Economical concrete mix design utilizing blended cements, performance-based specifications, and pay factors: Final Report 633

              Economical Concrete Mix Design Utilizing
Blended Cements, Performance-Based
Specifications, and Pay Factors
Final Report 633
May 2013
Arizona Department of Transportation
Research Center
Economical Concrete Mix Design
Utilizing Blended Cements,
Performance-Based Specifications,
and Pay Factors
Final Report 633
May 2013
Prepared by:
Mehdi Bakhshi, Graduate Research Associate
Busaba Laungrungrong, Graduate Research Associate
Aboozar Bonakdar, Postdoctoral Research Associate
Barzin Mobasher, Professor
Connie M. Borror, Professor, Math & Natural Sciences Division
Douglas C. Montgomery, Professor
Ira A. Fulton Schools of Engineering
Arizona State University
Tempe, AZ 85287-5306
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, AZ 85007
in cooperation with
U.S. Department of Transportation
Federal Highway Administration
This report was funded in part through grants from the Federal Highway Administration, U.S.
Department of Transportation. The contents of this report reflect the views of the authors, who
are responsible for the facts and the accuracy of the data, and for the use or adaptation of
previously published material, presented herein. The contents do not necessarily reflect the
official views or policies of the Arizona Department of Transportation or the Federal Highway
Administration, U.S. Department of Transportation. This report does not constitute a standard,
specification, or regulation. Trade or manufacturers’ names that may appear herein are cited
only because they are considered essential to the objectives of the report. The U.S. government
and the State of Arizona do not endorse products or manufacturers.
Technical Report Documentation Page
1. Report No.
FHWA-AZ-13-633
2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle
Economical Concrete Mix Design Utilizing Blended
Cements, Performance-Based Specifications, and Pay Factors
5. Report Date
May 2013
6. Performing Organization Code
7. Author(s)
M. Bakhshi, B. Laungrungrong, A. Bonakdar, B. Mobasher,
C.M. Borror, and D.C. Montgomery
8. Performing Organization Report No.
9. Performing Organization Name and Address
Ira A. Fulton Schools of Engineering
Arizona State University
Tempe, AZ 85287-5306
10. Work Unit No. (TRAIS)
11. Contract or Grant No.
SPR-PL1 (181) 633
12. Sponsoring Agency Name and Address
Research Center
Arizona Department of Transportation
206 S. 17th Ave. MD075R
Phoenix, AZ 85007
13. Type of Report and Period Covered
Final Report
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration
16. Abstract
This report showcases several new approaches of using materials science and structural mechanics to accomplish
sustainable design of concrete materials. The topics addressed include blended cements, fiber-reinforced concrete
(FRC), internal curing with lightweight aggregate, and statistical process control (SPC). Materials,
methodologies, and test methods to enhance the performance and durability of concrete are addressed. Properties
of pozzolans, blended cements, fly ashes, and other materials, along with proposed categories of high-performance
concrete (HPC) mixtures using high-volume fly ash are briefly described. Early-age cracking and
drying shrinkage are addressed in detail, as they both reduce load-carrying capacity and accelerate deterioration,
resulting in increased maintenance costs and reduced service life. New developments in HPC materials using
FRC are proposed, and it is shown that considerable cost savings can be realized by using fiber concrete
mixtures.
Internal curing techniques as a means of improving the quality of concrete using pre-soaked lightweight
aggregate as an internal water supply were studied. The superior results of internally cured samples with
lightweight aggregates, especially sintered bottom ash, indicate a great potential for using them in hot-weather
concreting or when external curing is not possible.
A new method for statistical data processing of concrete strength data also is presented. Technical tools were
developed to improve performance-based specifications and statistical process control methods using cumulative
sum (CUSUM) and exponentially weighted moving average (EWMA). Both of these approaches allow for
process control and quality control (QC) monitoring of the materials. This report concludes with specifications
for quality assurance (QA) and introduces quality measures as criteria for reducing the costs.
17. Key Words
Fiber-reinforced concrete, FRC, performance-based
specifications
18. Distribution Statement
No restrictions. This document is available to the public
through the National Technical Information Service,
Springfield, VA 22161.
19. Security Classification (of this report)
Unclassified
20. Security Classification (of this page)
Unclassified
21. No. of Pages
123
22. Price
FORM DOT F 1700.7 (8-72)
SI* (MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS
Symbol When You Know Multiply By To Find Symbol
LENGTH
in inches 25.4 millimeters mm
ft feet 0.305 meters m
yd yards 0.914 meters m
mi miles 1.61 kilometers km
AREA
in2 square inches 645.2 square millimeters mm2
ft2 square feet 0.093 square meters m2
yd2 square yard 0.836 square meters m2
ac acres 0.405 hectares ha
mi2 square miles 2.59 square kilometers km2
VOLUME
fl oz fluid ounces 29.57 milliliters mL
gal gallons 3.785 liters L
ft3 cubic feet 0.028 cubic meters m3
yd3 cubic yards 0.765 cubic meters m3
NOTE: volumes greater than 1000 L shall be shown in m3
MASS
oz ounces 28.35 grams g
lb pounds 0.454 kilograms kg
T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t")
TEMPERATURE (exact degrees)
oF Fahrenheit 5 (F-32)/9 Celsius oC
or (F-32)/1.8
ILLUMINATION
fc foot-candles 10.76 lux lx
fl foot-Lamberts 3.426 candela/m2 cd/m2
FORCE and PRESSURE or STRESS
lbf poundforce 4.45 newtons N
lbf/in2 poundforce per square inch 6.89 kilopascals kPa
APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol
LENGTH
mm millimeters 0.039 inches in
m meters 3.28 feet ft
m meters 1.09 yards yd
km kilometers 0.621 miles mi
AREA
mm2 square millimeters 0.0016 square inches in2
m2 square meters 10.764 square feet ft2
m2 square meters 1.195 square yards yd2
ha hectares 2.47 acres ac
km2 square kilometers 0.386 square miles mi2
VOLUME
mL milliliters 0.034 fluid ounces fl oz
L liters 0.264 gallons gal
m3 cubic meters 35.314 cubic feet ft3
m3 cubic meters 1.307 cubic yards yd3
MASS
g grams 0.035 ounces oz
kg kilograms 2.202 pounds lb
Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T
TEMPERATURE (exact degrees)
oC Celsius 1.8C+32 Fahrenheit oF
ILLUMINATION
lx lux 0.0929 foot-candles fc
cd/m2 candela/m2 0.2919 foot-Lamberts fl
FORCE and PRESSURE or STRESS
N newtons 0.225 poundforce lbf
kPa kilopascals 0.145 poundforce per square inch lbf/in2
*SI is the symbol for th International System of Units. Appropriate rounding should e be made to comply with Section 4 of ASTM E380.
(Revised March 2003)
TABLE OF CONTENTS
Chapter 1. Introduction ................................................................................................................... 1
Chapter 2. Concrete Materials for a Sustainable Infrastructure ...................................................... 3
A Case for Sustainable Infrastructure Systems ........................................................................... 3
Blended Cements........................................................................................................................ 3
High-performance Concrete ........................................................................................................ 7
Chapter 3. Fiber-reinforced Concrete ........................................................................................... 15
Introduction ............................................................................................................................... 15
Fiber Types ............................................................................................................................... 17
Three-Point Bending Tests ........................................................................................................ 17
Experimental Results of Three-point Bending Test .................................................................. 21
Inverse Analysis of Load-deflection Response ......................................................................... 28
Data Reduction by Average Residual Strength Method (ARS) ................................................ 37
Comparison between Post-peak Residual Strength and ARS Method ...................................... 37
Development of Design Equations for Flexural Response ....................................................... 39
Minimum Flexural Post-crack Tensile Strength Requirements ................................................ 39
Minimum Post-crack Tensile Strength for Shrinkage and Temperature................................... 40
Design Example for Slab on Grade ........................................................................................... 41
Conclusion ................................................................................................................................ 43
Chapter 4. Internal Curing ............................................................................................................ 45
Introduction ............................................................................................................................... 45
Curing Aspects of HPC ............................................................................................................. 45
Early-Age Shrinkage ................................................................................................................. 47
Experimental Program............................................................................................................... 48
Results and Discussion of Compressive Tests .......................................................................... 52
Conclusion ................................................................................................................................ 60
Chapter 5. High-Volume Fly Ash Concrete ................................................................................. 61
Introduction ............................................................................................................................... 61
Mechanical Properties ............................................................................................................... 61
Cracking Tendency of HVFA Concrete Due to Restrained Shrinkage ..................................... 65
Conclusions ............................................................................................................................... 67
Chapter 6. Enhancing Durability Characteristics of Concrete ...................................................... 69
Introduction ............................................................................................................................... 69
v
vi
Sulfate Attack and ASR ............................................................................................................ 69
Guidelines for Material Design ................................................................................................. 72
Chapter 7. Procedures for Statistical Quality Control .................................................................. 81
Introduction ............................................................................................................................... 81
Statistical Analysis for Quality Assurance ................................................................................ 83
Preliminary Study of Historical Data ........................................................................................ 91
Control Chart Design ................................................................................................................ 95
Performance of the Combined Control Charts .......................................................................... 96
Experimental Results and Further Discussion .......................................................................... 97
Further Comparisons of the CUSUM-Run and EWMA-Run Charts ...................................... 100
Pay Factor Criteria .................................................................................................................. 101
Conclusions ............................................................................................................................. 102
References .................................................................................................................................. 103
vii
LIST OF TABLES
Table 1. Sample Oxide Analysis for Fly Ash and Cement
(Portland Cement Association, 2009). ............................................................................................ 5
Table 2. Proposed HPC Classes Based on Specifications, Materials, Admixtures, and Testing
Methods........................................................................................................................................ 10
Table 3. Specifications for Type A HPC. ..................................................................................... 11
Table 4. Specifications for Type B HPC. ..................................................................................... 11
Table 5. Specifications for Type C HPC. ..................................................................................... 12
Table 6. Sample Specifications for Type C HPC. ........................................................................ 13
Table 7. Specifications for Type J HPC........................................................................................ 14
Table 8. Physical Properties of Fibers Used. ................................................................................ 18
Table 9. Mixture Proportions and Compressive Strength of all Mixes. ....................................... 20
Table 10. Summary of Flexural Tests of Plain and Glass Fiber Reinforced Concrete. ................ 22
Table 11. Summary of Experimental Analysis on Flexural Data of Polymeric Fibers. ............... 24
Table 12. Summary of Experimental Analysis on Flexural Data of Polymeric Fibers. ............... 26
Table 13. Summary of Experimental Analysis of Polymeric Fibers (Types 2, 3, 4 and 5). ......... 28
Table 14. Back-calculated Tensile Parameters of Flexural Samples Using a Plasticity Model. .. 34
Table 15. Back-calculated Tensile Parameters of Flexural Samples Using the Strain-softening
Model. .......................................................................................................................................... 36
Table 16. The Scope of the Test Program..................................................................................... 49
Table 17. Mix Design of All Mixes. ............................................................................................. 49
Table 18. Particle Size Distribution of the Lightweight Aggregates Used in This Study. ........... 51
Table 19. Specific Gravities, Absorption, and Void Content of LWAs Used in This Study. ...... 51
Table 20. Compression Data Summary (Low-strength Level). .................................................... 55
Table 21. Compression Data Summary (Mid-strength Level). ..................................................... 59
Table 22. Compression Data Summary (High-strength Level). ................................................... 60
Table 23. Mixture Proportions of HVFA Concrete. ..................................................................... 61
Table 24. Compression Test Results for the HVFA Concrete Samples at 7 and 28 Days. .......... 63
Table 25. Three-point Bending Test Results for HVFA Concrete Samples at 7 and 28 Days. .... 64
Table 26. Chemical and Physical Properties of Raw Cementitious Materials. ............................ 69
Table 27. Requirements to Protect against Damage to Concrete by Sulfate Attack (Takada et al.,
1998). ........................................................................................................................................... 72
viii
Table 28. Minimum Levels of Pozzolanic Replacement and Alkalinity that Will Provide Various
Levels of ASR Prevention (Thomas, Fournier & Folliard, 2008). ............................................... 73
Table 29. Allowed Alkali Contents to Provide Various Levels of ASR Prevention (Collins &
Sanjayan, 1999)............................................................................................................................ 73
Table 30. Protective Quality Based on Autoclam Air Permeability Index (Basheer, 1993). ....... 73
Table 31. Mixture Proportions of the AR Glass and Control Samples (lb/ft3). ............................ 74
Table 32. Mean Crack Width and Standard Deviation of Samples after 14, 21, and 28 Days. .... 79
Table 33. Sample Calculations of CUSUM with and without Resetting after an Out-of-control
Signal Is Detected. ........................................................................................................................ 86
Table 34. Sample Calculations of EWMA Chart (All Values Are in psi). ................................... 88
Table 35. ARL Performance of the Two-sided EWMA Control Chart with Varying L, λ, and
Shift Size. ..................................................................................................................................... 90
Table 36. ARL Performance of the One-sided CUSUM with Various Values of k and h
and with No Mean Shift. ............................................................................................................... 91
Table 37. Test Case Data Sets....................................................................................................... 93
Table 38. Statistics Summary for Samples A11, A12, A13, A21, A22, and A23. ....................... 95
Table 39. Test Case Summaries When Monitoring the Process Mean. ........................................ 97
Table 40. Test Case Summary Classification. ............................................................................ 100
ix
LIST OF FIGURES
Figure 1. Scanning Electron Microscope (SEM) Image and X-ray Diffraction Pattern for a
