Design of Continuously Reinforced 

Concrete Pavements Using Glass 

Fiber Reinforced Polymer Rebars

PUBLICATION NO. FHWA-HRT-05-081 OCTOBER 2005

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD 

This report, Design of Continuously Reinforced Concrete Pavements Using Glass Fiber 

Reinforced Polymer Rebars, investigates the effects on stress development in pavement 

and on critical design factors from substituting glass fiber reinforced polymer (GFRP) 

reinforcement for conventional steel reinforcement in continuously reinforced concrete 

pavements (CRCPs) in order to determine the performance characteristics of the GFRPreinforced concrete pavements. The results of this study target the design of CRCPs with 

GFRP rebars as an applicable reinforcement and the proposal of feasible GFRP-CRCP 

designs to be constructed. 

This report will be useful to those interested in the effect of GFRP reinforcing rebars on 

shrinkage and thermal stresses in concrete as studied using analytical and numerical 

methods as well as experimental measurements. This study proposes a series of designs 

for the GFRP-reinforced CRCP based on the numerical and mechanistic results, and 

reveals areas recommended for further investigation. 

Gary L. Henderson 

Director, Office of Infrastructure 

 Research and Development 

Notice

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

Transportation and the State of West Virginia in the interest of information exchange. The 

U.S. Government and the State of West Virginia assume no liability for the use of the 

information contained in this document. This report does not constitute a standard, 

specification, or regulation. 

The U.S. Government and the State of West Virginia do 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. 
1. Report No 2. Government Accession No. 3. Recipient's Catalog No. 

FHWA-HRT-05-081 N/A N/A 

4. Title and Subtitle 5. Report Date 

 October 2005 

 

6. Performing Organization Code 

Design of Continuously Reinforced Concrete Pavements Using Glass Fiber 

Reinforced Polymer Rebars

N/A 

7. Authors(s) 8. Performing Organization Report No. 

Jeong-Hoon Choi and Roger H. L. Chen, Ph.D. N/A 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 

N/A 

11. Contract or Grant No. 

DTFH61-99-X-00078 

13. Type of Report and Period Covered 

Department of Civil and Environmental Engineering 

West Virginia University 

Morgantown, WV 26506

Final 

12. Sponsoring Agency Name and Address 14. Sponsoring Agency Code 

 

Office of Research and Technology Services 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101 

 

15. Supplementary Notes 

The Contracting Officer’s Technical Representative on this contract was Peter Kopac, Pavement Materials and Construction Team. 

16. Abstract 

This is Task 3: Continuously Reinforced Concrete Pavement. The corrosion resistance characteristics of glass fiber reinforced polymer 

(GFRP) rebars make them a promising substitute for conventional steel reinforcing rebars in continuously reinforced concrete 

pavements (CRCPs). Studies are conducted on the effect of using GFRP rebars as reinforcement in CRCP on concrete stress 

development, which is directly related to the concrete crack formation that is inevitable in CRCP. Under restrained conditions,

concrete volume change because of shrinkage and temperature variations is known to cause early-age cracks in CRCP. In this study, 

an analytical model has been developed to simulate the shrinkage and thermal stress distributions in concrete due to the restraint 

provided by GFRP rebars in comparison with the stresses induced by steel rebars. The results show that the stress level in concrete 

is reduced with GFRP rebars because of a low Young’s modulus of GFRP. In addition, the analytical model has been used to 

estimate concrete strain variation in reinforced concrete slabs because of changes in concrete volume, and the results were 

compared with the experimental observation. Finite element (FE) methods are also developed to predict the stress distribution and 

crack width in the GFRP-reinforced CRCP section that is subjected to the concrete volume changes under various CRCP design 

considerations, such as the coefficient of thermal expansion (CTE) of concrete, the friction from the pavement's subbase, and the 

bond-slip between concrete and reinforcement. Based on the results from the FE simulation along with the mechanistic analysis, a

series of feasible designs of the GFRP-reinforced CRCP is proposed. The stress levels in the GFRP reinforcement, the crack widths,

and the crack spacings of the proposed pavements are shown to be within the allowable design requirements.

17. Key Words 18. Distribution Statement 

GLASS FIBER REINFORCED POLYMER, 

CONTINUOUSLY REINFORCED CONCRETE 

PAVEMENTS, REBARS, CONCRETE STRESS 

No restrictions. This document is available to the 

Public through the National Technical Information Service; 

Springfield, VA 22161 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

 Unclassified Unclassified 79 N/A 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized (art. 5/94)
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 oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Approp e riate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)

ii
TABLE OF CONTENTS 

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

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

OBJECTIVE AND SCOPE...................................................................................................... 2

CHAPTER 2. LITERATURE REVIEW.................................................................................... 3

CONTINUOUSLY REINFORCED CONCRETE PAVEMENT (CRCP)........................... 3

General................................................................................................................................... 3

AASHTO Design Guide and Limiting Criteria for CRCP ............................................... 5

Review of Mechanistic Analysis Program Development................................................... 6

FIBER REINFORCED POLYMER (FRP) REINFORCEMENT....................................... 6

CHAPTER 3. ANALYTICAL STUDY ....................................................................................... 9

ANALYTICAL MODEL FOR FREELY SUPPORTED REINFORCED CONCRETE 

SLAB.......................................................................................................................................... 9

MATERIAL PARAMETERS FOR ANALYTICAL APPROXIMATION ........................ 13

ANALYTICAL RESULTS AND DISCUSSION .................................................................. 13

COMPARISON WITH FINITE ELEMENT MODEL....................................................... 18

CHAPTER 4. EXPERIMENTAL STUDY ............................................................................... 21

ANALYTICAL SOLUTIONS EXPERIMENTALLY APPLICABLE TO FREELY 

SUPPORTED REINFORCED CONCRETE SLAB ........................................................... 21

CTE MEASUREMENT OF REINFORCEMENTS............................................................ 22

EXPERIMENT ON FREELY SUPPORTED REINFORCED CONCRETE SLAB 

SUBJECTED TO TEMPERATURE VARIATION ............................................................. 25

CHAPTER 5. FE STUDY OF DESIGN CONSIDERATIONS FOR CRCP......................... 35

FE ANALYSIS OF A 1.524-M (5-FT) CRCP SEGMENT................................................... 35

Effect of Concrete CTE on Stress Development in CRCP .............................................. 37

Effect of Bond-Slip between Concrete Slab and Subbase ............................................... 40

Effect of Bond-Slip between Concrete and Reinforcement............................................. 45

FE ANALYSIS OF CRCP SEGMENTS WITH DIFFERENT LENGTHS....................... 49

CHAPTER 6. MECHANISTIC STUDY OF GFRP-CRCP DESIGN ................................... 53

DESIGN INFORMATION OF STEEL-CRCP AND GFRPCRCP FOR MECHANISTIC ANALYSIS ........................................................................... 53

CRACK DEVELOPMENT AND REINFORCEMENT STRESS IN GFRPCRCP WITH VARYING CONCRETE COARSE AGGREGATE TYPE......................... 54

CRACK DEVELOPMENT AND REINFORCEMENT STRESS IN GFRPCRCP WITH VARYING SUBBASE TYPE ......................................................................... 58

iii
CHAPTER 7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS.................... 63

SUMMARY AND CONCLUSIONS...................................................................................... 63

RECOMMENDATIONS........................................................................................................ 64

ACKNOWLEDGMENTS.......................................................................................................... 65

REFERENCES............................................................................................................................ 67

iv
LIST OF FIGURES 

Figure 1. Photo. Typical example of reinforcement layout for CRCP (constructed on S.R. 288 in 

Virginia).................................................................................................................................... 3 

Figure 2. Equation. As. .................................................................................................................... 8 

Figure 3. Equation. Af,sh. ................................................................................................................. 8 

Figure 4. Equation. R. ..................................................................................................................... 9 

Figure 5. Drawing. Schematic details of representative reinforced concrete prism. ...................... 9 

Figure 6. Drawing. Schematic details of equivalent cylinder used in analyses............................ 10 

Figure 7. Equation. dP/dx. ............................................................................................................ 10 

Figure 8. Equation. τ(r)................................................................................................................. 10 

Figure 9. Equation. (u-v) in the form of integrating γ(r)................................................................11 

Figure 10. Equation. (u-v) in the solved form................................................................................11 

Figure 11. Equation. Co..................................................................................................................11 

Figure 12. Equation. d2P/dx2..........................................................................................................11 

Figure 13. Equation. εc,s(t). ............................................................................................................11 

Figure 14. Equation. εc,t. ................................................................................................................11 

Figure 15. Equation. εr,s. ............................................................................................................... 12 

Figure 16. Equation. εr,t................................................................................................................. 12 

Figure 17. Equation. (σc,s)avg......................................................................................................... 12 

Figure 18. Equation. (σc,t)avg. ........................................................................................................ 12 

Figure 19. Equation. β. ................................................................................................................. 13 

Figure 20. Equation. Ec(t). ............................................................................................................ 13 

Figure 21. Equation. Ec. ................................................................................................................ 13 

Figure 22. Graph. Maximum average tensile stress in concrete versus time (ρ = 0.00519 and L = 

1.524 m (60 inches)). .............................................................................................................. 15

Figure 23. Graph. Maximum average tensile stress in concrete versus time (L = 1.524 m (60 

inches)) and different GFRP reinforcing ratios, ρ ). ............................................................... 16

Figure 24. Graph. Maximum average tensile stress in concrete versus time (ρ = 0.00519 GFRP 

and different slab lengths, L). ................................................................................................. 16

v
Figure 25. Graph. Maximum average axial stress in concrete versus temperature change (ρ = 

0.00519 and L = 1.524 m (60 inches)).................................................................................... 17

Figure 26. Graph. Maximum average axial stress in concrete versus temperature change (ρ = 

0.00519 and L = 1.524 m (60 inches)).................................................................................... 18

Figure 27. Graph. Axial stress in concrete versus longitudinal location (comparison between 

analytical and FEM results). ................................................................................................... 19

Figure 28. Equation. (εc)gage.......................................................................................................... 21 

Figure 29. Equation. (εc,s)gage. ....................................................................................................... 21 

Figure 30. Equation. (εc,t)gage. ....................................................................................................... 21 

Figure 31. Photo. Number 4 steel rebar specimen for CTE measurement. .................................. 22 

Figure 32. Photo. Number 4 GFRP rebar specimen for CTE measurement................................. 23 

Figure 33. Photo. Titanium silicate strip specimen for CTE measurement. ................................. 23 

Figure 34. Equation. αT/M – αR/M................................................................................................... 24 

Figure 35. Equation. αT/M ΔT. ....................................................................................................... 24 

Figure 36. Graph. Coefficient of thermal expansion versus temperature for reinforcing rebars 

from third measurement.......................................................................................................... 25 

Figure 37. Drawing. Schematic details of concrete slabs used in experiment.............................. 27 

Figure 38. Photo. Concrete slab molds before concrete cast. ....................................................... 28 

Figure 39. Photo. Concrete slabs attached with strain gages........................................................ 28 

Figure 40. Graph. Axial concrete strain at midspan versus temperature change from analytical 

calculation............................................................................................................................... 29 

Figure 41. Graph. Axial concrete strain at midspan versus temperature change for plain concrete 

slab (reference temperature, To = about 42.39 oC (108.3 oF))................................................. 30 

Figure 42. Graph. Axial concrete strain at midspan versus temperature change for steelreinforced concrete slab (reference temperature, To = about 42.39 oC (108.3 o

F))................. 31 

Figure 43. Graph. Axial concrete strain at midspan versus temperature change for GFRPreinforced concrete slab (reference temperature, To = about 42.39 oC (108.3 o

F))................. 31

Figure 44. Drawing. Schematic details of a 2-D CRCP finite element model. ............................ 36 

Figure 45. Graph. Axial tensile stress on concrete surface versus longitudinal location of a 1.524-

m (5-ft) CRCP segment with ρ = 0.00739 and αc = 10.26 με/

o

C (5.7 με/

o

F)........................ 38 

vi
Figure 46. Graph. Axial tensile stress on concrete surface versus longitudinal location of a 1.524-

m (5-ft) CRCP segment with ρ = 0.00739 and αc = 14.40 με/

o

C (8.0 με/

o

F)......................... 38 

Figure 47. Graph. Axial stress in reinforcement versus longitudinal location of a 1.524-m (5-ft) 

CRCP segment with ρ = 0.00739 and αc = 10.26 με/

o

C (5.7 με/

o

F) ..................................... 39 

Figure 48. Graph. Axial stress in reinforcement versus longitudinal location of a 1.524-m (5-ft) 

CRCP segment with ρ = 0.00739 and αc = 14.40 με/

o

C (8.0 με/

o

F). ..................................... 40 

Figure 49. Graph. Axial stress at concrete bottom surface versus longitudinal location for two 

different subbase bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches))..................... 41 

Figure 50. Graph. Axial stress at concrete top surface versus longitudinal location for two 

different subbase bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). .................... 42 

Figure 51. Image. Axial stress in concrete versus longitudinal location of a 1.524-m (5-ft) CRCP 

segment with ρ = 0.00739, αc = 10.26 με/

o

C (5.7 με/

o

F), and a subbase bond-slip stiffness of 

0.236 MN/m (1,350 lbf/inch).................................................................................................. 43 

Figure 52. Image. Axial stress in concrete versus longitudinal location of a 1.524-m (5-ft) CRCP 

segment with ρ = 0.00739, αc = 10.26 με/

o

C (5.7 με/

o

F), and a subbase bond-slip stiffness of 

24.271 MN/m (138,600 lbf/inch)............................................................................................ 43 

Figure 53. Graph. Axial stress in GFRP rebar versus longitudinal location for two different 

subbase bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)).................................... 44 

Figure 54. Graph. Pavement depth versus crack width for two different subbase bond stiffnesses 

(ρ = 0.00739 and L = 1.524 m (60 inches)). ........................................................................... 45 

Figure 55. Graph. Axial tensile stress on concrete surface versus longitudinal location for 

different bond-stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)).................................. 46 

Figure 56. Graph. Axial stress in GFRP rebar versus longitudinal location for different bondstiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)).......................................................... 47 

Figure 57. Graph. Pavement depth versus crack width for different bond stiffnesses (ρ = 0.00739 

and L = 1.524 m (60 inches)).................................................................................................. 47 

Figure 58. Image. Axial stress in concrete versus longitudinal location of a 1.524-m (60-inch) 

CRCP segment with ρ = 0.00739, αc = 10.26 με/

o

C (5.7 με/

o

F), and a subbase bond-slip 

stiffness of 236.409 kN/m (1,350 lbf/inch; bond-break considered). ..................................... 48 

vii
Figure 59. Graph. Axial tensile stress on concrete surface versus longitudinal location for 

different slab segment lengths (ρ = 0.00739; bond-slip stiffness = 0.433 × 109

 N/m (2.474 ×

106

 lbf/inch)). .......................................................................................................................... 50

Figure 60. Graph. Axial stress in GFRP rebar versus longitudinal location for different slab 

segment lengths (ρ = 0.00739; bond-slip stiffness = 0.433 × 109 N/m 

(2.474 × 106 lbf/inch))............................................................................................................ 51 

Figure 61. Graph. Pavement depth versus crack width for different slab-segment lengths (ρ = 

0.00739; bond-slip stiffness = 0.433 × 109 N/m (2.474 × 106 lbf/in)).................................... 51 

Figure 62. Graph. Mean crack spacing versus type of coarse aggregate in concrete mix (ρ = 

0.0074; asphalt-stabilized subbase). ....................................................................................... 56 

Figure 63. Graph. Crack width versus type of coarse aggregate in concrete mix (ρ = 0.0074; 

asphalt-stabilized subbase)...................................................................................................... 57 

Figure 64. Graph. Tensile stress in reinforcement at crack versus type of coarse aggregate in 

concrete mix (ρ = 0.0074; asphalt-stabilized subbase).......................................................... 58 

Figure 65. Graph. Mean crack spacing and crack width versus bond-slip stiffness/unit area (ρ = 

0.0074; granite aggregate concrete)........................................................................................ 60 

Figure 66. Graph. Tensile stress in GFRP reinforcement at crack versus bond-slip stiffness/unit 

area (ρ = 0.0074; granite aggregate concrete). ...................................................................... 61 

viii
LIST OF TABLES 

Table 1. Model parameters and material properties used in analytical approximation. ... 14 

Table 2. Thermal outputs and CTEs of steel and GFRP rebars at different temperature 

levels (from third measurement). ............................................................................... 26 

Table 3. Thermal outputs of slabs at different temperature levels (TS: titanium silicate; 

PS: plain slab; S-RS: steel-reinforced slab; G-RS: GFRP-reinforced slab)............... 32

Table 4. Model parameters and material properties used in FE study. ............................. 36 

Table 5. Design parameters and material properties used in mechanistic analysis. ......... 54 

Table 6. Concrete material properties at 28 d used in mechanistic analysis (varied by 

using different types of coarse aggregate).................................................................. 55 

Table 7. Mechanistic prediction of crack development and reinforcement tensile stress at 

crack for GFRP-CRCP (varied with different types of subbase). .............................. 59

ix

CHAPTER 1. INTRODUCTION 

INTRODUCTION 

Many distresses occurring in concrete structures are attributed to the corrosion of steel 

reinforcing rebars, a condition to which steel-reinforced continuously reinforced concrete 

pavement (CRCP) is typically subjected. According to a CRCP performance report, 

corrosion has been a major deteriorative factor for CRCPs in Wisconsin, causing 

delamination, spalling, and steel rupture.(1) Therefore, glass fiber reinforced polymer 

(GFRP) rebars—which are increasingly gaining attention for structural application 

because of their noncorrosiveness and high longitudinal strength, light self-weight, and 

nonmagnetic quality—can also be viable alternatives to steel reinforcing rebars for CRCP. 

