSC-H columns. Overall, hybrid fiber
reinforced HSC column displayed better post-fire performance facilitated by beneficial effects
from both polypropylene and steel fibers.

5.6 Summary
Results from fire resistance tests show plain and fiber reinforced FAC columns exhibit lower fire
resistance than fiber reinforced HSC columns. The use of fibers enhances the fire resistance of
both FAC and HSC columns through spalling mitigation and enhanced mechanical properties.
The three columns tested for residual strength retained significant load carrying capacity that
ranged from 34.5 to 52% of ultimate strength capacity. As indicated by test results, this
serviceability of columns is helpful for their rehabilitation and restoration. Results from the fire
tests provide a better understanding of the response of plain and fiber reinforced HPC columns
under realistic fire, and load conditions. These tests provide valuable data for validating
computer models for tracing the fire response of HPC columns. The HPC columns can retain
much of their load carrying capacity after exposure to fire, particularly once different fibers are
used in the HPC mix.

204

Table 5.1 - Mix proportions for four batches of concrete.

Components

FAC

FAC-P

HSC-S

HSC-H

416

416

513

513

705

705

684

684

1041

1041

1078

1078

41

41

43

43

141

141

-

-

76

76

-

-

3

135

135

130

130

Water cement ratio (w/c)

0.33

0.33

0.25

0.25

3.8

3.8

-

-

High range water reducer/Superplasticizer – Type F,
3
kg/m

9.12

9.12

15

15

Slump, mm

150

100

100

90

-

2

-

2

-

-

42

42

2564

2530

2490

2464

7 days

76

72

66

68

28 days

102

81

67

68

90 days

107

100

72

75

Test day

107

100

77

80

Cement (Type I), kg/m
Fine aggregate, kg/m

3

3

Course aggregate (max size 10mm), kg/m
Silica fume, kg/m

3

3

Fly ash - Class C (25% replacement of cement), kg/m
Slag - Grade 120), kg/m
Water, kg/m

3

Retarding admixture – Type D, kg/m

3

3

Polypropylene fibers, kg/m (0.22% by volume)
3

Steel fibers, kg/m (0.54% by volume)
Unit weight of concrete, kg/m

3

3

Compressive strength (MPa)

205

Table 5.2 - Summary of test parameters for fire resistance test on columns.

Fire
exposure
(ASTM
E119 –
decay)

Total
test
time
(minute
s)

FAC

LF- decay
@4.16°C/
min

435

FAC-P

LF- decay
@4.16°C/
min

HSC-S

SF- decay
@11°C/mi
n

HSC-H

SF- decay
@11°C/mi
n

Column
designation

435

270

270

Concrete
strength (MPa)
28
Days

Test
day

102

107

81

72

75

100

77

80

Column
strength
(kN)

Load
ratio
(%)

Applie
d load
(kN)

Relative
humidity
(%)

Failure
times
(minutes)

Extent
of
spalling

Residual
strength
kN (%
of
ultimate
load
capacity)

2144

40

858

90

Failed
(165)

Severe

-

90.25

No
Failure
(435)

Nil

697
(34.5%)

91.25

No
Failure
(270)

Nil

839
(52%)

89.65

No
Failure
(270)

Nil

741
(44.5%)

2020

1612

1665

206

40

60

60

808

967

999

203 mm

4 #6 (19mm) rebars
#3 (10mm) ties

203 mm

Elevation

Cross-Section

Figure 5.1- Column elevation and cross-section showing design details

207

203 mm

3300 mm length

10 mm ties (135° @ 200 mm c/c
)

40 mm clear cover

50 mm effective
cover

Steel reinforcement cage
Formwork

Wires from TCs and SGs

Figure 5.2 - Steel cages inside column formwork with instruments wiring

Finishing of column
Formwork

Figure 5.3 - Casting and finishing of columns

208

TC 10
TC 1

TC 8

TC 7
TC 9

TC 4
TC 6
B

B

A

A

TC 3

TC 2
TC 5
Section BB

C

1981 mm

C

1626 mm

2762 mm

Section AA

TC 11

TC 12

TC 13
Section CC
Elevation

Cross-section

Figure 5.4 - Column cross-section showing location of thermocouples (TCs)

209

E

E
SG 1

D

D

1650 mm

2475 mm

HTSG 1

SG 3 HTSG 2

Section DD

SG 3

SG 2

Section EE

Cross-section

Elevation

Figure 5.5 - Column cross-section showing location of strain gauges (SGs)

Figure 5.6 - View of thermocouples in cross-section and strain gauges attached to steel rebars

210

Actuator

LPTNorth

Plate 406×406×25 mm

1650 mm

LPTEast

LPT-North

LPT-North

LPTEast

LPTWest
LPTNorth

LPTEast

Angle 100×100×12 mm

Vertical Displacement

LPT-North
1650 mm

Vertical Displacement

LPT-North

LPTWest

LPTEast

Lateral Displacement
West Column

Lateral Displacement
East Column

Plate 406×406×60 mm

Figure 5.7 - Column cross-section showing location of linear position transducers (LPTs)

211

(a) Picture of furnace and loading frame

305
460

(b) Schematic for column position relative to furnace
Figure 5.8 - Structural fire testing facility at MSU’s Civil Infrastructure Laboratory

212

Top linear position transducer
(LPT) for axial deformation
Wires from TCs and
Loading

Top steel plate
Steel angle attachments
Bottom steel plate

Figure 5.9 - End conditions for the columns before fire tests

Furnace temperature (°C)

1200
1000
800
600
ASTM E119

400

Design fire 1
200
Design fire 2
0
0

60

120

180

240

300

Time (minutes)
Figure 5.10 - Time temperature curve for fire scenario

213

360

420

2500

Furnace average
FAC-TC 1
FAC-TC 2
FAC-TC 3
FAC-TC 4
FAC-TC 5
FAC-TC 6
FAC-TC 7

Note: ° = (°
C
F-32)5/9

Temperature (°F)

2000

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.11 - Measured rebars and concrete temperatures for FAC column at Section AA
2500
Furnace average

Note: ° = (°
C
F-32)5/9

FAC-TC 8
Temperature (°F)

2000

FAC-TC 9
FAC-TC 10

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.12 - Measured rebars and concrete temperatures for FAC column at Section BB

214

2500
Note: ° = (°
C
F-32)5/9

Furnace average
FAC-TC 11

Temperature (°F)

2000

FAC-TC 12
FAC-TC 13

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.13 - Measured rebars and concrete temperatures for FAC column at Section CC
2500
Furnace average
FAC-P-TC 1
FAC-P-TC 2
FAC-P-TC 3
FAC-P-TC 4
FAC-P-TC 5
FAC-P-TC 6
FAC-P-TC 7

Note: ° = (°
C
F-32)5/9

Temperature (°F)

2000

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.14 - Measured rebars and concrete temperatures for FAC-P column at Section AA

215

2500
Note: ° = (°
C
F-32)5/9

Furnace average
FAC-P-TC 8

Temperature (°F)

2000

FAC-P-TC 9
FAC-P-TC 10

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.15 - Measured rebars and concrete temperatures for FAC-P column at Section BB
2500
Furnace average

Note: ° = (°
C
F-32)5/9

FAC-P-TC 11
Temperature (°F)

2000

FAC-P-TC 12
FAC-P-TC 13

1500

1000

500

0
0

100

200

300

400

500

Time (mins)
Figure 5.16 - Measured rebars and concrete temperatures for FAC-P column at Section CC

216

2500

Furnace average
HSC-S-TC 1
HSC-S-TC 2
HSC-S-TC 3
HSC-S-TC 4
HSC-S-TC 5
HSC-S-TC 6
HSC-S-TC 7

Note: ° = (°
C
F-32)5/9

Temperature (°F)

2000

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.17 - Measured rebars and concrete temperatures for HSC-S column at Section AA
2500
Note: ° = (°
C
F-32)5/9

Furnace average
HSC-S-TC 8

Temperature (°F)

2000

HSC-S-TC 9
HSC-S-TC 10

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.18 - Measured rebars and concrete temperatures for HSC-S column at Section BB

217

2500
Note: ° = (°
C
F-32)5/9

Furnace average
HSC-S-TC 11

Temperature (°F)

2000

HSC-S-TC 12
HSC-S-TC 13

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.19 - Measured rebars and concrete temperatures for HSC-S column at Section CC
2500

Furnace average
HSC-H-TC 1
HSC-H-TC 2
HSC-H-TC 3
HSC-H-TC 4
HSC-H-TC 5
HSC-H-TC 6
HSC-H-TC 7

Note: ° = (°
C
F-32)5/9

Temperature (°F)

2000

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.20 - Measured rebars and concrete temperatures for HSC-H column at Section AA

218

2500
Furnace average

Note: ° = (°
C
F-32)5/9

HSC-H-TC 8
Temperature (°F)

2000

HSC-H-TC 9
HSC-H-TC 10

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.21 - Measured rebars and concrete temperatures for HSC-H column at Section BB
2500
Furnace average

Note: ° = (°
C
F-32)5/9

HSC-H-TC 11
Temperature (°F)

2000

HSC-H-TC 12
HSC-H-TC 13

1500

1000

500

0
0

100

200

300

Time (mins)
Figure 5.22 - Measured rebars and concrete temperatures for HSC-H column at section CC

219

1400
Furnace
Rebar - FAC
Mid section - FAC
Rebar - FAC-P
Mid section - FAC-P

Temperature (°C)

1200
1000
800
600
400
200
0
0

100

200
300
Time (minutes)

400

500

Figure 5.23 - Comparison of measured temperature distribution for FAC and FACP columns
800

Temperature (°C)

700
600
500
Rebar - FAC
Mid section - FAC
Rebar - FAC-P
Mid section - FAC-P
Rebar - HSC-S
Mid section - HSC-S
Rebar - HSC-H
Mid section - HSC-H

400
300
200
100
0
0

100

200
300
Time (minutes)

400

500

Figure 5.24 - Comparison of temperature distribution for FAC and HSC columns

220

Axial deformation (mm)

4

FAC
FAC-P

0

HSC-S
HSC-H

-4
-8
-12
-16
0

100

200
300
Time (minutes)

400

500

Figure 5.25 - Measured axial deformations as a function of fire exposure time
FAC

Lateral deformation (mm)

120

FAC-P
HSC-S
90

HSC-H

60

30

0
0

90

180

270

360

450

Time (minutes)
Figure 5.26 - Measured lateral deformations as a function of fire exposure time in tested columns

221

Strain (micrometer/m)

500

0

-500

-1000
FAC HTSG 1
FAC HTSG 2
-1500
0

5

10
Time (min)

15

20

Figure 5.27 - Measured axial strains as a function of fire exposure time for FAC column at
Section DD

Strain (micrometer/m)

700
500
300
100
-100
-300
FAC SG 2
-500
0

4

8
Time (min)

12

Figure 5.28 - Measured axial strains as a function of fire exposure time for FAC column at
Section EE

222

2000
Strain (micrometer/m)

1500
1000
500
0
-500
FAC-P HTSG 1

-1000

FAC-P HTSG 2

-1500

FAC-P SG 3

-2000
0

50

100
Time (min)

150

Figure 5.29 - Measured axial strains as a function of fire exposure time for FAC-P column at
Section DD

Strain (micrometer/m)

1000
750
500
250
0
-250
FAC-P SG 3
-500
0

5

10

15
Time (min)

20

25

30

Figure 5.30 - Measured axial strains as a function of fire exposure time for FAC-P column at
Section EE

223

2000

Strain (micrometer/m)

1500
1000
500
0
-500
-1000
HSC S HTSG 1

-1500

HSC-S HTSG 2

-2000
0

5

10

15
Time (min)

20

25

30

Figure 5.31 - Measured axial strains as a function of fire exposure time for HSC-S column at
Section DD

Strain (micrometer/m)

500

250

0

-250
HSC S SG 1
HSC-S SG 2
-500
0

10

20
Time (min)

30

40

Figure 5.32 - Measured axial strains as a function of fire exposure time for HSC-S column at
Section EE

224

Strain (micrometer/m)

3000
2000
1000
0
-1000
HSC H HTSG 1
HSC-H HTSG 2

-2000

HSC-H SG 3
-3000
0

5

10
Time (min)

15

20

Figure 5.33 - Measured axial strains as a function of fire exposure time for HSC-H column at
Section DD
2500

Strain (micrometer/m)

2000
1500
1000
500
0
-500
HSC-H SG 1

-1000

HSC-H SG 2

-1500

HSC-H SG 3

-2000
0

10

20

30

40

Time (min)
Figure 5.34 - Measured axial strains as a function of fire exposure time for HSC-H column at
Section EE

225

FAC

FAC-P

HSC-S

HSC-H

Figure 5.35 – State of columns during fire test at 60 minutes into the test

FAC

FAC-P

(a) Typical column before test

HSC-S

(b) Columns after fire test

Figure 5.36 - State of columns before and after the fire resistance tests

226

HSC-H

FAC-P

HSC-S

HSC-H

Figure 5.37 - Columns after residual strength tests

Load (kN)

800

600

400
FAC-P

200

HSC-S
HSC-H

0
0

2

4
6
8
Deformation (mm)

10

12

Figure 5.38 - Load-deformation response of fire exposed columns during residual strength tests

227

CHAPTER 6
6

NUMERICAL MODEL

This chapter is mainly based on the following conference presentation and paper:
•

Khaliq, W., Raut, N. K., and Kodur, V. K. R. (2011). "Effect of tie configuration on fire
performance of high strength concrete columns." Proc., Conference presentation, ACI Fall
2011Conference.

•

Khaliq, W. and Kodur, V. K. R. (2012). "Effect of tie configuration on fire performance of
high strength concrete columns." SiF 2012 Conference at Zurich, Switzerland.

6.1 General
Fire response of concrete structures can be evaluated by applying heat transfer, thermodynamics,
and structural mechanics principles. For reliable fire response predictions, all influencing factors
including fire scenario, high temperature material properties, size of member, load, spalling, and
tie configuration have to be properly accounted for in fire resistance analysis. Developing a
numerical model for evaluating fire resistance is quite complex due to interdependency of many
of these significant parameters, as well as fire induced phenomenon such as cracking, spalling,
de-bonding and moisture migration that occurs in concrete structures. Currently available
commercial softwares are capable of accounting for complex structural geometry, but they are
not capable of fully accounting for microstructural phenomenon such as moisture migration, pore
pressure and spalling that occurs within a RC member under fire conditions.

228

Recently a macroscopic finite element (MFE) computer model was developed by Kodur et al.
(2009) and this model can account for most of the above mentioned factors and can capture the
fire response of RC beams and columns. However, this model does not account for high
temperature material properties of HPC (with and without fibers) and pore pressure induced tie
opening up in reinforced concrete columns. To enhance the capability two sub-models are
developed as part of current study. The first sub-model is to incorporate high temperature
properties of HPC and the second sub-model is to account the effect of tie configuration on fire
response of reinforced concrete columns.

6.2 Macroscopic Finite Element Model for Fire Resistance Analysis
6.2.1

General

The macroscopic finite element (MFE) based numerical model, developed by Kodur et al.
(2009), uses moment-curvature (Μ−κ) relations to trace the response of an RC structural
member (column or beam) in the entire range of loading up to failure under fire. In this model,
the RC structural member is divided into a number of segments along its length and the midsection of the segment is assumed to represent the behavior of the whole segment (Kodur et al.,
2009). The cross section, representing mid-section of each segment, is subdivided into elements
forming a two dimensional mesh. The fire resistance analysis is carried out by incrementing time
in intervals. The flowchart involving the various steps of analysis is shown in Figure 6.1.
At each time interval, the analysis is performed through three main steps namely, (1) establishing
temperatures due to fire, (2) carrying out heat transfer analysis to determine temperature
distribution in cross-section and (3) performing strength and deflection analysis. As part of step
three fire induced axial restraint force in RC structural member is calculated and then Μ−κ

229

relationship is generated based on axial and lateral forces computed in previous sub-step for each
segment and finally structural analysis of the member is performed to compute axial
deformations and internal forces.
Full details of the model, including derivation of equations and validation of the model are
comprehensively presented by Kodur et al. (2009) and Raut (2011). However, for the sake of
completeness, overall procedure used in the model and some of the main drawbacks in existing
model are presented here.
6.2.2

Fire Temperatures

First step in fire resistance analysis is calculation of fire temperatures. The fire temperature is
assumed to follow a standard fire curve such as ASTM E119 (ASTM E119-08b, 2008) or ISO
834 standard fire or any other design fire scenario. The time-temperature relationship for the
ASTM E119 and ISO 834 standard fire can be approximated by the following equations:

(

(

))

T f = T0 + 750 1 − exp − 3.79553 t h + 170.41 t h

(6.1)

T f = 20 + 345 log(8t + 1)

(6.2)

where th = time (hours), T0 = initial temperature (°C), and Tf = fire temperature (°C).
Any other design fire, standard hydrocarbon fire and user defined fire can be used in the model
based on the known time temperature relations.
6.2.3

Thermal Analysis

6.2.3.1 Cross-sectional Temperatures
The temperatures within the cross-section of each segment are computed using the finite element
approach. The fire exposure to columns can be from 1-, 2-, 3-, or all 4-sides and the fire

230

temperature established in Section 6.2.2 forms the input to thermal analysis. The cross-sectional
area of each segment (mid-section) is subdivided into a number of elements and temperature rise
in a column segment is derived by establishing a heat balance for each element. The temperature
is assumed to be uniform along the length of the segment and thus the calculations are performed
for a unit length of each segment. Steel reinforcement is not specifically considered in the
thermal analysis because it does not significantly influence the temperature distribution in the
column cross-section (Lie and Irwin, 1993). However, in the model, the location of the steel
reinforcement is accounted for while discretizing the column cross-section in to elements for
thermal analysis such that more accurate temperature distribution is obtained.
Based on the conservation of energy, the following equation can be obtained for one dimensional
heat transfer problems (Cook et al., 2007):

ρc

dT
dq
=−
+Q
dt
dx

(6.3)

Applying Fourier’s law, which relates the heat flux to the temperature gradients as q = − k

dT
,
dx

Eq. (6.3) can be written as

 dT 
d k

dT
 dx  + Q
=
ρc
dt
dx

(6.4)

Thus, the governing heat transfer equation within a rectangular column cross-section, that
represents a two dimensional problem, can be written as:

ρc

dT
= ∇k∇T + Q
dt

(6.5)

where k = thermal conductivity, ρc = heat capacity, T = fire temperature, t = time, Q = heat
source, and q = heat flux.