Typical Class F Fly Ash. ................................................................................................................. 5
Figure 2. Effect of Metakaolin in a) Increasing Compressive Strength, b) Reducing Water
Penetration (W.P.), Water Absorption (W.A), Gas Permeability (G.P.), and Electrical Resistivity
(E.R.) (Shekarchi et al., 2009). ....................................................................................................... 7
Figure 3. Effect of Metakaolin Replacement Level on ASR Expansion
(Shekarchi et al., 2009). .................................................................................................................. 7
Figure 4. HPC Use in the United States Transportation Sector as of 2006-07
(Triandafilou et al., 2007). .............................................................................................................. 8
Figure 5. Cleanup Operation for a Canal during Construction When an Occasional Rainfall
Results in Debris Accumulation and Grade Changes of the Prepared Base. Photo Courtesy of
Rich Shelly, Pulice Construction Co. ........................................................................................... 16
Figure 6. a) Closed-loop Flexural Test Setup, b) Measuring CMOD at the Notch by
Extensometer and Displacement at Mid-span by the LVDT. ....................................................... 18
Figure 7. Crack Growth in FRC Samples under a Three-point Bending Test. ............................. 19
Figure 8. Effect of AR Glass Fibers on Flexural Response after a) 1 Day and b) 7 Days of
Curing. ......................................................................................................................................... 21
Figure 9. Effect of Polymeric Fibers on Flexural Responses at a) 14 Days and b) 28 Days. ....... 23
Figure 10. Casting of Shotcrete FRC Samples for Flexural and Compressive Strength Testing. 25
Figure 11. Effect of Polymeric Fibers on Flexural Responses at 8, 16, and 36 Hours. ................ 25
Figure 12. Effect of Different Polymeric Fibers on the Flexural Response at 16 Hours. ............. 27
Figure 13. Stress-strain Material Model for FRC Strain Softening Materials: ............................. 29
Figure 14. Rectangular FRC Section and the Simplified Strain and Stress Variations in Bending
(Soranakom & Mobasher, 2007b)................................................................................................. 29
Figure 15. Closed-form Moment Curvature Relationship (for Tensile Strain-softening and
Hardening Response) and Applied for Calculation of Load Deflection of the Flexural Beam
(Mobasher, 2011). ......................................................................................................................... 31
Figure 16. a) Experimental Results and Simulated Flexural Load-deflection Response of
Concrete with Glass Fibers b) Back-calculated Stress-Strain Relationship for a Control
Sample at 7 Days. ......................................................................................................................... 33
Figure 17. a) Experimental Results and Simulated Flexural Load-deflection Response and b)
Back-calculated Stress-Strain Relationship for a Control Sample at 7 Days. .............................. 33
Figure 18. Experimental and Simulated Load-deflection Response and Back-calculated
Stress-Strain Relationship of Three Samples with Different Fiber Types and Contents
Tested at 28 Days. ......................................................................................................................... 35
x
Figure 19. Comparison of Stress Distribution Determined Using the Present Approach and the
ARS Method. ............................................................................................................................... 38
Figure 20. Comparison of Post-peak Strength with ARS for Various Types of Fibers. .............. 38
Figure 21. Grain Size Distribution of Fine Aggregate. ................................................................. 50
Figure 22. The Aggregates Used in This Study: a) Normal Weight Aggregate, b) Bottom Ash
Aggregate, and c) Sintered Bottom Ash Aggregate...................................................................... 50
Figure 23. Submerged Lightweight Aggregates in Water: a) Bottom Ash, b) Sintered Bottom
Ash, and c) Saturated Surface-dry Condition of Aggregates Prior to Use. .................................. 52
Figure 24. Casting Concrete with Lightweight Aggregate: a) Materials before Pouring into Mixer
and b) Materials after Mixing. ...................................................................................................... 52
Figure 25. Comparative Results of Compression Tests at 7 Days (Low-strength Level). ........... 53
Figure 26. Comparative Results of Compression Tests at 28 Days (Low-strength Level). ......... 54
Figure 27. Effect of Internal Curing on the Compressive Test Results (Low-strength Level). .... 54
Figure 28. Comparative Results of Compression Tests at 7 Days (Mid-strength Level). ............ 56
Figure 29. Comparative Results of Compression Tests at 28 Days (Mid-strength Level). .......... 56
Figure 30. Effect of Internal Curing on the Compressive Test Results (Mid-strength Level). .... 57
Figure 31. Comparative Results of Compression Tests at 7 Days (High-strength Level). ........... 57
Figure 32. Comparative Results of Compression Tests at 28 Days (High-strength Level). ......... 58
Figure 33. Effect of Internal Curing on the Compressive Test Results (High-strength Level). ... 58
Figure 34. Curing of Specimens in the Water Tank at a Constant Temperature of 70° F. ........... 62
Figure 35. Closed-loop Compression Test Setup. ........................................................................ 62
Figure 36. Compressive Stress vs. Axial Strain of HVFA Concrete at a) 7 Days
and b) 28 Days. ............................................................................................................................. 63
Figure 37. a) Closed-loop Flexural Test Setup; b) Measuring CMOD at the Notch by
Extensometer and Displacement at the Mid-span by LVDT. ....................................................... 64
Figure 38. Flexural Response of Load vs. CMOD of HVFA Concrete at 7 and 28 Days. ........... 65
Figure 39. Configuration and Geometry of the Ring Test Specimen. .......................................... 65
Figure 40. Shrinkage Chamber (with Cover Door Removed) Designed to Subject Restrained
Concrete Ring Samples to Low Humidity Conditions. ................................................................ 66
Figure 41. Strain Gauge Readings vs. Time for HVFA Concrete Specimen. .............................. 66
Figure 42. Examination of HVFA Concrete Specimens after Exposure to the Shrinkage
Chamber. ...................................................................................................................................... 67
Figure 43. Expansion Curves for Standard Size Paste Specimens with 30 Percent Fly Ash. ...... 70
Figure 44. SEM Images and EDS Spectra for Ettringite Formation in Sulfate Attack. ............... 70
Figure 45. Effect of 30 Percent Fly Ash Replacement on ASR Expansion (ASTM 1567). ......... 71
xi
Figure 46. SEM for a Typical ASR Gel Formed in Control Specimen. ....................................... 71
Figure 47. Typical Results Obtained Using a Strain Gauge Attached to a Steel Ring in a Plain
Concrete Sample. .......................................................................................................................... 75
Figure 48. Effect of an AR Glass Fiber Addition on Results Obtained Using Strain Gauges
Attached to Steel Rings. ................................................................................................................ 75
Figure 49. Digital Camera Used for Crack Investigations and Crack Width Measurement. ........ 76
Figure 50. Transverse Cracks Caused by Restrained Drying Shrinkage on a) Control Sample and
b) ARG5.0 Sample after Being Kept for 14 days in a Shrinkage Chamber. ................................ 76
Figure 51. Reconstructed Shrinkage Crack Images of Control Group and ARG5.0 Samples. .... 77
Figure 52. Steps in the Analysis of 1 of 8 Images Taken along the Bottom Side of a Crack. ...... 78
Figure 53. Mean and Standard Deviations of Shrinkage Crack Width of All Mixtures. ............. 80
Figure 54. Comparison of the CUSUM Chart for Table 33 with Resetting (C+
i w/reset and C-
i
w/reset) and without Resetting (C+
i and C-
i ) When an Out-of-control Signal Is Detected .......... 86
Figure 55. EWMA Chart for the Data (CL = Control Limit, UCL =Upper Control Limit, and
LCL = Lower Control Limit) in Table 34. .................................................................................... 89
Figure 56. Correlation of Data Representing the Specified Strength of Concrete Delivered to a
Job Site for a Single Ready-mix Producer. The Solid Line Represents a 1-to-1 Correlation...... 92
Figure 57. Probability Plot for Samples A11, A13, A21, A22, and A23 ..................................... 94
Figure 58. Plot of the Combined Control Charts for Project C21 (Subgroup Size=2) When f’c =
3,000 psi (N =16). ......................................................................................................................... 97
Figure 59. Plot of the Combined Chart for Project D12 (Subgroup Size=2) When f’c = 4,000 psi
(N=6). ........................................................................................................................................... 98
Figure 60. Plot of the Combined Chart for Project D13 (Subgroup Size=2) When f’c = 3,500 psi
(N=20). ......................................................................................................................................... 99
Figure 61. Plot of the Combined Chart for Project F4 (Subgroup Size=2) When f’c = 4,500 psi
(N=19). ......................................................................................................................................... 99
xii
xiii
LIST OF ABBREVIATIONS AND ACRONYMS
AASHTO American Association of State Highway and Transportation Officials
ACI American Concrete Institute
AD Anderson-Darling
ADOT Arizona Department of Transportation
AEA Air-entraining agent
Al2O3 Aluminum oxide
Al2Si2O7 Metakaolin
AR Alkali-resistant
ARL Average run length
ARPA Arizona Rock Products Association
ARS Average residual strength
ASR Alkali-silica reactivity
Caltrans California Department of Transportation
Ca(OH)2 Calcium hydroxide
CaO Free lime
CMOD Crack mouth opening deformation
CO2 Carbon dioxide
C-S-H Calcium silicate hydrate
CUSUM Cumulative sum
DOE Design of experiments
DTA Differential thermal analysis
E.R. Electrical resistivity
EDS Energy dispersive spectography
EWMA Exponentially weighted moving average
FAST Field office automation system
Fe2O3 Iron oxide
FHWA Federal Highway Administration
FRC Fiber-reinforced concrete
G.P. Gas permeability
HPC High-performance concrete
HVFA High-volume fly ash
K2O Potassium oxide
keV Kilo electron volts
KGA Alkalinity of cement, in kilograms
LBA Alkalinity of cement, in pounds
LOI Loss on ignition
LRFD Load and resistance factor design
LVDT Linear variable differential transformer
MgO Magnesium oxide
MK15 Metakaolin, 15 percent replacement level
MOR Modulus of rupture
Na2O Sodium oxide
NaOH Sodium hydroxide
xiv
NCHRP National Cooperative Highway Research Program
-O- Ether
-OH Hydroxyl
QA Quality assurance
QC Quality control
RCPT Rapid chloride permeability test
s/cm Sand/cement (ratio)
SCM Supplementary cementitious materials
SEM Scanning electron microscope
SFRC Steel fiber-reinforced concrete
SiO2 Silicon dioxide
SO3 Sulfur trioxide
SP Superplasticizer
SPC Statistical process control
SRA Shrinkage-reducing admixture
TBD To be determined
TGA Thermogravimetric analysis
W.A. Water absorption
W.P. Water penetration
w/b Water/binder (ratio)
w/c Water/cement (ratio)
w/cm Water/cementitious materials (ratio)
WWF Welded wire fabric
1
CHAPTER 1. INTRODUCTION
The “Economical Concrete” project, sponsored by the Arizona Department of Transportation
(ADOT) and carried out by researchers at Arizona State University, showcases several new
aspects of using materials science and structural mechanics to conduct a sustainable design of
concrete materials for use in the transportation sector. Many of the aspects discussed and
developed in this report also may be more broadly applicable to all structural concrete materials.
To consider both aspects of sustainability and economics, the transportation community must
first address material choices from technically feasible production and construction methods.
Furthermore, as the structures are put into service, life cycle maintenance costs of structural
systems become important. Traditional methods to design and construct reinforced concrete
structures based on simplified specifications and empirical design tools needs to be re-evaluated
as well. These methodologies ignore the tensile capacity of concrete, treat the cracking and
associated durability problems as an afterthought, and are inherently inefficient, wasteful, and
expensive. Using innovative materials and blended cement systems designed according to
fundamental aspects of materials science would allow for the design of more efficient structural
systems.
The topics addressed in this report include blended cements, fiber-reinforced concrete (FRC),
internal curing with lightweight aggregate, and statistical process control (SPC). The objective
was to address new specifications, analysis, and design guidelines so that material models can be
directly integrated into structural analysis software. Emphasis is placed on developing alternative
solutions that allow for sustainable development of infrastructure systems using blended
cements, mechanics of materials, SPC, and design for durability.
This report discusses materials, methodologies, and test methods to enhance the performance and
durability of concrete. Properties of pozzolans, blended cements, fly ashes, and other materials,
along with proposed categories of high-performance concrete (HPC) mixtures are briefly
described. The report also addresses early-age cracking and drying shrinkage, both of which
reduce load-carrying capacity and accelerate deterioration, resulting in increased maintenance
costs and reduced service life. The use of admixtures and supplementary cementitious materials
for quality improvement and cost reduction are addressed using formulations containing up to 35
percent class F fly ash as cement replacement. The effectiveness of different pozzolans in
making concrete a high-performance material was investigated by mechanical and durability
experiments (such as long-term sulfate attacks and alkali-silica reactivity [ASR] tests). The
current directives on the reduction of the maximum cement requirements, and increases in the
limits of the use of class F fly ash, can be used to specify mixtures that meet the sustainability
criteria and reduce the carbon footprint of cement use considerably.
The second aspect of this report addressed new developments in HPC materials using FRC.
Using a series of experimental and theoretical derivations, it is shown that considerable cost
savings can be realized by using high-volume fraction fiber mixtures, which can provide load-carrying
capacity and ductility. These mixtures can be used for canal lining, shotcrete
applications, elevated slabs, bridge decks, retaining wall sections, and many other applications
2
where heavy reinforcement and high flexural and shear loading cases are applied. As new
software tools for analyzing and designing FRC materials are developed, cost-effective
alternatives are identified that can reduce labor and mobilization expenses. This report presents
an evaluation of various fiber systems that can be used to design and analyze beams, slabs,
retaining walls, and buried structures. The authors present simple examples that are related
directly to the design of slabs with FRC.
This report also addresses internal curing techniques as a means of improving the quality of
normal- and high-strength concrete mixtures containing blended cements. As pozzolanic
materials such as fly ashes participate in slow acting reactions in a blended cement system, the
demand for curing water can be much greater than that of ordinary portland cement concrete.
When this water is not readily available (e.g., because of the emptying of the capillary porosity),
significant autogenous deformation and early-age cracking may result. On the other hand, most
high-performance concretes having a low water-to-binder (w/b) ratio contain insufficient mixing
water to maintain the water-filled coarse capillaries needed to sustain cement hydration and
pozzolanic reactions. Therefore, a method of curing based on internal water supply would be
very effective for this type of concrete. The researchers studied applications of pre-soaked
lightweight aggregate as an internal water supply for curing of concrete. The superior results of
internally cured samples with lightweight aggregates, especially sintered bottom ash, indicate a
great potential for them to be used in hot-weather concreting or when external curing is not
possible, practical, or economical.
New methods for statistical data processing of concrete strength data are proposed. Current
contract specifications prescribe concrete based on minimum acceptable strength measures and
force producers to supply excessively high-strength concrete mixtures to address the statistical
variations of the test results. In recent years, sustainability of infrastructure systems has been the
main cost driver for new materials and design methods. Furthermore, life cycle cost modeling
has shown the superiority of various construction alternatives simply because the total cost of the
project is reduced by choosing an alternative that may be more expensive than the traditional
reinforced concrete system while the cost of labor, mobilization, and placement is redcued.
Several technical tools were developed to improve the design, handling, and production process.
Performance-based specifications that address the serviceability, workability, and long-term
durability of test methods and procedures are presented using two new techniques—cumulative
sum (CUSUM) and exponentially weighted moving average (EWMA)—which allow for process
