Bond Behavior of Reinforcing Steel in 

Ultra-High Performance Concrete

October 2014

FHWA Publication No. FHWA-HRT-14-090
FOREWORD

With the ever increasing congestion and deterioration of our nation’s highway system, a need 

exists to develop highly durable and rapidly constructed infrastructure systems. Durable bridge 

structures that would require less intrusive maintenance and would exhibit longer life spans thus 

maximizing the use of the facility are highly desirable. Expediting bridge construction can 

minimize traffic flow disruptions. Ultra-high performance concrete (UHPC) is an advanced 

construction material which affords new opportunities to envision the future of the highway 

infrastructure. The Federal Highway Administration has been engaged in research on the optimal 

uses of UHPC in the highway bridge infrastructure since 2001 through its Bridge of the Future 

initiative. This report presents results of a study aimed at assessing the potential of using UHPCclass materials to anchor or lap splice deformed reinforcing bars in field-cast connections. This 

concept could potentially allow for the simplification of connection details in some prefabricated 

bridge systems, and may also allow for the development and deployment of expedited 

construction techniques.

This report corresponds to the TechBrief titled “Bond Behavior of Reinforcing Steel in UltraHigh Performance Concrete” (FHWA-HRT-089). This report is being distributed through the 

National Technical Information Service for informational purposes. The content in this report is 

being distributed “as is” and may contain editorial or grammatical errors.

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use of 

the information contained in this document.

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-14-090

2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Bond Behavior of Reinforcing Steel in Ultra-High 

Performance Concrete

5. Report Date

October 2014

6. Performing Organization Code: 

7. Author(s)

Jiqiu Yuan and Benjamin A. Graybeal

8. Performing Organization Report No. 

9. Performing Organization Name and Address

Office of Infrastructure Research & Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

10. Work Unit No.

11. Contract or Grant No.

12. Sponsoring Agency Name and Address

Office of Infrastructure Research & Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

March 2013 – March 2014

14. Sponsoring Agency Code

HRDI-40

15. Supplementary Notes

This document was developed by research staff at the Turner-Fairbank Highway Research Center. Portions of the

work were completed by PSI, Inc. under contract DTFH61-10-D-00017. Jiqiu Yuan of PSI, Inc. is a contract 

researcher on FHWA’s structural concrete research efforts and Ben Graybeal of FHWA both manages the FHWA 

Structural Concrete Research Program and leads the Bridge and Foundation Engineering Research team.

16. Abstract

Ultra-High Performance Concrete (UHPC) is a relatively new class of advanced cementitious composite 

materials, which exhibits high compressive [above 21.7 ksi (150 MPa)] and tensile [above 0.72 ksi (5 MPa)] 

strengths. The discrete steel fiber reinforcement included in UHPC allows the concrete to maintain tensile 

capacity beyond cracking of the cementitious matrix. The combination of the matrix and fiber performance allow 

for a reduction on the development length of reinforcing bar, thus providing the potential for a redesign of some 

structural systems such as field–cast connections between prefabricated bridge elements. The bond behavior of 

deformed reinforcing bar in UHPC is investigated in this study by conducting direct tension pullout tests. Over 

200 tests were completed and the effect of embedment length, concrete cover, bar spacing, concrete strength, bar 

size and type on bond strength were investigated. It was found that the development length of embedded 

reinforcement in UHPC can be significantly reduced. Guidance on the embedment of deformed reinforcing bars 

into UHPC is provided.

This report corresponds to the TechBrief titled “Bond Behavior of Reinforcing Steel in Ultra-High Performance 

Concrete” (FHWA-HRT-089).

17. Key Words

Ultra-high performance concrete, UHPC, fiberreinforced concrete, reinforcing bar, bond 

strength, anchorage, development length, splice 

length

18. Distribution Statement

No restrictions. This document is available through the 

National Technical Information Service, Springfield, VA 

22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

78

22. Price

N/A

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
ii

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) o

F Fahrenheit 5 (F-32)/9 Celsius o

C 

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) o

C Celsius 1.8C+32 Fahrenheit o

F 

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 the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
iii

TABLE OF CONTENTS

CHAPTER 1. INTRODUCTION ................................................................................................... 9

GENERAL...................................................................................................................................... 9

ULTRA-HIGH PERFORMANCE CONCRETE ..................................................................................... 10

LITERATURE REVIEW ON BOND STRENGTH BETWEEN DEFORMED REINFORCING STEEL AND UHPC

................................................................................................................................................... 10

OBJECTIVE.................................................................................................................................. 11

OUTLINE OF REPORT ................................................................................................................... 12

CHAPTER 2. EXPERIMENTAL INVESTIGATION................................................................. 13

INTRODUCTION........................................................................................................................... 13

UHPC FORMULATION .................................................................................................................. 13

UHPC COMPRESSIVE STRENGTH .................................................................................................. 14

REINFORCING STEEL ................................................................................................................... 14

TEST SETUP AND PROCEDURES.................................................................................................... 17

SPECIMEN PREPARATION ............................................................................................................ 20

TEST MATRIX.............................................................................................................................. 22

CHAPTER 3. PULLOUT TESTS RESULTS .............................................................................. 23

INTRODUCTION........................................................................................................................... 23

TERMINOLOGY AND SPECIMEN NOTATION .................................................................................. 23

CRACKING AND DAMAGE MECHANISM........................................................................................ 25

FACTORS AFFECTING BOND ........................................................................................................ 29

Casting Orientation............................................................................................................... 29

Effect of Embedment Length ................................................................................................. 31

Side Cover............................................................................................................................. 34

Bar Spacing........................................................................................................................... 39

UHPC Compressive Strength................................................................................................ 46

Reinforcing Bar Size ............................................................................................................. 52

Reinforcing Bar Type and Yielding Strength ........................................................................ 54

CHAPTER 4. DESIGN RECOMMENDATIONS FOR REINFORCING BAR EMBEDDED IN 

UHPC............................................................................................................................................ 59

MINIMUM BAR STRESS OF LESSER OF YIELD OR 75 KSI (517 MPA) ............................................. 59

MINIMUM BAR STRESS OF LESSER OF YIELD OR 75 KSI (517 MPA) – ALTERNATIVE........................ 63

BAR STRESS ABOVE 75 KSI (517 MPA) OR BAR RUPTURE BEFORE BOND FAILURE ...................... 67

CHAPTER 5. CONCLUSIONS ................................................................................................... 69

INTRODUCTION........................................................................................................................... 69

CONCLUSIONS ............................................................................................................................ 69

RECOMMENDED DESIGN ............................................................................................................. 70

FUTURE RESEARCH ..................................................................................................................... 71

ACKNOWLEDGMENTS ............................................................................................................ 73

REFERENCES.............................................................................................................................. 74
iv

LIST OF FIGURES

Figure 1. Graph. Tensile stress strain response of reinforcing bars.............................................. 15

Figure 2. Photo. Reinforcing bar rib pattern. ................................................................................ 17

Figure 3. Illustration. Overall configuration of test specimens..................................................... 18

Figure 4. Illustration. Pullout test specimens layout..................................................................... 18

Figure 5. Illustration. Loading setup............................................................................................. 19

Figure 6. Photograph. Loading setup. ........................................................................................... 20

Figure 7. Photograph. Displacement measurement via three LVDTs. ......................................... 20

Figure 8. Photograph. UHPC strip casting setup and orientation: (a) side pour setup; (b) side pour 

casting; (c) upright pour setup; and (d) upright pour casting. ........................................ 21

Figure 9. Illustration. Conceptual bar stress versus slip response................................................. 24

Figure 10. Equation. Average bond stress in reinforcing bar. ..................................................... 24

Figure 11. Illustration. Pullout tests: (a) forces on bars; and (b) crack patterns. .......................... 26

Figure 12. Photo. Crack patterns: (a) longitudinal splitting cracks to adjacent No. 8 bars; (b) 

splitting cracks to side face; (c) splitting cracks to side face and adjacent No. 8 bars; and 

(d) UHPC tensile failure with opened diagonal cracks. ................................................. 27

Figure 13. Photo. Diagonal crack observation: (a) visual inspection; and (b) crack inspection 

with denatured alcohol.................................................................................................... 28

Figure 14. Photo. Conical surface failure: (a) conical surface around the bar; and (b) conical 

surface extended to the side face. ................................................................................... 28

Figure 15. Graph. Effect of embedment length: fs,max versus embedment length ld. ..................... 34

Figure 16. Illustration. Bond splitting cracks: (a) csi > cso; and (b) csi < cso.................................. 35

Figure 17. Graph. Effect of side cover: bond strength μTEST versus side cover for specimens in 

Sets 1, 2 and 3. The csi is constant. ................................................................................. 38

Figure 18. Graph. Effect of side cover: bond strength μTEST versus side cover for specimens in 

Sets 4 and 5. The csi is constant. ..................................................................................... 39

Figure 19. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens in Set 1. 

The cso is constant. .......................................................................................................... 42

Figure 20. Illustration. Geometrical demonstration of lstan(θ) and 2csi........................................ 43

Figure 21. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens in Set 2. 

The cso is constant. .......................................................................................................... 44

Figure 22. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens in Set 3. 

The cso is constant. .......................................................................................................... 44

Figure 23. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens in Set 4. 

The cso is constant. .......................................................................................................... 45

Figure 24. Graph. Effect of UHPC compressive strength: bond (a) uTEST versus f’c and (b) uTEST

versus f’c

1/2 for specimens in Set 1. ................................................................................ 49

Figure 25. Graph. Effect of UHPC compressive strength: (a) uTEST versus f’c and (b) uTEST versus 

f’c

1/2 for specimens in Set 2............................................................................................. 50

Figure 26. Graph. Effect of UHPC compressive strength: (a) uTEST versus f’c and (b) uTEST versus 

f’c

1/2 for specimens in Set 3............................................................................................. 51
v

Figure 27. Chart. Bond strength versus bar size. .......................................................................... 54

Figure 28. Chart. Average bar stress at bond failure for different types of reinforcing bar. ........ 55

Figure 29. Graph. Bar stress at bond failure versus embedment length for all tests with A1035 

No. 5 bars........................................................................................................................ 60

Figure 30. Graph. Bar stress at bond failure versus embedment length for all tests with A1035 

No. 5 bars and with a side cover ≥ 2.7db......................................................................... 61

Figure 31. Graph. Bar stress at bond failure versus embedment length for tests with A1035 No. 7 

bars and epoxy coated No.8 bars. ................................................................................... 63

Figure 32. Chart. Bar stress at bond failure for all A1035 No.5 bars with different design details. 

All specimens had a bar clear spacing between 2db and lstan(θ).................................... 65

Figure 33. Chart. Bar stress at bond failure for all epoxy coated and uncoated No.5 bars with 

different design details. All specimens had a bar clear spacing between 2db and lstan(θ).

........................................................................................................................................ 66

Figure 34. Chart. Bar stress at bond failure for all A1035 No. 4 and No.7 bars and epoxy coated 

No. 8 bar with different design details. All specimens had a bar clear spacing between 

2db and lstan(θ). .............................................................................................................. 67
vi

LIST OF TABLES

Table 1. Typical field-cast UHPC material properties.................................................................. 11

Table 2. UHPC mix design. .......................................................................................................... 13

Table 3. Properties of Reinforcing Steel....................................................................................... 16

Table 4. Test Specimens – Effect of Casting Orientation............................................................. 30

Table 5. Test specimens – effect of embedment length................................................................ 32

Table 6. Test specimens – effect of side cover. ............................................................................ 36

Table 7. Test specimens – effect of bar spacing ........................................................................... 40

Table 8. Bond strength reduction for bar clear spacing out of the range of 2db < 2csi < lstan(θ)........ 45

Table 9. Test specimens – effect of UHPC compressive strength. ............................................... 47

Table 10. Test specimens – effect of bar size. .............................................................................. 53

Table 11. Test specimens – effect of bar type............................................................................... 56

Table 12. Bond stress reduction between different types of reinforcing bar. ............................... 58
vii

LIST OF ABBREVIATIONS AND NOTATION

ABBREVIATIONS

ABC Accelerated Bridge Construction

ASTM American Society For Testing and Materials

DOT Departments Of Transportation

FHWA Federal Highway Administration

LVDT Linear Variable Differential Transformer

PBES Prefabricated Bridge Elements And Systems

UHPC Ultra-High Performance Concrete

NOTATION

cso = side concrete cover for reinforcing bar

csi = one-half of the bar clear spacing

db = reinforcing bar diameter

f’c = concrete compressive strength

fs,crack = bar stress at first observed crack

fs,max = maximum bar stress at bond failure

ld = embedment length

ls = lap spliced length

s1 = bar slip at bond failure

μμTEST = average bond strength at bond failure

θ = angle between the diagonal cracks and testing bar

9

CHAPTER 1. INTRODUCTION

GENERAL

The use of accelerated bridge construction (ABC) techniques continues to grow as owners across 

the country look for construction solutions that reduce impacts on the users of the infrastructure. 

In ABC construction, one common technique used is prefabricated bridge elements and systems 

(PBES). In this practice, bridge elements are prefabricated offsite, then assembled and connected 

onsite during an expedited construction timeframe. The use of prefabricated bridge elements 

necessitates the use of field-applied connections between these elements. Field-cast concrete or 

other cementitious material connections have been deployed for decades by State departments of 

transportation (DOTs). However, decades of experience has led to the recognition that the fieldcast connections often prove to be susceptible to degradation that can lead to substandard 

performance of the overall bridge system. 

Connection systems for PBES are selected based on a variety of considerations. Critical 

properties of connection systems can include the rate of mechanical property development within 

the connection, the dimensional stability of the field-cast material, the durability of the field-cast 

material, and the ease of construction of the overall system.

(1) This document reports on research 

conducted through the Structural Concrete Research Program at the Federal Highway 

Administration Turner-Fairbank Highway Research Center. In this research project, connection 

details using different grout materials, including traditional non-shrinkage grout, epoxy grout, 

Ultra-High Performance Concrete (UHPC), and magnesium grout, are being evaluated. This 

report mainly focuses UHPC materials. 

UHPC is a relatively new class of cementitious composite materials. Since 2000, when UHPC 

became commercially available in the United States, a series of research projects has 

demonstrated the capabilities of the material. A handful of State DOTs have deployed UHPC 

components within their infrastructure, and many more are actively considering the use of 

UHPC. Many State DOTs, bridge design firms, and construction firms have expressed their 

interest of using UHPC in bridge construction, especially for field-cast connections deployed in 

the construction of PBES structures. As late 2013, 32 bridges in the United States have been 

constructed using field-cast UHPC connections.(2)

As opposed to conventional grouted connections which frequently contain complex 

reinforcement configurations, UHPC connections often involve much simpler reinforcement 

configurations such as the lap splicing of straight lengths of reinforcement. A few specific 

connection details, such as those discussed in Behavior of Field-Cast Ultra-High Performance 

Concrete Bridge Deck Connections Under Cyclic and Static Structural Loading and

Development of a Field-Cast Ultra-High Performance Concrete Composite Connection Detail 

for Precast Concrete Bridge Decks, have been rigorously tested at service and ultimate 

performance limits.(3,4) The advanced material properties of UHPC provide a potential to 

develop a simple and robust connection system for prefabricated bridge elements. The research
10

project discussed in this document investigated the bond performance between deformed 

reinforcing bar and UHPC. One objective of the research is to facilitate the development of 

design guidelines for using field-cast UHPC in innovative connection details. 

ULTRA-HIGH PERFORMANCE CONCRETE

Advances in the science of concrete materials have led to the development of a new class of 

advanced cementitious materials, namely UHPC. These concretes tend to contain high 

cementitious materials contents and very low water-to-cementitious materials ratio, and to 

exhibit high compressive and tensile strengths. The discrete steel fiber reinforcement included in 

UHPC allows the concrete to maintain tensile capacity beyond cracking of the cementitious

matrix. UHPC has been defined as follows:

UHPC is a cementitious composite material composed of an optimized gradation 

of granular constituents, a water-to-cementitious materials ratio less than 0.25, 

and a high percentage of discontinuous internal fiber reinforcement. The 

mechanical properties of UHPC include compressive strength greater than 

21.7 ksi (150 MPa) and sustained post-cracking tensile strength greater than 

0.72 ksi (5 MPa). UHPC has a discontinuous pore structure that reduces liquid 

ingress, significantly enhancing durability compared to conventional concrete.(2,5)

A typical field-cast UHPC material properties are presented in Table 1, which represents average 

values for a number of test parameters relevant to the use of UHPC as obtained from independent 

testing of a commercially available product.(6) This research published by the Federal Highway 

Administration in 2006 investigated a number of material properties of UHPC. The research 

analyzed both mechanical- and durability-based behaviors of UHPC to assess its potential for use 

in future highway and bridge construction projects. It should be noted that the UHPC 

investigated in that study was designed for precast applications with accelerated curing and thus 

exhibited a reduced compressive strength under field casting and curing applications as 

compared to current UHPC products.

LITERATURE REVIEW ON BOND STRENGTH BETWEEN DEFORMED 

REINFORCING STEEL AND UHPC

Limited research has investigated the bond performance of deformed reinforcing bar in UHPC. 