231

At the fire-column interface, the mechanism for heat transfer is through radiation and
convection. The heat flux on the boundary due to convection and radiation can be given by the
following two equations which relate the heat flux due to convection and radiation to the
temperature of fire (or ambient temperature for faces not exposed to fire):

(
)
qcon = hcon (T − T )
E

qrad = hrad T − T
E

(6.6)
(6.7)

where
qrad and qcon are radiative and convective heat fluxes,
hrad and hcon are radiative and convective heat transfer coefficient,

2
hrad = 4σε  T 2 + TE (T + TE ) ,





(6.8)

TE = temperature of the environment surrounding the boundary,
-8

2

4

σ = Stefan-Boltzmann constant taken as 5.67×10 (W/m .°K ), and
ε = emissivity factor.
Therefore, the total heat flux on the column boundaries (qb) can be given by the equation:

(

qb = (hcon + hrad ) T − T
E

)

(6.9)

Using Fourier’s Law, the governing heat transfer equation on the boundary of the column can be
written as:

 ∂T
∂T 
nz  = − h  T − T 
ny +
k

 ∂y
f 


∂z 



(6.10)

where

232

ny and nz = components of the vector normal to the boundary in the plane of the cross-section,
and
h = hrad + hcon
Since the column may be exposed to fire from any of the four sides, two types of boundary
equations are to be considered for thermal analysis, namely:
•

Fire exposed boundaries where the heat flux is governed by the following equation:

 ∂T
∂T 
nz  = − h f  T − T 
k ny +

 ∂y
f 


∂z 


•

(6.11)

Unexposed boundary where the heat flux equation is given by:

 ∂T
∂T 
nz  = −hc (T − T0 )
k ny +
 ∂y
∂z 



(6.12)

where
hf and hc are heat transfer coefficient of the fire side and the cold side, respectively, and
Tf and T0 are fire and cold side temperature, respectively.

6.2.3.2 Pore Pressure Calculations
The cross-sectional temperatures generated above are utilized to evaluate pore pressure in each
segment at each time step (Dwaikat, 2009; Dwaikat and Kodur, 2009; Raut, 2011). The pore
pressure calculations are quite complex in concrete medium and a number of assumptions are
made to deal the complications involved with moisture migration under elevated temperatures.
Some of the key assumptions are:

233

•

Concrete is a continuum medium. The solid skeleton (concrete structure) is assumed to be
undeformable. This is because the mechanical and thermal deformation of the solid phase
is small when compared to the volume changes due to other processes such as
evaporation.

•

Water vapor is an ideal gas, which is valid for most engineering applications (Harmathy,
1969; Harmathy, 1971; Huang, 1979).

•

Mobility of liquid water is ignored. This assumption is valid because Darcy’s coefficient
(permeability) for liquid water in concrete is much smaller than that for water vapor
(Harmathy, 1969; Sahota and Pagni, 1979).

•

The effect of air is ignored in the analysis. This assumption is considered to be valid
because the mass of air in concrete is much smaller than the mass of water.

•

Water is incompressible liquid. This assumption is valid because the volumetric
deformation of liquid water due to pressure is much smaller than the volumetric changes
due to other processes such as evaporation.

•

The effect of latent heat and heat of dehydration is not accounted for in the analysis.
Accounting for latent heat and heat of dehydration will slightly reduce the predicted
temperatures. Thus, latent heat and heat of dehydration can be conservatively ignored in
the analysis.

The governing equations for the calculation of vapor pressure in concrete are derived using four
main principles; namely:
•

Conservation of mass for liquid water,

•

Ideal gas law,

•

Total volume of all different components in a unit volume of concrete equals unity, and

234

•

Conservation of mass for water vapor.

The basic equations that govern the conservation of mass for liquid water is given by:

E = mLW 0 − mL + mD

(6.13)

where E = mass of evaporated water, mLW0 = mass of liquid water at time t = 0 (initial mass
of liquid water), mL = mass of liquid water at any time, t, and mD = mass of liquid water
formed due to dehydration.
The ideal gas law is used to relate the pressure, the volume, the mass, and the temperature for
water vapor. Equations are derived based on the conservation of mass of water vapor using
Darcy’s Law, which relates the mass flux to the pressure gradients. Mathematically solving
constitutive equations, a simplified equation is obtained for pore pressure calculations by
introducing three parameters, A, B, and C as follows:

dP
A V = ∇B∇P + C
V
dt

(6.14)

where


m  dm
V M
A = 1 − V  L + V 


RT 
 VV ρ L  dP
V


k
B = mV T
µV



1 − mV  − dmL + dmD  + mV + mV dρ L (m − m ) dT

C= 

D
L 
2
 VV ρ L  dT
dT  T
dt


VV ρ L dT


Finite difference analysis in space and time domains is utilized to solve Eq. 6.14 to compute the
pore pressure PV. The parameters A, B, C are based on a particular temperature and resultant

235

pore pressure is computed at target temperature. In equation 6.14 PV =pore pressure, mV = mass
of water vapor, R = gas constant, M = molar mass of water, VV = volume fraction of water vapor,
and T = temperature (°K) VL = volume fraction of liquid water, VD = volume fraction of
dehydrated liquid water, and ρL = density of liquid water, kT = intrinsic permeability of concrete
at temperature, T, and µV = dynamic viscosity of water vapor.

6.2.3.3 Initial Boundary Conditions
The initial boundary conditions for pore pressure calculations are assumed as follows:
•

Initial pore pressure (PV0) can be computed as:

P 0 = RH ⋅ PS 0
V

(6.15)

where RH = initial relative humidity in the concrete, and PS0 = initial saturation pressure
which can be computed based on the initial temperature of concrete.
•

On the boundaries (surface) of the column the water vapor is assumed to be transferred
through diffusion. Thus, the governing mass transfer equation of water vapor at the column
boundaries can be written as:


 ∂P
∂P
λ  V n y + V nz  = − D0 (ρV − ρV∞ )

 ∂y
∂z



(6.16)

where D0 = diffusion coefficient of water vapor at the boundaries of the column, ρV =
density of water vapor in the concrete boundaries, and ρV∞ = density of water vapor in the
surrounding environment. By assuming ρV∞ to be constant during fire exposure (due to the

236

lack of information on the changes that take place in the surrounding environment of the
column), Eq. (6.15) can be written as:


 ∂P
∂P
RTρV∞ 
D M
λ  V n y + V nz  = − 0  P −

V

 ∂y
∂z
M 
RT 



(6.17)

6.2.3.4 Finite Element Solution
Galerkin finite element formulation is applied to solve the heat transfer equation Eq. (6.5) and
the differential equation for pore pressure development Eq. (6.14). Both equations can be written
in the following form:

A1

du
= ∇B1∇u + C1
dt

(6.18)

The governing equation at the column boundaries for both heat and mass transfer can be written
as:

 ∂u
∂u 
A11 n y + nz  = − B11 (u − C11)
 ∂y
∂z 



(6.19)

The cross-section of an RC column is divided into elements as shown in Figure 6.2. According to
the finite element formulation, the material property matrices and the equivalent nodal heat or
mass flux (stiffness matrix Ke, mass matrix Me, and nodal heat or mass flux Fe) are generated for
each element. These matrices are given by the following equations (Williams, 2004)

 ∂N ∂N T
∂N ∂N T 
 dA + ∫ NB11N T ds
+ B1
Ke = ∫  B1
∂y ∂y 
Γ
A  ∂x ∂x



(6.20)

M e = ∫ A1NN T dA
A

(6.21)

237

Fe = ∫ NC1dA + ∫ NB11C11ds
A
Γ

(6.21)

where N = vector of the shape functions, A1, B1, C1, A11, B11 and C11 = parameters computed
by comparing equations (6.5), (6.11), (6.12), (6.14) and (6.17) with equations (6.18) and (6.19)
for heat and mass transfer, Γ = boundary of the column, and s = distance along the boundary Γ.
6.2.3.5 Spalling Calculations
Once the pore pressure in various concrete elements is calculated, a simplified approach is
applied to determine spalling. The computed pore pressure is compared against the temperature
dependent tensile strength of concrete as shown in Figure 2.18. When the effective pore pressure
exceeds the temperature dependent tensile strength at that time step, spalling is assumed to occur
in that concrete element; i.e.:

nPV > f tT

(6.23)

where: n is porosity of concrete and is equal to VV +VL, ftT = tensile strength of concrete for
temperature, T, VV is volume fraction of water vapor, VL is volume fraction of liquid water.
Once stress due to pore pressure exceeds the tensile strength, spalling occurs, the concrete
element is assumed to be lost (removed from the section) and the reduced concrete section and
new boundary surface is considered in the subsequent hydro-thermal and strength analyses. In
this way, the coupling between spalling and hydro-thermal analysis will be accounted for in the
model.

238

6.2.4

Strength Analysis

6.2.4.1 General Analysis
The third step in the numerical model is the strength analysis at the mid-section of each segment.
The cross-sectional temperature distribution generated from hydro-thermal analysis is used as
input to the strength analysis. For the strength analysis, the following assumptions are made:
Plane sections before bending remain plane after bending.
There is no bond-slip between steel reinforcement and concrete.
At each time step, the strength analysis is performed in three sub-steps; namely, estimating the
axial force in each segment of the restrained column, generating the M-κ relationship for each
segment, and carrying out nonlinear stiffness analysis to trace the response of the column under
fire conditions.
The strength calculations are carried out using the same mesh used for thermal analysis as shown
in Figure 6.2(d). The temperatures, deformations and stresses in each element are represented by
those at the center of the element. The temperature in each element is obtained by averaging the
nodal temperatures of rectangular elements. For steel rebars the temperature is assumed to be
that at the center of the rebar.
The total strain in a concrete element, at any fire exposure time, is taken as the sum of the
thermal expansion, the mechanical strain, the creep strain, and the transient strain:

ε t = ε th + ε me + ε cr + ε tr

(6.24)

where εt = total strain, εth = thermal strain, εme = mechanical strain, εcr = creep strain, and εtr =
transient strain in concrete.

239

Thermal strain (εth) is directly dependent on the temperature in the element and can be obtained
by knowing the temperature and thermal expansion of the concrete. Creep strain is assumed to be
function of time, temperature, and stress level, and is computed based on Harmathy’s (1993)
approach using the following expression:

σ
t ed (T −293)
ε cr = β1
f c,T
where β1 = 6.28×10

(6.25)

-6 -0.5

s

, d is a constant taken as 2.658×10

-3

-1

K , T = concrete temperature

(°K) at time t (s), fc,T = concrete compressive strength at temperature T, and σ = stress in the
concrete at the current temperature.
The transient strain (εtr), which is specific for concrete under fire conditions, is computed based
on the relationship proposed by Anderberg and Thelandersson (Anderberg and Thelandersson,
1976). The transient strain is related to thermal strain as follows:

∆ε tr = k2

σ
fc,20

∆ε th

(6.26)

where k2 = a constant ranges between 1.8 and 2.35 (a value of 2 will be used in the analysis),
∆εth = change in thermal strain, ∆εtr = change in transient strain, and fc,20 = concrete strength at
room temperature.
For steel reinforcement, the total strain, at any fire exposure time, is calculated as the sum of
three components, as given by the following equation:

ε ts = ε ths + ε mes + ε crs

(6.27)

240

where εts, εths, εmes and εcrs are total strain, thermal strain, mechanical strain, and creep strain in
the steel reinforcement, respectively.
Similar to concrete, thermal strain (εth) in steel can be directly calculated from the knowledge of
rebar temperature and the thermal expansion coefficient of the reinforcing steel. Creep strain
(εcr) in steel reinforcement is computed based on Dorn’s theory and the model proposed by
Harmathy (Harmathy, 1967) with some modifications made to account for different values of
yield strength of steel. According to Harmathy’s model, creep strain in steel is given by the
following expression:

13

ε crs =  3Zε t2 

0




θ 1 3 + Zθ

(6.28)

where

4.7

6.755 × 1019  σ 



 fy 



Z =

16  10.8 σ f y 

1.23 × 10  e





(

)


5 
≤
f y 12 

,
σ
5
> 
f y 12 


σ

1.75

σ 
−∆H RT dt ∆H =
ε t 0 = 0.016 
θ = ∫e
38900°K, t = time (hours),
,
 fy 
R



, σ = stress in

steel, and fy = yield strength of steel.
Figure 6.3 shows the distributions of total strain, stress, and internal forces for the column crosssection at any fire exposure time. The total strain in any element (concrete or rebar) can be
related to the curvature of the column by the following expression:

241

εt = ε0 + κ y

(6.29)

where: ε0 = total strain at the geometrical centroid of the column cross-section, κ = curvature,
and y = the distance from the geometrical centroid of the column cross-section.
In the model, Eq. (6.24) to Eq. (6.29) can be used to carry out strain computation of a segment at
any given fire exposure time. At any time step, and for an assumed value of ε0 and κ, the total
strain in each element (concrete or rebar) can be determined using Eq. (6.29). Then the thermal,
transient (for concrete only), and creep strains in the concrete and rebars are evaluated using
known temperatures and corresponding equations derived above. Using the knowledge of total,
thermal, transient, and creep strains, the mechanical strain in concrete or steel element can be
evaluated by rearranging Eqs. (6.24) to Eq. (6.27):

ε me = ε t − ε th − ε cr − ε tr

for concrete

(6.30)

ε mes = ε ts − ε ths − ε crs

for steel

(6.31)

Then for the estimated mechanical strain, the stress in the element can be established using the
temperature dependent stress-strain relations of steel and concrete. Detailed procedure for
evaluating thermal, mechanical, creep and transient strains in concrete and reinforcing steel is
given by Dwaikat (2009).
6.2.4.2 Calculation of Fire Induced Axial Force
RC columns can develop significant restraint forces under fire exposure. The degree of restraint
is dependent on the support conditions and will determine the behavior and fire resistance of an
RC column. Generally, the axial restraint force in an RC column is compressive during the
expansion phase of the column and tensile when the column starts contracting. Thus the axial
restraint force is computed as:
242

P r= kr ∆

(6.32)

where: Pr = axial restraint force, kr = axial restraint stiffness provided by adjoined beams
supported by the column, ∆ = axial deformation of the column.
For an assumed value of axial restraint force Pr, an iterative procedure is used to solve for
change in segment length in order to compute the axial strain in each segment. The constitutive
equations for calculating the total axial strain and axial strain in each segment and also the
governing compatibility equations are given by Dwaikat (2009). These equations are solved to
ensure the compatibility requirements with ∆ being calculated using Eq. (6.32). The value of Pr
is modified until compatibility conditions are satisfied within a pre-determined tolerance. The
error involved in the estimation of total axial strain and stain in segment becomes smaller if
shorter time steps are used.
6.2.4.3 Generation of Moment-Curvature Relationships
Once the axial restraint force in the column is computed, the moment-curvature (M-κ)
relationships for each segment of the beam or column are generated through an approach
analogous to the method used for the analysis of prestressed concrete beams. In this approach,
M-κ relationships are established by iterating the central total strain (ε0) and the curvature (κ).
At each time step, analysis starts with an assumed value of curvature and central total strain (in
concrete) are assumed. Then, the total strain in each of the rebars and concrete elements is
computed from the assumed strain and curvature. The stresses in the rebars and the concrete
elements are determined utilizing the constitutive laws for concrete and reinforcing steel. The
temperature in rebars is assumed to be equal to the temperature at the location of the center of the