control and help in quality control (QC) monitoring of the data. This report emphasizes
specifications for quality assurance (QA) and introduces quality measures as criteria for reducing
the cost of concrete.
3
CHAPTER 2. CONCRETE MATERIALS FOR A SUSTAINABLE
INFRASTRUCTURE
A CASE FOR SUSTAINABLE INFRASTRUCTURE SYSTEMS
Continuous maintenance and operation of civil infrastructure systems in support of prosperity,
safety, and economic productivity is a challenge faced by both state and federal governments. In
terms of building materials, concrete is the most commonly used throughout the world, and there
is a staggering demand for its production and utilization. The exponential growth of
infrastructure, especially in developing regions, further increases the demand for concrete
materials such that the worldwide production and use of concrete has surpassed 10 billion tons
per year (CEMBUREAU 2013). In the United States, concrete production almost doubled from
220 million cubic yards per year in the early 1990s to more than 430 million cubic yards in 2004.
Arizona utilized more than 15 million cubic yards of concrete products per year in 2004, and at a
cost ranging from of $100 to $400 per cubic yard, this number translates into an economic
impact of up to $6 billion (Damtoft et al., 2008).
Cement production generates one ton of carbon dioxide (CO2) per ton of cement and contributes
as much as 7 percent to the total production of greenhouse gases. The environmental
requirements applied to coal-burning power plants also have increased challenges for the use or
disposal of coal-burning by-products. Any optimization in the use of concrete products or long-term
increase in the durability of existing infrastructure systems will be beneficial in helping to
meet sustainability goals, reduce global CO2 emission, and improve quality of life (Yunovich,
Thompson & Virmani, 2004; Roy, 1999). The U.S. cement industry, led by the Portland Cement
Association, has adopted a year 2020 voluntary target of reducing CO2 emissions by 10 percent
(from a 1990 baseline) per ton of cementitious product produced or sold. Implementing methods
and recommendations for quality monitoring and control will have a direct impact on the
sustainability efforts of the cement production industry (Portland Cement Association, 2009).
The main topics addressed in this project may be categorized into four major groups: blended
cements, HPC, FRC, and the use of SPC procedures to monitor QC/QA of concrete construction.
Within these groups, the researchers considered mechanical properties, shrinkage cracking
tendency, high-volume fly ash (HVFA) concrete, and the effect of fly ash on enhancing the
performance of concrete against sulfate attack and ASR mitigation. These issues are addressed in
detail throughout this report and serve to integrate the need to better address materials used for
the next generation of transportation infrastructures.
BLENDED CEMENTS
Blended cement concretes, which are obtained by the partial replacement of portland cement
with pozzolanic materials, have improved mechanical properties and durability characteristics
compared to ordinary concrete formulations (Nikam, Rane & Deshmukh, 2005; American Coal
Ash Association, 2003; Mehta, 2004; Shekarchi et al., 2009). Blended cements have been used
for decades to improve the mechanical properties and durability characteristics of cement-based
materials. Using pozzolanic materials such as fly ash, silica fume, slag, and metakaolin
4
(Al2Si2O7) has resulted in economical and environmental benefits in the concrete industry
(Nikam, Rane & Deshmukh, 2005; American Coal Ash Association, 2003). To reduce
dependence on portland cement, the transportation industry needs to provide guidance and
promote the use of various blended cement formulations in accordance with the guidelines and
specifications of organizations such as the American Association of State Highway and
Transportation Officials (AASHTO), Federal Highway Administration (FHWA), American
Concrete Institute (ACI), and ASTM. This study investigated the potential benefits of using
blended cements in terms of both sustainability and durability, and this report addresses aspects
of using blended cements including sulfate attack, ASR mitigation, and internal curing.
Pozzolans
Pozzolanic materials improve the microstructure of concrete due to their particle size, and they
may alter chemical compositions and hydration reactions in blended cements. The pozzolanic
reactivity controls how much portlandite is consumed and converted to calcium silicate hydrate
(C-S-H) (Bentz & Garboczi, 1991). Over the past several decades, researchers have studied the
effectiveness of blended cement materials in reducing the level of damage from sulfate attack,
but the role of chemical composition of pozzolanic materials needs to be studied more precisely
(Tuthill, 1936; Kalousek, Porter & Benton, 1972; Monteiro & Kurtis, 2003). This report
addresses recent developments in the areas of use of blended cements and procedures to use
pozzolanic materials for ASR and sulfate attack mitigation.
Fly Ash
Coal-fired electric and steam-generating plants produce fly ash as a by-product. Typically, coal
is pulverized and blown with air into the boiler's combustion chamber where it ignites,
generating heat and producing a molten mineral residue. Boiler tubes extract heat from the
boiler, cooling the flue gas and causing the molten mineral residue to harden and form ash.
Coarse ash particles, referred to as bottom ash or slag, fall to the bottom of the combustion
chamber, while the lighter fine ash particles, termed fly ash, remain suspended in the flue gas.
Prior to exhausting the flue gas, particulate emission control devices, such as electrostatic
precipitators or filter fabric bag-houses, remove the fly ash (American Coal Ash Association,
2003). According to a Portland Cement Association report on fly ash, about 100 million tons of
fly ash is produced each year, of which only 20 percent is used in engineering applications such
as blended cements, road base stabilization, and land filling (Portland Cement Association,
2009). In addition to the economic and environmental benefits of using fly ash in concrete, there
is a technical advantage in increasing strength and improving mechanical properties (Nikam,
Rane & Deshmukh, 2005). Using fly ash reduces greenhouse gases, decreases life cycle costs,
and increases the concrete’s durability.
Class F fly ashes have a lower calcium oxide (CaO) content than class C fly ashes, as shown in
Table 1. This is a key factor in mitigating sulfate attack and ASR. Changes in the sources of coal
used in power generation plants result in changes in the quality of fly ash by-product. Figure 1
shows scanning electron microscope (SEM) micrograps of the small and characteristically round
fly ash particles. The figure also shows the X-ray diffraction pattern of class F fly ash,
5
illustrating the general amorphous nature of flyash containing quartz and mullite as the few
crystalline phases present.
Table 1. Sample Oxide Analysis for Fly Ash and Cement (Portland Cement Association,
2009).
Component
Compounds
Class F Fly Ash, % Class C Fly Ash, % Portland Cement, %
SiO2 55 40 23
Al2O3 26 17 4
Fe2O3 7 6 2
CaO 9 24 64
MgO 2 5 2
SO3 1 3 2
SiO2 = silicon dioxide; Al2O3 = aluminum oxide; Fe2O3 = iron oxide; MgO = magnesium oxide; SO3 =
sulfur trioxide
Figure 1. Scanning Electron Microscope (SEM) Image and X-ray Diffraction Pattern for a
Typical Class F Fly Ash.
Class C ashes generally are derived from sub-bituminous coals and consist mostly of calcium
alumino-sulfate glass, such as quartz (SiO2) and free lime (CaO). Class C ash sometimes is
referred to as high-calcium fly ash because it contains as much as 20 percent CaO. Typical
oxides of fly ash and their quantities are shown in Table 1.
High-Volume Fly Ash
In commercial practice, the dosage of fly ash is limited to 15 to 20 percent by mass of the total
cementitious material. Usually, this amount has a beneficial effect on the workability and
economy of concrete, but it may not be enough to improve durability sufficiently to address
sulfate attack, ASR, or shrinkage and thermal cracking. For this purpose, larger amounts of fly
6
ash, on the order of 25 to 35 percent, may be used. The dosage of fly ash in HVFA concrete can
exceed 50 percent and may change the chemistry and reactivity of the cementitious phase in
concrete (Malhotra & Mehta, 2005). Additional specifications are therefore required for its
implementation. Adoption of concrete mixtures with HVFA would enable the concrete
construction industry to become more sustainable, since incorporation of HVFA reduces water
demand, improves workability, minimizes cracking caused by thermal and drying shrinkage, and
enhances durability to reinforcement corrosion, sulfate attack, and ASR (Mehta, 2004). This
report addresses a limited study conducted to address HVFA with a cement replacement level in
the range of 35 percent.
Metakaolin
Commercially available since the mid-1990s, metakaolin (Al2Si2O7) has been used as a high-reactivity
pozzolan for HPC applications. Metakaolin is a thermally activated alumino-silicate
material that is manufactured primarily by calcination of kaolin clay in a temperature range of
1,300 to 1,560° F (700 to 850 °C) (Sabir, Wild & Khatib, 1996). It typically contains 50 to 55
percent SiO2 and 40 to 45 percent Al2O3 (Poon et al., 2001). A recent experimental program
evaluated the mechanical and durability properties of concrete with metakaolin (Shekarchi et al.,
2009). The researchers prepared concrete samples with 0, 5, 10 and 15 percent metakaolin (by
weight) replacement of portland cement. Results of samples with 15 percent replacement
(MK15) are shown in Figure 2a. The compressive strength of the control and metakaolin
mixtures ranged from 7,200 psi to 8,700 psi (50.0 MPa to 59.8 MPa), representing as much as a
20 percent increase for MK15. Water penetration decreased by as much as 50 percent for MK15,
and gas permeability decreased up to 40 percent. Also, in the MK15 mixture, the water
absorption potential decreased by 30 percent; the lowest absorption measured was 1.32±0.10
percent, as shown in Figure 2b. The ASR expansion decreased by 80 percent, as shown in Figure
3.
Copper Slag
Copper slag, which contains 50 to 75 percent Fe2O3 and 15 to 35 percent SiO2, can be used in
concrete as a cement or aggregate replacement. Since Arizona is the major producer of copper in
the United States (Leaming, 1998), mining operations in this state generate significant quantities
of copper slag. Replacing cement with slag lowers the cost of concrete and improves its
durability properties (Mobasher & Devaguptapu, 1993). Researchers at Arizona State University
have conducted significant research in this area (Tixier, Devaguptapu & Mobasher, 1997; Ariño
& Mobasher, 1999).
7
Figure 2. Effect of Metakaolin in a) Increasing Compressive Strength, b) Reducing Water
Penetration (W.P.), Water Absorption (W.A), Gas Permeability (G.P.), and Electrical
Resistivity (E.R.) (Shekarchi et al., 2009).
Figure 3. Effect of Metakaolin Replacement Level on ASR Expansion (Shekarchi et al.,
2009).
HIGH-PERFORMANCE CONCRETE
HPC is a high-strength concrete with characteristics that improve workability, strength, and
durability. The workability of HPC is such that the concrete can be mixed, transported, cast, and
finished easily and properly with minimum possible energy and labor. The strength
characteristics of HPC include high compressive strength (more than 6,000 psi) and high
ductility (energy absorption). The durability of HPC should cover a wide area of physical and
0 10 20 30
Time, Days
0
15
30
45
60
Compressive Strength, MPa
0
2000
4000
6000
8000
Compressive Strength, psi
Control
MK 5
MK10
MK15
0 5 10 15
MK Replacement Level
0
200
400
600
E. R., K.in
1.2
1.6
2
1.2
1.6
2
G. P. x10-3, in2
1.2
1.6
2
W. A., %
1.2
1.6
2
0.2
0.4
0.6
W. P., in
0 10 20 30
Time, Days
0
0.1
0.2
0.3
0.4
Linear Expansion, %
Control
MK5
MK10
MK15
(b)
0 5 10 15
MK Replacement Level, %
0
0.1
0.2
0.3
ASR 14-D Exp., %
0
0.1
0.2
0.3
ASR 28-D Exp., %
(a)
8
chemical causes for degradation, such as freeze/thaw, abrasion, fatigue, fire resistance, sulfate
attack, chloride ingress, carbonation, and ASR.
Use of HPC in transportation infrastructure systems leads to structures with longer spans, smaller
columns, thinner slabs, longer service life, and improved appearance. Several reports have been
published showing outstanding results from using HPC in high-rise buildings, bridges, and
pavements (Malhotra & Mehta, 2005). FHWA has played a key role in the HPC technology
transfer from research and development to routine practice for bridge and pavement design and
construction. The success has been largely due to a long-term continuing partnership between the
FHWA, state departments of transportation, AASHTO, local agencies, the private sector, and
academic organizations (Vanikar & Triandafilou, 2005). According to Vanikar and Triandafilou,
by 2005 HPC had been used in all states except Arizona, Idaho, North Dakota, Arkansas, and
Mississippi, as illustrated in Figure 4.
Figure 4. HPC Use in the United States Transportation Sector as of 2006-07 (Triandafilou
et al., 2007).
According to Aïtcin, there are five classes of HPC based on the compressive strength, starting
from a strength range of 7,200 to 11,800 psi (class I) and ending at a strength level of 21,800 psi
or above (class V) (Aïtcin, 1998). While HPC can be made using portland cement alone as a
cementitious material, a partial substitution of portland cement with one or more supplementary
cementitious materials can be advantageous. HPC usually has a water to cementitious materials
(w/cm) ratio of 0.42 or lower (down to 0.25), and high-range water reducers (superplasticizers)
often are used for enhancing workability. Short chopped fibers (natural, synthetic, or steel) can
be used for improving the tensile and flexural strengths (ductility) of HPC.
9
This study did not evaluate HPC directly through a systematic experimental program. However,
since it is segmented into various aspects of materials science, different aspects of HPC are
addressed based on the intended application. For example, Chapter 3 addresses high-early-strength
FRC for application to shotcrete applications, and Chapter 4 presents an internal curing
method as it relates to HPC, where the demand for curing water can be much greater than that in
a conventional portland cement concrete (Bentz, 2007). Most HPC have a low water-to-cement
(w/c) ratio and contain insufficient mixing water to maintain water-filled coarse capillaries
needed to sustain cement hydration and pozzolanic reactions; therefore, they require water curing
(Kovler & Jensen, 2007). However, the water-tightness and impermeability of the HPC mixtures
has a deleterious effect on the efficiency of traditional external curing, which depends primarily
on the moisture transport process. As the internal curing agent is dispersed finely and part of the
system, it can delineate the low permeability of cementitious systems with a low water to binder
(w/b) ratio. Internal water supply can therefore be considered as an efficient method of curing
HPC (Bentz, 2007).
According to a pending proposal to the joint task group by ADOT and Arizona Rock Products
Association (ARPA), HPC formulations could be classified as several different categories. Table
2 presents different classes of HPC based on the specifications, materials, use of admixtures, and
testing methods pertaining to each class.
Type A HPC
Type A HPC is specified for high early strength. The main specifications include a specific
strength at a certain age. Materials variables include cement type, cement content, and use of
specific proprietary admixtures such as superplacticizers, accelerator, and retarders. Within the
applicable ASTM standards, maturity testing is the primary method in asserting strength
development. Various sub-classes may be defined as shown in Table 3.
National Cooperative Highway Research Program (NCHRP) Report 540 addresses cases that are
designed to open early to traffic, joint repair, and selected slab replacement (Van Dam et al.,
2005). In the design of early-age strength, if a cement type other than specified is used, the long-term
durability of the mixture should be at the same level of a standard specified cement-based
system. Specimen conditioning is important for field-cured cylinders when tested in accordance
with ASTM C39. The best way to test this is to duplicate a field cure condition by means of
temperature matching (active, Sure cure, or passive, blanket, insulated box, etc.).
Typically, maturity testing in accordance with ASTM C1074 is specified. For example,
representative compressive strength specifications include 1,200 psi specified in Pennsylvania,
1,450 psi in 7 hours or 2,500 psi in 24 hours in Georgia, and 2,500 psi in 12 hours in Maryland
(Van Dam et al., 2005).
10
Table 2. Proposed HPC Classes Based on Specifications, Materials, Admixtures, and
Testing Methods.
Type Category Main Specifications Materials Admixtures Testing
A High early
strength
f’ c at specific age Cement type, content SP, accelerator,
retarders
Maturity, f’c
B Freeze/thaw f’ c + air content Max aggregate size Air entrainment ASTM C666,
ACI 211
C Low
permeability
w/c, air content,
curing
Type II cement SP, SRA,
pozzolans, AEA
RCPT
D f’ c > 5,000 pci f’ c, curing Cement, fly ash, SF,
special aggregates,
gradation
SP, retarders f’ c
E ASR + sulfate
attack
Cement II/V
+pozzolans,
geographic locations
Aggregates, cements SP, pozzolans,
lithium salts
Modified
C1260, C227,
C1012
F FRC, low fiber
content
Plastic shrinkage
cracking, impact,
durability
Fibers SP, water
reducers
C1399,
C1018, C1550
G FRC, high fiber
content
WWF, rebar
replacement impact,
durability
Fibers SP, water
reducers
C1399,
C1018, C1550
H Low shrinkage w/c, cement content,
air content, curing
Cement type,
shrinkage
compensating cement
admixtures
SRA, fibers, SP,
air
Mortar bars,
C157,
shrinkage
I Self-consolidating
concrete
Modified flow/
>8000 psi
Combined aggregate
grading
Viscosity
modifiers
Modified
slump,
rheometer
J Low cement
factor
f’ c at specific age Cement type SP, water
reducers,
pozzolans,
f’ c
K High fly ash f’c at specific age Fly ash to cement
replacement>25%
SP, water
reducers, blends
of pozzolans,
f’ c
L Internal curing f’c under adverse
curing conditions
Lightweight aggregate,
sintered bottom ash