New York State Department of Transportation performed pullout tests on reinforcing bar

embedded in 15.7 in. (400 mm) diameter UHPC cylinders.(5) The No. 4, 5, and 6 bars were 

embedded 2.9, 3.9, and 4.9 inches (75, 100, and 125 mm) into the UHPC, respectively, and all 

fractured before bond failure. 

Fehling et al. (7) performed pullout tests on 0.47 in. (12 mm) diameter bars with varied concrete 

cover and embedment length in UHPC. Their test results indicated that increasing concrete cover 

and increasing embedment length each resulted in an increase on the bond strength. For 
11

specimens with a concrete cover of 1.5ds (ds: diameter of reinforcing steel), an embedded length 

of 8ds would yield the bar with a yield strength of approximately 80 ksi (551 MPa). For 

specimens with a concrete cover of 2.5ds, an embedded length of 5ds would yield the bar. 

Table 1. Typical field-cast UHPC material properties. 

Material Characteristic Average Result

Density 2,480 kg/m3 (155 lb/ft3)

Compressive Strength (ASTM C39; 28-day strength) 126 MPa (18.3 ksi)

Modulus of Elasticity (ASTM C469; 28-day modulus) 42.7 GPa (6200 ksi)

Split Cylinder Cracking Strength (ASTM C496) 9.0 MPa (1.3 ksi)

Prism Flexure Cracking Strength (ASTM C1018; 305-mm (12-in.) span) 9.0 MPa (1.3 ksi)

Mortar Briquette Cracking Strength (AASHTO T132) 6.2 MPa (0.9 ksi)

Direct Tension Cracking Strength (Axial tensile load) 5.5–6.9 MPa (0.8–1.0 ksi)

Prism Flexural Tensile Toughness (ASTM C1018; 305-mm (12-in.) span) I30 = 48

Long-Term Creep Coefficient (ASTM C512; 77 MPa (11.2 ksi) load) 0.78

Long-Term Shrinkage (ASTM C157; initial reading after set) 555 microstrain

Total Shrinkage (Embedded vibrating wire gage) 790 microstrain

Coefficient of Thermal Expansion (AASHTO TP60–00) 14.7 x10–6 mm/mm/oC

(8.2 x10–6 in./in./oF)

Chloride Ion Penetrability (ASTM C1202; 28-day test) 360 coulombs

Chloride Ion Permeability (AASHTO T259; 12.7-mm (0.5-in.) depth) < 0.06 kg/m3 (< 0.10 lb/yd3)

Scaling Resistance (ASTM C672) No Scaling

Abrasion Resistance (ASTM C944 2x weight; ground surface) 0.73 grams lost (0.026 oz. lost)

Freeze-Thaw Resistance (ASTM C666A; 600 cycles) RDM = 112%

Alkali-Silica Reaction (ASTM C1260; tested for 28 days) Innocuous

Graybeal and Swenty (8) conducted pullout tests on No.4 reinforcing steel embedded into 6 in. 

(152 mm) cubes. Two types of UHPC were tested, with the test configuration including a 3 in. 

(76 mm) debond length and a 3 in. (76 mm) bond length along the centerline of the cube. One 

UHPC formulation resulted in bar yield before the ultimate pullout failure. The other UHPC

formulation resulted in bar rupture before bond failure. 

Pullout tests were also performed by Holschemacher et al. (9,10) and they observed that the bond 

strength and stiffness increases with testing ages.

OBJECTIVE

The objective of this research is to extensively evaluate the factors that affect bond strength 

between deformed reinforcing bar and UHPC and make recommendations for designs using

reinforcing steel in UHPC.
12

OUTLINE OF REPORT

The research discussed herein investigated the parameters that could affect bond strength 

between deformed bar and UHPC. Direct tension pullout tests were conducted and more than 

200 tests were included in this report. The parameters, including the structural characteristics like 

the embedment length, concrete side cover, bar spacing, bar size, and bar type and the materials 

properties like UHPC compressive strength and bar yielding strength, were considered in the 

study.

This report is divided into five chapters. Chapter 1 provides the introduction and the objective of 

the research. The background information about UHPC materials and the previous research on 

bond strength between deformed bar and UHPC are also included in Chapter 1. Then the 

experimental tests setup and the tests results are presented in Chapter 2 and Chapter 3, 

respectively. Design recommendations for using reinforcing steel in UHPC are presented in 

Chapter 4. At the end, Chapter 5 summarizes the conclusions based on this research. 
13

CHAPTER 2. EXPERIMENTAL INVESTIGATION

INTRODUCTION

The research discussed herein focuses on the assessment of bond performance of deformed bar in 

field-cast grout. This is an ongoing research program at the FHWA Turner-Fairbank Highway 

Research Center as part of a larger effort focused on developing innovative connection details for 

prefabricated bridge components. This report mainly presents the results of the bond behavior 

between deformed bar and UHPC. Direct tension pullout tests were conducted. The experimental 

setup is presented in this chapter. 

Details of the UHPC formulation investigated in this study, included the proportioning of the 

UHPC material and its compressive strength properties, are presented first. Then the deformed

steel bar properties are reported. Both normal strength Grade 60 bar, including uncoated and 

epoxy coated, and high strength Grade 120 uncoated bar were used in the study and their yield 

strength, tensile strength, and deformation properties are reported. Next, the details of the 

specimen preparation and the pullout tests configuration are presented. Finally, the design 

philosophy of the test matrix is introduced.

UHPC FORMULATION

The UHPC used for this research is a product produced by Lafarge North America. The specific 

product tested is Ductal JS1212 and mix proportions are shown in Table 2. 

Table 2. UHPC mix design.

Material Amount (lb/yd3 (kg/m3))

Premix Powder 3700 (2195)

Water 219 (130)

Premia 150* 30 (18)

Optima 100** 20 (12)

Turbocast 650A† 39 (23)

Steel Fibers (2%4) ‡ 263 (156)

* A modified phosphonate plasticizer; ** A modified polycarboxylate 

high-range water-reducing admixture; † A non-chloride accelerator ‡

Steel fibers content of 2% by volume.

As shown in Table 2, this UHPC formulation contains premix power, water, Premia 150 (a

modified phosphonate plasticizer), Optima 100 (a modified polycarboxylate high-range waterreducing admixture), Turbocast 650A (a non-chloride accelerator), and steel fibers. The steel 

fibers included in this mix design were nondeformed, cylindrical, high-tensile strength steel. 

They have a diameter of 0.008 in. (0.2 mm) with a length of 0.5 in. (12.7 mm). The steel tensile 

strength is specified to be greater than 290 ksi (2000 MPa). The steel fibers have a thin brass 
14

coating which provides lubrication during the drawing process and provides corrosion resistance 

for the raw fibers. A constant steel fiber content of two percent by volume was used in this study.

UHPC COMPRESSIVE STRENGTH

Alongside each batch of pullout test specimens, a set of three compression test cylinders were 

cast. All cylinders were 3 in. (76.2 mm) nominal diameter with approximately 6 in. (152.4 mm) 

lengths. These cylinders were cast at the same time as the pullout test specimens. After each 

cylinder mold was filled, the cylinder was briefly vibrated on a vibrating table to assist in the 

release of entrapped air. The cylinders were then finished with a magnesium hand float and 

covered in plastic. The cylinders were cured alongside the pullout test specimens in the ambient 

laboratory environment.

The compressive mechanical testing was completed through modified version of the ASTM C39 

Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens.(11)

The 

employed test method has been engaged multiple times in the past.(6,12,13) From the standpoint of the 

ASTM C39 test method, the load rate was increased from 35 psi/second (0.24 MPa/second) to 150 

psi/second (1.0 MPa/second) due to the high compressive strength of UHPC and the duration of test 

that would result from the slower load rate.

The compressive strength for each of UHPC batch is reported in Chapter 3, alongside the pullout 

test results. The UHPC used in this study had an average compressive strength of 13.5 ksi 

(93 MPa) at one day, with a minimum of 11.7 ksi (81 MPa) and a maximum of 14.2 (98 MPa) 

for 33 specimens tested in 11 batches. It had an average compressive strength of 19.4 ksi 

(133 MPa) at seven days, with a minimum of 18.5 ksi (128 MPa) and a maximum of 20.5 (141

MPa) for 21 specimens tested in 7 batches. It had an average compressive strength of 21.3 ksi 

(147 MPa) at 14 days, with a minimum of 20.3 ksi (140 MPa) and a maximum of 22.2 (153 

MPa) for six specimens tested in two batches. The majority of the tests in this study were 

conducted at one day or seven days after casting.

REINFORCING STEEL 

The properties of reinforcing steel used in this study are reported in this section. The bar type and 

size used in the study are presented first, then the yield strength and tensile strength for each bar are 

reported. The deformation properties and rib pattern of the reinforcing bar are also included in this 

section. 

Three types of reinforcing bar were tested in this study, including normal strength Grade 60 

uncoated and epoxy coated bar and high strength Grade 120 uncoated bar. All the Grade 60

uncoated and epoxy coated bar meet the specification of ASTM A615(14)

, and will be referred to 

as uncoated and epoxy coated bar, respectively; all the high strength Grade 120 uncoated bar

meets the specification of ASTM A1035(15)

, and will be referred to as A1035 bar in later 

discussions. The Grade 120 high strength bar is manufactured by MMFX Technologies 

Corporation. The bar sizes tested in the study include uncoated bar No.5, epoxy coated bar No.5 

and No.8, and A1035 bar No.4, No.5, and No.7. The steel bar mechanical properties were tested 
15

following ASTM A370(16). Two bars were tested for each nominal size used in the pull out 

specimens. Strain was measured with an 8 in. (203 mm) extensometer. The tests were conducted 

under displacement control. For the Grade 60 bars, the free-running rate of separation of the 

crosshead was adjusted to have a loading speed of 0.003 in. per min per inch until the strain in 

the extensometer reached 0.1%; then speed was adjusted to 0.002 in. per min per inch and the 

specimen was loaded until the strain reached 1%, and at the this point, the extensometer was 

removed; the test was then continued at a speed of 0.03 in. per min per inch until the bar fractured. 

For the Grade 120 bars, the free-running rate of separation of the crosshead was adjusted to have a 

loading speed of 0.006 in. per min per inch until the strain in the extensometer reached 0.5%; then 

speed was adjusted to 0.003 in. per min per inch and the specimen was loaded until the strain 

reached 2.5%, and at the this point, the extensometer was removed; the test was then continued at a 

speed of 0.03 in. per min per inch until the bar fractured. The yield strength was determined using 

the 0.2% offset method. The tensile stress versus strain curve for each type and size reinforcing bar

is presented in Figure 1, and the yield and tensile strengths are listed in Table 3. In general, as 

shown in Figure 1 and Table 3, the uncoated has a yield strength of approximately 75 ksi 

(517 MPa) and tensile strength of 118 ksi (814 MPa) while the yield and tensile strength of epoxy 

coated bar are 70 and 108 ksi (483 and 745 MPa), respectively. The A1035 bar has a yield strength 

(0.2% offset method) of approximately 130 ksi (896 MPa) and tensile strength of 170 ksi (1172 

MPa). All of the bar tested in this study exhibited nearly identical stress-strain response from the 

initiation of loading through the attainment of a tensile stress of 68 ksi (469 MPa).

Figure 1. Graph. Tensile stress strain response of reinforcing bars. 

0

138

276

414

552

690

827

965

1,103

1,241

1,379

0

20

40

60

80

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Engineering Stress (ksi)

Engineering Stress (MPa)

Engineering Strain

A1035 Rebar No.4

A1035 Rebar No.5

A1035 Rebar No.7

Uncoated Rebar No.5

Epoxy coated Rebar No.5

Epoxy coated Rebar No.8
16

Table 3. Properties of Reinforcing Steel

Bar 

Size

Bar 

Type

Yield 

Strength†

(ksi)

Tensile

Strength†

(ksi)

Mean 

height*

(in.)

Mean 

Spacing*

(in.)

Relative rib 

area**

No. 4 A1035 134 172 0.024 0.330 0.074

No. 5 A1035 126 167 0.037 0.417 0.088

No. 7 A1035 126 162 0.056 0.561 0.099

No. 5 Epoxy 68 108 0.034 0.408 0.083

No. 8 Epoxy 70 109 0.053 0.615 0.086

No. 5 Uncoated 75 118 0.034 0.402 0.085

† Per ASTM A370.

*Per ASTM A615 and A1035. 

**Per ACI 408R-03(17) and ACI 408.3R-09(18) for calculation of relative rib area.

Note: 1 in. = 2.54 cm, 1 ksi = 6.895 MPa.

The rib pattern for each type and size of the reinforcing bar used in the study is demonstrated in 

Figure 2. The A1035 high strength bar and the normal strength uncoated and epoxy coated bar were 

chosen to have similar rib patterns, as shown in Figure 2. The bar deformation, rib height and 

spacing, were measured following ASTM A615 and ASTM A1035. The height was determined from 

measurements made on three deformations. The spacing was determined by measuring the length of 

a minimum of ten spacings and dividing that length by the number of spaces included in the 

measurement; the average of two measurements was reported. The relative rib area, calculated as the 

ratio of the bearing area of bar deformations to the shear area between the deformations per ACI 

408R-03(17)

, is also presented in Table 3. As shown in Table 3, they all had similar relative rib areas, 

mostly in a range of 0.083 to 0.088 with the exception of A1035 No.4 and No.7 bars having a 

relative rib area of 0.074 and 0.099, respectively.
17

Figure 2. Photo. Reinforcing bar rib pattern.

TEST SETUP AND PROCEDURES

Direct tension pullout tests, with a novel test specimen design and associated loading apparatus, 

were conducted in this study. The test setup was developed so as to mimic the tension-tension 

lap splice configuration that may be encountered in a field-deployed connection system.

The pullout tests speicmens were UHPC strips cast on top of precast concrete slabs, as shown in 

Figure 3. The No.8 bars extended 8 in. (20.3 cm) from the pre-cast concrete slab. UHPC strips 

were cast on top of the precast slab with the No. 8 bars in the center of the strips. Each tested bar 

was situated so as to be embedded into the UHPC strip and located between two of the No. 8 bars.

Each precast concrete slab has dimensions of 4 × 8 × 1 ft (1.2 × 2.4 × 0.3 m) (width × length × 

depth) and the spacing between the extended No.8 bars in the longitudinal direction (along the 

UHPC strip as shown in Figure 4) is either 8 or 12 in. (20.3 or 30.5 cm). More details of 

specimen layout on the precast slab are illustrated in Figure 4. 

In Figure 3 and Figure 4, notations were assigned to represent dimension parameters, including 

cso for the clear side cover, 2csi for the clear spacing between the testing bar and the extended No. 

A1035 No.7

A1035 No.4

A1035 No.5

Uncoated No.5

Epoxy coated No.5

Epoxy coated No.8
18

8 bars, ld for the embedment length of testing bar measured from the top surface of the UHPC 

strip to the end of the testing bar, and ls for the lap splice length measured from the end of the 

testing bar to the end of extended No. 8 bars. These are also the main factors that will be 

investigated for their effect on bond strength in this study. The notations of csi, cso, ld, and ls are 

adopted from ACI 408 R-03 “Bond and Development of Staright Reinforcing Bars in 

Tension.”(17)

Figure 3. Illustration. Overall configuration of test specimens.

Figure 4. Illustration. Pullout test specimens layout.
19

The pullout tests were conducted using the fixture showing in Figure 5 and Figure 6. A hydraulic 

jack (Enerpac® Cylinder, Model RRH1508) was placed on a steel chair, and the steel chair stands 

on the precast slab. When a pullout force is applied, the fixture reacts against the precast slab. 

With such a setup, the reinforcing bars being tested as well as the extended No. 8 bars are both 

placed in tension. The UHPC surrounds these bars transfers the loads between them. This test 

setup simulates structural configurations wherein lap spliced reinforcement is loaded in tension.

Tests were conducted by applying a load to the free end of the embedded reinforcing bar. The 

load was applied under a closed-loop displacement control by adapting a servo valve into the 

system, which was attained with an MTS Flex Test GT controller uing a linear variable 

differential transformer (LVDT) for feedback. The jack was run at a constant displacment rate of 

0.2 in./min (5 mm/min) as measured by the LVDT which captured the displacement at the bar

chuck relative to the top of the jack. The top of the jack was approximately 30 in. (76 mm) above 

the precast slab and the bar chuck started approximately 36 in. (91 mm) above the top of the 

precast slab. A load cell located between the jack and the bar chuck measured the load applied to 

the bar. The bar displacement was measured at a location of approximately two inches (5.1 cm) 

above the top surface of UHPC strip, as shown in Figure 7. Three LVDTs were arranged in 120-

degree angle and the average displacement of the three LVDTs were used to offset the possible 

bending of the loaded bar. The load cell and all LVDTs were calibrated to the MTS DUC 

conditioner. The load cell used in this study was Strainset® model FL100U(C)-2DGKT (S/N 

08905-7) univeral flat load cell. The LVDTs used in this study were Omega® model LD300-150 

(for displacement control) and Omega® model LD320-25 (for displacement measurement at the 

bottom).