243

rebar. Once the stresses are known, the forces are computed in the concrete and the rebars. The
curvature is then iterated until equilibrium of forces is satisfied (internal force equal to the fire
induced axial restraint force). Once the equilibrium is satisfied, the moment and the
corresponding curvature are calculated. Thus, the values of moment and curvature are stored to
represent a point on the M-κ curve. The value of the central total strain is incremented to
generate subsequent points on the moment curvature curve. This procedure is repeated for each
time step of fire exposure and the values of the M-κ curves are stored as a point on moment
curvature curve at various time steps. The generated M-κ curves are used for tracing the behavior
of the column through nonlinear structural analysis. The generation of M-κ relationships is an
important part of the numerical model since these relationships form the basis for the fire
resistance analysis of the RC column.
6.2.4.4 Column Analysis
The M-κ relationships and the axial restraint force generated for various segments are utilized to
trace the response of the whole column exposed to fire. At each time step the deformations in the
column are evaluated through a stiffness approach. The secant stiffness for each segment is
determined from the M-κ relationships, based on the moment level reached in that particular
segment.
Each node in the idealized column is assumed to have five degrees of freedom (namely; two
rotations and three displacements) in the case of rectangular columns and three degrees of
freedom (namely; rotation and two displacements) in the case of circular columns. The
deformation of the column is computed using an iterative procedure described by Campbell and
Kodur (1990). Accordingly, an iterative column analysis is carried out at each time step first, a

244

linear analysis is carried out using the initial rigidity of the column (EI0) to determine the
moment distribution along the span of the column. The segment having the maximum bending
moment is selected to be the critical segment.
The second step is to increment the curvature in the critical segment and the curvature and
moment distributions along the span of the column (in each segment) are computed for each
increment of the curvature. An iterative procedure is employed to obtain the solution at each
increment of curvature such that equilibrium, compatibility, and convergence conditions are
satisfied, and the procedure is illustrated in Figure 6.4.
For each increment, a target curvature is selected for the critical segment. The column is
analyzed under a unit load and the bending moment and the curvature in each segment are
computed. The curvature in each segment is multiplied by a scaling factor that is computed
through dividing the target curvature in the critical element by the computed curvature in the
same element. The new secant rigidity for the next iteration can be computed from the generated
M-κ relationship. The iterative procedure continues until convergence is achieved where the
rigidity in each segment is approximately maintained within a certain tolerance.
In the iterative procedure described above, the stiffness matrix and the loading vector are
computed for each longitudinal segment. Then these matrices are assembled in the form of
nonlinear global stiffness equation, which can be written as:

K g δ = Pf + Ps

(6.332)

where: Kg = global stiffness matrix, δ = nodal displacements, Pf = equivalent nodal load vector
due to applied loading, and Ps = equivalent nodal load vector due to P-δ effect.

245

The effect of the second order moments, developed due to the axial restraint force, is calculated
using the following equation:

Ps = − K geoδ

(6.34)

where: Kgeo = geometric stiffness matrix, δ = nodal displacements, and Ps = equivalent nodal
load vector due to P-δ effect.
The second order moments are then added to the external loads in the stiffness analysis as given
by equation (6.33). Thus, for any given time step, the temperatures (in concrete and steel),
moment capacity and curvatures, as well as deformations in the column are known for a given
fire exposure. These output parameters are used to evaluate failure of the column either at local
(in each segment) or at global (whole column) levels.
6.2.4.5 Failure Limit State
The model generates various critical output parameters, such as temperatures, stresses, strains,
internal forces, and deformations at various fire exposure times. These output parameters are
used to check against predefined failure criteria. At every time step, each segment of the
structural member is checked against thermal, strength and deflection failure criteria. The
analysis is continued until strength failure of the structural member is reached. The different
failure limits incorporated into the model are:
•

The temperature in steel rebars exceeds the critical temperature which is 593°C for
reinforcing steel.

•

The applied load exceeds the load carrying capacity of the column.

•

Resultant axial deflections exceed the limiting deflection and rate of deflection.

246

The user has the option to specify any (or all) of the failure limit states mentioned above to
define failure.

6.3 Limitations of Existing Numerical Model
The model generates various critical output parameters, such as temperatures, stresses, strains,
axial restraint force, axial deformation, lateral deformation, and axial load and moment
capacities at various fire exposure times. The temperatures, capacity and deflections generated in
each time step are used to evaluate failure of the column at that time step. However, this
numerical model does not take in to account two important factors that influence the fire
resistance of HPC columns. These factors are (1) specific high temperature material properties of
HPC such as FAC and SCC (plain and with different fiber combinations) and (2) effect of
modified (135°) tie configuration on fire response of HPC columns. The two tie configurations
that are used for RC columns are show in Figure 6.5(a). It can be seen from Figure 6.5 that
modifying the tie configuration to 135° significantly reduces the spalling progression and thus
enhances fire performance of RC columns. Both of these factors are critical for accurate and
realistic fire resistance predictions for HPC columns.

6.4 Extension to Macroscopic Finite Element Model
The above presented MFE model is extended for fire resistance analysis of HPC columns by
incorporating two factors namely high temperature material properties of HPC, and the effect of
tie configuration on fire performance of columns. As part of this extension, two subroutines are
developed, one to capture the pertinent high temperature properties to HPC and second one for
accounting for the effect of tie configuration.

247

6.4.1

High Temperature Properties

As discussed in Chapter 2, columns made of HPC have lower fire resistance than conventional
concretes and it is due to different thermal and mechanical properties of HPC as compared to
conventional concrete. It is therefore imperative to incorporate specific HPC properties in the
numerical model to evaluate the fire resistance of RC columns made from that particular HPC.
For HPC namely HSC, FAC, SCC and FRC, various empirical property relations which have
been developed as part of characterization of high temperature material property tests presented
in Chapter 3 and 4 are incorporated into the model. These relations are thermal conductivity,
specific heat and thermal expansion, and compressive strength, splitting tensile strength, elastic
modulus and stress-strain curves. These high temperature material property relations are
incorporated as new subroutines in the MFE model that define high temperature material
properties in fire resistance calculations.
The thermal properties of HPC (HSC, FAC, SCC and fiber reinforced concrete) are added to
thermal part (thermal solver) of MFE model and given a material number at appropriate place.
Compressive and tensile strength of concrete are also incorporated in thermal solver of the MFE
model. Tensile strength relations are incorporated into thermal solver of the model for different
types of HPC so that spalling could be accurately predicted for specific concrete type. As shown
in Figure 6.1 the spalling is checked after thermal analysis and pore pressure calculations. At this
step the tensile strength of HPC (with and without fibers) is used against effective pore pressure,
if pore pressure overcomes the tensile strength of concrete it is assumed that spalling has
occurred and geometry of the cross-section of columns is updated for further calculations. The
mechanical properties comprising of compressive strength, tensile strength and elastic modulus
are also incorporated into structural part (structural solver) of the MFE model and given a

248

material number. The NSC and HPC columns are assumed to have a permeability of the order
-16

10

and 10

-18

2

m respectively. The melting of polypropylene fibers in concrete is taken into

account by varying the permeability of HPC from 10

-18

to 10

-17

m2 at 160°C when

polypropylene fibers melt away and enhance the permeability of HPC. With this addition, model
is able to predict realistic fire response of HPC columns by inputting unique high temperature
material properties of HSC, SCC, and FAC with and without fibers.
6.4.2

Approach to Model Tie Configuration

The beneficial effect of lateral confinement in concrete columns, both tie configuration (135°)
and closer spacing of ties, has been well recognized in seismic design of columns (Bayrak and
Sheikh, 2001; Pantazopoulou, 1998; Richart et al., 1929). This design philosophy is based on the
principle that the compressive strength of the confined concrete core of a column after stress
induced spalling should be equal to the strength of the gross section of the column before the
occurrence of spalling (Richart et al., 1929). The ties in column, when bent at 135°, achieve
sufficient lateral confinement and enhance ductility of column under seismic loading (Bayrak
and Sheikh, 2001; Berry and Eberhard, 2005; Pantazopoulou, 1998).
Similar approach, as that developed for seismic loading, can be applied to model the effect of tie
configuration on fire resistance of reinforced concrete columns. However, in the case of fire
conditions, additional stresses due to temperature induced vapor pressure and thermal strains are
to be considered along with mechanical stresses due to loading on the column. Also, bond
strength that develops at the tie-concrete interface deteriorates with temperature and also due to
occurrence of fire induced spalling. The force acting on the ties from pore pressure, mechanical

249

loading and thermal effects should be checked against this bond strength so as to ensure that the
ties have sufficient resistance and do not open-up through yielding.
When RC columns are exposed to fire, temperatures in concrete, steel reinforcement and ties
gradually increase. The increasing temperatures in concrete lead to build-up of pore pressure
which cannot be dissipated due to low permeability of concrete (characteristic of HSC). When
this pore pressure exceeds tensile strength of concrete, spalling occurs. The fire induced spalling
in concrete usually occurs in high strength concrete (HSC) structural members because of low
permeability associated with HSC. Such spalling not only leads to loss of cross-section in the
column, but also alters the bond resistance of the ties.
When exposed to fire, significant level of internal stresses are generated on ties and these stresses
result from load induced mechanical strains, temperature induced thermal expansion, and fire
induced vapor pressure as a result of water becoming vapor. The effective stress that is the sum
of three stresses (pore pressure, mechanical loading and thermal effects) acts as hoop stress on
ties. The resistance provided by ties against the effective stress is through the bond (strength)
action between tie and concrete interface, which also degrades with increasing temperatures.
When the force resulting from effective stress exceeds the bond strength of ties, the ties will
open-up (fail) through yielding of the ties.
The equations for confinement damage model under fire conditions can be derived based on
approach adopted in seismic analysis of concrete columns. Under axial load, concrete core
expands laterally and pushes against longitudinal rebars resulting in traverse loads. From
longitudinal rebars, these traverse loads are transferred to ties. At the tie level, where lateral
restraints are present, the lateral force is higher, whereas at the level between the two ties this
force will be smaller as the longitudinal rebars can deform outward and concrete core and

250

expand without restraint. The pressure exerted by the expanding concrete core in the form of
hoop stress on ties and the resultant confinement provided by ties to longitudinal rebars can be
used to model the tie behavior.
Free body diagram of various components of an RC column and forces acting on rebar and ties is
illustrated in Figure 6.6. The longitudinal rebar between the two ties is subjected to a force which
varies as sinusoidal wave function (Bayrak and Sheikh, 2001). At the level of ties a lateral
restraint is provided by tie corners, and the resulting force on longitudinal rebar is higher (Figure
6.6(a)). At the mid-level between the two ties, the force is the lowest as the concrete core can
expand relatively easily and thus exert force on longitudinal rebars. This force varies along the
longitudinal rebar and its variation can be taken as:

 2πx 
F( x) = F0 + Fv × cos
≥0
 s 

(6.35)

where F(x) is the force function acting along longitudinal rebar, F0 is the average force acting on
longitudinal rebar; Fv is the magnitude of variable part of force; (x) is the coordinate (distance)
along the length of rebar and (s) is tie spacing as shown in Figure 6.6(b) and (c). The unknowns
in Eq (6.35), F0 and Fv, at a given distance (x) can be determined by applying force equilibrium
and geometric boundary conditions. These two unknowns F0 and Fv, can be related to tie
spacing (s) and critical tie spacing (scr). Critical tie spacing, taken from the analogy used in
seismic design, is at the mid-height between two ties where effective confined concrete area is
assumed to be zero (Bayrak and Sheikh, 2001).

251

This implies that if s= scr at x = scr /2, the force exerted by ties on longitudinal rebars (F(x))
becomes zero, leading to variable part of the force Fv as:

 s
Fv = F0 
s
 cr






2
(6.36)

By substituting the value of Fv back to Eq. (6.35) the force acting on longitudinal bars can be
calculated as:

2
 

s 
 2πx 
 × cos 
F( x) = F0 1 + 

  scr 
 s 





(6.37)

The force developed in the ties can be obtained by integrating the force on longitudinal rebar
and applying relevant boundary conditions:

s
Ftie = 2 ∫0 / 2 F( x ) dx

(6.38)

Solving Eq (6.38) gives the total tie force acting on the corner of the longitudinal rebar which
translates to:

π 
Ftie = 2 Atie sin σ core
4

(6.39)

where Atie is cross sectional area of tie, σcore is stress resultant which is the sum of load induced
stress, thermal stress and pore pressure coming from concrete core.
Knowing the applied load on the column during fire exposure, load induced (mechanical) stress
can be evaluated at any given fire exposure time. It should be noted that this stress significantly
increases with increasing temperature due to degradation of strength properties of concrete and
steel. Further, if there is any fire induced spalling, the cross-section of column reduces and this
252

leads to higher mechanical stresses in column. The second component of the stress acting on the
ties is the fire induced thermal stress which can be evaluated knowing the temperatures in the
column. The thermal stress is evaluated by utilizing thermal expansion multiplied by the elastic
modulus of concrete both of which vary as a function of temperature.
The third component of the stress that is acting on the ties is the pore pressure in concrete which
can be evaluated through an hydrothermal model (Kodur et al., 2009). This model uses the
principles of mechanics and thermodynamics including the conservation of mass of liquid water
and water vapor to predict the pore pressure in the concrete exposed to fire (Dwaikat and Kodur,
2009). In the hydrothermal model, the mass transfer equation for water vapor inside heated
concrete can be written as:

 dP 
A  V  = ∇ B ∇ σP + C
V
 dt 
where:

(6.40)

σPV = pore pressure, t = time, A, B and C = parameters that depend on pore pressure,

temperature, rate of increase in temperature, permeability of concrete, initial moisture content,
and the isotherms used in the analysis. Isotherms are used to predict the liquid water inside
concrete as a function of pore pressure for a constant temperature.
Finite element analysis is used to solve Eq (6.40) and compute the pore pressure (σPV)
distribution within the elements of each segment along the length of the structural member. With
combination of the three stresses resulting from pore pressure (σPV), thermal expansion
(σthermal), and mechanical loading (σmechanical) resultant effective stress on tie is calculated. The
equation governing this condition at time T is given by:

253

σ core ,T = σ P
where

V

+ σ thermal + σ mechanical

(6.41)

σPV is stress due to pore pressure, σthermal is stress coming from thermal expansion of

concrete core and

σmechanical is stress resulting from axial load on column. With the effective

stress (σcore,T) at temperature T known in the tie, the force acting on ties (Ftie) is computed as:

π 
Ftie,T = 2 Atie sin σ core,T
4

(6.42)

The resisting force provided by the tie is the force developed between the tie and concrete
interface. This tie-concrete interface force is dependent on the length of the tie leg, the bar
diameter and the yield strength of the steel rebar used as ties. The bond strength therefore can be
related by taking into account the yield strength of the multiplied by the tie-concrete interaction
area which is given by the relation for room temperature calculations:

Fbond = ( 2πrl d )f y

(6.43)

where fy is the yield strength of steel at room temperature, ld is the development length of the leg
of the tie, and (r) is the radius of steel rebar used as tie. However, as steel strength also degrades
with temperature, the resulting resisting bond strength of the ties also decreases with temperature
and is given by the relation:

Fbond = ( 2 π rl d )f s ,T

(6.44)

where fs,T is the stress in steel at temperature T.
Knowing the force acting on ties and bond strength that develops in ties, the state of tie can be
checked and failure (opening up of ties) is said to occur when.
254

Ftie > Fbond

(6.45)

It can be seen that the resistance of tie (Fbond) is dependent on temperature as well as the bond
between tie-concrete interfaces; therefore it is highly dependent on cross-sectional integrity of
RC column. In case of fire induced spalling, the outer cover of cross-section spalls away leaving
the outer side of 90° tie exposed to fire and the tie-concrete interaction lost which leaves the
bond strength reduced to half. However, in the case of 135° tie, the legs of the tie are bent inside
concrete core and even in the case of fire induced spalling; the tie-concrete interaction is not lost
which is an advantage compared to 90° ties.

6.5 Computer Implementation
The macroscopic finite element (MFE) computer program described in Section 6.2 is extended
by incorporating new subroutines based on “high temperature material properties” and “tie submodel”. Figure 6.7 illustrates the flowchart showing schematic of main program and the
additional subroutines that are added. The high temperature thermal and mechanical properties of
HPC presented in Chapter 3 and 4 respectively, are incorporated into both thermal and structural
solvers of the MFE model (depicted by gray diamond boxes in main program in Figure 6.7).
These new material properties are utilized for carrying out thermal analysis, pore pressure and
spalling calculations, and strength analysis base on moment-curvature (M-κ) relationships. The
“tie sub-model” subroutine is incorporated in structural solver of the MFE model and is utilized
to further carry out calculation of tie forces (effective force on tie and bond strength) at each time
step. Upon calculating the M-κ response and after meeting the equilibrium and compatibility
conditions, the program carries out structural analysis at each time step based on failure limit
state (including tie failure). The iterative procedure continues till fire resistance is obtained based

255

failure time either due to failure of ties, or strength failure limit state. If any failure limit is not
attained the analysis continues to the end of investigation run-time.
For necessary computations to execute the program, the macroscopic finite element computer
model is developed in FORTRAN language. The details on idealization of structural member,
cross-sectional discretization, segment length, time domain, fire scenario, and exposure
conditions are explained in details by Raut (Raut, 2011) and Kodur et al. (Kodur et al., 2009).
6.5.1

Input Data

The basic input for the program consists of geometric properties, cross-sectional properties
(including tie configuration), material properties (including HPC), and general data such as the
number of time increments. The sequential order of the input data must be followed in the input
file. Consistent SI units must be used throughout input and analysis.
6.5.2

Output Results

The output from the program includes the results from thermal and structural analyses. At each
incremental time step, the temperature at each elemental node is computed by hydro-thermal
analysis. The output results include the fire resistance times based on failure or non-failure of
member, the M-κ curves, axial deformation, and rate of deflection, Ftie and Fbond at each time
step.