Conventional steel-reinforced CRCP has been built across the country since 1921, and its 

design can be found in a 1993 guide by the American Association of State Highway and 

Transportation Officials (AASHTO).(2) The behavior of conventional CRCP in response 

to concrete volume change has been well understood using mechanistic and numerical 

analysis methods, and its field performance has been monitored and analyzed as well; this 

has provided valuable information regarding some factors affecting the behavior and 

distresses deteriorating performance over time. (See references 1, 3, 4, and 5.) However, 

since little research concerning the replacement of steel reinforcing rebars with GFRP 

rebars in CRCP has been conducted, initial studies of mechanical behavior and design 

considerations for GFRP-reinforced CRCP need to be completed prior to any field 

application. 

At the onset of this study, the effects of using GFRP reinforcing rebars on shrinkage and 

thermal stress development in concrete were investigated. Shrinkage and thermal stresses 

in concrete have been known to cause incipient cracking in CRCPs or bridge decks. In 

order to optimally control concrete cracking (which has a strong influence on the 

performance and longevity of such structures), it is important to understand the 

development of these stresses in the structures. In the case of a freely supported 

reinforced concrete slab subjected to shrinkage or temperature variation, concrete stresses 

result from the restraint provided by the reinforcement. While concrete shrinkage causes 

tensile stresses in concrete, temperature variation can cause either tensile or compressive 

stresses in concrete, depending on whether the temperatures drop or rise and on the way 

of combining the coefficients of thermal expansion (CTEs) of the concrete and the 

reinforcement used.(6,7) The CTE of concrete varies primarily with the type of coarse 

aggregate used, and the CTE of the GFRP depends on the types of fibers and resins and 

the volume fraction of fiber used. In the case of slab on ground or bridge decks, however, 

other restraining forces acting on the concrete slab—such as friction from the subbase 

under concrete pavements, restraints from the girders underneath bridge decks, or 

restraints from reinforcement ties to neighboring slabs—need to be considered. When 

these restraints are considered, the overall resulting stress in the concrete will differ from 

that for a freely supported concrete slab (mostly by having a higher tensile stress level). 

1
In this report, analytical studies for a freely supported reinforced concrete slab are first 

presented to describe the effect of GFRP reinforcing rebars on shrinkage and thermal 

stresses in concrete, and the results are compared with the experimental measurements. 

A finite element (FE) model for the freely supported reinforced concrete slab was 

developed, and the results were verified by the analytical results. FE analyses were also 

conducted for the GFRP-reinforced CRCPs; transverse cracks were spaced at 1.524 

meters (m) (5 feet (ft)), which are subjected to both concrete shrinkage and temperature 

change. In the FE analyses, various CRCP design considerations (such as the CTE of 

concrete, the friction from the pavement's subbase, and the bond-slip between concrete 

and reinforcement) were studied to understand their effects on stress development and 

crack width in the CRCP; additional effects of crack spacing were studied using CRCP 

slab segments of lengths 1.067 meters (m) (3.5 feet (ft)), 1.524 m (5 ft), and 2.438 m (8 

ft).(8,9)

The FE analysis has also been employed to create a feasible longitudinal reinforcement 

design for a 25.4-centimeter- (cm-) (10-inch-) thick GFRP-reinforced CRCP as an 

example. Using number 6 GFRP rebars at 15-cm (6-inch) spacing at the middepth of the 

slab is shown to be an economically feasible design for GFRP-CRCP on a flexible 

subbase (or lime-treated clay subbase). Although a larger amount of GFRP reinforcement 

is sometimes required to satisfy the allowable crack spacing (1.067 to 2.438 m (3.5 to 8 

ft)), crack width (≤1 millimeter (mm) (0.04 inch)), and reinforcement stress level (20 

percent of GFRP ultimate tensile strength) comparable to those from number 6 steel 

rebars at a 15.24-cm (6-inch) spacing at the middepth, the proposed design for GFRPCRCP has been further examined using a mechanistic analysis program, CRCP8, and 

proven to perform satisfactorily for given material properties and design conditions 

provided by the Virginia Department of Transportation (VDOT). Other feasible designs 

for the given condition were also investigated, considering the effects of concrete coarse 

aggregate and subbase types on the development of crack by the mechanistic analysis. 

OBJECTIVE AND SCOPE 

The objective of this study is to investigate the effects on stress development in pavement 

and on critical design factors from substituting GFRP reinforcement for conventional 

steel reinforcement in CRCPs to determine the performance characteristics of the GFRPreinforced concrete pavements. The results of this study target the design of CRCP with 

GFRP rebars as an applicable reinforcement and propose feasible GFRP-CRCP designs to 

be constructed. 

The scope of this report includes studying the effect of GFRP reinforcing rebars on 

shrinkage and thermal stresses in concrete by analytical and numerical methods as well as 

by experimental measurements, and proposing a series of designs for the GFRPreinforced CRCP based on the numerical and mechanistic results. The study also reveals 

some areas where further studies are recommended. 

2
CHAPTER 2. LITERATURE REVIEW 

CONTINUOUSLY REINFORCED CONCRETE PAVEMENT (CRCP) 

General 

CRCP is a type of Portland cement concrete pavement reinforced with steel rebars 

throughout its length. The first CRCP was constructed in 1921 on Columbia Pike near 

Washington, D.C., for experimental purposes, and by the 1940s and 1950s many states 

began conducting extensive studies on the effects of various designs and construction 

factors on its performance.(10) The extensive use of CRCP began in the early 1960s during 

the heyday of the Interstate System construction program, and there are now over 45,080 

lane kilometers (km) (28,000 lane miles (mi)) of CRCP constructed in the United States 

throughout more than 35 states.(11) The use of continuous reinforcement generates the 

random cracks in the pavement, while obviating the need for transverse contraction joints 

that appear prone to joint-related distresses and failures. The cracks can be held tightly by 

the reinforcement and should be of no concern so long as they are uniformly spaced, 

maintaining the structural integrity of the pavement. Figure 1 shows the longitudinal steel 

rebars made continuous and the transverse steel rebars supporting the longitudinal 

rebars.(12) 

Figure 1. Photo. Typical example of reinforcement layout for CRCP 

(constructed on S.R. 288 in Virginia).

(12) 

3
The high durability and strength characteristics of CRCP, obtained through its unique 

design, assure its longevity and low-maintenance cost, and will provide an excellent 

support for future overlays. Also, the elimination of transverse contraction joints can offer 

high riding quality. In order to realize such a level of benefit, the CRCP needs to be 

designed and constructed properly. Otherwise, premature failure will occur when it is 

subjected to ever-increasing heavy traffic loading.(13) The design and construction 

features that considerably affect the performance of CRCP are reinforcement ratio, 

pavement thickness, concrete material properties decided by coarse aggregate type, 

water-to-cement ratio, chemo-thermo-mechanical behavior, subbase quality and drainage, 

and reinforcement placement. (See references 1, 14, 15, and 16.) A study indicated that 

many examples of CRCP over 50 years old were still in serviceable condition and were 

able to carry traffic loads in excess of their projected design loadings, possessing lowmaintenance cost and good riding quality.(16)

The distress most prevalent in CRCP is punchout failure at the pavement edge. There are 

four types and causes of distresses that commonly occur in CRCP: 

• “Pumping” is the ejection of base or subgrade materials by water through a crack 

caused by the deflection of slab under moving loads. This results in a progressive 

loss of pavement support. The upward warp and curl of the slab near cracks due to 

a gradient of concrete volume change contribute to the pumping condition. 

• “Faulting” is a difference of slab elevation across a crack. Faulting is caused by a 

buildup of loose materials under the trailing slab near the crack as well as at the 

depression of the leading slab. The buildup is caused by pumping due to heavy 

loading, and lack of load transfer contributes greatly to faulting. 

• “Spalling” of cracks is the cracking, breaking, or chipping of the slab edges within 

0.610 m (2 ft) of the crack. Spalling usually results from excessive stresses at the 

crack caused by infiltration of incompressible materials and subsequent expansion 

or traffic loading. It can also be caused by the disintegrated and weakened 

concrete at the crack caused by the reinforcement excessively stressed in tension. 

• “Punchout” is the major structural distress of CRCP. When the concrete slab 

cracks, the tensile stress in the reinforcement causes the fracture of surrounding 

concrete near the crack. The fracture of concrete reduces the stiffness of the slab 

and results in spalling on the crack surface under continuous traffic loadings, 

which consequently makes the crack open wide and results in the loss of load 

transfer across the crack. Without the load transfer, the slab between two closely 

spaced cracks, usually less than 0.610 m (2 ft) apart, acts as a cantilever beam, 

and as the applications of heavy truck load continue, a short, longitudinal crack 

forms between the two transverse cracks about 0.610 to 1.524 m (2 to 5 ft) from 

the pavement edge.(10)

Loss of subbase support is the fundamental cause of all the distresses. Instances where 

nonuniform support has precipitated localized short crack spacing, leading ultimately to 

4
punchout failure, have been reported in one study.(14) An optimum crack spacing between 

0.914 and 1.219 m (3 to 4 ft) was indicated because the maximum longitudinal and 

transverse bending stresses are minimized in terms of load transfer.(14) Maintaining high 

load transfer is critical to CRCP performance, particularly outside of this cracking 

interval, and is highly dependent on the crack width.(17) The other possible distresses are 

corrosion of steel reinforcement, blowup at transverse construction joint, and D-cracking 

adjacent and roughly parallel to cracks as well as along the slab edge.(1,10,18) The 

corrosion of steel reinforcement also leads to delamination, spalling, and steel rupture. 

AASHTO Design Guide and Limiting Criteria for CRCP 

The design for CRCP is based on empirical equations obtained from the AASHTO Road 

Test, and further modifications are based on theory and experience.(10) In the AASHTO 

design method, the procedure for determining the thickness of CRCP is the same as that 

used for conventional jointed pavement. The only difference in thickness design between 

the methods is that a slightly smaller load transfer coefficient (which implies more load 

transfer across the cracks) is used for CRCP, causing the thickness of the CRCP slab to be 

slightly smaller. However, according to a Portland Cement Association (PCA) report, the 

critical stresses and deflections in CRCP were about the same as those in conventional 

pavements, sometimes slightly larger and sometimes slightly smaller depending on the 

crack spacing, so the use of the same thickness has been recommended.(10, 19)

The AASHTO method for designing longitudinal reinforcement utilizes the nomographs 

developed by empirical equations. The input variables used for the design are concrete 

tensile strength, concrete shrinkage, CTE of concrete and steel rebar, rebar diameter, 

design temperature drop, and wheel load tensile stress. In addition, there are three 

limiting criteria which must be considered for the design: crack spacing, crack width, and 

reinforcement stress. The acceptable limits of these criteria (summarized below) can 

ensure satisfactory performance of CRCP under the anticipated environmental and 

vehicular loading conditions:(2)

• Crack spacing: The limits on crack spacing are established in consideration of 

spalling and punchout. To minimize crack spalling, the maximum spacing between 

consecutive cracks should be no more than 2.438 m (8 ft), whereas to minimize the 

potential for punchout, the minimum desirable spacing is 1.067 m (3.5 ft). 

• Crack width: The limit on crack width is based on a consideration of spalling and 

water penetration. The allowable crack width should not exceed 1 mm (0.04 inch). 

The crack width should be reduced as much as possible through the selection of a 

higher steel percentage or smaller diameter reinforcing rebars. 

• Reinforcement stress: Limiting criteria on reinforcement stress is intended to guard 

against steel fracture and excessive permanent deformation. To avoid these, a limiting 

stress of 75 percent of the ultimate tensile strength of steel rebar is recommended. 

5
The steel reinforcement ratio adopted varies from region to region. By far, the most 

commonly used amount of steel reinforcement is 0.6 percent. Under more severe weather 

conditions, 0.7 percent of steel amount is preferable.(1,3,20)

Review of Mechanistic Analysis Program Development 

In 1974, researchers at the University of Texas developed their first computer program 

for the mechanistic analysis of CRCP. Extensive field studies conducted to verify the 

validity of the program (CRCP1) indicated that the predictions from CRCP1 agreed with 

field observations. The effect of wheel load stresses was added to the CRCP behavior due 

to environmental loading, and the CRCP program was continuously improved by 

simulating material variance to concrete tensile strength and adding fatigue failure 

models.(3) Normalized concrete curing curves were determined for various coarse 

aggregates commonly used in Texas, and these curves and the calibrated failure 

prediction model were included.(5,21) Finally, all previous versions of the CRCP programs 

were integrated into one program (CRCP8) for simplification of the user input process.(22)

However, CRCP8 still had some limitations spawning from the simplified assumption of 

the one-dimensional analysis. In 1998, a new program, CRCP9 (which uses twodimensional finite element theories to create a mechanistic model) was developed.(4) 

The CRCP9 includes consideration of nonlinear variation in temperature and drying 

shrinkage through the depth of a concrete slab, the nonlinear bond-slip relationship 

between concrete and steel rebars, viscoelastic effects of concrete, curling and warping 

effects, and the ability to change locations of the longitudinal reinforcement. To improve 

the accuracy of the wheel load stress calculation, the program was updated once again by 

including the effect of the moving dynamic tandem axle loads (CRCP10).(23) 

FIBER REINFORCED POLYMER (FRP) REINFORCEMENT 

Steel reinforcement has been widely used for conventional concrete structure. In general, 

steel reinforcement is chemically protected by the high alkalinity (pH 12.5 to 13.5) of the 

concrete and physically protected by surrounding concrete cover against corrosion.(24)

However, for many structures exposed to aggressive environments (such as marine 

structures, bridges, loads, and parking garages), combinations of moisture, temperature, 

and chlorides reduce the alkalinity of the concrete and result in the corrosion of steel 

reinforcement. The corrosion process of steel reinforcement leads to concrete 

deterioration followed by the eventual loss of structural serviceability. To overcome 

corrosion problems, researchers have examined numerous options that can prevent 

corrosive agents from reaching the steel reinforcement surface, such as applications of 

epoxy coating and cathodic protection to the steel reinforcement, the use of sealers and 

membranes, lower permeability concrete, and corrosion-inhibiting chemical 

admixtures.(25) However, the potential of corrosion problems still remains with the 

constant presence of corrosive agents, and therefore the effectiveness of these options 

may vary considerably in the long run. 