SP, water
reducers
TGA/DTA X-ray,
SEM
f’c = compressive strength; SP = superplasticizer; SRA = shrinkage reducing admixtures; AEA = air-entraining
admixture, TGA = thermogravimetric analysis, DTA = differential thermal analysis, WWF = welded wire fabric,
RCPT = rapid chloride permeability test
11
Table 3. Specifications for Type A HPC.
Class Specifications* Cement Type
and amount
Admixtures Type,
Supplier
Ready Mix Test
Methods
A1 f’c =3,000 psi in
8 hrs.**
minimum
type II
740-900 lb/yd3
type III
660-825 lb/yd3
Non-chloride admixtures:
Accelerator,
Superplasticizer, hydration
control, AEA
Membrane
cure,
blankets
NCHRP
540 [25]
A2 f’c =3,000 psi in
12 hrs.
minimum
type II
740-900 lb/yd3
type III
660-825 lb/yd3
possibly fly ash
Non-chloride admixtures:
Accelerator,
Superplasticizer, hydration
control, AEA, fly ash,
metakaolin
Membrane
cure,
blankets
NCHRP
540
A3 f’c =3,000 psi in
24 hrs.
minimum
type II
740-900 lb/yd3
type III
660-825 lb/yd3
Non-chloride admixtures:
Accelerator,
Superplasticizer, hydration
control, AEA, mineral
admixture, fly ash,
metakaolin
Membrane
cure,
blankets
NCHRP
540
A4 Case by case
* Specifications include compressive strength, flexural strength, or maturity
** Sampled and cured by field conditions
Type B HPC
Type B HPC is specified for freeze/thaw resistance of concrete. The main specifications involve
a stated f’c and a minimum air content with various air spacing factors. Materials specifications
include minimum cement content, specific curing cycle, and a maximum aggregate size. The
primary admixture is an air entrainment agent (AEA). Testing is in accordance with ASTM C666
and the recently developed ACI 211 specifications for freeze/thaw resistance. Various sub-classes
may be defined, as shown in Table 4.
Table 4. Specifications for Type B HPC.
Class Specifications* Cement Admixtures Test Methods
B1 Up to 3% air TBD TBD ACI 211
B2 3-7% air TBD TBD ACI 211
B3 Freeze/thaw durability
(x=relative dynamic modulus
after 300 cycles)
TBD TBD AASHTO T161
Procedure A
B4 % air selected by contractor,
i.e. min 3%, max 9%
TBD TBD AASHTO T152
*Compressive strength, flexural strength or maturity, TBD = to be determined
12
Type C HPC
Type C HPC is specified for low permeability. The main specifications are w/c, air content, and
curing. The materials include type I/II cement and admixtures including SP, SRA, silica fume,
slag, fly ash, and AEA. The primary test method for characterization of permeability is the rapid
chloride permeability test. Various sub-classes may be defined, as shown in Table 5.
Table 5. Specifications for Type C HPC.
Class Specifications Cement Admixtures Test Methods
C1 w/c, curing duration TBD TBD TBD
C2 Chloride
permeability
TBD TBD ASTM C1202
AASHTO T277
C3 Bridge deck
applications
TBD TBD TBD
C4 Chloride
penetration depth
TBD TBD See AASHTO T259 modified,
Note A: Penetration 0.025% at
25mm
A sample set of specifications could be stated as shown in Table 6 (Stanish, Hooton & Thomas,
2000; Sprinkel, 2004).
The amount of electrical charge in amp-sec that pass through a 2-inch-long, 4-inch-diameter
saturated cylindrical sample when a DC voltage of 60 volts is applied across it is reported as an
indicator of concrete’s permeability. Concrete mixtures are required to undergo specific pre-conditioning,
including the following:
 For each sublot, the engineer will cast two 4- by 8-inch cylinder specimens. Samples 2 inches
thick will be cut from the center of each cylinder for testing. The average of the results for
the two test specimens for each sublot will be considered the sublot test value for
permeability.
 Latex-modified concrete samples shall be moist cured 2 days in the molds (1 day at job site
and 1 day in the lab), air cured 5 days in the molds in the laboratory, and 21 days out of the
molds at 100° F air temperature.
 Silica fume and other non-latex samples shall be moist cured 7 days in the molds (1 day at
job site and 6 days in the lab) and moist cured 21 days out of the molds in the laboratory at
100° F water temperature.
13
Table 6. Sample Specifications for Type C HPC.
Test Method Considers
Chloride
Ion
Movement
Constant
Temperature
Unaffected by
Conductors in
the Concrete
Approximate
Duration of Test
Procedure
Long
Term
AASHTO T259
(Salt Ponding)
Yes Yes Yes 90 days after curing
and conditioning
Bulk Diffusion
(Nordtest)
Yes Yes Yes 40-120 days after
curing and
conditioning
Short
Term
RCPT (T277) No No No 6 hours
Electrical
Migration
Yes Yes No Depends on the
voltage and concrete
Rapid
Migration
(CTH)
Yes Yes No 8 hours
Resistivity No Yes No 30 minutes
Pressure
Penetration
Yes Yes Yes Depends on pressure
(but potentially long)
Other Sorptivity-Lab No Yes Yes 1 week, including
conditioning
Sorptivity-
Field
No Yes Yes 30 minutes
Propan-2-ol
Counter-diffusion
No Yes Yes 14 days with thin
paste samples
Gas Diffusion No Yes Yes 2-3 hours
Type F and G HPC FRC with Low and High Fiber Content
Type F and G HPC represents concrete containing various levels and types of fibers, with their
experimental compressive and flexural properties, and methods to characterize the ductility.
These topics are addressed in detail in Chapter 3. Chapter 3 also presents other beneficial effects
of fiber addition in enhancing the durability characteristics of concrete, especially by controlling
early-age shrinkage cracking.
Type J HPC
Type J is a catch-all category addressing low cement factor mixtures. The main specifications
include variations in the cement type, content, fly ash to cement ratio, w/c, and curing. Testing
can be specified using a certain compressive strength at a specific age. Various sub-classes may
be defined, as shown in Table 7.
14
Table 7. Specifications for Type J HPC.
Class Specifications Cement Type,
Supplier
Admixtures Type,
Supplier
Test
Methods
J1 w/c, curing duration Type II TBD TBD
J2 Ultra high Flyash
Concrete
High fly ash
cement ratio
TBD TBD
J3 Bridge substructure
applications
TBD TBD
J4 Tertiary mixtures Class C fly ash TBD TBD
Low minimum cement content is being considered for different classes of concrete materials. For
example, the Maricopa Association of Government specifies a minimum of 420, 470, 520, and
600 lb/yd3 of cement for 2,000, 2,500, 3,000 and 4,000 psi concrete, respectively (Maricopa
Association of Government Standards, 2012). ADOT specifications for class S and class B
require a minimum of 564 lb/yd3 and 470 lb/yd3, respectively. For class K, a higher fly ash
content (>25 percent) must be used. Age at acceptance is another alternative by specifying
strength at 42 days or more from 28 days.
Recommendation for cement content may include terms that depend on the strength class. For
example, for classes of 4,000 psi and above, the total content of cementitious materials
(including fly ash) shall be 564 lb/yd3. For 3,000 to 4,000 psi, 517 lb/yd3 should be used, and for
2,500 psi, 470 lb/yd3 should be used. The minimum w/c recommended must be determined based
on durability, shrinkage potential, freeze/thaw, and sulfate attack potential. Acceptance of
concrete based on statistical mix design procedures and required strength based on ACI 318 will
lead to economical use of HPC materials (Laungrungrong, Mobasher & Montgomery, 2008;
American Concrete Institute, 2008).
Type K HPC
Type K HPC represents high fly ash concrete and specified as fly ash to cement replacement
levels above the current 25 percent level. This type is discussed in detail in Chapter 5.
Type L HPC
Type L HPC represents the concrete specified using criteria for internal curing. Preliminary test
data for these materials that may use lightweight aggregate, or sintered bottom ash under adverse
curing conditions, are discussed in Chapter 4.
15
CHAPTER 3. FIBER-REINFORCED CONCRETE
INTRODUCTION
Plain concrete has a low tensile strength and a low strain capacity at failure. Designers of
reinforced concrete overcome these shortcomings by adding reinforcing bars, welded wire
meshes, and prestressing steel. Reinforcing steel is continuous and is located in the structure
specifically to optimize performance. As an alternative to conventional reinforcement, fibers
have been used as reinforcement as well. Concrete materials produced with short, randomly
distributed fibers may be superior to forms of reinforcing concrete using welded wire mesh or
rebars. Both the tensile strength and toughness, especially the post-crack strength, are improved
(Bentur & Mindess, 1990). It has been shown that due to the reduced specific spacing, fibers
strengthen the composite at the micro level by bridging the microcracks before they reach the
critical flaw size (Mobasher & Li, 1996). The small diameter of the individual fibers ensures a
better and more uniform distribution of reinforcement. In addition, the high surface area offers
significant bond capability. Since the bond strength of glass, steel, or even polymeric fibers is far
superior to reinforcing bars, this increases the efficiency of reinforcement so that there is limited
crack opening due to the debonding and pullout of reinforcement. The fibers are distributed
randomly, offering efficiency in load transfer by the fiber phase. Finally, because the fibers that
bridge the matrix cracks are resilient and highly compliant, they can orient to carry the load
across the crack faces. This factor is expected to increase the durability of concrete substantially,
since the crack width control affects long-term durability.
Because of the flexibility in methods of fabrication, FRC can be an economic and useful
construction material. In architectural cladding panels, slabs on grade, mining, tunneling, and
excavation support applications, steel and synthetic FRC and shotcrete have been used in lieu of
welded wire fabric reinforcement (American Concrete Institute Committee 544, 1996). There are
numerous fiber types available for commercial and experimental use. It has been shown that
hybrid reinforcement systems utilizing two or more fiber lengths can also be used to optimize
composite performance for strength and ductility as a function of age (Mobasher, 2011). The
basic fiber categories are steel, glass, synthetic, and natural materials. The studies in this report
focused primarily on glass and polymeric FRC.
In addition to the general overview of FRC provided here, this chapter addresses mechanical
properties of FRC with different types of polymeric and glass fiber. Specifically, the response
under flexural bending tests is used to measure material properties that are needed in the design
of various sections. The three-point bending test methodology is described, and the results of
performing this test on different types of FRC are investigated. Due to the experimental and
analytical limitations of available test methods, the researchers present an inverse analysis of the
load-deflection response of these materials and for back-calculation of the stress-strain response
for various fiber reinforced concrete samples (Gopalaratnam & Gettu, 1995; Gopalaratnam et al.,
1991; Soranakom & Mobasher, 2007a). The chapter also presents a procedure that introduces a
guideline for designing flexural FRC members based on calculated residual strength. This
chapter also provides an examination of data reduction by the average residual strength (ARS)
method and compares ARS strength and back-calculated residual strength. A comparison of
16
back-calculated post-crack tensile strength with available ASTM test methods is provided. It is
shown that ASTM test methods may overestimate the residual strength (Soranakom &
Mobasher, 2010). Finally, design equations for flexural response are presented along with a
design example of slab on grade.
Economics of FRC
Use of FRC is associated with reduced labor costs, reduced potential for error at the job site, and
efficiency in placement and compaction. Therefore, fibers are more economical than steel
reinforcement and provide excellent strengthening mechanisms. Figure 5 shows the clean-up of
operation for a canal project during construction. Clean-up is required due to sudden rainfall and
its flow in the channel, resulting in debris accumulation and grade changes of the prepared base.
Application of FRC in a canal lining project significantly reduces labor requirements in the
construction phase since the rebar or mesh layout phase is eliminated. Instead of using a
longitudinal and transverse rebar layout or a welded wire mesh, an FRC mix can be specified to
meet system requirements at a much lower cost.
Figure 5. Cleanup Operation for a Canal during Construction When an Occasional
Rainfall Results in Debris Accumulation and Grade Changes of the Prepared Base. Photo
Courtesy of Rich Shelly, Pulice Construction Co.
Aerated FRC
Aerated concrete is a lightweight, noncombustible cement-based material manufactured from a
mixture of fly ash or other sources of silica, portland cement, quick lime, gypsum, water, and
aluminum powder or paste. These raw materials are mixed together and cast into large steel
molds where a chemical reaction takes place. Hydrogen gas is generated in the wet slurry
mixture, causing it to expand and form independent air cells. The chemical reaction caused by
the addition of aluminum makes the mixture expand to about twice its volume, resulting in a
highly porous structure. Approximately 80 percent of the volume of the hardened material is
made up of pores, 50 percent being macro-pores and 30 percent being micro-pores characterized
17
by their ability in capillary moisture transport. Due to the special cellular structure of this
material and its physical and mechanical properties, it is applicable in a variety of civil
engineering applications. Aerated FRC precast blocks and panels can be used as sound wall
systems along highways such as Arizona State Route 51 and Piestewa Peak, as well as in one-and
two-story buildings as structural components with thermal insulation properties.
High Early-Strength FRC
High early-strength FRC is made by adding fibers and accelerator admixtures. As the name
suggests, it has high early-age strength and high energy absorption capacity. This type of FRC is
suitable for shotcrete applications, which must achieve high early strength and ductility within 24
hours. Using a shotcrete lining system as a means of initial shaft support instead of the traditional
mesh and bolts increases the development speed (Vandewalle, 1993; Franzén, 1992). Several
elements must be considered, including alternative techniques to achieve adhesion, strength, and
ductility for the newly placed shotcrete materials.
FIBER TYPES
This study evaluated different types of non-metallic fibers. Table 8 lists the properties of a single
type of glass fiber and five different types of polymeric fibers. As shown in the table, the base,
specific gravity, modulus of elasticity, tensile strength, and length of fibers used cover a broad
range. In the labeling system used, G refers to alkali-resistant (AR) glass and P represents
polymeric. For example, FRC with AR glass fiber is a portland cement-based product that is
made by using a mortar matrix and low dosages of chopped AR glass fibers, referred to as G-Type1.
The various types of fibers used are identified as the base and refer to different
manufacturers.
THREE-POINT BENDING TESTS
To better monitor the flexural response of concrete samples using closed loop testing, samples
were pre-notched and loaded along the notch. The behavior of the specimen under flexure is
dominated by the cracking that initiates at the notch and grows along the depth of the specimen.
As the test progresses, the deformation localizes at the notch and is followed by crack
propagation. Since the critical deformations are the opening of the crack tip that may be
measured at the base of the notch, the best-controlled variable in flexure tests is the crack mouth
opening or a similar displacement.
18
Table 8. Physical Properties of Fibers Used.
Fiber
Type
G-Type 1 P-Type 1 P-Type 2
P-Type
3
P-Type 4 P-Type 5
Base
Alkali
Resistance
Glass
Fibrillated
Polypropylene
Monofilament
Polypropylene/
Polyethylene
blend
Modified
Olefin
Modified
Polypropylene
Blend
Fibrillated
Polypropylene
Fiber
Specific
Gravity
2.68 0.91 0.92 0.9-0.92 0.91 0.91
Modulus
of
Elasticity
10,000 ksi 493 ksi 725 ksi 1450 ksi 950 ksi 800 ksi
Tensile
Strength
250 ksi 87 ksi 87-94 ksi 80 ksi 95 ksi 60 ksi
Length
of Fiber
1 in 0.75 in 2 in 2 in 1.5 in 2 in
Flexural tests may be conducted under several loading configurations. In this study, beams were
loaded at a single point in the mid-span, which is known as the three-point bending test. The test
is performed under closed loop control with crack mouth opening deformation (CMOD) as the
controlled variable. Figure 6 represents the flexural test setup. In this test method, the CMOD
was measured across the face of notch using an extensometer and a linear variable differential
transformer (LVDT) with a 0.1-inch range measuring the deflection of the beam at the mid-span.
Figure 6. a) Closed-Loop Flexural Test Setup, b) Measuring CMOD at the Notch by
Extensometer and Displacement at Mid-span by the LVDT.
Three-point bending flexural tests were performed on 21- by 6- by 6-inch or 18- by 4- by 4-inch
beam specimens with an initial notch length of 0.5 or 1 inch and test span of 18 or 16 inches.
Figure 7 shows the typical concrete beam under a closed-loop three-point bending test. The
researchers observed that cracks initiate from the notch and extend up to the upper side of the
19
beam. However, the crack is bridged by the fibers, which are being pulled under this loading.
The presence of fiber significantly increases the ductility of the material and makes the crack
opening and deflection exceed 0.05 inches.
Figure 7. Crack Growth in FRC Samples under a Three-point Bending Test.
Mix Design and Compression Results
The researchers prepared and tested 14 mixtures under three-point bending tests, as shown in
Table 9. The results of compression tests also are shown in the table. The w/cm ratios are in the
range of 0.4 to 0.55, and cement content is 800 lb/yd3 except in two test series, in which the
cement content was 1,100 lb/yd3. The fly ash and silica fume were added to some of mixtures as
supplementary cementitious materials with dosages of 100 lb/yd3 and 25 lb/yd3, respectively.
The sand-to-cement (s/cm) ratio is 2 or 1.9 for all mixtures. Accelerator admixtures were added
to some of the mixtures, which led to gaining high early strength.
20
Table 9. Mixture Proportions and Compressive Strength of all Mixes.