6.6 Validation of Numerical Model
6.6.1

General

The previous version of the model has been earlier validated for NSC and HSC columns (Raut,
2011). However, further validations are required with the incorporation of high temperature

256

material properties for HPC. Six fire tested columns namely FAC, FAC-P, HSC2, HSC3, HSC5,
and HSC6 were analyzed for validation studies as part of current study. Two columns FAC and
FAC-P are selected from the experimental study presented in Chapter 5 and four columns HSC2,
HSC3, HSC5, and HSC6 were selected from fire test data reported by Kodur and McGrath
(2003) for validations of effect of tie configuration. Critical response parameters, such as crosssectional temperatures, axial deformation, failure times including tie failure, and effect of tie
configuration on fire response are compared with test data measured in fire resistance tests on
RC columns.
6.6.2

Validation Studies

The proposed model is being validated for RC columns by comparing predictions from the
model with measured data from fire tests. Recently characterized thermal and mechanical
properties for HPC (Chapter 3 and 4) are used in the analysis, whereas properties of reinforcing
steel used in the analysis are as per ASCE manual (1992). The validity of the macroscopic finite
element model for RC columns is established by comparing the predictions from the analysis
with the fire test data reported in Chapter 5 for columns FAC and FAC-P and test data published
earlier by Kodur and McGrath (2003) for columns HSC2, HSC3, HSC5 and HSC6. This selected
study is one of the few available in literature in which effect of tie configuration on fire response
of RC columns was experimentally investigated.
The geometric properties consisting of elevation and cross-section of FAC and FAC-P columns
are illustrated in Figure 6.8 and that of columns HSC2, HSC3, HSC5 and HSC6 are illustrated in
Figure 6.9. The columns are analyzed by exposing columns to the ASTM E119 (2008) standard
time-temperature curve. The fire resistance of the columns was evaluated based on both strength
failure and tie failure (yielding/opening) criteria. Predicted results from the analysis are

257

compared to the measured values from the fire tests in Figures 6.10 to 6.16 and also tabulated in
Table 1.
6.6.2.1 Temperature and Structural Response Predictions
Details on six columns including test parameters selected for predicting fire response of HPC
columns are given in Table 6.1. The table also shows the actual experimental test parameters
such as, column size, fire scenario, tie configuration, concrete strength, column strength and
applied load. Validation study on these columns is presented here:
For the analysis, the RC column was divided into 40 equal length segments along its length and
the mid-plane of each segment was assumed to represent the segmental behavior. The crosssection of each segment was divided with a 30x30 mesh of equal elemental size of with square
network of lines. This mesh can be coarsened or refined based on the accuracy of results desired
and availability of analysis time. For analyses of these columns the empirical relations on
thermal properties comprising of thermal conductivity, specific heat, thermal expansion, and
mechanical properties including compressive strength, splitting tensile strength and elastic
modulus presented used in Chapter 3 and 4 were used. The time domain was divided into
increments of one minute and the transient analysis was carried out at each time step. The
validity of the model is established by comparing predictions from the model with measured
temperatures, deflections and fire resistance times. Failure time was recorded when the column
was no longer capable of supporting the applied load or failure of tie occurs as per prescribed
criteria.
Two tested HPC columns (FAC and FAC-P) from current study reported in Chapter 5 were
analyzed using the macroscopic finite element model. Each column is analyzed under the fire

258

scenarios they were exposed to in tests which are given in Table 6.1. Figure 6.8 illustrates the
cross-sectional dimensions and layout of thermocouples for FAC and FAC-P columns. For
validation of temperatures three thermocouple positions at three places namely rebar, quarter
depth and mid depth of column cross-section were selected out of seven used in actual fire tests
as shown in Figure 6.8. Figures 6.10 and 6.11 illustrate the predicted and measured temperatures
as a function of fire exposure time for FAC and FAC-P columns. As FAC column suffered
spalling during the fire test therefore the rebar temperature went quite erratic during the fire test,
however the temperature predicted by the model in the rebar was quite high without showing any
noise in it. This stability in predicted temperature can be attributed to mathematical calculations
that can show higher temperatures but do not capture the extreme fluctuation in temperatures in
case of ongoing spalling in cross-section. These high temperature predictions however generally
lead to conservative fire resistance calculations. A slight difference can be observed between
measured and predicted temperatures of FAC-P column as shown in Figure 6.11. This is
attributed to the way the model handles the permeability parameters which could be different
form the actual permeability conditions in column on melting of polypropylene fibers.
Figure 6.12 illustrates the measured and predicted axial deformations of FAC and FAC-P
columns. The figure shows that there is a good agreement between the measured and the
predicted axial deformations for these columns. For FAC, FAC-P columns, the model predicted
about similar axial deformation with little conservative values for FAC-P. The comparison of
axial deformation for these columns illustrates that the numerical model handled material
properties for the new types of concrete very well and reasonably predicted the behavior of RC
columns made of new types of concrete.

259

The fire resistance predicted by model is compared to the measured fire resistance values for
FAC, FAC-P in Table 6.1. The model predicted the fire resistance of FAC and FAC-P columns
quite acceptable limits. The fire resistance time predicted by model for FAC column was 156
minutes as compared to 165 minutes measured time that was based on strength criteria and no tie
failure was predicted in this column. This can be attributed to the high cross-sectional
temperature profiles captured for FAC columns that resulted from spalling leading to this
conservative fire resistance prediction. FAC-P column did not fail in the fire tests and the model
prediction was also confirming the survival in the 270 minute analysis.
Though detailed comparisons are presented only for two columns, the predicted temperatures,
deformations, and fire resistance also compared well with test data for the other four columns
tested. Good comparison was observed between predicted and measured response parameters.
6.6.2.2 Tie Configuration
Four columns namely HSC2, HSC3, HSC5, and HSC6 were analyzed in the validation study on
effect of tie configuration on RC columns from fire test data reported by Kodur and McGrath
(2003). For validation purpose, similar parameters were used for analysis as were used for
experiments. As shown in Table 6.1, columns HSC2 and HSC3 had conventional 90° bent ties at
406 mm spacing, whereas HSC5 and HSC6 columns had 135° bent ties at 76 mm spacing. In the
case of columns HSC5 and HSC6 additional confinement was provided by adding middle tie leg
as shown in Figure 6.9. However, in the analysis it was neglected and analysis was run only for
main ties being critical. Columns HSC2 and HSC5 were axially loaded to 40% of their capacity,
while columns HSC3 and HSC6 were loaded to 60% of their room capacity. Concrete
compressive strength for these columns ranged from 86-120 MPa as shown in Table 6.1.
Specified yield strength of steel rebars was 420 MPa.
260

The thermal analysis is carried out by calculating cross-sectional temperatures and pore pressure.
In the analysis, when the pore pressure in an element exceeds temperature dependent tensile
strength of concrete, that element is removed from the cross-section for further analysis. Extent
of actual spalling data was not available for these columns from the test data; therefore for
purpose of calculations the outer concrete cover outside steel cage is assumed to have spalled in
first 60 minutes. Next, the strength and stiffness analysis is carried out by using high temperature
concrete and steel mechanical properties. The output parameters namely temperatures at various
locations (ties), mechanical stress, thermal stress and pore pressure are generated from the
model. Using these parameters effective stress is evaluated and the force acting on the tie is
computed using Eq 6.42. Also with increasing temperatures in ties and loss of concrete cover
bond strength degrades with fire exposure time. The force acting on the tie is then checked
against bond strength to evaluate failure of the ties. This procedure is repeated for each time step
till the failure of column occurs through reaching one of the failure limit states (Dwaikat and
Kodur, 2009).
Figure 6.13 illustrates the predicted development of pore pressure in the columns as a function of
fire exposure time. The pore pressure increases with fire exposure time, reaches a peak value and
then drops with time. The increase in pore pressure can be attributed to build-up of moisture clog
resulting from moisture movement inside concrete matrix. As the temperature in concrete
increases beyond 100°C, water present in concrete evaporates, leading to build-up of pore
pressure that increases with depth. This pore pressure build-up drives part of water vapor to
move away from heated surface deep into the inner layers of concrete member. This migrated
water vapor condensates and results in saturation of concrete microstructure. This phenomenon

261

is referred to as moisture clog and depending on concrete permeability (strength) this can result
in to significant variation in pore pressure during fire exposure (Dwaikat and Kodur, 2009).
Figure 6.13 shows that a peak pore pressure of 4.5 MPa gets developed in plain HSC concrete
column. In HSC columns, the lower permeability (Mindess et al., 2003; Noumowé et al., 2009)
does not facilitate the escape of water vapor and resultantly, higher pore pressure gets developed
in these columns. In addition to pore pressure development, another phenomenon that occurs
with increase in cross-sectional temperatures is the degradation of bond between reinforcement
(ties) and concrete. The degradation of bond strength for different tie configurations (10 mm ties)
is illustrated in Figure 6.14. The bond strength is dependent on the temperature in ties and any
loss of cross section due to fire induced spalling.
The significant drop in bond strength in 90° bent ties, at about 60 minutes, results from loss of
cover concrete from fire induced spalling. As a result of spalling, theh concrete cover outside ties
is lost, which results in significant reduction in bond strength in 90° bent ties (dropping to half of
the bond strength at that particular time) as interaction between tie legs and cover concrete is
lost. Such loss in bond strength is not encountered in 135° bent ties as the legs of the ties are bent
inward and embedded in to the concrete core. The drop in bond strength in HSC2 and HSC3
columns at 60 minutes into the fire exposure therefore occurs due to loss of concrete cover from
fire induced spalling.
The effective force (computed by Eq 6.42) that is acting on the ties results from a combination of
stresses generated from pore pressure, mechanical strain (loading) and thermal strain in fire
exposed columns. Figure 6.15 illustrates the development in effective force acting on ties with
fire exposure time plotted against the bond strength for columns HSC2 and HSC3, with 90° bent
ties. The predicted effective force acting on ties in column HSC3 is higher than that in column

262

HSC2 and this is due to higher loading ratio (0.6). As a result of higher loading ratio, the
effective force acting on ties in column HSC3 is higher than that in column HSC2. The analysis
shows that the ties (bent at 90°) failed due to opening-up (yielding) in column HSC3 at 120
minutes into the fire exposure time and this contributed to failure of this column. On the other
hand, ties did not fail in column HSC2, which can be attributed to lower mechanical stress
induced from loading in column HSC2.
Figure 6.16 illustrates the effective force on ties and resisting bond strength in 135° bent ties for
columns HSC5 and HSC6. Both of these columns had 135° bent ties and therefore exhibited
similar bond strength degradation in ties. However, as column HSC6 was subjected to higher
load ratio (0.6), the predicted effective tie force induced in column HSC6 was higher than that in
column HSC5. Although fire induced spalling was assumed in HSC5 and HSC6 columns at 60
minutes into the fire exposure, the predicted bond strength in ties was not lost as that in 90° bent
ties, this shows clear advantage of bending ties at 135° into concrete core over conventional 90°
bent ties. As a result of higher bond strength in 135° bent ties, the fire resistance of columns
HSC5 and HSC6 was significantly increased.
The results from fire resistance analysis show that the model predictions, based on high
temperature material properties and tie configuration sub-model, are in good agreement with
experimentally measured fire resistance values for the six HPC columns. Similar to the
observations in the tests, no failure was predicted in ties for column FAC-P. For the remaining
five columns (FAC, HSC2, HSC3, HSC5, HSC6) the predicted fire resistance values compared
well with the measured ones as shown in Table 6.1.

6.7 Summary

263

A macroscopic finite element model was extended to take in to account high temperature
properties for HPC (plain and with different fiber combinations) and effect of tie configuration
on fire response of RC columns. For this purpose a tie configuration sub-model was developed
based on principles used in seismic design. The effective stress resulting from fire induced pore
pressure, mechanical loading and thermal effects is evaluated and the effective force acting on tie
is computed and compared against the developed tie-concrete interface bond strength with fire
exposure time. The extended model is validated against fire test data on HPC columns, and it
shows that predictions from the model are in good agreement with test data from experiments.
Based on these validation studies, it is concluded that the capability of macroscopic finite
element model is enhanced for predicting the fire response of RC columns with incorporation of
“high temperature properties of HPC” and “tie-sub model” subroutines.

264

Table 6.1 - Parameters and results for RC columns tested at MSU used in the temperature and structural response validation study

S
No

Column
designa
tion

Size
(mm)

1

FAC

203

2

FAC-P

203

3

HSC2

406

4

HSC3

406

5

HSC5

305

6

HSC6

305

Fire
scenario
ASTM
E119 & EC
decay
@4.16°C/
min
ASTM
E119 & EC
decay
@4.16°C/
min
ASTM
E119
ASTM
E119
ASTM
E119
ASTM
E119

Tie
configurati
on

Concret
e
strength
Test day
(MPa)

Column
strength
(kN)

Load
ratio
(%)

Applie
d load
(kN)

Relative
humidit
y (%)

Fire
resistance
measured

Fire
resista
nce
predict
ed

Ties
failu
re

135°@h

107

2144

0.4

858

90

165

156

No

135°@h

100

2020

0.4

808

90.25

NF*

270

No

90°@h

86

5900

0.4

2406

86

224

213

No

90°@h

96

7400

0.6

4450

57

104

120

Yes

135°@h/4

120

3145

0.4

1250

68

290

282

No

135°@h/4

120

3145

0.6

1890

64

266

254

No

*No failure

265

Start
Input data
Increment time

Calculation of fire temperature
Thermal
properties

Thermal analysis

Pore pressure calculations

Calculate extent of
spalling

No

Yes
Update geometry and boundary
conditions
Mechanical
properties

M-K relationships

Structural analysis

Check Failure limit
state
No
Yes
End

Figure 6.1 - Flowchart showing the steps associated with analysis of fire exposed RC column

266

(c) Cross-section

(a) Column specimen

(b) Segmentation

(d) Discretization

Figure 6.2 - Layout of idealized RC column and discretization of its cross-section for fire
resistance analysis

267

Element area Am

Neutral axis

Element stress σm

Ct = Cs + Cc

Cs

εs,C

σs,C

h/2

Cc

P

y
ε0

h/2

Tc
1

κ εs,T

Geometrical centroidal axis
Cross section

Total strain
diagram

σs,T

Tt = Ts + Tc

Ts

Axis of zero mechanical strain
Stress
diagram

Internal
forces

Force Equilibrium
P = Tt+Ct

Figure 6.3 - Variation of strain, stress and internal forces in a cross-section of fire exposed RC column

268

M

Second iteration
First
iteration

EI12
1

EI0 EI11
1

EI13
1
Curvature normalization

1

Target curvature

k

(a) Moment curvature curve for a column segment

Critical segment
M3
M2
M1

(b) Column

(c) Bending moment diagram

Figure 6.4 - Illustration of Curvature Controlled Iterative Procedure used for Structural Analysis

269

90˚ Hook

135˚ Hook

Column with 90˚ ties

(a) Tie configuration

Column with 135˚ ties

(b) HSC columns after fire tests

Figure 6.5 - Comparison of fire performance of RC columns with conventional 90° ties and
modified 135° ties

270

Ftie

s
Ftie

135˚
Hook

Ftie

Ftie

s

F (x)

s

x

(a) Free body diagram of lateral and longitudinal reinforcement in an RC column
Figure 6.6 - Longitudinal rebar and transverse tie model and assumed forces

271

Fv

Fv

Fo

(b) Assumed force distribution in ties and longitudinal bars

y
Transverse tie level
Longitudinal bar

F (x)

x
Tie restraint
s

s

s

(c) The model for ties and longitudinal bar
Figure 6.6 - (cont’d) Longitudinal rebar and transverse tie model and assumed forces

272

Start
Input data
Increment time
Calculation of fire temperature
Thermal
properties

Start subroutine
Strains and
pore pressure
from previous
time step
Tie
configuration
model

Thermal analysis

Pore pressure calculations

Calculate thermal and
mechanical strains
Mechanical
properties

Calculate thermal, mechanical
stresses and pore pressure

Calculate extent
of spalling

No

Yes
Update geometry and
boundary conditions

Calculate total effective stress
and bond strength
Increment strains
and pore pressure
Check if effective stress > bond
strength