In recent efforts to solve the corrosion problems in concrete, nonmetallic materials such 

as fiber reinforced polymer (FRP) composites have become an alternative to reinforcing 

6
steel in various concrete structures. FRP reinforcement is primarily made of fibers 

embedded in a polymeric resin. The small diameter inorganic and organic fibers (e.g., 

glass, carbon, aramid, and polyvinyl alcohol) provide FRP reinforcement with strength 

and stiffness, whereas thermosetting polymer resins (e.g., polyester, vinylester, and 

epoxy) bind the fibers together. In addition, inorganic fillers (e.g., calcium carbonate, clay, 

and alumina trihydrate) can be mixed with the resins for cost reduction, property 

modification, and processing property control of FRP reinforcement. 

The FRP reinforcement has some advantages and disadvantages in its material 

characteristics when used in concrete structures:(26)

• Advantages 

• High longitudinal strength. 

• Nonmagnetic. 

• Corrosion resistance. 

• High fatigue endurance. 

• Light weight (about one-fifth to one-fourth the density of steel). 

• Low thermal and electric conductivity. 

• Disadvantages 

• High cost. 

• No yielding before brittle rupture. 

• Low transverse strength. 

• Low modulus of elasticity. 

• Susceptibility to damage due to ultra-violet radiation. 

• Low durability of glass fibers in a moist environment. 

• Low durability of some glass and aramid fibers in an alkaline environment. 

• High CTE perpendicular to the fibers, relative to concrete. 

• Susceptibility to fire, depending on matrix type and concrete cover. 

Therefore, the material characteristics of FRP need to be carefully considered when 

determining whether FRP reinforcement is suitable or necessary for a particular concrete 

structure. There are several commercially available FRP reinforcements made of 

continuous aramid (AFRP), carbon (CFRP) or glass (GFRP) fibers embedded in various 

resin materials. Also, FRP reinforcements can be sorted by the type of surface 

deformation system, such as exterior wound fibers, sand coating, or separately formed 

deformation. 

Currently, the structural performance and integrity of concrete structures reinforced with 

FRP rebars are being studied extensively by researchers in Japan, Europe, and North 

America in order to investigate FRP rebar structure capability and durability as 

reinforcement for concrete and to provide FRP design provisions for different 

applications. A preliminary design method of FRP reinforcement for jointed slabs on the 

ground is presented in an ACI committee report.(26) The subgrade drag method is 

7
frequently used to determine the amount of shrinkage and temperature steel 

reinforcement as: 

Figure 2. Equation. As. 

where As = cross-sectional area of steel (in2) per linear foot; fs = allowable stress in steel 

reinforcement (lbf/in2

), commonly taken as two-thirds to three-fourths of yielding stress 

level; μ = coefficient of subgrade friction (1.5 is recommended for floors on ground); L = 

distance between joints (ft); and w = dead weight of the slab (lbf/ft2

) per slab thickness. 

The drag equation is modified by considering the lower modulus of the FRP 

reinforcement. At the allowable stress, the strain in steel reinforcement is about 0.0012, 

and converting the same strain into the stress for FRP will give a stress of 0.0012Ef. 

Figure 2 can then be rewritten as: 

Figure 3. Equation. Af,sh. 

where Af,sh = the cross-sectional area of FRP reinforcement (in2) per linear foot; and Ef = 

Young’s modulus of FRP reinforcement (lbf/in2). Comparing figures 2 and 3, it can be 

noted that the ratio of the amount of FRP reinforcement required to be increased is the 

same as the ratio of steel to the GFRP Young’s modulus. However, according to the ACI 

report, this design approach still needs to be experimentally verified. More importantly, 

there is a need to consider the effects due to the difference in CTE and Young’s modulus 

between concrete and the types of reinforcement. An analytical study to address these 

effects will be presented in the next chapter. 

8
CHAPTER 3. ANALYTICAL STUDY 

ANALYTICAL MODEL FOR FREELY SUPPORTED REINFORCED 

CONCRETE SLAB 

To estimate the development of shrinkage and thermal stresses in a freely supported 

reinforced concrete slab, a representative concrete prismatic model containing a 

longitudinal reinforcing rebar at its center with width (or reinforcing space in CRCP) B, 

height (or thickness in CRCP) H, length L, and rebar diameter 2rr is considered. Then, for 

simplification of analysis, the model is modified into an equivalent cylinder with the 

corresponding equivalent diameter 2R accompanied by the same length and rebar 

diameter as those for the prismatic model. Schematic details of the models are shown in 

figures 5 and 6. 

Figure 4. Equation. R. 

Figure 5. Drawing. Schematic details of representative reinforced concrete prism. 

9
Figure 6. Drawing. Schematic details of equivalent cylinder used in analyses. 

Adopting the shear-lag theory, there are several assumptions applied to this analysis: (1) 

the concrete and reinforcement exhibit elastic behavior, (2) a perfect bond between 

concrete and reinforcement exists at an infinitely thin interface, (3) the stiffnesses of the 

concrete and the reinforcement in the radial (r-) direction are the same, (4) the strain in 

the concrete εc at a distance R from the x-axis is equivalent to the restraint-free concrete 

strain due to the shrinkage or temperature variation, and (5) the temperature distribution 

in the concrete and reinforcement is uniform in the radial direction.(27) The effects of 

concrete’s radial shrinkage on concrete stress development in the longitudinal (x-) 

direction are neglected. Also, the effects from the CTE discrepancies between concrete 

and reinforcement in the radial direction are neglected. 

When the concrete is subjected to a strain in the longitudinal (x-) direction, εc, the rate of 

transfer of load from concrete to reinforcement can be assumed as: 

Figure 7. Equation. dP/dx. 

where P = load in the reinforcement; Co = a constant; and v and u = axial displacements 

at r = R and r = rr , respectively. It is also known from force equilibrium that dP/dx = 

2π rτ, where τ is the axial shear stress varying along the radial direction. This gives: 

Figure 8. Equation. τ(r). 

10
The relative displacement between u and v can be obtained by: 

Figure 9. Equation. (u-v) in the form of integrating γ(r). 

where γ (r) = axial shear strain varying along the radial direction; and Gc = shear modulus 

of concrete. By solving figure 9, one then gets: 

Figure 10. Equation. (u-v) in the solved form. 

Hence, 

Figure 11. Equation. Co. 

Also, dv/dx = εc and du/dx = εr. Therefore, 

Figure 12. Equation. d2P/dx2. 

The restraint-free concrete axial strain, εc, in the above equation can be substituted with 

either shrinkage strain at any time t (in days (d)), εc,s(t), or thermal strain, εc,t, which are 

given by: 

Figure 13. Equation. εc,s(t). 

and 

Figure 14. Equation. εc,t. 

11
where (εc,s)ult = ultimate shrinkage strain for drying at 40 percent RH; ΔT = temperature 

variation; and αc = CTE of concrete. εc,s(t) is an empirical equation for moist cured 

concrete.(28) The reinforcement axial strains due to concrete shrinkage, εr,s, or due to 

temperature variation, εr,t, are shown as: 

Figure 15. Equation. εr,s. 

and 

Figure 16. Equation. εr,t. 

where Ar = reinforcement cross-sectional area; Er = Young’s modulus of the 

reinforcement; and αr = CTE of the reinforcement. 

Substituting figures 13–16 into figure 12 gives the governing differential equation for P, 

and then by solving the differential equation with the boundary conditions that P = 0 at x

= 0 and x = L, the reinforcement force, P(x), can be obtained. The axial force equilibrium 

with the average axial concrete stress, (σc)avg, must also be satisfied at any x location. In 

other words, P + (σc)avg Ac = 0, where Ac is the concrete cross-sectional area. Hence, the 

average axial concrete stress can be given as follows: 

Figure 17. Equation. (σc,s)avg. 

and 

Figure 18. Equation. (σc,t)avg. 

12
where (σc,s)avg and (σc,t)avg = average axial concrete stresses induced by concrete 

shrinkage and temperature variation, respectively; ρ = reinforcing ratio (Ar/Ac); and 

Figure 19. Equation. β. 

The negative values from figures 17 and 18 indicate compressive axial stresses in the 

concrete. The maximum axial stress in concrete can be simply found at the midpoint, 

x = L/2. 

MATERIAL PARAMETERS FOR ANALYTICAL APPROXIMATION 

In addition to the concrete shrinkage strain, εc,s(t), shown in figure 13, the Young’s 

modulus of concrete, Ec, is also employed as the time-dependent parameter in the 

shrinkage stress analysis. This leads the shrinkage stress analysis to be dependent on the 

elapsed time, t (d). The time-dependent Young’s modulus of concrete can be evaluated 

by: 

Figure 20. Equation. Ec(t). 

and 

Figure 21. Equation. Ec. 

where Ec,28 = Young’s modulus of concrete at 28 d.(29) In the thermal stress analysis, the 

concrete stresses at 28 d are estimated for different temperature variations; Ec,28 was 

therefore employed for the Young’s modulus of concrete in the analysis. Table 1 lists a set 

of model parameters and material properties used in the analytical study. The analytical 

model with a width of B = 15.24 cm (6 inches) and a height of H = 25.4 cm (10 inches) 

was examined in the study. Shown in the table are the Young’s moduli and CTEs of two 

different concretes whose types of coarse aggregate used are granite and siliceous river 

gravel, respectively. (30) In addition, the GFRP rebar used in the analyses is assumed to be 

C-BAR® deformed FRP rebar, manufactured by Marshall Industry Composite, Inc. 

ANALYTICAL RESULTS AND DISCUSSION 

In figure 22, the maximum average tensile stresses in the concrete due to concrete 

shrinkage are calculated over a period of time; the stresses induced by steel and GFRP 

13
reinforcements are shown in the figure for the purpose of comparison, and the granite 

aggregate concrete is used in the shrinkage stress analysis. In the calculation, number 5 

rebars with radii of 7.94 mm (0.3125 inch; ρ = 0.00519) are employed for the models 

having a length of L = 1.524 m (60 inches (5 ft)). The figure reveals that the maximum 

concrete stress level created by GFRP rebar is about one-fifth of that created by steel 

rebar, which is a ratio about the same as that of the longitudinal GFRP rebar’s elastic 

modulus to the steel rebar’s elastic modulus. The lower stress level by GFRP rebar results 

from the GFRP’s lower elastic modulus providing the concrete with less restraint while 

the concrete shrinks. 

Table 1. Model parameters and material properties used 

in analytical approximation. 

Parameter and Properties Value 

Width, B (cm (inches)) 15.24 (6.0) 

Height, H (cm (inches)) 25.40 (10.0) 

Length, L (m (inches)) 1.52 (60.0) 

Ultimate concrete shrinkage strain, (ε 800.00 c,s)ult (με) 

Young’s modulus of concrete at 28 d, Ec,28 (GPa (× 106 lbf/in2)) 33.10 (4.80)1

and 34.48 (5.0)2

Poisson’s ratio of concrete, ν 0.20 c

Young’s modulus of steel rebar (GPa (× 106 lbf/in2)) 200.00 (29.00) 

Longitudinal Young’s modulus of GFRP rebar (GPa (× 106 lbf/in2)) 40.00 (5.80) 

CTE of concrete, αc (με/

o

C (με/

o

F)) 10.26 (5.7)1

 

and 14.40 (8.0)2

CTE of steel rebar, αr,s (με/

o

C (με/

o

F)) 11.88 (6.6) 

CTE of GFRP rebar, αr,g (με/

o

C (με/

o

F)) 9.36 (5.2) 

1

Granite coarse aggregate. 

2

Siliceous river gravel coarse aggregate used. 

1 megapoundforce per square inch (106 lbf/in2) = 6.89 gigapascal (GPa) 

14
0

0.02

0.04

0.06

0.08

0.1

0.12

0 50 100 150 200 250 300 350 400 450

Time (days )

Max. Avg. Tensile Stress (ksi )

Steel Steel(FEM) GFRP GFRP(FEM)

1 kilopoundforce per square inch (ksi) = 6.89 megapascal (MPa) 

Figure 22. Graph. Maximum average tensile stress in concrete versus time 

(ρ = 0.00519 and L = 1.524 m (60 inches)). 

The cases for different sizes of GFRP rebars (numbers 3 through 6 (ρ = 0.00184 through 

0.00739)) are presented in figure 23, showing that the maximum concrete stress increases 

with an increase in the reinforcement ratio. This is because of the greater restraint 

provided to the concrete shrinkage by a higher reinforcement ratio. The maximum 

concrete stresses for different slab lengths, L, are examined in figure 24. The stresses 

increase with increases in length, L, increasingly converging to ρErεc,s(t) when L

approaches ∞. With the set of parameters (table 1) used, the maximum concrete stress 

already converges to ρErεc,s(t) as L reaches about 0.305 m (12 inches). 

The discrepancy in CTEs between the concrete and reinforcement causes thermal stresses 

in both the concrete and reinforcement as temperatures change. Figures 23 and 24 show 

the plots of the maximum average axial stress in concrete versus temperature increase 

(positive ΔT) for two different concrete CTEs. The CTE of granite aggregate concrete is 

lower than that of steel rebar and higher than that of GFRP rebar (table 1). As shown in 

figure 25, this CTE of concrete causes tensile concrete stress when using steel rebar and 

compressive concrete stress when using GFRP rebar as temperature increases; in the 

figure, the positive value represents the tensile stress, and the negative value the 

compressive stress. 

15
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 50 100 150 200 250 300 350 400 450

Time (days )

Max. Avg. Tensile Stress (ksi )

ρ = 0.00739 (#6; r r = 0.375 inch )

ρ = 0.00519 (#5; r r = 0.3125 inch )

ρ = 0.00334 (#4; r r = 0.25 inch )

ρ = 0.00184 (#3; r r = 0.1875 inch )

1 ksi = 6.89 MPa; 1 inch = 25.4 mm 

Figure 23. Graph. Maximum average tensile stress in concrete versus time 

(L = 1.524 m (60 inches)) and different GFRP reinforcing ratios, ρ ).

0

0.005

0.01

0.015

0.02

0.025

0 50 100 150 200 250 300 350 400 450

Time (days )

Max. Avg. Tensile Stress (ksi )

L = 3 inches

L = 6 in ches

L = 12 in ches

ρ E r ε c,s (t)

1 ksi = 6.89 MPa: 1 inch = 25.4 mm 

Figure 24. Graph. Maximum average tensile stress in concrete versus time 

(ρ = 0.00519 GFRP and different slab lengths, L). 

16
-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 5 10 15 20 25 30

ΔT (o F )

Max. Avg. Axial Stress (ksi )

Steel GFRP

α c = 5.7 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.2 με /

o F

1 (ΔT oF) = 0.56 (ΔT oC); 1 ksi = 6.89 MPa; 1 με/

o

F = 1.80 με/

o

C 

Figure 25. Graph. Maximum average axial stress in concrete versus temperature 

change (ρ = 0.00519 and L = 1.524 m (60 inches)). 

The siliceous river gravel aggregate concrete has a CTE higher than both CTEs of steel 

and GFRP rebars, and temperature increases lead to compressive stress development in 

the concrete for both reinforcement cases, as shown in figure 26. These compressive and 

tensile states are reversed as temperature decreases (negative ΔT). As can be seen in both 

figures 25 and 26, the absolute values of thermal concrete stresses from GFRP rebar are 

less than those from steel rebar, mainly because of GFRP rebar’s lower elastic modulus. 

In addition, both the magnitude and sign of the stress caused by temperature variation can 

be controlled by using different combinations of concrete and reinforcement CTEs. 

17
-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0 10 20 30 40 50 6

ΔT (o F )

Max. Avg. Axial Stress (ksi )

0

Steel GFRP Steel(FEM) GFRP(FEM)

α c = 8.0 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.2 με /

o F

1 (ΔT oF) = 0.56 (ΔT oC); 1 ksi = 6.89 MPa; 1 με/

o

F = 1.80 με/

o

C 

Figure 26. Graph. Maximum average axial stress in concrete versus temperature 

change (ρ = 0.00519 and L = 1.524 m (60 inches)). 