Figure 5. Illustration. Loading setup.
20

Figure 6. Photograph. Loading setup. 

Figure 7. Photograph. Displacement measurement via three LVDTs.

SPECIMEN PREPARATION

The UHPC materials tested in this study contained 2% (by volume) steel fibers. Casting 

technique can influence the dispersion and orientation of the fiber reinforcement. In this study, 

the UHPC strips were prepared using plywood forms. Two cast orientations were compared, as 
21

shown in Figure 8. The first orientation involved casting the specimen on its side as shown in 

Figure 8a and Figure 8b; the second orientation involved casting the specimen upright as shown 

in Figure 8c and Figure 8d, where the slab was placed with a small slope of approximately 1.5 

degree to facilitate the flow of the UHPC. For both orientations, the UHPC was first poured in 

from one end and allowed to flow until the forms were mostly filled. Thereafter, the UHPC was

poured in from the middle locations. The orientation of the casting was not observed to have a 

significant effect on bond behavior as will be discussed in Chapter 3. For the large majority of 

test specimens, the upright casting orientation was selected. 

Figure 8. Photograph. UHPC strip casting setup and orientation: (a) side pour setup; 

(b) side pour casting; (c) upright pour setup; and (d) upright pour casting.

The actual dimension of cso, 2csi, ld, and ls were measured. The side covers can be easily 

measured by taking the distance from the sides of the UHPC strip to the bar under consideration 

after forms are removed; the least side cover is reported as cso. The clear spacing between the 

1.5 °

(a) (b)

(c) (d)
22

testing bar and adjacent two No. 8 bars was determined by taking the difference between the 

spacing of the extended No. 8 bars before casting and the spacing of the testing bars after 

casting; the smaller value of the spacing to adjacent No.8 bars is used as 2csi. The actual 

embedment length (ld) was determined by substracting the exposed length of the bar after casting 

from the original length of the bar and the spliced length (ls) was calcuated as ld – (strip height –

8 in.), where the 8 in. (203 mm) is the length of No. 8 bars that is extended outside the precast 

slab. 

The forms were normally removed at 22 ± 1 hours after casting so the one-day testing can start at 

23 ± 1 hours after casting. 

TEST MATRIX

The objective of this study was to evaluate the bond behavior between the deformed reinforcing 

steel (lap spliced) and UHPC. The primary parameters investigated included the embedment 

length of reinforcing steel, concrete side cover, bar spacing, UHPC compressive strength, type of 

deformed bar, and size of deformed bar. Throughout the study, in order to better assess the 

influence of a particular variable, each individual parameter was varied while others remained 

constant. Each of the above mentioned variables will be evaluated and the results are presented 

in Chapter 3. The test matrix is provided in each section where the individual parameter is 

evaluated in Chapter 3. 
23

CHAPTER 3. PULLOUT TESTS RESULTS

INTRODUCTION

The test results from the physical testing of the pullout specimens are presented in this chapter. 

The terminology and specimen notation used in this study are first introduced. Then the cracking 

and damage mechanisms in bond for the pullout specimens are presented. Following that, the 

parameters that could affect bond performance, including casting orientation, embedment length, 

side cover, bar spacing, UHPC compressive strength, reinforcing bar size, and reinforcing bar 

type are analyzed and discussed. The test matrix, including all the information of the specimen 

design, UHPC compressive strength, and bar stress at bond failure, is reported in each section. 

TERMINOLOGY AND SPECIMEN NOTATION

Consistent terminology is used throughout this report in order to simplify the discussion of 

results. In terms of the bar stress versus bar slip response, the applied load and bar displacement 

were continuous recorded during the pullout test. The bar stress fs was then calculated as the 

applied load divided by the cross section area of the reinforcing bar. The displacement was 

measured along a loaded portion of the reinforcing bar at about two inches (5.1 cm) above the 

top surface of UHPC strip (shown in Figure 7). This displacement is used as a measure of the bar 

slip, with the understanding that the displacement also included the stretching of the reinforcing 

bar under the pullout force. The bar stress is plotted versus slip to characterize the bond behavior 

and a typical bar stress versus slip curve for reinforcing bar in UHPC in this study is presented in 

Figure 9. 

As shown in Figure 9, the point with the maximum bar stress was marked with (fs,max, s1), which 

refers to the bar stress and slip, respectively, at bond failure. During each test, the specimen 

surface was also continuously checked for signs of cracks and the bar stress at first observed 

crack was reported as fs,crack. Due to safety considerations, visual inspection was stopped when 

the load was close the estimated maximum load. In some cases, visual inspection was stopped 

before the first crack was observed. The bar stress at first observed crack (fs,crack), the maximum 

bar stress at bond failure (fs,max), and the bar slip at bond failure (s1) were reported for each 

specimen.
24

Figure 9. Illustration. Conceptual bar stress versus slip response.

Another term that has been often used in the report is the average bond strength at bond failure, 

μμTEST. In general, the load transfer between the reinforcing bar and the surrounding concrete 

materials is assumed as following. At the beginning of the axial loading of the reinforcing bar, 

the outermost lug exerts a bearing force on the surrounding concrete materials and this bearing 

force at the outermost lug plus the friction force and chemical adhesion contribute to the bond 

strength at this stage. As load increases, this bearing force causes crushing of concrete materials 

in the vicinity of the outermost lug, the bar slips, and most of the friction force and chemical 

adhesion are lost. The slip causes the bearing reaction of next adjacent lugs, which contribute to 

the resisting the applied axial load. At ultimate load, it is assumed that all the lugs bear against 

concrete and help resist the axial load and that the bond stress distribution is uniform. The 

average bond strength can be calculated by dividing the bond force at failure by the overall 

contact area, using the equation in Figure 10.

Figure 10. Equation. Average bond stress in reinforcing bar.

In this equation, ffs,max is the bar stress at bond failure, ddb is the bar diameter, and lld is the 

embedment length. The bond stress distribution for reinforcing bar in UHPC will be discussed in 

the later section where the effect of embedment length is investigated. 

0.0 1.3 2.5 3.8 5.1 6.4

0

138

276

414

552

690

827

0

20

40

60

80

100

120

0 0.05 0.1 0.15 0.2 0.25

Bar Slip (mm)

Bar Stress 

fs (MPa)

Bar Stress 

fs (ksi)

Bar Slip (in.) 

fs,crack

( fs,max, s1)

μμTTTTTTTT = ffss,mmmmmm ππddbb

2⁄4

ππddbb lldd

= ffss,mmmmmm ddbb

4lldd
25

As mentioned in the introduction and also will be discussed in later sections, there are many 

factors that affect bond strength. The main parameters that this study investigated include the bar

type and size, embedment length, side cover, bar spacing, and UHPC compressive strength. The 

specimens are named in a manner to be able illustrate all these variables. The specimen notation 

will be explained in an example in the following. Given an example specimen named B5-L6dS2d-Sp4-1D-B2S1, the first term B5 represents the type and the size of the reinforcing bar, and 

the letter is for the bar type (B for uncoated black reinforcing bar, M for A1035 high strength 

reinforcing bar, E for epoxy coated reinforcing bar) and the number is for the bar size (for 

example, 5 for No. 5 bar); L6d represents a designed embedment length of six times of the 

testing bar diameter; S2d represents a designed side cover of two times of the testing bar

diameter; Sp4 represents a designed center to center spacing of 4 in. (10.2 cm) between the 

testing bar and the nearest No.8 splice bar extending from the precast slab;1D represents the age 

(days) of the UHPC material at testing, which is one day in the example; B2S1 represents the 

Batch No. 2 of the UHPC casting and the specimens were cast on the precast Slab No. 1. The 

actual measurement of UHPC compressive strength at testing (f'c), bar embedment length (ld), bar

spliced length (ls), side cover (cso), and clear spacing to nearest No. 8 bar (2csi) are reported. The 

same notation will be used through the study.

It should be noted that the embedment length and side cover are defined in terms of bar diameter 

while the bar spacing is defined in terms of actual measurement in inches. The decision to define 

bar spacing in terms of a physical measurement results from the fact that the No. 8 bars 

extending from the precast slabs were spaced at either 8 or 12 in. (203 or 305 mm). In many 

cases, the testing bar was placed in the middle of the two No. 8 bars, therefore, the center-tocenter spacing was either 4 or 6 in. (102 or 152 mm).

CRACKING AND DAMAGE MECHANISM

In general, the transfer of force from the reinforcing steel to the surrounding concrete is mainly 

through mechanical anchorage or bearing of the reinforcing bar ribs against the concrete surface, 

with chemical adhesion and frictional forces between the bar and the concrete playing a minimal 

role. For the pullout tests in this study, the reinforcing bar are lap spliced, as shown in Figure 

11a, and the force on the testing bar is transferred to the concrete, which, in turn, transferred the 

force to adjacent No. 8 bars that extend from the precast concrete slab. The tensile forces due to 

this bearing effect could cause crack openings in a diagonal direction, as shown in Figure 11b. 

The wedging action of the deformations on the reinforcing bar could also cause hoop tensile 

stresses which can initiate splitting cracks as shown in Figure 11b. 
26

Figure 11. Illustration. Pullout tests: (a) forces on bars; and (b) crack patterns.

For tests in this study wherein the failure was not caused by reinforcing bar tensile rupture, the 

majority of the tests expressed a bond failure associated with splitting cracks, either split to the 

adjacent No.8 bars (Figure 12a), or to the side face (Figure 12b), or both (Figure 12c). In some 

cases, a UHPC tensile failure was observed wherein the tensile force separates a roughly planar

region of concrete from the rest of the specimen, as shown in Figure 12d. In general, the 

specimens with UHPC tensile failures had smaller concrete side cover, demonstrating less bond 

strength than those with splitting failures. It should be noted that in cases with splitting failure, 

diagonal cracks would still form but would not be the control failure mode as shown in Figure 

13. Figure 13a shows a few conical cracks observed with unaided vision; on this same specimen, 

when denatured alcohol was sprayed on the surface, more diagonal cracks appeared after the 

denatured alcohol evaporated from the surface, as shown in the Figure 13b. In almost all cases, 

the diagonal cracks like those in Figure 13 were observed. Conical surface failure around the 

reinforcing steel, as shown in Figure 14, was also observed in some cases. 

In most structural applications, splitting failure is more common (ACI 408 R-03) (17) and the 

majority of the tests in this study failed with splitting cracks. When the effect of different 

parameters on bond strength is evaluated in later sections of this chapter, the analysis only 

includes those with splitting failures (Figure 12a, b, and c) and those failed with splitting cracks 

combined with small conical surfaces failures (Figure 14). In the section where the design 
27

recommendations are developed, the specimens with UHPC tensile failures and the specimens 

with bar rupture are also included in the analysis.

Figure 12. Photo. Crack patterns: (a) longitudinal splitting cracks to adjacent No. 8 

bars; (b) splitting cracks to side face; (c) splitting cracks to side face and adjacent 

No. 8 bars; and (d) UHPC tensile failure with opened diagonal cracks.

(a) (b)

(c) (d)
28

Figure 13. Photo. Diagonal crack observation: (a) visual inspection; and (b) crack 

inspection with denatured alcohol.

Figure 14. Photo. Conical surface failure: (a) conical surface around the bar; and 

(b) conical surface extended to the side face.

(a) (b)

(a) (b)
29

FACTORS AFFECTING BOND

The factors affecting bond performance will be discussed in this section. The effect of casting 

orientation will be first presented. Then the parameters, including embedment length, concrete 

side cover, bar spacing, UHPC compressive strength, bar size, bar type, and bar yield strength, 

are evaluated. 

Casting Orientation

Two casting orientations, either cast on side or cast upright (see Figure 8), were compared. It 

should be noted that, other than the casting orientation, each pair of the comparison specimens 

were identical specimens that were cast at the same time. A total of nine pairs of specimens were 

tested and the results are presented in Table 4. 

As shown in Table 4, there was no appreciable difference between side-cast specimens and 

upright-cast specimens in eight of the nine pairs. In the one remaining pair, a difference of 

19.7% was observed. For the purpose of easy construction and casting, the upright orientation 

was used in the rest of the study.

In this early stage of investigation, it was noted that with an embedment length of only 6db and 

side cover of 2db (specimens B5-L6d-S2d-Sp4-1D-B2S1 and B5-L6d-S2d-Sp4-1D-B2S2), the 

bond strength was already close to, or even beyond the yield strength of Grade 60 uncoated bar. 

To minimize the effect of bar yielding on bond strength when investigating other factors, the 

majority of the tests were conducted using A1035 high strength bar. The effect of reinforcing bar

yielding before bond failure on bond strength will be discussed in the later section where the 

reinforcing bar type was evaluated.

During the investigation, it was also noted that the very end specimens that are close to the

casting point (where the large majority of the UHPC is poured into the formwork) consistently 

displayed lower bond strength than specimens at the other positions. This is probably due to the 

variation of fiber distribution inside the UHPC. The results from the end specimens close to 

casting point are included in the section wherein the design recommendations are developed, but

excluded from the sections of the report wherein the effect of different design parameters (ld, cso,

csi, f'c, etc.) on bond strength is analyzed. 
30

Table 4. Test Specimens – Effect of Casting Orientation.

Cast 

Orientation* Batch ID† f'c, ksi ld, in.

ls, 

in.

cso, 

in.

csi,

in. fs,max, ksi s, in. fs,crack,ksi

μTEST, 

ksi

Difference, 

%

Upright B5-L6d-S2d-Sp4-1D-B2S1 13.4 3.8 2.8 1.1 1.5 82 0.091 NA 3368 -19.7 Side B5-L6d-S2d-Sp4-1D-B2S2 13.4 3.9 2.9 1.2 1.3 67 0.061 20 2706

Upright B5-L8d-S2d-Sp4-1D-B2S1 13.4 5.3 4.3 1.2 1.5 96 0.205 24 2857 2.8 Side B5-L8d-S2d-Sp4-1D-B2S2 13.4 5.1 4.1 1.4 1.5 95 0.215 NA 2936

Upright B5-L10d-S2d-Sp4-1D-B2S1 13.4 6.3 5.3 1.2 1.6 94 0.128 22 2335 -6.2 Side B5-L10d-S2d-Sp4-1D-B2S2 13.4 6.3 5.3 1.4 1.5 88 0.167 NA 2189

Upright M5-L12d-S2d-Sp4-1D-B2S1 13.4 7.6 6.6 1.2 1.5 127 0.103 33 2603 1.6 Side M5-L12d-S2d-Sp4-1D-B2S2 13.4 7.6 6.6 1.3 1.6 129 0.090 30 2645

Upright B5-L8d-S2d-Sp4-7D-B2S1 19.5 5.1 4.1 1.1 1.5 94 0.162 21 2913 0.7 Side B5-L8d-S2d-Sp4-7D-B2S2 19.5 5.1 4.1 1.4 1.6 96 0.184 20 2933

Upright B5-L8d-S2d-Sp4-7D-B2S1 19.5 5.1 4.1 1.1 1.5 95 0.078 NA 2922 0.8 Side B5-L8d-S2d-Sp4-7D-B2S2 19.5 5.1 4.1 1.4 1.6 97 0.075 NA 2947

Upright B5-L10d-S2d-Sp4-7D-B2S1 19.5 6.3 5.3 1.2 1.4 rupture‡ 0.269 27 - - Side B5-L10d-S2d-Sp4-7D-B2S2 19.5 6.3 5.3 1.3 1.6 rupture‡ 0.262 NA -

Upright B5-L10d-S2d-Sp4-7D-B2S1 19.5 5.9 4.9 1.2 1.4 rupture‡ 0.161 21 - - Side B5-L10d-S2d-Sp4-7D-B2S2 19.5 6.3 5.3 1.4 1.6 rupture‡ 0.197 24 -

Upright M5-L12d-S2d-Sp4-7D-B2S1 19.5 7.6 6.6 1.2 1.4 rupture‡ 0.135 27 - - Side M5-L12d-S2d-Sp4-7D-B2S2 19.5 7.5 6.5 1.4 1.5 rupture‡ 0.152 NA - * Refer to Figure 8. ‡ Bar ruptured before bond failure. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm

†

The column headings are defined as follows:

• Batch ID notation example: B5-L6d-S2d-Sp4-1D-B2S1,the first term B5 represents the type and the size of the bar, and the letter is for the bar type (B 

for uncoated black bar, M for A1035 high strength bar, E for epoxy coated bar) and the number is for the bar size (for example, 5 for No. 5 bar); L6d 

represents a designed embedment length of six times of the testing bar diameter; S2d represents a designed side cover of two times of the testing bar

diameter; Sp4 represents a designed center to center spacing of 4 in. (10.2 cm) between the testing bar and the nearest No.8 splice bar extending from the 

precast slab;1D represents the age (days) of the UHPC material at testing, which is one day in the example; B2S1 represents the batch No. 2 of the UHPC 

casting and the specimens were cast on the pre-cast slab No. 1. 

• f'c: UHPC compressive strength at testing;

• ld, ls, cso and csi: actual measurement of embedment length, spliced length, side cover, and half the clear spacing to nearest No. 8 bar (refer to Figure 3).