Application Mix ID PC Fly Ash SF S CA W FB FB Type
AC,
%
w/cm s/cm
f’c,
psi
Shrinkage
Control
Plain
1,10
0
0 0
2,20
0
0 605 0 N/A 0 0.55 2
4,811
a
GlassF5
1,10
0
0 0
2,20
0
0 605 5
AR glass
Type1
0 0.55 2
4,670
a
Slabs on
Grade
PolyF9.5_Typ
e1
800 0 0
1,60
0
1,20
0
400 9.5 P-Type1 0 0.50 2
4,000
*
PolyF5_Type2 800 0 0
1,60
0
1,20
0
400 5 P-Type2 0 0.50 2
4,000
*
PolyF5_Type1 800 0 0
1,60
0
1,20
0
400 5 P-Type1 0 0.50 2
4,000
*
Shotcrete
B-CSA 800 100 25
1,85
0
800 390 10 P-Type3 4 0.42 2
4,860
b
B-CSB 800 100 25
1,85
0
800 390 12 P-Type3 4 0.42 2
4,680
b
B-HAS 800 100 25
1,85
0
800 390 10 P-Type3 8 0.42 2
6,170
b
B-HSB 800 100 25
1,85
0
800 390 15 P-Type3 8 0.42 2
5,840
b
1 800 100 25
1,75
0
670 375 10 P-Type 3 4 0.40 1.9
3,927
b
2 800 100 25
1,75
0
670 375 10 P-Type 2 4 0.40 1.9
4,208
b
3 800 100 25
1,75
0
670 375 10 P-Type 4 4 0.40 1.9
4,180
b
4 800 100 25
1,75
0
670 375
8.5
1.5
P-Type 3
P-Type 5
4 0.40 1.9
4,161
b
5 800 100 25
1,75
0
670 375
8.5
1.5
P-Type 4
P-Type 5
4 0.40 1.9
3,738
b
PC = portland cement; SF = silica fume; S = sand as fine aggregate; CA = coarse aggregate; W = water; FB = fiber—all expressed as lb/yd3. AC =
accelerator
*= not measured
a At 28 days
b At 24 hours
Specified 28 day strength
21
EXPERIMENTAL RESULTS OF THREE-POINT BENDING TEST
Results for AR Glass Fibers
General results indicate that AR glass fibers slightly delay the time of cracking but drastically
reduce the crack widths. Flexural responses of these mixtures were examined in this study, and
representative results of the three-point bending test for AR glass fibers are shown in Figure 8.
Results of the experimental analysis on flexural data of glass fiber are also summarized in Table
10. The addition of fibers increases the post-peak response because as the fibers bridge the crack
and pull out, additional energy is dissipated. Other studies have also examined the role of AR
glass fibers in extending the cracking resistance of concrete subjected to drying shrinkage
utilizing a ring-type restrained shrinkage test (Soranakom, Bakhshi & Mobasher, 2008). The area
under the load deflection diagram was integrated numerically and the results were presented as
flexural toughness.
Figure 8. Effect of AR Glass Fibers on Flexural Response after a) 1 Day and b) 7 Days of
Curing.
The results indicate that the elastic flexural stiffness of samples is as much as 11, 17, and 5
percent more than that of control samples (plain) after 1, 3, and 7 days of curing, respectively.
While fiber addition does not affect the deflections at maximum flexural load, maximum flexural
load and modulus of rupture (MOR) increase slightly at both 3 and 7 days. Finally, the flexural
toughness increases significantly with the addition of 5 lb/yd3 AR glass fibers. Results show that
average flexural toughness is 4.8, 4.9, and 4.2 times the flexural toughness of plain samples at 1,
3, and 7 days, respectively. The post cracking response in the strain softening region is the single
most important aspect of fiber reinforcement at these loading rates. This parameter can be
estimated for the closed loop testing using deflection or crack mouth opening displacement. The
added level of ductility can be used in the design of the composites using fibers, but appropriate
tools are needed to design based on ductility.
0 0.01 0.02 0.03 0.04 0.05
CMOD (Crack Opening), in
0
200
400
600
800
1000
Flexural Load, lb
Control: vf = 0 lb/yd3
ARG5.0: vf = 5 lb/yd3
w/c = 0.55
age: 1 day
0 0.01 0.02 0.03 0.04 0.05
CMOD (Crack Opening), in
0
200
400
600
800
1000
1200
Flexural Load, lb
ARG5.0: vf = 5 lb/yd3
Control: vf = 0 lb/yd3
w/c = 0.55
age: 7 days
22
Table 10. Summary of Flexural Tests of Plain and Glass Fiber Reinforced Concrete.
Mix ID
Age,
days
Statistical
Measure
Elastic Flexural
Stiffness,
kips/in
Deflection
at Max
Flexural
Load, in
Max
Flex.
Load, lbf
Modulus
of
Rupture,
psi
Flexural
Toughness,
lbf-in
Plain
1
Average 565 0.0016 834 409 2.64
Std. dev. 65 0.0001 21 10 0.10
3
Average 639 0.0016 918 450 2.60
Std. dev. 41 0.0001 4 2 0.15
7
Average 708 0.0016 952 467 3.02
Std. dev. 69 0.0001 16 8 0.28
GlassF5
1
Average 627 0.0016 829 406 12.73
Std. dev. 65 0.0002 25 12 1.22
3
Average 745 0.0016 979 480 12.80
Std. dev. 48 0.0000 21 11 3.04
7
Average 745 0.0018 1,014 497 12.46
Std. dev. 40 0.0002 13 6 0.52
Results for Polymeric Fibers (Type 1 and 2)
Results of three-point bending testing for polymeric fibers are shown in Figure 9. These results
are representative for each mixture; Results of experimental analysis on flexural data of
polymeric fibers are summarized in Table 11.
Results show that the average elastic flexural stiffness of PolyF9.5_Type1, PolyF5_Type2, and
PolyF5_Type1 samples increases by 70, 34, and 27 percent by extending the curing duration
from 14 days to 28 days. The maximum flexural load and MOR parameters show similar
increases when the curing time is extended. An analysis of the results indicates that average
MOR values for PolyF9.5_Type1, PolyF5_Type2, and PolyF5_Type1 samples increase by 13,
24, and 20 percent, respectively. The flexural toughness at 28 days was about double the
corresponding value at 14 days for all samples.
Comparing the results for the PolyF5_Type2 and PolyF5_Type1 mixtures at 14 and 28 days
indicates that both fiber types have similar effects on flexural toughness, maximum flexural load,
and MOR. However, the average flexural stiffness of samples with P-Type1 fiber is 46 and 40
percent higher than corresponding values of samples reinforced with P-Type2 fibers at 14 and 28
days, respectively.
Increasing the dosage of P-Type1 fibers from 5 lb/yd3 to 9.5 lb/yd3 had an inverse effect on all
parameters and resulted in a 30 to 50 percent reduction in stiffness, a 30 to 35 percent reduction
in maximum flexural load/MOR, and a 10 percent reduction in flexural toughness. The addition
of a high volume of fibers can decrease workability, compaction, and flowability of the concrete,
resulting in the creation of large pores in the microstructure and lowering the strength of FRC.
23
a) 14-day testing
b) 28-day testing
Figure 9. Effect of Polymeric Fibers on Flexural Responses at a) 14 Days and b) 28 Days.
0 0.01 0.02 0.03
CMOD (Crack Opening), in
0
400
800
1200
Flexural Load, lb
PolyF5-Type I
PolyF5-Type II
Effect of Fiber Type
on Flexural Toughness
and Post-Peak Strength
age: 14 days
0 0.005 0.01 0.015 0.02
CMOD (Crack Opening), in
0
400
800
1200
Flexural Load, lb
PolyF5-Type I
PolyF9.5-Type I
Effect of Fiber Dosage
on Flexural Toughness
and Post-Peak Strength
age: 14 days
0 0.02 0.04 0.06
CMOD (Crack Opening), in
0
400
800
1200
1600
Flexural Load, lb
PolyF5-Type I
PolyF5-Type II
Effect of Fiber Type
on Flexural Toughness
and Post-Peak Strength
age: 28 days
0 0.02 0.04 0.06
CMOD (Crack Opening), in
0
400
800
1200
1600
Flexural Load, lb
PolyF5-Type I
PolyF9.5-Type I
Effect of Fiber Dosage
on Flexural Toughness
and Post-Peak Strength
age: 28 days
24
Table 11. Summary of Experimental Analysis on Flexural Data of Polymeric Fibers.
Mix ID
Age,
days
Statistical
Measure
Elastic
Flexural
Stiffness,
kips/in
Deflection
at Max
Flexural
Load, in
Max
Flex.
Load, lbf
Modulus
of
Rupture
psi
Flexural
Toughness,
Lbf-in*
PolyF9.5_Type1
14
Average 351 0.0034 872 427 15.40
Std. dev. 13 0.0006 17 8 2.49
28
Average 597 0.0023 983 481 32.86
Std. dev. 88 0.0004 145 71 0.60
PolyF5_Type2
14
Average 473 0.0036 1,166 571 18.38
Std. dev. 18 0.0003 62 36 1.86
28
Average 631 0.0028 1,451 711 31.92
Std. dev. 197 0.0005 122 60 7.11
PolyF5_Type1
14
Average 690 0.0022 1,247 611 17.47
Std. dev. 79 0.0005 92 45 0.47
28
Average 880 0.00255 1,500 734.5 35.95
Std. dev. 45 0.0002 89 43 1.13
*Toughness measured as the area under the load deflection curve up until a deflection level of 0.1 in
Applications for Shotcrete with using Polymeric Fibers (Type 3) For Early-Age Strength
and Ductility
In areas where high early strength and ductility are important, one can develop mixtures that
have a rapid rate of strength gain. Examples include pavement repair or shotcrete applications, in
which the product must reach its full strength within 7 days of application. In areas of shotcrete
application, it is possible to use mixtures with a high dosage of accelerator. In these cases, the
early-age strength and ductility of fiber concrete become dominant factors. Applications for
shotcrete without any bolt and mesh applications need to consider rapid set times, early-age
strength, and ductility development because the fibers are the only mode of reinforcement
(Vandewalle, 1993). Early-age strength can be properly designed using chemical admixtures.
These are applicable to rapid repair of structures, pavements, slope stability, or rock slide
stabilization. Figure 10 shows an application for casting specimens using shotcrete mixtures. The
specimens were prepared for testing by flexural and round panel test methods.
Designing FRC requires the use of material properties that are obtained from an experimental
program. The test results are used to obtain material property data, which are incorporated in the
analytical, empirical, or computer simulation of design cases. The design procedures can be
developed based on models for flexural, tension, and compression behavior.
25
Figure 10. Casting of Shotcrete FRC Samples for Flexural and Compressive Strength
Testing.
The objective of this set of experiments was to document the different levels of energy
absorption and residual load capacity of FRC tested in accordance with the modified ASTM
C1609 procedure. It has been shown that the load in the post-crack range can be influenced by
the amount of fibers that offer resistance to crack opening. Methods of structural analysis are
being developed to design concrete slabs using the various degrees of strain softening exhibited
by the material. Researchers also are developing techniques for designing concrete slabs using
plastic analysis. These analytical approaches are also included in the present report.
Results of the three-point bending test for polymeric fibers for two alternative mixtures are
shown in Figure 11. Results of the experimental analysis on the flexural data of polymeric fibers
are summarized in Table 12.
Figure 11. Effect of Polymeric Fibers on Flexural Responses at 8, 16, and 36 Hours.
Results show that the average elastic flexural stiffness of both normal strength samples, B-CSA
and B-CSB, increases by 45 percent due to the curing from 8 to 16 hours. While there is no
significant change in flexural stiffness of B-CSA samples from 16 to 36 hours, there was a 30
percent increase in this parameter for B-CSB samples. No significant change in elastic flexural
0 0.03 0.06 0.09 0.12 0.15
CMOD, inch
0
500
1000
1500
2000
2500
3000
Load, lbf
Age
36 h
16 h
8 h
Mixture: B-HSA
0 0.03 0.06 0.09 0.12 0.15
CMOD, inch
0
500
1000
1500
2000
2500
Load, lbf
Age
36 h
16 h
8 h
Mixture: B-HSB
26
stiffness was observed for the high strength mixtures, B-HSA and B-HSB. There is no clear
trend for the change of deflection at maximum load for different mixtures by increasing the
curing from 8 to 16 hours, or from 16 to 36 hours. While this parameter increased by 11 to 17
percent for B-CSA mixture, it decreased by 7 to 12 percent for B-CSB samples and increased 17
to 60 percent for B-HSA samples.
Table 12. Summary of Experimental Analysis on Flexural Data of Polymeric Fibers.
Comparing the results for different mixtures at 8, 16, and 36 hours indicates that increasing the
curing time has a proportional effect on flexural toughness and maximum flexural load/MOR
parameters, especially for curing between 8 to 16 hours. The toughness from 8 to 16 hours
increased by 80, 20, 65, and 28 percent for the B-CSA, B-CSB, B-HSA, and B-HSB samples,
respectively. From 16 to 36 hours, the toughness increased only 18 and 11 percent for the B-CSA
and B-HSB samples, while it decreased slightly for the B-CSB and B-HAS samples. The
increase in maximum flexural load/MOR from 8 to 16 hours was 95, 50, 53, and 55 percent for
the B-CSA, B-CSB, B-HSA, and B-HSB samples, respectively. The increase was much lower
from 16 to 36 hours, indicating that due to the addition of accelerator admixtures, the mixtures
Sample
Code
Age,
hr
Statistical
Measure
Elastic
Flexural
Stiffness,
kips/in
Deflection
at Max
Flexural
Load, in
CMOD at
Max
Flexural
Load, in
Max Flex.
Load, lbf
MOR,
psi
Flexural
Toughness,
lbf in
B-CSA
8
Average 1,008 0.0017 0.0017 1,268 228 71.2
Std. dev. 201 0.0002 0.0003 171 31 0.42
16
Average 1,558 0.0018 0.0016 2,292 413 108.7
Std. dev. 66 0.0002 0.0002 160 29 3.68
36
Average 1,465 0.0020 0.0017 2,482 447 129.2
Std. dev. 34 0.0001 0.0002 107 19 6.15
B-CSB
8
Average 1,377 0.0016 0.0016 1,637 295 92.5
Std. dev. 162 0.0004 0.0003 13 2 2.54
16
Average 1,533 0.0019 0.0018 2,127 383 116.2
Std. dev. 87 0.0002 0.0002 191 34 0.49
36
Average 1,997 0.0015 0.0019 2,486 448 112.1
Std. dev. 254 0.0005 0.0004 23 4 12.02
B-HSA
8
Average 1,670 0.0013 0.0013 1,707 307 74.8
Std. dev. 458 0.0001 0.0002 288 52 0.71
16
Average 1,810 0.0019 0.0017 2,446 440 126.8
Std. dev. 121 0.0003 0.0001 88 16 30.40
36
Average 1,778 0.0022 0.0019 2,620 472 123.6
Std. dev. 234 0.0002 0.0006 37 7 17.6
B-HSB
8
Average 1,818 0.0013 0.0015 1,598 288 106.2
Std. dev. 411 7.07E-05 7.07E-05 97 18 13.43
16
Average 1,572 0.0020 0.0018 2,288 412 122.4
Std. dev. 34 0.0000 0.0000 91 16 22.06
36
Average 1,724 0.0019 0.0017 2,476 446 135.7
Std. dev. 143 0.0002 7.07E-05 214 39 13.08
27
gained early strength rapidly during the first 16 hours, after which time the rate of strength
increase slowed significantly.
Results for the B-CSA and B-CSB mixtures show that increasing the fiber dosage from 10 lb/yd3
to 12 lb/yd3 leads to a 30 percent increase in elastic flexural stiffness, maximum flexural
load/MOR parameters, and flexural toughness after 8 hours. However, at 16 and 36 hours, the
results for these two mixtures are similar. In the high-strength mixtures, B-HSA and B-HSB,
increasing the fiber dosage from 10 lb/yd3 to 15 lb/yd3 results in a decrease in all parameters at
all ages. The only exceptions are flexural stiffness and flexural toughness, which increased by 8
and 42 percent at 8 hours, respectively. This result may be attributable to the addition of a high
volume of fibers to the mixtures, which could decrease workability and flowability of the
concrete. This could then result in increasingly large pores and a decrease in the FRC strength.
These results show the importance of using adequate, but not excessive, amounts of fibers to
obtain a high-performance FRC.
Results for Polymeric Fibers (Type 2, 3, 4, and 5)
The previous section examined only one type of polymeric fiber (P-Type3). This section
examines a similar mixture of concrete reinforced with different polymeric fibers. The results of
three-point bending tests for all of the fibers are shown in Figure 12. A summary of the
experimental analysis for all flexural data is shown in Table 13.
Average flexural stiffness of mix 1 with P-Type 3 fibers is 17, 12, 5, and 6 percent higher than
mixes 2, 3, 4, and 5 with other types of fibers, respectively. Mix 1 reinforced with P-Type 3, and
mix 3 reinforced with P-Type 4, have the highest maximum flexural load/MOR. The flexural
toughness of mix 1 with P-Type3 fibers is 65, 29, 15, and 13 percent higher than that of mixes 2,
3, 4, and 5, respectively.
Figure 12. Effect of Different Polymeric Fibers on the Flexural Response at 16 Hours.
0 0.04 0.08 0.12 0.16
Deflection, in
0
500
1000
1500
2000
2500
Load, lbf
Mix 1
Mix 2
Mix 3
Mix 4
Mix 5
Age: 16 h
28
Table 13. Summary of Experimental Analysis of Polymeric Fibers (Types 2, 3, 4 and 5).
Mix
No.
Statistics
Stiffness,
kips/in
Defl. at
Max
Load, in
CMOD at
Max
Load, in
Max.
Load, lb
Modulus
of
Rupture
psi
Defl.
Capacity,
in
CMOD
Capacity,
in
Flex.
Tough.,
lbf.in
Mix
1
Average 1,603 0.0017 0.0017 2,228 401 0.0884 0.1506 139.72
Std. Dev. 32 0.0001 0.0002 129 23 0.0379 0.0667 73.31
Mix
2
Average 1,367 0.0018 0.0018 1,958 352 0.0900 0.1508 84.74
Std. Dev. 88 0.0001 0.0000 225 41 0.0030 0.0005 1.83
Mix
3
Average 1,434 0.0019 0.0018 2,241 404 0.0932 0.1502 108.47
Std. Dev. 159 0.0003 0.0003 11 2 0.026 0.0395 28.34
Mix
4
Average 1,534 0.0018 0.0024 1,992 359 0.0858 0.1504 121.89
Std. Dev. 466 0.0001 0.0012 47 9 0.021 0.0005 61.74
Mix
5
Average 1,517 0.0022 0.0020 1,836 331 0.0942 0.1501 124.02
Std. Dev. 166 0.0002 7.07E-05 91 16 0.019 7.07E-05 15.93
INVERSE ANALYSIS OF LOAD-DEFLECTION RESPONSE
The researchers have done extensive work in the development, design, analysis, and fieldwork
with FRC (Soranakom & Mobasher, 2007a; Soranakom & Mobasher, 2007b; Soranakom &
Mobasher, 2008). Traditionally, the compressive strength is a major design parameter in the
design of reinforced concrete structures. However, not all loading cases, applications, and
specifications translate directly into the compressive strength values. Accordingly, tensile
response has a dominant effect on the performance of FRC materials. Therefore, compressive
strength cannot be used as the sole measure of structural analysis, design, quality, and
performance. By using the design methodology in this section, the transportation community can
realize the potential for the use of fibers in improving ductility in tensile regions, which refers to
the zone below the neutral axis in a flexural beam. This work has culminated in a series of
formulations for simplified design and analysis procedures, incorporating the reliable stress-strain
relationship based on material behavior. ACI is considering several publications in this
area (such as ACI 544) as guides for use in designing FRC.
Figure 13 shows the bilinear elastic plastic model in compression and tension for an FRC
material. The tension and compressive stress and strain are both linear in the elastic range until
the first cracking strain, cr, is reached. Since the compressive strength is higher than tensile
strength, a non-dimensional parameter >1 is defined as the ratio of compressive to tensile
strength, and thus, cy = cr. After tensile cracking, the load-carrying capacity drops to a constant
level defined by Ecr. Two main parameters are therefore Young’s Modulus, E, and the first
cracking strain in tension, cr. The following normalized parameters define the characteristics of
the stress-strain curve:
 Compressive strain to tensile strain ratio at failure, = cy / cr.
 Tensile strain capacity, and tu.
29
 Compressive strain capacity, cu.
 Strain softening stiffness coefficient, -∞ < < 0.
 Stiffness ratio, = Ec / 