COMPARISON WITH FINITE ELEMENT MODEL 

Using the FE analysis program, ABAQUS, a finite element model (FEM) of a freely 

supported, reinforced concrete slab has been created, and the results from the shrinkage 

and thermal analytical models are compared with the FEM results. The concrete slab is 

modeled as four-node, 2-D elements under plane stress conditions, and the reinforcement 

is modeled as beam elements with circular cross sections. The thickness of the concrete 

2-D plane stress elements is the width, B, of the concrete prismatic model. The bond-slip 

between concrete and reinforcement is modeled by using horizontal spring elements, and 

the bond is assumed to be perfect. All of the material properties are assumed to be the 

same as those used in the analytical model (table 1); in this study, the spring stiffnesses 

used to simulate the perfect bond, which depend on Young’s modulus of concrete, are 

1.303 GN/m (7,443 kip/inch) and 1.251 GN/m (7,145 kip/inch) for granite concrete and 

siliceous river gravel concrete, respectively. The comparison (figures 20 and 24) between 

the analytical and FE methods shows a good agreement of the maximum average axial 

stresses in the concrete. 

The axial concrete stress distribution along the longitudinal (x-) direction for a GFRPreinforced slab with a temperature variation of –27.8 o

C (–50 oF) has also been calculated 

using both analytical and FE methods (figure 27). 

18
0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0 5 10 15 20 25 30 35 40 45 50 55 60

x (inches )

Axial Stress (ksi )

Analytical FEM1 FEM2 FEM3 FEM4 FEM5

 ρ = 0.00519

ΔT = -50 o F

α c = 5.7 με /

o F

α r,g = 5.2 με /

o F

1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT oF) = 0.56 (ΔT oC); 1 με/

o

F = 1.80 με/

o

C 

Figure 27. Graph. Axial stress in concrete versus longitudinal location 

(comparison between analytical and FEM results). 

Figure 27 shows the concrete stresses located at five different longitudinal layers of 

concrete. The layers are laterally located from the concrete surface to the interface 

between the concrete and reinforcement, and are represented by using the nomenclature 

of FEM1 through FEM5 in the figure; FEM1 represents the surface layer, and FEM5 

represents the layer closest to the reinforcement. The results show that the axial stresses 

from the analytical model, which are averaged in the radial (r-) direction, agree well with 

the axial stresses from all the layers of the concrete FE element as the x-location 

approaches the middle of the section. From the FE results, it can be seen that the axial 

stresses are varied through the depth around the ends of the slab. This is simply caused by 

the fact that, along the depth direction, the more drastic change in axial displacement 

occurs around the ends rather than around the middle section due to the restraint from the 

reinforcement. The comparison also shows that the analytical solution of average axial 

concrete stresses (figure 18) is valid throughout the longitudinal (x-) direction, especially 

in the vicinity of the slab’s middle section, proving the validity of the maximum average 

axial stresses in concrete at x = L/2 as previously shown.

19

CHAPTER 4. EXPERIMENTAL STUDY 

ANALYTICAL SOLUTIONS EXPERIMENTALLY APPLICABLE TO FREELY 

SUPPORTED REINFORCED CONCRETE SLAB 

In this study, a test to assess the validity of the analytical model was conducted. Since the 

experimental mechanical behavior of the reinforced concrete slab under concrete volume 

change can be estimated in terms of strain, the strain equation needs to be derived from 

the analytical model. The strain, (εc)gage, that can be measured by the strain gage on the 

reinforced concrete slab is the resulting concrete strain due to the concrete volume 

change, εc, and the restraint from reinforcement, (εc)avg. 

Figure 28. Equation. (εc)gage. 

where (εc)avg = (σc)avg/Ec. Thus, 

Figure 29. Equation. (εc,s)gage. 

and 

Figure 30. Equation. (εc,t)gage. 

where (εc,s)gage and (εc,t)gage are the strains due to concrete shrinkage and temperature 

variation, respectively. The (εc)avg in figure 28 is obtained from (σc)avg that is analytically 

derived for the averaged concrete stresses in the radial (r-) direction at any x-locations. 

Based on the previous discussion of FE model agreement (figure 27), this value can still 

adequately represent the reinforcement restraint-induced strain which is uniformly 

distributed throughout the lateral direction at around the longitudinal middle of the slab. 

The experiment was conducted considering the temperature variation-induced strain on 

21 
three laboratory slab specimens: a plain concrete slab, a steel (number 4 rebar with a 

radius of 6.35 mm (0.25 inch); ρ = 0.01695) reinforced concrete slab, and a GFRP 

(number 4 rebar) reinforced concrete slab. 

CTE MEASUREMENT OF REINFORCEMENTS 

The mechanical behavioral differences between the aforementioned slabs under a 

temperature change can be presented in terms of the differences in the deformations 

developed in the slabs. In order for the analytical model to predict the strain differences 

between the slabs under the temperature change, the CTEs of the reinforcements used in 

the slabs should be known. Therefore, an experiment to measure the CTEs of the steel 

and GFRP rebars using strain gages was conducted prior to the experiment on the slabs. 

The experimental method using strain gages has been standardized as an alternative 

method to accurately measure the CTEs of a test material with respect to that of any 

reference material having a known CTE.(31,32) Rebars—15.24 cm (6 inch) long number 4 

steel and GFRP—were prepared along with a reference material, titanium silicate, having 

an extremely low CTE (about 0.0 με/

o

F) over the temperature range of interest (from –29 o

C (–0.2 oF) to 49 oC (120.2 oF)); grade 60 deformed steel rebar and the GFRP rebar 

manufactured by Marshall Industry Composite, Inc., were employed. A strain gage (EA06-125BB-120; Measurement Group, Inc.) was attached at the middle of each of the steel 

and GFRP rebars in the longitudinal direction as well as at that of the titanium silicate 

strip, as shown in figures 31, 32, and 33. 

 

Figure 31. Photo. Number 4 steel rebar specimen for CTE measurement. 

22 
Figure 32. Photo. Number 4 GFRP rebar specimen for CTE measurement. 

Figure 33. Photo. Titanium silicate strip specimen for CTE measurement. 

23 
The steel and GFRP rebars were then housed in the environmental chamber along with 

the titanium silicate strip so that both rebars and the titanium silicate strip were subjected 

to the cyclic temperature change simultaneously. The rebars and titanium silicate strip 

were suspended from one end so that friction could not impede their expansion or 

contraction due to temperature change. The measurement was conducted three times for 

each of the steel and GFRP reinforcing rebars. Two cycles of temperature change were 

applied for each measurement. Each cycle of temperature change consisted of 43 o

C 

(109.4 o

F) → 49 oC (120.2 oF) → 22 oC (71.6 oF) → –29 oC (–20.2 oF) → 43 oC (109.4 o

F), would take about 5 d. 

The output of the strain gage induced by temperature change is defined as thermal output. 

The thermal output of the gage is caused by combined resistance changes resulting from 

(1) changes with temperature in the resistivity of the gage grid alloy, and (2) the 

mechanical strain of the strain grid by an amount equal to the difference in the expansion 

coefficient between the gage grid alloy and the test material. The thermal output does not 

directly represent genuine strain of the test material induced by the temperature change 

and must be adjusted accordingly. As given in figure 34, the strain of the test material can 

be obtained by rearranging the equation 

Figure 34. Equation. αT/M – αR/M. 

where αT/M and αR/M = CTEs of test and reference materials, respectively; and (εT/O)T/M

and (εT/O)R/M = thermal outputs of test and reference materials, respectively. Since the 

CTE of the reference material (titanium silicate) is 0.0 με/

o

F in this study, figure 34 

becomes 

αT/M ΔT = (εT/O)T/M – (εT/O)R/M. 

Figure 35. Equation. αT/M ΔT.

The difference between the thermal outputs of the test and reference materials, which are 

obtained experimentally, can then represent the strain of the test material induced by the 

temperature change. The CTE of the test material can thus be obtained since ΔT is 

experimentally known. For each measurement, the thermal output was set to 0 με at a 

reference temperature, To, of about 43o C (109.4 o

F). From each rebar as well as from 

titanium silicate strip, the thermal output was collected at each temperature level, and the 

CTE of each rebar was obtained. It was also observed from the measurements that the 

thermal outputs were highly repeatable at a similar measured temperature, and the CTE 

of each rebar was fairly consistent at different applied temperature levels as shown in 

table 2 and figure 36, which correlate to the third measurement. The average CTEs from 

the three measurements were about 11.88 με/

o

C (6.6 με/

o

F) for steel rebar and 9.18 με/

o

C 

(5.1 με/

o

F) for the GFRP rebar. 

24 
25 

0

-40 -20 0 20 40 60

Temperature (o

F )

1

2

3

4

5

6

7

8

80 100 120 140

Coefficient of Thermal Expansion (με /

o

F )

Steel1 Steel2 GFRP1 GFRP2

 Steel1 : steel rebar under 1st cycle of temp. change

 Steel2 : steel rebar under 2nd cycle of temp. change

GFRP1 : GFRP rebar under 1st cycle of temp. change

GFRP2 : GFRP rebar under 2nd cycle of temp. change

o

C = 5(oF – 32)/9; 1 με/

o

F = 1.80 με/

o

C 

Figure 36. Graph. Coefficient of thermal expansion versus temperature 

for reinforcing rebars from third measurement. 

EXPERIMENT ON FREELY SUPPORTED REINFORCED CONCRETE SLAB 

SUBJECTED TO TEMPERATURE VARIATION 

The three laboratory slab specimens were cast and cured for about 5 months at room 

temperature and 40~45 percent RH before the experiment. Drying shrinkage effect would 

be negligible during the experiment. A thermocouple was set in the center of each slab 

before the concrete cast, and a strain gage (N2A-06-40CBY-120; Measurement Group, 

Inc.) was attached in the center of the upper surface of each slab after the curing process. 

The slabs were then subjected to cyclic temperature changes in an environmental 

chamber with temperature and humidity control. The schematic details of the specimens 

are shown in figure 37, and photos are shown in figures 38 and 39.
Table 2. Thermal outputs and CTEs of steel and GFRP rebars at different temperature levels (from thi

Thermal Output 

(εT/O; με)

(εT/O) T/M – (

εT/O) R/M

(με)

(

Temperature 

(T; o

F1) 

Elapsed 

time 

(h) Titanium silicate Steel GFRP 

Δ

T2

=

T–

To

3

(

oF) Steel GFRP Stee

109.2 0 

0

0

0 ~ 

~

~

120.1 24 –74 –3 –21 10.9 70 53 6

72.7 48 247 –3 47 –36.5 –250 –199 6

–16.0 60 633 –198

6 –125.2 –831 –627 6

110.2 87 

2

0 –1 ~ 

~

~

109.7 94 1 0 –1 ~ 

~

~

120.5 144 -76 –4 –22 11.3 73 55 6

72.9 168 246 –2 48 –36.3 –248 –198 6

–15.9 180 631 –199

3 –125.1 –830 –628 6

110.0 207 1 0 1 ~ 

~

~

Average: 6

C); 

1 oC = 5(oF – 32)/9. 2 1 (ΔT oF) = 0.56 (

ΔT 

F). 

o

3 To = 42.9 oC (109.2 o

o 1 με/ F = 1.80 με/ C 4 o

26
1 inch = 25.4 mm; 1 ft = 0.305 m 

Figure 37. Drawing. Schematic details of concrete slabs used in experiment. 

27 
Figure 38. Photo. Concrete slab molds before concrete cast. 

Figure 39. Photo. Concrete slabs attached with strain gages. 

28 
In the concrete slab experiment, each slab was supported on three lubricated rollers in 

order to minimize the frictional effect. The experiment was also conducted three times, 

and, at each time, the slabs were subjected to two cycles of temperature change as the 

CTE measurement experiment was. The titanium silicate strip, now attached with a strain 

gage (N2A-06-40CBY-120) at its middle in a longitudinal direction, was also employed 

in the experiment on the slabs. The experiment followed the same procedure as 

previously mentioned. A concrete CTE of 9.36 με/

o o C (5.2 με/ F), which was an average 

of the CTEs measured from the plain concrete slab, was utilized for the analytical 

calculation using figure 31, and the results are shown in figure 40. In addition, the 

Young’s modulus of concrete of 30.5 GPa (4,420 ksi) used in the calculation was 

obtained experimentally from the results of the compressive tests of three 15.24- by 0.48-

cm (6- by 12-inch) concrete cylinders cast at the same time as the concrete slabs. In the 

figure, it is predicted that the axial concrete strains calculated for the steel-reinforced slab 

have higher contraction magnitudes (shown as negative values) than those for the plain 

and GFRP-reinforced slabs under temperature drop. This is reasonable since the CTE of 

the steel rebar is higher than those of the concrete and GFRP so that the steel 

reinforcement adds more contraction on the concrete. Since the GFRP rebar used has a 

CTE similar to that of the concrete, the strain values calculated for the GFRP-reinforced 

slab are also close to those for the plain slab. 

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

-140 -120 -100 -80 -60 -40 -20 0 20 40

ΔT (o

F )

Axial Concrete Strain (με )

steel-reinforced concrete slab

GFRP-reinforced concrete slab

plain concrete slab

1 (ΔT o o F) = 0.56 (ΔT C)

Figure 40. Graph. Axial concrete strain at midspan versus temperature change 

from analytical calculation. 

29 
In figures 41, 42, and 43, the axial concrete strains measured at the midspan of each slab 

over the temperature changes ranging from T = +49 o o o o C (+120.2 F) to –29 C (–20.2 F) 

are compared with the analytical calculations which employ the aforementioned material 

properties; some other material properties necessary for the analysis—such as the Poisson 

ratio of the concrete and the Young moduli of the steel and GFRP rebars—are the same as 

those listed in table 1. In the figure, the nomenclature of Test#X-Y represents the test 

results from the Yth temperature change cycle of Xth test. It is shown in the comparison 

that the experimentally obtained strains are fairly well distributed around the calculated 

strains, which are shown as solid lines. In addition, the measured strains under freezing 

temperatures seem to have contraction magnitudes that are somewhat smaller than the 

calculated values. This may result from the expansion of concrete and the higher Young’s 

modulus of concrete caused by moisture freezing in the concrete. The experimentally 

measured strains are tabulated in table 3. 

Similar results are also expected as the concrete shrinkage is considered. Therefore, the 

analytical model can be a useful means of evaluating the stress or strain level around the 

middle of a freely supported reinforced slab that is subjected to concrete shrinkage and 

temperature change. 

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

-140 -120 -100 -80 -60 -40 -20 0 20 40

ΔT (o

F )

Axial Concrete Strain (με )

Equation

Test#1-1

Test#1-2

Test#2-1

Test#2-2

Test#3-1

Test#3-2

o o 1 (ΔT F) = 0.56 (ΔT C) 

Figure 41. Graph. Axial concrete strain at midspan versus temperature change for 

plain concrete slab (reference temperature, To = about 42.39 o o C (108.3 F)). 

30 
31 

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

-140 -120 -100 -80 -60 -40 -20 0 20 40

Axial Concrete Strain (με )

ΔT (o

F )

Equation

Test#1-1

Test#1-2

Test#2-1

Test#2-2

Test#3-1

Test#3-2

1 (ΔT oF) = 0.56 (ΔT oC) 

Figure 42. Graph. Axial concrete strain at midspan versus temperature change for 

steel-reinforced concrete slab (reference temperature, To = about 42.39 oC (108.3 o

F)). 