Mechanical
properties

M-K relationships

Structural analysis
No

Check Failure limit
state

Tie opening / failure
Yes

Yes

End subroutine

End
Main Program

Subroutine

Figure 6.7 - Flowchart showing steps to calculate forces in tie configuration subroutine
273

No

203 mm

4 #6 (19mm) rebars

3350 mm length

10 mm ties (135° @ 200 mm c/c
)

#3 (10mm) ties

203 mm

203 mm

40 mm clear cover

50 mm effective
cover

Quarter depth
TCs
Mid depth
Rebar

Elevation

Cross-Section

Figure 6.8 - Physical details and location of thermocouples for columns FAC and FAC-P

274

40 mm clear cover

8 #8 (25mm) rebars

h= 406 mm

50 mm effective
cover

Cross-section HSC2 and HSC3 columns

8 #5 (15mm)
rebars
#3 (8mm) ties

h = 305 mm

3810 mm length

10 mm ties (90° and 135°) @ h mm c/c

#3 (8mm) ties

h = 406 mm

406 mm

h = 305 mm
Elevation

Cross-section HSC5 and HSC6 columns

Figure 6.9 - Physical details and location of thermocouples for columns HSC2, HSC3, HSC5 and
HSC6

275

1000

Temperature (°C)

800
600
FAC rebar (test)
FAC rebar (model)
FAC quarter depth (test)
FAC quarter depth (model)
FAC mid depth (test)
FAC mid depth (model)

400
200
0
0

60

120

180
240
Time (minutes)

300

360

420

Figure 6.10 - Comparison of measured and predicted temperatures in FAC column
800

Temperature (°C)

600

400

FAC-P rebar (test)
FAC-P rebar (model)
FAC-P quarter depth (test)
FAC-P quarter depth (model)
FAC-P mid depth (test)
FAC-P mid depth (model)

200

0
0

60

120

180
240
Time (minutes)

300

360

420

Figure 6.11 - Comparison of measured and predicted temperatures in FAC-P column

276

FAC (test)

Axial deformation (mm)

4

FAC (model)
0

FAC-P (test)
FAC-P (model)

-4
-8
-12
-16
0

100

200
300
Time (minutes)

400

500

Figure 6.12 - Comparison of measured and predicted axial deformations in FAC, FAC-P
columns
5

Pore pressure (MPa)

HSC2
4

HSC3
HSC5

3

HSC6

2
1
0
0

50

100
150
Time (min)

200

250

Figure 6.13 - Predicted pore pressure at cover depth HSC2, HSC3, HSC5, and HSC6 columns

277

Bond strength (kN)

1400

90° tie (HSC2)
90° tie (HSC3)
135° tie (HSC5)
135° tie (HSC6)

1200
1000
800
600
400
200
0
0

50

100
150
Time (min)

200

250

Figure 6.14 - Predicted bond strength offered by various ties in selected columns
1200

Eff tie force (HSC2)

Force (kN)

1000

Eff tie force (HSC3)
Bond strength 90° tie (HSC2)

800

Bond strength 90° tie (HSC3)
600
400
200
0
0

50

100
150
Time (min)

200

250

Figure 6.15 - Predicted effective tie force compared to bond strength in 90° tie in NSC, HSC1
and HSC2 columns

278

Eff tie force (HSC5)

1400

Eff tie force (HSC6)

1200

Force (kN)

Bond strength 135° tie (HSC5)
1000

Bond strength 135° tie (HSC6)

800
600
400
200
0
0

90

180
Time (min)

270

Figure 6.16 - Predicted effective tie force compared to bond strength in 135° tie in HSC3 and
HSC4

279

CHAPTER 7
7

PARAMETRIC STUDIES

This chapter is mainly based on the following conference presentation and paper:
•

Khaliq, W., Raut, N. K., and Kodur, V. K. R. (2011). "Effect of tie configuration on fire
performance of high strength concrete columns." Proc., Conference presentation, ACI Fall
2011Conference.

•

Khaliq, W. and Kodur, V. K. R. (2012). "Effect of tie configuration on fire performance of
high strength concrete columns." SiF 2012 Conference at Zurich, Switzerland.

7.1 General
Fire response of reinforced concrete columns, as discussed in Chapter 2, is influenced by
numerous of factors. Many of these influencing factors are interdependent and this makes fire
resistance predictions of RC columns quite complex. The effects of many of these factors on fire
response of RC columns are quantified in previous studies. However, the effect of tie
configuration on fire performance of HPC columns is not quantified. Further there is no
information on the extent of influence of specific high temperature properties of HPC on fire
resistance of HPC columns. To evaluate the effect of tie configuration and specific properties of
HPC on fire resistance of HPC columns, parametric studies are carried out in this chapter. The
fire resistance analysis is carried out utilizing the numerical model presented in Chapter 6. Also
the usefulness of numerical model in evaluating fire response of RC columns with different types
of HPC and tie configurations is demonstrated in this Chapter.

280

7.2 Factors influencing Fire Resistance
There are several factors that influence the fire response of RC columns. These factors have been
well studied through qualitative parametric studies (Ali et al., 2001; Kodur, 2003; Lie and
Woolerton, 1988; Raut, 2011). The main factors that have been quantified consist of:
Fire scenario
Size (cross-section) of column
Concrete cover thickness
Aggregate type
Load ratio
Reinforcement ratio
Load eccentricity (uniaxial and biaxial)
Fire exposure scenarios (1-, 2-, 3-, or 4-sides)
Concrete strength (or permeability)
However, the factors that influence the fire response of HPC columns and that have not been
studied include:
Effect of specific concrete type (HPC)
Effect of tie configuration (90° and 135° bent ties)
The effect of tie configuration (90° of 135°) on fire performance of RC columns is studied
previously through limited fire tests. However, there is no numerical approach to explain the
effect of tie configuration through principles of mechanics. Similarly, for fire resistance
predictions of the RC columns made of HPC, high temperature thermal and mechanical
properties specific to concrete type are to be incorporated in numerical models. The effect of

281

these factors on fire response of RC columns has been investigated as part of parametric studies
described below.

7.3 Parametric Studies
To generate data on the effect of tie configuration and high temperature material properties of
HPC (with and without fibers), fire resistance analyses are carried out by varying these
parameters in the practical range. Results from parametric studies are utilized to quantify the
effect of permeability (strength), effect of load ratio, use of fibers, and columns size on fire
response of RC columns based on different tie configurations.
7.3.1

Selection of RC Columns

For the fire resistance analysis, RC columns with square cross-section were selected and the
strength (permeability), high temperature properties of concrete, tie configuration, load ratio, and
type of fibers were varied within a pre-defined range. The elevation and cross-sectional details of
the selected columns are shown in Figure 7.1. The columns were designed as per ACI 318 (2008)
specifications with regards to size, reinforcement ratio, and cover thickness. For each column,
two tie configurations of 90° and 135° were assumed. For the analysis, the columns were
assumed to be fixed at both ends. High temperature property relations comprising of thermal
properties (thermal conductivity, specific heat, thermal expansion and mass loss ) as proposed in
Chapter 3 and mechanical properties (compressive strength, splitting tensile strength, and elastic
modulus) as proposed in Chapter 4 were used specific to HPC type. High temperature properties
for reinforcing steel followed the relations given in ASCE manual (1992).
7.3.2

Range of Parameters

The ranges of parameters varied for analysis include:

282

Three permeability values based on NSC and HPC (plain and with polypropylene fibers) by
changing three permeability coefficients 10

-16

, 10-17 and 10-18.

Two types of tie configuration (90° and 135°) with two tie sizes (#3 (10 mm) and #4 (13
mm))
Five load ratios (30%, 40%, 50%, 60%, 70%)
Three types of fibers (steel, polypropylene, and hybrid)
Three column sizes (305mm, 406 mm and 610 mm)
7.3.3

Analysis Procedure

The fire resistance analyses of RC columns were carried out using the extended MFE model at
one minute time increments. For the analysis, the column was divided into 40 equal segments
along its length. As the curvature variation along the length of the column depends on the length
and number of the segments, it was reported by Raut (2011) that 40 segments along column
length gave optimized results. Each column segment (represented by central section) was then
discretized into quadrilateral elements of 10 mm size for the analysis. The discretization and
analysis procedure is similar to that adopted in the validation of the model, which is presented in
detail in Chapter 6. The columns were exposed to ASTM E119 standard fire scenario (ASTM
E119-08b, 2008). Based on spalling information from literature on HSC (Dwaikat and Kodur,
2010; Yu et al., 2011), concrete cover of the columns was assumed to be lost due to occurrence
of fire induced spalling up to 60 minutes in to the fire exposure in plain HPC columns (HSC,
SCC, and FAC). The cross-sectional temperatures, pore pressure, mechanical stress due to
loading, thermal stress due to thermal effects, effective force on ties, and bond strength were
evaluated at every time step in fire resistance calculations. The fire resistance of the columns was
evaluated based on the failure of ties and strength failure limit state.

283

7.4 Results from Parametric Studies
Results from fire resistance analyses are presented in Tables 7.1 to 7.3 and in Figures 7.2 to 7.9.
The main factors that are studied are the effect of tie configuration (90° and 135°) and the effect
of high temperature properties of HPC on fire response of HPC columns. Other factors that
influence the effective force acting on ties, such as concrete strength (permeability), load ratio,
and use of fibers are also included in the parametric studies. The effect of various parameters on
fire response of RC columns is discussed below.
7.4.1

Effect of Permeability (Strength)

The strength in HPC is achieved through application of mineral and chemical admixtures that
consume the calcium hydroxide (CaOH2) which is produced in concrete matrix through process
of hydration. CaOH2 is a weak link in concrete and with addition of mineral admixtures such as
silica fume, flay ash and slag (silicates in nature), these react with CaOH2 over time to convert it
to primary binding cement gel, calcium silicate hydrate (C-S-H). In the process, the porosity gets
reduced and, very dense and impermeable microstructure of concrete develops, which imparts
higher strength and durability in concrete. Therefore strength in concrete can directly be related
to permeability, as higher the strength of concrete, lower is its permeability. Once exposed to
higher temperatures, this impermeability in concrete hinders dissipation of fire induced pore
pressure. This results in damage to dense microstructure, resulting in loss of strength and
stiffness of HPC. Thus impermeability which is beneficial for durability of HPC becomes a
disadvantage for HPC structural members under fire conditions.
There are generally two types of permeability associated with concrete: liquid permeability and
gas permeability (Boel et al., 2008; Mindess et al., 2003; Noumowé et al., 2009). Generally, gas
284

permeability is mostly used as representative property for concrete due to difficulties associated
for measuring liquid permeability in different HPC. Gas permeability is typically in the range of
2.4x10

-12

to 6.8x10

-16

-17

for NSC and 1.5x10

to 2.1x10

-18

for HSC (Boel et al., 2008; Dwaikat

and Kodur, 2009; Kalifa et al., 2001; Noumowé et al., 2009). In parametric studies, pore pressure
predictions were carried out for two initial (room temperature) permeability values of concrete:
high permeability of 2x10

-16

2

-18

m (representing NSC) and low permeability of 2x10

m

2

(representing HPC). These permeability values for NSC and HSC are kept constant (no variation
with temperature) throughout the fire resistance analysis. However, for polypropylene fiber
reinforced HPC, the initial permeability which is taken as 2x10
-17

permeability range for HPC), was increased to 2x10

-18

2

m (that represents the

2

m once polypropylene fibers melted at

170°C during.
Figure 7.2 illustrates that the accumulated pore pressure is highly dependent on permeability of
concrete. Results from the analysis shows that pore pressure increases with fire exposure time
until it reaches a peak value and then it decreases. The increase in pore pressure can be attributed
to build-up of moisture clog resulting from moisture movement inside concrete matrix. This
build-up of moisture clog can lead to significantly high pore pressure during fire exposure. It can
be seen from Figure 7.2 that a peak pore pressure of 4.5 MPa gets developed in HPC columns
with low permeability of 2x10

-18

2

-16

m , whereas in the case of higher permeability of 2x10

m

2

such as for NSC, the pore pressure can be as low as 2 MPa.
High permeability of concrete in the NSC column facilitates dissipation of water vapor and thus
there is lower build-up of pore pressure, whereas low permeability of concrete in HSC column,
does not facilitate the escape of water vapor and resultantly, higher pore pressure gets developed

285

in HSC columns (Mindess et al., 2003; Noumowé et al., 2009). With medium level of
permeability (2x10

-17

2

m ) assumed in polypropylene fiber reinforced column HSC1, resulting

from melting of polypropylene fibers around 170°C under fire conditions, it can be seen that
considerable reduction in pore pressure occurs. This reduction in pore pressure is beneficial in
mitigating fire induced spalling and also resulting in lower fire induced forces acting on ties.
As pore pressure is one of the primary contributors to total effective force that develops on ties,
therefore higher pore pressure will result in higher effective force acting on ties in the case of
columns made of HPC. This implies that a 90° bent tie with lower bond strength will have high
susceptibility to failure as compared to a 135° bent tie. On the other hand lower pore pressure
results in lower effective force acting on ties; therefore failure of 90° ties is not encountered in
NSC and polypropylene fibers reinforced HPC columns.
7.4.2

Effect of Tie Configuration

The degradation of bond strength for two types of tie configuration (90° and 135°) for tie sizes of
(#3 (10 mm) and #4 (13 mm)) is illustrated in Figure 7.3. With rise in cross-sectional
temperatures, bond between tie and concrete interface degrades. Two factors that contribute to
loss of bond strength are; (1) degradation in strength of ties (steel) with rise in temperature of
steel (ties) and (2) occurrence of fire induced spalling in concrete surrounding the ties. To
account for occurrence of fire induced spalling in plain HPC column, it is assumed that outer
concrete cover is lost and there is no tie-concrete interface at outer side of tie legs. In such a
scenario, the loss of concrete cover significantly affects the bond at tie-concrete interface and
thus bond strength is reduced.
Results shown in Figure 7.3 illustrate degradation of bond strength (at steel-concrete interface) in
RC columns with 90° and 135° bent ties as a function of fire exposure time. It can be seen that a

286

significant drop in bond strength occurs in 90° bent ties, at about 60 minutes, which results from
high temperatures developing in ties due to direct heating from fire (due to spalling off of
concrete cover) and loss of tie-concrete interface. As a result the bond strength reduces to half of
its original value. Such loss in bond strength is not encountered in 135° bent ties as the legs of
the ties are bent inward and embedded in to the concrete core and spalling outside the core do not
affect the bond between tie ends and concrete. This also helps in keeping the fire induced
spalling to outside of steel cage (concrete core) and mitigates further loss of cross-section
(concrete) in HPC columns. Increasing the size of the tie from #3 to #4 enhances the bond
strength of ties throughout fire exposure time; however, the variation in the loss of bond strength
with fire exposure time is similar to that in #3 ties. Even in the case of #4 ties, higher loss of
bond strength is encountered in 90° bent ties as compared to 135° bent ties.
Figure 7.4 illustrates the development of effective force acting on ties in an HSC column as a
function of fire exposure time. Also plotted in this graph is the degrading bond strength as a
function of time for 90° and 135° bent ties. It can be seen that the force acting on the ties
increases with fire exposure time and this is due to increase in resulting pore pressure. On the
other hand, strength and stiffness properties of HSC column also degrade with temperature,
which result in higher stresses due to applied loading. All the three fire induced stresses (pore
pressure, applied loading, and thermal effects) combined together act as effective stress (σcore)
on ties. From this stress (σcore), effective force acting on tie is evaluated using Eq 6.42. It can be
seen in Figure 7.4 that effective fore in tie increases from 230 kN at the start of the run to about
532 kN in 120 minutes thus taking over degrading bond strength of 90° ties at 120 minutes. This
leads to failure of 90° ties, whereas bond strength in 135° ties remains much higher than the
effective force on the tie and thus no failure occurs in 135° ties.