 represents the strain in the descending branch of stress after the cracking. By setting the
parameter =1 and  as an extremely small number, one can obtain the strain-softening
parameters from this model. The behavior of a specimen under flexure is dominated by the
cracking that initiates at the notch and grows along the depth of the specimen. As such a test
progresses, the deformation localizes at the notch due to crack propagation. The stress
transmitted thorough the cracked faces of sample is the tensile stress that is simplified as a
constant stress measure and depends on a parameter 0<<1, represented as a fraction of tensile
strength. For example,  = 0.3 indicates that the tensile post-cracking load-carrying capacity is
limited to 30 percent of the tensile strength of the specimen. Figure 14 shows the simplified
strain and stress variation along a cross section.
st
scr=crE
cr trn=cr tu=tucr
E E cr = 
(a)
E
sp=crE
0<<1
strain-softening
sc
c
scy=crE
cy=cr cu=cucr
(b)
Ec =E
t
Figure 13. Stress-strain Material Model for FRC Strain Softening Materials:
(a) Tension Model and (b) Compression Model.
Figure 14. Rectangular FRC Section and the Simplified
Strain and Stress Variations in Bending (Soranakom & Mobasher, 2007b).
30
Closed form solutions for the moment-curvature response were derived explicitly and published
recently (Mobasher, 2011). The procedure first identifies the potential interaction of parameters
and defining the stress-strain response according to the applied normalized maximum
compressive strain,  in three stages elastic tension and compression (0<<1 and 0<<1), post-peak
tension-elastic compression (1<, 1<<), and post-peak tension-plastic compression (1<
and < <  cu). The neutral axis depth ratio, k, is found by solving equilibrium of forces. The
moment capacity is then calculated from the tension and compression forces and the neutral axis
location; the corresponding curvature is obtained by dividing the maximum compressive strain
with the neutral axis depth. Finally, the moment, M, and curvature,  are expressed in terms of
the cracking moment and curvature, Mcr and cr, respectively, and their dimensionless
parameters, M’ and ’. Expressions for calculating neutral axis depth ratio, k, moment, and
curvature are obtained as follows.
For a given set of material parameters and beam dimensions (b and d are the width and the height
of the beam), the moment-curvature response can be generated by substituting any value of
normalized maximum tensile strain,  from zero up to the ultimate tensile strain,  cu . The model
presented in Figure 15 represents the derivations for moment-curvature responses of both a
stress-softening and strain-hardening material with different tensile and compressive responses.
For example, in the case where the tension response is in strain-softening mode while the
compression response is still elastic, one can calculate the location of k, the moment capacity,
and curvature. k is found by solving the equilibrium of net internal forces equal to zero:.
2
1 1
2
1
C C
k
C