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

-140 -120 -100 -80 -60 -40 -20 0

ΔT (o

F )

Axial Concrete Strain (με )

20 40

Equation

Test#1-1

Test#1-2

Test#2-1

Test#2-2

Test#3-1

Test#3-2

1 (ΔT oF) = 0.56 (ΔT oC) 

Figure 43. Graph. Axial concrete strain at midspan versus temperature change 

for GFRP-reinforced concrete slab (reference temperature,

To = about 42.39 oC (108.3 oF)).
Table 3. Thermal outputs of slabs at different temperature levels 

(TS: titanium silicate; PS: plain slab; S-RS: steel-reinforced slab; G-RS: GFRP-reinforced 

32

Thermal Output 

(εT/O; με) 

(ε

Temperature (T; oF1) Elapsed Time ΔT2=T–To o (h) TS PS S-RS G-RS ( F) PS 

108.0 0 0 0 0 0 ~ ~ 118.9 24 –68 –8 –22 –21 10.9 6

71.5 48 224 15 19 25 –36.5 –20

1st 

–14.6 60 564 –46 –64 –52 –122.6 –61

1st Test: Cycle 

107.0 87 2 10 16 10 ~ ~ 108.0 94 3 5 11 8 ~ ~ 118.4 144 –70 –13 –21 –18 10.4 5

72.4 168 223 15 24 28 –35.6 –20

–14.7 180 563 –47 –55 –47 –122.7 –61

To = 108.0oF 

2nd 

Cycle 

108.1 207 3 7 13 12 ~ ~ 108.3 0 0 0 0 0 ~ ~ 

119.0 24 –69 –13 –23 –22 10.7 5

73.7 48 223 22 29 29 –34.6 –20

1st 

–15.4 60 562 –34 –50 –36 –123.7 –59

Cycle 

108.6 87 2 4 5 –5 ~ ~ 108.7 94 0 –7 –6 –14 ~ ~ 

2nd Test: 

118.6 144 –73 –24 –33 –41 10.3 4

72.6 168 218 15 23 28 –35.7 –20

–15.2 180 559 –36 –56 –49 –123.5 –59

T = 108.3o o F 

2nd 

Cycle 

108.5 207 –1 1 2 –3 ~ ~ 

1 oC = 5(oF – 32)/9. 21 (ΔT o o F) = 0.56 (ΔT C)
Table 3. Thermal outputs of slabs at different temperature levels 

(TS: titanium silicate; PS: plain slab; S-RS: steel-reinforced slab; G-RS: GFRP-reinforced 

Continued 

Thermal Output 

(εT/O; με) 

(εT

Temperature (T; oF) Elapsed Time (h) TS PS S-RS G-RS ΔT=T–To (oF) PS 

108.5 0 0 0 0 0 ~ ~ 

119.0 24 –68 –15 –24 –19 10.5 5

73.0 48 222 25 31 33 –35.5 –19

–15.2 60 560 –27 –47 –37 –123.7 –58

1st 

Cycle 

109.0 87 0 –4 -6 -5 ~ ~ 108.7 94 –1 –12 –15 –10 ~ ~ 

118.9 144 –70 –31 –40 –30 10.4 3

73.2 168 220 20 25 28 –35.3 –20

–14.8 180 557 –30 –46 –32 –123.3 –58109.0 207 1 –7 -9 -6 ~ ~ 

2nd 

Cycle 

F

3rd Test: 

To = 108.5 o

33

CHAPTER 5. FE STUDY OF DESIGN CONSIDERATIONS FOR CRCP 

FE ANALYSIS OF A 1.524-M (5-FT) CRCP SEGMENT 

As can be seen in figures 22 through 26, the tensile stress levels in concrete caused by 

both concrete shrinkage and temperature variation are far below the tensile strength of 

normal concrete for the free slab. Other restraining forces acting on a given concrete slab, 

such as friction from the subbase under concrete pavements or restraints from 

reinforcement ties to neighboring slabs, need to be considered. When these restraints are 

considered, the overall resulting tensile stress level in the concrete will increase, possibly 

exceeding the concrete tensile strength and causing cracks in the concrete slab. 

The CRCPs considered in the FE analyses have been assumed to have transverse cracks 

equally spaced at 1.524 m (5 ft (60 inches)) and were subjected to the concrete shrinkage 

and temperature variation. Since the cracks in the CRCP are assumed to be spaced 

equally, the longitudinal reinforcement at the crack is constrained in both longitudinal and 

rotational directions. Therefore, only a representative slab segment was needed to model 

the CRCP. The length of the slab segment, L, is equal to the crack spacing. While 

longitudinal reinforcement of number 6 rebars with a radius (r) of 9.53 mm (0.375 inch) 

was considered in the FEM analysis, the influence of transverse reinforcement was 

ignored. The bond-slip behaviors between the concrete and reinforcement and between 

the concrete slab and subbase were modeled by using horizontal spring elements. The 

underlying layers are modeled as an elastic foundation with an elastic spring constant of 

108.583 megapascals per meter (MPa/m) (400 poundsforce per square inch per inch 

(lbf/in2

/inch)). The FE model of the CRCP slab segment has been assumed to be 

subjected to a concrete shrinkage at 28 d of 355.6 με and a temperature change (ΔT) of –

27.8 o o C (–50 F) and –16.7 o o C (–30 F) at the top and bottom of the slab segment, 

respectively. The temperature varies linearly from the top to the bottom. All of the other 

model parameters and material properties used are listed in table 4, and the schematic 

details of the FE model are depicted in figure 44; the properties of GFRP rebar are 

assumed in this analysis. 

35 
Table 4. Model parameters and material properties used in FE study. 

Parameter and Properties Value 

Width, B (cm (inches)) 15.24 (6)

Height, H (cm (inches)) 25.40 (10)

33.10 (4.80)1

Young’s modulus of concrete at 28 d, Ec,28 (GPa (× 106 lbf/in2)) 2 and 34.48 (5.00)

Poisson’s ratio of concrete, ν 0.20 c

Young’s modulus of steel rebar (GPa (× 106 2 lbf/in )) 200.00 (29.00)

Longitudinal Young’s modulus of GFRP rebar (GPa (× 106 lbf/in2)) 40.80 (5.92)

10.26 (5.7)1

CTE of concrete, α F)) o o c (με/ C (με/ 2 and 14.40 (8.0) o CTE of steel rebar, α ( με/ C (με/ F)) 11.88 (6.6) o r,s

o CTE of GFRP rebar, α (με/ C (με/ F)) 9.07 (5.04) o r,g 1

Granite coarse aggregate used. 

2

Siliceous river gravel coarse aggregate used. 

1 megapoundforce per square inch (106 lbf/in2) = 6.89 gigapascal (GPa) 

Figure 44. Drawing. Schematic details of a 2-D CRCP finite element model. 

36 
In the FE analysis, the CRCP design parameters—such as the CTE of concrete, the 

friction from the pavement's subbase, and the bond-slip between concrete and 

reinforcement—were studied to assist in understanding their effects on stress 

development and crack width in the CRCP.

Effect of Concrete CTE on Stress Development in CRCP 

Two different types of concrete, with granite aggregate or siliceous river gravel aggregate, 

have been adopted in the stress analysis of the CRCP slab segment. The CTEs of granite 

and siliceous river gravel concrete are 10.26 με/

o o o C (5.7 με/ F) and 14.40 με/ C (8.0 

με/

o

F), respectively.(30) In addition, the steel-reinforced CRCP slab segment is analyzed 

for comparison with the GFRP-reinforced one. The bond between the concrete and 

reinforcement is assumed to be perfect, and the bond-slip between the concrete slab and 

subbase was represented using a spring stiffness of 236.409 kilonewton per meter (kN/m) 

(1,350 poundsforce per inch (lbf/inch)), which is simulated for a flexible subbase or a 

lime-treated clay subbase, having the bond-slip stiffness per unit area of 40.719 MPa/m 

(150 lbf/in2/inch) with respect to the concrete slab. The spring stiffness corresponds to a 

concrete element with a horizontal length of 3.81 cm (1.5 inches) and a thickness in the zdirection of 15.24 cm (6 inches). 

Figures 45 and 46 show the FE results of axial tensile stresses developed on the concrete 

surface along the longitudinal (x-) direction, considering the aforementioned restraining 

conditions. The maximum tensile stress level for the GFRP-reinforced slab segment at the 

x-midpoint, shown in figure 42, is much higher compared with those for the freely 

supported reinforced concrete slab, shown in figures 22 through 26. As expected, 

considering those restraints in the CRCP model increases the tensile stress level in 

concrete. As can be seen in both figures 45 and 46, because of the low Young’s modulus 

in the GFRP rebar, the tensile stresses for the GFRP-reinforced concrete are always 

smaller than those for the steel ones. The use of GFRP rebar as the reinforcement might 

lead to larger crack spacings followed by wider crack widths in the CRCP. If it is 

necessary to shorten the crack spacing or narrow the crack width, it can be achieved by 

using a larger amount of reinforcement or by adjusting the concrete properties, the 

subbase restraints, or bonding between the concrete and reinforcement. For reference, 

AASHTO guidelines indicate that the crack spacing should be no more than 2.438 m (8 

ft) to minimize the incidence of crack spalling and no less than 1.067 m (3.5 ft) to 

minimize the potential for the development of punchouts, and the allowable crack width 

should not exceed 1 mm (0.04 inch) for the steel-reinforced CRCP.(2) 

37 
0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50

x (inches )

Axial Stress (ksi )

60

steel GFRP

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C 

Figure 45. Graph. Axial tensile stress on concrete surface versus longitudinal 

location of a 1.524-m (5-ft) CRCP segment with ρ = 0.00739 

and α o o c = 10.26 με/ C (5.7 με/ F). 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50

x (inches )

Axial Stress (ksi )

60

steel GFRP

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 8.0 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.04 με /

o F

1 inch = 25.4 mm; 1 ksi = 6.89 MPa1 (ΔT oF) = 0.56 (ΔT oC);1 με/

o

F = 1.80 με/

o

C 

Figure 46. Graph. Axial tensile stress on concrete surface versus longitudinal 

location of a 1.524-m (5-ft) CRCP segment with ρ = 0.00739 

and α o o c = 14.40 με/ C (8.0 με/ F). 

38 
It can be seen in the comparison between figures 45 and 46 that the tensile stress level in 

concrete for the granite concrete with a CTE of 10.26 με/

o o C (5.7 με/ F) is lower than that 

for the siliceous river gravel concrete with a CTE of 14.40 με/

o

C (8.0 με/

o

F). This is 

because the difference between CTEs of concrete and reinforcement for the granite 

concrete is smaller than that for the siliceous river gravel concrete. Therefore, the tensile 

stress in concrete can be reduced by using concrete with lower CTE. Regardless of the 

concrete CTEs, the maximum tensile stresses in concrete for both steel- and GFRPreinforced slab segments are much higher than the concrete tensile strength, and all the 

slab segments will presumably be cracked at their midspan due to the given temperature 

variation and shrinkage conditions. The concrete tensile strengths for the granite and 

siliceous river gravel concretes are about 2.90 MPa (420 lbf/in2

) and 2.55 MPa (370 

lbf/in2), respectively, with a concrete compressive strength, fc′, of about 27.58 MPa (4,000 

lbf/in2

). 

The axial stress distributions in the reinforcements along the longitudinal (x-) direction 

for two different concrete CTEs are shown in figures 47 and 48. While the reinforcements 

around the middle are under low compression, those around the crack (the ends of the 

slab segment) are under high tension. Because of the stiffness compatibility between 

GFRP and concrete, the tensile stresses in the GFRP reinforcements are lower than those 

in the steel reinforcements. The tensile reinforcement stress for the lower concrete CTE 

(figure 49) is also lower than that for the higher concrete CTE (figure 48). 

-20

0

20

40

60

80

100

120

0 10 20 30 40 50 6

x (inches )

Axial Stress (ksi )

0

steel GFRP

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C 

Figure 47. Graph. Axial stress in reinforcement versus longitudinal location 

of a 1.524-m (5-ft) CRCP segment with ρ = 0.00739 

and α o o c = 10.26 με/ C (5.7 με/ F). 

39 
-20

0

20

40

60

80

100

120

0 10 20 30 40 50 6

x (inches )

Axial Stress (ksi )

0

steel GFRP

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 8.0 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C 

Figure 48. Graph. Axial stress in reinforcement versus longitudinal location of a 

1.524-m (5-ft) CRCP segment with ρ = 0.00739 and α = 14.40 με/ C (8.0 με/ F). o o c

Figures 47 and 48 show that the reinforcements are subjected to higher tensile stresses 

than the limits of their allowable tensile stresses. While the stress limit for the grade 60 

number 6 steel rebar is about 75 percent of its ultimate tensile strength (379 MPa (55 

ksi)), the GFRP rebar’s allowable tensile stress is about 20 percent of its ultimate tensile 

strength under a harsh environment (124 MPa (18 ksi)).(2,26) The GFRP rebar’s allowable 

stress range is established for the prevention of any undesired early failure of GFRP 

rebars under sustained loads due to alkaline attacks on the glass fibers. 

Effect of Bond-Slip between Concrete Slab and Subbase 

Granite aggregate concrete was adopted for this analysis. The bond between the concrete 

and reinforcement was again assumed to be perfect, and two different values of the bondslip between the concrete slab and subbase were considered to study its effect on the 

stress development and crack width of the 1.524-m (5-ft) GFRP-reinforced CRCP slab 

segment; the spring stiffnesses used for the slab subbase bonds were 0.236 MN/m (1,350 

lbf/inch) and 24.271 MN/m (138,600 lbf/inch). The bond-slip stiffnesses were calculated 

for the concrete element with a horizontal length of 3.81 cm (1.5 inches) and a thickness 

of 15.24 cm (6 inches), and simulated for the bond-slip of the concrete slab with respect 

to the flexible (lime-treated clay) subbase and the cement-stabilized subbase, respectively. 

While the former was calculated from the bond-slip stiffness per unit area of 40.719 

MPa/m (150 lbf/in2

/inch), the latter was calculated from that of 4.180 GPa/m (15,400 

lbf/in2

/inch).(33) 

40 
Figures 49 and 50 show the FEM results of concrete stresses at the bottom surface and 

top surface of the GFRP-reinforced concrete pavement along the longitudinal (x-) 

direction, respectively, from varying the bond-slip stiffness between the concrete and 

subbase. As expected, the maximum tensile stresses in the concrete caused by the 

shrinkage and temperature variation have drastically increased after considering the 

aforementioned restraining conditions. Figure 49 shows that the tensile stress in the 

concrete for the higher subbase friction is larger than that for the lower one at the bottom 

of the CRCP slab segment. At the top of the slab segment, the reversed result of the 

concrete stress level has been observed (figure 50); smaller stress was found for the 

higher friction. The higher subbase friction creates more restraint against the concrete 

volume change at the bottom of the slab segment. More frictional reaction force is 

generated at the concrete bottom, leading to less concrete displacement with larger 

concrete stress at the bottom. Simultaneously, this causes less concrete displacement 

around the reinforcement and, consequently, less reaction force provided from the 

reinforcement to the concrete, leading to smaller concrete stresses around the 

reinforcement and at the top of the slab segment. 

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 6

x (inches )

Axial Stress (ksi )

0

1,350 lbf/inch 138,600 lbf/inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm;1ksi = 6.89 MPa; 1(ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C; 1lbf/inch = 175.12 N/m 

Figure 49. Graph. Axial stress at concrete bottom surface versus longitudinal 

location for two different subbase bond stiffnesses 

(ρ = 0.00739 and L = 1.524 m (60 inches)). 

41 
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

x (inches )

Axial Stress (ksi )

60

1,350 lbf/inch 138,600 lbf/inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to

bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

1 inch=25.4 mm;1 ksi=6.89 MPa; 1 (ΔT o oC); 1με/

o o F)=0.56 (ΔT F=1.80 με/ C; 1l bf/inch=175.12 N/m 

Figure 50. Graph. Axial stress at concrete top surface versus longitudinal location 

for two different subbase bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). 

Figures 51 and 52 show the axial concrete stress contours from the cases employing the 

two different subbase frictions. Figure 51, representing the lower friction case, shows that 

the stress variation is almost symmetrical with respect to the longitudinal center line on 

which the reinforcement is located; the stress contour is similar to that of the case without 

the subbase friction. On the other hand, the stress in figure 52, for the higher friction case, 

is observed to drastically change from the bottom to the top of the slab segment; the 

stress level at the bottom is much higher than that at the top. With such a high subbase 

friction, the CRCP is likely to have a chance to crack from its bottom area. In addition, 

the concrete stress at the bottom for the higher friction (figure 50) is larger than that at the 

top for the lower friction (figure 49). This implies that the CRCP with the higher subbase 

friction will have more cracks for a certain pavement length, in conjunction with smaller 

crack spacings. The high stress concentrations are also found around the reinforcement 

near the crack (the end of the slab segment) in figures 51 and 52. 