• fs,max and s1 represent the bar stress and bar slip at bond failure, respectively.

• fs,crack represents the bar stress when the first crack was observed.

• μTEST, refer to the equation in Figure 10.

• Difference, the percentage difference between the specimen cast on side and the specimen cast upright.

30
31

Effect of Embedment Length

The effect of embedment length on bond strength is analyzed in this section. It was evaluated by 

varying the embedment length while keeping other factors constant, including side cover, bar 

spacing, and concrete compressive strength. The test matrix is presented in Table 5. A total of 37 

tests (grouped into four sets) were included and all specimens used A1035 No. 5 bar. In the first 

set, the embedment lengths included 4db, 6db, 8db, and 10db; the side cover was designed to be 

constant at 2db; the center-to-center spacing between the testing bar and the nearest No. 8 bar 

was kept constant at 4 in. (10 cm); and the tests were conducted at one day after casting when the 

UHPC compressive strength averaged 13.7 ksi (90 MPa). In Set 2, similar specimens as those in 

Set 1 were tested except that the specimens were tested at seven days after casting and the 

compressive strength averaged 19.4 ksi (133 MPa). In Sets 3 and 4, while the embedment length 

was varied, the side cover was increased to 3.5db and 3db, respectively, compared with 2db in 

Sets 1 and 2. More details of the specimen design and actual measurement are presented in 

Table 5.

The bar stress at bond failure versus the embedment length for all the specimens is plotted in 

Figure 15. As shown in Figure 15, increasing the embedment length of a reinforcing bar 

increases the bond strength. The relationship between the bar stress at bond failure and the 

bonded length is nearly linear, similar to that observed in normal strength concrete 

(ACI 408 R-03) (17)

. The linear relationship between bond force and the bonded length in normal 

strength concrete is often explained based on the assumption that all lugs bear against concrete at 

the ultimate stage and help in resisting the applied axial force, therefore at ultimate the bond 

stress distribution is nearly uniform. However, the bond stress distribution in high strength 

conventional concrete, with compressive strength over 13 ksi (90 MPa) and without fiber 

reinforcement, was found to be not uniform based on a study conducted by Azizinamini et al. (19)

. 

Azizinamini et al. noted that for high strength concrete, the increase in bearing capacity is more 

than the increase in tensile strength, which in turn, would prevent crushing of the concrete in the 

vicinity of each lug to the extent that would otherwise take place in normal strength concrete. In 

other words, the high strength concrete would crack before crushing due to the less than 

proportional increase in tensile strength compared with bearing capacity. All lugs may not 

participate in resisting applied axial load before the concrete cracks, and the first few lugs

contribute the most. The linear relationship observed in this study implies that the behavior 

attributed to conventional high strength concretes by Azizinamini et al.(19) may not be present in 

UHPC, potentially due to the enhanced pre- and post-cracking tensile response of the UHPC. 
32

Table 5. Test specimens – effect of embedment length.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi

Set 1

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.56 1.56 1.19 1.53 43 0.033 NA

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.69 1.69 1.20 1.56 49 0.020 NA

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.69 3.44 1.16 1.56 77 0.042 45

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.81 3.56 1.16 1.38 84 0.053 42

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.81 2.81 1.29 1.38 82 0.053 58

M5-L8d-S2d-Sp4-1D-B3S1 13.2 5.00 4.00 1.23 1.44 96 0.065 58

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.60 3.60 1.25 1.47 108 0.057 68

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.94 3.94 1.10 1.53 106 0.050 NA

M5-L8d-S2d-Sp4-1D-B9S4 13.7 5.25 4.25 1.18 1.41 121 0.065 77

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.25 5.25 1.18 1.47 144 0.082 77

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.38 5.38 1.24 1.40 113 0.075 61

M5-L10d-S2d-Sp4-1D-B9S4 13.7 6.31 5.31 1.17 1.53 132 0.076 65

Set 2

M5-L4d-S2d-Sp4-7D-B1S1 19.9 2.36 1.36 1.18 1.49 67 0.036 NA

M5-L4d-S2d-Sp4-7D-B3S1 19.5 2.44 2.19 1.21 1.44 59 0.041 40

M5-L6d-S2d-Sp4-7D-B1S1 19.9 3.29 2.29 1.37 1.65 91 0.072 NA

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.75 3.50 1.25 1.56 91 0.068 52

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.81 2.81 1.20 1.50 90 0.052 58

M5-L6d-S2d-Sp4-7D-B4S2 19.2 3.88 2.88 1.14 1.44 83 0.047 65

M5-L8d-S2d-Sp4-7D-B3S1 19.5 5.06 4.06 1.22 1.56 114 0.059 58

M5-L8d-S2d-Sp4-7D-B9S4 18.8 5.00 4.00 1.12 1.50 127 0.070 NA

M5-L10d-S2d-Sp4-7D-B9S4 18.8 6.12 5.12 1.11 1.56 154 0.100 NA

M5-L10d-S2d-Sp4-7D-B9S4 18.8 6.06 5.06 1.15 1.47 153 0.115 NA

M5-L10d-S2d-Sp4-7D-B3S1 19.5 6.19 5.19 1.17 1.50 145 0.091 74

32
33

Table 5(cont’d). Test specimens – effect of embedment length.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi

Set 3

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.88 3.63 2.24 1.63 96 0.043 NA

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.81 2.81 2.25 1.56 90 0.045 79

M5-L8d-S3.5d-Sp4-1D-B4S2 13.6 5.06 4.06 2.35 1.56 136 0.080 65

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.13 4.13 2.08 1.56 137 0.068 97

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 6.06 2.20 1.56 155 0.108 90

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 5.31 2.24 1.63 166 0.161 68

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 5.31 2.33 1.56 158 0.099 125

Set 4

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.44 2.44 1.82 1.50 85 0.037 NA

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.75 2.75 1.83 1.53 84 0.051 NA

M5-L6.7d-S3d-Sp4-1D-B10S4 13.9 4.22 3.22 1.87 1.59 103 0.045 NA

M5-L6.7d-S3d-Sp4-1D-B10S4 13.9 4.13 3.13 1.85 1.50 115 0.060 NA

M5-L8d-S3d-Sp4-1D-B10S4 13.9 5.44 4.44 1.92 1.50 138 0.072 NA

M5-L8d-S3d-Sp4-1D-B10S4 13.9 5.25 4.25 1.86 1.59 134 0.080 NA

M5-L10d-S3d-Sp4-1D-B10S4 13.9 6.13 5.13 1.83 1.50 141 0.053 NA

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm. 

33
34

Figure 15. Graph. Effect of embedment length: fs,max versus embedment length ld.

Side Cover

Concrete cover and bar spacing play important roles in bond strength. An understanding of the 

bond behavior in normal non-fiber reinforced concrete is necessary. As stated in 

ACI 408 R-03(17), for bond failure involving splitting of the concrete, the nature of the splitting 

failure depends on whether the concrete cover, cso, is smaller than csi, which is 1/2 of the clear 

spacing to adjacent bar. The demonstration of cso and csi is presented in Figure 16 and also in

Figure 3 in Chapter 2. When cso is smaller than csi, the splitting crack occurs through the cover to 

the free surface, as shown in Figure 16a. When csi is smaller than cso, the splitting crack forms 

between the reinforcing bars as shown in Figure 16b. In ACI 318 Building Code Requirements 

for Structural Concrete,

(21) the actual values of csi are used for development length calculations. 

In the Canadian requirements for reinforced concrete design (CSA standard A23.3-94),

(21) a 

larger value defined as [(4/3)csi +(1/6)db] is used. Zuo and Darwin (1998) (22) suggested using 

either 1.6csi when using a multiple of csi or using csi + 0.25 in. (csi + 6.4 mm) when a constant 

value is added to csi. Darwin et al. (1996a) (23) explained that the reason why a larger value than 

the actual value of csi is used is most likely “due to the longer effective crack lengths that occur 

when concrete splits between bars.” The presence of fiber reinforcement in UHPC can be 

expected to increase the resistance to splitting crack between bars and thus an even larger value 

than the actual value of csi between bars may be necessary. In the present analysis, both the term 

csi representing 1/2 of the clear spacing as well as the actual clear spacing, 2csi, are compared 

with side cover cso. 

0 25 51 76 102 127 152 178

0

138

276

414

552

690

827

965

1,103

1,241

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7

Embedment Length, ld (mm)

Bar Stress at Bond Failure, fs,max (MPa)

Bar Stress at Bond Failure, fs,max (ksi)

Embedment Length, ld (in.)

Set 1

Set 2

Set 3

Set 4

Linear (Set 2)

Linear (Set 2)

Linear (Set 3)

Linear (Set 4)

Set 1, R2=0.90

Set 2, R2=0.95

Set 3, R2=0.96

Set 4, R2=0.89
35

(a) (b)

Figure 16. Illustration. Bond splitting cracks: (a) csi > cso; and (b) csi < cso.

Within this study, a total of 37 specimens were tested in five sets and the results are presented in 

Table 6. Using the same philosophy that has been used in previous sections, the specimens were 

designed to have the same parameters except for side cover. A1035 No. 5 bars were used and all 

specimens were designed to have the same bar spacing to the nearest No. 8 bar. As shown in 

Table 6, for Set 1 an embedment length of 6db was used and the side cover included nominal 

values of 2db, 2.7db, 3db, and 3.5db [corresponding to UHPC strip widths of 3 1/8, 4, 4 3/8, and 5 

in. (7.9 to 10.2, 11.1 and 12.7 cm), respectively]. Set 2 had the same design as Set 1, except that 

the embedment length was increased to 8db. In Set 3, specimens with a constant embedment 

length of 10db and a varied side cover of 2db and 3.5db were tested. All specimens in Sets 1, 2, 

and 3 were tested at one day after UHPC casting, with an average compressive strength of 13.7 

ksi (94 MPa). Specimens in Sets 4 and 5 were tested at seven days after the UHPC casting, with 

an average compressive strength of 19.4 ksi (133 MPa). Specimens in Set 4 had an embedment 

length of 6db and side covers of 2db, 3db, and 3.5db, while specimens in Set 5 had an embedment 

length of 8db and side covers of 2db and 3.5db. 

Based on the results shown in Table 6, it is clear that the maximum bar stress at bond failure 

increased as the side cover increased. For example, in Set 2 where a designed embedment length 

of 8db was used, the three specimens with a 2db side cover had bar stresses at bond failure of 

108, 106, and 121 ksi (741, 729 and 833 MPa); when the side cover was increased to 3.5db, the 

two specimens had bar stresses at bond failure of 136 and 137 ksi (940 and 943 MPa). 
36

Table 6. Test specimens – effect of side cover.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.69 3.44 1.16 1.56 77 0.042 45 3269

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.81 3.56 1.16 1.38 84 0.053 42 3430

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.81 2.81 1.29 1.38 82 0.053 58 3363

M5-L6d-S2.7d-Sp4-1D-B9S3 13.7 4.25 3.25 1.67 1.50 93 0.052 87 3420

M5-L6d-S2.7d-Sp4-1D-B9S3 13.7 4.13 3.13 1.66 1.53 98 0.057 90 3725

M5-L6d-S3d-Sp4-1D-B8S3 13.8 3.81 2.81 1.78 1.53 103 0.045 82 4211

M5-L6d-S3d-Sp4-1D-B8S3 13.8 3.81 2.81 1.78 1.56 88 0.039 86 3608

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.44 2.44 1.82 1.50 85 0.037 NA 3863

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.75 2.75 1.83 1.53 84 0.051 NA 3494

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.88 2.88 2.24 1.63 96 0.043 NA 3884

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.81 2.81 2.25 1.56 90 0.045 79 3707

Set 2

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.60 3.60 1.25 1.47 108 0.057 68 3649

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.94 3.94 1.10 1.53 106 0.050 0 3346

M5-L8d-S2d-Sp4-1D-B9S4 13.7 5.25 4.25 1.18 1.41 121 0.065 77 3595

M5-L8d-S2.7d-Sp4-1D-B9S3 13.7 5.31 4.31 1.55 1.47 129 0.074 87 3795

M5-L8d-S2.7d-Sp4-1D-B9S3 13.7 5.13 4.13 1.67 1.47 128 0.065 0 3906

M5-L8d-S3d-Sp4-1D-B8S3 13.8 5.13 4.13 1.49 1.47 134 0.073 95 4096

M5-L8d-S3d-Sp4-1D-B8S3 13.8 4.94 3.94 1.80 1.56 126 0.060 84 3974

M5-L8d-S3.5d-Sp4-1D-B4S2 13.6 5.06 4.06 2.35 1.56 136 0.080 65 4208

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.13 4.13 2.08 1.56 137 0.068 97 4168

36
37

Table 6 (cont’d).Test specimens – effect of side cover.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 3

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.25 5.25 1.18 1.47 144 0.082 77 3602

M5-L10d-S2d-Sp4-1D-B9S4 13.7 6.31 5.31 1.17 1.53 132 0.076 65 3276

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 6.06 2.20 1.56 155 0.108 90 3843

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 5.31 2.24 1.63 166 0.161 68 4116

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.31 5.31 2.33 1.56 158 0.099 125 3911

Set 4

M5-L6d-S2d-Sp4-7D-B1S1 19.9 3.29 2.29 1.37 1.65 91 0.072 NA 4326

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.75 3.50 1.25 1.56 91 0.068 52 3812

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.81 2.81 1.20 1.50 90 0.052 58 3695

M5-L6d-S2d-Sp4-7D-B4S2 19.2 3.88 2.88 1.14 1.44 83 0.047 65 3335

M5-L6d-S3d-Sp4-7D-B10S4 19.6 3.94 2.94 1.85 1.66 118 0.058 NA 4673

M5-L6d-S3d-Sp4-7D-B10S4 19.6 3.88 2.88 1.85 1.56 111 0.055 NA 4486

M5-L6d-S3d-Sp4-7D-B10S4 19.6 4.19 3.19 1.89 1.53 117 0.050 NA 4359

M5-L6d-S3.5d-Sp4-7D-B4S2 19.2 3.75 3.50 2.31 1.56 117 0.051 106 4876

M5-L6d-S3.5d-Sp4-7D-B4S2 19.2 3.75 2.75 2.31 1.56 124 0.061 106 5148

Set 5

M5-L8d-S2d-Sp4-7D-B3S1 19.5 5.06 4.06 1.22 1.56 114 0.059 58 3515

M5-L8d-S2d-Sp4-7D-B9S4 18.8 5.00 4.00 1.12 1.50 127 0.070 NA 3979

M5-L8d-S3.5d-Sp4-7D-B4S2 19.2 5.00 4.00 2.27 1.56 145 0.096 87 4521

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm. 

37
38

Note that specimens in Sets 1, 2, and 3 had the same design except for embedment length and 

side cover. The same is true for specimens in Sets 4 and 5. To create a bigger data pool, 

specimens in Sets 1, 2, and 3 and the specimens in Sets 4 and 5 are combined by converting bar 

stress at bond failure to bond stress to offset the effect of different embedment lengths (refer to 

equation in Figure 10). The bond stress is plotted versus side cover for specimens in Sets 1, 2 and 

3 and specimens in Sets 4 and 5 in Figure 17 and Figure 18, respectively. With constant bar 

spacing (2csi) for all specimens, straight lines representing the point where the side cover cso is 

equal to csi and 2csi are included in the figures.

As shown in Figure 17 and Figure 18, the bond strength increases as the side cover increases. It 

is noted that when the side cover (cso) is bigger than half of the clear spacing (csi), the bond 

strength still increases as the side cover increases, instead of being controlled by the constant 

value of csi. This proves the early assumption that a greater bar spacing value than csi should be 

used due to the presence of the fibers. All specimens had side covers (cso) less than the clear bar 

spacing (2csi). It is reasonable to predict that when the side cover is large enough, the bar spacing 

would become the controlling factor and the bond strength would reach a plateau.

Figure 17. Graph. Effect of side cover: bond strength μTEST versus side cover for 

specimens in Sets 1, 2 and 3. The csi is constant. 

0 25 51 76 102

17

21

24

28

31

34

38

2500

3000

3500

4000

4500

5000

5500

0 1 2 3 4

Side Cover, cso (mm)

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Side Cover, cso (in.)

Set 1

Set 2

Set 3

cso < csi csi < cso < 2csi cso > 2csi

csi

2csi
39

Figure 18. Graph. Effect of side cover: bond strength μTEST versus side cover for 

specimens in Sets 4 and 5. The csi is constant.

Bar Spacing

The effect of bar spacing on bond performance is analyzed in this section. Details for the 

specimens are presented in Table 7. A1035 bars were used and a total of 46 specimens were 

included in four sets. In each set of tests, the side cover (cso) and embedment length were 

designed to be constant while the bar spacing (csi) varied. It should be noted that the bar spacing 

to the nearest adjacent No. 8 bars was designed in terms of actual length in inches instead of bar 

diameter. In Set 1, a constant embedment length of 8db (A1035 No. 5 bar) and a constant side 

cover of 2db were used; the bar spacing, csi, varied from 0.1 to 5.7 in. (0.3 to 14.5 cm). All tests 

were conducted at one day after UHPC casting with an average compressive strength of 13.7 ksi 

(94.5 MPa). It should be pointed out that the specimens with a bar spacing of 0.1 in. (0.3 cm) 

were originally designed to have a contact lap splice, and the actual measurement indicated a bar 

spacing of 0.1 in. (0.3 cm). Given the small measured spacing value, these specimens were 

considered to have contact lap splices in the study. 