287

Figure 7.5 illustrates the development of effective force in 90° and 135° bent ties in NSC column
as a function of temperature. Because of continuous dissipation of pore pressure in NSC column,
the effective force acting on tie remains much lower and the bond strength that is degrading in
the case of 90° ties does not fall below the effective tie force. Therefore no failure of ties occurs
in NSC column even with provision of 90° bent ties. This leads to the conclusion that provision
of 90° and 135° bent ties will not make any difference in NSC columns under fire conditions.
7.4.3

Effect of Load Ratio (Level)

The effective force that is acting on ties of an RC column arises from a combination of three
stresses namely fire induced pore pressure, applied loading and temperature induced thermal
strain (from thermal effects). Depending on the load level, the mechanical stress from loading
can be significant component of effective stress acting on the ties. These stresses tend to increase
tremendously under fire conditions due to degradation of mechanical (strength) properties of
HPC column and this leads to significant increase in the effective force acting on ties. Figure 7.6
illustrates the development of effective force on ties as a function of fire exposure time in 305
mm size HPC columns (HSC1 to HSC5) under different load ratios of 0.3 to 0.7.
For comparison purpose, bond strength developed in columns with 90° and 135° bent ties is also
plotted as a function of fire exposure time in Figure 7.6. For 10% rise in load ratio, there is 1525% increase in peak effective force acting on ties. This shows stress from loading is a major
contributor to effective force on ties (next only to that from pore pressure). It can be seen from
the Figure 7.6 that, even at lower load ratio of 0.4 (in column HSC2), failure of ties can result in
columns with 90° ties. Conversely, in column (HSC3) with 135° bent ties no failure of ties
occurs for load levels up to 0.5 (load ratio), however, in the case of columns with 135° bent ties,
the ties fail by yielding/opening up under higher applied load ratios of 0.6 (column HSC4) and

288

0.7 (column HSC5). The predictions show that with each 10% increase in load ratio, the fire
resistance of HPC columns is reduced by an average of 25 minutes for columns provided with
135° ties.
Fire resistance of HPC columns (HSC1 to HSC5) under five load ratios (load levels) are
tabulated in Table 7.1. It can be seen that HSC columns with 90° bent ties can fail under lower
load ratio of 0.4. However, HSC columns provided with 135° bent ties can survive without
failure of ties till load ratio reaches 0.5. It can be seen that at 0.6 load ratio (60% load level) in
column HSC4, the fire resistance is 90 minutes and 126 minutes with 90° and 135° bend ties
respectively. It shows that in plain HPC columns, an improvement of about 35 minutes in fire
resistance can be achieved just by bending ties at 135°.
7.4.4

Effect of fibers

The presence of fibers can influence both thermal and structural response of HPC columns under
fire conditions. To illustrate this influence, ten HPC columns (with and without fibers) were
analyzed and the results of analysis are tabulated in Table 7.2. For illustrating thermal response,
cross-sectional temperatures at two locations (quarter depth and mid depth) are plotted in Figures
7.7 and 7.8 for HSC and FAC columns (plain and with different fiber combinations). Further to
illustrate the influence of fibers on pore pressure development in HSC and FAC columns (plain
and with different fiber combinations), pore pressure is plotted in Figure 7.9. Table 7.2 shows the
fire resistance predictions for these ten HPC columns made of three HPC types (HSC, SCC and
FAC) with different fiber combinations.
It can be seen from figures 7.7 and 7.8 that type of fibers has an effect on the resulting
temperature profiles in the column cross-section. The predicted temperatures are lower for fiber
reinforced concrete as compared to plain form of that specific concrete (HSC, SCC, or FAC).

289

This can be attributed to the thermal conductivity and specific heat properties of different HPC
types (plain and with fibers). The temperatures in the case of polypropylene and hybrid fibers
reinforced HPC are about 25-40°C lower than those in plain HPC columns throughout the fire
exposure time. This lowering of temperatures decreases pore pressure built up in the columns.
The lower temperature development leads to lower effective force acting on ties, thus an
enhancement of about 30 minutes is attained in fiber reinforced HPC columns.
It can be seen from Table 7.2 that the fire resistance of fiber reinforced HSC-P and HSC-H
columns increased to 218 and 230 minutes respectively as compared to 192 minutes for plain
HSC column. Similar improvement of about 30 minutes in fiber reinforced FAC and SCC
columns is observed in Table 7.2. Addition of steel fibers in the concrete mix also increase the
fire resistance of HPC columns to an average of 20 minutes which can be attributed to slower
degradation of tensile strength with temperature in steel fiber reinforced HPC.
Figure 7.9 illustrates development of pore pressure in fiber reinforced HPC columns (steel,
polypropylene, or hybrid fibers) as a function of fire exposure time. Significant reduction in pore
pressure occurs in polypropylene fiber reinforced HSC and FAC columns due to melting of
polypropylene fibers. The pore pressure drops from 5 MPs to about 3MPa in polypropylene and
hybrid fiber reinforced HSC and FAC columns. Pore pressure development in steel fiber
reinforced HSC column is similar to plain HPC column. However, slower degradation of tensile
strength in steel and hybrid fiber reinforced columns (HSC-S, HSC-H, SCC-S and SCC-H), leads
to higher fire resistance as shown in Table 7.2.
7.4.5

Effect of Column Size

To study the effect of pore pressure and effective tie force development in different column
sizes, three square columns namely HSC1, HSC2 and HSC3 (size 305 mm, 406 mm, and 610

290

mm) were analyzed. The elevation and cross-section details (properties of the section) of these
columns are given in Figure 7.1. The columns were analyzed under 90° and 135° tie
configuration and fire resistance analysis was carried out by exposing these columns to ASTM
E119 standard fire and subjecting them to axial load equivalent to 40% and 60% of their ultimate
capacity. Table 7.3 shows the design parameters and predicted fire resistance of the three
different size columns.
From Table 7.3 it can be seen that column HSC3 with 610 mm size and 0.4 load ratio, has the
highest fire resistance of 297 minutes among three columns based on strength failure criteria as
no tie failure occurred in these columns. On the other hand, columns HSC2 (406 mm sides) and
column HSC1 (305 mm sides) under 0.4 load ratio exhibited a fire resistance of 231 and
192minutes respectively. These results indicate fire resistance increases with increase in crosssectional size of the column. Further no tie failure occurred when the load ratio was 0.4. This is
as expected since larger mass of concrete acts as a heat sink and thus the overall temperature rise
within the column is lower in large size columns. However, when the above three columns
(HSC1, HSC2, and HSC3) were analyzed under higher load ratio of 0.6, failure of columns
HSC1 and HSC2 occurs through the failure of 90° ties at 159 and 188 minutes. However, in the
case of HSC3 column (610 mm sides) under 0.6 load ratio, no failure of ties (90° bent ties)
occurs and this column exhibits fire resistance of 270 minutes. This trend of increasing fire
resistance with increasing column size is well established in literature (Raut, 2011).
Figure 7.10 illustrates the development of pore pressure at 40 mm concrete depth in columns
HSC1, HSC2, and HSC3. It can be seen that there is no substantial difference in pore pressure
built-up in all three HPC columns with different cross-sectional sizes (305 mm, 406 mm, and

291

610 mm). As the model predicts the pore pressure at a predetermined concrete depth in column;
the build-up of pore pressure remains independent of column size.

7.5 Summary
Results of fire resistance analyses is presented to discuss the effect of tie configuration (90° and
135°) on the fire response of HPC columns. Based on the trends, it is evident that concrete
permeability has significant influence on pore pressure development under fire conditions, as
lower permeability (as in HPC columns) leads higher pore pressure development. A higher pore
pressure results in increased effective force on ties. Bond strength of ties (tie-concrete interface)
is not lost in 135° bent ties on occurrence of fire induced spalling. Load ratio also has significant
effect on failure/yielding of ties, since higher load ratio leads to higher effective force acting on
ties. Presence of steel, polypropylene, or hybrid fibers enhances fire resistance of HPC columns
in two ways; by mitigation of fire induced spalling and by slower degradation of tensile strength
in HPC. Increase in column size leads to increased fire resistance of HPC columns with no
influence on pore pressure development in HPC columns.

292

Table 7.1 - Results for HPC columns with different load ratios

Column
designation

Concre
te type

Size
(mm)

Column
strengt
h (kN)

Load
ratio
(%)

Applied
load
(kN)

Fire
resistance
predicted

Failure of ties

90°
HSC1
HSC
HSC2
HSC
HSC3
HSC
HSC4
HSC
HSC5
HSC
NF* - no failure

305
305
305
305
305

1636
1636
1636
1636
1636

0.3
0.4
0.5
0.6
0.7

490
655
818
980
1145

135°

90°

135°

NF
117
101
90
80

NF*
NF*
NF*
126
111

No
Yes
Yes
Yes
Yes

No
No
No
Yes
Yes

Table 7.2 - Results for HPC columns with different fiber combinations

Column
designation

Concret
e type

Size
(mm)

HSC
HSC-S
HSC-P
HSC-H
SCC
SCC-S
SCC-P
SCC-H
FAC
FAC-P

HSC
HSC
HSC
HSC
SCC
SCC
SCC
SCC
FAC
FAC

305
305
305
305
305
305
305
305
305
305

Concret
e
strength
(MPa)
81
89
71
67
61
57
56
57
72
74

293

Column
capacity
(kN)

Load
ratio
(%)

Applied
load
(kN)

Fire
resistance
predicted

1636
1798
1434
1354
1232
1152
1132
1152
1455
1495

0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4

655
719
754
542
493
461
453
461
582
598

192
205
218
230
185
196
210
224
190
215

Table 7.3 - Results for HPC columns with different column sizes

Column
designation

Concret
e type

Size
(mm)

HSC1
HSC2
HSC3
HSC1
HSC2
HSC3

HSC
HSC
HSC
HSC
HSC
HSC

305
406
610
305
406
610

Column
capacity
(kN)
1636
2350
5316
1636
2350
5316

Load
ratio
(%)
0.4
0.4
0.4
0.6
0.6
0.6

294

Applied
load
(kN)
655
940
2130
982
1410
3190

Fire
resistance
predicted
192
231
297
159
188
265

Tie/Strength
failure
Strength
Strength
Strength
Tie (90°)
Tie (90°)
Strength

Figure 7.1 - Elevation and cross-sections of RC columns used in parametric study
-sections

295

5
High perm (NSC) - 2e-16 m2
High perm - 2e-19 m2

Pore pressure (MPa)

Medium perm (HSC -pp fibers) - 2e-17 m2
Medium perm - 2e-18 m2
4

Low perm - 2e-16 m2
Low perm (plain HSC) - 2e-18 m2

3

pp fibers - polypropylene fibers

2

1

0
0

60

120
Time (min)

180

Figure 7.2 – Effect of permeability on pore pressure development in RC columns
Spalled area
90˚ Hook
90° tie (#3 tie)
90° tie (#4 tie)
135° tie (#3 tie)
135° tie (#4 tie)

1400

Bond strength (kN)

1200
1000
800

Spalled area

600

135˚ Hook

400
200
0
0

60

120

180

Time (min)

Figure 7.3 - Effect of tie size on bond strength in RC columns with 90° and 135° ties

296

90˚ Hook

1200

Force / Bond strength (kN)

Efftive force on ties (HSC)
Bond strength - 90° tie

1000

Bond strength - 135° tie

800
600
135˚ Hook

400
200
0
0

50

100
150
Time (min)

200

250

Figure 7.4 - Comparison of force acting on ties against bond strength in HSC column with 90°
and 135° ties
90˚ Hook

Force / Bond strength (kN)

1200
Efftive force on ties (NSC)
Bond strength - 90° tie
Bond strength - 135° tie

1000
800
600

135˚ Hook

400
200
0
0

50

100
150
Time (min)

200

250

Figure 7.5 - Comparison of force acting on ties against bond strength in NSC column with 90°
and 135° ties

297

Bond strength 90 tie
Bond strength 135 tie
Eff force - 30% load ratio
Eff force - 40% load ratio
Eff force - 50% load ratio
Eff force - 60% load ratio
Eff force - 70% load ratio

Force / Bond strength (kN)

1500
1200
900
600
300
0
0

120
180
Time (min)

60

240

300

Figure 7.6 - Effect of load level on the effective force acting on ties in RC columns

HSC - mid depth
HSC-S - mid depth
HSC-P - mid depth
HSC-H - mid depth
HSC - quarter depth
HSC-S - quarter depth
HSC-P - quarter depth
HSC-H - quarter depth

1200

Temperature ( C)

1000
800
600
400
200
0
0

60

120
Time (minutes)

180

240

Figure 7.7 - Temperature response HSC column with different fiber combinations

298

FAC - mid depth

1000
Temperature ( C)

FAC-P - mid depth
800

FAC - quarter depth
FAC-P - quarter depth

600
400
200
0
0

60

120
Time (minutes)

180

240

Figure 7.8 - Temperature response of FAC column with different fiber combinations
combinations

5
HSC
HSC-S

Pore pressure (MPa)

4

HSC-P
HSC-H

3

FAC
FAC-P

2
1
0
0

60

120
Time (min)

180

240

Figure 7.9 - Pore pressure development in RC columns with different fiber combinations

299

6

305 mm - HSC1
406 mm - HSC2
610 mm - HSC3

Pore pressure (MPa)

5
4
3
2
1
0
0

50

100
Time (min)

150

Figure 7.10 - Effect of column size on development of pore pressure at 40 mm depth

300

CHAPTER 8
8

CONCLUSIONS AND RECOMMENDATIONS

8.1 General
The experimental and numerical studies presented in this thesis provide data and high
temperature property relations for evaluating the fire performance of RC columns made of high
performance concrete. The thermal properties consisting of thermal conductivity, specific heat,
thermal expansion, and mass loss and mechanical properties consisting of compressive strength,
splitting tensile strength, elastic modulus, and stress-strain curves were generated in 20-800°C
for different types of HPC. Simple empirical relations, obtained through regression analysis on
measured test data, are proposed for high temperature properties of HPC (with and without
fibers). Also, a numerical approach is developed to account for the effect of tie configuration on
fire resistance predictions of RC columns and the sub-model is built into an existing macroscopic
finite element (MFE) model for fire resistance analysis of RC columns. The extended model was
validated against data generated from fire resistance tests on HPC columns. The validated MFE
model was then utilized to undertake parametric studies to quantify the effect of strength
(permeability), tie configuration, load ratio, fibers, and column sizes on fire resistance of HPC
columns.

8.2 Key Findings
Based on the information presented in this study, the following are the key conclusions:
•

Data generated from high temperature thermal property tests on HPC indicate that:

301

-

Temperature has significant influence on thermal conductivity and specific heat of HSC,
FAC, and SCC and these properties decrease with temperature in a similar fashion as that
of conventional NSC. Specific heat of all these three concretes (HSC, SCC, and FAC)
remains almost constant up to about 400°C, and there after increases up to about 650°C
before following a constant trend in 650-800°C range.

-

Thermal expansion increases with temperature for HSC, SCC, and FAC in entire 20800°C. Thermal expansion is about 25% higher in case SCC as compared to HSC in 400800°C temperature range.

-

No significant mass loss occurs in HSC, SCC, and FAC up to 600°C. The mass loss
increases beyond 600°C, and at 800°C, mass loss reaches to about 90% of initial mass for
FAC and SCC and to about 80% of initial mass in the case of HSC.

-

The addition of steel, polypropylene, or hybrid fibers to HSC, SCC, and FAC batch
mixes does not significantly alter the thermal conductivity in 20-800°C temperature
range. The addition of these fibers to HSC, SCC, and FAC also does not alter the specific
heat in 20-400°C; however, the presence of fibers do increase the specific heat of these
concretes in 400-800°C temperature range.

-

Presence of fibers (steel, polypropylene or hybrid) in SCC increases thermal expansion in
200-800°C, however in the case of HSC and FAC the presence of fibers decreases the
thermal expansion of concretes throughout 200-800°C range.

-

The presence of steel, polypropylene or hybrid fibers does not influence the mass loss of
HSC, SCC and FAC in the entire 20-800°C temperature range.

•

Data generated from high temperature mechanical property tests on HPC indicate that:

302

-

Compressive strength, tensile strength and elastic modulus of HSC, SCC, and FAC
degrade with temperature at a faster rate as compared to conventional NSC. Among high
performance concretes, SCC (plain and with fibers) retains higher compressive strength
as compared to FAC and HSC (plain and with fibers) throughout 20-800°C temperature
range. At 800°C, SCC retains of 40-45% of its initial room temperature compressive
strength while HSC and FAC retain only 10-20% of initial strength.

-

Splitting tensile strength of HSC, SCC and FAC degrade with temperature, and the loss
in tensile strength is lower in case of SCC than that in HSC and FAC in 20-800°C
temperature range. SCC retains about 90% of its initial splitting tensile strength at
400°C, and 20% of its initial splitting tensile strength at 800°C. Conversely, HSC and
FAC retain only 50% of initial splitting tensile strength at 400°C and this degradation
reaches to 10% in HSC and zero in FAC at 800°C.

-

Elastic modulus of SCC and FAC does not degrade significantly up to 200°C; however
rapid deterioration of elastic modulus occurs in 200-800°C, and reaches to zero at 800°C.

-

Both plain SCC and plain FAC exhibit stiff stress-strain response throughout 20-800°C
range with higher peak stress developing at lower (peak) strains. Addition of steel,
polypropylene or hybrid fibers to HPC transforms the stiffer stress-strain response to a
ductile mode.

-

Addition of steel, polypropylene, or hybrid fibers to HPC mixes does not have much
influence on high temperature compressive strength of HSC, SCC, and FAC. However,
presence of steel and hybrid fibers in HPC mixes slows down degradation in tensile
strength of HSC and SCC up to 400°C, beyond which there is little influence of fibers.

303

-

Presence of polypropylene fibers in HPC mixes does not have much effect on high
temperature stress-strain response of SCC-P; however, ductility of SCC-S and SCC-H at
high temperature increases in the presence of steel fibers in the concrete. Presence of
fibers in FAC-P also leads to attainment of higher peak strains in 200-800°C.

•

Results from fire resistance tests on FAC and HSC columns indicate that:
-

Plain FAC column experiences significant fire induced spalling and thus fire resistance of
FAC column decreases to about 60% as that of polypropylene fiber reinforced FAC-P
column.