42 
1 lbf/in2 = 6.89 kilopascal (kPa) 

Figure 51. Image. Axial stress in concrete versus longitudinal location of a 1.524-m 

(5-ft) CRCP segment with ρ = 0.00739, α o o c = 10.26 με/ C (5.7 με/ F), and 

a subbase bond-slip stiffness of 0.236 MN/m (1,350 lbf/inch). 

1 lbf/in2 = 6.89 kPa 

Figure 52. Image. Axial stress in concrete versus longitudinal location of a 1.524-m 

(5-ft) CRCP segment with ρ = 0.00739, α o o c = 10.26 με/ C (5.7 με/ F), and 

a subbase bond-slip stiffness of 24.271 MN/m (138,600 lbf/inch). 

43 
The stress distributions in the GFRP reinforcement for the two different subbase frictions 

are plotted in figure 53. The compressive stresses (negative value in the figure) are 

developed around the middle of the slab segment in the longitudinal (x-) direction for 

both friction cases. The compressive stress level for the higher friction, about 6.46 MPa 

(0.94 ksi), is slightly lower than that for the lower friction, about 7.81 MPa (1.13 ksi). At 

the cracks, a tensile stress of about 222.31 MPa (32.24 ksi) is developed for the higher 

friction and is also lower than that of about 237.09 MPa (34.39 ksi) for the lower friction. 

As mentioned before, the subbase with the higher friction applies more frictional reaction 

force to the bottom of the slab segment as the concrete volume change occurs, leading to 

less concrete displacements both at the bottom and around the reinforcement. The lesser 

concrete displacement around the reinforcement releases the force applied to the 

reinforcement, leading to lower compressive reinforcement stresses around the middle in 

the longitudinal (x-) direction and lower tensile reinforcement stresses at the crack. 

The variation of crack width through the depth of the slab segment is observed in figure 

54. The crack width at the bottom for the higher friction is narrower than that for the 

lower friction because of greater restraint from the subbase. The crack width for the 

higher friction is narrower up to about middepth of the slab (where the reinforcement is 

located) and becomes wider at the top, presenting more drastic variations through the 

depth. In the figure, the protrusion on the graph is found at the middepth because of the 

restraint from the reinforcement, and the crack width at the top of the pavement is shown 

to be wider than that at the bottom since the magnitude of the temperature drop (ΔT) is 

larger at the top than at the bottom and the restraint from the subbase exists at the bottom. 

The crack widths for both cases are below the allowable limitation of 1 mm (0.04 inch).(2) 

-5

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 6

x (inches )

Axial Stress (ksi )

0

1,350 lbf/inch 138,600 lbf/inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm;1 ksi = 6.89 MPa; 1(ΔT F) = 0.56 (ΔT C); 1με/o

F = 1.80 με/

o

C; 1lbf/inch = 175.12 N/m 

Figure 53. Graph. Axial stress in GFRP rebar versus longitudinal location for two 

different subbase bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). 

44 
0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Crack Width (inch )

Pavement Depth (inches )

1,350 lbf/inch 138,600 lbf/inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to

bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

 o o 1 inch = 25.4 mm; 1 (ΔT F) = 0.56 (ΔT C); 1 με/

o

F = 1.80 με/

o

C; 1lbf/inch = 175.12 N/m 

Figure 54. Graph. Pavement depth versus crack width for two different subbase 

bond stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). 

Effect of Bond-Slip between Concrete and Reinforcement 

The FE analysis was also conducted for CRCP slab segments with different bond-slip 

stiffness between the concrete and the reinforcement. The bond-slip stiffness between 

concrete and reinforcement varies from 1.344 × 109 N/m (7.675 × 106 lbf/inch), 0.433 ×

109

 N/m (2.474 × 106 lbf/inch), and 0.175 × 109 N/m (1.0 × 106 lbf/inch), where the first 

value corresponds to the perfect bond case, the second corresponds to the bond-slip 

stiffness between the concrete and steel reinforcement, and the third is arbitrarily selected 

to about 40 percent of the second value. These bond-slip stiffnesses correspond to the 

bond-slip stiffness per unit area of 589.5 × 103

 MPa/m (2.172 × 106 lbf/in2/inch), 190.0 ×

103

 MPa/m (0.7 × 106 lbf/in2/inch), and 76.86 × 103 MPa/m (0.283 × 106 lbf/in2/inch), 

respectively. A spring stiffness between the concrete slab and subbase (a flexible subbase 

or a lime-treated clay subbase) of 236.409 kN/m (1,350 lbf/inch), which corresponds to 

the bond-slip stiffness per unit area of 40.719 MPa/m (150 lbf/in2

/inch), was applied for 

the analyses. 

Figure 55 shows that the concrete stress level from a larger bond-slip stiffness is higher 

than that from a smaller stiffness since the tighter bond between the concrete and 

reinforcement provides more restraint to the concrete’s volume change. It can therefore 

be anticipated that using reinforcement that provides the concrete with a tighter bond can 

cause more cracks in a certain length of CRCP, leading to smaller crack spacing and a 

narrower crack width. Under the given conditions, only the maximum concrete stress for 

the bond-slip stiffness of 0.175 × 109

 N/m (1.0 × 106 lbf/inch) is below the tensile 

45 
strength of the concrete. Figure 56 shows the axial stress distributions in the GFRP 

reinforcement for the different bond-slip stiffnesses. The stress level around the crack 

decreases as the bond-slip stiffness decreases. The tensile stress levels for all the bondslip cases are higher than the allowable stress limit for the GFRP rebar. Employing 

reinforcement with a lower bond-slip stiffness might be one way to reduce the stress 

levels in both concrete and reinforcement in the CRCP. It is noted that the bond between 

the concrete and GFRP reinforcement cannot be perfect, and for practical purposes it can 

be assumed to be between the second and third bond cases. Stress development in the 

CRCP is sensitive to the bond between the concrete and the reinforcement. 

The variation of crack width throughout the pavement depth for the crack spacing, L, of 

1.524 m (5 ft) is shown in figure 57. The crack width for the higher bond-slip stiffness is 

narrower than that for the lower ones as a result of having more restraint against the 

concrete volume change. Also, the crack width for steel reinforcement is narrower than 

that for GFRP reinforcement at a bond-slip stiffness due to the higher Young’s modulus 

of the steel reinforcement. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

x (inches )

Axial Stress (ksi )

60

perfect bond

2.474E6 lbf/inch

1.0E6 lbf/inch

perfect bond with bond-break at a relative displacement of 0.004 inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch=25.4 mm; 1 ksi=6.89 MPa; 1 (ΔT F)=0.56 (ΔT C); 1 με/o o F=1.80 με/ C; 1 lbf/inch=175.12 N/m 

Figure 55. Graph. Axial tensile stress on concrete surface versus longitudinal 

location for different bond-stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). 

46 
-5

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 6

x (inches )

Axial Stress (ksi )

0

perfect bond

2.474E6 lbf/inch

1.0E6 lbf/inch

perfect bond with bond-break at a relative displacement of 0.004 inch

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch=25.4 mm; 1 ksi=6.89 MPa; 1 (ΔT F)=0.56 (ΔT C); 1 με/o o F=1.80 με/ C; 1 lbf/inch=175.12 N/m 

Figure 56. Graph. Axial stress in GFRP rebar versus longitudinal location for 

different bond-stiffnesses (ρ = 0.00739 and L = 1.524 m (60 inches)). 

0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Crack Width (inch )

Pavement Depth (inches )

Steel(perfect bond) Steel(2.474E6 lbf/inch)

Steel(1.0E6 lbf/inch) GFRP(perfect bond)

GFRP(2.474E6 lbf/inch) GFRP(1.0E6 lbf/inch)

GFRP(perfect bond;bond-break)

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 5.7 με /

o F

α r,s = 6.6 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C; 1 lbf/inch = 175.12 N/m 

Figure 57. Graph. Pavement depth versus crack width for different bond stiffnesses 

(ρ = 0.00739 and L = 1.524 m (60 inches)). 

47 
In figure 57, the protrusions on the graph are found at the middepth of the pavement 

(where the reinforcement is located), and the graph is observed to be more protruded with 

the higher bond-slip stiffness. This results from the fact that the concrete volume change 

is restrained most at the middepth by the reinforcement and is subjected to more restraint 

as the bond-slip stiffness increases. The crack width at the top of the pavement is wider 

than that at the bottom of the pavement since the magnitude of the temperature drop (ΔT) 

is larger at the top than at the bottom, and the restraint from the subbase exists at the 

bottom. The crack widths throughout the pavement depth for all the cases are below 1 

mm (0.04 inch), which is the assumed maximum allowable crack width to prevent the 

loss of concrete aggregate interlock. 

The high stress concentration caused by the perfect bond assumption between the 

concrete and reinforcement, as found around the reinforcement near the crack in figures 

51 and 52, is not realistic; the bond between the concrete and reinforcement will actually 

break near the crack, relieving the stress concentration as shown in figure 58, whose FE 

model is equivalent to that of figure 51 except that the bond-slip springs between 

concrete and reinforcement are modeled to yield when the relative spring displacement 

between concrete and reinforcement exceeds 0.1 mm (0.004 inch). The calculated bondbreak appears at the first spring element; hence, the bond-break length is less than 3.81 

cm (1.5 inches) starting from the surface of the crack. The bond-break near the crack also 

lowers the overall stress level in concrete (as shown in figure 58). 

1 lbf/in2 = 6.89 kPa

Figure 58. Image. Axial stress in concrete versus longitudinal location of a 1.524-m 

(60-inch) CRCP segment with ρ = 0.00739, α o o c = 10.26 με/ C (5.7 με/ F), 

and a subbase bond-slip stiffness of 236.409 kN/m 

(1,350 lbf/inch; bond-break considered). 

48 
This effect of bond-break can also be seen in figures 55 and 56. While the bond-break 

near the crack decreases the tensile concrete stress from about 6.33 MPa (0.92 ksi) to 

4.15 MPa (0.60 ksi) on the concrete surface, it increases the tensile reinforcement stress 

from about 237.09 MPa (34.39 ksi) to 285.94 MPa (41.47 ksi) at the cracks, and the 

compressive reinforcement stress from about 7.81 MPa (1.13 ksi) to 10.49 MPa (1.52 ksi) 

at the midspan. If bond-break length increases, which will make more spring elements 

yield, the maximum tensile stress in the reinforcement will reduce. In addition, the effect 

of the bond-break on the crack width variation in the case of GFRP reinforcement is 

shown in figure 57. Since the bond breaks near the crack, the crack widths throughout the 

pavement depth become wider than those without the bond-break assumption; note that 

the maximum crack width of the 1.524-m (5-ft) CRCP segment is about 0.83 mm (0.033 

inch) on the top surface, which is just under the allowable crack width limitation, 1 mm 

(0.04 inch). 

FE ANALYSIS OF CRCP SEGMENTS WITH DIFFERENT LENGTHS 

The previous FE results show that, in most cases, not only do the concrete stresses exceed 

the concrete tensile strength, but the reinforcement stresses around the crack also exceed 

the limit of allowable working stress of GFRP rebar under the given conditions. As 

previously shown, the lower bond-slip stiffness between concrete and reinforcement, as 

well as the smaller CTE and Young’s modulus of concrete, can lower the stress levels in 

the concrete and reinforcement. Therefore, the bond-slip stiffness of 0.433 × 109 N/m 

(2.474 × 106 lbf/inch), instead of perfect bond, is employed for a design example, along 

with a concrete CTE of 6.84 με/

o o C (3.8 με/ F) and Young’s modulus of 24.8 GPa (3.6 ×

106 lbf/in2) for a limestone aggregate concrete. The bond-slip stiffness between concrete 

and subbase for flexible subbase (or lime-treated clay subbase) is applied for the example. 

In addition, the CRCP segments at three different lengths—1.067 m (3.5 ft), 1.524 m (5 

ft), and 2.438 m (8 ft)—are modeled to represent the range of the crack spacing 

anticipated from the conventional CRCP design, which is 1.067 to 2.438 m (3.5 to 8.0 ft). 

The other conditions for the example are the same as previously adopted. 

The axial tensile concrete stress distribution at the top of the slab segment, along the 

longitudinal direction, has been plotted for each slab length (figure 59). As shown in the 

figure, the concrete stress level of the longer slab segment is higher than that of the 

shorter slab segment. The maximum stress levels in the concrete for the lengths of 1.067 

m (3.5 ft), 1.524 m (5 ft), and 2.438 m (8 ft) are about 1.86 MPa (270 lbf/in2

), 3.08 MPa 

(447 lbf/in2 2 ), and 6.16 MPa (893 lbf/in ), respectively. The stress level for L = 2.438 m (8 

ft) is well above the tensile strength, about 2.41 MPa (350 lbf/in2

), of the limestone 

concrete approximated with a concrete compressive strength, fc′, of about 27.58 MPa 

(4,000 lbf/in2

). This slab segment will crack at the middle. On the other hand, the slab 

segments with lengths shorter than 1.067 m (3.5 ft) will not crack at the middle; the 

maximum stress level for L = 1.067 m (3.5 ft) does not reach the tensile strength of 

concrete. The stress level for L = 1.524 m (5 ft) is assumed to be roughly on the verge of 

the cracking point or has slightly passed the point. Therefore, the crack spacing for the 

example is anticipated to be between 1.067 m (3.5 ft) and 1.524 m (5 ft). 

49 
Figure 60 shows the axial stress distributions in the GFRP reinforcement for the different 

slab segment lengths. Around the crack, the stress levels in the GFRP reach around 

113.83 MPa (16.51 ksi), 192.70 MPa (27.95 ksi), and 387.59 MPa (56.21 ksi) for the 

lengths of 1.067 m (3.5 ft), 1.524 m (5 ft), and 2.438 m (8 ft), respectively. Except for the 

case of L = 1.067 m (3.5 ft), the GFRP reinforcement is subjected to higher stress levels 

than its limit of allowable tensile stress (124 MPa; 18 ksi); with the anticipated crack 

spacing of this example, shorter than 1.524 m (5 ft), the stress level could meet its limit. 

The variation of crack width along the pavement depth is shown in figure 61. The crack 

width for the longer slab segment is wider than that for the shorter one. Except for the 

case of L = 2.438 m (8 ft), the crack widths for all cases are below the limit of allowable 

crack width, 1 mm (0.04 inch). 

It can be understood in this chapter that the behavior of the CRCP can be adjusted by 

varying the concrete material properties, subbase type, and the bond characteristics 

between concrete and reinforcement. For example, if it is necessary to have a smaller 

crack spacing in the CRCP (which can be attained by creating higher concrete stress 

level), concrete with a larger CTE and Young’s modulus, a subbase providing the 

concrete slab with higher friction, reinforcement which bonds better with concrete, or a 

combination of the three may need to be employed. This study reveals that careful 

consideration of these parameters can provide favorable control of the stresses in the 

concrete and reinforcement followed by the control of cracking in the CRCP, allowing for 

a sound design of the GFRP-reinforced CRCP. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 10

x (inches )

Axial Stress (ksi )

0

L=3.5 ft L=5 ft L=8 ft

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from

top to bottom.)

α c = 3.8 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C; 1 ft = 0.305 m 

Figure 59. Graph. Axial tensile stress on concrete surface versus longitudinal 

location for different slab segment lengths (ρ = 0.00739; bond-slip 

stiffness = 0.433 × 109 6 N/m (2.474 × 10 lbf/inch)). 

50 
-10

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 10

x (inches )

Axial Stress (ksi )

0

L=3.5 ft L=5 ft L=8 ft

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly from top to bottom.)