All four sets specimens demonstrated similar trends and the results from Set 1 are discussed first

here. As shown in Table 7, the bar stress at bond failure was only about 83 ksi (572 MPa) for a 

contact lap splice (the first two specimens in Set 1), and it increased to over 95 ksi (655 MPa) 

when csi was increased from zero to the range of 0.5 to 2.6 in. (1.3 to 6.6 cm). When csi was

increased to over 3.5 in. (8.9 cm), the bar stress at bond failure dropped to as low as 70 ksi 

(483 MPa). 

0 25 51 76 102

17

21

24

28

31

34

38

41

2500

3000

3500

4000

4500

5000

5500

6000

0 1 2 3 4

Side Cover, cso (mm)

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Side Cover, cso (in.)

Set 4

Set 5

cso < csi csi < cso < 2csi cso > 2csi

csi 2csi
40

Table 7. Test specimens – effect of bar spacing

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

M5-L8d-S2d-Sp0-1D-B6S7 13.9 5.0 4.0 1.3 0.1 82 0.037 NA 2576

M5-L8d-S2d-Sp0-1D-B6S7 13.9 5.1 4.1 1.2 0.1 83 0.036 NA 2575

M5-L8d-S2d-Sp2-1D-B11S4 13.6 5.1 4.1 1.2 0.5 119 0.050 77 3642

M5-L8d-S2d-Sp2-1D-B11S4 13.6 4.8 3.8 1.3 0.6 109 0.065 71 3594

M5-L8d-S2d-Sp4-1D-B3S1 13.2 5.0 4.0 1.2 1.4 96 0.065 58 2995

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.6 3.6 1.2 1.5 108 0.057 68 3649

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.9 3.9 1.1 1.5 106 0.050 NA 3346

M5-L8d-S2d-Sp6-1D-B3S6 13.2 5.1 4.1 1.4 2.6 101 0.075 52 3075

M5-L8d-S2d-Sp6-1D-B6S7 13.9 5.1 4.1 1.2 2.6 96 0.072 48 2965

M5-L8d-S2d-Sp6-1D-B6S7 13.9 5.0 4.0 1.3 2.6 95 0.074 58 2968

M5-L8d-S2d-Sp8-1D-B8S4 13.8 4.8 3.8 1.2 3.6 78 0.068 69 2545

M5-L8d-S2d-Sp8-1D-B8S4 13.8 5.0 4.0 1.2 3.5 82 0.066 NA 2571

M5-L8d-S2d-Sp8-1D-B11S4 13.6 5.0 4.0 1.2 3.5 86 0.076 57 2691

M5-L8d-S2d-Sp8-1D-B11S4 13.6 5.1 4.1 1.2 3.6 94 0.120 54 2866

M5-L8d-S2d-Sp12-1D-B6S7 13.9 5.0 4.0 1.3 5.6 70 0.081 45 2178

M5-L8d-S2d-Sp12-1D-B11S4 13.6 5.0 4.0 1.2 5.7 85 0.124 55 2646

Set 2

M5-L8d-S3.5d-Sp0-1D-B7S7 13.5 4.9 3.9 2.1 0.1 105 0.000 NA 3372

M5-L8d-S3.5d-Sp0-1D-B7S7 13.5 5.3 4.3 2.2 0.1 109 0.000 NA 3245

M5-L8d-S3.5d-Sp2-1D-B11S6 13.6 5.1 4.1 2.2 0.6 159 0.059 58 4858

M5-L8d-S3.5d-Sp2-1D-B11S6 13.6 5.1 4.1 2.2 0.7 149 0.084 68 4528

M5-L8d-S3.5d-Sp4-1D-B4S2 13.6 5.1 4.1 2.4 1.6 136 0.000 NA 4208

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.1 4.1 2.1 1.6 137 0.000 NA 4168

40
41

Table 7 (cont’d) Test specimens – effect of bar spacing

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 2

M5-L8d-S3.5d-Sp6-1D-B7S7 13.5 5.1 4.1 2.2 2.5 137 0.032 90 4180

M5-L8d-S3.5d-Sp6-1D-B7S7 13.5 5.3 4.3 2.1 2.4 145 0.048 NA 4314

M5-L8d-S3.5d-Sp8-1D-B7S3 13.5 5.2 4.2 2.0 3.4 115 0.131 81 3452

M5-L8d-S3.5d-Sp8-1D-B7S3 13.5 4.9 3.9 2.0 3.7 108 0.092 106 3434

M5-L8d-S3.5d-Sp12-1D-B7S7 13.5 5.1 4.1 2.2 5.8 129 0.080 65 3925

M5-L8d-S3.5d-Sp12-1D-B7S7 13.5 4.9 3.9 2.2 5.4 103 0.068 97 3288

M5-L8d-S3.5d-Sp12-1D-B11S6 13.6 5.1 4.1 2.2 5.5 107 0.082 74 3260

Set 3

M5-L6d-S2d-Sp0-7D-B5S1 18.9 3.9 2.9 1.1 0.0 78 0.093 100 3142

M5-L6d-S2d-Sp0-7D-B5S1 18.9 3.8 2.8 1.1 0.0 84 0.086 55 3506

M5-L6d-S2d-Sp2-7D-B5S1 18.9 3.8 2.8 1.1 0.6 88 0.079 81 3589

M5-L6d-S2d-Sp2-7D-B5S1 18.9 3.8 2.8 1.1 0.7 99 NA 81 4131

M5-L6d-S2d-Sp4-7D-B1S1 19.9 3.3 2.3 1.4 1.6 91 0.085 87 4326

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 2.8 1.2 1.6 91 0.112 61 3812

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 2.8 1.2 1.5 90 NA NA 3695

M5-L6d-S2d-Sp4-7D-B4S2 19.2 3.9 2.9 1.1 1.4 83 0.131 NA 3335

M5-L6d-S2d-Sp8-7D-B5S1 18.9 4.0 3.0 1.1 3.5 77 0.091 74 2999

Set 4

M4-L6d-S3.5d-Sp0-1D-B12S5 11.9 2.9 1.9 1.7 0.1 90 0.108 60 3894

M4-L6d-S3.5d-Sp0-1D-B12S5 11.9 3.1 2.1 1.8 0.1 99 0.000 NA 4051

M4-L6d-S3.5d-Sp2-1D-B12S5 11.9 3.1 2.1 1.7 0.5 111 0.000 NA 4516

M4-L6d-S3.5d-Sp4-1D-B12S5 11.9 3.1 2.1 1.7 1.6 106 0.032 NA 4243

M4-L6d-S3.5d-Sp4-1D-B12S5 11.9 3.1 2.1 1.6 1.4 97 0.036 NA 3867

M4-L6d-S3.5d-Sp8-1D-B12S5 11.9 2.7 1.7 1.7 3.5 81 0.042 NA 3751

M4-L6d-S3.5d-Sp8-1D-B12S5 11.9 3.1 2.1 1.7 3.6 85 0.041 NA 3483

M4-L6d-S3.5d-Sp8-1D-B12S5 11.9 3.1 2.1 1.7 3.6 97 0.038 NA 3867

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm. 

41
42

The bond stress (μTEST) is plotted versus bar clear spacing (2csi) for specimens in Set 1 in 

Figure 19. The bond stress (μTEST) is used in Figure 19 to account for the different embedment 

length of the compared specimens. It should be noted that the specimens in Set 1 were designed 

to have the same nominal embedment length, though the actual embedment length varied slightly 

between 4.8 and 5.1 in. (12.2 and 13.0 cm) with one having 4.6 in. (11.7 cm). The bar clear 

spacing (2csi) was chosen for the reason stated in previous section that a greater bar spacing 

value than csi should be used due to the presence of the fibers. The actual clear spacing 2csi was 

used in current study. Figure 19 also includes two straight lines, representing the points of 

2csi = cso and 2csi = lstan(θ), respectively. The meaning of 2csi and lstan(θ) are demonstrated in 

Figure 20. The 2csi represents the clear spacing to the nearest bar; ls is the lap splice length 

(instead of embedded length ld); and θ is the angle between the diagonal cracks and testing bar. 

The angle θ for the A1035 No.5 bar tested in this study was measured to be approximately 55 

degrees. The hypothesis of adding the two straight lines is as follows: when 2csi ≤ cso, where cso

has constant values in each set of comparison, the bond strength is controlled by the bar spacing 

2csi, with larger bar spacing resulting in higher bond strength; when cso < 2csi ≤ lstan(θ), the bond 

strength is controlled by constant side cover cso; and when 2csi > lstan(θ), the diagonal cracks 

would not intersect with the near No. 8 bars. In this last situation, the adjacent No.8 bars would 

not help to stop the propagation of the diagonal cracks and the bond strength would likely be 

primarily dependent on the mechanical performance of the UHPC. 

Figure 19. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens 

in Set 1. The cso is constant.

0 51 102 152 203 254 305

0

7

14

21

28

34

0

1000

2000

3000

4000

5000

0 2 4 6 8 10 12

Clear Spacing to Nearest No.8 Bar, 2csi (mm) 

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Clear Spacing to Nearest No.8 Bar, 2csi (in.) 

cso lstan(θ)

2csi < cso cso<2csi < lstan(θ) 2csi > lstan(θ)
43

Figure 20. Illustration. Geometrical demonstration of lstan(θ) and 2csi.

The bond strength is plotted versus 2csi in Figure 19, and as shown, only a very limited number 

of specimens fell in the range of 2csi < cso. When the testing bar was in contact with extended

No.8 bars (2csi near to zero), it expressed less bond strength than those with larger spacing. The 

bond strength for the two contact lap splice specimens was 2575 and 2576 psi (17.8 and 

17.8 MPa), respectively. For the specimens with bar spacing greater than zero but less than 

lstan(θ), the observed bond strength was about the same, close to or greater than 3000 psi (20.7 

MPa). Note that, other than the contact lap splice, the least bar spacing (center-to-center) that 

was tested in the study was 2 in. (5.1 cm), which is approximately 2db bar clear spacing. When 

the testing bar was placed further than lstan(θ) away from the adjacent No. 8 bars, the bond 

strength decreased, with an average bond stress of 2583 psi (17.8 MPa) for the six specimens in 

Set 1. 

The similar trend was also observed in the other three sets of specimens. The bond strength 

versus bar clear spacing curve for specimens in Sets 2, 3, and 4 are presented in Figure 21, 

Figure 22, and Figure 23, respectively. The specimens in Set 2 had similar design as those in 

Set 1, except that the side cover was increased from 2db to 3.5db. The specimens in Set 3 had a 

nominal embedment length of 6db and side cover of 2db and all tests were conducted at 7 days 

after UHPC casting, with an average compressive strength of 19.2 ksi (132 MPa). While A1035

No. 5 bars were used in Sets 1, 2 and 3, A1035 No. 4 bars were used in Set 4, with an 

embedment length of 6db and side cover of 3.5db. The bar spacing for specimens in Sets 2, 3, and 

4 was varied. The trend that can be noted from these series of tests is that specimens with the bar 

spacing between 2db and lstan(θ) have higher bond strength than those with a contact lap splice

and those with bar spacing bigger than lstan(θ). The bar spacing of 2db is the least clear spacing, 

other than contact lap splice, investigated in this study.
44

Figure 21. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens 

in Set 2. The cso is constant.

Figure 22. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens 

in Set 3. The cso is constant.

0 51 102 152 203 254 305

0

7

14

21

28

34

0

1000

2000

3000

4000

5000

0 2 4 6 8 10 12

Clear Spacing to Nearest No.8 Bar, 2csi (mm) 

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Clear Spacing to Nearest No.8 Bar, 2csi (in.) 

cso lstan(θ)

2csi < cso cso<2csi < lstan(θ) 2csi > lstan(θ)

0 51 102 152 203

0

7

14

21

28

34

0

1000

2000

3000

4000

5000

0 2 4 6 8

Clear Spacing to Nearest No.8 Bar, 2csi (mm) 

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Clear Spacing to Nearest No.8 Bar, 2csi (in.) 

cso lstan(θ)

2csi < cso cso<2csi < lstan(θ) 2csi > lstan(θ)
45

Figure 23. Graph. Effect of bar spacing: bond strength μTEST versus 2csi for specimens 

in Set 4. The cso is constant.

The average bond strength for specimens with bar spacing between 2db and lstan(θ) was 

compared with those with bar spacing out of the range and the results are presented in Table 8. 

As shown in Table 8, the reduction of bond strength is over twenty percent in most cases. The 

decrease on bond stress for contacted lap splice specimens is probably due to decreased contact 

area between the reinforcing bar and UHPC materials, especially considering the dispersion of 

the fiber reinforcement into the spaces near closely spaced bars, which is needed to locally 

enhance the mechanical resistance of the UHPC. This is contrary to early studies in normal nonfiber reinforced concrete (23,24,25)

, where it was concluded that tied spliced (zero spacing) bars had 

similar or even better bond strength than non-contact lap splices. When the bar clear spacing is 

larger than lstan(θ), the induced diagonal cracks from the pullout force will not intersect with the 

adjacent bar and the bond strength is primarily dependent on the performance of the individual 

bar in the UHPC.

Table 8. Bond strength reduction for bar clear spacing out of the range of 2db < 2csi < lstan(θ).

Bar clear spacing 2db< 2csi<lstan(θ) Contact lap splice 2csi>lstan(θ)

Avg. μTEST, psi Avg. μTEST, psi Reduction, % Avg. μTEST, psi Reduction, %

Set 1 3279 2575 21 2583 21

Set 2 4376 3309 24 3472 21

Set 3 3815 3324 13 2999 21

Set 4 NA 4154 NA 3842 NA

0 51 102 152 203

0

7

14

21

28

34

0

1000

2000

3000

4000

5000

0 2 4 6 8

Clear Spacing to Nearest No.8 Bar, 2csi (mm) 

Bond Strength, 

μTEST (MPa)

Bond Strength, 

μTEST (psi)

Clear Spacing to Nearest No.8 Bar, 2csi (in.) 

cso lstan(θ)

2csi < cso cso<2csi < lstan(θ) 2csi > lstan(θ)
46

UHPC Compressive Strength

The effect of UHPC compressive strength on bond strength is analyzed in this section. For the 

UHPC materials tested in this study, the average compressive strength was 13.5 ksi (93 MPa) at 

one day, 17.0 ksi (117 MPa) at three days, 19.4 ksi (133 MPa) at seven days, and 21.3 ksi 

(147 MPa) at 14 days.

A total of 41 specimens were included and all specimens were tested with A1035 No.5 bars. The 

details of all specimens are presented in Table 9. The specimens were grouped into three sets

based on side cover, and specimens with different embedment lengths were included in the same 

set. The specimens were grouped so that the specimens in each set can be either directly 

compared to those with the same embedment length or indirectly compared by comparing the

bond strength μTEST for all specimens. As shown in Table 9, in Set 1 a side cover of 2db with a 

constant bar spacing [center to center 4 in. (10 cm)] was used; specimens with embedment length 

of 4db, 6db, 8db, 10db, and 12db were tested at either 1, 3, or 7 days after casting. Set 2 specimens 

had a side cover of 3db with embedment length of either 6db or 6.7db and they were tested at 

either 1 or 7 days. Similarly, Set 3 specimens had a side cover of 3.5db and embedment length of 

either 6db or 8db; they were tested at either 1 or 7 days. 

As expected, an increase in the compressive strength increases the bond strength, as shown in 

Table 9. For example, for specimens with embedment length of 6db and side cover of 2db in Set 

1, the average bar stress at bond failure increased from 81 to 89 ksi (558 to 613 MPa) when the 

compressive strength increased from 13.5 to 19.5 ksi (93 to 135 MPa). In a separate comparison, 

when the embedment length was 12db with the UHPC compressive strength at 13.4 ksi 

(92 MPa), the average bar stress at bond failure was 128 ksi (883 MPa); increasing the UHPC 

compressive strength to 19.5 ksi (135 MPa) resulted in bar rupture, with bar stress over 160 ksi 

(1103 MPa) before bond failure. 

The relationship between the bond strength and UHPC compressive strength was also assessed. 