-

The presence of fibers (steel, polypropylene or hybrid fibers) enhances fire resistance of
HPC columns and the addition of any of these fiber types are equally effective in
mitigating fire induced spalling in HPC columns.

-

Steel, polypropylene or hybrid fiber reinforced HPC columns can retain significant
residual strength capacity after fire damage (exposure). HPC columns with steel,
polypropylene, or hybrid fibers can have residual strength capacity that is in the range of
34 to 52% of original capacity, even after exposure to severe fire scenarios (similar to
that used in the fire tests).

•

The proposed tie sub-model, based on mechanics principles, accounts for significant fire
induced forces resulting from pore pressure, mechanical loading and thermal strains.

•

Results from parametric studies indicate that the factors such as concrete strength
(permeability), tie configuration, and load ratio, have significant influence on effective force
acting on ties in fire exposed HPC columns. Specifically:
-

Increased impermeability (concrete strength) leads to higher pore pressure in HPC
columns. The pore pressure in typical high strength concrete columns can reach about 5

304

MPa, while that in conventional normal strength concrete columns can reach about 1
MPa.
-

The effective stress acting on ties increases with load level and when the load level
reaches 40%, failure of ties can occur in plain HPC columns with 90° bent ties. The fire
resistance can decrease by about 15 minutes with each 10% increase in load level.

-

The size (cross-sectional size) of columns does not have much effect on pore pressure
development in HPC columns. However, with increased column size, fire resistance gets
higher since the area farthest away from fire in the central concrete core of large size
columns is less exposed to detrimental effects (temperature) of fire.

-

Presence of polypropylene fibers in HPC columns reduces pore pressure accumulation
thus leading to lower effective force on ties, which in turn enhances the fire resistance.

8.3 Recommendations for Future Research
While this research has advanced the state-of-the-art with respect to fire response of HPC both at
material and at structural levels, further studies are required to fully characterize the complex
material behavior and structural members of HPC. The following are some of the key
recommendations for further research in this area:
•

The material properties of HPC can be further refined by taking into account the significant
factors such as change in permeability (pore structure), and moisture content as a function of
temperature. Effect of cooling phase of fire on the properties should also be established so
that model predictions can be enhanced for accuracy under design fire scenarios.

•

There is lack of test data in the literature on the fire performance of fiber reinforced fly ash
and self-consolidating concrete columns. Further fire resistance tests should be carried out on
fiber reinforced fly ash and self-consolidating concrete columns.

305

•

Strain gauge measurements in fire resistance tests can be highly useful in validating
computer models under combined effects of applied load and fire. The high temperature
strain gages used in the current study did not provide reliable measurements under fire
exposure due limitations of these gauges at high temperatures (above 300°C). Thus there is a
need for developing reliable procedure to obtain high temperature strains in rebars.

8.4 Research Impact
The information developed as part of this research will have significant impact on use of high
performance concrete in building applications. HPC offer excellent strength and durability
characteristics, but are much more susceptible to faster degradation of strength properties and
fire induced spalling and thus have lower fire resistance. This aspect can be overcome either
through the addition of fibers or by reconfiguring the ties through bending the ends of ties at
135° into the concrete core. Since mixing and placing the fiber reinforced concrete in a job site
can be labor intensive, bending the ties at 135° can offer a practical and economical solution in
many situations.
The proposed extensions to macroscopic finite element model take into account the high
temperature thermal and mechanical properties of different HPC (plain and with different
combination of fibers), and the effect of tie configuration in fire resistance evaluation of HPC
columns. These enhancements will help to recognize the inherent fire resistance in HPC
columns. Overall, this research will lead to wider application and use of HPC in building
applications.

306

APPENDIX A

307

APPENDIX A

Equipment Techniques for Measurement of Thermal Properties
A.1 Hot Disk Technique
This appendix gives a brief theoretical description of the Hot Disk Thermal Constants Analyzer
used to measure the thermal conductivity and specific heat of different HPC in this study. Hot
Disk is relatively new equipment and it combines the measurements of three heat transfer
properties (thermal conductivity, thermal diffusivity, and specific heat) in a single test unlike
existing test techniques of separately evaluating these properties. The use of Hot Disk equipment
is also simple with major effort in sample preparation and high temperature equipment
installation. The high temperature mica sensors need more care as these are fragile and brittle
due to mica coating and these sensors get burned and consumes in a single high temperature
measurement of 20-800°C. Extra care is needed for proper installation of mica sensors with
specified resistance between 5 to 10 ohms. The input parameters first need to be evaluated at
room temperature for establishing room temperature thermal properties and then these
parameters are used as input for high temperature properties evaluation.
Based on the theory of the Transient Plane Source (TPS) technique, recognized in ISO 22007-2
(2008), the Hot Disk Thermal Constants Analyzer utilizes a sensor element in the shape of a
double spiral. This Hot Disk sensor acts both as a heat source for increasing the temperature of
the sample and a ”resistance thermometer” for recording the time dependent temperature
increase. In most cases the sensor element is made of a 10 µm thick Nickel-metal double spiral,
with precisely designed dimensions (width, number of windings and their radii). This spiral is
supported by a material to protect its particular shape, to give it mechanical strength and keep it

308

electrically insulated. The polyimide “Kapton” is such a material, which can be used throughout
the temperature range from 10 K to 500 K. A “Mica” material is also available as
supporting/insulating material and in that case the upper limit of the temperature range is
extended to 1000 K.
The encapsulated Ni-spiral sensor is then sandwiched between two halves of the sample (solid
samples). During a pre-set time, 200 resistance recordings are taken, and from these the relation
between temperature and time is established. A few parameters, like the Heating power to
increase the temperature of the spiral, the measurement time for recording 200 point and the size
of the sensor are used to optimize the settings for the experiment so that thermal conductivities
from 0.005 W/mK to 500 W/mK can be measured. Measurements on standard materials ranging
from Polystyrene to Aluminum metal show that the accuracy over the whole range of Thermal
Conductivities is within +/- 5% and the reproducibility is within +/- 2%.
The Hot Disk sensor is clamped between two pieces of the sample, with two flat sides facing the
sensor. They are clamped together, completely covering the sensor. The mounting pressure or
surface roughness is not important, but the thermal contact between the sample and the sensor
should be fair for hard samples, in particular for moderately- and high-conducting materials.
The sensor and sample are initially allowed to settle at isothermal conditions. Then, a constant
electrical power is applied to the Hot Disk heating element. The heat that is generated in the
heating elements will then dissipate into the surrounding sample. Simultaneously, the
temperature increase in the sensor is recorded as a function of time. This temperature increase
data is then used to estimate the bulk thermal transport properties of the material.
The heating power applied causes an initial temperature increase. Several important factors – not
related to the bulk properties of the sample – influence the recorded temperature increase. They
309

are: the sensor insulation, the interfacial thermal contact resistance between sensor and sample
surface (influenced by surface roughness, mounting pressure, etc.) as well as possible thin
surface layers on the sample surface (e.g. thin oxidation layers). All these factors have a
considerable impact on the recorded temperature increase.
If we assume that the thermal transport properties are constant in the radial direction with respect
to the plane of the sensor, but different from the thermal transport properties in the axial
direction, one can derive the following model to be used for the analysis and curve-fitting
procedure.



P0

 ⋅ D ⋅ (τ )
∆Ti =
 λ ⋅ λ ⋅π 3 / 2 ⋅ r  0 i
 r a


where

and

τi =
r2
θ=
ar

ti − tcorr

θ

(A.1)

is a dimensionless “time”

is the characteristic time of the experiment.

Index i denotes the data points, which range from 1 to 200, and the indices a and r refer to axial
and radial thermal transport properties, respectively. Parameter A incorporates the imperfect
thermal contact conditions in a measurement, while the remainder of Eq (A.1) is in accordance
with the ideal theory assuming perfect thermal contact conditions, and zero specific heat capacity
of the sensor itself. This remainder of Eq (A.1) is referred to as the ideal model.
Figure A.1 displays a typical average temperature increase as a function of D0(τ). The model
fitted to experimental data results in a straight-line fitting – where the intercept at time zero

310

represents the steady-state temperature difference across the interfacial layers and interfacial
thermal resistances between the heating elements and the bulk surface of the sample, including
the thermal contact resistance. Also, low conducting surface layers, such as thin oxidation layers,
are compensated for in parameter A. The sensor insulation requires typically a settling time of the
2
order dsensor /asensor, where dsensor represents the thickness and asensor the thermal

diffusivity of the sensor insulation. However, the establishment of a constant heating power is
not instantaneous. Both these phenomena are treated with the use of a time correction, and initial
points deviating from the model fitting should be omitted in the analysis.

∆T sensor

∆T

∆T surface (sensor)

Experimental data

∆T surface (sample)

∆T ideal

Ains
At.c.r

Ideal model

D0(τ )
c

Alayer
Time window for analysis
The thermal penetration
Parameter A has settled,
depth reaches the first
i.e. the contact resistance
lateral sample boundary
influence becomes
Figure A.1 - The average temperature response as a function of D0(τ)

311

Eq A.1, gives a straight-line curve fitting, where parameter A is modeled as a sum of different
constant contributions to the total thermal resistance between the sensor heating element and the
bulk surface.
It should be noted that the recorded temperature increase is often appreciably higher than the
maximum temperature increase of the sample surface itself, particularly for high-conducting
samples. Now, as all these interfacial influences may be summed up in the constant A, and thus
be separated from the properties inside the bulk of the sample, we see that the bulk thermal
conductivity may be found in the slope of the straight-line fit, and the thermal diffusivity in the
1/2

best-model fitting of the D0(τ) function. For isotropic samples, λ=(λr·λa)

and a = ar , and the

volumetric specific heat may be obtained as ρcp = λ/a.
The model, Eq (A.1), represents the experimental data very well. For instance, with a
temperature increase of about 1 degree K, a standard deviation for all curve-fitted points of the
order 10

-5

K is commonly obtained, if the sample is homogeneous. This result in standard
1/2

deviations of the order of (or better than) 0.1% for the bulk thermal conductivity (λrλa)

even

if the sample is dismounted and remounted with different mounting pressures (which results in
rather scattered values of A from measurement to measurement), or the sensor insulation may
creep between measurements. So far it is obvious that the sensitivity is limited by the
performance of the electronics used in the measuring system.
Non-ideal experimental conditions like sensor heat capacity, heat losses through sensor leads and
variation in output of power during the transient, all of these influences normally within 1% of
the total output of heating power and are compensated for accurately in the Hot Disk software.

312

Other non-ideal conditions may appear when the insulating layer of the sensor is comparatively
large, say 100 µm or larger. However, these geometry deviations are small for sensors of larger
diameter, and at present, a calibration approach (against a well-known, homogeneous reference
material with known anisotropy and heat capacity) makes it possible to calibrate different
sensors to obtain full consistency in all estimated properties within 0.1-0.4%, independent of the
sensor used. Uncalibrated sensors of various kinds reproduce thermal conductivity results within
typically 1% between different types of sensors, and thermal diffusivity within typically 3-4%.

A.2 Thermomechanical Analysis (TMA) Technique
In the TMA technique thermal expansion properties of the sample are monitored against time or
temperature under a specified programmed atmosphere an follows ASTM test procedure (ASTM
E831, 2006). TMA measures deformation of the sample under non-oscillating load. The applied
load is kept very low to measure the dimension change of the sample also called thermo
dilatometry. Usually a small load of 2kN is sufficient to keep the probe in place over sample. A
typical system of TMA is shown in Figure 3.5a. The sample is placed on the inert surface
pedestal and probe is allowed to rest upon it exerting load controlled be the force controller as
shown in Figure 3.5c. The movement of the probe resulting from specimen changes is measure
by a linear variable differential transducer (LVDT) which produces electrical signal related to
position of the probe. The programmed controller controls the rate of heating and temperatures
are measured by thermocouples in furnace and at pedestal. Data from LVDT and the
thermocouples are stored and processed in real time by computer.
TMA basically uses the modulated temperature techniques to carry thermal analysis. In
modulated temperature thermal analysis, a sinusoidal temperature “forcing function” is added to
the traditional linear (or isothermal) underlying heating rate. This forcing function induces in the
313

sample a sinusoidal response that may be de-convoluted to yield reversing and non-reversing
information.
When applied to thermo-mechanical analysis (TMA), the temperature modulation produces a
sinusoidal change in test specimen length. Figure A.2, for example, shows the modulated
temperature at the figure bottom and the length change at the top both as their first derivatives.
Discrete Fourier transformation is applied in real time to continuously determine the average

24

Derivative of modulated dimension
change (µm/min)

2
1

16
0
-1

8

-2
0
-3
-4

-8
40

80

120

[------] Derivative of moduated temperture
(°C/min)

value and the amplitude value for each signal (Price, 1998).

160

Temperature (°C)
Figure A.2 - Modulated temperature (bottom) and the length change (top) both as their first
derivatives.
The governing equation for modulated TMA is given by
dL/dt = A dT/dt + f (t, T)

A.2

where L is length, T is temperature, t is time, A is expansivity, and f(x) is “function of time and
Temperature”. The left hand term of equation 1, known as the total length change rate, is shown

314

on the right to be composed of two parts; a reversing contribution proportional to the time rate of
change of the independent parameter (temperature) and a non-reversing contribution from the
absolute value of that independent parameter.
Of course in TMA, the dependent parameter measured is length (not the time rate of change of
length) so the governing equation takes on the form of:
Ltotal =Lreversing + Lnonreversing

A.3

where Ltotal is the average length from the Fourier de-convolution, Lreversing is the (length
amplitude / temperature amplitude) ∫ dT/dt K. The “average length”, “length amplitude” and
“temperature amplitude” are the signals derived from the Fourier transformation process. ∫ dT/dt
is the underlying heating rate averaged over a single period while K is a calibration constant
close to unity. The non-reversing length is obtained from the difference between the total and
reversing contributions.
Lnonreversing = Ltotal – Lreversing

A.4

There is always a “lag” between the applications of the forcing function and the resultant
response. The use of sinusoidal forcing functions provides for the easy measurement and
interpretation of the magnitude of this lag through the use of a Lissajous plot. Evaluation of the
midpoint and extrema values of the Lissajous plot yields the phase lag. In modulated TMA, this
lag is rather large compared to other modulated temperature techniques, about 28 s, due to the
large thermal mass and low thermal conductivity of the quartz sample stage and measuring
probe. A practical rule-of-thumb is that the period of the applied forcing function should be
about ten times the time constant. So for modulated TMA, a period of about 300 seconds (5mins)
is used. The applied temperature amplitude is selected based upon the value of the expansivity

315

value A in equation A.2, but is typically ± 5°C. And as with all modulated temperature
approaches, at least 5 cycles is required across a transition in order to have reliable Fourier deconvolution. This results in the typical underlying heating rate of 2°C/min or less. The value of
the calibration coefficient is determined, as is the length change calibration of the TMA, from the
use of a reference material with a known coefficient of thermal expansion (CTE) value (Blaine
and Hahn, 1998).

316

APPENDIX B

317

APPENDIX B

Design of Column Specimens
B.1 Column Capacity Calculations
This appendix summarizes the design calculations using ACI 318 (2008) and ACI 216.1 (2007)
provisions for FAC, FAC-P, HSC-S, and HSC-H columns. Dimensions for design of columns
are mainly dictated by fire test furnace in with these columns were to be tested. Table B.1 gives
the dimensions and properties of the steel used in calculations. Calculations for one column each
from set of FAC and HSC columns is presented here and ultimate strength and factored design
capacity is summarized for all columns in Table B.2 and B.5 for FAC and HSC columns
respectively.
Table B.1 - Design parameters used for the columns
Design parameter

Notation

Value

Gross area (Cross-section = 203x203 mm)

Ag

41209 mm

Steel yield strength

fy

420 MPa

Steel area (4 # 6 bars)

Ast

4 × 285 = 1140 mm

Length of column

l

3300 mm

Concrete cover to main rebars for
minimum 2 hours fire resistance

-

50 mm (ACI 216.1 2.5.3)

Column end conditions

-

Pin-pin

2

2

Note: Maximum usable strain at extreme concrete compressive fiber shall be assumed equal to

(ACI 10.2.3)

0.003.