α c = 3.8 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 ksi = 6.89 MPa; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C; 1 ft = 0.305 m 

Figure 60. Graph. Axial stress in GFRP rebar versus longitudinal location 

for different slab segment lengths (ρ = 0.00739; bond-slip 

stiffness = 0.433 × 109 6 N/m (2.474 × 10 lbf/inch)). 

0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03 0.04 0.05 0.06

Crack Width (inch )

Pavement Depth (inches )

L=3.5 ft L=5 ft L=8 ft

ε c,s (28) = 355.6 με

ΔT at top of slab = -50 o F

ΔT at bottom of slab = -30 o F

(Temperature changes linearly

from top to bottom.)

α c = 3.8 με /

o F

α r,g = 5.04 με /

o F

o o 1 inch = 25.4 mm; 1 (ΔT F) = 0.56 (ΔT C); 1 με/o

F = 1.80 με/

o

C; 1 ft = 0.305 m 

Figure 61. Graph. Pavement depth versus crack width for different slab-segment 

lengths (ρ = 0.00739; bond-slip stiffness = 0.433 × 109 6 N/m (2.474 × 10 lbf/inch)). 

51 
Design considerations related to crack spacing (1.067 to 2.438 m; 3.5 to 8 ft), crack width 

limitation (≤1 mm (0.04 inch)), and the allowable stress limit of GFRP reinforcement 

were also presented in this chapter, and the results indicated that GFRP-reinforced CRCP 

can satisfy these requirements. For cost considerations, the reinforcement amount used in 

the proposed design (≈0.74 percent) was chosen to be the same as a traditional steelreinforced CRCP. Typical reinforcement amounts for steel-reinforced CRCP can range 

between 0.5 and 0.7 percent, depending on the weather conditions.(20) Increasing the 

reinforcement amount will reduce the reinforcement stress, which may be a simple and 

necessary consideration for the GFRP-reinforced CRCP when the pavement is likely to 

be subjected to a harsh environment with high temperature variations and alkaline attack. 

The current design example using number 6 rebars at 15.2-cm (6-inch) spacing in the 

longitudinal direction and number 5 at 121.9-cm (4-ft) spacing in the transverse direction 

in a 3.658-m- (12-ft) wide lane shows feasible performance under an extreme 

temperature variation (ΔT = –27.8 o o C (–50 F) at the top surface of the pavement and ΔT

= –16.7 o o C (–30 F) at the bottom surface), with a concrete shrinkage of 355.6 με at 28 d. 

By careful consideration of concrete properties, proper bond between GFRP rebar and 

concrete, reinforcement amount, and subbase friction, the above design shows 

satisfactory performance.

52 
CHAPTER 6. MECHANISTIC STUDY OF GFRP-CRCP DESIGN 

DESIGN INFORMATION OF STEEL-CRCP AND GFRP-CRCP FOR 

MECHANISTIC ANALYSIS 

The Virginia Department of Transportation planned to construct a steel-reinforced CRCP 

on S.R. 288 in June 2003.(12) The CRCP would consist of two lanes: one 4.267-m- 

(14-ft-) wide travel lane, and a 3.658-m- (12-ft-) wide passing lane. The CRCP section is 

25.4 cm (10 inch) thick, and it is reinforced with a steel reinforcing ratio of about 0.74 

percent, which corresponds to number 6 longitudinal reinforcements spaced at 15.24 cm 

(6 inches). Number 5 steel rebars were used for the transverse reinforcement at a spacing 

of 121.9 cm (48 inches). Below the pavement section is a 7.62-cm- (3-inch-) thick 

asphalt-stabilized open graded drainage layer (OGDL; number 57 AASHTO gradation, 

treated with 2.5 percent asphalt by weight), which is then supported by a 15.24-cm- (6-

inch-) thick layer of cement-treated aggregate (dense aggregate type I, size 21A, treated 

with 4 percent cement by weight). The coarse aggregate of metamorphosed granite is 

used for concrete mix. The design parameters and material properties of the VDOT’s 

CRCP are listed in table 5; the table also includes the GFRP material properties and the 

assumed bond property between concrete and subbase for the following mechanistic 

study of a GFRP-reinforced CRCP. 

The performance of the steel-reinforced CRCP at 28 d in terms of crack spacing, crack 

width, and tensile stress level in steel reinforcement at crack was predicted by using the 

mechanistic analysis program, CRCP8.(22) A mean crack spacing of 1.058 m (3.47 ft), a 

crack width of 0.49 mm (0.0193 inch), and a reinforcement tensile stress at crack of 

288.56 MPa (41.850 ksi) were obtained. The crack spacing is acceptable even though the 

crack spacing of 1.058 m (3.47 ft) barely meets its allowable lower limit of 1.067 m (3.5 

ft) since the punchout failure, which is first characterized by a loss of aggregate interlock 

at one or two closely spaced cracks (usually less than 0.610 m (2 ft)), can be avoided 

provided that the crack width is narrow enough (≤ 1 mm (0.04 inch)).(2,10) Also, the steel 

reinforcement stress at crack is lower than its maximum allowable limit of 379 MPa (55 

ksi), which is about 75 percent of the ultimate tensile strength for the grade 60 number 6 

steel rebar.(2)

In the following section, based on the design parameters and material properties of 

VDOT’s CRCP (table 5), except for replacing number 6 steel reinforcement with number 

6 GFRP reinforcement, the performance of GFRP-reinforced CRCP will be predicted 

over various types of concrete and subbase. This mechanistic prediction shows the effect 

of using different types of concretes and subbases on the pavement’s performance, which 

the FE analysis previously conducted could not explicitly indicate. In addition, the 

performance of the GFRP-CRCP will be compared with that of the steel-CRCP in this 

chapter. The ideal situation is to come up with a feasible GFRP-CRCP design that 

performs comparable to the steel-CRCP without raising the GFRP reinforcement ratio. 

Considered in the mechanistic simulation of GFRP-CRCP is also the same GFRP rebar 

properties utilized in the FE analysis in Chapter 5. 

53 
Table 5. Design parameters and material properties used in mechanistic analysis. 

1 Parameters and Properties Value 

Longitudinal reinforcement spacing (cm (inches)) 15.24 (6.0)

Pavement thickness (cm (inches)) 25.4 (10.0)

Young’s modulus of concrete at 28 d (GPa (× 106 lbf/in2)) 31.44 (4.56)

2 Compressive strength of concrete at 28 d (MPa (lbf/in )) 32.13 (4,660)

Tensile strength of concrete at 28 d (MPa (lbf/in2)) 3.86 (560)

Total shrinkage of concrete (με) 394

Young’s modulus of steel rebar (GPa (× 106 2 lbf/in )) 200.00 (29)

41.37 (6.0) 

(≈40.80 (5.92)) Longitudinal Young’s modulus of GFRP rebar (GPa (× 106

 lbf/in2)) 

Ultimate tensile strength of GFRP rebar (MPa (ksi)) 620 (90)

CTE of concrete, αc (με/

o o C (με/ F)) 10.33 (5.74)

o o CTE of steel rebar, αr,s (με/ C (με/ F)) 11.88 (6.6)

CTE of GFRP rebar, αr,g (με/

o

C (με/

o

F)) 9.07 (5.04)

Bond-slip stiffness/unit area bet. concrete and subbase 15.17 (55.88) (MPa/m (lbf/in2

/inch)) 

o 43.3 (110), Curing, minimum temperature ( C ( F)) o

–3.89 (25)

4,540 (10,000), 

15.24 (6.0) Static single wheel load (kg (lb)), wheel base radius (cm (inches)) 

1

Granite aggregate is used for concrete mix; number rebar is considered; asphalt- 

 stabilized subbase is used. 

CRACK DEVELOPMENT AND REINFORCEMENT STRESS IN GFRP-CRCP 

WITH VARYING CONCRETE COARSE AGGREGATE TYPE 

The material properties of concrete (such as CTE and Young’s modulus) are primarily a 

function of the type of coarse aggregate, and since these properties are interdependent, a 

consistent set of properties that are representative of the concrete mixture to be used 

should be carefully selected for the concrete pavement design and analysis.(30) The 

approximate sets of concrete material properties are listed in table 6. Except for that of 

granite concrete, the compressive strengths are assumed to be 31.03 MPa (4,500 lbf/in2

) 

to approximate the values of indirect tensile strength, followed by the flexural strength 

and drying shrinkage values. The concrete material properties and their approximate 

relationship have been identified by other researchers.(30) In table 6, it is shown that the 

coarse aggregate types are listed in order of lowest to highest concrete CTE, which are 

6.84 με/

o o o C (3.8 με/ F) for limestone concrete and 14.40 με/ C (8.0 με/o

F) for siliceous 

river gravel concrete, respectively. 

54 
Table 6. Concrete material properties at 28 d used in mechanistic analysis (varied by 

using different types of coarse aggregate). (30)

Young's 

Modulus 

Coefficient 

of Thermal 

Expansion 

Drying 

Shrinkage

Coarse 

Aggregate 

Type 

Compressive 

Strength 

Tensile 

Strength 

Flexural 

Strength (× 106

(με/ lbf/in oF1) (lbf/in2 2) 2

) (lbf/in2

) (lbf/in2) (με)

Limestone 3.8 4,500 3.6 387 625 626

Basalt 4.8 4,500 3.8 486 992 471

Granite 5.74 4,660 4.56 560 610 394

Dolomite 5.9 4,500 4.8 495 895 458

Sandstone 6.5 4,500 3.8 468 762 498

Quartz 6.6 4,500 4.5 495 868 458

Siliceous 

River Gravel 8.0 4,500 5.0 419 697 572

1 1 με/o

F = 1.80 με/

o

C. 2

 1 lbf/in2 = 0.00689 MPa. 

Figure 62 shows the prediction of mean crack spacing for the GFRP-CRCP over various 

types of concrete coarse aggregate as well as that for the steel-GFRP with granite coarse 

aggregate, which is the VDOT’s CRCP. It can be easily understood that the GFRP-CRCP 

with granite concrete has larger crack spacing (2.115 m (6.94 ft)) than does the VDOT’s 

steel-CRCP (1.058 m (3.47 ft)) since the Young’s modulus of GFRP is smaller than that 

of steel. Among the GFRP-CRCPs, the CRCP using basalt concrete is predicted to have 

the largest crack spacing of 2.457 m (8.06 ft), which slightly exceeds the upper limit of 

allowable crack spacing of 2.438 m (8 ft). This is reasonable since the basalt concrete has 

a relatively low CTE and Young’s modulus, which cause low tensile stress development 

in concrete and result in less cracks in the CRCP. On the other hand, using the siliceous 

river gravel concrete creates the smallest crack spacing of 1.003 m (3.29 ft), which results 

from its high CTE, high Young’s modulus, and large shrinkage; this is still acceptable, 

despite slightly deviating from the lower allowable limit of 1.067 m (3.5 ft) for reasons 

discussed at the beginning of this chapter. 

It is found in the prediction that even though the limestone concrete has the lowest CTE 

and Young’s modulus, the crack spacing is smaller than those for the basalt, granite, 

dolomite, and quartz concretes (a result of this type having the lowest tensile strength and 

largest shrinkage). It can therefore be understood that the material properties of each type 

of concrete must be collectively considered and used in the CRCP design. From the 

comparison in crack spacing between the GFRP-CRCPs and VDOT’s steel-CRCP, it is 

55 
also found that the GFRP-CRCPs using the sandstone and the siliceous river gravel 

concretes have crack spacings comparable to that for VDOT’s steel-CRCP without 

increasing the amount of GFRP reinforcement. In addition to the comparable GFRPCRCPs, the GFRP-CRCP using the limestone concrete has a crack spacing of 1.814 m 

(5.95 ft), which is within the acceptable range for the criteria of crack spacing. 

5.95

8.06

6.94

3.47

6.25

4.46

6.25

3.29

0

1

2

3

4

5

6

7

8

9

Limestone Basalt Granite Granite (for

steel-CRCP)

Dolomite Sandstone Quartz Siliceous

River Gravel

Type of Coarse Aggregate in Concrete Mix

Mean Crack Spacing (ft )

1 ft = 0.305 m 

Figure 62. Graph. Mean crack spacing versus type of coarse aggregate 

in concrete mix (ρ = 0.0074; asphalt-stabilized subbase). 

In figure 63, the crack widths were predicted and compared over various concrete coarse 

aggregate types. In general, the crack widths appear to be wider as their corresponding 

crack spacings are larger. Also, a larger volume change in concrete appears to contribute 

to developing a wider crack width. The comparison in crack widths between the 

limestone and siliceous river gravel cases shows that the crack width for the limestone 

case, 0.54 mm (0.0211 inch), is narrower than that for the siliceous river gravel case, 0.67 

mm (0.0263 inch), although the crack spacing for the limestone case, 1.814 m (5.95 ft), is 

larger than that for the siliceous river gravel case, 1.003 m (3.29 ft). This can be 

explained by considering the much larger concrete volume change of siliceous river 

gravel concrete, which is mainly induced by its much higher CTE. The same explanation 

can be applied to the comparison between the dolomite and quartz cases. 

Among all crack widths which meet the maximum limiting criteria of ≤ 1 mm (0.04 inch), 

the crack widths for the limestone, sandstone, and siliceous river gravel cases can provide 

a reliable concrete aggregate interlock at crack. In addition, tighter cracks can be 

56 
generally expected with the steel reinforcement, since the steel reinforcement (having a 

higher Young’s modulus) can better restrain the concrete volume change and hold the 

crack more tightly. 

0.0211

0.0365

0.0388

0.0193

0.0361

0.0283

0.0402

0.0263

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Limestone Basalt Granite Granite (for

steel-CRCP)

Dolomite Sandstone Quartz Siliceous

River Gravel

Type of Coarse Aggregate in Concrete Mix

Crack Width (in .)

1 inch = 25.4 mm 

Figure 63. Graph. Crack width versus type of coarse aggregate in concrete mix 

(ρ = 0.0074; asphalt-stabilized subbase). 

Figure 64 shows the tensile stress level in reinforcement at crack for various types of 

concrete coarse aggregate. The tensile stress levels in GFRP reinforcement are in the 

range of about 137.90 to 172.38 MPa (20 to 25 ksi), levels that are somewhat higher than 

the GFRP rebar’s allowable tensile stress limit of 124 MPa (18 ksi), which is about 20 

percent of its ultimate tensile strength under a harsh environment; this adverse result 

could be resolved by using a new type of GFRP rebar such as alkaline-resistant GFRP 

rebar (such as AdvantexTM glass GFRP) which has an allowable stress limit that can be 

higher than 20 percent.(26) The stress levels in GFRP reinforcement appear to correlate 

with their corresponding crack widths. In the case of steel-CRCP, the reinforcement stress 

level is 288.56 MPa (41.850 ksi), which is lower than its limit of 379 MPa (55 ksi) and 

about 75 percent of the ultimate tensile strength of steel rebar.(2) The higher reinforcement 

stress for steel-CRCP is attributed to the higher Young’s modulus of steel. 

From the results, any of the GFRP-CRCPs with the limestone, sandstone, and siliceous 

river gravel concrete seems to perform satisfactorily without raising the reinforcement 

ratio under the given conditions provided by VDOT design data. In addition, even though 

the results show that the GFRP-CRCP with the granite concrete can satisfy the limiting 

57 
criteria, one may still want to increase the reinforcement ratio to avoid the possibility of 

violating the limiting criteria due to environmental variations. 

19.891

25.175 25.466

41.850

24.350

21.441

25.564

19.686

0

5

10

15

20

25

30

35

40

45

Limestone Basalt Granite Granite (for

steel-CRCP)

Dolomite Sandstone Quartz Siliceous

River Gravel

Type of Coarse Aggregate in Concrete Mix

Tensile Stress in Reinf. at Crack (ksi )

1 ksi = 6.89 MPa 

Figure 64. Graph. Tensile stress in reinforcement at crack versus type of coarse 

aggregate in concrete mix (ρ = 0.0074; asphalt-stabilized subbase). 