Traditionally, the effect of concrete properties on bond strength is represented by the square root 

of the compressive strength f’c

1/2, which is related to tensile strength of the concrete. This

representation is normally limited to a maximum concrete strength of 8000 psi (55 MPa) 

(ACI 408 R-03) (17)

. The relationship between the bond strength and the UHPC compressive 

strength is evaluated here. The bond strength μμTEST is plotted versus f’c and f’c

1/2 for specimens in 

Sets 1, 2, and 3 in Figure 24, Figure 25, and Figure 26, respectively. As shown in the figures, the 

correlation coefficient (R2

) values for all three sets of tests are low, no matter it is between μμTEST 

and f’c or between μμTEST and f’c

1/2. Since the UHPC material investigated is both high strength 

and fiber reinforced, other material properties besides compressive strength should be involved 

in the evaluating of bond strength. 
47

Table 9. Test specimens – effect of UHPC compressive strength.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.6 1.6 1.2 1.5 43 0.033 NA 2640

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.7 1.7 1.2 1.6 49 0.020 NA 2828

M5-L4d-S2d-Sp4-7D-B1S1 19.9 2.4 1.4 1.2 1.5 67 0.036 NA 4449

M5-L4d-S2d-Sp4-7D-B3S1 19.5 2.4 2.2 1.2 1.4 59 0.041 40 3781

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.7 3.4 1.2 1.6 77 0.042 45 3269

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 3.6 1.2 1.4 84 0.053 42 3430

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 2.8 1.3 1.4 82 0.053 58 3363

M5-L6d-S2d-Sp4-7D-B1S1 19.9 3.3 2.3 1.4 1.6 91 0.072 NA 4326

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 3.5 1.2 1.6 91 0.068 52 3812

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 2.8 1.2 1.5 90 0.052 58 3695

M5-L6d-S2d-Sp4-7D-B4S2 19.2 3.9 2.9 1.1 1.4 83 0.047 65 3335

M5-L8d-S2d-Sp4-1D-B3S1 13.2 5.0 4.0 1.2 1.4 96 0.065 58 2995

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.6 3.6 1.2 1.5 108 0.057 68 3649

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.9 3.9 1.1 1.5 106 0.050 NA 3346

M5-L8d-S2d-Sp4-3D-B1S1 17.3 4.8 3.8 1.4 1.3 108 0.075 NA 3506

M5-L8d-S2d-Sp4-3D-B9S4 16.6 5.2 4.2 1.3 1.4 111 0.066 NA 3330

M5-L8d-S2d-Sp4-7D-B3S1 19.5 5.1 4.1 1.2 1.6 114 0.059 58 3515

M5-L8d-S2d-Sp4-7D-B9S4 18.8 5.0 4.0 1.1 1.5 127 0.070 NA 3979

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.3 5.3 1.2 1.5 144 0.082 77 3602

M5-L10d-S2d-Sp4-1D-B9S4 13.7 6.3 5.3 1.2 1.5 132 0.076 65 3276

M5-L10d-S2d-Sp4-7D-B3S1 19.5 6.2 5.2 1.2 1.5 145 0.091 74 3653

M5-L10d-S2d-Sp4-7D-B9S4 18.8 6.1 5.1 1.1 1.6 154 0.100 NA 3935

M5-L10d-S2d-Sp4-7D-B9S4 18.8 6.1 5.1 1.2 1.5 153 0.115 NA 3944

47
48

Table 9 (cont’d). Test specimens – effect of UHPC compressive strength.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

M5-L12d-S2d-Sp4-1D-B2S1 13.4 7.6 6.6 1.2 1.5 127 0.103 106 2603

M5-L12d-S2d-Sp4-1D-B2S2 13.4 7.6 6.6 1.3 1.6 129 0.090 97 2645

M5-L12d-S2d-Sp4-7D-B2S1 19.5 7.6 6.6 1.2 1.4 bar rupture (>160 ksi) 0.135 87 NA

M5-L12d-S2d-Sp4-7D-B2S2 19.5 7.5 6.5 1.4 1.5 bar rupture (>160 ksi) 0.152 NA NA

Set 2

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.4 2.4 1.8 1.5 85 0.037 NA 3863

M5-L6d-S3d-Sp4-1D-B10S4 13.9 3.8 2.8 1.8 1.5 84 0.051 NA 3494

M5-L6d-S3d-Sp4-7D-B10S4 19.6 3.9 2.9 1.8 1.7 118 0.058 NA 4673

M5-L6d-S3d-Sp4-7D-B10S4 19.6 3.9 2.9 1.9 1.6 111 0.055 NA 4486

M5-L6.7d-S3d-Sp4-1D-B10S4 13.9 4.2 3.2 1.9 1.6 103 0.045 NA 3800

M5-L6.7d-S3d-Sp4-1D-B10S4 13.9 4.1 3.1 1.8 1.5 115 0.060 NA 4365

M5-L6.7d-S3d-Sp4-7D-B10S4 19.6 4.3 3.3 1.9 1.6 130 0.061 NA 4775

M5-L6.7d-S3d-Sp4-7D-B10S4 19.6 4.2 3.2 1.9 1.5 117 0.050 NA 4359

Set 3

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.9 3.6 2.2 1.6 96 0.043 NA 3884

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.8 2.8 2.2 1.6 90 0.045 79 3707

M5-L6d-S3.5d-Sp4-7D-B4S2 19.2 3.8 3.5 2.3 1.6 117 0.051 106 4876

M5-L6d-S3.5d-Sp4-7D-B4S2 19.2 3.8 2.8 2.3 1.6 124 0.061 106 5148

M5-L8d-S3.5d-Sp4-1D-B4S2 13.6 5.1 4.1 2.4 1.6 136 0.080 65 4208

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.1 4.1 2.1 1.6 137 0.068 97 4168

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.1 4.1 1.8 1.5 113 0.054 100 3477

M5-L8d-S3.5d-Sp4-7D-B4S2 19.2 5.0 4.0 2.3 1.6 145 0.096 87 4521

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm.

48
49

(a)

(b)

Figure 24. Graph. Effect of UHPC compressive strength: bond (a) uTEST versus f’c

and (b) uTEST versus f’c

1/2 for specimens in Set 1.

μTEST = 0.13 f'c + 1420 (psi)

R2 = 0.55

83 97 110 124 138 152

14

17

21

24

28

31

34

2000

2500

3000

3500

4000

4500

5000

12000 14000 16000 18000 20000 22000

UHPC Compressive Strength, f'c (MPa)

Bond Strength, 

uTEST (MPa)

Bond Strength, 

uTEST (psi)

UHPC Compressive Strength, f'c (psi)

Ld_4d

Ld_6d

Ld_8d

Ld_10d

ld = 4db

ld = 6db

ld = 8db

ld = 10db

μTEST = 32.63 f'c

1/2 - 650 (psi)

R2 = 0.55

0.69 0.76 0.83 0.90 0.97 1.03

14

17

21

24

28

31

34

2000

2500

3000

3500

4000

4500

5000

100 110 120 130 140 150

UHPC Compressive Strength, f'c

1/2 (MPa)

Bond Strength, 

uTEST (MPa)

Bond Strength, 

uTEST (psi)

UHPC Compressive Strength, f'c

1/2 (psi)

Ld_4d

Ld_6d

Ld_8d

Ld_10d

ld = 4db

ld = 6db

ld = 8db

ld = 10db
50

(a)

(b)

Figure 25. Graph. Effect of UHPC compressive strength: (a) uTEST versus f’c and (b) 

uTEST versus f’c

1/2 for specimens in Set 2.

μTEST = 0.16 f'c + 1,750 (psi)

R2 = 0.75

83 97 110 124 138

14

17

21

24

28

31

34

38

2000

2500

3000

3500

4000

4500

5000

5500

12000 14000 16000 18000 20000

UHPC Compressive Strength, f'c (MPa)

Bond Strength, 

uTES

T (MPa)

Bond Strength, 

uTES

T (psi)

UHPC compressive strength, f'c (psi)

Ld_6d

l

Ld_8d d = 8db

ld = 6db

μTEST = 41.96 f'c

1/2 - 910 (psi)

R2 = 0.75

0.69 0.76 0.83 0.90 0.97 1.03

14

17

21

24

28

31

34

38

2000

2500

3000

3500

4000

4500

5000

5500

100 110 120 130 140 150

UHPC Compressive Strength, f'c

1/2 (MPa)

Bond Strength, 

uTES

T (MPa)

Bond Strength, 

uTES

T (psi)

UHPC compressive strength, f'c

1/2 (psi)

Ld_6d

lLd_8d d = 8db

ld = 6db
51

(a)

(b)

Figure 26. Graph. Effect of UHPC compressive strength: (a) uTEST versus f’c and (b) 

uTEST versus f’c

1/2 for specimens in Set 3.

μTEST = 0.12 f'c + 2,210 (psi)

R2 = 0.66

83 97 110 124 138

14

17

21

24

28

31

34

38

2000

2500

3000

3500

4000

4500

5000

5500

12000 14000 16000 18000 20000

UHPC Compressive Strength, f'c (MPa)

Bond Strength, 

uTES

T (MPa)

Bond Strength, 

uTES

T (psi)

UHPC compressive strength, f'c (psi)

Ld_6d

l

Ld_6.7d d = 8db

ld = 6db

μTEST = 31.74 f'c

1/2 + 180

R2 = 0.66

0.69 0.76 0.83 0.90 0.97 1.03

14

17

21

24

28

31

34

38

2000

2500

3000

3500

4000

4500

5000

5500

100 110 120 130 140 150

UHPC Compressive Strength, f'c

1/2 (MPa)

Bond Strength, 

uTES

T (MPa)

Bond Strength, 

uTES

T (psi)

UHPC compressive strength, f'c

1/2 (psi)

Ld_6d

lLd_8d d = 8db

ld = 6db
52

Reinforcing Bar Size

The majority of the tests in the study were conducted with A1035 No. 5 bar to serve as the 

baseline. In this section, the effect of bar size on bond strength is evaluated. Tests on A1035 No.

4, No. 5 and No. 7 bar were used in this analysis.

With the consideration that the design (development length, concrete cover, and bar spacing) is 

often defined in terms of bar diameter (db) in design codes, the embedment length and 

confinement used for different size bar will also be based on individual bar diameter in this 

section. For example, No. 4 bar with 2db side cover, which is 1 in. (2.5 cm), will be compared 

with the No. 5 bar with 2db side cover, which is 1.25 in. (3.2 cm), and they are considered to 

have the same side cover. Also as discussed previously, specimens with the bar spacing between 

2db and lstan(θ) are recognized as demonstrating similar performance. All specimens in this 

section had bar spacing in this range and the effect of bar spacing is assumed to be minimal and 

will be neglected in this analysis. 

A total of 27 tests were included in this section, divided into two sets as shown in Table 10. Set 1 

included specimens with No. 5 and No. 4 bars and Set 2 included specimens with No. 5 and No.

7 bars. Specimens in each set had the same design for side cover and had varied embedment 

lengths. Specimens in each set can be either directly compared among those with the same 

design of embedment length or compared as a whole by comparing the bond strength uTEST , 

which included the embedment length in the calculation. All specimens were tested at one day 

after UHPC casting to ensure a similar compressive strength. 

A direct comparison between the specimens with the same design reveals that, in general, higher 

bar stress was developed for smaller bars at bond failure. For example, for the specimen with 

No. 4 bar embedded 8db (specimen ID M4-L8d-S3.5d-Sp4-1D-B9S3) in Set 1, the bar stress at 

bond failure was 147 ksi (1014 MPa), higher than the 136 and 137 ksi (938 and 945 MPa) for the 

two specimens with No. 5 bars (specimen ID M5-L8d-S3.5d-Sp4-1D-B4S2 and M5-L8d-S3.5dSp4-1D-B7S3). Similarly, for the five specimens with No.7 bars embedded 8db in Set 2, the bar 

stress at bond failure ranged from 81 to 109 ksi (558 to 752 MPa) with an average of 99 ksi 

(686 MPa), compared with 96 to 121 ksi (662 to 834 MPa) with an average of 107 ksi (741 MPa) 

for the corresponding specimens with No. 5 bars. 
53

Table 10. Test specimens – effect of bar size.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

M4-L8d-S3.5d-Sp4-1D-B9S3 13.7 4.1 3.1 1.7 1.5 147 0.073 NA 4460

M5-L8d-S3.5d-Sp4-1D-B4S2 13.6 5.1 4.1 2.4 1.6 136 0.080 65 4208

M5-L8d-S3.5d-Sp4-1D-B7S3 13.5 5.1 4.1 2.1 1.6 137 0.068 97 4168

M4-L6d-S3.5d-Sp4-1D-B12S5 11.9 3.1 2.1 1.7 1.6 106 0.041 NA 4243

M4-L6d-S3.5d-Sp4-1D-B12S5 11.9 3.1 2.1 1.6 1.4 97 0.038 NA 3867

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.9 2.9 2.2 1.6 96 0.043 NA 3884

M5-L6d-S3.5d-Sp4-1D-B4S2 13.6 3.8 2.8 2.2 1.6 90 0.045 79 3707

M4-L10d-S3.5d-Sp4-1D-B9S3 13.7 5.2 4.2 1.7 1.6 156 0.105 NA 3757

M4-L10d-S3.5d-Sp4-1D-B9S3 13.7 5.2 4.2 1.7 1.6 165 0.144 NA 3978

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.3 5.3 2.2 1.6 155 0.108 90 3843

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.3 5.3 2.2 1.6 166 0.161 68 4116

M5-L10d-S3.5d-Sp4-1D-B4S2 13.6 6.3 5.3 2.3 1.6 158 0.099 125 3911

Set 2

M7-L8d-S2d-Sp2-1D-B12S5 11.9 6.9 5.9 2.0 0.6 109 0.058 NA 3462

M7-L8d-S2d-Sp6-1D-B12S5 11.9 6.8 5.8 1.9 2.4 81 0.068 NA 2609

M7-L8d-S2d-Sp6-1D-B12S5 11.9 7.0 6.0 1.9 2.1 122 0.111 NA 3824

M7-L8d-S2d-Sp6-1D-B12S5 11.9 7.0 6.0 1.9 2.5 92 0.080 NA 2875

M7-L8d-S2d-Sp4-1D-B8S3 13.8 7.2 6.2 1.7 1.5 93 0.036 NA 2823

M5-L8d-S2d-Sp4-1D-B3S1 13.2 5.0 4.0 1.2 1.4 96 0.065 58 2995

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.6 3.6 1.2 1.5 108 0.057 68 3649

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.9 3.9 1.1 1.5 106 0.050 NA 3346

M5-L8d-S2d-Sp4-1D-B9S4 13.7 5.3 4.3 1.2 1.4 121 0.065 77 3595

M7-L6d-S2d-Sp4-1D-B8S3 13.8 5.3 4.3 1.6 1.3 60 0.021 NA 2510

M7-L6d-S2d-Sp4-1D-B8S3 13.8 5.0 4.0 1.6 1.4 61 0.042 NA 2657

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.7 3.4 1.2 1.6 77 0.042 45 3269

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.8 2.8 1.3 1.6 70 0.058 55 2876

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 3.6 1.2 1.4 84 0.053 42 3430

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 2.8 1.3 1.4 82 0.053 58 3363

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm.

53
54

The bond stress at bond failure was also calculated for each specimen and is presented in 

Table 10. The average bond stress for all No. 4 and No. 5 bars in Set 1 and for all No. 7 and No. 

5 bars in Set 2 were compared in Figure 27. In addition to the average values of bond strength, 

the figure also shows the maximum and minimum values for the included specimens and the 

number of tests conducted. As shown in Figure 27, No. 4 bars had slightly higher average bond 

strength than the No. 5 bars in Set 1, and No. 5 bars had higher average bond strength than the 

No. 7 bars in Set 2. Note that all the comparisons are made between specimens with a similar 

design which is based on the individual bar diameter. With these conditions, the tests results 

indicated that for bars with larger diameter, the bond strength decreased and a longer embedment

length should considered.

Figure 27. Chart. Bond strength versus bar size.

Reinforcing Bar Type and Yielding Strength

As demonstrated in previous sections, a reinforcing bar embedded only 6db in UHPC (with 

appropriate cover) can achieve a bar stress over 70 ksi (483 MPa) before bond failure. To 

minimize the effect of reinforcing bar yielding on bond strength when other factors were 

evaluated, the majority of the tests in the study were conducted using A1035 Grade 120 bar. The 

effect of bar type and the effect of bar yielding prior to bond failure are evaluated in this section. 

A total of 46 tests are included in this section and the tests were grouped into six sets based on 

embedment length as shown in Table 11. Each set had three types of reinforcing bar, uncoated, 

epoxy coated, and A1035, except for Set 6 having only uncoated and A1035 bar. The six sets are 

presented in an order from low bond strength to high bond strength. In each set, the bond 

strength of different types of bar can be compared directly with the fact they had the same 

0

7

14

21

28

34

0

1000

2000

3000

4000

5000

Bond Strength, 

uTEST (MPa)

Bond Strength, 

uTEST (psi)

#5 #4 #5 #7

Set 1

max

min

Set 2

No. of tests: (7) (5) (8) (7)
55

design. The reinforcing bar properties, including yield and tensile strengths and relative rib area, 

can be found in Table 2 and the rib pattern can be found in Figure 2. As the relative rib area is 

one of the main factors when looking at different types reinforcing bar, it should be noted that 

the No.5 uncoated, epoxy coated, and A1035 bar used in this study had similar relative rib areas, 

with values of 0.085, 0.083 and 0.088, respectively. 

The average bar stress at bond failure for each type of bar in each set is presented in Figure 28. 