318

Notations:

d΄

b

Pn

yˊ

e
Aˊ
s

d h

As
Geometric
centroid

c = distance to neutral axis
‫ = ݕ‬distance to geometric centroid
ത
εs = steel strain in tension side
ε’s = steel strain in compression side

e = eccentricity of load to geometric centroid
e’ = eccentricity of load to tension steel
d’ = effective cover of compression steel
Figure B.1 - Notations used in calculations

319

e΄
Geometric
centroid

4 #6 (19mm)
rebars
#3 (10mm)
ties

εc = 0.003

ε's

0.85 f´c

Cs
Cc

c

Cs
Cc
d - d´

Ts

Ts

εs
Strains
d −c
c
c − d'
ε 's = 0.003
c

ε s = 0.003

Stresses
f s = E sε s ≤ f y
f ' s = E sε ' s ≤ f y

Figure B.2 - Stress-strains and forces in columns

320

Internal forces
Cc = 0.85 f 'c ba
Cs = A's f 's
Ct = As f s

B.2 P-M interaction Diagram for FAC column
Table B.2 - Calculated factored capacities of FAC and FAC-P columns
Column
FAC

Factored strength property

Value

Compressive strength (f’c)

107 MPa

Ultimate load (Pu)

2144 kN

Ultimate moment (Mu)

68.12 kN.m

Compressive strength (f’c)

100 MPa

Ultimate load (Pu)

2020 kN

Ultimate moment

68.65 kN.m

FAC-P

Point 1 - (depth of neutral axis > d)
c = infinity

203mm

Pn = 0.8(Anet × 0.85 f´c + Ast fy)

= 0.8 × (40069×0.85×107+1140×420)/1000 = 3298 kN

4 #6 (19mm)
rebars
#3 (10mm)
ties

φPn = 0.65 × = 2144 kN
Mn = 0

Point 2 - (depth of neutral axis at d)

Figure B.3 - Cross-section of RC column

at c = d = 153 mm

0.003ሺܿ െ ݀ᇱ ሻ
݂ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ‫ ݏ‬ൌ 200000
൑ ݂‫ݕ‬
ܿ
ᇱ

ᇱ

݂ ᇱ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ᇱ ‫ ݏ‬ൌ 200000

203 mm

50 mm

0.003ሺ153 െ 50ሻ
153

321

ൌ 403 ‫ ܽܲܯ‬൏ 420 ‫ܽܲܯ‬
‫ ݏܥ‬ൌ ‫ܣ‬ᇱ ‫ ݏ‬ൈ ݂ ᇱ ‫ ݏ‬ൌ 570 ൈ

403
ൌ 230 ݇ܰ
1000

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ
݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ = 0
ܶ‫ ݏ‬ൌ 0
‫ ܿܥ‬ൌ 0.85 ൈ ݂ ᇱ ܿ ൈ ߚ ൈ ܽ ൈ ܾ
ൌ 0.85 ൈ 107 ൈ 203 ൈ 0.85 ൈ

153
ൌ 2401.09 ݇ܰ
1000

ܲ݊ ൌ ‫ ܿܥ‬൅ ‫ ݏܥ‬െ ܶ‫ ݏ‬ൌ 2401.09 ൅ 230 െ 0 ൌ 2631.33 ݇ܰ
φPn = 0.65 × 2631.33 = 1710.36 kN
ܽ
തሻ
ത
‫ ݊ܯ‬ൌ ‫ ܿܥ‬ቀ‫ ݕ‬െ ቁ ൅ ‫ݏܥ‬ሺ‫ ݕ‬െ ݀ ᇱ ሻ ൅ ܶ‫ ݏ‬ሺ݀ െ ‫ݕ‬
ത
2

Mn = 99.43 kN.m
φMn = 0.65 × 99.43 = 64.63 kN.m

(ACI 9.3.2)

Point 3 - (depth of neutral axis < d)
at c = d = 122.4 mm

݂ ᇱ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ᇱ ‫ݏ‬
ൌ 200000

଴.଴଴ଷ൫௖ିௗᇲ ൯
௖

൑ ݂‫ݕ‬

(ACI 10.2.4)

322

݂ ᇱ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ᇱ ‫ ݏ‬ൌ 200000

0.003ሺ122.4 െ 50ሻ
122.4

ൌ 354.90 ൏ 420 ‫ܽܲܯ‬

354.90
1000

‫ ݏܥ‬ൌ ‫ܣ‬ᇱ ‫ ݏ‬ൈ ݂ ᇱ ‫ ݏ‬ൌ 570 ൈ
ൌ 202.29 ݇ܰ

(ACI 10.2.4)

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ
଴.଴଴ଷሺଵହଷିଵଶଶ.ସሻ

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000
ܶ‫ ݏ‬ൌ ‫ ݏܣ‬ൈ ݂‫075 = ݏ‬ൈ

ଷହସ.ଽଷ
ଵ଴଴଴

ଵଶଶ.ସ

= 354.93 MPa < 420 MPa

ൌ 85.5 ݇ܰ

‫ ܿܥ‬ൌ 0.85 ൈ ݂ ᇱ ܿ ൈ ߚ ൈ ܿ ൈ ܾ
ൌ 0.85 ൈ 107 ൈ 0.85 ൈ 122.4 ൈ 203/1000 ൌ 1920.87 ݇ܰ
ܲ݊ ൌ ‫ ܿܥ‬൅ ‫ ݏܥ‬െ ܶ‫ ݏ‬ൌ 1920.87 ൅ 202.29 െ 85.5
ൌ 2037.7 ݇ܰ

(ACI 10.3.6)

φPn = 0.65 × 2037.7 = 1324.5 kN

(ACI 9.3.2)

ܽ
‫ ݊ܯ‬ൌ ‫ ܿܥ‬ቀ‫ ݕ‬െ ቁ ൅ ‫ݏܥ‬ሺ‫ ݕ‬െ ݀ ᇱ ሻ ൅ ܶ‫ ݏ‬ሺ݀ െ ‫ݕ‬
ത
തሻ
ത
2
Mn = 109.87 kN.m
φMn = 0.65 × 109.87 = 71.41 kN.m

(ACI 9.3.2)

Obtain more points for P-M diagram at given in Table B.3

323

Table B.3 - Calculation of nominal load and moment for P-M diagram for FAC column
Point #

c (mm)

Pn (kN)

φPn (kN)

Mn (kN.m)

1
2
3
4
5
6
7

inf
153.00
122.40
91.80
61.20
30.60
0.01

3298.46
2631.33
2037.67
1368.38
783.63
24.00
-478.64

2144.00
1710.36
1324.48
889.45
509.36
15.60
-311.12

0.00
99.44
109.87
109.78
88.06
43.66
0.02

φMn
(kN.m)
0.00
64.63
71.41
71.36
57.24
28.38
0.01

From all these points we get the load-moment (P-M) interaction diagram for FAC column as
plotted in Figure B.4.
2000

Load Pu (kN)

1500
1000
500
0
-500
0

20
40
Moment Mu (kN.m)

Figure B.4 - Load-moment interaction diagram for FAC column

Calculate the critical buckling load of the column
Pin ended (k = 1)
Check slenderness

324

60

Radius of gyration r = 0 .3 × h
Where h = dimension of column
h = 203 mm
r = 0.3 × 203 = 60.9
lu = 3350 mm = 3.35 m
klu = 1*3350 = 3350 mm
௞௟ೠ
௥

൑ 40

(ACI 10.10)

Slenderness ratio = 3350/60.9 = 55 >40
Hence the column is slender and moment magnification method should be used.
Calculate buckling load – concentrically loaded slender column

‫ܧ‬ி஺஼ ൌ 3.32ඥ݂ ᇱ ܿ ൅ 6895ሺ‫ݓ‬௖ /2320ሻଵ.ହ
‫ܧ‬ி஺஼ ൌ 3.32√107/1000 ൅ 6895ሺ2564/2320ሻଵ.ହ = 42352 MPa
ܾ݀ଷ
‫ܫ‬௚ ൌ
ൌ 141515140.1 ݉݉ସ
12
(ACI 10.15)

Flexural rigidity = EI

‫ ܫܧ‬ൌ

଴.ସா௖ூ೒
ଵାఉ೏

‫ܫܧ‬ி஺஼ ൌ

0.4 ൈ 42352 ൈ 141515140.1
ൌ 1.62݁ଵଶ ‫ܽܲܯ‬
ሺ1 ൅ 0.5ሻ1000
(ACI 10.13)

Euler buckling Load Pc

325

ߨ ଶ ‫ܫܧ‬
ܲ௖ୀ
ሺ݈݇௨ ሻଶ
ܲ௖ ி஺஼ୀ 1408.89 ݇ܰ
Calculate the load and moment capacity of the column, the moment calculated by moment
magnification factor will be checked against P-M diagram. Capacity is calculated by using
iterations by assuming different Pu and then calculation of ߜ௡௦ as tabulated in Table B.4:

ߜ௡௦ ൌ ‫/݉ܥ‬ሺ1 െ

ܲ‫ݑ‬
ሻ
0.75ܲܿ

Table B.4 - Load and moment capacity calculated by moment magnification method.
Mu (kN.m)

Pu (kN)

ࢾ࢔࢙

e (mm)

0.00
5.63
14.04
27.95
55.35
56.17
57.01
68.54

0.00
222.40
444.80
667.20
889.60
894.05
898.50
951.87

1.00
1.20
1.49
1.98
2.94
2.97
3.00
3.40

0.00
25.65
31.75
42.16
62.74
63.50
64.01
72.64

Superimposing the calculated Pu and Mu against P-M diagram of the column gives the capacity
of the column.

326

2500

Load Pu (kN)

2000
1500
1000
500
0
-500
0

20
40
Moment Mu (kN.m)

60

80

Figure B.5 - Calculation of ultimate load from load-moment interaction diagram for FAC column

B.3 P-M interaction Diagram for HSC-S and HSC-H column
Design parameters for HSC-S and HSC-H are same as given in table B.1.
Table B.5 - Calculated factored capacities of HSC-S and HSC-H columns
HAC-S
Compressive strength (f’c)

77 MPa

Ultimate load (Pu)

1612 kN

Ultimate moment (Mu)

50.84 kN.m

Compressive strength (f’c)

80 MPa

Ultimate load (Pu)

1665 kN

Ultimate moment (Mu)

53.45 kN.m

HAC-H

Point 1 - (depth of neutral axis > d)
327

c = infinity
Pn = 0.8(Anet × 0.85 f´c + Ast fy)
= 0.8 × (40069×0.85×77+1140×420)/1000 = 2481.05 kN
φPn = 0.65 × = 1612 kN
Mn = 0
Point 2 - (depth of neutral axis at d)
at c = d = 153 mm

0.003ሺܿ െ ݀ ᇱ ሻ
൑ ݂‫ݕ‬
݂ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ‫ ݏ‬ൌ 200000
ܿ
ᇱ

ᇱ

݂ ᇱ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ᇱ ‫ ݏ‬ൌ 200000
‫ ݏܥ‬ൌ ‫ܣ‬ᇱ ‫ ݏ‬ൈ ݂ ᇱ ‫ ݏ‬ൌ 570 ൈ

0.003ሺ153 െ 50ሻ
ൌ 403 ‫ ܽܲܯ‬൏ 420 ‫ܽܲܯ‬
153

403
ൌ 230 ݇ܰ
1000

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ
݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ = 0
ܶ‫ ݏ‬ൌ 0
‫ ܿܥ‬ൌ 0.85 ൈ ݂ ᇱ ܿ ൈ ߚ ൈ ܽ ൈ ܾ
ൌ 0.85 ൈ 77 ൈ 203 ൈ 0.85 ൈ

153
ൌ 1727.89 ݇ܰ
1000

ܲ݊ ൌ ‫ ܿܥ‬൅ ‫ ݏܥ‬െ ܶ‫ ݏ‬ൌ 1727.89 ൅ 230 െ 0 ൌ 1958.13 ݇ܰ
φPn = 0.65 × 1958.13 = 1272.78 kN
ܽ
തሻ
ത
‫ ݊ܯ‬ൌ ‫ ܿܥ‬ቀ‫ ݕ‬െ ቁ ൅ ‫ݏܥ‬ሺ‫ ݕ‬െ ݀ ᇱ ሻ ൅ ܶ‫ ݏ‬ሺ݀ െ ‫ݕ‬
ത
2
328

Mn = 74.88 kN.m
φMn = 0.65 × 74.88 = 48.67 kN.m

(ACI 9.3.2)

Point 3 - (depth of neutral axis < d)
at c = d = 122.4 mm
ᇱ

ᇱ

݂ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ‫ ݏ‬ൌ 200000
݂ ᇱ ‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ߝ ᇱ ‫ ݏ‬ൌ 200000
‫ ݏܥ‬ൌ ‫ܣ‬ᇱ ‫ ݏ‬ൈ ݂ ᇱ ‫ ݏ‬ൌ 570 ൈ

଴.଴଴ଷ൫௖ିௗᇲ ൯
௖

൑ ݂‫ݕ‬

(ACI 10.2.4)

0.003ሺ122.4 െ 50ሻ
ൌ 354.90 ൏ 420 ‫ܽܲܯ‬
122.4

354.90
1000

ൌ 202.29 ݇ܰ

(ACI 10.2.4)

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000 ሺ0.003ሺ݀ െ ܿሻሻ/ܿ
଴.଴଴ଷሺଵହଷିଵଶଶ.ସሻ

݂‫ ݏ‬ൌ ‫ ݏܧ‬ൈ ݂‫ ݏ‬ൌ 200000
ܶ‫ ݏ‬ൌ ‫ ݏܣ‬ൈ ݂‫075 = ݏ‬ൈ

ଷହସ.ଽଷ
ଵ଴଴଴

ଵଶଶ.ସ

= 354.93 MPa < 420 MPa

ൌ 85.5 ݇ܰ

‫ ܿܥ‬ൌ 0.85 ൈ ݂ ᇱ ܿ ൈ ߚ ൈ ܿ ൈ ܾ
ൌ 0.85 ൈ 77 ൈ 0.85 ൈ 122.4 ൈ 203/1000 ൌ 1382.31 ݇ܰ
ܲ݊ ൌ ‫ ܿܥ‬൅ ‫ ݏܥ‬െ ܶ‫ ݏ‬ൌ 1382.31 ൅ 202.29 െ 85.5 ൌ 1499. 11 ݇ܰ

(ACI 10.3.6)

φPn = 0.65 × 1499. 11 = 974.41 kN

(ACI 9.3.2)

ܽ
‫ ݊ܯ‬ൌ ‫ ܿܥ‬ቀ‫ ݕ‬െ ቁ ൅ ‫ݏܥ‬ሺ‫ ݕ‬െ ݀ ᇱ ሻ ൅ ܶ‫ ݏ‬ሺ݀ െ ‫ݕ‬
ത
തሻ
ത
2
Mn = 83.22 kN.m

329

φMn = 0.65 × 83.22 = 54.10 kN.m

(ACI 9.3.2)

Obtain more points for P-M diagram as given in Table B.6
Table B.6 - Calculation of nominal load and moment for P-M diagram for HSC-S column
Point #

c

Pn

φPn

Mn

φMn

1
2
3
4
5
6
7

infinity
153.00
122.40
91.80
61.20
30.60
0.01

2481.05
1958.13
1499.11
964.46
514.34
-110.65
-478.69

1612.68
1272.78
974.42
626.90
334.32
-71.92
-311.15

0.00
74.88
83.22
84.54
67.73
31.74
0.01

0.00
48.67
54.09
54.95
44.02
20.63
0.01

From all these points we get the P-M diagram
2000

Load Pu (kN)

1500
1000
500
0
-500
0

20
40
Moment Mu (kN.m)

60

Figure B.6 - Load-moment interaction diagram for HSC-S column
Calculate buckling load – concentrically loaded slender column

E୊୅େ ൌ 3.32√f ᇱ c ൅ 6895ሺwୡ /2320ሻଵ.ହ
E୊୅େ ൌ 3.32√107/1000 ൅ 6895ሺ2530/2320ሻଵ.ହ = 37142.88 MPa
330

bdଷ
I୥ ൌ
ൌ 141515140.1 mmସ
12
(ACI 10.15)

Flexural rigidity = EI

EI ൌ

଴.ସ୉ୡ୍ౝ
ଵାஒౚ

EI୊୅େ ൌ

0.4 ൈ 37142.88 ൈ 141515140.1
ൌ 1.40eଵଶ MPa
ሺ1 ൅ 0.5ሻ1000
(ACI 10.13)

Euler buckling Load Pc

ߨ ଶ ‫ܫܧ‬
ܲ௖ୀ
ሺ݈݇௨ ሻଶ
ܲ௖ ுௌ஼ିௌୀ 1232.7 ݇ܰ
Calculate the load and moment capacity of the column, the moment calculated by moment
magnification factor will be checked against P-M diagram. Capacity is calculated by using
iterations by assuming different Pu and then calculation of ߜ௡௦ as tabulated in Table B.7:
δ୬ୱ ൌ Cm/ሺ1 െ

Pu
ሻ
0.75Pc

Table B.7 - Load and moment capacity calculated by moment magnification method.
Mu (kN.m)

Pu (kN)

ࢾ࢔࢙

e (mm)

0.00
5.64
14.11
28.22
56.45
65.86
68.00

0
222.4
444.8
667.2
889.6
934.08
942.976

1
1.2
1.5
2
3
3.3
3.4

0
25.4
33.02
43.18
63.5
71.12
73.66

Superimposing the calculated Pu and Mu against P-M diagram of the column gives the capacity
of the column.

331

2000

Load Pu (kN)

1500
1000
500
0
-500
0

20
40
Moment Mu (kN.m)

60

Figure B.7 - Calculation of ultimate load from load-moment interaction diagram for HSC-S
column

332

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