CRACK DEVELOPMENT AND REINFORCEMENT STRESS IN GFRP-CRCP 

WITH VARYING SUBBASE TYPE 

The comparison of the performances of GFRP-reinforced CRCP on various subbase types 

was simulated in this section. The linear bond-slip relationships between the concrete 

slabs and various subbase types, in terms of bond-slip stiffness per unit area of slab base 

(GPa/m (lbf/in2/inch)), were utilized for the simulation; the relationships were obtained 

experimentally by a group of researchers at the University of Texas.(33,34,35) The subbase 

types considered are untreated clay, asphalt stabilized, flexible, lime-treated clay, and 

cement stabilized, listed in order of lowest to highest bond-slip stiffness/unit area (GPa/m 

(lbf/in2

/inch)). The value of bond-slip stiffness/unit area for each type is shown in table 7. 

In addition to the cases of the aforementioned subbase types, hypothetical bond-slip cases 

of 0.136, 0.271, 0.543, 1.357, and 2.715 GPa/m (500, 1,000, 2,000, 5,000, and 10,000 

lbf/in2

/inch, respectively) were also simulated to find the appropriate range of bond-slip 

for the considered CRCP that eventually satisfies the limit of crack spacing, crack width, 

and the reinforcement stress level at crack. Granite aggregate concrete was used in this 

simulation based on material properties listed in table 5. 

58 
Table 7 and figure 65 show the predicted mean crack spacing and crack width over the 

bond-slip stiffness/unit area. It can be seen from figure 65 that the higher bond-slip 

results in smaller crack spacing, which in turn causes narrower crack widths. This result 

is reasonable since the higher bond-slip from the subbase provides the concrete slab with 

more restraint, causing higher tensile concrete stress under the concrete shrinkage and 

temperature drop and thus creating more cracks in a certain length of the slab. 

Table 7. Mechanistic prediction of crack development and reinforcement tensile 

stress at crack for GFRP-CRCP (varied with different types of subbase). 

Mean 

Crack 

Spacing 

Crack 

Width 

Reinf. Tensile 

Stress at Crack 

Bond-Slip 

Stiffness/Unit Area 1 Subbase Type

(lbf/in2

/inch) (inch) (ksi) (ft) 

Untreated clay 21.95 8.62 0.0478 28.501

Asphalt stabilized 55.88 6.94 0.0388 25.466

Flexible 145.45 6.94 0.0388 25.468

Lime-treated clay 154.55 6.76 0.0378 24.769

~ 500 5.95 0.0334 23.255

~ 1,000 5.68 0.0318 22.893

~ 2,000 4.64 0.026 20.887

~ 5,000 3.57 0.0201 18.256

~ 10,000 2.91 0.0164 16.250

Cement stabilized 15,400 2.45 0.0139 14.871

1

Granite aggregate is used for concrete mix; number 6 GFRP rebar is considered. 

 1 lbf/in2

/inch = 0.271 MPa/m; 1 ft = 0.305 m; 1 inch = 25.4 mm; 1 ksi = 6.89 MPa 

In the prediction, the asphalt-stabilized subbase results in a mean crack spacing of 2.115 

m (6.94 ft) and a crack width of 0.99 mm (0.0388 inch); these results are on the verge of 

the upper limit. Therefore, the asphalt-stabilized subbase appears to approximately 

provide the minimum allowable bond-slip (15.169 MPa/m (55.88 lbf/in2

/inch)) necessary 

to avoid spalling distress of the given CRCP. The cement-stabilized subbase was found to 

have nearly the maximum allowable bond-slip, resulting in a mean crack spacing of 

0.747 m (2.45 ft) and a crack width of 0.35 mm (0.0139 inch). The mean crack spacing 

for the cement-stabilized subbase is somewhat small compared with its limit of about 

1.067 m (3.5 ft), having the possibility of punchout distress. 

59 
0

1

2

3

4

5

6

7

8

9

10

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000

Bond-Slip Stiffness/Unit Area (lbf /in 2/inch )

Mean Crack Spacing (ft )

0

0.01

0.02

0.03

0.04

0.05

0.06

Crack Width (inch )

Mean C.S. C.W.

Note:

1. longitudinal GFRP reinforcement (#6) spaced at 6 inches

2. Bond-Slip Stifness/Unit Area

 Untreated Clay : 21.95 lbf /in 2

/inch

 Asphalt-Stabilized : 55.88 lbf /in 2

/inch

 Flexible : 145.45 lbf /in 2

/inch

 Lime-Treated Clay : 154.55 lbf /in 2

/inch

 Cememt-Stabilized : 15,400 lbf /in 2

/inch

1 lbf/in2/inch = 0.271 MPa/m; 1 ft = 0.305 m; 1 inch = 25.4 mm 

Figure 65. Graph. Mean crack spacing and crack width versus bond-slip 

stiffness/unit area (ρ = 0.0074; granite aggregate concrete). 

The tensile stresses in the GFRP reinforcement at cracks were also predicted over various 

subbase types (figure 66). As can be seen in the figure, higher bond-slip causes lower 

tensile stress in the reinforcement at the crack since the smaller crack spacing is expected 

with the higher bond-slip. The tensile stresses in the reinforcement corresponding to the 

subbase types range from about 103.43 to 199.96 MPa (15 to 29 ksi). The tensile stress 

levels for most subbase types, except for that of the cement-stabilized, exceed the 

allowable tensile stress of 124 MPa (18 ksi). The allowable tensile stress, as can be seen 

from the figure, is attained at a bond-slip of about 1.357 GPa/m (5,000 lbf/in2

/inch). 

Therefore, in order to avoid both spalling distress and early failure of GFRP 

reinforcement in the CRCP, the bond-slip should be held by at least 1.357 GPa/m (5,000 

lbf/in2

/inch). Only the cement-stabilized subbase meets this criterion, even though it may 

have some possibility of causing punchout distress in the CRCP. In this simulation 

calculated by the CRCP8 program, the bond stress between the concrete and 

reinforcement leads to stress changes in the concrete and reinforcement, and the bond 

stress varies in the bond development zone; the location of this zone is determined by 

solving the system of governing equations with the assumed bond stress distribution 

function and the reinforcement boundary condition.(3)

The performance of the GFRP-CRCP design presumably proposed by FE analysis in 

chapter 5 was also mechanistically examined by CRCP8. Since the design was 

60 
established with the limestone concrete with a compressive strength, fc′, of 27.58 MPa 

(4,000 psi), the concrete material properties become a little different from those shown in 

table 6, which are based on fc′ = 31.03 MPa (4,500 psi). The concrete material properties 

of tensile strength, flexural strength, and drying shrinkage change to 2.37 MPa (344 psi), 

3.83 MPa (556 psi), and 712 με, respectively. However, the CTE of 6.84 με/

o

C (3.8 

με/

o

F) and Young’s modulus of 24.8 GPa (3.6 × 106 lbf/in2) are assumed to remain the 

same when fc′ = 27.58 MPa (4,000 lbf/in2). The temperature input for the mechanistic 

exam also remains the same as that in table 6. This proposed GFRP-CRCP, which is 

designed utilizing a flexible subbase (or lime-treated clay subbase), is predicted to create 

a mean crack spacing of 1.466 m (4.81 ft), a crack width of 0.44 mm (0.0173 inch), and a 

reinforcement tensile stress at crack of 123.93 MPa (17.974 ksi). All of the results appear 

to be within their own limits and, therefore, the proposed GFRP-CRCP is expected to 

perform successfully. 

12

14

16

18

20

22

24

26

28

30

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000

Bond-Slip Stiffness/Unit Area (lbf /in 2/inch )

Tensile Stress in Reinf. at Crack (ksi )

Note:

1. longitudinal GFRP reinforcement (#6) spaced at 6 inches

2. Bond-Slip Stifness/Unit Area

 Untreated Clay : 21.95 lbf /in 2

/inch

 Asphalt-Stabilized : 55.88 lbf /in 2

/inch

 Flexible : 145.45 lbf /in 2

/inch

 Lime-Treated Clay : 154.55 lbf /in 2

/inch

 Cememt-Stabilized : 15,400 lbf /in 2

/inch

1 lbf/in2/inch = 0.271 MPa/m; 1 ksi = 6.89 MPa; 1 inch = 25.4 mm 

Figure 66. Graph. Tensile stress in GFRP reinforcement at crack versus bond-slip 

stiffness/unit area (ρ = 0.0074; granite aggregate concrete). 

The performance of GFRP-CRCP in response to traffic loading is mainly dependent on 

the overall stiffness of the CRCP system. It is generally known that the flexural stiffness 

of the slab can be significantly influenced by the slab thickness rather than the 

reinforcement.(30) The thickness design, which determines the pavement stiffness, is 

accordingly dependent on load transfer coefficient, so it is currently thought that as long 

as the load transfer capability of GFRP-CRCP is satisfactory, the thickness of GFRPCRCP may be able to remain the same, providing a pavement stiffness comparable to that 

61 
of steel-CRCP. (2) Currently, the thickness design procedure of steel-CRCP follows that of 

conventional jointed pavement, and the thickness of steel-CRCP is also recommended to 

be the same as that of conventional jointed pavement.(2,10) However, it is still necessary to 

investigate the performance of GFRP-CRCP in the field to verify this preliminary 

concept of GFRP-CRCP thickness design. In addition, it is noted that CRCP8 was 

designed for steel-CRCP with empirical data collected from the field with only steelreinforced CRCPs. Hence, the GFRP-CRCP performance predicted from CRCP8 needs 

to be verified by monitoring of future construction of a GFRP-reinforced CRCP in the 

field. It is noted that the current AASHTO limiting criterion of 1 mm crack width is 

developed from the steel-reinforced CRCP. Field investigation report(36) of steelreinforced CRCPs shows that high load transfer efficiency (LTE) (about 90%) is 

maintained for CRCPs at different ages, and the LTE is not influenced by the amount of 

reinforcement used (0.5% to 0.75%) or the crack spacings (0.5 to 2.5 m). Further research 

is needed to investigate the relationship between the crack width and its corresponding 

LTE of a GFRP-reinforced CRCP. 

A possible future construction of 27.94-cm- (11-inch-) thick GFRP-reinforced and steelreinforced CRCP sections are being planned in Elkins, West Virginia, in 2005. Under a 

given construction condition from the West Virginia Department of Transportation 

(WVDOT), using number 7 longitudinal GFRP rebars at 15.24-cm (6-inch) spacing on 

the line about 2.54 cm (1 inch) above the middepth of the slab is predicted to be an 

economically applicable design for GFRP-CRCP with limestone concrete on the asphaltstabilized subbase. In addition, number 6 GFRP rebars spaced at 1.219 m (48 inches (4 

ft)) will be installed as transverse reinforcement. For the steel-reinforced CRCP, number 

6 longitudinal steel rebars spaced at 15.24 cm (6 inches) will be adopted on the same 

subbase along with number 5 transverse steel rebars spaced at 1.219 m (48 inches (4 ft)). 

After the construction, the field monitoring of both the CRCPs will be followed to 

compare and evaluate the performance of the GFRP-CRCP in terms of crack spacing, 

crack width, and the number of distresses (such as spalling and punchout). 

62 
CHAPTER 7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 

SUMMARY AND CONCLUSIONS 

In this report, the concrete stresses induced in a GFRP-reinforced concrete slab due to 

concrete shrinkage and temperature variations have been analytically calculated in 

comparison to those induced in a steel-reinforced concrete slab, and the validity of the 

analytical model has been verified numerically and experimentally. The analytical 

solution indicates that a low Young’s modulus of GFRP rebar results in a stress reduction 

in concrete slabs. The thermal stress in concrete can be either tensile or compressive, 

depending on temperature variation and the CTEs of the concrete and the GFRP 

reinforcement used. 

From comparison with the finite element calculation, the analytical solution of average 

axial concrete stresses is shown to be valid throughout the longitudinal (x-) direction, 

especially in the vicinity of the slab’s middle section, where the maximum average axial 

stresses in concrete appeared. Meanwhile, the comparison also reveals the applicability of 

the FE method to the CRCP analysis. A 1.524-m (5-ft) CRCP segment FE model was 

built to simulate the behavior of the CRCP and to study the effects of CRCP design 

considerations (such as the CTE of concrete, the friction from the pavement's subbase, 

and the bond-slip between concrete and reinforcement) on stress development and crack 

width in the CRCP. It is shown that using concrete with a lower CTE reduces the 

concrete’s tensile stress level when exposed to temperature drop, and a weaker bond 

between the concrete and reinforcement also decreases the concrete tensile stress level in 

the CRCP and the tensile reinforcement stress level at its cracks. With a higher subbase 

friction, the CRCP is more likely to crack from its bottom area since the concrete stress 

level at the bottom will be higher than that at the top. The results give ways to favorably 

control the larger crack spacing and wider cracks of the GFRP-reinforced CRCP caused 

by the GFRP’s low elastic modulus; in order to satisfy the limiting criteria, with a given 

CTE of concrete, one can choose to (1) increase the amount of reinforcement, (2)increase 

the bond between concrete and reinforcement, and/or (3) increase the bond between 

concrete slab and subbase. 

From the FE study, a feasible longitudinal reinforcement design of 25.4-cm- (10-inch-) 

thick GFRP-reinforced CRCP has been proposed for a given condition by evaluating 

concrete stress developments in the 1.067-m (3.5-ft), 1.524-m (5-ft), and 2.438-m- (8-ft-) 

long CRCP slab segments with limestone concrete. Using number 6 longitudinal GFRP 

rebars at 15.24-cm (6-in.) spacing at the middepth of the slab is shown to be an 

economically feasible design for GFRP-CRCP on the flexible subbase (or lime-treated 

clay subbase). In addition, number 5 GFRP rebars spaced at 1.219 m (48 inches (4 ft)) 

will be adequate as transverse reinforcement. 

The mechanistic analysis program has been used to analyze the GFRP-CRCPs with 

different types of concrete coarse aggregate and subbase. Higher CTE, higher Young’s 

modulus, lower tensile strength, and larger drying shrinkage of concrete appear to reduce 

63 
the crack spacing in the CRCP. However, even though the crack width is generally 

narrower as the crack spacing is smaller, it can open wider after the crack formation 

settles down. This occurs when ambient temperature and air humidity levels drop enough 

to cause large concrete volume change so that the crack width of those smaller crack 

spacing sections will become larger. Higher subbase friction always causes smaller crack 

spacing followed by narrower crack width. From the mechanistic analysis results, the 

GFRP-CRCPs with the limestone, sandstone, or siliceous river gravel concrete on 

asphalt-stabilized subbase seems to perform satisfactorily without raising the GFRPreinforcement ratio under a given design condition provided by VDOT. In addition, the 

subbase that can provide a bond-slip of about 1.357 GPa/m (5,000 lbf/in2/inch) is able to 

provide a satisfactory performance of the GFRP-CRCP with granite concrete. 

Currently, the designs of a 27.94-cm- (11-inch-) thick GFRP-reinforced CRCP and a 

steel-reinforced CRCP section have been prepared and are waiting to be constructed in 

West Virginia in 2006. 

RECOMMENDATIONS 

• Further studies of the effect of a high transverse CTE of the GFRP rebar on its bond 

with concrete at various temperatures and on cracking in the GFRP-reinforced CRCP 

are necessary. 

• Investigations into the effect due to the low transverse (shear) strength of the GFRP 

rebar on the load transfer at the cracks generated in the GFRP-reinforced CRCP 

should be conducted. Investigation of the relationship between the load transfer 

efficiency and the crack width is required. 

• Developing the previously mentioned alternative reinforcement position for 

minimizing the amount of GFRP reinforcement needed while still favorably 

controlling the cracking in the GFRP-reinforced CRCP would be economically 

beneficial. 

• Development of standard design guidelines to clearly specify the limiting criteria 

(such as crack spacing, crack width, and reinforcement stress level for the GFRPreinforced CRCP) is needed. Currently, the AASHTO guideline for the steelreinforced CRCP design can only serve as a reference. 

64 
ACKNOWLEDGMENTS 

The authors acknowledge the assistance provided by the Constructed Facilities Center, 

West Virginia University (WVU), during this study. This report also constitutes part of Mr. 

Jeong-Hoon Choi’s Ph.D. dissertation at WVU. 

65 

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