; where  2 
C1    2 1  2 1 (Eq. 1)
The nominal moment capacity, Mn, is obtained by taking the first moment of force about the
neutral axis, Mn = Fc1yc1 + Ft1yt1 + Ft2yt2, and expressed as a product of the normalized nominal
moment, m’, and the cracking moment, Mcr, as follows:
Mn  m'Mcr
2
6
cr
cr
bh
M
s
 (Eq. 2)
2 3
2 2
2 1 2
'
1
k k k
m C
k


 
 

where 2
C2  C1  2C1  (Eq. 3)
2
6
cr
cr
bh
M
s
 (Eq. 4)
31
2
' cr
cr cr d

     (Eq. 5)
Mmax
M Mfail cr Mmax1
Mlow
Mmax2
Moment
Curvature
(j-1,Mj-1
(j,Mj
loading
unloading
localized
zone
non-localized
zone
S S/2
cS
localized
zone
non-localized
zone P/2
Axis of Symmetry
P/2
Figure 15. Closed-form Moment Curvature Relationship (for Tensile Strain-softening and
Hardening Response) and Applied for Calculation of Load Deflection of the Flexural Beam
(Mobasher, 2011).
The methodology used in the design of conventional reinforced concrete according to ACI 318 is
adopted next (ACI Committee 318, 2005). The nominal moment capacity of a flexural member,
Mn, must be decreased by a reduction factor to account for variability in materials and
workmanships. The reduced capacity must be greater than the ultimate moment, Mu, due to
factored loading:
rMn  Mu (Eq. 6)
where r is the reduction factor for strain-softening FRC and taken within the range of 0.7 to
0.85, equal to the reduction factor for compressive failure of plain concrete stipulated by ACI
318. Despite the fact that post-crack flexural response of FRC is ductile such that it can sustain
large deflections after cracking, it may fail abruptly with little warning after passing the ultimate
moment. For this reason, a conservative reduction factor for compressive failure is adopted.
One can show that the post-crack normalized moment curvature response depends mainly on the
normalized post-crack tensile strength parameter, . The moment-curvature response becomes
elastic-perfectly plastic when  reaches the critical value of crit, given by:
3 1 crit





(Eq. 7)

crit represents the transition from a deflection-softening to a deflection-hardening material. For
typical steel fiber-reinforced concrete (SFRC) with  between 6 and 12, crit varies in a narrow
range from 0.353 to 0.343. This indicates that the post-crack tensile strength in FRC must be at
least 35 percent of its tensile strength before it can exhibit deflection hardening. This value is in
agreement with the values reported by other researchers (Nemegeer-Harelbeke, 1998; Barros et
al., 2005).
32
Back-calculation of Material Properties from Flexural Tests
This section introduces a theoretical method to utilize the load deflection results of flexural
specimens for obtaining tensile material properties. This section also presents a comparison of
the material properties with the available ASTM approaches. By utilizing the back-calculation
procedure, the researchers sought to determine equivalent material properties used in the
procedures proposed in calculation for moment curvature and load deflection. This approach
forms the basis for the development of design equations for various structural elements.
Due to the lack of a comprehensive testing program prior to the design and construction phase,
many material properties used in current design procedures are estimated based on relationships
with uniaxial compressive strength, f’c. This may not be a realistic approach to capture the
mechanisms of tensile failure using compressive strength properties; hence, new procedures are
needed. Several test methods are available to characterize post-crack tensile strength of FRC.
Gopalaratnam addressed the experimental and analytical merits and drawbacks of these methods
(Gopalaratnam, 1995).
In the conventional approach, material properties are estimated based on prior experience and
verified through testing. As samples are tested to meet the specified strength in design
calculations, the strength of a flexural member is correlated empirically with its compressive and
tensile strength, and then verified during the construction quality control phase. Other test
methods developed for the characterization of ductility and toughness may be applicable to
differentiate in-between various comparative samples; however, their utility for design purposes
are questionable. It would be ideal to obtain fundamental tensile properties from flexural tests,
but it is imperative that the discrepancy between the two be addressed in design calculations and
actual values obtained from testing be subjected to appropriate safety factors.
To verify the theoretical derivations for flexural loading, the researchers studied the model
applied to FRC beams under several cases of deflection-softening and deflection-hardening
under the three-point and four-point bending tests, for which tensile data may not have been
available. The closed-form solutions for moment-curvature diagrams can be used to predict load
deformation response and can be followed through a back-calculation procedure to measure
material properties from flexural tests. The researchers found the material parameters for tension
models by fitting the model to simulate the flexural response. If tension results are available, one
can use a forward calculation to predict the flexural response. If such results are not available,
one can use the flexural data to obtain effective tensile properties. Since the material parameters
for compression model are less dominant in the prediction of the load deflection, they can be
estimated from the uniaxial compressive strength or tensile data. To capture the post-peak
response, especially in low-volume fraction composites, tests need to be conducted under closed-loop
control with the CMOD as the controlled variable. In this test, the CMOD is measured
across the face of the notch using an extensometer. The loading procedure also measures the
fracture toughness parameter, Gf, defined as the area under the load-deflection response.
Representative back-calculations of stress-strain responses using a plasticity model for AR glass
fibers are shown in Figure 16 and compared with control experiments in Figure 17. Back-
33
calculated tensile parameters of flexural samples using the plasticity model are shown in Table
14.
Figure 16. a) Experimental Results and Simulated Flexural Load-deflection Response of
Concrete with Glass Fibers b) Back-calculated Stress-Strain Relationship for a Control
Sample at 7 Days.
Figure 17. a) Experimental Results and Simulated Flexural Load-deflection Response and
b) Back-calculated Stress-Strain Relationship for a Control Sample at 7 Days.
0 0.01 0.02 0.03 0.04 0.05
LVDT Deflection, in
0
300
600
900
1200
Flexural Load, lb
Experiment
ASU Model
ARG5.0: Vf = 5 lb/yd3
sample 1, age:7 days
0 0.004 0.008 0.012 0.016 0.02
Strain, in/in
0
50
100
150
200
Stress, psi
ARG5.0 : Vf = 5 lb/yd3
0
50
100
150
200
250
0 0.0002 0.0004 0.0006 0.0008 0.001
Strain (in/in)
Tensile Stress-Strain
Relationship
sample 1, age: 7 days
Back calculated method
0 0.004 0.008 0.012 0.016
LVDT Deflection, in
0
200
400
600
800
1000
Flexural Load, lb
Experiment
ASU Model
Control: vf = 0 lb/yd3
sample 1, age:7 days
0 0.002 0.004 0.006 0.008
Strain, in/in
0
50
100
150
200
Stress, psi
Control : Vf = 0 lb/yd3
0
50
100
150
200
250
0 0.0002 0.0004 0.0006 0.0008 0.001
Strain (in/in)
Tensile Stress-Strain
Relationship
sample 1, age: 7 days
LVDT back calculated method
34
Table 14. Back-calculated Tensile Parameters of Flexural Samples Using a Plasticity Model.
Mix ID
Sample
Code
Age,
days
First
Crack
Tensile
Strain
( cr), str
Young’s
Modulus
(E), ksi
First Crack
Tensile
Strength
(scr), psi
Normalized
Post-Crack
Tensile
Strength ()
Normalized
Transition
Tensile
Strain ()
Transition
Tensile
Strain,
( trn), str
Ultimate
Tensile
Strain ( tu),
str
Plain
Plain_WC.55_1d_1 1 56 3,949 220 0.02 7 389 6,631
Plain_WC.55_1d_2 1 57 3,668 210 0.02 7 400 6,001
Plain_WC.55_1d_3 1 58 3,949 230 0.02 6 349 6,998
Average 1 57 3,855 220 0.02 7 379 6,543
Plain_WC.55_3d_1 3 54 4,344 235 0.02 12 649 7,001
Plain_WC.55_3d_2 3 62 3,949 245 0.02 9 558 6,998
Average 3 58 4,147 240 0.02 11 604 6,999
Plain_WC.55_7d_1 7 55 4,344 240 0.02 12 663 6,497
Plain_WC.55_7d_2 7 57 4,344 245 0.02 12 682 7,500
Average 7 56 4,344 243 0.02 12 672.5 6,999
GlassF5 GlassF5_WC.55_1d_
1
1 57 3,949 225 0.20 7 399 17,999
GlassF5_WC.55_1d_
2
1 60 3,949 235 0.17 7 417 18,002
GlassF5_WC.55_1d_
2
1 54 3,949 215 0.22 7 382 18,999
Average 1 57 3,949 225 0.20 7 399 18,333
GlassF5_WC.55_3d_
1
3 50 4,739 238 0.24 12 603 8,999*
GlassF5_WC.55_3d_
2
3 53 4,739 250 0.17 12 633 19,496
Average 3 51 4,739 244 0.21 12 618 19,496
GlassF5_WC.55_7d_
1
7 52 4,739 245 0.17 15 775 19,501
GlassF5_WC.55_7d_
2
7 52 4,739 245 0.17 15 775 19,000
Average 7 52 4,739 245 0.17 15 775 19,250
* Ultimate tensile strain of this sample is back-calculated only up to 0.02 in, where the LVDT stopped recording
35
Inverse Analysis of Load Deflection Response of Polymeric Fibers (Type 1 and 2)
Representative back-calculations of stress-strain responses using the bilinear elastic-plastic
model for polymeric fibers are shown in Figure 18. Back-calculated tensile parameters of
flexural samples using the model are also shown in Table 15.
Figure 18. Experimental and Simulated Load-deflection Response and Back-calculated
Stress-Strain Relationship of Three Samples with Different Fiber Types and Contents
Tested at 28 Days.
0 0.02 0.04 0.06
Deflection, in
0
200
400
600
800
1000
Flexural Load, lb
Experiment
Simulation
PolyF9.5-Type I
sample 1
age: 28 days
0 0.01 0.02 0.03
Strain, in/in
0
40
80
120
160
Stress, psi
PolyF9.5-Type I
sample 1
age: 28 days
Stress-Strain Relationship
0 0.01 0.02 0.03 0.04 0.05
Deflection, in
0
400
800
1200
1600
Flexural Load, lb
Experiment
Simulation
PolyF5-Type II
sample 1
age: 28 days
0 0.005 0.01 0.015 0.02 0.025
Strain, in/in
0
50
100
150
200
250
Stress, psi
PolyF5-Type II
sample 1
age: 28 days
Stress-Strain Relationship
0 0.02 0.04 0.06
Deflection, in
0
400
800
1200
1600
Flexural Load, lb
Experiment
Simulation
PolyF5-type I
sample 1
age: 28 days
0 0.01 0.02 0.03
Strain, in/in
0
100
200
300
Stress, psi
PolyF5-Type I
sample 1
age: 28 days
Stress-Strain Relationship
36
Table 15. Back-calculated Tensile Parameters of Flexural Samples Using the Strain-softening Model.
Mix ID
Sample
Code
Age,
days
First Crack
Tensile
Strain ( cr),
str
Young’s
Modulus
(E), ksi
First Crack
Tensile
Strength
(scr), psi
Normalized
Post-Crack
Tensile
Strength ()
Normalized
Transition
Tensile
Strain ()
Transition
Tensile
Strain, ( trn),
str
Ultimate
Tensile
Strain ( tu),
str
PolyF9.5_Type1
PolyF9.5_Type1_14d_1 14 102 1,622 165* 0.39 12 1,224 20,308
PolyF9.5_Type1_14d_2 14 96 1,622 155* 0.43 16 1,536 20,352
Average 14 99 1,622 160 0.41 14 1,380 20,330
PolyF9.5_Type1_28d_1 28 44 3,605 160* 0.45 12 528 26,765
PolyF9.5_Type1_28d_2 28 44 4,326 190* 0.43 16 704 20,288
Average 28 44 3,965.5 175 0.44 14 616 23,526
PolyF5_Type2
PolyF5_Type2_14d_1 14 48 3,824 185 0.2 50 2,400 20,088
Average 14 48 3,824 185 0.2 50 2,400 20,088
PolyF5_Type2_28d_1 28 44 5,544 245 0.23 45 1,980 20,161
PolyF5_Type2_28d_2 28 58 3,824 220 0.30 40 2,320 25,201
Average 28 51 4,684 233 0.265 42.5 2,150 22,681
PolyF5_Type1
PolyF5_Type1_14d_1 14 71 2,868 205 0.20 32 2,272 20,114
PolyF5_Type1_14d_2 14 52 3,824 200 0.23 25 1,300 20,129
Average 14 62 3,346 203 0.22 29 1,786 20,122
PolyF5_Type1_28d_1 28 67 3,824 255 0.27 32 2,144 27,128
PolyF5_Type1_28d_2 28 75 3,250 245 0.29 25 1,875 25,867
Average 28 71 3,537 250 0.28 29 2,010 26,498
37
Note that the present approach can reliably simulate the response of the specimens for different
fiber contents. The bilinear elastic-plastic model presented here as a design approach captures the
location of the neutral axis, the linear compressive stress, and the residual tensile stress.
DATA REDUCTION BY AVERAGE RESIDUAL STRENGTH METHOD (ARS)
ASTM test methods C1399 and C1609 present alternative ways to measure the post-cracking
characteristics of FRC and report the results in terms of ARS values. The popularity of ASTM
C1399 is due to the fact that the experimental portion of the test can be accomplished using an
open-loop testing machine that is available in many material testing labs (Nemkumar & Ashish,
1999; Nemkumar & Ashish, 2000; ASTM, 1999a). According to the ASTM C1399 method, first
a steel plate is placed underneath a concrete beam and the specimen is loaded under a four-point
bending setup until the concrete cracks. Then, the steel plate is removed and the cracked
specimen is reloaded to obtain post-crack flexural strengths at deflection levels of 0.02, 0.03,
0.04, and 0.05 inches. Finally, the equivalent stress results are averaged to represent an ARS
value. This parameter has been used to compare different material formulations, but some
designers have been using it as a tensile strength measure. It is imperative to note that the ARS
value is not an equivalent elastic stress and cannot be associated with the post-crack tensile
strength, or with the tensile residual strength parameter. The ARS method has been extended to
ASTM C1609 (ASTM, 1999b). As the post-peak response is averaged, the residual load is used
in the elastically equivalent flexural stress using the section modulus of the uncracked beam to
calculate a stress measure. In doing so, the load is divided by the equivalent elastic section
modulus. The ARS value is reported as an equivalent elastic stress in a specimen that is no
longer elastic. The properties are measured in accordance with a flexural neutral axis assumed at
the centroid of the specimen, whereas due to cracking the neutral axis has shifted significantly
toward the compression zone. The ARS method therefore overestimates the residual uniaxial
tensile strength obtained based on the present approach.
To illustrate the fundamental differences between the two methods, the stress distribution during
the late stage of loading composites is presented across the depth of the cross section. The strain
distribution across the cross section is shown in Figure 19. Note that, according to the ARS
method, the stress distribution is linear and the neutral axis remains at the center of the section.
However, in accordance with the bilinear elastic plastic model (also called the bilinear softening
model), the neutral axis moves toward the compression zone and a uniform tensile stress
distribution is distributed over the tensile zone. Figure 19 implies that the residual flexural
strength cannot be a substitute for residual tensile strength in design, since the residual flexural
strength is just an equivalent form of stress and not a material property.
COMPARISON BETWEEN POST-PEAK RESIDUAL STRENGTH AND ARS METHOD
Direct correlation of residual strength from ASTM C1399 and the bilinear elastic-plastic method,
shown in Figure 20, indicates that the ARS method overestimates the residual tensile strength by
as much as two to three times. The experimental test data were reduced using both methods, and
the plot of residual strength in accordance to ARS values was plotted vs. the post peak residual
strength obtained by the bilinear elastic-plastic method. The simplifications due to the
assumption of the location of neutral axis lead to very high nominal flexural stress levels in the
38
far tension fiber, which are far greater than the actual tensile strength. Extreme caution must be
exercised in applying the ARS method to design and analysis of FRC sections. In fact, the ARS
parameter is merely an equivalent elastic stress of the true nonlinear stress of the material. Thus,
this parameter can serve only as a residual tensile strength index.
Figure 19. Comparison of Stress Distribution Determined Using the Present Approach and
the ARS Method.
Figure 20. Comparison of Post-peak Strength
with ARS for Various Types of Fibers.
0 400 800 1200 1600
Stress, psi
-2
-1
0
1
2
Distance along depth, in
ARS Method,
Linear Elastic
Present Method,
Elastic Softening
Stress Distribution
in Softening Zone
N.A. (ARS method)
N.A. (Present Method)
0 4 8
Stress, MPa
-60
-40
-20
0
20
40
60
Distance along depth, mm
20 40 60 80 100
Post Peak Residual Strength (scr), psi
50
100
150
200
250
300
350
Residual Strength, ASTM-C1399 Equivalent, psi
Glass Fiber
Equation Y = 2.05 * X + 24.54
R-squared = 0.73
Polymer Fiber - Type I
Equation Y = 3.74 * X + 33.11
R-squared = 0.99
Polymer Fiber - Type II
Equation Y = 5.14 * X - 63.30
R-squared = 0.67 Polymer Fiber - Type III
Equation Y = 2.76 * X + 41.62
R-squared = 0.76
Polymer Fiber - Type IV and Hybrid
Equation Y = 3.49 * X - 27.56
R-squared = 0.80
39
DEVELOPMENT OF DESIGN EQUATIONS FOR FLEXURAL RESPONSE
A tensile stress-strain model also can be obtained directly from a uniaxial tension test. However,
the test procedure is difficult to control and normally underestimates the flexural strength due to
the size effect between uniform stress in direct tension tests and gradient stress in bending tests
(Soranakom & Mobasher, 2007a; Soranakom & Mobasher, 2007b). To predict flexural
behaviors, the back-calculation of tensile properties from the load-deflection curve of the four-point
bending test is an option that indirectly incorporates the size effect in material properties.
The design equations for flexural response are presented here with a minimum number of
independent variables and dimensionless parameters. Cracking tensile strength and Young’s
modulus can be estimated according to ACI 318 (American Concrete Institute, 2005):
(Eq. 8)
(Eq. 9)
Cracking tensile strain for FRC members can be calculated from Hooke’s law as:
(Eq. 10)
The yield compressive strength parameter, σcy = 0.85fc’ from RILEM, is adopted here, in which
fc’ is the ultimate uniaxial cylinder compressive strength (RILEM Technical Committee 162-
TDF, 2003). Using the compressive strength as an input, the parameter  is defined as the ratio
of compressive strength to tensile strength and was reported in Tables 14 and 15. Applying the
ACI-recommended equations for compressive and tensile strength, this function can be estimated
as =0.85(fc’)
0.5/6.7. By defining the initial cracking moment, Mcr=scrbh
2/6 , and the resistance
factor defined in accordance with load and resistance factor design (LRFD) guidelines as p, the
expression for factored nominal moment capacity as an elastic material is shown in Figure 13.
The moment capacity using an elastic-residual strength approach is represented by a function
that utilizes the post-crack tensile strength, , and ultimate compressive strength, f’c, is
represented by Equation 12 (Chuang & Mai, 1989; Wee, Lu & Swaddiwudhipong, 2000):
1
6
2
 pMn   pscrbh ( elastic analysis )
(Eq. 11)
15 8 1 32
'
c 2 ' '
p n p cr c c
'
c
f
M bh . for f in psi, . for f in MPa
+2 f