The maximum and minimum values for included specimens in each group are also presented. As 

shown in Figure 28, for specimens with ultimate bar stress at bond failure below or close to the 

yield strength of the uncoated bar (Sets 1 and 2), the A1035 and uncoated bar had similar bond 

strength. When the bar stress at bond failure was greater than the yield strength of the uncoated 

bar, the A1035 bar had higher ultimate bar stress than the corresponding uncoated bar. In all 

cases, the epoxy coated bar had lower ultimate bar stress than the corresponding uncoated and 

A1035 bar. It is reasonable to predict the bond performance of the Grade 60 uncoated bar based 

on the tests of A1035 bar, up to at least the yield strength of the Grade 60 uncoated bar; beyond 

the yield, it is important to realize the fact that bars that yielded before bond failures produced 

average bond stress lower than A1035 bars in similar test specimens. The epoxy coated bar had 

lower bond strength than uncoated bar.

Figure 28. Chart. Average bar stress at bond failure for different types of reinforcing bar.

0

138

276

414

552

690

827

965

0

20

40

60

80

100

120

140

Set 1 Set 2 Set 3 Set 4 Set 5 Set 6

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

A1035

Uncoated

Epoxy coated

Yield strength of 

uncoated bar

ld : 4db 6db 6db 8db 8db 10db

f'c (ksi): 13.9 13.6 19.4 13.7 19.5 13.7

No. of tests:(2)(2)(2) (4)(4)(1) (4)(3)(3) (4)(2)(2) (3)(4)(1) (4)(2)
56

Table 11. Test specimens – effect of bar type.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 1

B5-L4d-S2d-Sp4-1D-B5S2 13.9 2.6 1.6 1.1 1.6 46 0.032 NA 2719

B5-L4d-S2d-Sp4-1D-B5S2 13.9 2.5 1.5 1.2 1.5 48 0.033 NA 3014

E5-L4d-S2d-Sp4-1D-B5S2 13.9 2.6 1.6 1.0 1.5 38 0.051 NA 2233

E5-L4d-S2d-Sp4-1D-B5S2 13.9 2.6 1.6 1.2 1.5 37 0.045 NA 2177

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.6 1.6 1.2 1.5 43 0.033 NA 2640

M5-L4d-S2d-Sp4-1D-B5S2 13.9 2.7 1.7 1.2 1.6 49 0.020 NA 2828

Set 2

B5-L6d-S2d-Sp4-1D-B2S1 13.4 3.8 2.8 1.1 1.5 82 0.091 NA 3368

B5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 2.8 1.3 1.4 76 0.087 44 3156

B5-L6d-S2d-Sp4-1D-B6S3 13.9 3.4 2.4 1.2 1.3 70 0.055 65 3222

B5-L6d-S2d-Sp4-1D-B6S3 13.9 3.8 2.8 1.1 1.4 83 0.090 55 3393

E5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 2.8 1.2 1.4 57 0.055 42 2378

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.7 3.4 1.2 1.6 77 0.042 45 3269

M5-L6d-S2d-Sp4-1D-B3S1 13.2 3.8 2.8 1.3 1.6 70 0.058 55 2876

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 3.6 1.2 1.4 84 0.053 42 3430

M5-L6d-S2d-Sp4-1D-B4S2 13.6 3.8 2.8 1.3 1.4 82 0.053 58 3363

Set 3

B5-L6d-S2d-Sp4-7D-B2S2 19.5 3.9 2.9 1.3 1.6 73 0.067 65 2901

B5-L6d-S2d-Sp4-7D-B4S2 19.2 3.8 2.8 1.3 1.4 81 0.101 47 3337

B5-L6d-S2d-Sp4-7D-B5S2 18.9 3.8 2.8 1.2 1.5 73 0.066 52 3037

E5-L6d-S2d-Sp4-7D-B1S1 19.9 3.6 2.6 1.3 1.5 71 0.059 NA 3112

E5-L6d-S2d-Sp4-7D-B4S2 19.2 3.8 2.8 1.3 1.4 64 0.031 NA 2651

E5-L6d-S2d-Sp4-7D-B5S2 18.9 3.8 2.8 1.1 1.6 66 0.063 58 2742

M5-L6d-S2d-Sp4-7D-B1S1 19.9 3.3 2.3 1.4 1.6 91 0.072 NA 4326

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 3.5 1.2 1.6 91 0.068 52 3812

M5-L6d-S2d-Sp4-7D-B3S1 19.5 3.8 2.8 1.2 1.5 90 0.052 58 3695

M5-L6d-S2d-Sp4-7D-B4S2 19.2 3.9 2.9 1.1 1.4 83 0.047 65 3335

56
57

Table 11 (cont’d). Test specimens – effect of bar type.

Batch ID f'c, ksi ld, in. ls, in. cso, in. csi, in. fs,max, ksi s1, in. fs,crack, ksi μTEST, psi

Set 4

B5-L8d-S2d-Sp4-1D-B2S1 13.4 5.3 4.3 1.2 1.5 96 0.205 77 2857

B5-L8d-S2d-Sp4-1D-B2S2 13.4 5.1 4.1 1.4 1.5 95 0.215 NA 2936

E5-L8d-S2d-Sp4-1D-B6S3 13.9 4.7 3.7 1.2 1.4 78 0.090 58 2612

E5-L8d-S2d-Sp4-1D-B6S3 13.9 5.1 4.1 1.2 1.3 83 0.106 55 2553

M5-L8d-S2d-Sp4-1D-B3S1 13.2 5.0 4.0 1.2 1.4 96 0.065 58 2995

M5-L8d-S2d-Sp4-1D-B6S3 13.9 4.6 3.6 1.2 1.5 108 0.057 68 3649

M5-L8d-S2d-Sp4-1D-B8S4 13.8 4.9 3.9 1.1 1.5 106 0.050 NA 3346

M5-L8d-S2d-Sp4-1D-B9S4 13.7 5.3 4.3 1.2 1.4 121 0.065 77 3595

Set 5

B5-L8d-S2d-Sp4-7D-B2S1 19.5 5.1 4.1 1.1 1.5 94 0.162 68 2913

B5-L8d-S2d-Sp4-7D-B2S1 19.5 5.1 4.1 1.1 1.5 95 0.078 NA 2922

B5-L8d-S2d-Sp4-7D-B2S2 19.5 5.1 4.1 1.4 1.6 96 0.184 65 2933

B5-L8d-S2d-Sp4-7D-B2S2 19.5 5.1 4.1 1.4 1.6 97 0.075 NA 2947

E5-L8d-S2d-Sp4-7D-B1S1 19.9 4.9 3.9 1.5 1.6 92 0.167 NA 2935

M5-L8d-S2d-Sp4-7D-B1S1 19.9 4.8 3.8 1.1 1.4 125 0.087 NA 4069

M5-L8d-S2d-Sp4-7D-B3S1 19.5 5.1 4.1 1.2 1.6 114 0.059 58 3515

M5-L8d-S2d-Sp4-7D-B9S4 18.8 5.0 4.0 1.1 1.5 127 0.070 NA 3979

Set 6

B5-L10d-S2d-Sp4-1D-B2S1 13.4 6.3 5.3 1.2 1.6 94 0.128 71 2335

B5-L10d-S2d-Sp4-1D-B2S2 13.4 6.3 5.3 1.4 1.5 88 0.167 NA 2189

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.3 5.3 1.2 1.5 144 0.082 77 3602

M5-L10d-S2d-Sp4-1D-B6S3 13.9 6.4 5.4 1.2 1.4 113 0.075 61 2760

M5-L10d-S2d-Sp4-1D-B9S4 13.7 6.3 5.3 1.2 1.5 132 0.076 65 3276

Note: For explanation of the specimen ID and each parameter, see note for Table 4. 1 ksi = 6.895 MPa; 1 in. = 2.54 cm

57
58

The average bond stress μTEST for each type of reinforcing bar in each set is calculated and 

presented in Table 12, as well as the bond stress reduction between different reinforcing bar. As 

shown in Table 12, the uncoated bars in Sets 1 and 2 had about the same bond stress as A1035

bars, with a slight difference of 4.9% and 1.6%, respectively; when the maximum bar stress at 

bond failure exceeded the yield strength of the uncoated bar, as those in Sets 3, 4, 5, and 6, the 

A1035 bars had much higher ultimate bond stress than that of uncoated bars, ranging from 

14.7% to 29.6% with an average of 21.7% higher. Another noted trend is that the reduction on 

bond strength due to the yielding of uncoated bar is amplified as the ultimate bar stress at bond 

failure increases. The reduction on bond stress were 18.5%, 14.7%, 24.0%, and 29.6% following 

the order of Sets 3, 4, 5, and 6, which are grouped in the order of increasing ultimate bar stress at 

bond failure.

The bond stress reduction of epoxy coated bar compared with uncoated bar is also presented in 

Table 12. The reductions were 23.1% and 27.6% in Sets 1 and 2 where the ultimate bar stress at 

bond failure is below or close to yield strength of the uncoated bar. The difference seemed to be 

minimized when there is a sufficient embedment length that the bar yielded before bond failure, 

with 8.3% and 10.8% reduction in Sets 3 and 4 and almost no reductions in Set 5. 

Table 12. Bond stress reduction between different types of reinforcing bar.

Average μTEST, psi Reduction, %

A1035 Uncoated Epoxy (A1035-

Uncoated)/A1035

(UncoatedEpoxy)/Uncoated

Set 1 2734 2867 2205 -4.9 23.1

Set 2 3235 3285 2378 -1.6 27.6

Set 3 3792 3092 2835 18.5 8.3

Set 4 3396 2896 2583 14.7 10.8

Set 5 3854 2929 2935 24.0 -0.2

Set 6 3213 2262 - 29.6 -
59

CHAPTER 4. DESIGN RECOMMENDATIONS FOR REINFORCING BAR 

EMBEDDED IN UHPC

One of the main goals of the research is to develop design details for reinforcing bar embedded 

in UHPC, which would provide guidance for engineers using reinforced UHPC in innovative 

applications. In this report, the focus has been on a widely available UHPC product containing 

2% steel fiber (by volume). Reinforcing bar sizes ranging from No. 4 to No. 8 and bar type 

including A615 Grade 60 uncoated and epoxy coated bar and A1035 Grade 120 bar were 

included in the study.

One design detail that would reach at least the lesser of the bar yield stress or 75 ksi (517 MPa) 

at bond failure for different bar type and size tested in this study is first presented. Other design 

details that would also attain a similar stress level are then presented. Finally, details relevant to 

an alternative design concept wherein the bar stress reaches a significantly higher stress level 

alongside an ensured ductility prior to bond failure is presented.

MINIMUM BAR STRESS OF LESSER OF YIELD OR 75 ksi (517 MPa) 

The fundamental design concept embedded into the reinforcing steel development and splice 

length provisions of the AASHTO LRFD Bridge Design Specification and the ACI 318 Building 

Code is to allow for the attainment of the yield strength of the mild steel reinforcement. The 

research studies on which these provisions are based were primarily conducted on structural 

components wherein the stress in the reinforcement at failure was below the yield stress of the 

bar. These results allowed for extrapolation of the observed bar stress at failure up to the yield 

strength of the bar. Aside from special provisions that ensure ductility by limiting the locations 

of splices or anchorages, these design specifications do not specifically ensure ductility of 

spliced or embedded reinforcing bars beyond the initial yielding of the bar.

Given this construct, the results obtained in this study were analyzed so as to create design guidance 

that parallels the existing provisions in these design specifications. Specifically, test results were 

analyzed to ensure that the bar could attain the lesser of its yield stress or 75 ksi (517 MPa). 

As mentioned earlier in the report, there were specimens that were intentionally excluded from 

previously discussed analyses, including those end specimens close to the casting point and those 

specimens that failed with UHPC tensile failures. In this present section wherein design guidance 

is developed, all test specimens were included in the analysis.

First, the bar stress at bond failure is plotted versus embedment length in Figure 29 for all the A1035

No. 5 bars tested in study, with those end specimens close to casting point and those with UHPC 

tensile failures included. The specimens had a variety of side cover and bar spacing. For the side 

cover, values of 2db, 2.7db, 3db ,and 3.5db were included; for the bar spacing to the nearest No. 8 bars, 

values of 0, 2, 4, 6, 8, and 12 in. (0, 5.1, 10.2, 15.2, 20.3 and 30.5 cm) were used. The specimens 

were grouped into two base categories, one with side over equal to 2db and the other one with side 
60

cover greater than or equal to 2.7db, as shown in Figure 29. Then, the specimens with those specific

conditions, including the zero bar spacing, bar spacing greater than lstan(θ), end specimens close to 

casting point, and specimens with UHPC tensile failures were marked on top of the base categories, 

as explained in the note of Figure 29. For those without any mark on top, they all had bar spacing 

between 2db and lstan(θ). It is also important to note that all the tests included were conducted at one 

day after casting with a UHPC compressive strength of approximately 13.5 ksi (93.1 MPa).

As shown in Figure 29, in general, the bar stress at bond failure increases as the embedment 

length increases. The large majority of the specimens had a bar stress at bond failure over 80 ksi 

(552 MPa); the ones with bar stress at bond failure below 80 ksi (552 MPa) were those with a 

side cover of 2db, combined with either a short embedment length of 4db and 6db or 

disadvantageous spacing (bar spacing = 0 or bar spacing > lstan(θ)). It is also important to note 

that for the specimens with a side cover of 2db, combined with sufficient embedment length 

(≥8db) and appropriate bar spacing (between 2db and lstan(θ) in this study), they all have reached 

a bar stress of at least 80 ksi (552 MPa). 

Note: * Specimens were grouped into two base categories based in side cover, one with side cover equal to 2db and

the other one with side cover greater than or equal to 2.7db. The specimens with specific conditions, including bar 

spacing equal to zero, bar spacing greater than lstan(θ), end specimens close to casting point, and specimens with 

UHPC tensile failures were marked on top of that. For example, refers to a specimen with side cover of 2db and 

with a specific condition of end specimen close to the casting point; refers to a specimen with side cover ≥ 

2.7db, and with specific conditions of zero bar spacing to nearest bar and end specimen close to the casting point. 

For those without any mark on top, they had bar spacing between 2db and lstan(θ).

Figure 29. Graph. Bar stress at bond failure versus embedment length for all tests with 

A1035 No. 5 bars.

0

138

276

414

552

690

827

965

1,103

1,241

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

Embedment Length, ×db

side cover ≥ 2.7

side cover = 2

bar spacing = 0

bar spacing > Lstan(θ)

end specimen close to casting point

UHPC tensile failure

*

*

ls tan(θ)

*

*

db

*

db
61

Based on Figure 29, the plot of bar stress at bond failure versus embedment length is modified by 

excluding the specimens with a side cover of 2db, and the results are shown in Figure 30. As 

shown in Figure 30, all specimens exhibited a bar stress higher than 80 ksi (552 MPa), with the 

specimens with bar spacing equal to zero or greater than lstan(θ) and/or end specimens close to 

casting point generally exhibiting lesser bar stresses at bond failure. It should be noted that there 

is only one specimen that failed with UHPC tensile failure in this group while the majority of the 

specimens failed with UHPC tensile failure were those with a side cover only 2db, as shown in 

Figure 29. The specimens with an embedment length of 8db and a side cover of 3db are identified 

in Figure 30 with a red diamond; all of them have reached a bar stress over 100 ksi (690 MPa) at 

bond failure; those with appropriate bar spacing [between 2db and lstan(θ)] reached a bar stress 

over 120 ksi (827 MPa). 

Figure 30. Graph. Bar stress at bond failure versus embedment length for all tests with 

A1035 No. 5 bars and with a side cover ≥ 2.7db.

Based on Figure 29 and Figure 30, a design detail that will allow for the attainment of the lesser 

of the bar yield strength or 75 ksi (517 MPa) before bond failure in this UHPC material for all 

the bar types and bar sizes tested in this study is developed and verified in the following. A 

review of some of the findings presented in previous sections is necessary here. As discussed

earlier, for bars with larger diameter, the bond strength decreased and a longer embedment length 

should be used. Uncoated bar that yielded before bond failure tends to have lower ultimate bond 

0

138

276

414

552

690

827

965

1,103

1,241

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

Embedment Length, ×db

side cover ≥ 2.7db

L8dS3d

bar spacing = 0

bar spacing > Lstan(θ)

end specimen close to casting point

UHPC tensile failure

*

db

ls tan(θ)

ld = 8db, side cover = 3db

*

*

*

* refer to the note for Figure 29.
62

strength than corresponding high strength reinforcing bar that does not yield. Epoxy coated 

reinforcing bar, in general, has less bond strength than uncoated bar. Given these considerations, 

the design with a minimum embedment length of 8db, minimum side cover of 3db, bar spacing 

between 2db and lstan(θ), and minimum UHPC compressive strength of 13.5 ksi (93 MPa) is 

recommended. The crack angle θ for the bar tested in this study is about 55 degrees. In general, 

the angle of inclination can vary from 45° to 80° and depends on whether the reinforcing bar ribs 

are lateral, diagonal, or wavy with respect to the axis of the bar.