  s  

 
    
 
 
(Eq. 12)
MINIMUM FLEXURAL POST-CRACK TENSILE STRENGTH REQUIREMENTS
In reinforced concrete structures, the minimum flexural reinforcement is enforced to avoid a
sudden failure of a beam when its post-cracking strength is lower than its cracking moment. In
an FRC system, the sudden drop in the moment capacity after cracking refers to the deflection-
' ' scr  E cr  6.7 fc (psi) (or  0.56 fc (MPa))
' ' E  57,000 fc (psi) (or  4,733 fc (MPa))
' '
' '
6.7 0.56
118
57000 4733
cr c c
cr
c c
f f
str
E f f
s
     
40
softening response. The critical normalized post-crack tensile strength level, crit, that maintains
a load-carrying capacity equivalent to the cracking strength level (Mu = Mcr) is obtained by
solving Equation 4 with a reduction factor p = 1.
(Eq. 13)
For typical FRC materials, the compressive-tensile strain ratio, ω, varies between 6 and 12.
Thus, crit varies in a narrow range between 0.34 and 0.35. Since the actual tensile strength and
the strength used in the design calculations may be different by a factor of
, a slightly conservative value that ensures the post-crack capacity is
always greater than the first cracking level of an actual flexural member is proposed as:
(Eq. 14)
MINIMUM POST-CRACK TENSILE STRENGTH FOR SHRINKAGE AND
TEMPERATURE
Due to temperature and shrinkage conditions occurring during the curing process, a concrete slab
with a large surface-to-volume ratio can be subjected to severe cracking due to restrained
shrinkage stresses. To control crack width, minimum reinforcement for shrinkage and
temperature must be placed perpendicular to the main flexural reinforcement. According to ACI
318, the minimum ratio of reinforcement to gross section area, min_ST, is:
(Eq. 15)
where fy is the yield strength of steel. When steel rebars or welded wire mesh are replaced with
FRC, the minimum normalized post-crack tensile strength, μmin_ST, guarantees that the same
tensile performance can be determined by the equivalent tensile capacity for the same reliability
index.
(Eq. 16)
Here we can assume a reduction factor identical to the one mentioned in ACI 318 for bending
structural members (b=0.90). In these members, failure is controlled by reinforcement failure.
On the other hand, the reduction factor p = 0.70 is used for a member in which the tensile failure
is controlled by the post-crack capacity of the FRC. The use of higher and lower reduction
factors in Equation 3.16 ensures the reliability index is maintained when the steel reinforcement
is replaced with FRC. Conservative values of ρmin_ST = 0.0018 and fy = 60,000 psi are substituted
3 1
crit





' ' 7.5 fc / 6.7 fc 1.12
min_ flex  0.40
min_
0.0020 40 < 50 , deformed bar
0.0018 = 60 ,welded-wire fabric (smooth or deformed)
0.0018 60,000
0.0014 > 60 ksi at = 0.35%
y
ST y
y sy
y
ksi f ksi
f ksi
f
f




< 
 

  

bmin_ ST f ybh  pmin_ STscrbh
41
in Equation 16 to produce highest tension force and solve for μmin_ST:
(Eq. 17)
DESIGN EXAMPLE FOR SLAB ON GRADE
The design procedure for strain-softening FRC is best suited to thin structural applications, such
as slab systems in which the size effect is minimal and the internal forces are relatively low
compared to the moment capacity. An example of slab on grade is presented to demonstrate the
design calculations. Typically, slabs on grade are designed based on minimum shrinkage and
temperature steel. Loads on slabs are not critical and are transferred directly to stiff compacted
base materials. These slabs are allowed to crack but not disintegrate. Other types of slabs on
grade and pavements that are designed based on applied load and subgrade modulus are not
studied here.
The concrete slab is 5 inches thick, reinforced at mid-depth with #4 steel rebars placed 18 inches
apart on center. The materials used are concrete with a compressive strength of 3,000 psi and
steel with a yield strength of 60 ksi. In this analysis, this existing design is replaced with steel
fiber reinforced concrete (SFRC) that has a compressive strength of 4,000 psi.
The slab is designed based on a 1-foot strip, and the amount of reinforcement, As, is calculated
as:
(Eq. 18)
The plastic compressive zone is calculated according to the ACI stress block concept:
(Eq. 19)
The factored ultimate moment, Mu, is then equal to the reduced nominal moment capacity, bMn:
(Eq. 20)
min_
140 0.97
ST (psi) (or (MPa))
cr cr

s s
 
2 2 2 12 0.5 12 in
0.131
4 4 18 ft
s
d
A
spacing
 
  
0.131 60
0.257
0.85 ' 0.85 3 12
s y
c
A f
a
f b

  
 
2
u b n b s y
a
M  M  A f d
 
    
 
0.257 1
0.9 0.131 60(2.5 ) 1.40 kips-ft/ft
2 12
    
42
Equivalent Moment Capacity with SFRC, fc’ = 4,000 psi
Calculate the cracking tensile strength of SFRC according to the following equation:
(Eq. 21)
Calculate the cracking moment:
(Eq. 22)
Calculate the compressive-tensile strength ratio by:
(Eq. 23)
Determine the normalized post-crack tensile strength as demand and solve for required post-crack
residual strength:
(Eq. 24)
It can be verified that the reduced nominal moment capacity of the SFRC slab is equal to the
ultimate moment determined from the reinforced concrete slab:
(Eq. 25)
(Eq. 26)
However, the required  must be checked against the minimum post-crack tensile strength for
flexure, defined in Equation 13, min_flex = 0.40. Thus, use  = 0.40.
' s cr  6.7 fc  6.7 4000  424 psi
2 2 424 12 5 1
1.77 kips-ft/ft
6 6 12000
cr
cr
bh
M
s  
  
0.85 4000
8.02
424
cy
cr
s

s

  
1.40 8.02
0.395
3 3 8.02 0.7 1.77 1.40
u
p cr u
M
M M




  
    
15 8
'
c 2
p n p cr
'
c
f
M bh
. +2 f

  s

 
  
 
 
0 395 4000 2 1
0 7 424 12 5 1 40
15 8 0 395 2 4000 12000
.
. ( )( )( ) . kips-ft/ft
. ( . )
 
   
  
43
Equivalent Tensile Capacity
Assume plain concrete in the reinforced concrete slab has no residual strength; thus, the amount
of reinforcement will be replaced with an SFRC having the same tensile capacity:
(Eq. 27)
The post-crack tensile strength is calculated as:
(Eq. 28)
The minimum normalized post-crack tensile strength for shrinkage and temperature can be
calculated by the following equation:
(Eq. 29)
The calculations in this example point to several potential design approaches. If the goal is to
replace the existing reinforced concrete slab with an SFRC system and still have the same
performance and reliability index as the original design, the post-crack tensile strength must be
0.40 based on the minimum flexural strength. However, if only shrinkage and temperature
cracking are of concern, the required strength can be reduced to 0.33. In this case, a parameter of
 = 0.40 is specified to meet a performance level that is equivalent to the reinforced concrete
slab. The specified post-crack tensile strength for material testing must be calculated using the
same cracking tensile strength used in the design calculations, which may be different from the
actual value obtained from testing. According to th