(27) To simplify the design and 

also to be conservative, the angle of 45° is used and the bar spacing is then recommended to be 

between 2db and ls. For all the A1035 No.5 bars tested in this study, when the recommended 

design condition were met, they all had a bar stress at bond failure over 120 ksi (827 MPa), as 

shown in Figure 30. For different type and size bars, it will be discussed in the following. 

For situations where the above design recommendation is problematic, alternate recommendations 

can be developed. Addressing the effect of bar type first, the previous analysis has indicated that 

the yielding of reinforcing bar would reduce the ultimate bar stress at bond failure as compared to a 

similar bar with a higher yield strength. The research also indicated that the performance of A1035

can be used to well predict the performance of normal strength uncoated bar up to at least the yield 

strength of the uncoated bar. It would be conservative to predict that the uncoated bar would yield 

if the corresponding A1035 high strength reinforcing bar reached an ultimate bar stress well over 

the yield strength of the uncoated bar. For epoxy coated bar, the research indicated minimal 

reduction compared with uncoated bar when there was a sufficient embedment length that the bar

yielded before bond failure. In fact, there were two epoxy coated bar specimens with an 

embedment length of 8db and side cover of only 2db in this study (Table 11 Set 4), and they had bar 

stress at bond failure of 78 and 83 ksi (538 and 572 MPa), which is above the yield strength; if the 

side cover was increased to 3db as recommended, a higher bar stress at bond failure would be 

expected. 

The analysis in previous sections indicated that larger size bar tends to have lower bar stress at 

bond failure compared with smaller bars with the same design in terms of individual bar

diameter. However, the reduction is minimal. To verify the selected design having sufficient bond 

strength for larger bars, the tests with A1035 No.7 bar and epoxy coated No. 8 bar were examined 

and the results are presented in Figure 31. Most of the tests were conducted using A1035 No.7 bar,

with a side cover of either 2db or 2.35db, corresponding to a UHPC strip width of 4-3/8 and 5 in. 

(11.1 and 12.7 cm), respectively. One specimen with epoxy coated No.8 bar was tested as the 

possible weakest case in this study. As shown in Figure 31, for the A1035 No.7 bar with a 6db

embedment length, the bar stress at bond failure was only about 60 ksi (414 MPa) for specimens 

with 2db side cover; it increased to about 77 ksi (531 MPa) when the side cover was increased to 

2.35db. With a 8db embedment length and 2db side cover, all A1035 No.7 bars have reached a bar 

stress of 80 ksi (552 MPa) or more, except for the two end specimens close to the casting point

having bar stress of 68 and 76 ksi (469 and 524 MPa). For the specimen cast with No. 8 epoxy 

coated bar, it had an embedment length of 8db and a side cover of 2db, and it reached a bar stress of 

91 ksi (627 MPa) at bond failure. Therefore, for larger bars, up to No. 8 in this study, it would be
63

conservative to expect bar stress at bond failure to be at least the lesser of 75 ksi (517 MPa) or the 

bar yield strength with an embedment length of 8db and side cover of 3db.

Figure 31. Graph. Bar stress at bond failure versus embedment length for tests with A1035

No. 7 bars and epoxy coated No.8 bars.

MINIMUM BAR STRESS OF LESSER OF YIELD OR 75 ksi (517 MPa) – ALTERNATIVE 

The design with a minimum embedment length of 8db, a minimum side cover of 3db, a bar clear 

spacing between 2db and ls, and a minimum UHPC compressive strength of 13.5 ksi (93.1 MPa)

is recommended for general application of deformed bar to reach the lesser of the bar yield 

strength or 75 ksi (517 MPa) at bond failure. In some cases, reinforcing bar would reach a much 

higher bar stress at bond failure with this design detail. For example, the A1035 No. 5 bars tested 

in the study reached a bar stress over 120 ksi (827 MPa) at bond failure. For specific applications 

with different bar type, bar size, and UHPC compressive strength, designers may want to 

consider refinements of these recommendations based on the test results. For example, if a larger 

side cover is provided or/and UHPC with a higher compressive strength is used, the embedment 

length can be reduced. For this purpose, the following three figures were developed for reference 

when modification of the recommended design is needed. 

0

138

276

414

552

690

827

965

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

Embedment Length, ×db

side cover = 2.35

side cover = 2

Epoxy No.8 bar

bar spacing = 0

end specimen close to the casting point

db

db

**

*

*

*refer to the note for Figure 29. ** Test with epoxy coated No.8 bar, all other tests were with A1035 No.7 bar.
64

The average bar stress at bond failure for different design details is presented in Figure 32

through Figure 34. Figure 32 included the tests with A1035 high strength No. 5 bars, Figure 33

presented the specimens with normal strength epoxy coated and uncoated No.5 bars, and Figure 

34 had the specimens with A1035 No. 4 and No. 7 bars and epoxy coated No. 8 bars. For each 

design detail, the average bar stress at bond failure and the maximum and minimum values for 

involved specimens are presented in the bar chart. Below each bar chart, the design detail, 

including embedment length, concrete cover, UHPC compressive strength, and number of tests 

conducted are presented. For general information, the specimens were tested either at 1, 7, or 14 

days after casting, corresponding to compressive strength of approximately of 13, 19, and 21 ksi 

(90, 131, and 145 MPa), respectively.

All specimens in the three figures have a bar clear spacing between 2db and lstan(θ). It is 

important to consider this, because, as demonstrated in an earlier section, the specimens with bar 

clear spacing that is too small or too large tend to exhibit lower bond strengths, with the potential 

for a twenty percent or more reduction. It should also be noted that the specimens with UHPC 

tensile failure and the end specimens close to casting point are all included in the three figures; in 

fact, these specimens were the main reason why some of the results have a large range (the range 

between the maximum and minimum values showing in each figure). The UHPC tensile failure 

is attributable to insufficient UHPC cross sectional area to carry applied force and thus can 

generally be minimized by providing sufficient concrete side cover (≥3db). The specimens that 

failed with bar rupture before bond failure are outlined in red. 

With the design of a minimum embedment length of 8db, a minimum side cover of 3db, a bar 

clear spacing between 2db and ls, and a minimum UHPC compressive strength of 13.5 ksi 

(93.1 MPa) as the baseline, minor adjustment can be made based the limited test results shown in 

Figure 32 through Figure 34 per practical need. For example, for situations where the above 

conditions are met except that the minimum side cover is between 2db and 3db, the minimum 

embedment length can be increased to 10db. Based on Figure 32, for A1035 No. 5 bars, both the 

design with an embedment length of 6db accompanied with a side cover of 3db and the design 

with an embedment length of 8db accompanied with a side cover of 2db could reach a bar stress 

of at least 75 ksi (517 MPa) before bond failure at one day after casting with UHPC compressive 

strength of 13.8 ksi (95 MPa). If sufficient UHPC compressive strength was gained, for example 

at 14 days after casting, the uncoated No.5 bar with an embedment length of 6db and a side cover 

of 2db could also reach a bar stress equal to the lesser of the yield strength or 75 ksi (517 MPa) 

before bond failure (see Figure 33). 
65

Figure 32. Chart. Bar stress at bond failure for all A1035 No.5 bars with different design details. All specimens had a bar 

clear spacing between 2db and lstan(θ).

0

138

276

414

552

690

827

965

1,103

1,241

0

20

40

60

80

100

120

140

160

180

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

1 Day

7 Day

side cover: 2db 3db 2db 3db 3.5db 2db 3.5db 2db

f'c (ksi ): 13.4 19.2 13.9 19.6 13.7 19.3 13.9 13.6 13.8 19.3 13.6 13.4 19.5

No. of Tests: (4) (8) (4) (2) (10) (5) (4) (8) (4) (6) (4) (2) (2)

6db 8db 10db 12db ld :

Max

Min

75 ksi

bar rupture

65
66

Figure 33. Chart. Bar stress at bond failure for all epoxy coated and uncoated No.5 bars with different design details. All 

specimens had a bar clear spacing between 2db and lstan(θ).

0

138

276

414

552

690

827

0

20

40

60

80

100

120

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

Epoxy coated-1 Day

Epoxy coated-7 Day

Black-1 Day

Black-7 Day

Black-14 Day

Side cover : 2db 2db 2db

f'c (ksi): 13.6 19.3 13.6 19.3 21.3 13.9 19.9 13.4 19.5 21.4 19.9 13.4 19.5

No. of Tests: (1) (3) (5) (4) (2) (2) (1) (2) (4) (3) (2) (2) (4)

6db 8db 10db ld :

Epoxy

Max

Min

Black

75 ksi

bar rupture bar rupture

Epoxy Black Epoxy Black

66
67

Figure 34. Chart. Bar stress at bond failure for all A1035 No. 4 and No.7 bars and epoxy 

coated No. 8 bar with different design details. All specimens had a bar clear spacing 

between 2db and lstan(θ).

BAR STRESS ABOVE 75 ksi (517 MPa) OR BAR RUPTURE BEFORE BOND FAILURE

In some design cases, such as seismic design, the ductility of reinforcing steel beyond the yield 

point is also considered. For this purpose, a few embedment configurations relevant to 

attainment of a bar stress beyond 75 ksi (517 MPa), or even allowing for bar rupture before bond 

failure, are discussed in this section based on the limited tests in this study. 

For details engaging high strength reinforcing bars that do not exhibit a defined yield plateau, the 

results presented in Figure 32 are quite instructive. For example, for A1035 No.5 bars, the 

results indicate that when there is a minimum side cover of 3db and a minimum UHPC 

compressive strength of 19.5 ksi (134 MPa), specimens with embedment length of at least 6db

reached a bar stress greater than 100 ksi (690 MPa).

For details engaging normal strength reinforcing bars, a limited set of test configurations resulted 

in sufficient bar stress and ductility that the rupture of the reinforcing bar occurred before bond 

failure. The relevant test configurations that achieved bar rupture for both normal and high 

strength reinforcing bar are as follows:

0

138

276

414

552

690

827

965

1,103

1,241

0

20

40

60

80

100

120

140

160

180

Bar Stress at Bond Failure, 

fs,max (MPa)

Bar Stress at Bond Failure, 

fs,max (ksi)

1 Day

ld: 6db 8db 10db 10db 6db 8db 8db 

Side cover : 3.5db 3.5db 3.5db 4.5db 2db 2db 2db 

f'c (ksi): 11.9 13.7 13.7 13.5 13.8 12.5 13.6 

No. of Tests: (3) (2) (2) (2) (2) (6) (1) 

A1035 No. 4 bar bar rupture A1035 No. 7 bar Epoxy No. 8 bar

Max

Min

75 ksi
68

• A615 Grade 60 No. 5 uncoated bar with an embedment length of 8db, side cover of 2db, 

and UHPC compressive strength of 21.4 ksi (148 MPa).

• A615 Grade 60 No. 5 uncoated bar with an embedment length of 10db, side cover of 2db, 

and UHPC compressive strength of 19.5 ksi (134 MPa).

• A615 Grade 60 No. 5 epoxy coated bar with an embedment length of 10db, side cover of 

2db, and UHPC compressive strength of 19.9 ksi (137 MPa).

• A1035 Grade 120 No. 5 uncoated bar with an embedment length of 12db, side cover of 

2db, and UHPC compressive strength of 19.5 ksi (134 MPa).

• A1035 Grade 120 No. 4 uncoated bar with an embedment length of 10db, side cover of 

4.5db, and UHPC compressive strength of 13.5 ksi (93 MPa).
69

CHAPTER 5. CONCLUSIONS 

INTRODUCTION

The research discussed herein focused on assessing the bond strength of deformed reinforcing 

steel in UHPC. Deformed reinforcing steel, including ASTM A615 Grade 60 uncoated No. 5 bar 

and epoxy coated No. 5 and No.8 bars and ASTM A1035 Grade 120 No.4, No.5, and No.7 bars, 

were tested. The specific UHPC material used in this study had a steel fiber content of two 

percent by volume and an average compressive strength of 13.5 ksi (93 MPa) at one day, 17.0 ksi 

(117 MPa) at three days, 19.4 ksi (133 MPa) at seven days, and 21.3 ksi (147 MPa) at 14 days. 

The main factors affecting bond performance, including the structural characteristics like the 

embedment length, concrete side cover, bar spacing, bar size, and bar type, and materials 

properties such as UHPC compressive strength and bar yield strength are investigated. The 

summary of the findings are presented in this chapter. Design details for using deformed 

reinforcing steel in UHPC are then recommended. At the end, the proposed future research on 

this topic is included. 

CONCLUSIONS

The following conclusions are based on the research presented in this report for deformed 

reinforcing steel embedded in UHPC. 

• Increasing the embedment length of the bar increases bond strength. 

• The relationship between the bond strength and the bonded length for reinforcing bar

embedded in UHPC is nearly linear, indicating that UHPC exhibits enhanced 

performance as compared to conventional high strength concrete.

• Bond strength increases as the side cover increases. 

• Non-contact lap splice specimens, where the bar spacing is less than lstan(θ) †

, exhibit 

higher bond strength than contact lap splice specimens; when the bar clear spacing is bigger 

than lstan(θ), the bond strength decreases as compared to those having lesser spacing. 

• The decrease in bond stress for contact lap splice specimens is probably due to decreased 

contact area between the reinforcing bar and UHPC materials. Tight spacing between bars 

limits the ability of the fiber reinforcement to locally enhance the mechanical resistance of 

the UHPC.

• When the bar clear spacing is bigger than lstan(θ), the induced diagonal cracks from the 

pullout force will not intersect with the adjacent bar. The adjacent bar will not help stop 

the propagation of the diagonal cracks. The bond strength becomes a function of the 

mechanical properties of the UHPC.

 

†

 lstan(θ): refer to Figure 20. 
70

• Models that use bar spacing and bar cover to predict bond stress may need to be 

reevaluated in consideration of the added crack propagation resistance provided by fiber 

reinforcement in UHPC. 

• An increase on the compressive strength of the UHPC results in an increased bond strength.

• The effect of UHPC properties on bond strength cannot be effectively represented by the 

compressive strength f’c, or the square root of its compressive strength f’c

1/2. Other UHPC 

mechanical properties, particularly those relevant to the post-cracking tensile behavior of 

UHPC, may be more appropriate for evaluating the bond strength of reinforcing bar in 

UHPC.

• For bars with larger diameter, the bond strength decreases.

• Bars that yield before bond failure have less ultimate bond strength than high strength 

bars that do not yield before bond failure; the reduction in bond strength is amplified as 

the ultimate bond strength increases.

• The epoxy coated bar had lower bond strength than uncoated bar; the reduction was

minimized when there is a sufficient embedment length that the bar yields before bond 

failure.

RECOMMENDED DESIGN

One of the main goals of the research is to develop design recommendations for reinforcing bar

embedded in UHPC, thus providing guidance for designers using reinforced UHPC in innovative 

applications. This study focused on a widely available UHPC product containing 2% steel fiber 

(by volume). Reinforcing bar sizes ranging from No. 4 to No. 8 and bar type including A615 

Grade 60 uncoated and epoxy coated bar and A1035 Grade 120 bar were included in the study. 

Deformed reinforcing bar embedded in UHPC can attain the lesser of the bar yield strength or 

75 ksi (517 MPa) at bond failure when the following conditions are met:

• Bar size from No. 4 to No. 8,

• Uncoated or epoxy coated bar,

• Minimum embedment length of 8db,

• Minimum side cover of 3db,

• Bar clear spacing between 2db and ls, and

• Minimum UHPC compressive strength of 13.5 ksi (93 MPa).

For lap splice reinforcement configurations, a minimum lap splice length of 75 percent of the 

embedment length is suggested, which is the range into which most of tests in this study fell. 

Note that db is the bar diameter and ls is the lap splice length.

For situations wherein the above conditions are met except that the minimum side cover is 

between 2db and 3db, the minimum embedment length should be increased to 10db.
71

Refinements of the recommended design can be made for specific applications. For example, if a 

larger side cover is provided or/and UHPC has gained higher compressive strength, an 

embedment length reduction may be possible; if a longer embedment length is provided, the side 

cover can be correspondingly reduced with caution. Figure 32, Figure 33, and Figure 34 provide 

supporting information. 

FUTURE RESEARCH

The research in this study mainly focuses on one specific UHPC material. Future research in this 

topic area may also consider the following:

• Bond performance in other UHPC materials and other grout materials, such as traditional 

non-shrinkage grout and epoxy grout. 

• Investigation of the mechanical properties that are predictive of the bond performance of 

UHPC materials.

• Development of a general expression to estimate the bond strength of deformed steel 

reinforcing bars in UHPC materials with different fiber content. 

73

ACKNOWLEDGMENTS

The research which is the subject of this document was funded by the U.S. Federal Highway 

Administration. This support is gratefully acknowledged. 

This research project could not have been completed were it not for the dedicated support of the 

federal and contract staff associated with the FHWA Structural Concrete Research Program. 

Recognition also goes to the technical staff who assisted with specimen fabrication and testing. 

PSI, Inc. provided laboratory support to FHWA under contract DTFH61-10-D-00017 through 

the duration of this research project. 
74

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